%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU608^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 2.52s 1.71s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 2460 ( 682 equ; 0 cnn)
% Maximal formula atoms : 126 ( 87 avg)
% Number of connectives : 1229 ( 36 ~; 16 |; 385 &; 158 @)
% ( 3 <=>; 631 =>; 0 <=; 0 <~>)
% Maximal formula depth : 134 ( 40 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 : 60 ( 0 ^; 42 !; 18 ?; 60 :)
% 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_156,type,
sP0: $i > $i > $o ).
thf(func_def_157,type,
sP1: $i > $o ).
thf(func_def_158,type,
sP2: $i > $i > $o ).
thf(func_def_159,type,
sP3: $i > $i > $o ).
thf(func_def_170,type,
sK14: $i > $i > $i ).
thf(func_def_171,type,
sK15: $i > $i > $i ).
thf(func_def_172,type,
sK16: $i > $i > $i ).
thf(func_def_173,type,
sK17: $i > $i > $i ).
thf(func_def_174,type,
sK18: $i > $i > $i > $i ).
thf(func_def_175,type,
sK19: $i > $i ).
thf(func_def_176,type,
sK20: $i > $i ).
thf(func_def_177,type,
sK21: $i > $i ).
thf(func_def_178,type,
sK22: $i > $i ).
thf(func_def_179,type,
sK23: $i > $i > $i ).
thf(func_def_180,type,
sK24: $i > $i > $i > $i ).
thf(func_def_181,type,
sK25: $i > $i > $i > $i ).
thf(func_def_182,type,
sK26: $i > $i > $i ).
thf(func_def_183,type,
sK27: $i > $i > $i ).
thf(func_def_184,type,
sK28: $i > $i ).
thf(func_def_185,type,
sK29: $i > $i > $i ).
thf(func_def_187,type,
sK31: $i > $i ).
thf(func_def_188,type,
sK32: $i > $i ).
thf(func_def_195,type,
sK39: $i > $i > $i ).
thf(func_def_213,type,
sK57: $i > $o ).
thf(func_def_214,type,
sK58: ( $i > $o ) > $i ).
thf(func_def_218,type,
sK62: $i > $i ).
thf(func_def_243,type,
sK87: $i > $o ).
thf(func_def_244,type,
sK88: $i > $i ).
thf(func_def_245,type,
sK89: ( $i > $o ) > $i ).
thf(func_def_255,type,
sK99: $i > $o ).
thf(func_def_278,type,
sK122: $i > $i > $o ).
thf(func_def_280,type,
sK124: $i > $i ).
thf(func_def_281,type,
sK125: $i > $i ).
thf(func_def_282,type,
sK126: $i > ( $i > $i > $o ) > $i ).
thf(func_def_283,type,
sK127: $i > ( $i > $i > $o ) > $i ).
thf(func_def_284,type,
sK128: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_287,type,
sK131: $i > $i ).
thf(func_def_288,type,
sK132: ( $i > $o ) > $i > $i ).
thf(func_def_290,type,
sK134: $i > $o ).
thf(func_def_294,type,
sK138: $i > $i > $i ).
thf(func_def_299,type,
sK143: $i > $i > $i ).
thf(func_def_314,type,
sK158: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_315,type,
sK159: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_316,type,
sK160: $i > $o ).
thf(func_def_317,type,
sK161: $i > $o ).
thf(func_def_323,type,
sK167: $i > $i ).
thf(func_def_327,type,
sK171: $i > $o ).
thf(func_def_328,type,
sK172: $i > $o ).
thf(func_def_329,type,
sK173: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_330,type,
sK174: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_336,type,
sK180: $i > $o ).
thf(func_def_338,type,
sK182: ( $i > $o ) > $i ).
thf(func_def_339,type,
sK183: ( $i > $o ) > $i ).
thf(func_def_340,type,
sK184: $i > $i > $i ).
thf(func_def_347,type,
sK191: $i > $o ).
thf(func_def_348,type,
sK192: $i > $i ).
thf(func_def_349,type,
sK193: ( $i > $o ) > $i ).
thf(func_def_355,type,
sK199: $i > $o ).
thf(func_def_358,type,
sK202: $i > ( $i > $o ) > $i ).
thf(func_def_359,type,
sK203: $i > $i ).
thf(func_def_361,type,
sK205: $i > $o ).
thf(func_def_366,type,
sK210: $i > $o ).
thf(func_def_372,type,
sK216: $i > $o ).
thf(func_def_385,type,
sK229: $i > $i ).
thf(func_def_391,type,
sK235: $i > $i > $i ).
thf(func_def_392,type,
sK236: $i > $i > $i ).
thf(func_def_402,type,
sK246: $i > $o ).
thf(func_def_407,type,
sK251: $i > $o ).
thf(func_def_410,type,
sK254: $i > $o ).
thf(func_def_411,type,
sK255: $i > $i > $i ).
thf(func_def_418,type,
sK262: $i > $o ).
thf(func_def_423,type,
sK267: ( $i > $o ) > $i > $i ).
thf(func_def_425,type,
sK269: $i > $o ).
thf(func_def_427,type,
sK271: $i > ( $i > $o ) > $i ).
thf(func_def_428,type,
sK272: $i > $o ).
thf(func_def_431,type,
sK275: $i > $o ).
thf(func_def_432,type,
sK276: $i > $o ).
thf(func_def_433,type,
sK277: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_434,type,
sK278: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_436,type,
sK280: $i > $o ).
thf(func_def_442,type,
sK286: $i > $o ).
thf(func_def_445,type,
sK289: $i > ( $i > $o ) > $i ).
thf(func_def_447,type,
sK291: $i > $i ).
thf(func_def_449,type,
sK293: $i > $i ).
thf(func_def_453,type,
sK297: $i > $o ).
thf(func_def_455,type,
sK299: $i > ( $i > $o ) > $i ).
thf(func_def_456,type,
sK300: $i > $o ).
thf(func_def_460,type,
sK304: ( $i > $o ) > $i > $i ).
thf(func_def_462,type,
sK306: $i > $o ).
thf(func_def_466,type,
sK310: $i > $i > $i ).
thf(func_def_470,type,
sK314: $o > $i > $i > $i ).
thf(func_def_473,type,
sK317: $i > $o ).
thf(func_def_475,type,
sK319: $i > ( $i > $o ) > $i ).
thf(func_def_478,type,
sK322: $i > $o ).
thf(func_def_484,type,
sK328: $i > $i > $i ).
thf(func_def_489,type,
sK333: $i > $o ).
thf(func_def_499,type,
ph343:
!>[X0: $tType] : X0 ).
thf(f1883,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1873]) ).
thf(f1873,plain,
$true != $true,
inference(superposition,[status(thm)],[f1854,f1541]) ).
thf(f1541,plain,
( $true
= ( in @ sK244 @ sK245 ) ),
inference(cnf_transformation,[status(thm)],[f964]) ).
thf(f964,plain,
( ( subsetemptysetimpeq = $true )
& ( omega0Ax = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( binunionE = $true )
& ( foundationAx = $true )
& ( in__Cong = $true )
& ( vacuousDall = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectLsub = $true )
& ( nonemptyImpWitness = $true )
& ( exuE3e = $true )
& ( setadjoin__Cong = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan1 = $true )
& ( setminusILneg = $true )
& ( subsetRefl = $true )
& ( exuEu = $true )
& ( binintersectI = $true )
& ( notinsingleton = $true )
& ( binintersectSubset1 = $true )
& ( emptyE1 = $true )
& ( setunionI = $true )
& ( setminusER = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan2 = $true )
& ( uniqinunit = $true )
& ( omegaSAx = $true )
& ( setadjoinIR = $true )
& ( upairsetIR = $true )
& ( upairset2IR = $true )
& ( subPowSU = $true )
& ( prop2set2propI = $true )
& ( binintersectEL = $true )
& ( sepSubset = $true )
& ( upairsetIL = $true )
& ( omegaIndAx = $true )
& ( emptysetimpfalse = $true )
& ( exuI1 = $true )
& ( binunionIL = $true )
& ( nonemptyI = $true )
& ( setminusEL = $true )
& ( setoftrueEq = $true )
& ( subsetE2 = $true )
& ( emptysetAx = $true )
& ( setextAx = $true )
& ( setunion__Cong = $true )
& ( noeltsimpempty = $true )
& ( binintersectSubset5 = $true )
& ( binintersectER = $true )
& ( quantDeMorgan4 = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( binunionIR = $true )
& ( eqinunit = $true )
& ( setadjoinAx = $true )
& ( setminusI = $true )
& ( setbeta = $true )
& ( disjointsetsI1 = $true )
& ( $true
= ( in @ sK244 @ ( setminus @ sK243 @ sK245 ) ) )
& ( $true
= ( in @ sK244 @ sK245 ) )
& ( subsetE = $true )
& ( setunionE = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( emptyset__Cong = $true )
& ( wellorderingAx = $true )
& ( setadjoinOr = $true )
& ( descr__Cong = $true )
& ( exuE1 = $true )
& ( powersetE1 = $true )
& ( descrp = $true )
& ( subsetTrans = $true )
& ( powersetI1 = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstrI = $true )
& ( dsetconstr__Cong = $true )
& ( subset2powerset = $true )
& ( notdallE = $true )
& ( binintersectSubset2 = $true )
& ( notsubsetI = $true )
& ( setunionAx = $true )
& ( emptyinPowerset = $true )
& ( setadjoinSub2 = $true )
& ( inCongP = $true )
& ( notequalI1 = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset2 = $true )
& ( prop2setI = $true )
& ( exu__Cong = $true )
& ( nonemptyE1 = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( singletonsswitch = $true )
& ( powersetAx = $true )
& ( setadjoinSub = $true )
& ( notdexE = $true )
& ( notinemptyset = $true )
& ( exuI3 = $true )
& ( exuE3u = $true )
& ( upairsetE = $true )
& ( setadjoinIL = $true )
& ( setextsub = $true )
& ( notequalI2 = $true )
& ( binintersectSubset3 = $true )
& ( bs114d = $true )
& ( nonemptyI1 = $true )
& ( emptyI = $true )
& ( sepInPowerset = $true )
& ( emptyinunitempty = $true )
& ( powerset__Cong = $true )
& ( binunionEcases = $true )
& ( binunionLsub = $true )
& ( binintersectRsub = $true )
& ( setminusERneg = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset2 = $true )
& ( setminusELneg = $true )
& ( dsetconstrEL = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( inPowerset = $true )
& ( exuI2 = $true )
& ( setadjoinE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK243,sK244,sK245])],[f505,f963]) ).
thf(f963,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
=> ( ( $true
= ( in @ sK244 @ ( setminus @ sK243 @ sK245 ) ) )
& ( $true
= ( in @ sK244 @ sK245 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f505,plain,
( ( subsetemptysetimpeq = $true )
& ( omega0Ax = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( binunionE = $true )
& ( foundationAx = $true )
& ( in__Cong = $true )
& ( vacuousDall = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectLsub = $true )
& ( nonemptyImpWitness = $true )
& ( exuE3e = $true )
& ( setadjoin__Cong = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan1 = $true )
& ( setminusILneg = $true )
& ( subsetRefl = $true )
& ( exuEu = $true )
& ( binintersectI = $true )
& ( notinsingleton = $true )
& ( binintersectSubset1 = $true )
& ( emptyE1 = $true )
& ( setunionI = $true )
& ( setminusER = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan2 = $true )
& ( uniqinunit = $true )
& ( omegaSAx = $true )
& ( setadjoinIR = $true )
& ( upairsetIR = $true )
& ( upairset2IR = $true )
& ( subPowSU = $true )
& ( prop2set2propI = $true )
& ( binintersectEL = $true )
& ( sepSubset = $true )
& ( upairsetIL = $true )
& ( omegaIndAx = $true )
& ( emptysetimpfalse = $true )
& ( exuI1 = $true )
& ( binunionIL = $true )
& ( nonemptyI = $true )
& ( setminusEL = $true )
& ( setoftrueEq = $true )
& ( subsetE2 = $true )
& ( emptysetAx = $true )
& ( setextAx = $true )
& ( setunion__Cong = $true )
& ( noeltsimpempty = $true )
& ( binintersectSubset5 = $true )
& ( binintersectER = $true )
& ( quantDeMorgan4 = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( binunionIR = $true )
& ( eqinunit = $true )
& ( setadjoinAx = $true )
& ( setminusI = $true )
& ( setbeta = $true )
& ( disjointsetsI1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
& ( subsetE = $true )
& ( setunionE = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( emptyset__Cong = $true )
& ( wellorderingAx = $true )
& ( setadjoinOr = $true )
& ( descr__Cong = $true )
& ( exuE1 = $true )
& ( powersetE1 = $true )
& ( descrp = $true )
& ( subsetTrans = $true )
& ( powersetI1 = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstrI = $true )
& ( dsetconstr__Cong = $true )
& ( subset2powerset = $true )
& ( notdallE = $true )
& ( binintersectSubset2 = $true )
& ( notsubsetI = $true )
& ( setunionAx = $true )
& ( emptyinPowerset = $true )
& ( setadjoinSub2 = $true )
& ( inCongP = $true )
& ( notequalI1 = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset2 = $true )
& ( prop2setI = $true )
& ( exu__Cong = $true )
& ( nonemptyE1 = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( singletonsswitch = $true )
& ( powersetAx = $true )
& ( setadjoinSub = $true )
& ( notdexE = $true )
& ( notinemptyset = $true )
& ( exuI3 = $true )
& ( exuE3u = $true )
& ( upairsetE = $true )
& ( setadjoinIL = $true )
& ( setextsub = $true )
& ( notequalI2 = $true )
& ( binintersectSubset3 = $true )
& ( bs114d = $true )
& ( nonemptyI1 = $true )
& ( emptyI = $true )
& ( sepInPowerset = $true )
& ( emptyinunitempty = $true )
& ( powerset__Cong = $true )
& ( binunionEcases = $true )
& ( binunionLsub = $true )
& ( binintersectRsub = $true )
& ( setminusERneg = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset2 = $true )
& ( setminusELneg = $true )
& ( dsetconstrEL = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( inPowerset = $true )
& ( exuI2 = $true )
& ( setadjoinE = $true ) ),
inference(flattening,[status(thm)],[f504]) ).
thf(f504,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f385]) ).
thf(f385,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f201]) ).
thf(f201,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f200]) ).
thf(f200,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f128]) ).
thf(f128,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ! [X3: $i,X1: $i,X4: $i] :
( ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
thf(f127,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ! [X3: $i,X1: $i,X4: $i] :
( ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UhuhNbW7fO/DTF2THF_3995.p',setminusIRneg) ).
thf(f1854,plain,
( $true
!= ( in @ sK244 @ sK245 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1853]) ).
thf(f1853,plain,
( ( $true
!= ( in @ sK244 @ sK245 ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f1835,f1578]) ).
thf(f1578,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f964]) ).
thf(f1835,plain,
( ( $true
!= ( in @ sK244 @ sK245 ) )
| ( setminusER != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1830]) ).
thf(f1830,plain,
( ( $true != $true )
| ( setminusER != $true )
| ( $true
!= ( in @ sK244 @ sK245 ) ) ),
inference(superposition,[status(thm)],[f1347,f1542]) ).
thf(f1542,plain,
( $true
= ( in @ sK244 @ ( setminus @ sK243 @ sK245 ) ) ),
inference(cnf_transformation,[status(thm)],[f964]) ).
thf(f1347,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f810]) ).
thf(f810,plain,
( ( ( setminusER = $true )
| ( ( $true
= ( in @ sK154 @ sK153 ) )
& ( ( in @ sK154 @ ( setminus @ sK152 @ sK153 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) ) )
| ( setminusER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153,sK154])],[f808,f809]) ).
thf(f809,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
=> ( ( $true
= ( in @ sK154 @ sK153 ) )
& ( ( in @ sK154 @ ( setminus @ sK152 @ sK153 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f808,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f807]) ).
thf(f807,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f414]) ).
thf(f414,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f404]) ).
thf(f404,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X0 @ X1 ) ) )
=> ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f329]) ).
thf(f329,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X0 @ X1 ) ) )
=> ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f328]) ).
thf(f328,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
inference(rectify,[status(thm)],[f122]) ).
