%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU568^1 : 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 : n016.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 09:35:19 AM UTC 2026
% Result : Theorem 0.22s 1.59s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 1601 ( 448 equ; 0 cnn)
% Maximal formula atoms : 87 ( 114 avg)
% Number of connectives : 760 ( 21 ~; 0 |; 262 &; 46 @)
% ( 0 <=>; 431 =>; 0 <=; 0 <~>)
% Maximal formula depth : 94 ( 53 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 197 ( 194 usr; 89 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 15 !; 9 ?; 24 :)
% 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_113,type,
sP1: $i > $i > $o ).
thf(func_def_114,type,
sP2: $i > $o ).
thf(func_def_115,type,
sP3: $i > $i > $o ).
thf(func_def_116,type,
sP4: $i > $i > $o ).
thf(func_def_117,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_119,type,
sK7: $i > $o ).
thf(func_def_121,type,
sK9: $i > $o ).
thf(func_def_122,type,
sK10: $i > $i ).
thf(func_def_126,type,
sK14: $i > $i > $i ).
thf(func_def_131,type,
sK19: $i > $i > $i ).
thf(func_def_136,type,
sK24: $i > $o ).
thf(func_def_137,type,
sK25: $i > $o ).
thf(func_def_139,type,
sK27: $i > $o ).
thf(func_def_140,type,
sK28: $i > $o ).
thf(func_def_141,type,
sK29: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_142,type,
sK30: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_143,type,
sK31: $i > $o ).
thf(func_def_144,type,
sK32: $i > $o ).
thf(func_def_145,type,
sK33: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_146,type,
sK34: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_148,type,
sK36: $i > $o ).
thf(func_def_149,type,
sK37: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK41: ( $i > $o ) > $i ).
thf(func_def_154,type,
sK42: $i > $o ).
thf(func_def_155,type,
sK43: $i > $i ).
thf(func_def_160,type,
sK48: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_161,type,
sK49: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_164,type,
sK52: $i > $o ).
thf(func_def_165,type,
sK53: $i > $o ).
thf(func_def_181,type,
sK69: $i > $o ).
thf(func_def_187,type,
sK75: $i > $o ).
thf(func_def_194,type,
sK82: $i > $o ).
thf(func_def_197,type,
sK85: $i > ( $i > $o ) > $i ).
thf(func_def_206,type,
sK94: $i > $o ).
thf(func_def_208,type,
sK96: $i > ( $i > $o ) > $i ).
thf(func_def_209,type,
sK97: $i > ( $i > $o ) > $i ).
thf(func_def_210,type,
sK98: $i > $o ).
thf(func_def_213,type,
sK101: $i > $i > $o ).
thf(func_def_215,type,
sK103: $i > $i ).
thf(func_def_216,type,
sK104: $i > $i ).
thf(func_def_217,type,
sK105: $i > ( $i > $i > $o ) > $i ).
thf(func_def_218,type,
sK106: $i > ( $i > $i > $o ) > $i ).
thf(func_def_219,type,
sK107: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_229,type,
sK117: $i > $o ).
thf(func_def_232,type,
sK120: $i > ( $i > $o ) > $i ).
thf(func_def_234,type,
sK122: $i > $i ).
thf(func_def_237,type,
sK125: $i > $i > $i ).
thf(func_def_245,type,
sK133: $i > $o ).
thf(func_def_248,type,
sK136: $i > $i ).
thf(func_def_249,type,
sK137: $i > $o ).
thf(func_def_251,type,
sK139: ( $i > $o ) > $i ).
thf(func_def_252,type,
sK140: ( $i > $o ) > $i ).
thf(func_def_253,type,
sK141: $i > $i > $i ).
thf(func_def_259,type,
sK147: $i > $i > $i ).
thf(func_def_265,type,
sK153: $i > $i > $i ).
thf(func_def_266,type,
sK154: $i > $i > $i ).
thf(func_def_269,type,
sK157: $o > $i > $i > $i ).
thf(func_def_276,type,
sK164: $i > $o ).
thf(func_def_278,type,
sK166: $i > $i ).
thf(func_def_280,type,
sK168: $i > $o ).
thf(func_def_288,type,
sK176: ( $i > $o ) > $i > $i ).
thf(func_def_290,type,
sK178: $i > $o ).
thf(func_def_294,type,
sK182: $i > $i > $i ).
