%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU607^1 : 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 : n012.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 2.51s 1.72s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 2433 ( 674 equ; 0 cnn)
% Maximal formula atoms : 125 ( 90 avg)
% Number of connectives : 1216 ( 39 ~; 16 |; 382 &; 152 @)
% ( 2 <=>; 625 =>; 0 <=; 0 <~>)
% Maximal formula depth : 133 ( 41 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 246 ( 243 usr; 131 con; 0-4 aty)
% Number of variables : 57 ( 0 ^; 39 !; 18 ?; 57 :)
% 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_155,type,
sP0: $i > $i > $o ).
thf(func_def_156,type,
sP1: $i > $o ).
thf(func_def_157,type,
sP2: $i > $i > $o ).
thf(func_def_158,type,
sP3: $i > $i > $o ).
thf(func_def_164,type,
sK9: $i > $o ).
thf(func_def_169,type,
sK14: $i > $i > $i ).
thf(func_def_179,type,
sK24: $i > $o ).
thf(func_def_181,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_182,type,
sK27: $i > $o ).
thf(func_def_188,type,
sK33: $i > ( $i > $o ) > $i ).
thf(func_def_189,type,
sK34: $i > $o ).
thf(func_def_192,type,
sK37: $i > $i > $i ).
thf(func_def_201,type,
sK46: $i > $i > $i ).
thf(func_def_205,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_206,type,
sK51: $i > $o ).
thf(func_def_207,type,
sK52: $i > $i ).
thf(func_def_210,type,
sK55: $i > $o ).
thf(func_def_216,type,
sK61: $i > $i ).
thf(func_def_218,type,
sK63: $i > $o ).
thf(func_def_219,type,
sK64: ( $i > $o ) > $i ).
thf(func_def_225,type,
sK70: $i > $i ).
thf(func_def_227,type,
sK72: $i > $i > $i ).
thf(func_def_228,type,
sK73: $i > $i > $i ).
thf(func_def_229,type,
sK74: $i > $i > $i ).
thf(func_def_230,type,
sK75: $i > $i > $i ).
thf(func_def_231,type,
sK76: $i > $i > $i ).
thf(func_def_232,type,
sK77: $i > $i > $i > $i ).
thf(func_def_233,type,
sK78: $i > $i ).
thf(func_def_234,type,
sK79: $i > $i ).
thf(func_def_235,type,
sK80: $i > $i ).
thf(func_def_236,type,
sK81: $i > $i ).
thf(func_def_237,type,
sK82: $i > $i > $i ).
thf(func_def_238,type,
sK83: $i > $i > $i > $i ).
thf(func_def_239,type,
sK84: $i > $i > $i > $i ).
thf(func_def_240,type,
sK85: $i > $i > $i ).
thf(func_def_241,type,
sK86: $i > $i > $i ).
thf(func_def_242,type,
sK87: $i > $i ).
thf(func_def_244,type,
sK89: $i > $i ).
thf(func_def_245,type,
sK90: $i > $i ).
thf(func_def_246,type,
sK91: $i > ( $i > $o ) > $i ).
thf(func_def_247,type,
sK92: $i > $o ).
thf(func_def_254,type,
sK99: $i > $i > $i ).
thf(func_def_258,type,
sK103: $o > $i > $i > $i ).
thf(func_def_271,type,
sK116: $i > $o ).
thf(func_def_273,type,
sK118: $i > $i > $i ).
thf(func_def_274,type,
sK119: $i > $i > $i ).
thf(func_def_280,type,
sK125: $i > $i > $i ).
thf(func_def_281,type,
sK126: $i > $i ).
thf(func_def_286,type,
sK131: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_287,type,
sK132: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_290,type,
sK135: $i > $o ).
thf(func_def_291,type,
sK136: $i > $o ).
thf(func_def_293,type,
sK138: $i > $o ).
thf(func_def_305,type,
sK150: $i > $o ).
thf(func_def_308,type,
sK153: $i > $i > $i ).
thf(func_def_311,type,
sK156: ( $i > $o ) > $i ).
thf(func_def_312,type,
sK157: ( $i > $o ) > $i ).
thf(func_def_313,type,
sK158: $i > $o ).
thf(func_def_315,type,
sK160: $i > ( $i > $o ) > $i ).
thf(func_def_316,type,
sK161: $i > $o ).
thf(func_def_327,type,
sK172: $i > $o ).
thf(func_def_328,type,
sK173: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_329,type,
sK174: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_330,type,
sK175: $i > $o ).
thf(func_def_331,type,
sK176: $i > $o ).
thf(func_def_336,type,
sK181: $i > $o ).
thf(func_def_338,type,
sK183: $i > $o ).
thf(func_def_340,type,
sK185: ( $i > $o ) > $i > $i ).
thf(func_def_364,type,
sK209: $i > $o ).
thf(func_def_381,type,
sK226: $i > $o ).
thf(func_def_388,type,
sK233: $i > ( $i > $o ) > $i ).
thf(func_def_389,type,
sK234: $i > $o ).
thf(func_def_392,type,
sK237: $i > $o ).
thf(func_def_393,type,
sK238: $i > $i ).
thf(func_def_394,type,
sK239: ( $i > $o ) > $i ).
thf(func_def_398,type,
sK243: $i > $o ).
thf(func_def_429,type,
sK274: $i > ( $i > $o ) > $i ).
thf(func_def_430,type,
sK275: $i > $o ).
thf(func_def_436,type,
sK281: $i > $i > $i ).
thf(func_def_438,type,
sK283: $i > $i ).
thf(func_def_444,type,
sK289: $i > $i > $o ).
thf(func_def_446,type,
sK291: $i > $i ).
thf(func_def_447,type,
sK292: $i > $i ).
thf(func_def_448,type,
sK293: $i > ( $i > $i > $o ) > $i ).
thf(func_def_449,type,
sK294: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_450,type,
sK295: $i > ( $i > $i > $o ) > $i ).
thf(func_def_453,type,
sK298: $i > $o ).
thf(func_def_456,type,
sK301: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_457,type,
sK302: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_458,type,
sK303: $i > $o ).
thf(func_def_459,type,
sK304: $i > $o ).
thf(func_def_468,type,
sK313: $i > $i ).
thf(func_def_481,type,
sK326: $i > ( $i > $o ) > $i ).
thf(func_def_482,type,
sK327: $i > $o ).
thf(func_def_485,type,
sK330: $i > $i ).
thf(func_def_487,type,
sK332: $i > $i ).
thf(func_def_495,type,
ph340:
!>[X0: $tType] : X0 ).
thf(f1852,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1850]) ).
thf(f1850,plain,
$true != $true,
inference(superposition,[status(thm)],[f1667,f1834]) ).
thf(f1834,plain,
( ( in @ sK316 @ sK317 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1833]) ).
thf(f1833,plain,
( ( ( in @ sK316 @ sK317 )
= $true )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f1832,f1594]) ).
thf(f1594,plain,
setminusEL = $true,
inference(cnf_transformation,[status(thm)],[f1076]) ).
thf(f1076,plain,
( ( emptyE1 = $true )
& ( binunionEcases = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrEL = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinIR = $true )
& ( binintersectLsub = $true )
& ( emptysetE = $true )
& ( notdallE = $true )
& ( wellorderingAx = $true )
& ( powerset__Cong = $true )
& ( foundationAx = $true )
& ( binunionE = $true )
& ( binunionIL = $true )
& ( quantDeMorgan2 = $true )
& ( omega__Cong = $true )
& ( omegaIndAx = $true )
& ( powersetE = $true )
& ( nonemptyImpWitness = $true )
& ( setextsub = $true )
& ( $true
= ( in @ sK316 @ ( setminus @ sK317 @ sK318 ) ) )
& ( ( in @ sK316 @ sK317 )
!= $true )
& ( notinemptyset = $true )
& ( notsubsetI = $true )
& ( omega0Ax = $true )
& ( setadjoinAx = $true )
& ( binintersectER = $true )
& ( prop2setI = $true )
& ( exuI2 = $true )
& ( emptysetAx = $true )
& ( upairsetIR = $true )
& ( exuE3u = $true )
& ( upairsetIL = $true )
& ( subsetTrans = $true )
& ( subsetI2 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectEL = $true )
& ( sepSubset = $true )
& ( descr__Cong = $true )
& ( prop2set2propI = $true )
& ( noeltsimpempty = $true )
& ( subPowSU = $true )
& ( quantDeMorgan3 = $true )
& ( emptyInPowerset = $true )
& ( binintersectSubset5 = $true )
& ( notinsingleton = $true )
& ( setadjoinE = $true )
& ( subsetRefl = $true )
& ( emptyinPowerset = $true )
& ( descrp = $true )
& ( exuI3 = $true )
& ( powersetI = $true )
& ( eqinunit = $true )
& ( setunionE = $true )
& ( inPowerset = $true )
& ( setunion__Cong = $true )
& ( subsetI1 = $true )
& ( powersetE1 = $true )
& ( bs114d = $true )
& ( replAx = $true )
& ( setminusI = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( exuI1 = $true )
& ( eqimpsubset2 = $true )
& ( prop2setE = $true )
& ( binintersectRsub = $true )
& ( uniqinunit = $true )
& ( setunionAx = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan4 = $true )
& ( powersetsubset = $true )
& ( setadjoinSub2 = $true )
& ( emptysetsubset = $true )
& ( binunionIR = $true )
& ( exuEu = $true )
& ( dsetconstrI = $true )
& ( omegaSAx = $true )
& ( notequalI2 = $true )
& ( setminusER = $true )
& ( binintersectSubset1 = $true )
& ( singletonsswitch = $true )
& ( binunionRsub = $true )
& ( nonemptyI1 = $true )
& ( vacuousDall = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusSubset2 = $true )
& ( subsetE2 = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub = $true )
& ( notequalI1 = $true )
& ( setoftrueEq = $true )
& ( nonemptyE1 = $true )
& ( exuE2 = $true )
& ( setminusEL = $true )
& ( setadjoinIL = $true )
& ( dsetconstr__Cong = $true )
& ( disjointsetsI1 = $true )
& ( emptyset__Cong = $true )
& ( dsetconstrER = $true )
& ( notdexE = $true )
& ( exuE1 = $true )
& ( powersetI1 = $true )
& ( subsetE = $true )
& ( subset2powerset = $true )
& ( binunionLsub = $true )
& ( setunionI = $true )
& ( binintersectSubset3 = $true )
& ( in__Cong = $true )
& ( emptyinunitempty = $true )
& ( upairsetE = $true )
& ( setextAx = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( upairset2IR = $true )
& ( nonemptyI = $true )
& ( sepInPowerset = $true )
& ( setminusELneg = $true )
& ( inCongP = $true )
& ( emptysetimpfalse = $true )
& ( binintersectI = $true )
& ( setminusERneg = $true )
& ( setbeta = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK316,sK317,sK318])],[f459,f1075]) ).
thf(f1075,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) ) )
=> ( ( $true
= ( in @ sK316 @ ( setminus @ sK317 @ sK318 ) ) )
& ( ( in @ sK316 @ sK317 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f459,plain,
( ( emptyE1 = $true )
& ( binunionEcases = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrEL = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinIR = $true )
& ( binintersectLsub = $true )
& ( emptysetE = $true )
& ( notdallE = $true )
& ( wellorderingAx = $true )
& ( powerset__Cong = $true )
& ( foundationAx = $true )
& ( binunionE = $true )
& ( binunionIL = $true )
& ( quantDeMorgan2 = $true )
& ( omega__Cong = $true )
& ( omegaIndAx = $true )
& ( powersetE = $true )
& ( nonemptyImpWitness = $true )
& ( setextsub = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) ) )
& ( notinemptyset = $true )
& ( notsubsetI = $true )
& ( omega0Ax = $true )
& ( setadjoinAx = $true )
& ( binintersectER = $true )
& ( prop2setI = $true )
& ( exuI2 = $true )
& ( emptysetAx = $true )
& ( upairsetIR = $true )
& ( exuE3u = $true )
& ( upairsetIL = $true )
& ( subsetTrans = $true )
& ( subsetI2 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectEL = $true )
& ( sepSubset = $true )
& ( descr__Cong = $true )
& ( prop2set2propI = $true )
& ( noeltsimpempty = $true )
& ( subPowSU = $true )
& ( quantDeMorgan3 = $true )
& ( emptyInPowerset = $true )
& ( binintersectSubset5 = $true )
& ( notinsingleton = $true )
& ( setadjoinE = $true )
& ( subsetRefl = $true )
& ( emptyinPowerset = $true )
& ( descrp = $true )
& ( exuI3 = $true )
& ( powersetI = $true )
& ( eqinunit = $true )
& ( setunionE = $true )
& ( inPowerset = $true )
& ( setunion__Cong = $true )
& ( subsetI1 = $true )
& ( powersetE1 = $true )
& ( bs114d = $true )
& ( replAx = $true )
& ( setminusI = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( exuI1 = $true )
& ( eqimpsubset2 = $true )
& ( prop2setE = $true )
& ( binintersectRsub = $true )
& ( uniqinunit = $true )
& ( setunionAx = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan4 = $true )
& ( powersetsubset = $true )
& ( setadjoinSub2 = $true )
& ( emptysetsubset = $true )
& ( binunionIR = $true )
& ( exuEu = $true )
& ( dsetconstrI = $true )
& ( omegaSAx = $true )
& ( notequalI2 = $true )
& ( setminusER = $true )
& ( binintersectSubset1 = $true )
& ( singletonsswitch = $true )
& ( binunionRsub = $true )
& ( nonemptyI1 = $true )
& ( vacuousDall = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusSubset2 = $true )
& ( subsetE2 = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub = $true )
& ( notequalI1 = $true )
& ( setoftrueEq = $true )
& ( nonemptyE1 = $true )
& ( exuE2 = $true )
& ( setminusEL = $true )
& ( setadjoinIL = $true )
& ( dsetconstr__Cong = $true )
& ( disjointsetsI1 = $true )
& ( emptyset__Cong = $true )
& ( dsetconstrER = $true )
& ( notdexE = $true )
& ( exuE1 = $true )
& ( powersetI1 = $true )
& ( subsetE = $true )
& ( subset2powerset = $true )
& ( binunionLsub = $true )
& ( setunionI = $true )
& ( binintersectSubset3 = $true )
& ( in__Cong = $true )
& ( emptyinunitempty = $true )
& ( upairsetE = $true )
& ( setextAx = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( upairset2IR = $true )
& ( nonemptyI = $true )
& ( sepInPowerset = $true )
& ( setminusELneg = $true )
& ( inCongP = $true )
& ( emptysetimpfalse = $true )
& ( binintersectI = $true )
& ( setminusERneg = $true )
& ( setbeta = $true ) ),
inference(flattening,[status(thm)],[f458]) ).
thf(f458,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) ) )
& ( 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)],[f386]) ).
thf(f386,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f192]) ).
thf(f192,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f191]) ).
thf(f191,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ X1 )
=> ~ ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f127]) ).
thf(f127,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
=> ! [X1: $i,X3: $i,X4: $i] :
( ~ ( in @ X1 @ X3 )
=> ~ ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f126]) ).
thf(f126,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
=> ! [X1: $i,X3: $i,X4: $i] :
( ~ ( in @ X1 @ X3 )
=> ~ ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3WLPAKKuIJ/DTF2THF_3246.p',setminusILneg) ).
thf(f1832,plain,
( ( setminusEL != $true )
| ( ( in @ sK316 @ sK317 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1827]) ).
thf(f1827,plain,
( ( setminusEL != $true )
| ( ( in @ sK316 @ sK317 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1172,f1668]) ).
thf(f1668,plain,
( $true
= ( in @ sK316 @ ( setminus @ sK317 @ sK318 ) ) ),
inference(cnf_transformation,[status(thm)],[f1076]) ).
thf(f1172,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( setminusEL != $true )
| ( $true
= ( in @ X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f613]) ).
thf(f613,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
| ( setminusEL != $true ) )
& ( ( setminusEL = $true )
| ( ( $true
!= ( in @ sK43 @ sK45 ) )
& ( $true
= ( in @ sK43 @ ( setminus @ sK45 @ sK44 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45])],[f611,f612]) ).
thf(f612,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X5 ) )
& ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) ) )
=> ( ( $true
!= ( in @ sK43 @ sK45 ) )
& ( $true
= ( in @ sK43 @ ( setminus @ sK45 @ sK44 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f611,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
| ( setminusEL != $true ) )
& ( ( setminusEL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X5 ) )
& ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f610]) ).
thf(f610,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
| ( setminusEL != $true ) )
& ( ( setminusEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f492]) ).
thf(f492,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
<=> ( setminusEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f213]) ).
thf(f213,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
=> ( $true
= ( in @ X0 @ X2 ) ) )
<=> ( setminusEL = $true ) ),
inference(fool_elimination,[status(thm)],[f212]) ).
thf(f212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
=> ( in @ X0 @ X2 ) )
= setminusEL ),
inference(rectify,[status(thm)],[f121]) ).
thf(f121,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( in @ X1 @ ( setminus @ X3 @ X4 ) )
=> ( in @ X1 @ X3 ) )
= setminusEL ),
file('/export/starexec/sandbox/tmp/tmp.3WLPAKKuIJ/DTF2THF_3246.p',setminusEL) ).
thf(f1667,plain,
( ( in @ sK316 @ sK317 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU607^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n012.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 12:28:15 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.38 thf(spec,logic,$$dhol).