thf(f122,axiom,
! [X3: $i,X4: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X3 @ X4 ) )
=> ~ ( in @ X1 @ X4 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.UhuhNbW7fO/DTF2THF_3995.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU608^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n004.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:28:11 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU608^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : (! A:i.! B:i.! x:i.in x B -> ~(in x (setminus A B)))
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC110g [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % 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 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 270 ( 126 unt; 143 typ; 126 def)
% 0.16/0.39 % Number of atoms : 672 ( 182 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 126 ( 5 avg)
% 0.16/0.39 % Number of connectives : 1068 ( 39 ~; 6 |; 28 &; 683 @)
% 0.16/0.39 % ( 14 <=>; 298 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 133 ( 2 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 146 ( 143 usr; 128 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 366 ( 30 ^; 307 !; 29 ?; 366 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=463
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu_type,type,
% 0.16/0.39 exu: ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu,definition,
% 0.16/0.39 ( exu
% 0.16/0.39 = ( ^ [Xphi: $i > $o] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx_type,type,
% 0.16/0.39 setextAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx,definition,
% 0.16/0.39 ( setextAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xx @ B ) )
% 0.16/0.39 => ( A = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx_type,type,
% 0.16/0.39 emptysetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx,definition,
% 0.16/0.39 ( emptysetAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx_type,type,
% 0.16/0.39 setadjoinAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx,definition,
% 0.16/0.39 ( setadjoinAx
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 <=> ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset_type,type,
% 0.16/0.39 powerset: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx_type,type,
% 0.16/0.39 powersetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx,definition,
% 0.16/0.39 ( powersetAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 <=> ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion_type,type,
% 0.16/0.39 setunion: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx_type,type,
% 0.16/0.39 setunionAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx,definition,
% 0.16/0.39 ( setunionAx
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 <=> ? [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega_type,type,
% 0.16/0.39 omega: $i ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax_type,type,
% 0.16/0.39 omega0Ax: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax,definition,
% 0.16/0.39 ( omega0Ax
% 0.16/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx_type,type,
% 0.16/0.39 omegaSAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx,definition,
% 0.16/0.39 ( omegaSAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx_type,type,
% 0.16/0.39 omegaIndAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx,definition,
% 0.16/0.39 ( omegaIndAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( ( in @ emptyset @ A )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ omega )
% 0.16/0.39 & ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(replAx_type,type,
% 0.16/0.39 replAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(replAx,definition,
% 0.16/0.39 ( replAx
% 0.16/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 <=> ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx_type,type,
% 0.16/0.39 foundationAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx,definition,
% 0.16/0.39 ( foundationAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ( ( in @ B @ A )
% 0.16/0.39 & ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx_type,type,
% 0.16/0.39 wellorderingAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx,definition,
% 0.16/0.39 ( wellorderingAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ? [B: $i] :
% 0.16/0.39 ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) ) )
% 0.16/0.39 & ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ A )
% 0.16/0.39 & ( in @ Xy @ A ) )
% 0.16/0.39 => ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ( ( in @ Xx @ C )
% 0.16/0.39 <=> ( in @ Xy @ C ) ) )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 & ! [C: $i,D: $i] :
% 0.16/0.39 ( ( ( in @ C @ B )
% 0.16/0.39 & ( in @ D @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ D ) )
% 0.16/0.39 | ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ D )
% 0.16/0.39 => ( in @ Xx @ C ) ) ) )
% 0.16/0.39 & ! [C: $i] :
% 0.16/0.39 ( ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.39 => ? [D: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ D @ B )
% 0.16/0.39 & ( in @ Xx @ C )
% 0.16/0.39 & ~ ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ D )
% 0.16/0.39 & ( in @ Xy @ C ) )
% 0.16/0.39 & ! [E: $i] :
% 0.16/0.39 ( ( in @ E @ B )
% 0.16/0.39 => ( ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ E )
% 0.16/0.39 => ( in @ Xy @ D ) )
% 0.16/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr_type,type,
% 0.16/0.39 descr: ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(descrp_type,type,
% 0.16/0.39 descrp: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descrp,definition,
% 0.16/0.39 ( descrp
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( Xphi
% 0.16/0.39 @ ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr_type,type,
% 0.16/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI_type,type,
% 0.16/0.39 dsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI,definition,
% 0.16/0.39 ( dsetconstrI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL_type,type,
% 0.16/0.39 dsetconstrEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL,definition,
% 0.16/0.39 ( dsetconstrEL
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER_type,type,
% 0.16/0.39 dsetconstrER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER,definition,
% 0.16/0.39 ( dsetconstrER
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1_type,type,
% 0.16/0.39 exuE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1,definition,
% 0.16/0.39 ( exuE1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set_type,type,
% 0.16/0.39 prop2set: $o > $i ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE_type,type,
% 0.16/0.39 prop2setE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE,definition,
% 0.16/0.39 ( prop2setE
% 0.16/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE_type,type,
% 0.16/0.39 emptysetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE,definition,
% 0.16/0.39 ( emptysetE
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse_type,type,
% 0.16/0.39 emptysetimpfalse: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse,definition,
% 0.16/0.39 ( emptysetimpfalse
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => $false ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset_type,type,
% 0.16/0.39 notinemptyset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset,definition,
% 0.16/0.39 ( notinemptyset
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e_type,type,
% 0.16/0.39 exuE3e: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e,definition,
% 0.16/0.39 ( exuE3e
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setext_type,type,
% 0.16/0.39 setext: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setext,definition,
% 0.16/0.39 ( setext
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( A = B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI_type,type,
% 0.16/0.39 emptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI,definition,
% 0.16/0.39 ( emptyI
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty_type,type,
% 0.16/0.39 noeltsimpempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty,definition,
% 0.16/0.39 ( noeltsimpempty
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta_type,type,
% 0.16/0.39 setbeta: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta,definition,
% 0.16/0.39 ( setbeta
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty_type,type,
% 0.16/0.39 nonempty: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty,definition,
% 0.16/0.39 ( nonempty
% 0.16/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1_type,type,
% 0.16/0.39 nonemptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1,definition,
% 0.16/0.39 ( nonemptyE1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI_type,type,
% 0.16/0.39 nonemptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI,definition,
% 0.16/0.39 ( nonemptyI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( nonempty
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1_type,type,
% 0.16/0.39 nonemptyI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1,definition,
% 0.16/0.39 ( nonemptyI1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL_type,type,
% 0.16/0.39 setadjoinIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL,definition,
% 0.16/0.39 ( setadjoinIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty_type,type,
% 0.16/0.39 emptyinunitempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty,definition,
% 0.16/0.39 ( emptyinunitempty
% 0.16/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR_type,type,
% 0.16/0.39 setadjoinIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR,definition,
% 0.16/0.39 ( setadjoinIR
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE_type,type,
% 0.16/0.39 setadjoinE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE,definition,
% 0.16/0.39 ( setadjoinE
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ( ( Xy = Xx )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => ( ( ( in @ Xy @ A )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr_type,type,
% 0.16/0.39 setadjoinOr: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr,definition,
% 0.16/0.39 ( setadjoinOr
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq_type,type,
% 0.16/0.39 setoftrueEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq,definition,
% 0.16/0.39 ( setoftrueEq
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : $true )
% 0.16/0.39 = A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI_type,type,
% 0.16/0.39 powersetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI,definition,
% 0.16/0.39 ( powersetI
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset_type,type,
% 0.16/0.39 emptyinPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset,definition,
% 0.16/0.39 ( emptyinPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset_type,type,
% 0.16/0.39 emptyInPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset,definition,
% 0.16/0.39 ( emptyInPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE_type,type,
% 0.16/0.39 powersetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE,definition,
% 0.16/0.39 ( powersetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI_type,type,
% 0.16/0.39 setunionI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI,definition,
% 0.16/0.39 ( setunionI
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE_type,type,
% 0.16/0.39 setunionE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE,definition,
% 0.16/0.39 ( setunionE
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ! [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU_type,type,
% 0.16/0.39 subPowSU: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU,definition,
% 0.16/0.39 ( subPowSU
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2_type,type,
% 0.16/0.39 exuE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2,definition,
% 0.16/0.39 ( exuE2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness_type,type,
% 0.16/0.39 nonemptyImpWitness: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness,definition,
% 0.16/0.39 ( nonemptyImpWitness
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & $true ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit_type,type,
% 0.16/0.39 uniqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit,definition,
% 0.16/0.39 ( uniqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton_type,type,
% 0.16/0.39 notinsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton,definition,
% 0.16/0.39 ( notinsingleton
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx != Xy )
% 0.16/0.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit_type,type,
% 0.16/0.39 eqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit,definition,
% 0.16/0.39 ( eqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch_type,type,
% 0.16/0.39 singletonsswitch: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch,definition,
% 0.16/0.39 ( singletonsswitch
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE_type,type,
% 0.16/0.39 upairsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE,definition,
% 0.16/0.39 ( upairsetE
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xx )
% 0.16/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL_type,type,
% 0.16/0.39 upairsetIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL,definition,
% 0.16/0.39 ( upairsetIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR_type,type,
% 0.16/0.39 upairsetIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR,definition,
% 0.16/0.39 ( upairsetIR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1_type,type,
% 0.16/0.39 emptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1,definition,
% 0.16/0.39 ( emptyE1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = emptyset )
% 0.16/0.39 => $false ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall_type,type,
% 0.16/0.39 vacuousDall: $o ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall,definition,
% 0.16/0.39 ( vacuousDall
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1_type,type,
% 0.16/0.39 quantDeMorgan1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1,definition,
% 0.16/0.39 ( quantDeMorgan1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2_type,type,
% 0.16/0.39 quantDeMorgan2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2,definition,
% 0.16/0.39 ( quantDeMorgan2
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3_type,type,
% 0.16/0.39 quantDeMorgan3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3,definition,
% 0.16/0.39 ( quantDeMorgan3
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4_type,type,
% 0.16/0.39 quantDeMorgan4: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4,definition,
% 0.16/0.39 ( quantDeMorgan4
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI_type,type,
% 0.16/0.39 prop2setI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI,definition,
% 0.16/0.39 ( prop2setI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(set2prop_type,type,
% 0.16/0.39 set2prop: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI_type,type,
% 0.16/0.39 prop2set2propI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI,definition,
% 0.16/0.39 ( prop2set2propI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE_type,type,
% 0.16/0.39 notdexE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE,definition,
% 0.16/0.39 ( notdexE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE_type,type,
% 0.16/0.39 notdallE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE,definition,
% 0.16/0.39 ( notdallE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1_type,type,
% 0.16/0.39 exuI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1,definition,
% 0.16/0.39 ( exuI1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3_type,type,
% 0.16/0.39 exuI3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3,definition,
% 0.16/0.39 ( exuI3
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.16/0.39 => ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2_type,type,
% 0.16/0.39 exuI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2,definition,
% 0.16/0.39 ( exuI2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP_type,type,
% 0.16/0.39 inCongP: $o ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP,definition,
% 0.16/0.39 ( inCongP
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong_type,type,
% 0.16/0.39 in__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong,definition,
% 0.16/0.39 ( in__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u_type,type,
% 0.16/0.39 exuE3u: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u,definition,
% 0.16/0.39 ( exuE3u
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong_type,type,
% 0.16/0.39 exu__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong,definition,
% 0.16/0.39 ( exu__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 <=> ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong_type,type,
% 0.16/0.39 emptyset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong,definition,
% 0.16/0.39 ( emptyset__Cong
% 0.16/0.39 = ( emptyset = emptyset ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong_type,type,
% 0.16/0.39 setadjoin__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong,definition,
% 0.16/0.39 ( setadjoin__Cong
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ! [Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( Xz = Xu )
% 0.16/0.39 => ( ( setadjoin @ Xx @ Xz )
% 0.16/0.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong_type,type,
% 0.16/0.39 powerset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong,definition,
% 0.16/0.39 ( powerset__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( powerset @ A )
% 0.16/0.39 = ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong_type,type,
% 0.16/0.39 setunion__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong,definition,
% 0.16/0.39 ( setunion__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( setunion @ A )
% 0.16/0.39 = ( setunion @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong_type,type,
% 0.16/0.39 omega__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong,definition,
% 0.16/0.39 ( omega__Cong
% 0.16/0.39 = ( omega = omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu_type,type,
% 0.16/0.39 exuEu: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu,definition,
% 0.16/0.39 ( exuEu
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong_type,type,
% 0.16/0.39 descr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong,definition,
% 0.16/0.39 ( descr__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.16/0.39 => ( ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong_type,type,
% 0.16/0.39 dsetconstr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong,definition,
% 0.16/0.39 ( dsetconstr__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.16/0.39 => ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( dsetconstr @ B
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset_type,type,
% 0.16/0.39 subset: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(disjoint_type,type,
% 0.16/0.39 disjoint: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setsmeet_type,type,
% 0.16/0.39 setsmeet: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1_type,type,
% 0.16/0.39 subsetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1,definition,
% 0.16/0.39 ( subsetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2_type,type,
% 0.16/0.39 eqimpsubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2,definition,
% 0.16/0.39 ( eqimpsubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1_type,type,
% 0.16/0.39 eqimpsubset1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1,definition,
% 0.16/0.39 ( eqimpsubset1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2_type,type,
% 0.16/0.39 subsetI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2,definition,
% 0.16/0.39 ( subsetI2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset_type,type,
% 0.16/0.39 emptysetsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset,definition,
% 0.16/0.39 ( emptysetsubset
% 0.16/0.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE_type,type,
% 0.16/0.39 subsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE,definition,
% 0.16/0.39 ( subsetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2_type,type,
% 0.16/0.39 subsetE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2,definition,
% 0.16/0.39 ( subsetE2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI_type,type,
% 0.16/0.39 notsubsetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI,definition,
% 0.16/0.39 ( notsubsetI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1_type,type,
% 0.16/0.39 notequalI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1,definition,
% 0.16/0.39 ( notequalI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ~ ( subset @ A @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2_type,type,
% 0.16/0.39 notequalI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2,definition,
% 0.16/0.39 ( notequalI2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetRefl_type,type,
% 0.16/0.39 subsetRefl: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetRefl,definition,
% 0.16/0.39 ( subsetRefl
% 0.16/0.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetTrans_type,type,
% 0.16/0.39 subsetTrans: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetTrans,definition,
% 0.16/0.39 ( subsetTrans
% 0.16/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( subset @ B @ C )
% 0.16/0.39 => ( subset @ A @ C ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub_type,type,
% 0.16/0.39 setadjoinSub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub,definition,
% 0.16/0.39 ( setadjoinSub
% 0.16/0.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub2_type,type,
% 0.16/0.39 setadjoinSub2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub2,definition,
% 0.16/0.39 ( setadjoinSub2
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset2powerset_type,type,
% 0.16/0.39 subset2powerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subset2powerset,definition,
% 0.16/0.39 ( subset2powerset
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextsub_type,type,
% 0.16/0.39 setextsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextsub,definition,
% 0.16/0.39 ( setextsub
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( subset @ B @ A )
% 0.16/0.39 => ( A = B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetemptysetimpeq_type,type,
% 0.16/0.39 subsetemptysetimpeq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetemptysetimpeq,definition,
% 0.16/0.39 ( subsetemptysetimpeq
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( subset @ A @ emptyset )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI1_type,type,
% 0.16/0.39 powersetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI1,definition,
% 0.16/0.39 ( powersetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ B @ A )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE1_type,type,
% 0.16/0.39 powersetE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE1,definition,
% 0.16/0.39 ( powersetE1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(inPowerset_type,type,
% 0.16/0.39 inPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(inPowerset,definition,
% 0.16/0.39 ( inPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetsubset_type,type,
% 0.16/0.39 powersetsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetsubset,definition,
% 0.16/0.39 ( powersetsubset
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sepInPowerset_type,type,
% 0.16/0.39 sepInPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(sepInPowerset,definition,
% 0.16/0.39 ( sepInPowerset
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( in
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sepSubset_type,type,
% 0.16/0.39 sepSubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(sepSubset,definition,
% 0.16/0.39 ( sepSubset
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( subset
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunion_type,type,
% 0.16/0.39 binunion: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIL_type,type,
% 0.16/0.39 binunionIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIL,definition,
% 0.16/0.39 ( binunionIL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2IR_type,type,
% 0.16/0.39 upairset2IR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2IR,definition,
% 0.16/0.39 ( upairset2IR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIR_type,type,
% 0.16/0.39 binunionIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionIR,definition,
% 0.16/0.39 ( binunionIR
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionEcases_type,type,
% 0.16/0.39 binunionEcases: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionEcases,definition,
% 0.16/0.39 ( binunionEcases
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.16/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.39 => ( ( ( in @ Xx @ A )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => ( ( ( in @ Xx @ B )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionE_type,type,
% 0.16/0.39 binunionE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionE,definition,
% 0.16/0.39 ( binunionE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionLsub_type,type,
% 0.16/0.39 binunionLsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionLsub,definition,
% 0.16/0.39 ( binunionLsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunionRsub_type,type,
% 0.16/0.39 binunionRsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binunionRsub,definition,
% 0.16/0.39 ( binunionRsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersect_type,type,
% 0.16/0.39 binintersect: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectI_type,type,
% 0.16/0.39 binintersectI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectI,definition,
% 0.16/0.39 ( binintersectI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset5_type,type,
% 0.16/0.39 binintersectSubset5: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset5,definition,
% 0.16/0.39 ( binintersectSubset5
% 0.16/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.39 ( ( subset @ C @ A )
% 0.16/0.39 => ( ( subset @ C @ B )
% 0.16/0.39 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectEL_type,type,
% 0.16/0.39 binintersectEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectEL,definition,
% 0.16/0.39 ( binintersectEL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectLsub_type,type,
% 0.16/0.39 binintersectLsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectLsub,definition,
% 0.16/0.39 ( binintersectLsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset2_type,type,
% 0.16/0.39 binintersectSubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset2,definition,
% 0.16/0.39 ( binintersectSubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( binintersect @ A @ B )
% 0.16/0.39 = A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset3_type,type,
% 0.16/0.39 binintersectSubset3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset3,definition,
% 0.16/0.39 ( binintersectSubset3
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( ( binintersect @ A @ B )
% 0.16/0.39 = B )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectER_type,type,
% 0.16/0.39 binintersectER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectER,definition,
% 0.16/0.39 ( binintersectER
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(disjointsetsI1_type,type,
% 0.16/0.39 disjointsetsI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(disjointsetsI1,definition,
% 0.16/0.39 ( disjointsetsI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( in @ Xx @ B ) )
% 0.16/0.39 => ( ( binintersect @ A @ B )
% 0.16/0.39 = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectRsub_type,type,
% 0.16/0.39 binintersectRsub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectRsub,definition,
% 0.16/0.39 ( binintersectRsub
% 0.16/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset4_type,type,
% 0.16/0.39 binintersectSubset4: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset4,definition,
% 0.16/0.39 ( binintersectSubset4
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ B @ A )
% 0.16/0.39 => ( ( binintersect @ A @ B )
% 0.16/0.39 = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset1_type,type,
% 0.16/0.39 binintersectSubset1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(binintersectSubset1,definition,
% 0.16/0.39 ( binintersectSubset1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( ( binintersect @ A @ B )
% 0.16/0.39 = A )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(bs114d_type,type,
% 0.16/0.39 bs114d: $o ).