thf(func_def_300,type,
sK188: $i > ( $i > $o ) > $i ).
thf(func_def_301,type,
sK189: $i > $o ).
thf(func_def_307,type,
sK195: $i > $o ).
thf(func_def_309,type,
sK197: ( $i > $o ) > $i > $i ).
thf(func_def_318,type,
sK206: $i > $o ).
thf(func_def_324,type,
sK212: $i > $o ).
thf(func_def_327,type,
sK215: $i > $i ).
thf(func_def_330,type,
sK218: $i > $i ).
thf(func_def_332,type,
sK220: $i > $i ).
thf(func_def_333,type,
sK221: $i > $o ).
thf(func_def_334,type,
sK222: $i > $i ).
thf(func_def_335,type,
sK223: ( $i > $o ) > $i ).
thf(func_def_336,type,
sK224: $i > $i > $i ).
thf(func_def_337,type,
sK225: $i > $i > $i ).
thf(func_def_338,type,
sK226: $i > $i > $i ).
thf(func_def_339,type,
sK227: $i > $i > $i ).
thf(func_def_340,type,
sK228: $i > $i > $i ).
thf(func_def_341,type,
sK229: $i > $i > $i > $i ).
thf(func_def_342,type,
sK230: $i > $i ).
thf(func_def_343,type,
sK231: $i > $i ).
thf(func_def_344,type,
sK232: $i > $i ).
thf(func_def_345,type,
sK233: $i > $i ).
thf(func_def_346,type,
sK234: $i > $i > $i > $i ).
thf(func_def_347,type,
sK235: $i > $i > $i > $i ).
thf(func_def_348,type,
sK236: $i > $i > $i ).
thf(func_def_349,type,
sK237: $i > $i > $i ).
thf(func_def_350,type,
sK238: $i > $i > $i ).
thf(func_def_351,type,
sK239: $i > $i ).
thf(func_def_353,type,
sK241: $i > $i ).
thf(func_def_354,type,
sK242: $i > $i ).
thf(func_def_357,type,
ph245:
!>[X0: $tType] : X0 ).
thf(f1747,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1368,f954]) ).
thf(f954,plain,
( ( in @ sK110 @ sK109 )
= $true ),
inference(cnf_transformation,[status(thm)],[f555]) ).
thf(f555,plain,
( ( wellorderingAx = $true )
& ( nonemptyI = $true )
& ( powerset__Cong = $true )
& ( setunion__Cong = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrEL = $true )
& ( prop2setI = $true )
& ( dsetconstr__Cong = $true )
& ( exuI3 = $true )
& ( setadjoinIR = $true )
& ( eqimpsubset2 = $true )
& ( emptyInPowerset = $true )
& ( subsetI2 = $true )
& ( exuEu = $true )
& ( subsetI1 = $true )
& ( setadjoinOr = $true )
& ( setadjoinIL = $true )
& ( exu__Cong = $true )
& ( upairsetIL = $true )
& ( emptyI = $true )
& ( setunionE = $true )
& ( nonemptyImpWitness = $true )
& ( powersetAx = $true )
& ( notdallE = $true )
& ( notsubsetI = $true )
& ( setextAx = $true )
& ( setunionI = $true )
& ( omegaIndAx = $true )
& ( emptysetAx = $true )
& ( dsetconstrI = $true )
& ( upairsetIR = $true )
& ( setunionAx = $true )
& ( replAx = $true )
& ( quantDeMorgan3 = $true )
& ( subsetE2 = $true )
& ( vacuousDall = $true )
& ( exuE3e = $true )
& ( powersetE = $true )
& ( emptyinPowerset = $true )
& ( prop2setE = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( emptyset__Cong = $true )
& ( exuE2 = $true )
& ( in__Cong = $true )
& ( setoftrueEq = $true )
& ( notinsingleton = $true )
& ( nonemptyE1 = $true )
& ( descr__Cong = $true )
& ( notinemptyset = $true )
& ( omega0Ax = $true )
& ( prop2set2propI = $true )
& ( emptysetimpfalse = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( emptysetE = $true )
& ( setadjoin__Cong = $true )
& ( omega__Cong = $true )
& ( exuI1 = $true )
& ( quantDeMorgan1 = $true )
& ( eqimpsubset1 = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ( $true
!= ( in @ sK110 @ sK108 ) )
& ( sK108 = sK109 )
& ( ( in @ sK110 @ sK109 )
= $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( setadjoinAx = $true )
& ( descrp = $true )
& ( emptysetsubset = $true )
& ( powersetI = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyI1 = $true )
& ( emptyE1 = $true )
& ( uniqinunit = $true )
& ( setext = $true )
& ( notequalI1 = $true )
& ( exuE3u = $true )
& ( exuI2 = $true )
& ( inCongP = $true )
& ( notdexE = $true )
& ( singletonsswitch = $true )
& ( subPowSU = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108,sK109,sK110])],[f306,f554]) ).