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 % File : SEU607^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.38 % Domain : Set Theory
% 0.16/0.38 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.16/0.38 % Version : Especial.
% 0.16/0.38 % English : (! A:i.! B:i.! x:i.~(in x A) -> ~(in x (setminus A B)))
% 0.16/0.38
% 0.16/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.38 % Source : [Bro08]
% 0.16/0.38 % Names : ZFC109g [Bro08]
% 0.16/0.38
% 0.16/0.38 % Status : Theorem
% 0.16/0.38 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.16/0.38 % Syntax : Number of formulae : 268 ( 125 unt; 142 typ; 125 def)
% 0.16/0.38 % Number of atoms : 667 ( 181 equ; 0 cnn)
% 0.16/0.38 % Maximal formula atoms : 125 ( 5 avg)
% 0.16/0.38 % Number of connectives : 1059 ( 38 ~; 6 |; 28 &; 677 @)
% 0.16/0.38 % ( 14 <=>; 296 =>; 0 <=; 0 <~>)
% 0.16/0.38 % Maximal formula depth : 132 ( 2 avg)
% 0.16/0.38 % Number of types : 2 ( 0 usr)
% 0.16/0.38 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.16/0.38 % Number of symbols : 145 ( 142 usr; 127 con; 0-2 aty)
% 0.16/0.38 % Number of variables : 363 ( 30 ^; 304 !; 29 ?; 363 :)
% 0.16/0.38 % SPC : TH0_THM_EQU_NAR
% 0.16/0.38
% 0.16/0.38 % Comments : http://mathgate.info/detsetitem.php?id=462
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 thf(in_type,type,
% 0.16/0.38 in: $i > $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(exu_type,type,
% 0.16/0.38 exu: ( $i > $o ) > $o ).
% 0.16/0.38
% 0.16/0.38 thf(exu,definition,
% 0.16/0.38 ( exu
% 0.16/0.38 = ( ^ [Xphi: $i > $o] :
% 0.16/0.38 ? [Xx: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 & ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setextAx_type,type,
% 0.16/0.38 setextAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setextAx,definition,
% 0.16/0.38 ( setextAx
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 <=> ( in @ Xx @ B ) )
% 0.16/0.38 => ( A = B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyset_type,type,
% 0.16/0.38 emptyset: $i ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetAx_type,type,
% 0.16/0.38 emptysetAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetAx,definition,
% 0.16/0.38 ( emptysetAx
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoin_type,type,
% 0.16/0.38 setadjoin: $i > $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinAx_type,type,
% 0.16/0.38 setadjoinAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinAx,definition,
% 0.16/0.38 ( setadjoinAx
% 0.16/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.38 <=> ( ( Xy = Xx )
% 0.16/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powerset_type,type,
% 0.16/0.38 powerset: $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(powersetAx_type,type,
% 0.16/0.38 powersetAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetAx,definition,
% 0.16/0.38 ( powersetAx
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.38 <=> ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setunion_type,type,
% 0.16/0.38 setunion: $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(setunionAx_type,type,
% 0.16/0.38 setunionAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setunionAx,definition,
% 0.16/0.38 ( setunionAx
% 0.16/0.38 = ( ! [A: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.38 <=> ? [B: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(omega_type,type,
% 0.16/0.38 omega: $i ).
% 0.16/0.38
% 0.16/0.38 thf(omega0Ax_type,type,
% 0.16/0.38 omega0Ax: $o ).
% 0.16/0.38
% 0.16/0.38 thf(omega0Ax,definition,
% 0.16/0.38 ( omega0Ax
% 0.16/0.38 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(omegaSAx_type,type,
% 0.16/0.38 omegaSAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(omegaSAx,definition,
% 0.16/0.38 ( omegaSAx
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ omega )
% 0.16/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(omegaIndAx_type,type,
% 0.16/0.38 omegaIndAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(omegaIndAx,definition,
% 0.16/0.38 ( omegaIndAx
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( ( in @ emptyset @ A )
% 0.16/0.38 & ! [Xx: $i] :
% 0.16/0.38 ( ( ( in @ Xx @ omega )
% 0.16/0.38 & ( in @ Xx @ A ) )
% 0.16/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.38 => ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ omega )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(replAx_type,type,
% 0.16/0.38 replAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(replAx,definition,
% 0.16/0.38 ( replAx
% 0.16/0.38 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( exu
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.38 => ? [B: $i] :
% 0.16/0.38 ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 <=> ? [Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ A )
% 0.16/0.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(foundationAx_type,type,
% 0.16/0.38 foundationAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(foundationAx,definition,
% 0.16/0.38 ( foundationAx
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.38 => ? [B: $i] :
% 0.16/0.38 ( ( in @ B @ A )
% 0.16/0.38 & ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(wellorderingAx_type,type,
% 0.16/0.38 wellorderingAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(wellorderingAx,definition,
% 0.16/0.38 ( wellorderingAx
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ? [B: $i] :
% 0.16/0.38 ( ! [C: $i] :
% 0.16/0.38 ( ( in @ C @ B )
% 0.16/0.38 => ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ C )
% 0.16/0.38 => ( in @ Xx @ A ) ) )
% 0.16/0.38 & ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( ( in @ Xx @ A )
% 0.16/0.38 & ( in @ Xy @ A ) )
% 0.16/0.38 => ( ! [C: $i] :
% 0.16/0.38 ( ( in @ C @ B )
% 0.16/0.38 => ( ( in @ Xx @ C )
% 0.16/0.38 <=> ( in @ Xy @ C ) ) )
% 0.16/0.38 => ( Xx = Xy ) ) )
% 0.16/0.38 & ! [C: $i,D: $i] :
% 0.16/0.38 ( ( ( in @ C @ B )
% 0.16/0.38 & ( in @ D @ B ) )
% 0.16/0.38 => ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ C )
% 0.16/0.38 => ( in @ Xx @ D ) )
% 0.16/0.38 | ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ D )
% 0.16/0.38 => ( in @ Xx @ C ) ) ) )
% 0.16/0.38 & ! [C: $i] :
% 0.16/0.38 ( ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ C )
% 0.16/0.38 => ( in @ Xx @ A ) )
% 0.16/0.38 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.38 => ? [D: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ D @ B )
% 0.16/0.38 & ( in @ Xx @ C )
% 0.16/0.38 & ~ ? [Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ D )
% 0.16/0.38 & ( in @ Xy @ C ) )
% 0.16/0.38 & ! [E: $i] :
% 0.16/0.38 ( ( in @ E @ B )
% 0.16/0.38 => ( ! [Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ E )
% 0.16/0.38 => ( in @ Xy @ D ) )
% 0.16/0.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(descr_type,type,
% 0.16/0.38 descr: ( $i > $o ) > $i ).
% 0.16/0.38
% 0.16/0.38 thf(descrp_type,type,
% 0.16/0.38 descrp: $o ).
% 0.16/0.38
% 0.16/0.38 thf(descrp,definition,
% 0.16/0.38 ( descrp
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ( Xphi
% 0.16/0.38 @ ( descr
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstr_type,type,
% 0.16/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrI_type,type,
% 0.16/0.38 dsetconstrI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrI,definition,
% 0.16/0.38 ( dsetconstrI
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 => ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrEL_type,type,
% 0.16/0.38 dsetconstrEL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrEL,definition,
% 0.16/0.38 ( dsetconstrEL
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrER_type,type,
% 0.16/0.38 dsetconstrER: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrER,definition,
% 0.16/0.38 ( dsetconstrER
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuE1_type,type,
% 0.16/0.38 exuE1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuE1,definition,
% 0.16/0.38 ( exuE1
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 & ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(prop2set_type,type,
% 0.16/0.38 prop2set: $o > $i ).
% 0.16/0.38
% 0.16/0.38 thf(prop2setE_type,type,
% 0.16/0.38 prop2setE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(prop2setE,definition,
% 0.16/0.38 ( prop2setE
% 0.16/0.38 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.38 => Xphi ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetE_type,type,
% 0.16/0.38 emptysetE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetE,definition,
% 0.16/0.38 ( emptysetE
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ emptyset )
% 0.16/0.38 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetimpfalse_type,type,
% 0.16/0.38 emptysetimpfalse: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetimpfalse,definition,
% 0.16/0.38 ( emptysetimpfalse
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ emptyset )
% 0.16/0.38 => $false ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notinemptyset_type,type,
% 0.16/0.38 notinemptyset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notinemptyset,definition,
% 0.16/0.38 ( notinemptyset
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuE3e_type,type,
% 0.16/0.38 exuE3e: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuE3e,definition,
% 0.16/0.38 ( exuE3e
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setext_type,type,
% 0.16/0.38 setext: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setext,definition,
% 0.16/0.38 ( setext
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ B ) )
% 0.16/0.38 => ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) )
% 0.16/0.38 => ( A = B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyI_type,type,
% 0.16/0.38 emptyI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyI,definition,
% 0.16/0.38 ( emptyI
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ~ ( in @ Xx @ A )
% 0.16/0.38 => ( A = emptyset ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(noeltsimpempty_type,type,
% 0.16/0.38 noeltsimpempty: $o ).
% 0.16/0.38
% 0.16/0.38 thf(noeltsimpempty,definition,
% 0.16/0.38 ( noeltsimpempty
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ~ ( in @ Xx @ A )
% 0.16/0.38 => ( A = emptyset ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setbeta_type,type,
% 0.16/0.38 setbeta: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setbeta,definition,
% 0.16/0.38 ( setbeta
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.38 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonempty_type,type,
% 0.16/0.38 nonempty: $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonempty,definition,
% 0.16/0.38 ( nonempty
% 0.16/0.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyE1_type,type,
% 0.16/0.38 nonemptyE1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyE1,definition,
% 0.16/0.38 ( nonemptyE1
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( nonempty @ A )
% 0.16/0.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyI_type,type,
% 0.16/0.38 nonemptyI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyI,definition,
% 0.16/0.38 ( nonemptyI
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 => ( nonempty
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyI1_type,type,
% 0.16/0.38 nonemptyI1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyI1,definition,
% 0.16/0.38 ( nonemptyI1
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.38 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIL_type,type,
% 0.16/0.38 setadjoinIL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIL,definition,
% 0.16/0.38 ( setadjoinIL
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyinunitempty_type,type,
% 0.16/0.38 emptyinunitempty: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyinunitempty,definition,
% 0.16/0.38 ( emptyinunitempty
% 0.16/0.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIR_type,type,
% 0.16/0.38 setadjoinIR: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIR,definition,
% 0.16/0.38 ( setadjoinIR
% 0.16/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ A )
% 0.16/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinE_type,type,
% 0.16/0.38 setadjoinE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinE,definition,
% 0.16/0.38 ( setadjoinE
% 0.16/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.38 => ! [Xphi: $o] :
% 0.16/0.38 ( ( ( Xy = Xx )
% 0.16/0.38 => Xphi )
% 0.16/0.38 => ( ( ( in @ Xy @ A )
% 0.16/0.38 => Xphi )
% 0.16/0.38 => Xphi ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinOr_type,type,
% 0.16/0.38 setadjoinOr: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinOr,definition,
% 0.16/0.38 ( setadjoinOr
% 0.16/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.38 => ( ( Xy = Xx )
% 0.16/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setoftrueEq_type,type,
% 0.16/0.38 setoftrueEq: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setoftrueEq,definition,
% 0.16/0.38 ( setoftrueEq
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xx: $i] : $true )
% 0.16/0.38 = A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powersetI_type,type,
% 0.16/0.38 powersetI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetI,definition,
% 0.16/0.38 ( powersetI
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) )
% 0.16/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyinPowerset_type,type,
% 0.16/0.38 emptyinPowerset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyinPowerset,definition,
% 0.16/0.38 ( emptyinPowerset
% 0.16/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyInPowerset_type,type,
% 0.16/0.38 emptyInPowerset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyInPowerset,definition,
% 0.16/0.38 ( emptyInPowerset
% 0.16/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powersetE_type,type,
% 0.16/0.38 powersetE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetE,definition,
% 0.16/0.38 ( powersetE
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.38 => ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setunionI_type,type,
% 0.16/0.38 setunionI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setunionI,definition,
% 0.16/0.38 ( setunionI
% 0.16/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( ( in @ B @ A )
% 0.16/0.38 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setunionE_type,type,
% 0.16/0.38 setunionE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setunionE,definition,
% 0.16/0.38 ( setunionE
% 0.16/0.38 = ( ! [A: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.38 => ! [Xphi: $o] :
% 0.16/0.38 ( ! [B: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( ( in @ B @ A )
% 0.16/0.38 => Xphi ) )
% 0.16/0.38 => Xphi ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subPowSU_type,type,
% 0.16/0.38 subPowSU: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subPowSU,definition,
% 0.16/0.38 ( subPowSU
% 0.16/0.38 = ( ! [A: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuE2_type,type,
% 0.16/0.38 exuE2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuE2,definition,
% 0.16/0.38 ( exuE2
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyImpWitness_type,type,
% 0.16/0.38 nonemptyImpWitness: $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyImpWitness,definition,
% 0.16/0.38 ( nonemptyImpWitness
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( nonempty @ A )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & $true ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(uniqinunit_type,type,
% 0.16/0.38 uniqinunit: $o ).
% 0.16/0.38
% 0.16/0.38 thf(uniqinunit,definition,
% 0.16/0.38 ( uniqinunit
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notinsingleton_type,type,
% 0.16/0.38 notinsingleton: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notinsingleton,definition,
% 0.16/0.38 ( notinsingleton
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx != Xy )
% 0.16/0.38 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(eqinunit_type,type,
% 0.16/0.38 eqinunit: $o ).
% 0.16/0.38
% 0.16/0.38 thf(eqinunit,definition,
% 0.16/0.38 ( eqinunit
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(singletonsswitch_type,type,
% 0.16/0.38 singletonsswitch: $o ).
% 0.16/0.38
% 0.16/0.38 thf(singletonsswitch,definition,
% 0.16/0.38 ( singletonsswitch
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetE_type,type,
% 0.16/0.38 upairsetE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetE,definition,
% 0.16/0.38 ( upairsetE
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.38 => ( ( Xz = Xx )
% 0.16/0.38 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetIL_type,type,
% 0.16/0.38 upairsetIL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetIL,definition,
% 0.16/0.38 ( upairsetIL
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetIR_type,type,
% 0.16/0.38 upairsetIR: $o ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetIR,definition,
% 0.16/0.38 ( upairsetIR
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyE1_type,type,
% 0.16/0.38 emptyE1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyE1,definition,
% 0.16/0.38 ( emptyE1
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( Xphi @ Xx ) )
% 0.16/0.38 => ( ( ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 = emptyset )
% 0.16/0.38 => $false ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(vacuousDall_type,type,
% 0.16/0.38 vacuousDall: $o ).