% 0.16/0.39
% 0.16/0.39 thf(bs114d,definition,
% 0.16/0.39 ( bs114d
% 0.16/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.39 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.16/0.39 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(regular_type,type,
% 0.16/0.39 regular: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminus_type,type,
% 0.16/0.39 setminus: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setminusI_type,type,
% 0.16/0.39 setminusI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusI,definition,
% 0.16/0.39 ( setminusI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusEL_type,type,
% 0.16/0.39 setminusEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusEL,definition,
% 0.16/0.39 ( setminusEL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusER_type,type,
% 0.16/0.39 setminusER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusER,definition,
% 0.16/0.39 ( setminusER
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.39 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusSubset2_type,type,
% 0.16/0.39 setminusSubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusSubset2,definition,
% 0.16/0.39 ( setminusSubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( setminus @ A @ B )
% 0.16/0.39 = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusERneg_type,type,
% 0.16/0.39 setminusERneg: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusERneg,definition,
% 0.16/0.39 ( setminusERneg
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusELneg_type,type,
% 0.16/0.39 setminusELneg: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusELneg,definition,
% 0.16/0.39 ( setminusELneg
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusILneg_type,type,
% 0.16/0.39 setminusILneg: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setminusILneg,definition,
% 0.16/0.39 ( setminusILneg
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ A )
% 0.16/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setminusIRneg,conjecture,
% 0.16/0.39 ( setextAx
% 0.16/0.39 => ( emptysetAx
% 0.16/0.39 => ( setadjoinAx
% 0.16/0.39 => ( powersetAx
% 0.16/0.39 => ( setunionAx
% 0.16/0.39 => ( omega0Ax
% 0.16/0.39 => ( omegaSAx
% 0.16/0.39 => ( omegaIndAx
% 0.16/0.39 => ( replAx
% 0.16/0.39 => ( foundationAx
% 0.16/0.39 => ( wellorderingAx
% 0.16/0.39 => ( descrp
% 0.16/0.39 => ( dsetconstrI
% 0.16/0.39 => ( dsetconstrEL
% 0.16/0.39 => ( dsetconstrER
% 0.16/0.39 => ( exuE1
% 0.16/0.39 => ( prop2setE
% 0.16/0.39 => ( emptysetE
% 0.16/0.39 => ( emptysetimpfalse
% 0.16/0.39 => ( notinemptyset
% 0.16/0.39 => ( exuE3e
% 0.16/0.39 => ( setext
% 0.16/0.39 => ( emptyI
% 0.16/0.39 => ( noeltsimpempty
% 0.16/0.39 => ( setbeta
% 0.16/0.39 => ( nonemptyE1
% 0.16/0.39 => ( nonemptyI
% 0.16/0.39 => ( nonemptyI1
% 0.16/0.39 => ( setadjoinIL
% 0.16/0.39 => ( emptyinunitempty
% 0.16/0.39 => ( setadjoinIR
% 0.16/0.39 => ( setadjoinE
% 0.16/0.39 => ( setadjoinOr
% 0.16/0.39 => ( setoftrueEq
% 0.16/0.39 => ( powersetI
% 0.16/0.39 => ( emptyinPowerset
% 0.16/0.39 => ( emptyInPowerset
% 0.16/0.39 => ( powersetE
% 0.16/0.39 => ( setunionI
% 0.16/0.39 => ( setunionE
% 0.16/0.39 => ( subPowSU
% 0.16/0.39 => ( exuE2
% 0.16/0.39 => ( nonemptyImpWitness
% 0.16/0.39 => ( uniqinunit
% 0.16/0.39 => ( notinsingleton
% 0.16/0.39 => ( eqinunit
% 0.16/0.39 => ( singletonsswitch
% 0.16/0.39 => ( upairsetE
% 0.16/0.39 => ( upairsetIL
% 0.16/0.39 => ( upairsetIR
% 0.16/0.39 => ( emptyE1
% 0.16/0.39 => ( vacuousDall
% 0.16/0.39 => ( quantDeMorgan1
% 0.16/0.39 => ( quantDeMorgan2
% 0.16/0.39 => ( quantDeMorgan3
% 0.16/0.39 => ( quantDeMorgan4
% 0.16/0.39 => ( prop2setI
% 0.16/0.39 => ( prop2set2propI
% 0.16/0.39 => ( notdexE
% 0.16/0.39 => ( notdallE
% 0.16/0.39 => ( exuI1
% 0.16/0.39 => ( exuI3
% 0.16/0.39 => ( exuI2
% 0.16/0.39 => ( inCongP
% 0.16/0.39 => ( in__Cong
% 0.16/0.39 => ( exuE3u
% 0.16/0.39 => ( exu__Cong
% 0.16/0.39 => ( emptyset__Cong
% 0.16/0.39 => ( setadjoin__Cong
% 0.16/0.39 => ( powerset__Cong
% 0.16/0.39 => ( setunion__Cong
% 0.16/0.39 => ( omega__Cong
% 0.16/0.39 => ( exuEu
% 0.16/0.39 => ( descr__Cong
% 0.16/0.39 => ( dsetconstr__Cong
% 0.16/0.39 => ( subsetI1
% 0.16/0.39 => ( eqimpsubset2
% 0.16/0.39 => ( eqimpsubset1
% 0.16/0.39 => ( subsetI2
% 0.16/0.39 => ( emptysetsubset
% 0.16/0.39 => ( subsetE
% 0.16/0.39 => ( subsetE2
% 0.16/0.39 => ( notsubsetI
% 0.16/0.39 => ( notequalI1
% 0.16/0.39 => ( notequalI2
% 0.16/0.39 => ( subsetRefl
% 0.16/0.39 => ( subsetTrans
% 0.16/0.39 => ( setadjoinSub
% 0.16/0.39 => ( setadjoinSub2
% 0.16/0.39 => ( subset2powerset
% 0.16/0.39 => ( setextsub
% 0.16/0.39 => ( subsetemptysetimpeq
% 0.16/0.39 => ( powersetI1
% 0.16/0.39 => ( powersetE1
% 0.16/0.39 => ( inPowerset
% 0.16/0.39 => ( powersetsubset
% 0.16/0.39 => ( sepInPowerset
% 0.16/0.39 => ( sepSubset
% 0.16/0.39 => ( binunionIL
% 0.16/0.39 => ( upairset2IR
% 0.16/0.39 => ( binunionIR
% 0.16/0.39 => ( binunionEcases
% 0.16/0.39 => ( binunionE
% 0.16/0.39 => ( binunionLsub
% 0.16/0.39 => ( binunionRsub
% 0.16/0.39 => ( binintersectI
% 0.16/0.39 => ( binintersectSubset5
% 0.16/0.39 => ( binintersectEL
% 0.16/0.39 => ( binintersectLsub
% 0.16/0.39 => ( binintersectSubset2
% 0.16/0.39 => ( binintersectSubset3
% 0.16/0.39 => ( binintersectER
% 0.16/0.39 => ( disjointsetsI1
% 0.16/0.39 => ( binintersectRsub
% 0.16/0.39 => ( binintersectSubset4
% 0.16/0.39 => ( binintersectSubset1
% 0.16/0.39 => ( bs114d
% 0.16/0.39 => ( setminusI
% 0.16/0.39 => ( setminusEL
% 0.16/0.39 => ( setminusER
% 0.16/0.39 => ( setminusSubset2
% 0.16/0.39 => ( setminusERneg
% 0.16/0.39 => ( setminusELneg
% 0.16/0.39 => ( setminusILneg
% 0.16/0.39 => ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.48/1.51 ---- Embedded in THF ---
% 2.48/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.48/1.51 %%% Generated on Tue Feb 24 12:28:12 EST 2026
% 2.48/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.48/1.51 %%% Logic specification used:
% 2.48/1.51 %%% thf(spec, logic, $$dhol).
% 2.48/1.51
% 2.48/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.UhuhNbW7fO/DTF2DTF3995.p
% See solution above
% 2.48/1.51 ------------------------
% 2.48/1.53 ---- Cleaned THF ---
% 2.48/1.53 thf(in_type,type,
% 2.48/1.53 in: $i > $i > $o ).
% 2.48/1.53
% 2.48/1.53 thf(exu_type,type,
% 2.48/1.53 exu: ( $i > $o ) > $o ).
% 2.48/1.53
% 2.48/1.53 thf(exu,definition,
% 2.48/1.53 ( exu
% 2.48/1.53 = ( ^ [Xphi: $i > $o] :
% 2.48/1.53 ? [Xx: $i] :
% 2.48/1.53 ( ( Xphi @ Xx )
% 2.48/1.53 & ! [Xy: $i] :
% 2.48/1.53 ( ( Xphi @ Xy )
% 2.48/1.53 => ( Xx = Xy ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setextAx_type,type,
% 2.48/1.53 setextAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setextAx,definition,
% 2.48/1.53 ( setextAx
% 2.48/1.53 = ( ! [A: $i,B: $i] :
% 2.48/1.53 ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ A )
% 2.48/1.53 <=> ( in @ Xx @ B ) )
% 2.48/1.53 => ( A = B ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(emptyset_type,type,
% 2.48/1.53 emptyset: $i ).
% 2.48/1.53
% 2.48/1.53 thf(emptysetAx_type,type,
% 2.48/1.53 emptysetAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(emptysetAx,definition,
% 2.48/1.53 ( emptysetAx
% 2.48/1.53 = ( ! [Xx: $i] :
% 2.48/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoin_type,type,
% 2.48/1.53 setadjoin: $i > $i > $i ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinAx_type,type,
% 2.48/1.53 setadjoinAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinAx,definition,
% 2.48/1.53 ( setadjoinAx
% 2.48/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.48/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.48/1.53 <=> ( ( Xy = Xx )
% 2.48/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(powerset_type,type,
% 2.48/1.53 powerset: $i > $i ).
% 2.48/1.53
% 2.48/1.53 thf(powersetAx_type,type,
% 2.48/1.53 powersetAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(powersetAx,definition,
% 2.48/1.53 ( powersetAx
% 2.48/1.53 = ( ! [A: $i,B: $i] :
% 2.48/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.48/1.53 <=> ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ B )
% 2.48/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setunion_type,type,
% 2.48/1.53 setunion: $i > $i ).
% 2.48/1.53
% 2.48/1.53 thf(setunionAx_type,type,
% 2.48/1.53 setunionAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setunionAx,definition,
% 2.48/1.53 ( setunionAx
% 2.48/1.53 = ( ! [A: $i,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.48/1.53 <=> ? [B: $i] :
% 2.48/1.53 ( ( in @ Xx @ B )
% 2.48/1.53 & ( in @ B @ A ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(omega_type,type,
% 2.48/1.53 omega: $i ).
% 2.48/1.53
% 2.48/1.53 thf(omega0Ax_type,type,
% 2.48/1.53 omega0Ax: $o ).
% 2.48/1.53
% 2.48/1.53 thf(omega0Ax,definition,
% 2.48/1.53 ( omega0Ax
% 2.48/1.53 = ( in @ emptyset @ omega ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(omegaSAx_type,type,
% 2.48/1.53 omegaSAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(omegaSAx,definition,
% 2.48/1.53 ( omegaSAx
% 2.48/1.53 = ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ omega )
% 2.48/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(omegaIndAx_type,type,
% 2.48/1.53 omegaIndAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(omegaIndAx,definition,
% 2.48/1.53 ( omegaIndAx
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ( ( ( in @ emptyset @ A )
% 2.48/1.53 & ! [Xx: $i] :
% 2.48/1.53 ( ( ( in @ Xx @ omega )
% 2.48/1.53 & ( in @ Xx @ A ) )
% 2.48/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.48/1.53 => ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ omega )
% 2.48/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(replAx_type,type,
% 2.48/1.53 replAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(replAx,definition,
% 2.48/1.53 ( replAx
% 2.48/1.53 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.48/1.53 ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ A )
% 2.48/1.53 => ( exu
% 2.48/1.53 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.48/1.53 => ? [B: $i] :
% 2.48/1.53 ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ B )
% 2.48/1.53 <=> ? [Xy: $i] :
% 2.48/1.53 ( ( in @ Xy @ A )
% 2.48/1.53 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(foundationAx_type,type,
% 2.48/1.53 foundationAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(foundationAx,definition,
% 2.48/1.53 ( foundationAx
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.48/1.53 => ? [B: $i] :
% 2.48/1.53 ( ( in @ B @ A )
% 2.48/1.53 & ~ ? [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ B )
% 2.48/1.53 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(wellorderingAx_type,type,
% 2.48/1.53 wellorderingAx: $o ).
% 2.48/1.53
% 2.48/1.53 thf(wellorderingAx,definition,
% 2.48/1.53 ( wellorderingAx
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ? [B: $i] :
% 2.48/1.53 ( ! [C: $i] :
% 2.48/1.53 ( ( in @ C @ B )
% 2.48/1.53 => ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ C )
% 2.48/1.53 => ( in @ Xx @ A ) ) )
% 2.48/1.53 & ! [Xx: $i,Xy: $i] :
% 2.48/1.53 ( ( ( in @ Xx @ A )
% 2.48/1.53 & ( in @ Xy @ A ) )
% 2.48/1.53 => ( ! [C: $i] :
% 2.48/1.53 ( ( in @ C @ B )
% 2.48/1.53 => ( ( in @ Xx @ C )
% 2.48/1.53 <=> ( in @ Xy @ C ) ) )
% 2.48/1.53 => ( Xx = Xy ) ) )
% 2.48/1.53 & ! [C: $i,D: $i] :
% 2.48/1.53 ( ( ( in @ C @ B )
% 2.48/1.53 & ( in @ D @ B ) )
% 2.48/1.53 => ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ C )
% 2.48/1.53 => ( in @ Xx @ D ) )
% 2.48/1.53 | ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ D )
% 2.48/1.53 => ( in @ Xx @ C ) ) ) )
% 2.48/1.53 & ! [C: $i] :
% 2.48/1.53 ( ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ C )
% 2.48/1.53 => ( in @ Xx @ A ) )
% 2.48/1.53 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.48/1.53 => ? [D: $i,Xx: $i] :
% 2.48/1.53 ( ( in @ D @ B )
% 2.48/1.53 & ( in @ Xx @ C )
% 2.48/1.53 & ~ ? [Xy: $i] :
% 2.48/1.53 ( ( in @ Xy @ D )
% 2.48/1.53 & ( in @ Xy @ C ) )
% 2.48/1.53 & ! [E: $i] :
% 2.48/1.53 ( ( in @ E @ B )
% 2.48/1.53 => ( ! [Xy: $i] :
% 2.48/1.53 ( ( in @ Xy @ E )
% 2.48/1.53 => ( in @ Xy @ D ) )
% 2.48/1.53 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(descr_type,type,
% 2.48/1.53 descr: ( $i > $o ) > $i ).