thf(f554,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( X0 = X1 )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( $true
!= ( in @ sK110 @ sK108 ) )
& ( sK108 = sK109 )
& ( ( in @ sK110 @ sK109 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f306,plain,
( ( wellorderingAx = $true )
& ( nonemptyI = $true )
& ( powerset__Cong = $true )
& ( setunion__Cong = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrEL = $true )
& ( prop2setI = $true )
& ( dsetconstr__Cong = $true )
& ( exuI3 = $true )
& ( setadjoinIR = $true )
& ( eqimpsubset2 = $true )
& ( emptyInPowerset = $true )
& ( subsetI2 = $true )
& ( exuEu = $true )
& ( subsetI1 = $true )
& ( setadjoinOr = $true )
& ( setadjoinIL = $true )
& ( exu__Cong = $true )
& ( upairsetIL = $true )
& ( emptyI = $true )
& ( setunionE = $true )
& ( nonemptyImpWitness = $true )
& ( powersetAx = $true )
& ( notdallE = $true )
& ( notsubsetI = $true )
& ( setextAx = $true )
& ( setunionI = $true )
& ( omegaIndAx = $true )
& ( emptysetAx = $true )
& ( dsetconstrI = $true )
& ( upairsetIR = $true )
& ( setunionAx = $true )
& ( replAx = $true )
& ( quantDeMorgan3 = $true )
& ( subsetE2 = $true )
& ( vacuousDall = $true )
& ( exuE3e = $true )
& ( powersetE = $true )
& ( emptyinPowerset = $true )
& ( prop2setE = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( emptyset__Cong = $true )
& ( exuE2 = $true )
& ( in__Cong = $true )
& ( setoftrueEq = $true )
& ( notinsingleton = $true )
& ( nonemptyE1 = $true )
& ( descr__Cong = $true )
& ( notinemptyset = $true )
& ( omega0Ax = $true )
& ( prop2set2propI = $true )
& ( emptysetimpfalse = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( emptysetE = $true )
& ( setadjoin__Cong = $true )
& ( omega__Cong = $true )
& ( exuI1 = $true )
& ( quantDeMorgan1 = $true )
& ( eqimpsubset1 = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( X0 = X1 )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( setadjoinAx = $true )
& ( descrp = $true )
& ( emptysetsubset = $true )
& ( powersetI = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyI1 = $true )
& ( emptyE1 = $true )
& ( uniqinunit = $true )
& ( setext = $true )
& ( notequalI1 = $true )
& ( exuE3u = $true )
& ( exuI2 = $true )
& ( inCongP = $true )
& ( notdexE = $true )
& ( singletonsswitch = $true )
& ( subPowSU = $true ) ),
inference(flattening,[status(thm)],[f305]) ).
thf(f305,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $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)],[f258]) ).
thf(f258,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( X0 != X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f138]) ).
thf(f138,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( X0 != X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f137]) ).
thf(f137,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X0 )
=> ( X0 != X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f88]) ).
thf(f88,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
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ( X3 != X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f87]) ).
thf(f87,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
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ( X3 != X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.F3Lz7gYs5d/DTF2THF_7946.p',notequalI2) ).
thf(f1368,plain,
( ( in @ sK110 @ sK109 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f956,f955]) ).
thf(f955,plain,
sK108 = sK109,
inference(cnf_transformation,[status(thm)],[f555]) ).