% 0.16/0.38
% 0.16/0.38 thf(vacuousDall,definition,
% 0.16/0.38 ( vacuousDall
% 0.16/0.38 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ emptyset )
% 0.16/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan1_type,type,
% 0.16/0.38 quantDeMorgan1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan1,definition,
% 0.16/0.38 ( quantDeMorgan1
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ~ ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan2_type,type,
% 0.16/0.38 quantDeMorgan2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan2,definition,
% 0.16/0.38 ( quantDeMorgan2
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ~ ( Xphi @ Xx ) )
% 0.16/0.38 => ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan3_type,type,
% 0.16/0.38 quantDeMorgan3: $o ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan3,definition,
% 0.16/0.38 ( quantDeMorgan3
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( Xphi @ Xx ) )
% 0.16/0.38 => ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan4_type,type,
% 0.16/0.38 quantDeMorgan4: $o ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan4,definition,
% 0.16/0.38 ( quantDeMorgan4
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ~ ( Xphi @ Xx ) )
% 0.16/0.38 => ~ ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(prop2setI_type,type,
% 0.16/0.38 prop2setI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(prop2setI,definition,
% 0.16/0.38 ( prop2setI
% 0.16/0.38 = ( ! [Xphi: $o] :
% 0.16/0.38 ( Xphi
% 0.16/0.38 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(set2prop_type,type,
% 0.16/0.38 set2prop: $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(prop2set2propI_type,type,
% 0.16/0.38 prop2set2propI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(prop2set2propI,definition,
% 0.16/0.38 ( prop2set2propI
% 0.16/0.38 = ( ! [Xphi: $o] :
% 0.16/0.38 ( Xphi
% 0.16/0.38 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notdexE_type,type,
% 0.16/0.38 notdexE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notdexE,definition,
% 0.16/0.38 ( notdexE
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( Xphi @ Xx ) )
% 0.16/0.38 => ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notdallE_type,type,
% 0.16/0.38 notdallE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notdallE,definition,
% 0.16/0.38 ( notdallE
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ~ ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuI1_type,type,
% 0.16/0.38 exuI1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuI1,definition,
% 0.16/0.38 ( exuI1
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 & ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) )
% 0.16/0.38 => ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuI3_type,type,
% 0.16/0.38 exuI3: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuI3,definition,
% 0.16/0.38 ( exuI3
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.16/0.38 => ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 => ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) )
% 0.16/0.38 => ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuI2_type,type,
% 0.16/0.38 exuI2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuI2,definition,
% 0.16/0.38 ( exuI2
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] :
% 0.16/0.38 ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 <=> ( Xy = Xx ) )
% 0.16/0.38 => ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(inCongP_type,type,
% 0.16/0.38 inCongP: $o ).
% 0.16/0.38
% 0.16/0.38 thf(inCongP,definition,
% 0.16/0.38 ( inCongP
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(in__Cong_type,type,
% 0.16/0.38 in__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(in__Cong,definition,
% 0.16/0.38 ( in__Cong
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( ( in @ Xx @ A )
% 0.16/0.38 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuE3u_type,type,
% 0.16/0.38 exuE3u: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuE3u,definition,
% 0.16/0.38 ( exuE3u
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 => ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exu__Cong_type,type,
% 0.16/0.38 exu__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exu__Cong,definition,
% 0.16/0.38 ( exu__Cong
% 0.16/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.38 => ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 <=> ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyset__Cong_type,type,
% 0.16/0.38 emptyset__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyset__Cong,definition,
% 0.16/0.38 ( emptyset__Cong
% 0.16/0.38 = ( emptyset = emptyset ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoin__Cong_type,type,
% 0.16/0.38 setadjoin__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoin__Cong,definition,
% 0.16/0.38 ( setadjoin__Cong
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ! [Xz: $i,Xu: $i] :
% 0.16/0.38 ( ( Xz = Xu )
% 0.16/0.38 => ( ( setadjoin @ Xx @ Xz )
% 0.16/0.38 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powerset__Cong_type,type,
% 0.16/0.38 powerset__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powerset__Cong,definition,
% 0.16/0.38 ( powerset__Cong
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ( ( powerset @ A )
% 0.16/0.38 = ( powerset @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setunion__Cong_type,type,
% 0.16/0.38 setunion__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setunion__Cong,definition,
% 0.16/0.38 ( setunion__Cong
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ( ( setunion @ A )
% 0.16/0.38 = ( setunion @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(omega__Cong_type,type,
% 0.16/0.38 omega__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(omega__Cong,definition,
% 0.16/0.38 ( omega__Cong
% 0.16/0.38 = ( omega = omega ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuEu_type,type,
% 0.16/0.38 exuEu: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuEu,definition,
% 0.16/0.38 ( exuEu
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 => ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(descr__Cong_type,type,
% 0.16/0.38 descr__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(descr__Cong,definition,
% 0.16/0.38 ( descr__Cong
% 0.16/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.38 => ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.16/0.38 => ( ( descr
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 = ( descr
% 0.16/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstr__Cong_type,type,
% 0.16/0.38 dsetconstr__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstr__Cong,definition,
% 0.16/0.38 ( dsetconstr__Cong
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ! [Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ B )
% 0.16/0.38 => ( ( Xx = Xy )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 <=> ( 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,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 => ! [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 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.44/1.52 ---- Embedded in THF ---
% 2.44/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.44/1.52 %%% Generated on Tue Feb 24 12:28:16 EST 2026
% 2.44/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.44/1.52 %%% Logic specification used:
% 2.44/1.52 %%% thf(spec, logic, $$dhol).
% 2.44/1.52
% 2.44/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3WLPAKKuIJ/DTF2DTF3246.p
% See solution above
% 2.44/1.52 ------------------------
% 2.44/1.54 ---- Cleaned THF ---
% 2.44/1.54 thf(in_type,type,
% 2.44/1.54 in: $i > $i > $o ).
% 2.44/1.54
% 2.44/1.54 thf(exu_type,type,
% 2.44/1.54 exu: ( $i > $o ) > $o ).
% 2.44/1.54
% 2.44/1.54 thf(exu,definition,
% 2.44/1.54 ( exu
% 2.44/1.54 = ( ^ [Xphi: $i > $o] :
% 2.44/1.54 ? [Xx: $i] :
% 2.44/1.54 ( ( Xphi @ Xx )
% 2.44/1.54 & ! [Xy: $i] :
% 2.44/1.54 ( ( Xphi @ Xy )
% 2.44/1.54 => ( Xx = Xy ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setextAx_type,type,
% 2.44/1.54 setextAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setextAx,definition,
% 2.44/1.54 ( setextAx
% 2.44/1.54 = ( ! [A: $i,B: $i] :
% 2.44/1.54 ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ A )
% 2.44/1.54 <=> ( in @ Xx @ B ) )
% 2.44/1.54 => ( A = B ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(emptyset_type,type,
% 2.44/1.54 emptyset: $i ).
% 2.44/1.54
% 2.44/1.54 thf(emptysetAx_type,type,
% 2.44/1.54 emptysetAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(emptysetAx,definition,
% 2.44/1.54 ( emptysetAx
% 2.44/1.54 = ( ! [Xx: $i] :
% 2.44/1.54 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoin_type,type,
% 2.44/1.54 setadjoin: $i > $i > $i ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinAx_type,type,
% 2.44/1.54 setadjoinAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinAx,definition,
% 2.44/1.54 ( setadjoinAx
% 2.44/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.44/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.44/1.54 <=> ( ( Xy = Xx )
% 2.44/1.54 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(powerset_type,type,
% 2.44/1.54 powerset: $i > $i ).
% 2.44/1.54
% 2.44/1.54 thf(powersetAx_type,type,
% 2.44/1.54 powersetAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(powersetAx,definition,
% 2.44/1.54 ( powersetAx
% 2.44/1.54 = ( ! [A: $i,B: $i] :
% 2.44/1.54 ( ( in @ B @ ( powerset @ A ) )
% 2.44/1.54 <=> ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ B )
% 2.44/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setunion_type,type,
% 2.44/1.54 setunion: $i > $i ).
% 2.44/1.54
% 2.44/1.54 thf(setunionAx_type,type,
% 2.44/1.54 setunionAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setunionAx,definition,
% 2.44/1.54 ( setunionAx
% 2.44/1.54 = ( ! [A: $i,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 2.44/1.54 <=> ? [B: $i] :
% 2.44/1.54 ( ( in @ Xx @ B )
% 2.44/1.54 & ( in @ B @ A ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(omega_type,type,
% 2.44/1.54 omega: $i ).
% 2.44/1.54
% 2.44/1.54 thf(omega0Ax_type,type,
% 2.44/1.54 omega0Ax: $o ).
% 2.44/1.54
% 2.44/1.54 thf(omega0Ax,definition,
% 2.44/1.54 ( omega0Ax
% 2.44/1.54 = ( in @ emptyset @ omega ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(omegaSAx_type,type,
% 2.44/1.54 omegaSAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(omegaSAx,definition,
% 2.44/1.54 ( omegaSAx
% 2.44/1.54 = ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ omega )
% 2.44/1.54 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(omegaIndAx_type,type,
% 2.44/1.54 omegaIndAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(omegaIndAx,definition,
% 2.44/1.54 ( omegaIndAx
% 2.44/1.54 = ( ! [A: $i] :
% 2.44/1.54 ( ( ( in @ emptyset @ A )
% 2.44/1.54 & ! [Xx: $i] :
% 2.44/1.54 ( ( ( in @ Xx @ omega )
% 2.44/1.54 & ( in @ Xx @ A ) )
% 2.44/1.54 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.44/1.54 => ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ omega )
% 2.44/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(replAx_type,type,
% 2.44/1.54 replAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(replAx,definition,
% 2.44/1.54 ( replAx
% 2.44/1.54 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.44/1.54 ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ A )
% 2.44/1.54 => ( exu
% 2.44/1.54 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.44/1.54 => ? [B: $i] :
% 2.44/1.54 ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ B )
% 2.44/1.54 <=> ? [Xy: $i] :
% 2.44/1.54 ( ( in @ Xy @ A )
% 2.44/1.54 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(foundationAx_type,type,
% 2.44/1.54 foundationAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(foundationAx,definition,
% 2.44/1.54 ( foundationAx
% 2.44/1.54 = ( ! [A: $i] :
% 2.44/1.54 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.44/1.54 => ? [B: $i] :
% 2.44/1.54 ( ( in @ B @ A )
% 2.44/1.54 & ~ ? [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ B )
% 2.44/1.54 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(wellorderingAx_type,type,
% 2.44/1.54 wellorderingAx: $o ).
% 2.44/1.54
% 2.44/1.54 thf(wellorderingAx,definition,
% 2.44/1.54 ( wellorderingAx
% 2.44/1.54 = ( ! [A: $i] :
% 2.44/1.54 ? [B: $i] :
% 2.44/1.54 ( ! [C: $i] :
% 2.44/1.54 ( ( in @ C @ B )
% 2.44/1.54 => ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ C )
% 2.44/1.54 => ( in @ Xx @ A ) ) )
% 2.44/1.54 & ! [Xx: $i,Xy: $i] :
% 2.44/1.54 ( ( ( in @ Xx @ A )
% 2.44/1.54 & ( in @ Xy @ A ) )
% 2.44/1.54 => ( ! [C: $i] :
% 2.44/1.54 ( ( in @ C @ B )
% 2.44/1.54 => ( ( in @ Xx @ C )
% 2.44/1.54 <=> ( in @ Xy @ C ) ) )
% 2.44/1.54 => ( Xx = Xy ) ) )
% 2.44/1.54 & ! [C: $i,D: $i] :
% 2.44/1.54 ( ( ( in @ C @ B )
% 2.44/1.54 & ( in @ D @ B ) )
% 2.44/1.54 => ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ C )
% 2.44/1.54 => ( in @ Xx @ D ) )
% 2.44/1.54 | ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ D )
% 2.44/1.54 => ( in @ Xx @ C ) ) ) )
% 2.44/1.54 & ! [C: $i] :
% 2.44/1.54 ( ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ C )
% 2.44/1.54 => ( in @ Xx @ A ) )
% 2.44/1.54 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.44/1.54 => ? [D: $i,Xx: $i] :
% 2.44/1.54 ( ( in @ D @ B )
% 2.44/1.54 & ( in @ Xx @ C )
% 2.44/1.54 & ~ ? [Xy: $i] :
% 2.44/1.54 ( ( in @ Xy @ D )
% 2.44/1.54 & ( in @ Xy @ C ) )
% 2.44/1.54 & ! [E: $i] :
% 2.44/1.54 ( ( in @ E @ B )
% 2.44/1.54 => ( ! [Xy: $i] :
% 2.44/1.54 ( ( in @ Xy @ E )
% 2.44/1.54 => ( in @ Xy @ D ) )
% 2.44/1.54 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(descr_type,type,
% 2.44/1.54 descr: ( $i > $o ) > $i ).
% 2.44/1.54
% 2.44/1.54 thf(descrp_type,type,
% 2.44/1.54 descrp: $o ).
% 2.44/1.54
% 2.44/1.54 thf(descrp,definition,
% 2.44/1.54 ( descrp
% 2.44/1.54 = ( ! [Xphi: $i > $o] :
% 2.44/1.54 ( ( exu
% 2.44/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.54 => ( Xphi
% 2.44/1.54 @ ( descr
% 2.44/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(dsetconstr_type,type,
% 2.44/1.54 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.44/1.54
% 2.44/1.54 thf(dsetconstrI_type,type,
% 2.44/1.54 dsetconstrI: $o ).
% 2.44/1.54
% 2.44/1.54 thf(dsetconstrI,definition,
% 2.44/1.54 ( dsetconstrI
% 2.44/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ A )
% 2.44/1.54 => ( ( Xphi @ Xx )
% 2.44/1.54 => ( in @ Xx
% 2.44/1.54 @ ( dsetconstr @ A
% 2.44/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(dsetconstrEL_type,type,
% 2.44/1.54 dsetconstrEL: $o ).
% 2.44/1.54
% 2.44/1.54 thf(dsetconstrEL,definition,
% 2.44/1.54 ( dsetconstrEL
% 2.44/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx
% 2.44/1.54 @ ( dsetconstr @ A
% 2.44/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.44/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(dsetconstrER_type,type,
% 2.44/1.54 dsetconstrER: $o ).
% 2.44/1.54
% 2.44/1.54 thf(dsetconstrER,definition,
% 2.44/1.54 ( dsetconstrER
% 2.44/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx
% 2.44/1.54 @ ( dsetconstr @ A
% 2.44/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.44/1.54 => ( Xphi @ Xx ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(exuE1_type,type,
% 2.44/1.54 exuE1: $o ).
% 2.44/1.54
% 2.44/1.54 thf(exuE1,definition,
% 2.44/1.54 ( exuE1
% 2.44/1.54 = ( ! [Xphi: $i > $o] :
% 2.44/1.54 ( ( exu
% 2.44/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.54 => ? [Xx: $i] :
% 2.44/1.54 ( ( Xphi @ Xx )
% 2.44/1.54 & ! [Xy: $i] :
% 2.44/1.54 ( ( Xphi @ Xy )
% 2.44/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(prop2set_type,type,
% 2.44/1.54 prop2set: $o > $i ).
% 2.44/1.54
% 2.44/1.54 thf(prop2setE_type,type,
% 2.44/1.54 prop2setE: $o ).