% 2.48/1.53
% 2.48/1.53 thf(descrp_type,type,
% 2.48/1.53 descrp: $o ).
% 2.48/1.53
% 2.48/1.53 thf(descrp,definition,
% 2.48/1.53 ( descrp
% 2.48/1.53 = ( ! [Xphi: $i > $o] :
% 2.48/1.53 ( ( exu
% 2.48/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.53 => ( Xphi
% 2.48/1.53 @ ( descr
% 2.48/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(dsetconstr_type,type,
% 2.48/1.53 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.48/1.53
% 2.48/1.53 thf(dsetconstrI_type,type,
% 2.48/1.53 dsetconstrI: $o ).
% 2.48/1.53
% 2.48/1.53 thf(dsetconstrI,definition,
% 2.48/1.53 ( dsetconstrI
% 2.48/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ A )
% 2.48/1.53 => ( ( Xphi @ Xx )
% 2.48/1.53 => ( in @ Xx
% 2.48/1.53 @ ( dsetconstr @ A
% 2.48/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(dsetconstrEL_type,type,
% 2.48/1.53 dsetconstrEL: $o ).
% 2.48/1.53
% 2.48/1.53 thf(dsetconstrEL,definition,
% 2.48/1.53 ( dsetconstrEL
% 2.48/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx
% 2.48/1.53 @ ( dsetconstr @ A
% 2.48/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.48/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(dsetconstrER_type,type,
% 2.48/1.53 dsetconstrER: $o ).
% 2.48/1.53
% 2.48/1.53 thf(dsetconstrER,definition,
% 2.48/1.53 ( dsetconstrER
% 2.48/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx
% 2.48/1.53 @ ( dsetconstr @ A
% 2.48/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.48/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(exuE1_type,type,
% 2.48/1.53 exuE1: $o ).
% 2.48/1.53
% 2.48/1.53 thf(exuE1,definition,
% 2.48/1.53 ( exuE1
% 2.48/1.53 = ( ! [Xphi: $i > $o] :
% 2.48/1.53 ( ( exu
% 2.48/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.53 => ? [Xx: $i] :
% 2.48/1.53 ( ( Xphi @ Xx )
% 2.48/1.53 & ! [Xy: $i] :
% 2.48/1.53 ( ( Xphi @ Xy )
% 2.48/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(prop2set_type,type,
% 2.48/1.53 prop2set: $o > $i ).
% 2.48/1.53
% 2.48/1.53 thf(prop2setE_type,type,
% 2.48/1.53 prop2setE: $o ).
% 2.48/1.53
% 2.48/1.53 thf(prop2setE,definition,
% 2.48/1.53 ( prop2setE
% 2.48/1.53 = ( ! [Xphi: $o,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.48/1.53 => Xphi ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(emptysetE_type,type,
% 2.48/1.53 emptysetE: $o ).
% 2.48/1.53
% 2.48/1.53 thf(emptysetE,definition,
% 2.48/1.53 ( emptysetE
% 2.48/1.53 = ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ emptyset )
% 2.48/1.53 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(emptysetimpfalse_type,type,
% 2.48/1.53 emptysetimpfalse: $o ).
% 2.48/1.53
% 2.48/1.53 thf(emptysetimpfalse,definition,
% 2.48/1.53 ( emptysetimpfalse
% 2.48/1.53 = ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ emptyset )
% 2.48/1.53 => $false ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(notinemptyset_type,type,
% 2.48/1.53 notinemptyset: $o ).
% 2.48/1.53
% 2.48/1.53 thf(notinemptyset,definition,
% 2.48/1.53 ( notinemptyset
% 2.48/1.53 = ( ! [Xx: $i] :
% 2.48/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(exuE3e_type,type,
% 2.48/1.53 exuE3e: $o ).
% 2.48/1.53
% 2.48/1.53 thf(exuE3e,definition,
% 2.48/1.53 ( exuE3e
% 2.48/1.53 = ( ! [Xphi: $i > $o] :
% 2.48/1.53 ( ( exu
% 2.48/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.53 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setext_type,type,
% 2.48/1.53 setext: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setext,definition,
% 2.48/1.53 ( setext
% 2.48/1.53 = ( ! [A: $i,B: $i] :
% 2.48/1.53 ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ A )
% 2.48/1.53 => ( in @ Xx @ B ) )
% 2.48/1.53 => ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ B )
% 2.48/1.53 => ( in @ Xx @ A ) )
% 2.48/1.53 => ( A = B ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(emptyI_type,type,
% 2.48/1.53 emptyI: $o ).
% 2.48/1.53
% 2.48/1.53 thf(emptyI,definition,
% 2.48/1.53 ( emptyI
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ( ! [Xx: $i] :
% 2.48/1.53 ~ ( in @ Xx @ A )
% 2.48/1.53 => ( A = emptyset ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(noeltsimpempty_type,type,
% 2.48/1.53 noeltsimpempty: $o ).
% 2.48/1.53
% 2.48/1.53 thf(noeltsimpempty,definition,
% 2.48/1.53 ( noeltsimpempty
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ( ! [Xx: $i] :
% 2.48/1.53 ~ ( in @ Xx @ A )
% 2.48/1.53 => ( A = emptyset ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setbeta_type,type,
% 2.48/1.53 setbeta: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setbeta,definition,
% 2.48/1.53 ( setbeta
% 2.48/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ A )
% 2.48/1.53 => ( ( in @ Xx
% 2.48/1.53 @ ( dsetconstr @ A
% 2.48/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.48/1.53 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(nonempty_type,type,
% 2.48/1.53 nonempty: $i > $o ).
% 2.48/1.53
% 2.48/1.53 thf(nonempty,definition,
% 2.48/1.53 ( nonempty
% 2.48/1.53 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(nonemptyE1_type,type,
% 2.48/1.53 nonemptyE1: $o ).
% 2.48/1.53
% 2.48/1.53 thf(nonemptyE1,definition,
% 2.48/1.53 ( nonemptyE1
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ( ( nonempty @ A )
% 2.48/1.53 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(nonemptyI_type,type,
% 2.48/1.53 nonemptyI: $o ).
% 2.48/1.53
% 2.48/1.53 thf(nonemptyI,definition,
% 2.48/1.53 ( nonemptyI
% 2.48/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ A )
% 2.48/1.53 => ( ( Xphi @ Xx )
% 2.48/1.53 => ( nonempty
% 2.48/1.53 @ ( dsetconstr @ A
% 2.48/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(nonemptyI1_type,type,
% 2.48/1.53 nonemptyI1: $o ).
% 2.48/1.53
% 2.48/1.53 thf(nonemptyI1,definition,
% 2.48/1.53 ( nonemptyI1
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.48/1.53 => ( nonempty @ A ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinIL_type,type,
% 2.48/1.53 setadjoinIL: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinIL,definition,
% 2.48/1.53 ( setadjoinIL
% 2.48/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(emptyinunitempty_type,type,
% 2.48/1.53 emptyinunitempty: $o ).
% 2.48/1.53
% 2.48/1.53 thf(emptyinunitempty,definition,
% 2.48/1.53 ( emptyinunitempty
% 2.48/1.53 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinIR_type,type,
% 2.48/1.53 setadjoinIR: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinIR,definition,
% 2.48/1.53 ( setadjoinIR
% 2.48/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.48/1.53 ( ( in @ Xy @ A )
% 2.48/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinE_type,type,
% 2.48/1.53 setadjoinE: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinE,definition,
% 2.48/1.53 ( setadjoinE
% 2.48/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.48/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.48/1.53 => ! [Xphi: $o] :
% 2.48/1.53 ( ( ( Xy = Xx )
% 2.48/1.53 => Xphi )
% 2.48/1.53 => ( ( ( in @ Xy @ A )
% 2.48/1.53 => Xphi )
% 2.48/1.53 => Xphi ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinOr_type,type,
% 2.48/1.53 setadjoinOr: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setadjoinOr,definition,
% 2.48/1.53 ( setadjoinOr
% 2.48/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.48/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.48/1.53 => ( ( Xy = Xx )
% 2.48/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setoftrueEq_type,type,
% 2.48/1.53 setoftrueEq: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setoftrueEq,definition,
% 2.48/1.53 ( setoftrueEq
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ( ( dsetconstr @ A
% 2.48/1.53 @ ^ [Xx: $i] : $true )
% 2.48/1.53 = A ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(powersetI_type,type,
% 2.48/1.53 powersetI: $o ).
% 2.48/1.53
% 2.48/1.53 thf(powersetI,definition,
% 2.48/1.53 ( powersetI
% 2.48/1.53 = ( ! [A: $i,B: $i] :
% 2.48/1.53 ( ! [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ B )
% 2.48/1.53 => ( in @ Xx @ A ) )
% 2.48/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(emptyinPowerset_type,type,
% 2.48/1.53 emptyinPowerset: $o ).
% 2.48/1.53
% 2.48/1.53 thf(emptyinPowerset,definition,
% 2.48/1.53 ( emptyinPowerset
% 2.48/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(emptyInPowerset_type,type,
% 2.48/1.53 emptyInPowerset: $o ).
% 2.48/1.53
% 2.48/1.53 thf(emptyInPowerset,definition,
% 2.48/1.53 ( emptyInPowerset
% 2.48/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(powersetE_type,type,
% 2.48/1.53 powersetE: $o ).
% 2.48/1.53
% 2.48/1.53 thf(powersetE,definition,
% 2.48/1.53 ( powersetE
% 2.48/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.48/1.53 => ( ( in @ Xx @ B )
% 2.48/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setunionI_type,type,
% 2.48/1.53 setunionI: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setunionI,definition,
% 2.48/1.53 ( setunionI
% 2.48/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.48/1.53 ( ( in @ Xx @ B )
% 2.48/1.53 => ( ( in @ B @ A )
% 2.48/1.53 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(setunionE_type,type,
% 2.48/1.53 setunionE: $o ).
% 2.48/1.53
% 2.48/1.53 thf(setunionE,definition,
% 2.48/1.53 ( setunionE
% 2.48/1.53 = ( ! [A: $i,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.48/1.53 => ! [Xphi: $o] :
% 2.48/1.53 ( ! [B: $i] :
% 2.48/1.53 ( ( in @ Xx @ B )
% 2.48/1.53 => ( ( in @ B @ A )
% 2.48/1.53 => Xphi ) )
% 2.48/1.53 => Xphi ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(subPowSU_type,type,
% 2.48/1.53 subPowSU: $o ).
% 2.48/1.53
% 2.48/1.53 thf(subPowSU,definition,
% 2.48/1.53 ( subPowSU
% 2.48/1.53 = ( ! [A: $i,Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ A )
% 2.48/1.53 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(exuE2_type,type,
% 2.48/1.53 exuE2: $o ).
% 2.48/1.53
% 2.48/1.53 thf(exuE2,definition,
% 2.48/1.53 ( exuE2
% 2.48/1.53 = ( ! [Xphi: $i > $o] :
% 2.48/1.53 ( ( exu
% 2.48/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.53 => ? [Xx: $i] :
% 2.48/1.53 ! [Xy: $i] :
% 2.48/1.53 ( ( Xphi @ Xy )
% 2.48/1.53 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(nonemptyImpWitness_type,type,
% 2.48/1.53 nonemptyImpWitness: $o ).
% 2.48/1.53
% 2.48/1.53 thf(nonemptyImpWitness,definition,
% 2.48/1.53 ( nonemptyImpWitness
% 2.48/1.53 = ( ! [A: $i] :
% 2.48/1.53 ( ( nonempty @ A )
% 2.48/1.53 => ? [Xx: $i] :
% 2.48/1.53 ( ( in @ Xx @ A )
% 2.48/1.53 & $true ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(uniqinunit_type,type,
% 2.48/1.53 uniqinunit: $o ).
% 2.48/1.53
% 2.48/1.53 thf(uniqinunit,definition,
% 2.48/1.53 ( uniqinunit
% 2.48/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.48/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(notinsingleton_type,type,
% 2.48/1.53 notinsingleton: $o ).
% 2.48/1.53
% 2.48/1.53 thf(notinsingleton,definition,
% 2.48/1.53 ( notinsingleton
% 2.48/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.53 ( ( Xx != Xy )
% 2.48/1.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(eqinunit_type,type,
% 2.48/1.53 eqinunit: $o ).
% 2.48/1.53
% 2.48/1.53 thf(eqinunit,definition,
% 2.48/1.53 ( eqinunit
% 2.48/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.53 ( ( Xx = Xy )
% 2.48/1.53 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(singletonsswitch_type,type,
% 2.48/1.53 singletonsswitch: $o ).
% 2.48/1.53
% 2.48/1.53 thf(singletonsswitch,definition,
% 2.48/1.53 ( singletonsswitch
% 2.48/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.48/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(upairsetE_type,type,
% 2.48/1.53 upairsetE: $o ).
% 2.48/1.53
% 2.48/1.53 thf(upairsetE,definition,
% 2.48/1.53 ( upairsetE
% 2.48/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.48/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.48/1.53 => ( ( Xz = Xx )
% 2.48/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(upairsetIL_type,type,
% 2.48/1.53 upairsetIL: $o ).
% 2.48/1.53
% 2.48/1.53 thf(upairsetIL,definition,
% 2.48/1.53 ( upairsetIL
% 2.48/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.48/1.53
% 2.48/1.53 thf(upairsetIR_type,type,
% 2.48/1.53 upairsetIR: $o ).
% 2.48/1.53
% 2.48/1.53 thf(upairsetIR,definition,
% 2.48/1.53 ( upairsetIR
% 2.48/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(emptyE1_type,type,
% 2.48/1.54 emptyE1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(emptyE1,definition,
% 2.48/1.54 ( emptyE1
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( ? [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 & ( Xphi @ Xx ) )
% 2.48/1.54 => ( ( ( dsetconstr @ A
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 = emptyset )
% 2.48/1.54 => $false ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(vacuousDall_type,type,
% 2.48/1.54 vacuousDall: $o ).
% 2.48/1.54
% 2.48/1.54 thf(vacuousDall,definition,
% 2.48/1.54 ( vacuousDall
% 2.48/1.54 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ emptyset )
% 2.48/1.54 => ( Xphi @ Xx ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(quantDeMorgan1_type,type,
% 2.48/1.54 quantDeMorgan1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(quantDeMorgan1,definition,
% 2.48/1.54 ( quantDeMorgan1
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( ~ ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( Xphi @ Xx ) )
% 2.48/1.54 => ? [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(quantDeMorgan2_type,type,
% 2.48/1.54 quantDeMorgan2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(quantDeMorgan2,definition,
% 2.48/1.54 ( quantDeMorgan2
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ~ ( Xphi @ Xx ) )
% 2.48/1.54 => ~ ? [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(quantDeMorgan3_type,type,
% 2.48/1.54 quantDeMorgan3: $o ).
% 2.48/1.54
% 2.48/1.54 thf(quantDeMorgan3,definition,
% 2.48/1.54 ( quantDeMorgan3
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( ~ ? [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 & ( Xphi @ Xx ) )
% 2.48/1.54 => ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(quantDeMorgan4_type,type,
% 2.48/1.54 quantDeMorgan4: $o ).
% 2.48/1.54
% 2.48/1.54 thf(quantDeMorgan4,definition,
% 2.48/1.54 ( quantDeMorgan4
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( ? [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 & ~ ( Xphi @ Xx ) )
% 2.48/1.54 => ~ ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(prop2setI_type,type,
% 2.48/1.54 prop2setI: $o ).
% 2.48/1.54
% 2.48/1.54 thf(prop2setI,definition,
% 2.48/1.54 ( prop2setI
% 2.48/1.54 = ( ! [Xphi: $o] :
% 2.48/1.54 ( Xphi
% 2.48/1.54 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(set2prop_type,type,
% 2.48/1.54 set2prop: $i > $o ).
% 2.48/1.54
% 2.48/1.54 thf(prop2set2propI_type,type,
% 2.48/1.54 prop2set2propI: $o ).