thf(f956,plain,
( $true
!= ( in @ sK110 @ sK108 ) ),
inference(cnf_transformation,[status(thm)],[f555]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU568^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n016.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 12:27:36 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
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU568^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : (! A:i.! B:i.! x:i.in x A -> ~(in x B) -> ~(A = B))
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC070g [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 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, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 186 ( 86 unt; 99 typ; 86 def)
% 0.16/0.39 % Number of atoms : 473 ( 133 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 87 ( 5 avg)
% 0.16/0.39 % Number of connectives : 755 ( 29 ~; 5 |; 27 &; 462 @)
% 0.16/0.39 % ( 14 <=>; 218 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 93 ( 2 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 102 ( 99 usr; 88 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 267 ( 28 ^; 211 !; 28 ?; 267 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=439
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu_type,type,
% 0.16/0.39 exu: ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu,definition,
% 0.16/0.39 ( exu
% 0.16/0.39 = ( ^ [Xphi: $i > $o] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx_type,type,
% 0.16/0.39 setextAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx,definition,
% 0.16/0.39 ( setextAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xx @ B ) )
% 0.16/0.39 => ( A = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx_type,type,
% 0.16/0.39 emptysetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx,definition,
% 0.16/0.39 ( emptysetAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx_type,type,
% 0.16/0.39 setadjoinAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx,definition,
% 0.16/0.39 ( setadjoinAx
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 <=> ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset_type,type,
% 0.16/0.39 powerset: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx_type,type,
% 0.16/0.39 powersetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx,definition,
% 0.16/0.39 ( powersetAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 <=> ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion_type,type,
% 0.16/0.39 setunion: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx_type,type,
% 0.16/0.39 setunionAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx,definition,
% 0.16/0.39 ( setunionAx
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 <=> ? [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega_type,type,
% 0.16/0.39 omega: $i ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax_type,type,
% 0.16/0.39 omega0Ax: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax,definition,
% 0.16/0.39 ( omega0Ax
% 0.16/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx_type,type,
% 0.16/0.39 omegaSAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx,definition,
% 0.16/0.39 ( omegaSAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx_type,type,
% 0.16/0.39 omegaIndAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx,definition,
% 0.16/0.39 ( omegaIndAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( ( in @ emptyset @ A )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ omega )
% 0.16/0.39 & ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(replAx_type,type,
% 0.16/0.39 replAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(replAx,definition,
% 0.16/0.39 ( replAx
% 0.16/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 <=> ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx_type,type,
% 0.16/0.39 foundationAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx,definition,
% 0.16/0.39 ( foundationAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ( ( in @ B @ A )
% 0.16/0.39 & ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx_type,type,
% 0.16/0.39 wellorderingAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx,definition,
% 0.16/0.39 ( wellorderingAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ? [B: $i] :
% 0.16/0.39 ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) ) )
% 0.16/0.39 & ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ A )
% 0.16/0.39 & ( in @ Xy @ A ) )
% 0.16/0.39 => ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ( ( in @ Xx @ C )
% 0.16/0.39 <=> ( in @ Xy @ C ) ) )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 & ! [C: $i,D: $i] :
% 0.16/0.39 ( ( ( in @ C @ B )
% 0.16/0.39 & ( in @ D @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ D ) )
% 0.16/0.39 | ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ D )
% 0.16/0.39 => ( in @ Xx @ C ) ) ) )
% 0.16/0.39 & ! [C: $i] :
% 0.16/0.39 ( ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.39 => ? [D: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ D @ B )
% 0.16/0.39 & ( in @ Xx @ C )
% 0.16/0.39 & ~ ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ D )
% 0.16/0.39 & ( in @ Xy @ C ) )
% 0.16/0.39 & ! [E: $i] :
% 0.16/0.39 ( ( in @ E @ B )
% 0.16/0.39 => ( ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ E )
% 0.16/0.39 => ( in @ Xy @ D ) )
% 0.16/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr_type,type,
% 0.16/0.39 descr: ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(descrp_type,type,
% 0.16/0.39 descrp: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descrp,definition,
% 0.16/0.39 ( descrp
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( Xphi
% 0.16/0.39 @ ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr_type,type,
% 0.16/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI_type,type,
% 0.16/0.39 dsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI,definition,
% 0.16/0.39 ( dsetconstrI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL_type,type,
% 0.16/0.39 dsetconstrEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL,definition,
% 0.16/0.39 ( dsetconstrEL
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER_type,type,
% 0.16/0.39 dsetconstrER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER,definition,
% 0.16/0.39 ( dsetconstrER
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1_type,type,
% 0.16/0.39 exuE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1,definition,
% 0.16/0.39 ( exuE1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set_type,type,
% 0.16/0.39 prop2set: $o > $i ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE_type,type,
% 0.16/0.39 prop2setE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE,definition,
% 0.16/0.39 ( prop2setE
% 0.16/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE_type,type,
% 0.16/0.39 emptysetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE,definition,
% 0.16/0.39 ( emptysetE
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse_type,type,
% 0.16/0.39 emptysetimpfalse: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse,definition,
% 0.16/0.39 ( emptysetimpfalse