% 2.44/1.54
% 2.44/1.54 thf(prop2setE,definition,
% 2.44/1.54 ( prop2setE
% 2.44/1.54 = ( ! [Xphi: $o,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.44/1.54 => Xphi ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(emptysetE_type,type,
% 2.44/1.54 emptysetE: $o ).
% 2.44/1.54
% 2.44/1.54 thf(emptysetE,definition,
% 2.44/1.54 ( emptysetE
% 2.44/1.54 = ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ emptyset )
% 2.44/1.54 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(emptysetimpfalse_type,type,
% 2.44/1.54 emptysetimpfalse: $o ).
% 2.44/1.54
% 2.44/1.54 thf(emptysetimpfalse,definition,
% 2.44/1.54 ( emptysetimpfalse
% 2.44/1.54 = ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ emptyset )
% 2.44/1.54 => $false ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(notinemptyset_type,type,
% 2.44/1.54 notinemptyset: $o ).
% 2.44/1.54
% 2.44/1.54 thf(notinemptyset,definition,
% 2.44/1.54 ( notinemptyset
% 2.44/1.54 = ( ! [Xx: $i] :
% 2.44/1.54 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(exuE3e_type,type,
% 2.44/1.54 exuE3e: $o ).
% 2.44/1.54
% 2.44/1.54 thf(exuE3e,definition,
% 2.44/1.54 ( exuE3e
% 2.44/1.54 = ( ! [Xphi: $i > $o] :
% 2.44/1.54 ( ( exu
% 2.44/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.54 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setext_type,type,
% 2.44/1.54 setext: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setext,definition,
% 2.44/1.54 ( setext
% 2.44/1.54 = ( ! [A: $i,B: $i] :
% 2.44/1.54 ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ A )
% 2.44/1.54 => ( in @ Xx @ B ) )
% 2.44/1.54 => ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ B )
% 2.44/1.54 => ( in @ Xx @ A ) )
% 2.44/1.54 => ( A = B ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(emptyI_type,type,
% 2.44/1.54 emptyI: $o ).
% 2.44/1.54
% 2.44/1.54 thf(emptyI,definition,
% 2.44/1.54 ( emptyI
% 2.44/1.54 = ( ! [A: $i] :
% 2.44/1.54 ( ! [Xx: $i] :
% 2.44/1.54 ~ ( in @ Xx @ A )
% 2.44/1.54 => ( A = emptyset ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(noeltsimpempty_type,type,
% 2.44/1.54 noeltsimpempty: $o ).
% 2.44/1.54
% 2.44/1.54 thf(noeltsimpempty,definition,
% 2.44/1.54 ( noeltsimpempty
% 2.44/1.54 = ( ! [A: $i] :
% 2.44/1.54 ( ! [Xx: $i] :
% 2.44/1.54 ~ ( in @ Xx @ A )
% 2.44/1.54 => ( A = emptyset ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setbeta_type,type,
% 2.44/1.54 setbeta: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setbeta,definition,
% 2.44/1.54 ( setbeta
% 2.44/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ A )
% 2.44/1.54 => ( ( in @ Xx
% 2.44/1.54 @ ( dsetconstr @ A
% 2.44/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.44/1.54 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(nonempty_type,type,
% 2.44/1.54 nonempty: $i > $o ).
% 2.44/1.54
% 2.44/1.54 thf(nonempty,definition,
% 2.44/1.54 ( nonempty
% 2.44/1.54 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(nonemptyE1_type,type,
% 2.44/1.54 nonemptyE1: $o ).
% 2.44/1.54
% 2.44/1.54 thf(nonemptyE1,definition,
% 2.44/1.54 ( nonemptyE1
% 2.44/1.54 = ( ! [A: $i] :
% 2.44/1.54 ( ( nonempty @ A )
% 2.44/1.54 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(nonemptyI_type,type,
% 2.44/1.54 nonemptyI: $o ).
% 2.44/1.54
% 2.44/1.54 thf(nonemptyI,definition,
% 2.44/1.54 ( nonemptyI
% 2.44/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ A )
% 2.44/1.54 => ( ( Xphi @ Xx )
% 2.44/1.54 => ( nonempty
% 2.44/1.54 @ ( dsetconstr @ A
% 2.44/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(nonemptyI1_type,type,
% 2.44/1.54 nonemptyI1: $o ).
% 2.44/1.54
% 2.44/1.54 thf(nonemptyI1,definition,
% 2.44/1.54 ( nonemptyI1
% 2.44/1.54 = ( ! [A: $i] :
% 2.44/1.54 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.44/1.54 => ( nonempty @ A ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinIL_type,type,
% 2.44/1.54 setadjoinIL: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinIL,definition,
% 2.44/1.54 ( setadjoinIL
% 2.44/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(emptyinunitempty_type,type,
% 2.44/1.54 emptyinunitempty: $o ).
% 2.44/1.54
% 2.44/1.54 thf(emptyinunitempty,definition,
% 2.44/1.54 ( emptyinunitempty
% 2.44/1.54 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinIR_type,type,
% 2.44/1.54 setadjoinIR: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinIR,definition,
% 2.44/1.54 ( setadjoinIR
% 2.44/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.44/1.54 ( ( in @ Xy @ A )
% 2.44/1.54 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinE_type,type,
% 2.44/1.54 setadjoinE: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinE,definition,
% 2.44/1.54 ( setadjoinE
% 2.44/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.44/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.44/1.54 => ! [Xphi: $o] :
% 2.44/1.54 ( ( ( Xy = Xx )
% 2.44/1.54 => Xphi )
% 2.44/1.54 => ( ( ( in @ Xy @ A )
% 2.44/1.54 => Xphi )
% 2.44/1.54 => Xphi ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinOr_type,type,
% 2.44/1.54 setadjoinOr: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setadjoinOr,definition,
% 2.44/1.54 ( setadjoinOr
% 2.44/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.44/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.44/1.54 => ( ( Xy = Xx )
% 2.44/1.54 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setoftrueEq_type,type,
% 2.44/1.54 setoftrueEq: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setoftrueEq,definition,
% 2.44/1.54 ( setoftrueEq
% 2.44/1.54 = ( ! [A: $i] :
% 2.44/1.54 ( ( dsetconstr @ A
% 2.44/1.54 @ ^ [Xx: $i] : $true )
% 2.44/1.54 = A ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(powersetI_type,type,
% 2.44/1.54 powersetI: $o ).
% 2.44/1.54
% 2.44/1.54 thf(powersetI,definition,
% 2.44/1.54 ( powersetI
% 2.44/1.54 = ( ! [A: $i,B: $i] :
% 2.44/1.54 ( ! [Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ B )
% 2.44/1.54 => ( in @ Xx @ A ) )
% 2.44/1.54 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(emptyinPowerset_type,type,
% 2.44/1.54 emptyinPowerset: $o ).
% 2.44/1.54
% 2.44/1.54 thf(emptyinPowerset,definition,
% 2.44/1.54 ( emptyinPowerset
% 2.44/1.54 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(emptyInPowerset_type,type,
% 2.44/1.54 emptyInPowerset: $o ).
% 2.44/1.54
% 2.44/1.54 thf(emptyInPowerset,definition,
% 2.44/1.54 ( emptyInPowerset
% 2.44/1.54 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(powersetE_type,type,
% 2.44/1.54 powersetE: $o ).
% 2.44/1.54
% 2.44/1.54 thf(powersetE,definition,
% 2.44/1.54 ( powersetE
% 2.44/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.54 ( ( in @ B @ ( powerset @ A ) )
% 2.44/1.54 => ( ( in @ Xx @ B )
% 2.44/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setunionI_type,type,
% 2.44/1.54 setunionI: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setunionI,definition,
% 2.44/1.54 ( setunionI
% 2.44/1.54 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.44/1.54 ( ( in @ Xx @ B )
% 2.44/1.54 => ( ( in @ B @ A )
% 2.44/1.54 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(setunionE_type,type,
% 2.44/1.54 setunionE: $o ).
% 2.44/1.54
% 2.44/1.54 thf(setunionE,definition,
% 2.44/1.54 ( setunionE
% 2.44/1.54 = ( ! [A: $i,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 2.44/1.54 => ! [Xphi: $o] :
% 2.44/1.54 ( ! [B: $i] :
% 2.44/1.54 ( ( in @ Xx @ B )
% 2.44/1.54 => ( ( in @ B @ A )
% 2.44/1.54 => Xphi ) )
% 2.44/1.54 => Xphi ) ) ) ) ).
% 2.44/1.54
% 2.44/1.54 thf(subPowSU_type,type,
% 2.44/1.54 subPowSU: $o ).
% 2.44/1.54
% 2.44/1.54 thf(subPowSU,definition,
% 2.44/1.54 ( subPowSU
% 2.44/1.54 = ( ! [A: $i,Xx: $i] :
% 2.44/1.54 ( ( in @ Xx @ A )
% 2.44/1.54 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(exuE2_type,type,
% 2.44/1.55 exuE2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(exuE2,definition,
% 2.44/1.55 ( exuE2
% 2.44/1.55 = ( ! [Xphi: $i > $o] :
% 2.44/1.55 ( ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 => ? [Xx: $i] :
% 2.44/1.55 ! [Xy: $i] :
% 2.44/1.55 ( ( Xphi @ Xy )
% 2.44/1.55 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(nonemptyImpWitness_type,type,
% 2.44/1.55 nonemptyImpWitness: $o ).
% 2.44/1.55
% 2.44/1.55 thf(nonemptyImpWitness,definition,
% 2.44/1.55 ( nonemptyImpWitness
% 2.44/1.55 = ( ! [A: $i] :
% 2.44/1.55 ( ( nonempty @ A )
% 2.44/1.55 => ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & $true ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(uniqinunit_type,type,
% 2.44/1.55 uniqinunit: $o ).
% 2.44/1.55
% 2.44/1.55 thf(uniqinunit,definition,
% 2.44/1.55 ( uniqinunit
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.44/1.55 => ( Xx = Xy ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(notinsingleton_type,type,
% 2.44/1.55 notinsingleton: $o ).
% 2.44/1.55
% 2.44/1.55 thf(notinsingleton,definition,
% 2.44/1.55 ( notinsingleton
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xx != Xy )
% 2.44/1.55 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(eqinunit_type,type,
% 2.44/1.55 eqinunit: $o ).
% 2.44/1.55
% 2.44/1.55 thf(eqinunit,definition,
% 2.44/1.55 ( eqinunit
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xx = Xy )
% 2.44/1.55 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(singletonsswitch_type,type,
% 2.44/1.55 singletonsswitch: $o ).
% 2.44/1.55
% 2.44/1.55 thf(singletonsswitch,definition,
% 2.44/1.55 ( singletonsswitch
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.44/1.55 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(upairsetE_type,type,
% 2.44/1.55 upairsetE: $o ).
% 2.44/1.55
% 2.44/1.55 thf(upairsetE,definition,
% 2.44/1.55 ( upairsetE
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.44/1.55 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.44/1.55 => ( ( Xz = Xx )
% 2.44/1.55 | ( Xz = Xy ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(upairsetIL_type,type,
% 2.44/1.55 upairsetIL: $o ).
% 2.44/1.55
% 2.44/1.55 thf(upairsetIL,definition,
% 2.44/1.55 ( upairsetIL
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(upairsetIR_type,type,
% 2.44/1.55 upairsetIR: $o ).
% 2.44/1.55
% 2.44/1.55 thf(upairsetIR,definition,
% 2.44/1.55 ( upairsetIR
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(emptyE1_type,type,
% 2.44/1.55 emptyE1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(emptyE1,definition,
% 2.44/1.55 ( emptyE1
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & ( Xphi @ Xx ) )
% 2.44/1.55 => ( ( ( dsetconstr @ A
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 = emptyset )
% 2.44/1.55 => $false ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(vacuousDall_type,type,
% 2.44/1.55 vacuousDall: $o ).
% 2.44/1.55
% 2.44/1.55 thf(vacuousDall,definition,
% 2.44/1.55 ( vacuousDall
% 2.44/1.55 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ emptyset )
% 2.44/1.55 => ( Xphi @ Xx ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(quantDeMorgan1_type,type,
% 2.44/1.55 quantDeMorgan1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(quantDeMorgan1,definition,
% 2.44/1.55 ( quantDeMorgan1
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( ~ ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( Xphi @ Xx ) )
% 2.44/1.55 => ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(quantDeMorgan2_type,type,
% 2.44/1.55 quantDeMorgan2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(quantDeMorgan2,definition,
% 2.44/1.55 ( quantDeMorgan2
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ~ ( Xphi @ Xx ) )
% 2.44/1.55 => ~ ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(quantDeMorgan3_type,type,
% 2.44/1.55 quantDeMorgan3: $o ).
% 2.44/1.55
% 2.44/1.55 thf(quantDeMorgan3,definition,
% 2.44/1.55 ( quantDeMorgan3
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( ~ ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & ( Xphi @ Xx ) )
% 2.44/1.55 => ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(quantDeMorgan4_type,type,
% 2.44/1.55 quantDeMorgan4: $o ).
% 2.44/1.55
% 2.44/1.55 thf(quantDeMorgan4,definition,
% 2.44/1.55 ( quantDeMorgan4
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & ~ ( Xphi @ Xx ) )
% 2.44/1.55 => ~ ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(prop2setI_type,type,
% 2.44/1.55 prop2setI: $o ).
% 2.44/1.55
% 2.44/1.55 thf(prop2setI,definition,
% 2.44/1.55 ( prop2setI
% 2.44/1.55 = ( ! [Xphi: $o] :
% 2.44/1.55 ( Xphi
% 2.44/1.55 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(set2prop_type,type,
% 2.44/1.55 set2prop: $i > $o ).
% 2.44/1.55
% 2.44/1.55 thf(prop2set2propI_type,type,
% 2.44/1.55 prop2set2propI: $o ).
% 2.44/1.55
% 2.44/1.55 thf(prop2set2propI,definition,
% 2.44/1.55 ( prop2set2propI
% 2.44/1.55 = ( ! [Xphi: $o] :
% 2.44/1.55 ( Xphi
% 2.44/1.55 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(notdexE_type,type,
% 2.44/1.55 notdexE: $o ).
% 2.44/1.55
% 2.44/1.55 thf(notdexE,definition,
% 2.44/1.55 ( notdexE
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( ~ ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & ( Xphi @ Xx ) )
% 2.44/1.55 => ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(notdallE_type,type,
% 2.44/1.55 notdallE: $o ).
% 2.44/1.55
% 2.44/1.55 thf(notdallE,definition,
% 2.44/1.55 ( notdallE
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( ~ ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( Xphi @ Xx ) )
% 2.44/1.55 => ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(exuI1_type,type,
% 2.44/1.55 exuI1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(exuI1,definition,
% 2.44/1.55 ( exuI1
% 2.44/1.55 = ( ! [Xphi: $i > $o] :
% 2.44/1.55 ( ? [Xx: $i] :
% 2.44/1.55 ( ( Xphi @ Xx )
% 2.44/1.55 & ! [Xy: $i] :
% 2.44/1.55 ( ( Xphi @ Xy )
% 2.44/1.55 => ( Xx = Xy ) ) )
% 2.44/1.55 => ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(exuI3_type,type,
% 2.44/1.55 exuI3: $o ).
% 2.44/1.55
% 2.44/1.55 thf(exuI3,definition,
% 2.44/1.55 ( exuI3
% 2.44/1.55 = ( ! [Xphi: $i > $o] :
% 2.44/1.55 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.44/1.55 => ( ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xphi @ Xx )
% 2.44/1.55 => ( ( Xphi @ Xy )
% 2.44/1.55 => ( Xx = Xy ) ) )
% 2.44/1.55 => ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(exuI2_type,type,
% 2.44/1.55 exuI2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(exuI2,definition,
% 2.44/1.55 ( exuI2
% 2.44/1.55 = ( ! [Xphi: $i > $o] :
% 2.44/1.55 ( ? [Xx: $i] :
% 2.44/1.55 ! [Xy: $i] :
% 2.44/1.55 ( ( Xphi @ Xy )
% 2.44/1.55 <=> ( Xy = Xx ) )
% 2.44/1.55 => ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(inCongP_type,type,
% 2.44/1.55 inCongP: $o ).