% 2.48/1.54
% 2.48/1.54 thf(prop2set2propI,definition,
% 2.48/1.54 ( prop2set2propI
% 2.48/1.54 = ( ! [Xphi: $o] :
% 2.48/1.54 ( Xphi
% 2.48/1.54 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(notdexE_type,type,
% 2.48/1.54 notdexE: $o ).
% 2.48/1.54
% 2.48/1.54 thf(notdexE,definition,
% 2.48/1.54 ( notdexE
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( ~ ? [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 & ( Xphi @ Xx ) )
% 2.48/1.54 => ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(notdallE_type,type,
% 2.48/1.54 notdallE: $o ).
% 2.48/1.54
% 2.48/1.54 thf(notdallE,definition,
% 2.48/1.54 ( notdallE
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( ~ ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( Xphi @ Xx ) )
% 2.48/1.54 => ? [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(exuI1_type,type,
% 2.48/1.54 exuI1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(exuI1,definition,
% 2.48/1.54 ( exuI1
% 2.48/1.54 = ( ! [Xphi: $i > $o] :
% 2.48/1.54 ( ? [Xx: $i] :
% 2.48/1.54 ( ( Xphi @ Xx )
% 2.48/1.54 & ! [Xy: $i] :
% 2.48/1.54 ( ( Xphi @ Xy )
% 2.48/1.54 => ( Xx = Xy ) ) )
% 2.48/1.54 => ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(exuI3_type,type,
% 2.48/1.54 exuI3: $o ).
% 2.48/1.54
% 2.48/1.54 thf(exuI3,definition,
% 2.48/1.54 ( exuI3
% 2.48/1.54 = ( ! [Xphi: $i > $o] :
% 2.48/1.54 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.48/1.54 => ( ! [Xx: $i,Xy: $i] :
% 2.48/1.54 ( ( Xphi @ Xx )
% 2.48/1.54 => ( ( Xphi @ Xy )
% 2.48/1.54 => ( Xx = Xy ) ) )
% 2.48/1.54 => ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(exuI2_type,type,
% 2.48/1.54 exuI2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(exuI2,definition,
% 2.48/1.54 ( exuI2
% 2.48/1.54 = ( ! [Xphi: $i > $o] :
% 2.48/1.54 ( ? [Xx: $i] :
% 2.48/1.54 ! [Xy: $i] :
% 2.48/1.54 ( ( Xphi @ Xy )
% 2.48/1.54 <=> ( Xy = Xx ) )
% 2.48/1.54 => ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(inCongP_type,type,
% 2.48/1.54 inCongP: $o ).
% 2.48/1.54
% 2.48/1.54 thf(inCongP,definition,
% 2.48/1.54 ( inCongP
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( A = B )
% 2.48/1.54 => ! [Xx: $i,Xy: $i] :
% 2.48/1.54 ( ( Xx = Xy )
% 2.48/1.54 => ( ( in @ Xx @ A )
% 2.48/1.54 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(in__Cong_type,type,
% 2.48/1.54 in__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(in__Cong,definition,
% 2.48/1.54 ( in__Cong
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( A = B )
% 2.48/1.54 => ! [Xx: $i,Xy: $i] :
% 2.48/1.54 ( ( Xx = Xy )
% 2.48/1.54 => ( ( in @ Xx @ A )
% 2.48/1.54 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(exuE3u_type,type,
% 2.48/1.54 exuE3u: $o ).
% 2.48/1.54
% 2.48/1.54 thf(exuE3u,definition,
% 2.48/1.54 ( exuE3u
% 2.48/1.54 = ( ! [Xphi: $i > $o] :
% 2.48/1.54 ( ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 => ! [Xx: $i,Xy: $i] :
% 2.48/1.54 ( ( Xphi @ Xx )
% 2.48/1.54 => ( ( Xphi @ Xy )
% 2.48/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(exu__Cong_type,type,
% 2.48/1.54 exu__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(exu__Cong,definition,
% 2.48/1.54 ( exu__Cong
% 2.48/1.54 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.48/1.54 ( ! [Xx: $i,Xy: $i] :
% 2.48/1.54 ( ( Xx = Xy )
% 2.48/1.54 => ( ( Xphi @ Xx )
% 2.48/1.54 <=> ( Xpsi @ Xy ) ) )
% 2.48/1.54 => ( ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 <=> ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(emptyset__Cong_type,type,
% 2.48/1.54 emptyset__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(emptyset__Cong,definition,
% 2.48/1.54 ( emptyset__Cong
% 2.48/1.54 = ( emptyset = emptyset ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setadjoin__Cong_type,type,
% 2.48/1.54 setadjoin__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setadjoin__Cong,definition,
% 2.48/1.54 ( setadjoin__Cong
% 2.48/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.54 ( ( Xx = Xy )
% 2.48/1.54 => ! [Xz: $i,Xu: $i] :
% 2.48/1.54 ( ( Xz = Xu )
% 2.48/1.54 => ( ( setadjoin @ Xx @ Xz )
% 2.48/1.54 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(powerset__Cong_type,type,
% 2.48/1.54 powerset__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(powerset__Cong,definition,
% 2.48/1.54 ( powerset__Cong
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( A = B )
% 2.48/1.54 => ( ( powerset @ A )
% 2.48/1.54 = ( powerset @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setunion__Cong_type,type,
% 2.48/1.54 setunion__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setunion__Cong,definition,
% 2.48/1.54 ( setunion__Cong
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( A = B )
% 2.48/1.54 => ( ( setunion @ A )
% 2.48/1.54 = ( setunion @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(omega__Cong_type,type,
% 2.48/1.54 omega__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(omega__Cong,definition,
% 2.48/1.54 ( omega__Cong
% 2.48/1.54 = ( omega = omega ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(exuEu_type,type,
% 2.48/1.54 exuEu: $o ).
% 2.48/1.54
% 2.48/1.54 thf(exuEu,definition,
% 2.48/1.54 ( exuEu
% 2.48/1.54 = ( ! [Xphi: $i > $o] :
% 2.48/1.54 ( ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 => ! [Xx: $i,Xy: $i] :
% 2.48/1.54 ( ( Xphi @ Xx )
% 2.48/1.54 => ( ( Xphi @ Xy )
% 2.48/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(descr__Cong_type,type,
% 2.48/1.54 descr__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(descr__Cong,definition,
% 2.48/1.54 ( descr__Cong
% 2.48/1.54 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.48/1.54 ( ! [Xx: $i,Xy: $i] :
% 2.48/1.54 ( ( Xx = Xy )
% 2.48/1.54 => ( ( Xphi @ Xx )
% 2.48/1.54 <=> ( Xpsi @ Xy ) ) )
% 2.48/1.54 => ( ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 => ( ( exu
% 2.48/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.48/1.54 => ( ( descr
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 = ( descr
% 2.48/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(dsetconstr__Cong_type,type,
% 2.48/1.54 dsetconstr__Cong: $o ).
% 2.48/1.54
% 2.48/1.54 thf(dsetconstr__Cong,definition,
% 2.48/1.54 ( dsetconstr__Cong
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( A = B )
% 2.48/1.54 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.48/1.54 ( ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ! [Xy: $i] :
% 2.48/1.54 ( ( in @ Xy @ B )
% 2.48/1.54 => ( ( Xx = Xy )
% 2.48/1.54 => ( ( Xphi @ Xx )
% 2.48/1.54 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.48/1.54 => ( ( dsetconstr @ A
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 = ( dsetconstr @ B
% 2.48/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(subset_type,type,
% 2.48/1.54 subset: $i > $i > $o ).
% 2.48/1.54
% 2.48/1.54 thf(disjoint_type,type,
% 2.48/1.54 disjoint: $i > $i > $o ).
% 2.48/1.54
% 2.48/1.54 thf(setsmeet_type,type,
% 2.48/1.54 setsmeet: $i > $i > $o ).
% 2.48/1.54
% 2.48/1.54 thf(subsetI1_type,type,
% 2.48/1.54 subsetI1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(subsetI1,definition,
% 2.48/1.54 ( subsetI1
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( in @ Xx @ B ) )
% 2.48/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(eqimpsubset2_type,type,
% 2.48/1.54 eqimpsubset2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(eqimpsubset2,definition,
% 2.48/1.54 ( eqimpsubset2
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( A = B )
% 2.48/1.54 => ( subset @ B @ A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(eqimpsubset1_type,type,
% 2.48/1.54 eqimpsubset1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(eqimpsubset1,definition,
% 2.48/1.54 ( eqimpsubset1
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( A = B )
% 2.48/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(subsetI2_type,type,
% 2.48/1.54 subsetI2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(subsetI2,definition,
% 2.48/1.54 ( subsetI2
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ! [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( in @ Xx @ B ) )
% 2.48/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(emptysetsubset_type,type,
% 2.48/1.54 emptysetsubset: $o ).
% 2.48/1.54
% 2.48/1.54 thf(emptysetsubset,definition,
% 2.48/1.54 ( emptysetsubset
% 2.48/1.54 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(subsetE_type,type,
% 2.48/1.54 subsetE: $o ).
% 2.48/1.54
% 2.48/1.54 thf(subsetE,definition,
% 2.48/1.54 ( subsetE
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( ( in @ Xx @ A )
% 2.48/1.54 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(subsetE2_type,type,
% 2.48/1.54 subsetE2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(subsetE2,definition,
% 2.48/1.54 ( subsetE2
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( ~ ( in @ Xx @ B )
% 2.48/1.54 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(notsubsetI_type,type,
% 2.48/1.54 notsubsetI: $o ).
% 2.48/1.54
% 2.48/1.54 thf(notsubsetI,definition,
% 2.48/1.54 ( notsubsetI
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( ~ ( in @ Xx @ B )
% 2.48/1.54 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(notequalI1_type,type,
% 2.48/1.54 notequalI1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(notequalI1,definition,
% 2.48/1.54 ( notequalI1
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ~ ( subset @ A @ B )
% 2.48/1.54 => ( A != B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(notequalI2_type,type,
% 2.48/1.54 notequalI2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(notequalI2,definition,
% 2.48/1.54 ( notequalI2
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( ~ ( in @ Xx @ B )
% 2.48/1.54 => ( A != B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(subsetRefl_type,type,
% 2.48/1.54 subsetRefl: $o ).
% 2.48/1.54
% 2.48/1.54 thf(subsetRefl,definition,
% 2.48/1.54 ( subsetRefl
% 2.48/1.54 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(subsetTrans_type,type,
% 2.48/1.54 subsetTrans: $o ).
% 2.48/1.54
% 2.48/1.54 thf(subsetTrans,definition,
% 2.48/1.54 ( subsetTrans
% 2.48/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( ( subset @ B @ C )
% 2.48/1.54 => ( subset @ A @ C ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setadjoinSub_type,type,
% 2.48/1.54 setadjoinSub: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setadjoinSub,definition,
% 2.48/1.54 ( setadjoinSub
% 2.48/1.54 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setadjoinSub2_type,type,
% 2.48/1.54 setadjoinSub2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setadjoinSub2,definition,
% 2.48/1.54 ( setadjoinSub2
% 2.48/1.54 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(subset2powerset_type,type,
% 2.48/1.54 subset2powerset: $o ).
% 2.48/1.54
% 2.48/1.54 thf(subset2powerset,definition,
% 2.48/1.54 ( subset2powerset
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setextsub_type,type,
% 2.48/1.54 setextsub: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setextsub,definition,
% 2.48/1.54 ( setextsub
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( ( subset @ B @ A )
% 2.48/1.54 => ( A = B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(subsetemptysetimpeq_type,type,
% 2.48/1.54 subsetemptysetimpeq: $o ).
% 2.48/1.54
% 2.48/1.54 thf(subsetemptysetimpeq,definition,
% 2.48/1.54 ( subsetemptysetimpeq
% 2.48/1.54 = ( ! [A: $i] :
% 2.48/1.54 ( ( subset @ A @ emptyset )
% 2.48/1.54 => ( A = emptyset ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(powersetI1_type,type,
% 2.48/1.54 powersetI1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(powersetI1,definition,
% 2.48/1.54 ( powersetI1
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( subset @ B @ A )
% 2.48/1.54 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(powersetE1_type,type,
% 2.48/1.54 powersetE1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(powersetE1,definition,
% 2.48/1.54 ( powersetE1
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( in @ B @ ( powerset @ A ) )
% 2.48/1.54 => ( subset @ B @ A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(inPowerset_type,type,
% 2.48/1.54 inPowerset: $o ).
% 2.48/1.54
% 2.48/1.54 thf(inPowerset,definition,
% 2.48/1.54 ( inPowerset
% 2.48/1.54 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(powersetsubset_type,type,
% 2.48/1.54 powersetsubset: $o ).
% 2.48/1.54
% 2.48/1.54 thf(powersetsubset,definition,
% 2.48/1.54 ( powersetsubset
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(sepInPowerset_type,type,
% 2.48/1.54 sepInPowerset: $o ).
% 2.48/1.54
% 2.48/1.54 thf(sepInPowerset,definition,
% 2.48/1.54 ( sepInPowerset
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( in
% 2.48/1.54 @ ( dsetconstr @ A
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 @ ( powerset @ A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(sepSubset_type,type,
% 2.48/1.54 sepSubset: $o ).
% 2.48/1.54
% 2.48/1.54 thf(sepSubset,definition,
% 2.48/1.54 ( sepSubset
% 2.48/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.54 ( subset
% 2.48/1.54 @ ( dsetconstr @ A
% 2.48/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.54 @ A ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binunion_type,type,
% 2.48/1.54 binunion: $i > $i > $i ).
% 2.48/1.54
% 2.48/1.54 thf(binunionIL_type,type,
% 2.48/1.54 binunionIL: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binunionIL,definition,
% 2.48/1.54 ( binunionIL
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(upairset2IR_type,type,
% 2.48/1.54 upairset2IR: $o ).
% 2.48/1.54
% 2.48/1.54 thf(upairset2IR,definition,
% 2.48/1.54 ( upairset2IR
% 2.48/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binunionIR_type,type,
% 2.48/1.54 binunionIR: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binunionIR,definition,
% 2.48/1.54 ( binunionIR
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ B )
% 2.48/1.54 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binunionEcases_type,type,
% 2.48/1.54 binunionEcases: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binunionEcases,definition,
% 2.48/1.54 ( binunionEcases
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.48/1.54 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.48/1.54 => ( ( ( in @ Xx @ A )
% 2.48/1.54 => Xphi )
% 2.48/1.54 => ( ( ( in @ Xx @ B )
% 2.48/1.54 => Xphi )
% 2.48/1.54 => Xphi ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binunionE_type,type,
% 2.48/1.54 binunionE: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binunionE,definition,
% 2.48/1.54 ( binunionE
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.48/1.54 => ( ( in @ Xx @ A )
% 2.48/1.54 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binunionLsub_type,type,
% 2.48/1.54 binunionLsub: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binunionLsub,definition,
% 2.48/1.54 ( binunionLsub
% 2.48/1.54 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binunionRsub_type,type,
% 2.48/1.54 binunionRsub: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binunionRsub,definition,
% 2.48/1.54 ( binunionRsub
% 2.48/1.54 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersect_type,type,
% 2.48/1.54 binintersect: $i > $i > $i ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectI_type,type,
% 2.48/1.54 binintersectI: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectI,definition,
% 2.48/1.54 ( binintersectI
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( ( in @ Xx @ B )
% 2.48/1.54 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset5_type,type,
% 2.48/1.54 binintersectSubset5: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset5,definition,
% 2.48/1.54 ( binintersectSubset5
% 2.48/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 2.48/1.54 ( ( subset @ C @ A )
% 2.48/1.54 => ( ( subset @ C @ B )
% 2.48/1.54 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectEL_type,type,
% 2.48/1.54 binintersectEL: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectEL,definition,
% 2.48/1.54 ( binintersectEL
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.48/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectLsub_type,type,
% 2.48/1.54 binintersectLsub: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectLsub,definition,
% 2.48/1.54 ( binintersectLsub
% 2.48/1.54 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset2_type,type,
% 2.48/1.54 binintersectSubset2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset2,definition,
% 2.48/1.54 ( binintersectSubset2
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( ( binintersect @ A @ B )
% 2.48/1.54 = A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset3_type,type,
% 2.48/1.54 binintersectSubset3: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset3,definition,
% 2.48/1.54 ( binintersectSubset3
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( ( binintersect @ A @ B )
% 2.48/1.54 = B )
% 2.48/1.54 => ( subset @ B @ A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectER_type,type,
% 2.48/1.54 binintersectER: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectER,definition,
% 2.48/1.54 ( binintersectER
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.48/1.54 => ( in @ Xx @ B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(disjointsetsI1_type,type,
% 2.48/1.54 disjointsetsI1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(disjointsetsI1,definition,
% 2.48/1.54 ( disjointsetsI1
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ~ ? [Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 & ( in @ Xx @ B ) )
% 2.48/1.54 => ( ( binintersect @ A @ B )
% 2.48/1.54 = emptyset ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectRsub_type,type,
% 2.48/1.54 binintersectRsub: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectRsub,definition,
% 2.48/1.54 ( binintersectRsub
% 2.48/1.54 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset4_type,type,
% 2.48/1.54 binintersectSubset4: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset4,definition,
% 2.48/1.54 ( binintersectSubset4
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( subset @ B @ A )
% 2.48/1.54 => ( ( binintersect @ A @ B )
% 2.48/1.54 = B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset1_type,type,
% 2.48/1.54 binintersectSubset1: $o ).