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => $false ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset_type,type,
% 0.16/0.39 notinemptyset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset,definition,
% 0.16/0.39 ( notinemptyset
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e_type,type,
% 0.16/0.39 exuE3e: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e,definition,
% 0.16/0.39 ( exuE3e
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setext_type,type,
% 0.16/0.39 setext: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setext,definition,
% 0.16/0.39 ( setext
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( A = B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI_type,type,
% 0.16/0.39 emptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI,definition,
% 0.16/0.39 ( emptyI
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty_type,type,
% 0.16/0.39 noeltsimpempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty,definition,
% 0.16/0.39 ( noeltsimpempty
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta_type,type,
% 0.16/0.39 setbeta: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta,definition,
% 0.16/0.39 ( setbeta
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty_type,type,
% 0.16/0.39 nonempty: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty,definition,
% 0.16/0.39 ( nonempty
% 0.16/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1_type,type,
% 0.16/0.39 nonemptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1,definition,
% 0.16/0.39 ( nonemptyE1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI_type,type,
% 0.16/0.39 nonemptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI,definition,
% 0.16/0.39 ( nonemptyI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( nonempty
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1_type,type,
% 0.16/0.39 nonemptyI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1,definition,
% 0.16/0.39 ( nonemptyI1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL_type,type,
% 0.16/0.39 setadjoinIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL,definition,
% 0.16/0.39 ( setadjoinIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty_type,type,
% 0.16/0.39 emptyinunitempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty,definition,
% 0.16/0.39 ( emptyinunitempty
% 0.16/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR_type,type,
% 0.16/0.39 setadjoinIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR,definition,
% 0.16/0.39 ( setadjoinIR
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE_type,type,
% 0.16/0.39 setadjoinE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE,definition,
% 0.16/0.39 ( setadjoinE
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ( ( Xy = Xx )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => ( ( ( in @ Xy @ A )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr_type,type,
% 0.16/0.39 setadjoinOr: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr,definition,
% 0.16/0.39 ( setadjoinOr
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq_type,type,
% 0.16/0.39 setoftrueEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq,definition,
% 0.16/0.39 ( setoftrueEq
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : $true )
% 0.16/0.39 = A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI_type,type,
% 0.16/0.39 powersetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI,definition,
% 0.16/0.39 ( powersetI
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset_type,type,
% 0.16/0.39 emptyinPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset,definition,
% 0.16/0.39 ( emptyinPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset_type,type,
% 0.16/0.39 emptyInPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset,definition,
% 0.16/0.39 ( emptyInPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE_type,type,
% 0.16/0.39 powersetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE,definition,
% 0.16/0.39 ( powersetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI_type,type,
% 0.16/0.39 setunionI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI,definition,
% 0.16/0.39 ( setunionI
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE_type,type,
% 0.16/0.39 setunionE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE,definition,
% 0.16/0.39 ( setunionE
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ! [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU_type,type,
% 0.16/0.39 subPowSU: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU,definition,
% 0.16/0.39 ( subPowSU
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2_type,type,
% 0.16/0.39 exuE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2,definition,
% 0.16/0.39 ( exuE2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness_type,type,
% 0.16/0.39 nonemptyImpWitness: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness,definition,
% 0.16/0.39 ( nonemptyImpWitness
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & $true ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit_type,type,
% 0.16/0.39 uniqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit,definition,
% 0.16/0.39 ( uniqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton_type,type,
% 0.16/0.39 notinsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton,definition,
% 0.16/0.39 ( notinsingleton
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx != Xy )
% 0.16/0.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit_type,type,
% 0.16/0.39 eqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit,definition,
% 0.16/0.39 ( eqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch_type,type,
% 0.16/0.39 singletonsswitch: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch,definition,
% 0.16/0.39 ( singletonsswitch
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE_type,type,
% 0.16/0.39 upairsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE,definition,
% 0.16/0.39 ( upairsetE
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xx )
% 0.16/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL_type,type,
% 0.16/0.39 upairsetIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL,definition,
% 0.16/0.39 ( upairsetIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR_type,type,
% 0.16/0.39 upairsetIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR,definition,
% 0.16/0.39 ( upairsetIR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1_type,type,
% 0.16/0.39 emptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1,definition,
% 0.16/0.39 ( emptyE1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = emptyset )
% 0.16/0.39 => $false ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall_type,type,
% 0.16/0.39 vacuousDall: $o ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall,definition,
% 0.16/0.39 ( vacuousDall
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1_type,type,
% 0.16/0.39 quantDeMorgan1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1,definition,
% 0.16/0.39 ( quantDeMorgan1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2_type,type,