% 2.44/1.55
% 2.44/1.55 thf(inCongP,definition,
% 2.44/1.55 ( inCongP
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( A = B )
% 2.44/1.55 => ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xx = Xy )
% 2.44/1.55 => ( ( in @ Xx @ A )
% 2.44/1.55 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(in__Cong_type,type,
% 2.44/1.55 in__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(in__Cong,definition,
% 2.44/1.55 ( in__Cong
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( A = B )
% 2.44/1.55 => ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xx = Xy )
% 2.44/1.55 => ( ( in @ Xx @ A )
% 2.44/1.55 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(exuE3u_type,type,
% 2.44/1.55 exuE3u: $o ).
% 2.44/1.55
% 2.44/1.55 thf(exuE3u,definition,
% 2.44/1.55 ( exuE3u
% 2.44/1.55 = ( ! [Xphi: $i > $o] :
% 2.44/1.55 ( ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 => ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xphi @ Xx )
% 2.44/1.55 => ( ( Xphi @ Xy )
% 2.44/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(exu__Cong_type,type,
% 2.44/1.55 exu__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(exu__Cong,definition,
% 2.44/1.55 ( exu__Cong
% 2.44/1.55 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.44/1.55 ( ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xx = Xy )
% 2.44/1.55 => ( ( Xphi @ Xx )
% 2.44/1.55 <=> ( Xpsi @ Xy ) ) )
% 2.44/1.55 => ( ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 <=> ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(emptyset__Cong_type,type,
% 2.44/1.55 emptyset__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(emptyset__Cong,definition,
% 2.44/1.55 ( emptyset__Cong
% 2.44/1.55 = ( emptyset = emptyset ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setadjoin__Cong_type,type,
% 2.44/1.55 setadjoin__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setadjoin__Cong,definition,
% 2.44/1.55 ( setadjoin__Cong
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xx = Xy )
% 2.44/1.55 => ! [Xz: $i,Xu: $i] :
% 2.44/1.55 ( ( Xz = Xu )
% 2.44/1.55 => ( ( setadjoin @ Xx @ Xz )
% 2.44/1.55 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(powerset__Cong_type,type,
% 2.44/1.55 powerset__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(powerset__Cong,definition,
% 2.44/1.55 ( powerset__Cong
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( A = B )
% 2.44/1.55 => ( ( powerset @ A )
% 2.44/1.55 = ( powerset @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setunion__Cong_type,type,
% 2.44/1.55 setunion__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setunion__Cong,definition,
% 2.44/1.55 ( setunion__Cong
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( A = B )
% 2.44/1.55 => ( ( setunion @ A )
% 2.44/1.55 = ( setunion @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(omega__Cong_type,type,
% 2.44/1.55 omega__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(omega__Cong,definition,
% 2.44/1.55 ( omega__Cong
% 2.44/1.55 = ( omega = omega ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(exuEu_type,type,
% 2.44/1.55 exuEu: $o ).
% 2.44/1.55
% 2.44/1.55 thf(exuEu,definition,
% 2.44/1.55 ( exuEu
% 2.44/1.55 = ( ! [Xphi: $i > $o] :
% 2.44/1.55 ( ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 => ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xphi @ Xx )
% 2.44/1.55 => ( ( Xphi @ Xy )
% 2.44/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(descr__Cong_type,type,
% 2.44/1.55 descr__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(descr__Cong,definition,
% 2.44/1.55 ( descr__Cong
% 2.44/1.55 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.44/1.55 ( ! [Xx: $i,Xy: $i] :
% 2.44/1.55 ( ( Xx = Xy )
% 2.44/1.55 => ( ( Xphi @ Xx )
% 2.44/1.55 <=> ( Xpsi @ Xy ) ) )
% 2.44/1.55 => ( ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 => ( ( exu
% 2.44/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.44/1.55 => ( ( descr
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 = ( descr
% 2.44/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(dsetconstr__Cong_type,type,
% 2.44/1.55 dsetconstr__Cong: $o ).
% 2.44/1.55
% 2.44/1.55 thf(dsetconstr__Cong,definition,
% 2.44/1.55 ( dsetconstr__Cong
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( A = B )
% 2.44/1.55 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.44/1.55 ( ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ! [Xy: $i] :
% 2.44/1.55 ( ( in @ Xy @ B )
% 2.44/1.55 => ( ( Xx = Xy )
% 2.44/1.55 => ( ( Xphi @ Xx )
% 2.44/1.55 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.44/1.55 => ( ( dsetconstr @ A
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 = ( dsetconstr @ B
% 2.44/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(subset_type,type,
% 2.44/1.55 subset: $i > $i > $o ).
% 2.44/1.55
% 2.44/1.55 thf(disjoint_type,type,
% 2.44/1.55 disjoint: $i > $i > $o ).
% 2.44/1.55
% 2.44/1.55 thf(setsmeet_type,type,
% 2.44/1.55 setsmeet: $i > $i > $o ).
% 2.44/1.55
% 2.44/1.55 thf(subsetI1_type,type,
% 2.44/1.55 subsetI1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(subsetI1,definition,
% 2.44/1.55 ( subsetI1
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( in @ Xx @ B ) )
% 2.44/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(eqimpsubset2_type,type,
% 2.44/1.55 eqimpsubset2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(eqimpsubset2,definition,
% 2.44/1.55 ( eqimpsubset2
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( A = B )
% 2.44/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(eqimpsubset1_type,type,
% 2.44/1.55 eqimpsubset1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(eqimpsubset1,definition,
% 2.44/1.55 ( eqimpsubset1
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( A = B )
% 2.44/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(subsetI2_type,type,
% 2.44/1.55 subsetI2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(subsetI2,definition,
% 2.44/1.55 ( subsetI2
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ! [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( in @ Xx @ B ) )
% 2.44/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(emptysetsubset_type,type,
% 2.44/1.55 emptysetsubset: $o ).
% 2.44/1.55
% 2.44/1.55 thf(emptysetsubset,definition,
% 2.44/1.55 ( emptysetsubset
% 2.44/1.55 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(subsetE_type,type,
% 2.44/1.55 subsetE: $o ).
% 2.44/1.55
% 2.44/1.55 thf(subsetE,definition,
% 2.44/1.55 ( subsetE
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( ( in @ Xx @ A )
% 2.44/1.55 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(subsetE2_type,type,
% 2.44/1.55 subsetE2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(subsetE2,definition,
% 2.44/1.55 ( subsetE2
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( ~ ( in @ Xx @ B )
% 2.44/1.55 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(notsubsetI_type,type,
% 2.44/1.55 notsubsetI: $o ).
% 2.44/1.55
% 2.44/1.55 thf(notsubsetI,definition,
% 2.44/1.55 ( notsubsetI
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( ~ ( in @ Xx @ B )
% 2.44/1.55 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(notequalI1_type,type,
% 2.44/1.55 notequalI1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(notequalI1,definition,
% 2.44/1.55 ( notequalI1
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ~ ( subset @ A @ B )
% 2.44/1.55 => ( A != B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(notequalI2_type,type,
% 2.44/1.55 notequalI2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(notequalI2,definition,
% 2.44/1.55 ( notequalI2
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( ~ ( in @ Xx @ B )
% 2.44/1.55 => ( A != B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(subsetRefl_type,type,
% 2.44/1.55 subsetRefl: $o ).
% 2.44/1.55
% 2.44/1.55 thf(subsetRefl,definition,
% 2.44/1.55 ( subsetRefl
% 2.44/1.55 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(subsetTrans_type,type,
% 2.44/1.55 subsetTrans: $o ).
% 2.44/1.55
% 2.44/1.55 thf(subsetTrans,definition,
% 2.44/1.55 ( subsetTrans
% 2.44/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( ( subset @ B @ C )
% 2.44/1.55 => ( subset @ A @ C ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setadjoinSub_type,type,
% 2.44/1.55 setadjoinSub: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setadjoinSub,definition,
% 2.44/1.55 ( setadjoinSub
% 2.44/1.55 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setadjoinSub2_type,type,
% 2.44/1.55 setadjoinSub2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setadjoinSub2,definition,
% 2.44/1.55 ( setadjoinSub2
% 2.44/1.55 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(subset2powerset_type,type,
% 2.44/1.55 subset2powerset: $o ).
% 2.44/1.55
% 2.44/1.55 thf(subset2powerset,definition,
% 2.44/1.55 ( subset2powerset
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setextsub_type,type,
% 2.44/1.55 setextsub: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setextsub,definition,
% 2.44/1.55 ( setextsub
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( ( subset @ B @ A )
% 2.44/1.55 => ( A = B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(subsetemptysetimpeq_type,type,
% 2.44/1.55 subsetemptysetimpeq: $o ).
% 2.44/1.55
% 2.44/1.55 thf(subsetemptysetimpeq,definition,
% 2.44/1.55 ( subsetemptysetimpeq
% 2.44/1.55 = ( ! [A: $i] :
% 2.44/1.55 ( ( subset @ A @ emptyset )
% 2.44/1.55 => ( A = emptyset ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(powersetI1_type,type,
% 2.44/1.55 powersetI1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(powersetI1,definition,
% 2.44/1.55 ( powersetI1
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( subset @ B @ A )
% 2.44/1.55 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(powersetE1_type,type,
% 2.44/1.55 powersetE1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(powersetE1,definition,
% 2.44/1.55 ( powersetE1
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.44/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(inPowerset_type,type,
% 2.44/1.55 inPowerset: $o ).
% 2.44/1.55
% 2.44/1.55 thf(inPowerset,definition,
% 2.44/1.55 ( inPowerset
% 2.44/1.55 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(powersetsubset_type,type,
% 2.44/1.55 powersetsubset: $o ).
% 2.44/1.55
% 2.44/1.55 thf(powersetsubset,definition,
% 2.44/1.55 ( powersetsubset
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(sepInPowerset_type,type,
% 2.44/1.55 sepInPowerset: $o ).
% 2.44/1.55
% 2.44/1.55 thf(sepInPowerset,definition,
% 2.44/1.55 ( sepInPowerset
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( in
% 2.44/1.55 @ ( dsetconstr @ A
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 @ ( powerset @ A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(sepSubset_type,type,
% 2.44/1.55 sepSubset: $o ).
% 2.44/1.55
% 2.44/1.55 thf(sepSubset,definition,
% 2.44/1.55 ( sepSubset
% 2.44/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.55 ( subset
% 2.44/1.55 @ ( dsetconstr @ A
% 2.44/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.55 @ A ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binunion_type,type,
% 2.44/1.55 binunion: $i > $i > $i ).
% 2.44/1.55
% 2.44/1.55 thf(binunionIL_type,type,
% 2.44/1.55 binunionIL: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binunionIL,definition,
% 2.44/1.55 ( binunionIL
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(upairset2IR_type,type,
% 2.44/1.55 upairset2IR: $o ).
% 2.44/1.55
% 2.44/1.55 thf(upairset2IR,definition,
% 2.44/1.55 ( upairset2IR
% 2.44/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binunionIR_type,type,
% 2.44/1.55 binunionIR: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binunionIR,definition,
% 2.44/1.55 ( binunionIR
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ B )
% 2.44/1.55 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binunionEcases_type,type,
% 2.44/1.55 binunionEcases: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binunionEcases,definition,
% 2.44/1.55 ( binunionEcases
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.44/1.55 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.44/1.55 => ( ( ( in @ Xx @ A )
% 2.44/1.55 => Xphi )
% 2.44/1.55 => ( ( ( in @ Xx @ B )
% 2.44/1.55 => Xphi )
% 2.44/1.55 => Xphi ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binunionE_type,type,
% 2.44/1.55 binunionE: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binunionE,definition,
% 2.44/1.55 ( binunionE
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.44/1.55 => ( ( in @ Xx @ A )
% 2.44/1.55 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binunionLsub_type,type,
% 2.44/1.55 binunionLsub: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binunionLsub,definition,
% 2.44/1.55 ( binunionLsub
% 2.44/1.55 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binunionRsub_type,type,
% 2.44/1.55 binunionRsub: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binunionRsub,definition,
% 2.44/1.55 ( binunionRsub
% 2.44/1.55 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersect_type,type,
% 2.44/1.55 binintersect: $i > $i > $i ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectI_type,type,
% 2.44/1.55 binintersectI: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectI,definition,
% 2.44/1.55 ( binintersectI
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( ( in @ Xx @ B )
% 2.44/1.55 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset5_type,type,
% 2.44/1.55 binintersectSubset5: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset5,definition,
% 2.44/1.55 ( binintersectSubset5
% 2.44/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.44/1.55 ( ( subset @ C @ A )
% 2.44/1.55 => ( ( subset @ C @ B )
% 2.44/1.55 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectEL_type,type,
% 2.44/1.55 binintersectEL: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectEL,definition,
% 2.44/1.55 ( binintersectEL
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.44/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectLsub_type,type,
% 2.44/1.55 binintersectLsub: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectLsub,definition,
% 2.44/1.55 ( binintersectLsub
% 2.44/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset2_type,type,
% 2.44/1.55 binintersectSubset2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset2,definition,
% 2.44/1.55 ( binintersectSubset2
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( ( binintersect @ A @ B )
% 2.44/1.55 = A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset3_type,type,
% 2.44/1.55 binintersectSubset3: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset3,definition,
% 2.44/1.55 ( binintersectSubset3
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( ( binintersect @ A @ B )
% 2.44/1.55 = B )
% 2.44/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectER_type,type,
% 2.44/1.55 binintersectER: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectER,definition,
% 2.44/1.55 ( binintersectER
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.44/1.55 => ( in @ Xx @ B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(disjointsetsI1_type,type,
% 2.44/1.55 disjointsetsI1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(disjointsetsI1,definition,
% 2.44/1.55 ( disjointsetsI1
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ~ ? [Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 & ( in @ Xx @ B ) )
% 2.44/1.55 => ( ( binintersect @ A @ B )
% 2.44/1.55 = emptyset ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectRsub_type,type,
% 2.44/1.55 binintersectRsub: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectRsub,definition,
% 2.44/1.55 ( binintersectRsub
% 2.44/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset4_type,type,
% 2.44/1.55 binintersectSubset4: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset4,definition,
% 2.44/1.55 ( binintersectSubset4
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( subset @ B @ A )
% 2.44/1.55 => ( ( binintersect @ A @ B )
% 2.44/1.55 = B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset1_type,type,
% 2.44/1.55 binintersectSubset1: $o ).
% 2.44/1.55
% 2.44/1.55 thf(binintersectSubset1,definition,
% 2.44/1.55 ( binintersectSubset1
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( ( binintersect @ A @ B )
% 2.44/1.55 = A )
% 2.44/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(bs114d_type,type,
% 2.44/1.55 bs114d: $o ).
% 2.44/1.55
% 2.44/1.55 thf(bs114d,definition,
% 2.44/1.55 ( bs114d
% 2.44/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.44/1.55 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.44/1.55 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(regular_type,type,
% 2.44/1.55 regular: $i > $o ).
% 2.44/1.55
% 2.44/1.55 thf(setminus_type,type,
% 2.44/1.55 setminus: $i > $i > $i ).