% 2.48/1.54
% 2.48/1.54 thf(binintersectSubset1,definition,
% 2.48/1.54 ( binintersectSubset1
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( ( binintersect @ A @ B )
% 2.48/1.54 = A )
% 2.48/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(bs114d_type,type,
% 2.48/1.54 bs114d: $o ).
% 2.48/1.54
% 2.48/1.54 thf(bs114d,definition,
% 2.48/1.54 ( bs114d
% 2.48/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 2.48/1.54 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.48/1.54 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(regular_type,type,
% 2.48/1.54 regular: $i > $o ).
% 2.48/1.54
% 2.48/1.54 thf(setminus_type,type,
% 2.48/1.54 setminus: $i > $i > $i ).
% 2.48/1.54
% 2.48/1.54 thf(setminusI_type,type,
% 2.48/1.54 setminusI: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setminusI,definition,
% 2.48/1.54 ( setminusI
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ A )
% 2.48/1.54 => ( ~ ( in @ Xx @ B )
% 2.48/1.54 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setminusEL_type,type,
% 2.48/1.54 setminusEL: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setminusEL,definition,
% 2.48/1.54 ( setminusEL
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.48/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setminusER_type,type,
% 2.48/1.54 setminusER: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setminusER,definition,
% 2.48/1.54 ( setminusER
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.48/1.54 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setminusSubset2_type,type,
% 2.48/1.54 setminusSubset2: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setminusSubset2,definition,
% 2.48/1.54 ( setminusSubset2
% 2.48/1.54 = ( ! [A: $i,B: $i] :
% 2.48/1.54 ( ( subset @ A @ B )
% 2.48/1.54 => ( ( setminus @ A @ B )
% 2.48/1.54 = emptyset ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setminusERneg_type,type,
% 2.48/1.54 setminusERneg: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setminusERneg,definition,
% 2.48/1.54 ( setminusERneg
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.48/1.54 => ( ( in @ Xx @ A )
% 2.48/1.54 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setminusELneg_type,type,
% 2.48/1.54 setminusELneg: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setminusELneg,definition,
% 2.48/1.54 ( setminusELneg
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.48/1.54 => ( ~ ( in @ Xx @ B )
% 2.48/1.54 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setminusILneg_type,type,
% 2.48/1.54 setminusILneg: $o ).
% 2.48/1.54
% 2.48/1.54 thf(setminusILneg,definition,
% 2.48/1.54 ( setminusILneg
% 2.48/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ~ ( in @ Xx @ A )
% 2.48/1.54 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.48/1.54
% 2.48/1.54 thf(setminusIRneg,conjecture,
% 2.48/1.54 ( setextAx
% 2.48/1.54 => ( emptysetAx
% 2.48/1.54 => ( setadjoinAx
% 2.48/1.54 => ( powersetAx
% 2.48/1.54 => ( setunionAx
% 2.48/1.54 => ( omega0Ax
% 2.48/1.54 => ( omegaSAx
% 2.48/1.54 => ( omegaIndAx
% 2.48/1.54 => ( replAx
% 2.48/1.54 => ( foundationAx
% 2.48/1.54 => ( wellorderingAx
% 2.48/1.54 => ( descrp
% 2.48/1.54 => ( dsetconstrI
% 2.48/1.54 => ( dsetconstrEL
% 2.48/1.54 => ( dsetconstrER
% 2.48/1.54 => ( exuE1
% 2.48/1.54 => ( prop2setE
% 2.48/1.54 => ( emptysetE
% 2.48/1.54 => ( emptysetimpfalse
% 2.48/1.54 => ( notinemptyset
% 2.48/1.54 => ( exuE3e
% 2.48/1.54 => ( setext
% 2.48/1.54 => ( emptyI
% 2.48/1.54 => ( noeltsimpempty
% 2.48/1.54 => ( setbeta
% 2.48/1.54 => ( nonemptyE1
% 2.48/1.54 => ( nonemptyI
% 2.48/1.54 => ( nonemptyI1
% 2.48/1.54 => ( setadjoinIL
% 2.48/1.54 => ( emptyinunitempty
% 2.48/1.54 => ( setadjoinIR
% 2.48/1.54 => ( setadjoinE
% 2.48/1.54 => ( setadjoinOr
% 2.48/1.54 => ( setoftrueEq
% 2.48/1.54 => ( powersetI
% 2.48/1.54 => ( emptyinPowerset
% 2.48/1.54 => ( emptyInPowerset
% 2.48/1.54 => ( powersetE
% 2.48/1.54 => ( setunionI
% 2.48/1.54 => ( setunionE
% 2.48/1.54 => ( subPowSU
% 2.48/1.54 => ( exuE2
% 2.48/1.54 => ( nonemptyImpWitness
% 2.48/1.54 => ( uniqinunit
% 2.48/1.54 => ( notinsingleton
% 2.48/1.54 => ( eqinunit
% 2.48/1.54 => ( singletonsswitch
% 2.48/1.54 => ( upairsetE
% 2.48/1.54 => ( upairsetIL
% 2.48/1.54 => ( upairsetIR
% 2.48/1.54 => ( emptyE1
% 2.48/1.54 => ( vacuousDall
% 2.48/1.54 => ( quantDeMorgan1
% 2.48/1.54 => ( quantDeMorgan2
% 2.48/1.54 => ( quantDeMorgan3
% 2.48/1.54 => ( quantDeMorgan4
% 2.48/1.54 => ( prop2setI
% 2.48/1.54 => ( prop2set2propI
% 2.48/1.54 => ( notdexE
% 2.48/1.54 => ( notdallE
% 2.48/1.54 => ( exuI1
% 2.48/1.54 => ( exuI3
% 2.48/1.54 => ( exuI2
% 2.48/1.54 => ( inCongP
% 2.48/1.54 => ( in__Cong
% 2.48/1.54 => ( exuE3u
% 2.48/1.54 => ( exu__Cong
% 2.48/1.54 => ( emptyset__Cong
% 2.48/1.54 => ( setadjoin__Cong
% 2.48/1.54 => ( powerset__Cong
% 2.48/1.54 => ( setunion__Cong
% 2.48/1.54 => ( omega__Cong
% 2.48/1.54 => ( exuEu
% 2.48/1.54 => ( descr__Cong
% 2.48/1.54 => ( dsetconstr__Cong
% 2.48/1.54 => ( subsetI1
% 2.48/1.54 => ( eqimpsubset2
% 2.48/1.54 => ( eqimpsubset1
% 2.48/1.54 => ( subsetI2
% 2.48/1.54 => ( emptysetsubset
% 2.48/1.54 => ( subsetE
% 2.48/1.54 => ( subsetE2
% 2.48/1.54 => ( notsubsetI
% 2.48/1.54 => ( notequalI1
% 2.48/1.54 => ( notequalI2
% 2.48/1.54 => ( subsetRefl
% 2.48/1.54 => ( subsetTrans
% 2.48/1.54 => ( setadjoinSub
% 2.48/1.54 => ( setadjoinSub2
% 2.48/1.54 => ( subset2powerset
% 2.48/1.54 => ( setextsub
% 2.48/1.54 => ( subsetemptysetimpeq
% 2.48/1.54 => ( powersetI1
% 2.48/1.54 => ( powersetE1
% 2.48/1.54 => ( inPowerset
% 2.48/1.54 => ( powersetsubset
% 2.48/1.54 => ( sepInPowerset
% 2.48/1.54 => ( sepSubset
% 2.48/1.54 => ( binunionIL
% 2.48/1.54 => ( upairset2IR
% 2.48/1.54 => ( binunionIR
% 2.48/1.54 => ( binunionEcases
% 2.48/1.54 => ( binunionE
% 2.48/1.54 => ( binunionLsub
% 2.48/1.54 => ( binunionRsub
% 2.48/1.54 => ( binintersectI
% 2.48/1.54 => ( binintersectSubset5
% 2.48/1.54 => ( binintersectEL
% 2.48/1.54 => ( binintersectLsub
% 2.48/1.54 => ( binintersectSubset2
% 2.48/1.54 => ( binintersectSubset3
% 2.48/1.54 => ( binintersectER
% 2.48/1.54 => ( disjointsetsI1
% 2.48/1.54 => ( binintersectRsub
% 2.48/1.54 => ( binintersectSubset4
% 2.48/1.54 => ( binintersectSubset1
% 2.48/1.54 => ( bs114d
% 2.48/1.54 => ( setminusI
% 2.48/1.54 => ( setminusEL
% 2.48/1.54 => ( setminusER
% 2.48/1.54 => ( setminusSubset2
% 2.48/1.54 => ( setminusERneg
% 2.48/1.54 => ( setminusELneg
% 2.48/1.54 => ( setminusILneg
% 2.48/1.54 => ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.54 ( ( in @ Xx @ B )
% 2.48/1.54 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.48/1.54 ------------------------
% 2.48/1.56 % (4097)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_3995 for (2999ds/2Mi)
% 2.48/1.56 % (4093)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/183Mi)
% 2.48/1.56 % (4099)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/18Mi)
% 2.48/1.56 % (4095)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_3995 for (2999ds/27Mi)
% 2.48/1.56 % (4098)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_3995 for (2999ds/275Mi)
% 2.48/1.56 % (4096)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/2Mi)
% 2.48/1.56 % (4094)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_3995 for (2999ds/4Mi)
% 2.48/1.56 % (4097)Instruction limit reached!
% 2.48/1.56 % (4097)------------------------------
% 2.48/1.56 % (4097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.56 % (4097)Termination reason: Unknown
% 2.48/1.56 % (4097)Termination phase: shuffling
% 2.48/1.56
% 2.48/1.56 % (4097)Memory used [KB]: 1151
% 2.48/1.56 % (4097)Time elapsed: 0.003 s
% 2.48/1.56 % (4097)Instructions burned: 2 (million)
% 2.48/1.56 % (4097)------------------------------
% 2.48/1.56 % (4097)------------------------------
% 2.48/1.56 % (4096)Instruction limit reached!
% 2.48/1.56 % (4096)------------------------------
% 2.48/1.56 % (4096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.56 % (4096)Termination reason: Unknown
% 2.48/1.56 % (4096)Termination phase: shuffling
% 2.48/1.56
% 2.48/1.56 % (4096)Memory used [KB]: 1151
% 2.48/1.56 % (4096)Time elapsed: 0.003 s
% 2.48/1.56 % (4096)Instructions burned: 3 (million)
% 2.48/1.56 % (4096)------------------------------
% 2.48/1.56 % (4096)------------------------------
% 2.48/1.56 % (4094)Instruction limit reached!
% 2.48/1.56 % (4094)------------------------------
% 2.48/1.56 % (4094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.56 % (4094)Termination reason: Unknown
% 2.48/1.56 % (4094)Termination phase: shuffling
% 2.48/1.56
% 2.48/1.56 % (4094)Memory used [KB]: 1279
% 2.48/1.56 % (4094)Time elapsed: 0.004 s
% 2.48/1.56 % (4094)Instructions burned: 5 (million)
% 2.48/1.56 % (4094)------------------------------
% 2.48/1.56 % (4094)------------------------------
% 2.48/1.57 % (4099)Instruction limit reached!
% 2.48/1.57 % (4099)------------------------------
% 2.48/1.57 % (4099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.57 % (4099)Termination reason: Unknown
% 2.48/1.57 % (4099)Termination phase: Preprocessing 3
% 2.48/1.57
% 2.48/1.57 % (4099)Memory used [KB]: 1535
% 2.48/1.57 % (4099)Time elapsed: 0.010 s
% 2.48/1.57 % (4099)Instructions burned: 18 (million)
% 2.48/1.57 % (4099)------------------------------
% 2.48/1.57 % (4099)------------------------------
% 2.48/1.57 % (4095)Instruction limit reached!
% 2.48/1.57 % (4095)------------------------------
% 2.48/1.57 % (4095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.57 % (4095)Termination reason: Unknown
% 2.48/1.57 % (4095)Termination phase: Property scanning
% 2.48/1.57
% 2.48/1.57 % (4095)Memory used [KB]: 1535
% 2.48/1.57 % (4095)Time elapsed: 0.014 s
% 2.48/1.57 % (4095)Instructions burned: 27 (million)
% 2.48/1.57 % (4095)------------------------------
% 2.48/1.57 % (4095)------------------------------
% 2.48/1.58 % (4100)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/3Mi)
% 2.48/1.58 % (4101)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_3995 for (2999ds/37Mi)
% 2.48/1.58 % (4100)Instruction limit reached!
% 2.48/1.58 % (4100)------------------------------
% 2.48/1.58 % (4100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.58 % (4102)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_3995 for (2999ds/15Mi)
% 2.48/1.58 % (4100)Termination reason: Unknown
% 2.48/1.58 % (4100)Termination phase: shuffling
% 2.48/1.58
% 2.48/1.58 % (4100)Memory used [KB]: 1279
% 2.48/1.58 % (4100)Time elapsed: 0.004 s
% 2.48/1.58 % (4100)Instructions burned: 5 (million)
% 2.48/1.58 % (4100)------------------------------
% 2.48/1.58 % (4100)------------------------------
% 2.48/1.59 % (4103)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_3995 for (2999ds/3Mi)
% 2.48/1.59 % (4102)Instruction limit reached!
% 2.48/1.59 % (4102)------------------------------
% 2.48/1.59 % (4102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.59 % (4102)Termination reason: Unknown
% 2.48/1.59 % (4102)Termination phase: Preprocessing 1
% 2.48/1.59
% 2.48/1.59 % (4102)Memory used [KB]: 1407
% 2.48/1.59 % (4102)Time elapsed: 0.009 s
% 2.48/1.59 % (4102)Instructions burned: 16 (million)
% 2.48/1.59 % (4102)------------------------------
% 2.48/1.59 % (4102)------------------------------
% 2.48/1.59 % (4103)Instruction limit reached!
% 2.48/1.59 % (4103)------------------------------
% 2.48/1.59 % (4103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.59 % (4103)Termination reason: Unknown
% 2.48/1.59 % (4103)Termination phase: shuffling
% 2.48/1.59
% 2.48/1.59 % (4103)Memory used [KB]: 1151
% 2.48/1.59 % (4103)Time elapsed: 0.003 s
% 2.48/1.59 % (4103)Instructions burned: 3 (million)
% 2.48/1.59 % (4103)------------------------------
% 2.48/1.59 % (4103)------------------------------
% 2.48/1.59 % (4104)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_3995 for (2999ds/1041Mi)
% 2.48/1.59 % (4101)Instruction limit reached!
% 2.48/1.59 % (4101)------------------------------
% 2.48/1.59 % (4101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.59 % (4101)Termination reason: Unknown
% 2.48/1.59 % (4101)Termination phase: Property scanning
% 2.48/1.59
% 2.48/1.59 % (4101)Memory used [KB]: 1663
% 2.48/1.59 % (4101)Time elapsed: 0.018 s
% 2.48/1.59 % (4101)Instructions burned: 38 (million)
% 2.48/1.59 % (4101)------------------------------
% 2.48/1.59 % (4101)------------------------------
% 2.48/1.59 % (4105)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/7Mi)
% 2.52/1.60 % (4105)Instruction limit reached!
% 2.52/1.60 % (4105)------------------------------
% 2.52/1.60 % (4105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.60 % (4105)Termination reason: Unknown
% 2.52/1.60 % (4105)Termination phase: shuffling
% 2.52/1.60
% 2.52/1.60 % (4105)Memory used [KB]: 1279
% 2.52/1.60 % (4105)Time elapsed: 0.005 s
% 2.52/1.60 % (4105)Instructions burned: 7 (million)
% 2.52/1.60 % (4105)------------------------------
% 2.52/1.60 % (4105)------------------------------
% 2.52/1.60 % (4106)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/16Mi)
% 2.52/1.60 % (4107)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_3995 for (2999ds/3Mi)
% 2.52/1.60 % (4107)Instruction limit reached!