% 0.16/0.39 quantDeMorgan2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2,definition,
% 0.16/0.39 ( quantDeMorgan2
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3_type,type,
% 0.16/0.39 quantDeMorgan3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3,definition,
% 0.16/0.39 ( quantDeMorgan3
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4_type,type,
% 0.16/0.39 quantDeMorgan4: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4,definition,
% 0.16/0.39 ( quantDeMorgan4
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI_type,type,
% 0.16/0.39 prop2setI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI,definition,
% 0.16/0.39 ( prop2setI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(set2prop_type,type,
% 0.16/0.39 set2prop: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI_type,type,
% 0.16/0.39 prop2set2propI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI,definition,
% 0.16/0.39 ( prop2set2propI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE_type,type,
% 0.16/0.39 notdexE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE,definition,
% 0.16/0.39 ( notdexE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE_type,type,
% 0.16/0.39 notdallE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE,definition,
% 0.16/0.39 ( notdallE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1_type,type,
% 0.16/0.39 exuI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1,definition,
% 0.16/0.39 ( exuI1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3_type,type,
% 0.16/0.39 exuI3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3,definition,
% 0.16/0.39 ( exuI3
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.16/0.39 => ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2_type,type,
% 0.16/0.39 exuI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2,definition,
% 0.16/0.39 ( exuI2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP_type,type,
% 0.16/0.39 inCongP: $o ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP,definition,
% 0.16/0.39 ( inCongP
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong_type,type,
% 0.16/0.39 in__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong,definition,
% 0.16/0.39 ( in__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u_type,type,
% 0.16/0.39 exuE3u: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u,definition,
% 0.16/0.39 ( exuE3u
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong_type,type,
% 0.16/0.39 exu__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong,definition,
% 0.16/0.39 ( exu__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 <=> ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong_type,type,
% 0.16/0.39 emptyset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong,definition,
% 0.16/0.39 ( emptyset__Cong
% 0.16/0.39 = ( emptyset = emptyset ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong_type,type,
% 0.16/0.39 setadjoin__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong,definition,
% 0.16/0.39 ( setadjoin__Cong
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ! [Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( Xz = Xu )
% 0.16/0.39 => ( ( setadjoin @ Xx @ Xz )
% 0.16/0.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong_type,type,
% 0.16/0.39 powerset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong,definition,
% 0.16/0.39 ( powerset__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( powerset @ A )
% 0.16/0.39 = ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong_type,type,
% 0.16/0.39 setunion__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong,definition,
% 0.16/0.39 ( setunion__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( setunion @ A )
% 0.16/0.39 = ( setunion @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong_type,type,
% 0.16/0.39 omega__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong,definition,
% 0.16/0.39 ( omega__Cong
% 0.16/0.39 = ( omega = omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu_type,type,
% 0.16/0.39 exuEu: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu,definition,
% 0.16/0.39 ( exuEu
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong_type,type,
% 0.16/0.39 descr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong,definition,
% 0.16/0.39 ( descr__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.16/0.39 => ( ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong_type,type,
% 0.16/0.39 dsetconstr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong,definition,
% 0.16/0.39 ( dsetconstr__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.16/0.39 => ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( dsetconstr @ B
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset_type,type,
% 0.16/0.39 subset: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(disjoint_type,type,
% 0.16/0.39 disjoint: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setsmeet_type,type,
% 0.16/0.39 setsmeet: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1_type,type,
% 0.16/0.39 subsetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1,definition,
% 0.16/0.39 ( subsetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2_type,type,
% 0.16/0.39 eqimpsubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2,definition,
% 0.16/0.39 ( eqimpsubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1_type,type,
% 0.16/0.39 eqimpsubset1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1,definition,
% 0.16/0.39 ( eqimpsubset1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2_type,type,
% 0.16/0.39 subsetI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2,definition,
% 0.16/0.39 ( subsetI2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset_type,type,
% 0.16/0.39 emptysetsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset,definition,
% 0.16/0.39 ( emptysetsubset
% 0.16/0.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE_type,type,
% 0.16/0.39 subsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE,definition,
% 0.16/0.39 ( subsetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2_type,type,
% 0.16/0.39 subsetE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2,definition,
% 0.16/0.39 ( subsetE2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI_type,type,
% 0.16/0.39 notsubsetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI,definition,
% 0.16/0.39 ( notsubsetI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1_type,type,
% 0.16/0.39 notequalI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1,definition,
% 0.16/0.39 ( notequalI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ~ ( subset @ A @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2,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 => ! [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 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 0.22/1.50 ---- Embedded in THF ---
% 0.22/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.22/1.50 %%% Generated on Tue Feb 24 12:27:37 EST 2026
% 0.22/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.22/1.50 %%% Logic specification used:
% 0.22/1.50 %%% thf(spec, logic, $$dhol).