% 2.44/1.55
% 2.44/1.55 thf(setminusI_type,type,
% 2.44/1.55 setminusI: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setminusI,definition,
% 2.44/1.55 ( setminusI
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ A )
% 2.44/1.55 => ( ~ ( in @ Xx @ B )
% 2.44/1.55 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setminusEL_type,type,
% 2.44/1.55 setminusEL: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setminusEL,definition,
% 2.44/1.55 ( setminusEL
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.44/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setminusER_type,type,
% 2.44/1.55 setminusER: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setminusER,definition,
% 2.44/1.55 ( setminusER
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.44/1.55 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setminusSubset2_type,type,
% 2.44/1.55 setminusSubset2: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setminusSubset2,definition,
% 2.44/1.55 ( setminusSubset2
% 2.44/1.55 = ( ! [A: $i,B: $i] :
% 2.44/1.55 ( ( subset @ A @ B )
% 2.44/1.55 => ( ( setminus @ A @ B )
% 2.44/1.55 = emptyset ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setminusERneg_type,type,
% 2.44/1.55 setminusERneg: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setminusERneg,definition,
% 2.44/1.55 ( setminusERneg
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.44/1.55 => ( ( in @ Xx @ A )
% 2.44/1.55 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setminusELneg_type,type,
% 2.44/1.55 setminusELneg: $o ).
% 2.44/1.55
% 2.44/1.55 thf(setminusELneg,definition,
% 2.44/1.55 ( setminusELneg
% 2.44/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.44/1.55 => ( ~ ( in @ Xx @ B )
% 2.44/1.55 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.55
% 2.44/1.55 thf(setminusILneg,conjecture,
% 2.44/1.55 ( setextAx
% 2.44/1.55 => ( emptysetAx
% 2.44/1.55 => ( setadjoinAx
% 2.44/1.55 => ( powersetAx
% 2.44/1.55 => ( setunionAx
% 2.44/1.55 => ( omega0Ax
% 2.44/1.55 => ( omegaSAx
% 2.44/1.55 => ( omegaIndAx
% 2.44/1.55 => ( replAx
% 2.44/1.55 => ( foundationAx
% 2.44/1.55 => ( wellorderingAx
% 2.44/1.55 => ( descrp
% 2.44/1.55 => ( dsetconstrI
% 2.44/1.55 => ( dsetconstrEL
% 2.44/1.55 => ( dsetconstrER
% 2.44/1.55 => ( exuE1
% 2.44/1.55 => ( prop2setE
% 2.44/1.55 => ( emptysetE
% 2.44/1.55 => ( emptysetimpfalse
% 2.44/1.55 => ( notinemptyset
% 2.44/1.55 => ( exuE3e
% 2.44/1.55 => ( setext
% 2.44/1.55 => ( emptyI
% 2.44/1.55 => ( noeltsimpempty
% 2.44/1.55 => ( setbeta
% 2.44/1.55 => ( nonemptyE1
% 2.44/1.55 => ( nonemptyI
% 2.44/1.55 => ( nonemptyI1
% 2.44/1.55 => ( setadjoinIL
% 2.44/1.55 => ( emptyinunitempty
% 2.44/1.55 => ( setadjoinIR
% 2.44/1.55 => ( setadjoinE
% 2.44/1.55 => ( setadjoinOr
% 2.44/1.55 => ( setoftrueEq
% 2.44/1.55 => ( powersetI
% 2.44/1.55 => ( emptyinPowerset
% 2.44/1.55 => ( emptyInPowerset
% 2.44/1.55 => ( powersetE
% 2.44/1.55 => ( setunionI
% 2.44/1.55 => ( setunionE
% 2.44/1.55 => ( subPowSU
% 2.44/1.55 => ( exuE2
% 2.44/1.55 => ( nonemptyImpWitness
% 2.44/1.55 => ( uniqinunit
% 2.44/1.55 => ( notinsingleton
% 2.44/1.55 => ( eqinunit
% 2.44/1.55 => ( singletonsswitch
% 2.44/1.55 => ( upairsetE
% 2.44/1.55 => ( upairsetIL
% 2.44/1.55 => ( upairsetIR
% 2.44/1.55 => ( emptyE1
% 2.44/1.55 => ( vacuousDall
% 2.44/1.55 => ( quantDeMorgan1
% 2.44/1.55 => ( quantDeMorgan2
% 2.44/1.55 => ( quantDeMorgan3
% 2.44/1.55 => ( quantDeMorgan4
% 2.44/1.55 => ( prop2setI
% 2.44/1.55 => ( prop2set2propI
% 2.44/1.55 => ( notdexE
% 2.44/1.55 => ( notdallE
% 2.44/1.55 => ( exuI1
% 2.44/1.55 => ( exuI3
% 2.44/1.55 => ( exuI2
% 2.44/1.55 => ( inCongP
% 2.44/1.55 => ( in__Cong
% 2.44/1.55 => ( exuE3u
% 2.44/1.55 => ( exu__Cong
% 2.44/1.55 => ( emptyset__Cong
% 2.44/1.55 => ( setadjoin__Cong
% 2.44/1.55 => ( powerset__Cong
% 2.44/1.55 => ( setunion__Cong
% 2.44/1.55 => ( omega__Cong
% 2.44/1.55 => ( exuEu
% 2.44/1.55 => ( descr__Cong
% 2.44/1.55 => ( dsetconstr__Cong
% 2.44/1.55 => ( subsetI1
% 2.44/1.55 => ( eqimpsubset2
% 2.44/1.55 => ( eqimpsubset1
% 2.44/1.55 => ( subsetI2
% 2.44/1.55 => ( emptysetsubset
% 2.44/1.55 => ( subsetE
% 2.44/1.55 => ( subsetE2
% 2.44/1.55 => ( notsubsetI
% 2.44/1.55 => ( notequalI1
% 2.44/1.55 => ( notequalI2
% 2.44/1.55 => ( subsetRefl
% 2.44/1.55 => ( subsetTrans
% 2.44/1.55 => ( setadjoinSub
% 2.44/1.55 => ( setadjoinSub2
% 2.44/1.55 => ( subset2powerset
% 2.44/1.55 => ( setextsub
% 2.44/1.55 => ( subsetemptysetimpeq
% 2.44/1.55 => ( powersetI1
% 2.44/1.55 => ( powersetE1
% 2.44/1.55 => ( inPowerset
% 2.44/1.55 => ( powersetsubset
% 2.44/1.55 => ( sepInPowerset
% 2.44/1.55 => ( sepSubset
% 2.44/1.55 => ( binunionIL
% 2.44/1.55 => ( upairset2IR
% 2.44/1.55 => ( binunionIR
% 2.44/1.55 => ( binunionEcases
% 2.44/1.55 => ( binunionE
% 2.44/1.55 => ( binunionLsub
% 2.44/1.55 => ( binunionRsub
% 2.44/1.55 => ( binintersectI
% 2.44/1.55 => ( binintersectSubset5
% 2.44/1.55 => ( binintersectEL
% 2.44/1.55 => ( binintersectLsub
% 2.44/1.55 => ( binintersectSubset2
% 2.44/1.55 => ( binintersectSubset3
% 2.44/1.55 => ( binintersectER
% 2.44/1.55 => ( disjointsetsI1
% 2.44/1.55 => ( binintersectRsub
% 2.44/1.55 => ( binintersectSubset4
% 2.44/1.55 => ( binintersectSubset1
% 2.44/1.55 => ( bs114d
% 2.44/1.55 => ( setminusI
% 2.44/1.55 => ( setminusEL
% 2.44/1.55 => ( setminusER
% 2.44/1.55 => ( setminusSubset2
% 2.44/1.55 => ( setminusERneg
% 2.44/1.55 => ( setminusELneg
% 2.44/1.55 => ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.55 ( ~ ( in @ Xx @ A )
% 2.44/1.55 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.44/1.55 ------------------------
% 2.44/1.57 % (3345)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/183Mi)
% 2.44/1.57 % (3347)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_3246 for (2999ds/27Mi)
% 2.44/1.57 % (3348)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/2Mi)
% 2.44/1.57 % (3346)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_3246 for (2999ds/4Mi)
% 2.44/1.57 % (3350)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_3246 for (2999ds/275Mi)
% 2.44/1.57 % (3349)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_3246 for (2999ds/2Mi)
% 2.44/1.57 % (3351)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/18Mi)
% 2.44/1.57 % (3348)Instruction limit reached!
% 2.44/1.57 % (3348)------------------------------
% 2.44/1.57 % (3348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.57 % (3348)Termination reason: Unknown
% 2.44/1.57 % (3349)Instruction limit reached!
% 2.44/1.57 % (3349)------------------------------
% 2.44/1.57 % (3349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.57 % (3349)Termination reason: Unknown
% 2.44/1.57 % (3349)Termination phase: shuffling
% 2.44/1.57
% 2.44/1.57 % (3349)Memory used [KB]: 1151
% 2.44/1.57 % (3349)Time elapsed: 0.003 s
% 2.44/1.57 % (3349)Instructions burned: 3 (million)
% 2.44/1.57 % (3349)------------------------------
% 2.44/1.57 % (3349)------------------------------
% 2.44/1.57 % (3348)Termination phase: shuffling
% 2.44/1.57
% 2.44/1.57 % (3348)Memory used [KB]: 1151
% 2.44/1.57 % (3348)Time elapsed: 0.003 s
% 2.44/1.57 % (3348)Instructions burned: 3 (million)
% 2.44/1.57 % (3348)------------------------------
% 2.44/1.57 % (3348)------------------------------
% 2.44/1.57 % (3346)Instruction limit reached!
% 2.44/1.57 % (3346)------------------------------
% 2.44/1.57 % (3346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.57 % (3346)Termination reason: Unknown
% 2.44/1.57 % (3346)Termination phase: shuffling
% 2.44/1.57
% 2.44/1.57 % (3346)Memory used [KB]: 1279
% 2.44/1.57 % (3346)Time elapsed: 0.004 s
% 2.44/1.57 % (3346)Instructions burned: 4 (million)
% 2.44/1.57 % (3346)------------------------------
% 2.44/1.57 % (3346)------------------------------
% 2.44/1.58 % (3351)Instruction limit reached!
% 2.44/1.58 % (3351)------------------------------
% 2.44/1.58 % (3351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.58 % (3351)Termination reason: Unknown
% 2.44/1.58 % (3351)Termination phase: Preprocessing 3
% 2.44/1.58
% 2.44/1.58 % (3351)Memory used [KB]: 1535
% 2.44/1.58 % (3351)Time elapsed: 0.011 s
% 2.44/1.58 % (3351)Instructions burned: 19 (million)
% 2.44/1.58 % (3351)------------------------------
% 2.44/1.58 % (3351)------------------------------
% 2.44/1.58 % (3347)Instruction limit reached!
% 2.44/1.58 % (3347)------------------------------
% 2.44/1.58 % (3347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.58 % (3347)Termination reason: Unknown
% 2.44/1.58 % (3347)Termination phase: Property scanning
% 2.44/1.58
% 2.44/1.58 % (3347)Memory used [KB]: 1535
% 2.44/1.58 % (3347)Time elapsed: 0.014 s
% 2.44/1.58 % (3347)Instructions burned: 27 (million)
% 2.44/1.58 % (3347)------------------------------
% 2.44/1.58 % (3347)------------------------------
% 2.44/1.59 % (3352)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/3Mi)
% 2.44/1.59 % (3353)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_3246 for (2999ds/37Mi)
% 2.44/1.59 % (3354)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_3246 for (2999ds/15Mi)
% 2.44/1.59 % (3352)Instruction limit reached!
% 2.44/1.59 % (3352)------------------------------
% 2.44/1.59 % (3352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.59 % (3352)Termination reason: Unknown
% 2.44/1.59 % (3352)Termination phase: shuffling
% 2.44/1.59
% 2.44/1.59 % (3352)Memory used [KB]: 1151
% 2.44/1.59 % (3352)Time elapsed: 0.003 s
% 2.44/1.59 % (3352)Instructions burned: 3 (million)
% 2.44/1.59 % (3352)------------------------------
% 2.44/1.59 % (3352)------------------------------
% 2.51/1.60 % (3354)Instruction limit reached!
% 2.51/1.60 % (3354)------------------------------
% 2.51/1.60 % (3354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (3354)Termination reason: Unknown
% 2.51/1.60 % (3354)Termination phase: Preprocessing 1
% 2.51/1.60 % (3355)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_3246 for (2999ds/3Mi)
% 2.51/1.60
% 2.51/1.60 % (3354)Memory used [KB]: 1407
% 2.51/1.60 % (3354)Time elapsed: 0.009 s
% 2.51/1.60 % (3354)Instructions burned: 16 (million)
% 2.51/1.60 % (3354)------------------------------
% 2.51/1.60 % (3354)------------------------------
% 2.51/1.60 % (3355)Instruction limit reached!
% 2.51/1.60 % (3355)------------------------------
% 2.51/1.60 % (3355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (3355)Termination reason: Unknown
% 2.51/1.60 % (3355)Termination phase: shuffling
% 2.51/1.60
% 2.51/1.60 % (3355)Memory used [KB]: 1151
% 2.51/1.60 % (3355)Time elapsed: 0.003 s
% 2.51/1.60 % (3355)Instructions burned: 3 (million)
% 2.51/1.60 % (3355)------------------------------
% 2.51/1.60 % (3355)------------------------------
% 2.51/1.60 % (3356)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_3246 for (2999ds/1041Mi)
% 2.51/1.60 % (3353)Instruction limit reached!
% 2.51/1.60 % (3353)------------------------------
% 2.51/1.60 % (3353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (3353)Termination reason: Unknown
% 2.51/1.60 % (3353)Termination phase: Property scanning
% 2.51/1.60
% 2.51/1.60 % (3353)Memory used [KB]: 1663
% 2.51/1.60 % (3353)Time elapsed: 0.018 s
% 2.51/1.60 % (3353)Instructions burned: 37 (million)
% 2.51/1.60 % (3353)------------------------------
% 2.51/1.60 % (3353)------------------------------
% 2.51/1.61 % (3357)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/7Mi)
% 2.51/1.61 % (3357)Instruction limit reached!
% 2.51/1.61 % (3357)------------------------------
% 2.51/1.61 % (3357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.61 % (3357)Termination reason: Unknown
% 2.51/1.61 % (3357)Termination phase: shuffling
% 2.51/1.61
% 2.51/1.61 % (3357)Memory used [KB]: 1279
% 2.51/1.61 % (3357)Time elapsed: 0.005 s
% 2.51/1.61 % (3357)Instructions burned: 8 (million)
% 2.51/1.61 % (3357)------------------------------
% 2.51/1.61 % (3357)------------------------------
% 2.51/1.61 % (3358)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/16Mi)
% 2.51/1.61 % (3359)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_3246 for (2999ds/3Mi)
% 2.51/1.62 % (3359)Instruction limit reached!
% 2.51/1.62 % (3359)------------------------------
% 2.51/1.62 % (3359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.62 % (3359)Termination reason: Unknown
% 2.51/1.62 % (3359)Termination phase: shuffling
% 2.51/1.62
% 2.51/1.62 % (3359)Memory used [KB]: 1151
% 2.51/1.62 % (3359)Time elapsed: 0.003 s
% 2.51/1.62 % (3359)Instructions burned: 3 (million)
% 2.51/1.62 % (3359)------------------------------
% 2.51/1.62 % (3359)------------------------------
% 2.51/1.62 % (3358)Instruction limit reached!
% 2.51/1.62 % (3358)------------------------------
% 2.51/1.62 % (3358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.62 % (3358)Termination reason: Unknown
% 2.51/1.62 % (3358)Termination phase: shuffling
% 2.51/1.62
% 2.51/1.62 % (3358)Memory used [KB]: 1535
% 2.51/1.62 % (3358)Time elapsed: 0.009 s
% 2.51/1.62 % (3358)Instructions burned: 17 (million)
% 2.51/1.62 % (3358)------------------------------
% 2.51/1.62 % (3358)------------------------------
% 2.51/1.62 % (3360)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_3246 for (2999ds/3Mi)
% 2.51/1.62 % (3360)Instruction limit reached!