% 2.52/1.60 % (4107)------------------------------
% 2.52/1.60 % (4107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.60 % (4107)Termination reason: Unknown
% 2.52/1.60 % (4107)Termination phase: shuffling
% 2.52/1.60
% 2.52/1.60 % (4107)Memory used [KB]: 1151
% 2.52/1.60 % (4107)Time elapsed: 0.003 s
% 2.52/1.60 % (4107)Instructions burned: 3 (million)
% 2.52/1.60 % (4107)------------------------------
% 2.52/1.60 % (4107)------------------------------
% 2.52/1.61 % (4106)Instruction limit reached!
% 2.52/1.61 % (4106)------------------------------
% 2.52/1.61 % (4106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.61 % (4106)Termination reason: Unknown
% 2.52/1.61 % (4106)Termination phase: shuffling
% 2.52/1.61
% 2.52/1.61 % (4106)Memory used [KB]: 1535
% 2.52/1.61 % (4106)Time elapsed: 0.009 s
% 2.52/1.61 % (4106)Instructions burned: 16 (million)
% 2.52/1.61 % (4106)------------------------------
% 2.52/1.61 % (4106)------------------------------
% 2.52/1.61 % (4108)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_3995 for (2999ds/3Mi)
% 2.52/1.61 % (4108)Instruction limit reached!
% 2.52/1.61 % (4108)------------------------------
% 2.52/1.61 % (4108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.61 % (4108)Termination reason: Unknown
% 2.52/1.61 % (4108)Termination phase: shuffling
% 2.52/1.61
% 2.52/1.61 % (4108)Memory used [KB]: 1151
% 2.52/1.61 % (4108)Time elapsed: 0.003 s
% 2.52/1.61 % (4108)Instructions burned: 3 (million)
% 2.52/1.61 % (4108)------------------------------
% 2.52/1.61 % (4108)------------------------------
% 2.52/1.61 % (4109)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/7Mi)
% 2.52/1.62 % (4109)Instruction limit reached!
% 2.52/1.62 % (4109)------------------------------
% 2.52/1.62 % (4109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.62 % (4109)Termination reason: Unknown
% 2.52/1.62 % (4109)Termination phase: shuffling
% 2.52/1.62
% 2.52/1.62 % (4109)Memory used [KB]: 1279
% 2.52/1.62 % (4109)Time elapsed: 0.005 s
% 2.52/1.62 % (4109)Instructions burned: 9 (million)
% 2.52/1.62 % (4109)------------------------------
% 2.52/1.62 % (4109)------------------------------
% 2.52/1.62 % (4110)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/3Mi)
% 2.52/1.62 % (4110)Instruction limit reached!
% 2.52/1.62 % (4110)------------------------------
% 2.52/1.62 % (4110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.62 % (4110)Termination reason: Unknown
% 2.52/1.62 % (4110)Termination phase: shuffling
% 2.52/1.62
% 2.52/1.62 % (4110)Memory used [KB]: 1151
% 2.52/1.62 % (4110)Time elapsed: 0.003 s
% 2.52/1.62 % (4110)Instructions burned: 3 (million)
% 2.52/1.62 % (4110)------------------------------
% 2.52/1.62 % (4110)------------------------------
% 2.52/1.63 % (4111)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/4Mi)
% 2.52/1.63 % (4112)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/18Mi)
% 2.52/1.63 % (4111)Instruction limit reached!
% 2.52/1.63 % (4111)------------------------------
% 2.52/1.63 % (4111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.63 % (4111)Termination reason: Unknown
% 2.52/1.63 % (4111)Termination phase: shuffling
% 2.52/1.63
% 2.52/1.63 % (4111)Memory used [KB]: 1279
% 2.52/1.63 % (4111)Time elapsed: 0.004 s
% 2.52/1.63 % (4111)Instructions burned: 5 (million)
% 2.52/1.63 % (4111)------------------------------
% 2.52/1.63 % (4111)------------------------------
% 2.52/1.63 % (4113)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/710Mi)
% 2.52/1.64 % (4112)Instruction limit reached!
% 2.52/1.64 % (4112)------------------------------
% 2.52/1.64 % (4112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.64 % (4112)Termination reason: Unknown
% 2.52/1.64 % (4112)Termination phase: Property scanning
% 2.52/1.64
% 2.52/1.64 % (4112)Memory used [KB]: 1535
% 2.52/1.64 % (4112)Time elapsed: 0.010 s
% 2.52/1.64 % (4112)Instructions burned: 19 (million)
% 2.52/1.64 % (4112)------------------------------
% 2.52/1.64 % (4112)------------------------------
% 2.52/1.64 % (4114)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/6Mi)
% 2.52/1.64 % (4114)Instruction limit reached!
% 2.52/1.64 % (4114)------------------------------
% 2.52/1.64 % (4114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.64 % (4114)Termination reason: Unknown
% 2.52/1.64 % (4114)Termination phase: shuffling
% 2.52/1.64
% 2.52/1.64 % (4114)Memory used [KB]: 1279
% 2.52/1.64 % (4114)Time elapsed: 0.004 s
% 2.52/1.64 % (4114)Instructions burned: 6 (million)
% 2.52/1.64 % (4114)------------------------------
% 2.52/1.64 % (4114)------------------------------
% 2.52/1.64 % (4093)Instruction limit reached!
% 2.52/1.64 % (4093)------------------------------
% 2.52/1.64 % (4093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.64 % (4093)Termination reason: Unknown
% 2.52/1.64 % (4093)Termination phase: Saturation
% 2.52/1.64
% 2.52/1.64 % (4093)Memory used [KB]: 6908
% 2.52/1.64 % (4093)Time elapsed: 0.085 s
% 2.52/1.64 % (4093)Instructions burned: 183 (million)
% 2.52/1.64 % (4093)------------------------------
% 2.52/1.64 % (4093)------------------------------
% 2.52/1.64 % (4115)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_3995 for (2999ds/902Mi)
% 2.52/1.65 % (4116)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_3995 for (2999ds/21Mi)
% 2.52/1.66 % (4117)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3995 for (2999ds/5Mi)
% 2.52/1.66 % (4117)Instruction limit reached!
% 2.52/1.66 % (4117)------------------------------
% 2.52/1.66 % (4117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.66 % (4117)Termination reason: Unknown
% 2.52/1.66 % (4117)Termination phase: shuffling
% 2.52/1.66
% 2.52/1.66 % (4117)Memory used [KB]: 1279
% 2.52/1.66 % (4117)Time elapsed: 0.004 s
% 2.52/1.66 % (4117)Instructions burned: 6 (million)
% 2.52/1.66 % (4117)------------------------------
% 2.52/1.66 % (4117)------------------------------
% 2.52/1.66 % (4118)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_3995 for (2999ds/6Mi)
% 2.52/1.66 % (4116)Instruction limit reached!
% 2.52/1.66 % (4116)------------------------------
% 2.52/1.66 % (4116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.66 % (4116)Termination reason: Unknown
% 2.52/1.66 % (4116)Termination phase: Property scanning
% 2.52/1.66
% 2.52/1.66 % (4116)Memory used [KB]: 1535
% 2.52/1.66 % (4116)Time elapsed: 0.011 s
% 2.52/1.66 % (4116)Instructions burned: 21 (million)
% 2.52/1.66 % (4116)------------------------------
% 2.52/1.66 % (4116)------------------------------
% 2.52/1.66 % (4118)Instruction limit reached!
% 2.52/1.66 % (4118)------------------------------
% 2.52/1.66 % (4118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.66 % (4118)Termination reason: Unknown
% 2.52/1.66 % (4118)Termination phase: shuffling
% 2.52/1.66
% 2.52/1.66 % (4118)Memory used [KB]: 1279
% 2.52/1.66 % (4118)Time elapsed: 0.004 s
% 2.52/1.66 % (4118)Instructions burned: 6 (million)
% 2.52/1.66 % (4118)------------------------------
% 2.52/1.66 % (4118)------------------------------
% 2.52/1.67 % (4119)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3995 for (2998ds/377Mi)
% 2.52/1.68 % (4121)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_3995 for (2998ds/19Mi)
% 2.52/1.68 % (4120)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_3995 for (2998ds/779Mi)
% 2.52/1.69 % (4121)Instruction limit reached!
% 2.52/1.69 % (4121)------------------------------
% 2.52/1.69 % (4121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.69 % (4121)Termination reason: Unknown
% 2.52/1.69 % (4121)Termination phase: Property scanning
% 2.52/1.69
% 2.52/1.69 % (4121)Memory used [KB]: 1535
% 2.52/1.69 % (4121)Time elapsed: 0.010 s
% 2.52/1.69 % (4121)Instructions burned: 19 (million)
% 2.52/1.69 % (4121)------------------------------
% 2.52/1.69 % (4121)------------------------------
% 2.52/1.70 % (4098)Instruction limit reached!
% 2.52/1.70 % (4098)------------------------------
% 2.52/1.70 % (4098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.70 % (4098)Termination reason: Unknown
% 2.52/1.70 % (4098)Termination phase: Saturation
% 2.52/1.70
% 2.52/1.70 % (4098)Memory used [KB]: 7803
% 2.52/1.70 % (4098)Time elapsed: 0.140 s
% 2.52/1.70 % (4098)Instructions burned: 276 (million)
% 2.52/1.70 % (4098)------------------------------
% 2.52/1.70 % (4098)------------------------------
% 2.52/1.70 % (4122)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3995 for (2998ds/879Mi)
% 2.52/1.71 % (4115)First to succeed.
% 2.52/1.71 % (4115)Refutation found. Thanks to Tanya!
% 2.52/1.71 % SZS status Theorem for DTF2THF_3995
% 2.52/1.71 % SZS output start Proof for DTF2THF_3995
% 2.52/1.71 thf(func_def_0, type, in: $i > $i > $o).
% 2.52/1.71 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.52/1.71 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.52/1.71 thf(func_def_8, type, powerset: $i > $i).
% 2.52/1.71 thf(func_def_10, type, setunion: $i > $i).
% 2.52/1.71 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.52/1.71 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_26, type, prop2set: $o > $i).
% 2.52/1.71 thf(func_def_36, type, nonempty: $i > $o).
% 2.52/1.71 thf(func_def_69, type, set2prop: $i > $o).
% 2.52/1.71 thf(func_def_88, type, subset: $i > $i > $o).
% 2.52/1.71 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.52/1.71 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.52/1.71 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.52/1.71 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.52/1.71 thf(func_def_135, type, regular: $i > $o).
% 2.52/1.71 thf(func_def_136, type, setminus: $i > $i > $i).
% 2.52/1.71 thf(func_def_156, type, sP0: $i > $i > $o).
% 2.52/1.71 thf(func_def_157, type, sP1: $i > $o).
% 2.52/1.71 thf(func_def_158, type, sP2: $i > $i > $o).
% 2.52/1.71 thf(func_def_159, type, sP3: $i > $i > $o).
% 2.52/1.71 thf(func_def_170, type, sK14: $i > $i > $i).
% 2.52/1.71 thf(func_def_171, type, sK15: $i > $i > $i).
% 2.52/1.71 thf(func_def_172, type, sK16: $i > $i > $i).
% 2.52/1.71 thf(func_def_173, type, sK17: $i > $i > $i).
% 2.52/1.71 thf(func_def_174, type, sK18: $i > $i > $i > $i).
% 2.52/1.71 thf(func_def_175, type, sK19: $i > $i).
% 2.52/1.71 thf(func_def_176, type, sK20: $i > $i).
% 2.52/1.71 thf(func_def_177, type, sK21: $i > $i).
% 2.52/1.71 thf(func_def_178, type, sK22: $i > $i).
% 2.52/1.71 thf(func_def_179, type, sK23: $i > $i > $i).
% 2.52/1.71 thf(func_def_180, type, sK24: $i > $i > $i > $i).
% 2.52/1.71 thf(func_def_181, type, sK25: $i > $i > $i > $i).
% 2.52/1.71 thf(func_def_182, type, sK26: $i > $i > $i).
% 2.52/1.71 thf(func_def_183, type, sK27: $i > $i > $i).
% 2.52/1.71 thf(func_def_184, type, sK28: $i > $i).
% 2.52/1.71 thf(func_def_185, type, sK29: $i > $i > $i).
% 2.52/1.71 thf(func_def_187, type, sK31: $i > $i).
% 2.52/1.71 thf(func_def_188, type, sK32: $i > $i).
% 2.52/1.71 thf(func_def_195, type, sK39: $i > $i > $i).
% 2.52/1.71 thf(func_def_213, type, sK57: $i > $o).
% 2.52/1.71 thf(func_def_214, type, sK58: ($i > $o) > $i).
% 2.52/1.71 thf(func_def_218, type, sK62: $i > $i).
% 2.52/1.71 thf(func_def_243, type, sK87: $i > $o).
% 2.52/1.71 thf(func_def_244, type, sK88: $i > $i).
% 2.52/1.71 thf(func_def_245, type, sK89: ($i > $o) > $i).
% 2.52/1.71 thf(func_def_255, type, sK99: $i > $o).
% 2.52/1.71 thf(func_def_278, type, sK122: $i > $i > $o).
% 2.52/1.71 thf(func_def_280, type, sK124: $i > $i).
% 2.52/1.71 thf(func_def_281, type, sK125: $i > $i).
% 2.52/1.71 thf(func_def_282, type, sK126: $i > ($i > $i > $o) > $i).
% 2.52/1.71 thf(func_def_283, type, sK127: $i > ($i > $i > $o) > $i).
% 2.52/1.71 thf(func_def_284, type, sK128: $i > $i > ($i > $i > $o) > $i).
% 2.52/1.71 thf(func_def_287, type, sK131: $i > $i).
% 2.52/1.71 thf(func_def_288, type, sK132: ($i > $o) > $i > $i).
% 2.52/1.71 thf(func_def_290, type, sK134: $i > $o).
% 2.52/1.71 thf(func_def_294, type, sK138: $i > $i > $i).
% 2.52/1.71 thf(func_def_299, type, sK143: $i > $i > $i).
% 2.52/1.71 thf(func_def_314, type, sK158: ($i > $o) > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_315, type, sK159: ($i > $o) > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_316, type, sK160: $i > $o).
% 2.52/1.71 thf(func_def_317, type, sK161: $i > $o).
% 2.52/1.71 thf(func_def_323, type, sK167: $i > $i).
% 2.52/1.71 thf(func_def_327, type, sK171: $i > $o).
% 2.52/1.71 thf(func_def_328, type, sK172: $i > $o).
% 2.52/1.71 thf(func_def_329, type, sK173: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.52/1.71 thf(func_def_330, type, sK174: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.52/1.71 thf(func_def_336, type, sK180: $i > $o).
% 2.52/1.71 thf(func_def_338, type, sK182: ($i > $o) > $i).
% 2.52/1.71 thf(func_def_339, type, sK183: ($i > $o) > $i).
% 2.52/1.71 thf(func_def_340, type, sK184: $i > $i > $i).
% 2.52/1.71 thf(func_def_347, type, sK191: $i > $o).
% 2.52/1.71 thf(func_def_348, type, sK192: $i > $i).
% 2.52/1.71 thf(func_def_349, type, sK193: ($i > $o) > $i).
% 2.52/1.71 thf(func_def_355, type, sK199: $i > $o).
% 2.52/1.71 thf(func_def_358, type, sK202: $i > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_359, type, sK203: $i > $i).
% 2.52/1.71 thf(func_def_361, type, sK205: $i > $o).
% 2.52/1.71 thf(func_def_366, type, sK210: $i > $o).
% 2.52/1.71 thf(func_def_372, type, sK216: $i > $o).
% 2.52/1.71 thf(func_def_385, type, sK229: $i > $i).
% 2.52/1.71 thf(func_def_391, type, sK235: $i > $i > $i).
% 2.52/1.71 thf(func_def_392, type, sK236: $i > $i > $i).
% 2.52/1.71 thf(func_def_402, type, sK246: $i > $o).
% 2.52/1.71 thf(func_def_407, type, sK251: $i > $o).
% 2.52/1.71 thf(func_def_410, type, sK254: $i > $o).
% 2.52/1.71 thf(func_def_411, type, sK255: $i > $i > $i).
% 2.52/1.71 thf(func_def_418, type, sK262: $i > $o).
% 2.52/1.71 thf(func_def_423, type, sK267: ($i > $o) > $i > $i).