% 0.22/1.50
% 0.22/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.F3Lz7gYs5d/DTF2DTF7946.p
% See solution above
% 0.22/1.50 ------------------------
% 0.22/1.52 ---- Cleaned THF ---
% 0.22/1.52 thf(in_type,type,
% 0.22/1.52 in: $i > $i > $o ).
% 0.22/1.52
% 0.22/1.52 thf(exu_type,type,
% 0.22/1.52 exu: ( $i > $o ) > $o ).
% 0.22/1.52
% 0.22/1.52 thf(exu,definition,
% 0.22/1.52 ( exu
% 0.22/1.52 = ( ^ [Xphi: $i > $o] :
% 0.22/1.52 ? [Xx: $i] :
% 0.22/1.52 ( ( Xphi @ Xx )
% 0.22/1.52 & ! [Xy: $i] :
% 0.22/1.52 ( ( Xphi @ Xy )
% 0.22/1.52 => ( Xx = Xy ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setextAx_type,type,
% 0.22/1.52 setextAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setextAx,definition,
% 0.22/1.52 ( setextAx
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 <=> ( in @ Xx @ B ) )
% 0.22/1.52 => ( A = B ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptyset_type,type,
% 0.22/1.52 emptyset: $i ).
% 0.22/1.52
% 0.22/1.52 thf(emptysetAx_type,type,
% 0.22/1.52 emptysetAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptysetAx,definition,
% 0.22/1.52 ( emptysetAx
% 0.22/1.52 = ( ! [Xx: $i] :
% 0.22/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoin_type,type,
% 0.22/1.52 setadjoin: $i > $i > $i ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinAx_type,type,
% 0.22/1.52 setadjoinAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinAx,definition,
% 0.22/1.52 ( setadjoinAx
% 0.22/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.22/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.22/1.52 <=> ( ( Xy = Xx )
% 0.22/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(powerset_type,type,
% 0.22/1.52 powerset: $i > $i ).
% 0.22/1.52
% 0.22/1.52 thf(powersetAx_type,type,
% 0.22/1.52 powersetAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(powersetAx,definition,
% 0.22/1.52 ( powersetAx
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ( in @ B @ ( powerset @ A ) )
% 0.22/1.52 <=> ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ B )
% 0.22/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setunion_type,type,
% 0.22/1.52 setunion: $i > $i ).
% 0.22/1.52
% 0.22/1.52 thf(setunionAx_type,type,
% 0.22/1.52 setunionAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setunionAx,definition,
% 0.22/1.52 ( setunionAx
% 0.22/1.52 = ( ! [A: $i,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 0.22/1.52 <=> ? [B: $i] :
% 0.22/1.52 ( ( in @ Xx @ B )
% 0.22/1.52 & ( in @ B @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(omega_type,type,
% 0.22/1.52 omega: $i ).
% 0.22/1.52
% 0.22/1.52 thf(omega0Ax_type,type,
% 0.22/1.52 omega0Ax: $o ).