% 2.51/1.62 % (3360)------------------------------
% 2.51/1.62 % (3360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.62 % (3360)Termination reason: Unknown
% 2.51/1.62 % (3360)Termination phase: shuffling
% 2.51/1.62
% 2.51/1.62 % (3360)Memory used [KB]: 1151
% 2.51/1.62 % (3360)Time elapsed: 0.003 s
% 2.51/1.62 % (3360)Instructions burned: 3 (million)
% 2.51/1.62 % (3360)------------------------------
% 2.51/1.62 % (3360)------------------------------
% 2.51/1.63 % (3361)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/7Mi)
% 2.51/1.63 % (3361)Instruction limit reached!
% 2.51/1.63 % (3361)------------------------------
% 2.51/1.63 % (3361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.63 % (3361)Termination reason: Unknown
% 2.51/1.63 % (3361)Termination phase: shuffling
% 2.51/1.63
% 2.51/1.63 % (3361)Memory used [KB]: 1279
% 2.51/1.63 % (3361)Time elapsed: 0.005 s
% 2.51/1.63 % (3361)Instructions burned: 8 (million)
% 2.51/1.63 % (3361)------------------------------
% 2.51/1.63 % (3361)------------------------------
% 2.51/1.63 % (3362)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/3Mi)
% 2.51/1.63 % (3362)Instruction limit reached!
% 2.51/1.63 % (3362)------------------------------
% 2.51/1.63 % (3362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.63 % (3362)Termination reason: Unknown
% 2.51/1.63 % (3362)Termination phase: shuffling
% 2.51/1.63
% 2.51/1.63 % (3362)Memory used [KB]: 1151
% 2.51/1.63 % (3362)Time elapsed: 0.003 s
% 2.51/1.63 % (3362)Instructions burned: 4 (million)
% 2.51/1.63 % (3362)------------------------------
% 2.51/1.63 % (3362)------------------------------
% 2.51/1.64 % (3363)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/4Mi)
% 2.51/1.64 % (3364)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/18Mi)
% 2.51/1.64 % (3363)Instruction limit reached!
% 2.51/1.64 % (3363)------------------------------
% 2.51/1.64 % (3363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.64 % (3363)Termination reason: Unknown
% 2.51/1.64 % (3363)Termination phase: shuffling
% 2.51/1.64
% 2.51/1.64 % (3363)Memory used [KB]: 1279
% 2.51/1.64 % (3363)Time elapsed: 0.004 s
% 2.51/1.64 % (3363)Instructions burned: 6 (million)
% 2.51/1.64 % (3363)------------------------------
% 2.51/1.64 % (3363)------------------------------
% 2.51/1.64 % (3365)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/710Mi)
% 2.51/1.65 % (3364)Instruction limit reached!
% 2.51/1.65 % (3364)------------------------------
% 2.51/1.65 % (3364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.65 % (3364)Termination reason: Unknown
% 2.51/1.65 % (3364)Termination phase: Property scanning
% 2.51/1.65
% 2.51/1.65 % (3364)Memory used [KB]: 1535
% 2.51/1.65 % (3364)Time elapsed: 0.010 s
% 2.51/1.65 % (3364)Instructions burned: 19 (million)
% 2.51/1.65 % (3364)------------------------------
% 2.51/1.65 % (3364)------------------------------
% 2.51/1.65 % (3366)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/6Mi)
% 2.51/1.65 % (3366)Instruction limit reached!
% 2.51/1.65 % (3366)------------------------------
% 2.51/1.65 % (3366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.65 % (3366)Termination reason: Unknown
% 2.51/1.65 % (3366)Termination phase: shuffling
% 2.51/1.65
% 2.51/1.65 % (3366)Memory used [KB]: 1279
% 2.51/1.65 % (3366)Time elapsed: 0.004 s
% 2.51/1.65 % (3366)Instructions burned: 6 (million)
% 2.51/1.65 % (3366)------------------------------
% 2.51/1.65 % (3366)------------------------------
% 2.51/1.65 % (3367)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_3246 for (2999ds/902Mi)
% 2.51/1.66 % (3345)Instruction limit reached!
% 2.51/1.66 % (3345)------------------------------
% 2.51/1.66 % (3345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.66 % (3345)Termination reason: Unknown
% 2.51/1.66 % (3345)Termination phase: Saturation
% 2.51/1.66
% 2.51/1.66 % (3345)Memory used [KB]: 7036
% 2.51/1.66 % (3345)Time elapsed: 0.087 s
% 2.51/1.66 % (3345)Instructions burned: 183 (million)
% 2.51/1.66 % (3345)------------------------------
% 2.51/1.66 % (3345)------------------------------
% 2.51/1.66 % (3368)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_3246 for (2999ds/21Mi)
% 2.51/1.67 % (3369)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3246 for (2999ds/5Mi)
% 2.51/1.67 % (3369)Instruction limit reached!
% 2.51/1.67 % (3369)------------------------------
% 2.51/1.67 % (3369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.67 % (3369)Termination reason: Unknown
% 2.51/1.67 % (3369)Termination phase: shuffling
% 2.51/1.67
% 2.51/1.67 % (3369)Memory used [KB]: 1279
% 2.51/1.67 % (3369)Time elapsed: 0.004 s
% 2.51/1.67 % (3369)Instructions burned: 6 (million)
% 2.51/1.67 % (3369)------------------------------
% 2.51/1.67 % (3369)------------------------------
% 2.51/1.67 % (3370)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_3246 for (2999ds/6Mi)
% 2.51/1.67 % (3368)Instruction limit reached!
% 2.51/1.67 % (3368)------------------------------
% 2.51/1.67 % (3368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.67 % (3368)Termination reason: Unknown
% 2.51/1.67 % (3368)Termination phase: Property scanning
% 2.51/1.67
% 2.51/1.67 % (3368)Memory used [KB]: 1535
% 2.51/1.67 % (3368)Time elapsed: 0.011 s
% 2.51/1.67 % (3368)Instructions burned: 21 (million)
% 2.51/1.67 % (3368)------------------------------
% 2.51/1.67 % (3368)------------------------------
% 2.51/1.68 % (3370)Instruction limit reached!
% 2.51/1.68 % (3370)------------------------------
% 2.51/1.68 % (3370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.68 % (3370)Termination reason: Unknown
% 2.51/1.68 % (3370)Termination phase: shuffling
% 2.51/1.68
% 2.51/1.68 % (3370)Memory used [KB]: 1279
% 2.51/1.68 % (3370)Time elapsed: 0.005 s
% 2.51/1.68 % (3370)Instructions burned: 8 (million)
% 2.51/1.68 % (3370)------------------------------
% 2.51/1.68 % (3370)------------------------------
% 2.51/1.69 % (3371)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3246 for (2998ds/377Mi)
% 2.51/1.69 % (3372)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_3246 for (2998ds/779Mi)
% 2.51/1.69 % (3373)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_3246 for (2998ds/19Mi)
% 2.51/1.70 % (3373)Instruction limit reached!
% 2.51/1.70 % (3373)------------------------------
% 2.51/1.70 % (3373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.70 % (3373)Termination reason: Unknown
% 2.51/1.70 % (3373)Termination phase: Property scanning
% 2.51/1.70
% 2.51/1.70 % (3373)Memory used [KB]: 1535
% 2.51/1.70 % (3373)Time elapsed: 0.010 s
% 2.51/1.70 % (3373)Instructions burned: 19 (million)
% 2.51/1.70 % (3373)------------------------------
% 2.51/1.70 % (3373)------------------------------
% 2.51/1.71 % (3350)Instruction limit reached!
% 2.51/1.71 % (3350)------------------------------
% 2.51/1.71 % (3350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.71 % (3350)Termination reason: Unknown
% 2.51/1.71 % (3350)Termination phase: Saturation
% 2.51/1.71
% 2.51/1.71 % (3350)Memory used [KB]: 7803
% 2.51/1.71 % (3350)Time elapsed: 0.138 s
% 2.51/1.71 % (3350)Instructions burned: 275 (million)
% 2.51/1.71 % (3350)------------------------------
% 2.51/1.71 % (3350)------------------------------
% 2.51/1.71 % (3367)First to succeed.
% 2.51/1.72 % (3374)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3246 for (2998ds/879Mi)
% 2.51/1.72 % (3367)Refutation found. Thanks to Tanya!
% 2.51/1.72 % SZS status Theorem for DTF2THF_3246
% 2.51/1.72 % SZS output start Proof for DTF2THF_3246
% 2.51/1.72 thf(func_def_0, type, in: $i > $i > $o).
% 2.51/1.72 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.51/1.72 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.51/1.72 thf(func_def_8, type, powerset: $i > $i).
% 2.51/1.72 thf(func_def_10, type, setunion: $i > $i).
% 2.51/1.72 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.51/1.72 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_26, type, prop2set: $o > $i).
% 2.51/1.72 thf(func_def_36, type, nonempty: $i > $o).
% 2.51/1.72 thf(func_def_69, type, set2prop: $i > $o).
% 2.51/1.72 thf(func_def_88, type, subset: $i > $i > $o).
% 2.51/1.72 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.51/1.72 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.51/1.72 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.51/1.72 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.51/1.72 thf(func_def_135, type, regular: $i > $o).
% 2.51/1.72 thf(func_def_136, type, setminus: $i > $i > $i).
% 2.51/1.72 thf(func_def_155, type, sP0: $i > $i > $o).
% 2.51/1.72 thf(func_def_156, type, sP1: $i > $o).
% 2.51/1.72 thf(func_def_157, type, sP2: $i > $i > $o).
% 2.51/1.72 thf(func_def_158, type, sP3: $i > $i > $o).
% 2.51/1.72 thf(func_def_164, type, sK9: $i > $o).
% 2.51/1.72 thf(func_def_169, type, sK14: $i > $i > $i).
% 2.51/1.72 thf(func_def_179, type, sK24: $i > $o).
% 2.51/1.72 thf(func_def_181, type, sK26: $i > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_182, type, sK27: $i > $o).
% 2.51/1.72 thf(func_def_188, type, sK33: $i > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_189, type, sK34: $i > $o).
% 2.51/1.72 thf(func_def_192, type, sK37: $i > $i > $i).
% 2.51/1.72 thf(func_def_201, type, sK46: $i > $i > $i).
% 2.51/1.72 thf(func_def_205, type, sK50: ($i > $o) > $i).
% 2.51/1.72 thf(func_def_206, type, sK51: $i > $o).
% 2.51/1.72 thf(func_def_207, type, sK52: $i > $i).
% 2.51/1.72 thf(func_def_210, type, sK55: $i > $o).
% 2.51/1.72 thf(func_def_216, type, sK61: $i > $i).
% 2.51/1.72 thf(func_def_218, type, sK63: $i > $o).
% 2.51/1.72 thf(func_def_219, type, sK64: ($i > $o) > $i).
% 2.51/1.72 thf(func_def_225, type, sK70: $i > $i).
% 2.51/1.72 thf(func_def_227, type, sK72: $i > $i > $i).
% 2.51/1.72 thf(func_def_228, type, sK73: $i > $i > $i).
% 2.51/1.72 thf(func_def_229, type, sK74: $i > $i > $i).
% 2.51/1.72 thf(func_def_230, type, sK75: $i > $i > $i).
% 2.51/1.72 thf(func_def_231, type, sK76: $i > $i > $i).
% 2.51/1.72 thf(func_def_232, type, sK77: $i > $i > $i > $i).
% 2.51/1.72 thf(func_def_233, type, sK78: $i > $i).
% 2.51/1.72 thf(func_def_234, type, sK79: $i > $i).
% 2.51/1.72 thf(func_def_235, type, sK80: $i > $i).
% 2.51/1.72 thf(func_def_236, type, sK81: $i > $i).
% 2.51/1.72 thf(func_def_237, type, sK82: $i > $i > $i).
% 2.51/1.72 thf(func_def_238, type, sK83: $i > $i > $i > $i).
% 2.51/1.72 thf(func_def_239, type, sK84: $i > $i > $i > $i).
% 2.51/1.72 thf(func_def_240, type, sK85: $i > $i > $i).
% 2.51/1.72 thf(func_def_241, type, sK86: $i > $i > $i).
% 2.51/1.72 thf(func_def_242, type, sK87: $i > $i).
% 2.51/1.72 thf(func_def_244, type, sK89: $i > $i).
% 2.51/1.72 thf(func_def_245, type, sK90: $i > $i).
% 2.51/1.72 thf(func_def_246, type, sK91: $i > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_247, type, sK92: $i > $o).
% 2.51/1.72 thf(func_def_254, type, sK99: $i > $i > $i).
% 2.51/1.72 thf(func_def_258, type, sK103: $o > $i > $i > $i).
% 2.51/1.72 thf(func_def_271, type, sK116: $i > $o).
% 2.51/1.72 thf(func_def_273, type, sK118: $i > $i > $i).
% 2.51/1.72 thf(func_def_274, type, sK119: $i > $i > $i).
% 2.51/1.72 thf(func_def_280, type, sK125: $i > $i > $i).
% 2.51/1.72 thf(func_def_281, type, sK126: $i > $i).
% 2.51/1.72 thf(func_def_286, type, sK131: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.51/1.72 thf(func_def_287, type, sK132: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.51/1.72 thf(func_def_290, type, sK135: $i > $o).
% 2.51/1.72 thf(func_def_291, type, sK136: $i > $o).
% 2.51/1.72 thf(func_def_293, type, sK138: $i > $o).
% 2.51/1.72 thf(func_def_305, type, sK150: $i > $o).
% 2.51/1.72 thf(func_def_308, type, sK153: $i > $i > $i).
% 2.51/1.72 thf(func_def_311, type, sK156: ($i > $o) > $i).
% 2.51/1.72 thf(func_def_312, type, sK157: ($i > $o) > $i).
% 2.51/1.72 thf(func_def_313, type, sK158: $i > $o).
% 2.51/1.72 thf(func_def_315, type, sK160: $i > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_316, type, sK161: $i > $o).
% 2.51/1.72 thf(func_def_327, type, sK172: $i > $o).
% 2.51/1.72 thf(func_def_328, type, sK173: ($i > $o) > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_329, type, sK174: ($i > $o) > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_330, type, sK175: $i > $o).
% 2.51/1.72 thf(func_def_331, type, sK176: $i > $o).
% 2.51/1.72 thf(func_def_336, type, sK181: $i > $o).
% 2.51/1.72 thf(func_def_338, type, sK183: $i > $o).
% 2.51/1.72 thf(func_def_340, type, sK185: ($i > $o) > $i > $i).
% 2.51/1.72 thf(func_def_364, type, sK209: $i > $o).
% 2.51/1.72 thf(func_def_381, type, sK226: $i > $o).
% 2.51/1.72 thf(func_def_388, type, sK233: $i > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_389, type, sK234: $i > $o).
% 2.51/1.72 thf(func_def_392, type, sK237: $i > $o).
% 2.51/1.72 thf(func_def_393, type, sK238: $i > $i).
% 2.51/1.72 thf(func_def_394, type, sK239: ($i > $o) > $i).
% 2.51/1.72 thf(func_def_398, type, sK243: $i > $o).
% 2.51/1.72 thf(func_def_429, type, sK274: $i > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_430, type, sK275: $i > $o).
% 2.51/1.72 thf(func_def_436, type, sK281: $i > $i > $i).
% 2.51/1.72 thf(func_def_438, type, sK283: $i > $i).
% 2.51/1.72 thf(func_def_444, type, sK289: $i > $i > $o).
% 2.51/1.72 thf(func_def_446, type, sK291: $i > $i).
% 2.51/1.72 thf(func_def_447, type, sK292: $i > $i).
% 2.51/1.72 thf(func_def_448, type, sK293: $i > ($i > $i > $o) > $i).
% 2.51/1.72 thf(func_def_449, type, sK294: $i > $i > ($i > $i > $o) > $i).
% 2.51/1.72 thf(func_def_450, type, sK295: $i > ($i > $i > $o) > $i).
% 2.51/1.72 thf(func_def_453, type, sK298: $i > $o).
% 2.51/1.72 thf(func_def_456, type, sK301: ($i > $o) > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_457, type, sK302: ($i > $o) > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_458, type, sK303: $i > $o).