% 2.52/1.71 thf(func_def_425, type, sK269: $i > $o).
% 2.52/1.71 thf(func_def_427, type, sK271: $i > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_428, type, sK272: $i > $o).
% 2.52/1.71 thf(func_def_431, type, sK275: $i > $o).
% 2.52/1.71 thf(func_def_432, type, sK276: $i > $o).
% 2.52/1.71 thf(func_def_433, type, sK277: ($i > $o) > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_434, type, sK278: ($i > $o) > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_436, type, sK280: $i > $o).
% 2.52/1.71 thf(func_def_442, type, sK286: $i > $o).
% 2.52/1.71 thf(func_def_445, type, sK289: $i > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_447, type, sK291: $i > $i).
% 2.52/1.71 thf(func_def_449, type, sK293: $i > $i).
% 2.52/1.71 thf(func_def_453, type, sK297: $i > $o).
% 2.52/1.71 thf(func_def_455, type, sK299: $i > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_456, type, sK300: $i > $o).
% 2.52/1.71 thf(func_def_460, type, sK304: ($i > $o) > $i > $i).
% 2.52/1.71 thf(func_def_462, type, sK306: $i > $o).
% 2.52/1.71 thf(func_def_466, type, sK310: $i > $i > $i).
% 2.52/1.71 thf(func_def_470, type, sK314: $o > $i > $i > $i).
% 2.52/1.71 thf(func_def_473, type, sK317: $i > $o).
% 2.52/1.71 thf(func_def_475, type, sK319: $i > ($i > $o) > $i).
% 2.52/1.71 thf(func_def_478, type, sK322: $i > $o).
% 2.52/1.71 thf(func_def_484, type, sK328: $i > $i > $i).
% 2.52/1.71 thf(func_def_489, type, sK333: $i > $o).
% 2.52/1.71 thf(func_def_499, type, ph343: !>[X0: $tType]:(X0)).
% 2.52/1.71 thf(f1883,plain,(
% 2.52/1.71 $false),
% 2.52/1.71 inference(trivial_inequality_removal,[status(thm)],[f1873])).
% 2.52/1.71 thf(f1873,plain,(
% 2.52/1.71 ($true != $true)),
% 2.52/1.71 inference(superposition,[status(thm)],[f1854,f1541])).
% 2.52/1.71 thf(f1541,plain,(
% 2.52/1.71 ($true = (in @ sK244 @ sK245))),
% 2.52/1.71 inference(cnf_transformation,[status(thm)],[f964])).
% 2.52/1.71 thf(f964,plain,(
% 2.52/1.71 (subsetemptysetimpeq = $true) & (omega0Ax = $true) & (powersetE = $true) & (omega__Cong = $true) & (binunionE = $true) & (foundationAx = $true) & (in__Cong = $true) & (vacuousDall = $true) & (powersetI = $true) & (quantDeMorgan3 = $true) & (binintersectLsub = $true) & (nonemptyImpWitness = $true) & (exuE3e = $true) & (setadjoin__Cong = $true) & (binunionRsub = $true) & (quantDeMorgan1 = $true) & (setminusILneg = $true) & (subsetRefl = $true) & (exuEu = $true) & (binintersectI = $true) & (notinsingleton = $true) & (binintersectSubset1 = $true) & (emptyE1 = $true) & (setunionI = $true) & (setminusER = $true) & (powersetsubset = $true) & (quantDeMorgan2 = $true) & (uniqinunit = $true) & (omegaSAx = $true) & (setadjoinIR = $true) & (upairsetIR = $true) & (upairset2IR = $true) & (subPowSU = $true) & (prop2set2propI = $true) & (binintersectEL = $true) & (sepSubset = $true) & (upairsetIL = $true) & (omegaIndAx = $true) & (emptysetimpfalse = $true) & (exuI1 = $true) & (binunionIL = $true) & (nonemptyI = $true) & (setminusEL = $true) & (setoftrueEq = $true) & (subsetE2 = $true) & (emptysetAx = $true) & (setextAx = $true) & (setunion__Cong = $true) & (noeltsimpempty = $true) & (binintersectSubset5 = $true) & (binintersectER = $true) & (quantDeMorgan4 = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (binunionIR = $true) & (eqinunit = $true) & (setadjoinAx = $true) & (setminusI = $true) & (setbeta = $true) & (disjointsetsI1 = $true) & (($true = (in @ sK244 @ (setminus @ sK243 @ sK245))) & ($true = (in @ sK244 @ sK245))) & (subsetE = $true) & (setunionE = $true) & (replAx = $true) & (subsetI1 = $true) & (emptyset__Cong = $true) & (wellorderingAx = $true) & (setadjoinOr = $true) & (descr__Cong = $true) & (exuE1 = $true) & (powersetE1 = $true) & (descrp = $true) & (subsetTrans = $true) & (powersetI1 = $true) & (binintersectSubset4 = $true) & (dsetconstrI = $true) & (dsetconstr__Cong = $true) & (subset2powerset = $true) & (notdallE = $true) & (binintersectSubset2 = $true) & (notsubsetI = $true) & (setunionAx = $true) & (emptyinPowerset = $true) & (setadjoinSub2 = $true) & (inCongP = $true) & (notequalI1 = $true) & (emptysetsubset = $true) & (eqimpsubset2 = $true) & (prop2setI = $true) & (exu__Cong = $true) & (nonemptyE1 = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (singletonsswitch = $true) & (powersetAx = $true) & (setadjoinSub = $true) & (notdexE = $true) & (notinemptyset = $true) & (exuI3 = $true) & (exuE3u = $true) & (upairsetE = $true) & (setadjoinIL = $true) & (setextsub = $true) & (notequalI2 = $true) & (binintersectSubset3 = $true) & (bs114d = $true) & (nonemptyI1 = $true) & (emptyI = $true) & (sepInPowerset = $true) & (emptyinunitempty = $true) & (powerset__Cong = $true) & (binunionEcases = $true) & (binunionLsub = $true) & (binintersectRsub = $true) & (setminusERneg = $true) & (emptyInPowerset = $true) & (setminusSubset2 = $true) & (setminusELneg = $true) & (dsetconstrEL = $true) & (setext = $true) & (exuE2 = $true) & (emptysetE = $true) & (inPowerset = $true) & (exuI2 = $true) & (setadjoinE = $true)),
% 2.52/1.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK243,sK244,sK245])],[f505,f963])).
% 2.52/1.71 thf(f963,plain,(
% 2.52/1.71 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) & ($true = (in @ X1 @ X2))) => (($true = (in @ sK244 @ (setminus @ sK243 @ sK245))) & ($true = (in @ sK244 @ sK245)))),
% 2.52/1.71 introduced(definition,[],[choice_axiom])).
% 2.52/1.71 thf(f505,plain,(
% 2.52/1.71 (subsetemptysetimpeq = $true) & (omega0Ax = $true) & (powersetE = $true) & (omega__Cong = $true) & (binunionE = $true) & (foundationAx = $true) & (in__Cong = $true) & (vacuousDall = $true) & (powersetI = $true) & (quantDeMorgan3 = $true) & (binintersectLsub = $true) & (nonemptyImpWitness = $true) & (exuE3e = $true) & (setadjoin__Cong = $true) & (binunionRsub = $true) & (quantDeMorgan1 = $true) & (setminusILneg = $true) & (subsetRefl = $true) & (exuEu = $true) & (binintersectI = $true) & (notinsingleton = $true) & (binintersectSubset1 = $true) & (emptyE1 = $true) & (setunionI = $true) & (setminusER = $true) & (powersetsubset = $true) & (quantDeMorgan2 = $true) & (uniqinunit = $true) & (omegaSAx = $true) & (setadjoinIR = $true) & (upairsetIR = $true) & (upairset2IR = $true) & (subPowSU = $true) & (prop2set2propI = $true) & (binintersectEL = $true) & (sepSubset = $true) & (upairsetIL = $true) & (omegaIndAx = $true) & (emptysetimpfalse = $true) & (exuI1 = $true) & (binunionIL = $true) & (nonemptyI = $true) & (setminusEL = $true) & (setoftrueEq = $true) & (subsetE2 = $true) & (emptysetAx = $true) & (setextAx = $true) & (setunion__Cong = $true) & (noeltsimpempty = $true) & (binintersectSubset5 = $true) & (binintersectER = $true) & (quantDeMorgan4 = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (binunionIR = $true) & (eqinunit = $true) & (setadjoinAx = $true) & (setminusI = $true) & (setbeta = $true) & (disjointsetsI1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) & ($true = (in @ X1 @ X2))) & (subsetE = $true) & (setunionE = $true) & (replAx = $true) & (subsetI1 = $true) & (emptyset__Cong = $true) & (wellorderingAx = $true) & (setadjoinOr = $true) & (descr__Cong = $true) & (exuE1 = $true) & (powersetE1 = $true) & (descrp = $true) & (subsetTrans = $true) & (powersetI1 = $true) & (binintersectSubset4 = $true) & (dsetconstrI = $true) & (dsetconstr__Cong = $true) & (subset2powerset = $true) & (notdallE = $true) & (binintersectSubset2 = $true) & (notsubsetI = $true) & (setunionAx = $true) & (emptyinPowerset = $true) & (setadjoinSub2 = $true) & (inCongP = $true) & (notequalI1 = $true) & (emptysetsubset = $true) & (eqimpsubset2 = $true) & (prop2setI = $true) & (exu__Cong = $true) & (nonemptyE1 = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (singletonsswitch = $true) & (powersetAx = $true) & (setadjoinSub = $true) & (notdexE = $true) & (notinemptyset = $true) & (exuI3 = $true) & (exuE3u = $true) & (upairsetE = $true) & (setadjoinIL = $true) & (setextsub = $true) & (notequalI2 = $true) & (binintersectSubset3 = $true) & (bs114d = $true) & (nonemptyI1 = $true) & (emptyI = $true) & (sepInPowerset = $true) & (emptyinunitempty = $true) & (powerset__Cong = $true) & (binunionEcases = $true) & (binunionLsub = $true) & (binintersectRsub = $true) & (setminusERneg = $true) & (emptyInPowerset = $true) & (setminusSubset2 = $true) & (setminusELneg = $true) & (dsetconstrEL = $true) & (setext = $true) & (exuE2 = $true) & (emptysetE = $true) & (inPowerset = $true) & (exuI2 = $true) & (setadjoinE = $true)),
% 2.52/1.71 inference(flattening,[status(thm)],[f504])).
% 2.52/1.71 thf(f504,plain,(
% 2.52/1.71 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) & ($true = (in @ X1 @ X2))) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.52/1.71 inference(ennf_transformation,[status(thm)],[f385])).
% 2.52/1.71 thf(f385,plain,(
% 2.52/1.71 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ((in @ X1 @ (setminus @ X0 @ X2)) != $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.52/1.71 inference(flattening,[status(thm)],[f201])).
% 2.52/1.71 thf(f201,plain,(
% 2.52/1.71 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ~((in @ X1 @ (setminus @ X0 @ X2)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.52/1.71 inference(fool_elimination,[status(thm)],[f200])).
% 2.52/1.71 thf(f200,plain,(
% 2.52/1.71 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ~(in @ X1 @ (setminus @ X0 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.52/1.71 inference(rectify,[status(thm)],[f128])).
% 2.52/1.71 thf(f128,negated_conjecture,(
% 2.52/1.71 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => ! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X4) => ~(in @ X1 @ (setminus @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.52/1.71 inference(negated_conjecture,[status(cth)],[f127])).
% 2.52/1.71 thf(f127,conjecture,(
% 2.52/1.71 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => ! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X4) => ~(in @ X1 @ (setminus @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.52/1.71 file('/export/starexec/sandbox/tmp/tmp.UhuhNbW7fO/DTF2THF_3995.p',setminusIRneg)).
% 2.52/1.71 thf(f1854,plain,(
% 2.52/1.71 ($true != (in @ sK244 @ sK245))),
% 2.52/1.71 inference(trivial_inequality_removal,[status(thm)],[f1853])).
% 2.52/1.71 thf(f1853,plain,(
% 2.52/1.71 ($true != (in @ sK244 @ sK245)) | ($true != $true)),
% 2.52/1.71 inference(forward_demodulation,[status(thm)],[f1835,f1578])).
% 2.52/1.71 thf(f1578,plain,(
% 2.52/1.71 (setminusER = $true)),
% 2.52/1.71 inference(cnf_transformation,[status(thm)],[f964])).
% 2.52/1.71 thf(f1835,plain,(
% 2.52/1.71 ($true != (in @ sK244 @ sK245)) | (setminusER != $true)),
% 2.52/1.71 inference(trivial_inequality_removal,[status(thm)],[f1830])).
% 2.52/1.71 thf(f1830,plain,(
% 2.52/1.71 ($true != $true) | (setminusER != $true) | ($true != (in @ sK244 @ sK245))),
% 2.52/1.71 inference(superposition,[status(thm)],[f1347,f1542])).
% 2.52/1.71 thf(f1542,plain,(
% 2.52/1.71 ($true = (in @ sK244 @ (setminus @ sK243 @ sK245)))),
% 2.52/1.71 inference(cnf_transformation,[status(thm)],[f964])).
% 2.52/1.71 thf(f1347,plain,(
% 2.52/1.71 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (setminus @ X3 @ X4))) | ((in @ X5 @ X4) != $true) | (setminusER != $true)) )),
% 2.52/1.71 inference(cnf_transformation,[status(thm)],[f810])).
% 2.52/1.71 thf(f810,plain,(
% 2.52/1.71 ((setminusER = $true) | (($true = (in @ sK154 @ sK153)) & ((in @ sK154 @ (setminus @ sK152 @ sK153)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) != $true) | ($true != (in @ X5 @ (setminus @ X3 @ X4)))) | (setminusER != $true))),
% 2.52/1.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153,sK154])],[f808,f809])).
% 2.52/1.71 thf(f809,plain,(
% 2.52/1.71 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X2 @ (setminus @ X0 @ X1)))) => (($true = (in @ sK154 @ sK153)) & ((in @ sK154 @ (setminus @ sK152 @ sK153)) = $true))),
% 2.52/1.71 introduced(definition,[],[choice_axiom])).
% 2.52/1.71 thf(f808,plain,(
% 2.52/1.71 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X2 @ (setminus @ X0 @ X1))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) != $true) | ($true != (in @ X5 @ (setminus @ X3 @ X4)))) | (setminusER != $true))),
% 2.52/1.71 inference(rectify,[status(thm)],[f807])).
% 2.52/1.71 thf(f807,plain,(
% 2.52/1.71 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X2 @ (setminus @ X0 @ X1))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ (setminus @ X0 @ X1)))) | (setminusER != $true))),
% 2.52/1.71 inference(nnf_transformation,[status(thm)],[f414])).
% 2.52/1.71 thf(f414,plain,(
% 2.52/1.71 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ (setminus @ X0 @ X1))))),
% 2.52/1.71 inference(ennf_transformation,[status(thm)],[f404])).
% 2.52/1.71 thf(f404,plain,(
% 2.52/1.71 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X0 @ X1))) => ((in @ X2 @ X1) != $true)) <=> (setminusER = $true)),
% 2.52/1.71 inference(flattening,[status(thm)],[f329])).
% 2.52/1.71 thf(f329,plain,(
% 2.52/1.71 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X0 @ X1))) => ~((in @ X2 @ X1) = $true)) <=> (setminusER = $true)),
% 2.52/1.71 inference(fool_elimination,[status(thm)],[f328])).
% 2.52/1.71 thf(f328,plain,(
% 2.52/1.71 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 2.52/1.71 inference(rectify,[status(thm)],[f122])).
% 2.52/1.71 thf(f122,axiom,(
% 2.52/1.71 (! [X3 : $i,X4 : $i,X1 : $i] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)) = setminusER)),
% 2.52/1.71 file('/export/starexec/sandbox/tmp/tmp.UhuhNbW7fO/DTF2THF_3995.p',setminusER)).
% 2.52/1.71 % SZS output end Proof for DTF2THF_3995
% 2.52/1.71 % (4115)------------------------------
% 2.52/1.71 % (4115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.71 % (4115)Termination reason: Refutation
% 2.52/1.71
% 2.52/1.71 % (4115)Memory used [KB]: 7419
% 2.52/1.71 % (4115)Time elapsed: 0.067 s
% 2.52/1.71 % (4115)Instructions burned: 127 (million)
% 2.52/1.71 % (4115)------------------------------
% 2.52/1.71 % (4115)------------------------------
% 2.52/1.71 % (4092)Success in time 0.159 s
%------------------------------------------------------------------------------