% 2.51/1.72 thf(func_def_459, type, sK304: $i > $o).
% 2.51/1.72 thf(func_def_468, type, sK313: $i > $i).
% 2.51/1.72 thf(func_def_481, type, sK326: $i > ($i > $o) > $i).
% 2.51/1.72 thf(func_def_482, type, sK327: $i > $o).
% 2.51/1.72 thf(func_def_485, type, sK330: $i > $i).
% 2.51/1.72 thf(func_def_487, type, sK332: $i > $i).
% 2.51/1.72 thf(func_def_495, type, ph340: !>[X0: $tType]:(X0)).
% 2.51/1.72 thf(f1852,plain,(
% 2.51/1.72 $false),
% 2.51/1.72 inference(trivial_inequality_removal,[status(thm)],[f1850])).
% 2.51/1.72 thf(f1850,plain,(
% 2.51/1.72 ($true != $true)),
% 2.51/1.72 inference(superposition,[status(thm)],[f1667,f1834])).
% 2.51/1.72 thf(f1834,plain,(
% 2.51/1.72 ((in @ sK316 @ sK317) = $true)),
% 2.51/1.72 inference(trivial_inequality_removal,[status(thm)],[f1833])).
% 2.51/1.72 thf(f1833,plain,(
% 2.51/1.72 ((in @ sK316 @ sK317) = $true) | ($true != $true)),
% 2.51/1.72 inference(forward_demodulation,[status(thm)],[f1832,f1594])).
% 2.51/1.72 thf(f1594,plain,(
% 2.51/1.72 (setminusEL = $true)),
% 2.51/1.72 inference(cnf_transformation,[status(thm)],[f1076])).
% 2.51/1.72 thf(f1076,plain,(
% 2.51/1.72 (emptyE1 = $true) & (binunionEcases = $true) & (exu__Cong = $true) & (quantDeMorgan1 = $true) & (dsetconstrEL = $true) & (powersetAx = $true) & (setadjoin__Cong = $true) & (setadjoinIR = $true) & (binintersectLsub = $true) & (emptysetE = $true) & (notdallE = $true) & (wellorderingAx = $true) & (powerset__Cong = $true) & (foundationAx = $true) & (binunionE = $true) & (binunionIL = $true) & (quantDeMorgan2 = $true) & (omega__Cong = $true) & (omegaIndAx = $true) & (powersetE = $true) & (nonemptyImpWitness = $true) & (setextsub = $true) & (($true = (in @ sK316 @ (setminus @ sK317 @ sK318))) & ((in @ sK316 @ sK317) != $true)) & (notinemptyset = $true) & (notsubsetI = $true) & (omega0Ax = $true) & (setadjoinAx = $true) & (binintersectER = $true) & (prop2setI = $true) & (exuI2 = $true) & (emptysetAx = $true) & (upairsetIR = $true) & (exuE3u = $true) & (upairsetIL = $true) & (subsetTrans = $true) & (subsetI2 = $true) & (binintersectSubset4 = $true) & (binintersectEL = $true) & (sepSubset = $true) & (descr__Cong = $true) & (prop2set2propI = $true) & (noeltsimpempty = $true) & (subPowSU = $true) & (quantDeMorgan3 = $true) & (emptyInPowerset = $true) & (binintersectSubset5 = $true) & (notinsingleton = $true) & (setadjoinE = $true) & (subsetRefl = $true) & (emptyinPowerset = $true) & (descrp = $true) & (exuI3 = $true) & (powersetI = $true) & (eqinunit = $true) & (setunionE = $true) & (inPowerset = $true) & (setunion__Cong = $true) & (subsetI1 = $true) & (powersetE1 = $true) & (bs114d = $true) & (replAx = $true) & (setminusI = $true) & (emptyI = $true) & (eqimpsubset1 = $true) & (exuI1 = $true) & (eqimpsubset2 = $true) & (prop2setE = $true) & (binintersectRsub = $true) & (uniqinunit = $true) & (setunionAx = $true) & (setadjoinOr = $true) & (quantDeMorgan4 = $true) & (powersetsubset = $true) & (setadjoinSub2 = $true) & (emptysetsubset = $true) & (binunionIR = $true) & (exuEu = $true) & (dsetconstrI = $true) & (omegaSAx = $true) & (notequalI2 = $true) & (setminusER = $true) & (binintersectSubset1 = $true) & (singletonsswitch = $true) & (binunionRsub = $true) & (nonemptyI1 = $true) & (vacuousDall = $true) & (subsetemptysetimpeq = $true) & (setminusSubset2 = $true) & (subsetE2 = $true) & (binintersectSubset2 = $true) & (setadjoinSub = $true) & (notequalI1 = $true) & (setoftrueEq = $true) & (nonemptyE1 = $true) & (exuE2 = $true) & (setminusEL = $true) & (setadjoinIL = $true) & (dsetconstr__Cong = $true) & (disjointsetsI1 = $true) & (emptyset__Cong = $true) & (dsetconstrER = $true) & (notdexE = $true) & (exuE1 = $true) & (powersetI1 = $true) & (subsetE = $true) & (subset2powerset = $true) & (binunionLsub = $true) & (setunionI = $true) & (binintersectSubset3 = $true) & (in__Cong = $true) & (emptyinunitempty = $true) & (upairsetE = $true) & (setextAx = $true) & (exuE3e = $true) & (setext = $true) & (upairset2IR = $true) & (nonemptyI = $true) & (sepInPowerset = $true) & (setminusELneg = $true) & (inCongP = $true) & (emptysetimpfalse = $true) & (binintersectI = $true) & (setminusERneg = $true) & (setbeta = $true)),
% 2.51/1.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK316,sK317,sK318])],[f459,f1075])).
% 2.51/1.72 thf(f1075,plain,(
% 2.51/1.72 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) & ($true != (in @ X0 @ X1))) => (($true = (in @ sK316 @ (setminus @ sK317 @ sK318))) & ((in @ sK316 @ sK317) != $true))),
% 2.51/1.72 introduced(definition,[],[choice_axiom])).
% 2.51/1.72 thf(f459,plain,(
% 2.51/1.72 (emptyE1 = $true) & (binunionEcases = $true) & (exu__Cong = $true) & (quantDeMorgan1 = $true) & (dsetconstrEL = $true) & (powersetAx = $true) & (setadjoin__Cong = $true) & (setadjoinIR = $true) & (binintersectLsub = $true) & (emptysetE = $true) & (notdallE = $true) & (wellorderingAx = $true) & (powerset__Cong = $true) & (foundationAx = $true) & (binunionE = $true) & (binunionIL = $true) & (quantDeMorgan2 = $true) & (omega__Cong = $true) & (omegaIndAx = $true) & (powersetE = $true) & (nonemptyImpWitness = $true) & (setextsub = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) & ($true != (in @ X0 @ X1))) & (notinemptyset = $true) & (notsubsetI = $true) & (omega0Ax = $true) & (setadjoinAx = $true) & (binintersectER = $true) & (prop2setI = $true) & (exuI2 = $true) & (emptysetAx = $true) & (upairsetIR = $true) & (exuE3u = $true) & (upairsetIL = $true) & (subsetTrans = $true) & (subsetI2 = $true) & (binintersectSubset4 = $true) & (binintersectEL = $true) & (sepSubset = $true) & (descr__Cong = $true) & (prop2set2propI = $true) & (noeltsimpempty = $true) & (subPowSU = $true) & (quantDeMorgan3 = $true) & (emptyInPowerset = $true) & (binintersectSubset5 = $true) & (notinsingleton = $true) & (setadjoinE = $true) & (subsetRefl = $true) & (emptyinPowerset = $true) & (descrp = $true) & (exuI3 = $true) & (powersetI = $true) & (eqinunit = $true) & (setunionE = $true) & (inPowerset = $true) & (setunion__Cong = $true) & (subsetI1 = $true) & (powersetE1 = $true) & (bs114d = $true) & (replAx = $true) & (setminusI = $true) & (emptyI = $true) & (eqimpsubset1 = $true) & (exuI1 = $true) & (eqimpsubset2 = $true) & (prop2setE = $true) & (binintersectRsub = $true) & (uniqinunit = $true) & (setunionAx = $true) & (setadjoinOr = $true) & (quantDeMorgan4 = $true) & (powersetsubset = $true) & (setadjoinSub2 = $true) & (emptysetsubset = $true) & (binunionIR = $true) & (exuEu = $true) & (dsetconstrI = $true) & (omegaSAx = $true) & (notequalI2 = $true) & (setminusER = $true) & (binintersectSubset1 = $true) & (singletonsswitch = $true) & (binunionRsub = $true) & (nonemptyI1 = $true) & (vacuousDall = $true) & (subsetemptysetimpeq = $true) & (setminusSubset2 = $true) & (subsetE2 = $true) & (binintersectSubset2 = $true) & (setadjoinSub = $true) & (notequalI1 = $true) & (setoftrueEq = $true) & (nonemptyE1 = $true) & (exuE2 = $true) & (setminusEL = $true) & (setadjoinIL = $true) & (dsetconstr__Cong = $true) & (disjointsetsI1 = $true) & (emptyset__Cong = $true) & (dsetconstrER = $true) & (notdexE = $true) & (exuE1 = $true) & (powersetI1 = $true) & (subsetE = $true) & (subset2powerset = $true) & (binunionLsub = $true) & (setunionI = $true) & (binintersectSubset3 = $true) & (in__Cong = $true) & (emptyinunitempty = $true) & (upairsetE = $true) & (setextAx = $true) & (exuE3e = $true) & (setext = $true) & (upairset2IR = $true) & (nonemptyI = $true) & (sepInPowerset = $true) & (setminusELneg = $true) & (inCongP = $true) & (emptysetimpfalse = $true) & (binintersectI = $true) & (setminusERneg = $true) & (setbeta = $true)),
% 2.51/1.72 inference(flattening,[status(thm)],[f458])).
% 2.51/1.72 thf(f458,plain,(
% 2.51/1.72 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) & ($true != (in @ X0 @ X1))) & (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)),
% 2.51/1.72 inference(ennf_transformation,[status(thm)],[f386])).
% 2.51/1.72 thf(f386,plain,(
% 2.51/1.72 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) => ((in @ X0 @ (setminus @ X1 @ X2)) != $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.51/1.72 inference(flattening,[status(thm)],[f192])).
% 2.51/1.72 thf(f192,plain,(
% 2.51/1.72 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (~($true = (in @ X0 @ X1)) => ~((in @ X0 @ (setminus @ X1 @ X2)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.51/1.72 inference(fool_elimination,[status(thm)],[f191])).
% 2.51/1.72 thf(f191,plain,(
% 2.51/1.72 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ X1) => ~(in @ X0 @ (setminus @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.51/1.72 inference(rectify,[status(thm)],[f127])).
% 2.51/1.72 thf(f127,negated_conjecture,(
% 2.51/1.72 ~(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 => ! [X1 : $i,X3 : $i,X4 : $i] : (~(in @ X1 @ X3) => ~(in @ X1 @ (setminus @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.51/1.72 inference(negated_conjecture,[status(cth)],[f126])).
% 2.51/1.72 thf(f126,conjecture,(
% 2.51/1.72 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 => ! [X1 : $i,X3 : $i,X4 : $i] : (~(in @ X1 @ X3) => ~(in @ X1 @ (setminus @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.51/1.72 file('/export/starexec/sandbox/tmp/tmp.3WLPAKKuIJ/DTF2THF_3246.p',setminusILneg)).
% 2.51/1.72 thf(f1832,plain,(
% 2.51/1.72 (setminusEL != $true) | ((in @ sK316 @ sK317) = $true)),
% 2.51/1.72 inference(trivial_inequality_removal,[status(thm)],[f1827])).
% 2.51/1.72 thf(f1827,plain,(
% 2.51/1.72 (setminusEL != $true) | ((in @ sK316 @ sK317) = $true) | ($true != $true)),
% 2.51/1.72 inference(superposition,[status(thm)],[f1172,f1668])).
% 2.51/1.72 thf(f1668,plain,(
% 2.51/1.72 ($true = (in @ sK316 @ (setminus @ sK317 @ sK318)))),
% 2.51/1.72 inference(cnf_transformation,[status(thm)],[f1076])).
% 2.51/1.72 thf(f1172,plain,(
% 2.51/1.72 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setminus @ X2 @ X1))) | (setminusEL != $true) | ($true = (in @ X0 @ X2))) )),
% 2.51/1.72 inference(cnf_transformation,[status(thm)],[f613])).
% 2.51/1.72 thf(f613,plain,(
% 2.51/1.72 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) | ($true != (in @ X0 @ (setminus @ X2 @ X1)))) | (setminusEL != $true)) & ((setminusEL = $true) | (($true != (in @ sK43 @ sK45)) & ($true = (in @ sK43 @ (setminus @ sK45 @ sK44)))))),
% 2.51/1.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45])],[f611,f612])).
% 2.51/1.72 thf(f612,plain,(
% 2.51/1.72 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ X5)) & ($true = (in @ X3 @ (setminus @ X5 @ X4)))) => (($true != (in @ sK43 @ sK45)) & ($true = (in @ sK43 @ (setminus @ sK45 @ sK44))))),
% 2.51/1.72 introduced(definition,[],[choice_axiom])).
% 2.51/1.72 thf(f611,plain,(
% 2.51/1.72 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) | ($true != (in @ X0 @ (setminus @ X2 @ X1)))) | (setminusEL != $true)) & ((setminusEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ X5)) & ($true = (in @ X3 @ (setminus @ X5 @ X4)))))),
% 2.51/1.72 inference(rectify,[status(thm)],[f610])).
% 2.51/1.72 thf(f610,plain,(
% 2.51/1.72 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) | ($true != (in @ X0 @ (setminus @ X2 @ X1)))) | (setminusEL != $true)) & ((setminusEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ($true = (in @ X0 @ (setminus @ X2 @ X1)))))),
% 2.51/1.72 inference(nnf_transformation,[status(thm)],[f492])).
% 2.51/1.72 thf(f492,plain,(
% 2.51/1.72 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) | ($true != (in @ X0 @ (setminus @ X2 @ X1)))) <=> (setminusEL = $true)),
% 2.51/1.72 inference(ennf_transformation,[status(thm)],[f213])).
% 2.51/1.72 thf(f213,plain,(
% 2.51/1.72 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) => ($true = (in @ X0 @ X2))) <=> (setminusEL = $true)),
% 2.51/1.72 inference(fool_elimination,[status(thm)],[f212])).
% 2.51/1.72 thf(f212,plain,(
% 2.51/1.72 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => (in @ X0 @ X2)) = setminusEL)),
% 2.51/1.72 inference(rectify,[status(thm)],[f121])).
% 2.51/1.72 thf(f121,axiom,(
% 2.51/1.72 (! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ (setminus @ X3 @ X4)) => (in @ X1 @ X3)) = setminusEL)),
% 2.51/1.72 file('/export/starexec/sandbox/tmp/tmp.3WLPAKKuIJ/DTF2THF_3246.p',setminusEL)).
% 2.51/1.72 thf(f1667,plain,(
% 2.51/1.72 ((in @ sK316 @ sK317) != $true)),
% 2.51/1.72 inference(cnf_transformation,[status(thm)],[f1076])).
% 2.51/1.72 % SZS output end Proof for DTF2THF_3246
% 2.51/1.72 % (3367)------------------------------
% 2.51/1.72 % (3367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.72 % (3367)Termination reason: Refutation
% 2.51/1.72
% 2.51/1.72 % (3367)Memory used [KB]: 7291
% 2.51/1.72 % (3367)Time elapsed: 0.064 s
% 2.51/1.72 % (3367)Instructions burned: 123 (million)
% 2.51/1.72 % (3367)------------------------------
% 2.51/1.72 % (3367)------------------------------
% 2.51/1.72 % (3344)Success in time 0.156 s
%------------------------------------------------------------------------------