% 0.22/1.52
% 0.22/1.52 thf(omega0Ax,definition,
% 0.22/1.52 ( omega0Ax
% 0.22/1.52 = ( in @ emptyset @ omega ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(omegaSAx_type,type,
% 0.22/1.52 omegaSAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(omegaSAx,definition,
% 0.22/1.52 ( omegaSAx
% 0.22/1.52 = ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ omega )
% 0.22/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(omegaIndAx_type,type,
% 0.22/1.52 omegaIndAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(omegaIndAx,definition,
% 0.22/1.52 ( omegaIndAx
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ( ( ( in @ emptyset @ A )
% 0.22/1.52 & ! [Xx: $i] :
% 0.22/1.52 ( ( ( in @ Xx @ omega )
% 0.22/1.52 & ( in @ Xx @ A ) )
% 0.22/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.22/1.52 => ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ omega )
% 0.22/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(replAx_type,type,
% 0.22/1.52 replAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(replAx,definition,
% 0.22/1.52 ( replAx
% 0.22/1.52 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( exu
% 0.22/1.52 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.22/1.52 => ? [B: $i] :
% 0.22/1.52 ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ B )
% 0.22/1.52 <=> ? [Xy: $i] :
% 0.22/1.52 ( ( in @ Xy @ A )
% 0.22/1.52 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(foundationAx_type,type,
% 0.22/1.52 foundationAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(foundationAx,definition,
% 0.22/1.52 ( foundationAx
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.22/1.52 => ? [B: $i] :
% 0.22/1.52 ( ( in @ B @ A )
% 0.22/1.52 & ~ ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ B )
% 0.22/1.52 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(wellorderingAx_type,type,
% 0.22/1.52 wellorderingAx: $o ).
% 0.22/1.52
% 0.22/1.52 thf(wellorderingAx,definition,
% 0.22/1.52 ( wellorderingAx
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ? [B: $i] :
% 0.22/1.52 ( ! [C: $i] :
% 0.22/1.52 ( ( in @ C @ B )
% 0.22/1.52 => ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ C )
% 0.22/1.52 => ( in @ Xx @ A ) ) )
% 0.22/1.52 & ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( ( in @ Xx @ A )
% 0.22/1.52 & ( in @ Xy @ A ) )
% 0.22/1.52 => ( ! [C: $i] :
% 0.22/1.52 ( ( in @ C @ B )
% 0.22/1.52 => ( ( in @ Xx @ C )
% 0.22/1.52 <=> ( in @ Xy @ C ) ) )
% 0.22/1.52 => ( Xx = Xy ) ) )
% 0.22/1.52 & ! [C: $i,D: $i] :
% 0.22/1.52 ( ( ( in @ C @ B )
% 0.22/1.52 & ( in @ D @ B ) )
% 0.22/1.52 => ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ C )
% 0.22/1.52 => ( in @ Xx @ D ) )
% 0.22/1.52 | ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ D )
% 0.22/1.52 => ( in @ Xx @ C ) ) ) )
% 0.22/1.52 & ! [C: $i] :
% 0.22/1.52 ( ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ C )
% 0.22/1.52 => ( in @ Xx @ A ) )
% 0.22/1.52 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.22/1.52 => ? [D: $i,Xx: $i] :
% 0.22/1.52 ( ( in @ D @ B )
% 0.22/1.52 & ( in @ Xx @ C )
% 0.22/1.52 & ~ ? [Xy: $i] :
% 0.22/1.52 ( ( in @ Xy @ D )
% 0.22/1.52 & ( in @ Xy @ C ) )
% 0.22/1.52 & ! [E: $i] :
% 0.22/1.52 ( ( in @ E @ B )
% 0.22/1.52 => ( ! [Xy: $i] :
% 0.22/1.52 ( ( in @ Xy @ E )
% 0.22/1.52 => ( in @ Xy @ D ) )
% 0.22/1.52 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(descr_type,type,
% 0.22/1.52 descr: ( $i > $o ) > $i ).
% 0.22/1.52
% 0.22/1.52 thf(descrp_type,type,
% 0.22/1.52 descrp: $o ).
% 0.22/1.52
% 0.22/1.52 thf(descrp,definition,
% 0.22/1.52 ( descrp
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 => ( Xphi
% 0.22/1.52 @ ( descr
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstr_type,type,
% 0.22/1.52 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstrI_type,type,
% 0.22/1.52 dsetconstrI: $o ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstrI,definition,
% 0.22/1.52 ( dsetconstrI
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( ( Xphi @ Xx )
% 0.22/1.52 => ( in @ Xx
% 0.22/1.52 @ ( dsetconstr @ A
% 0.22/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstrEL_type,type,
% 0.22/1.52 dsetconstrEL: $o ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstrEL,definition,
% 0.22/1.52 ( dsetconstrEL
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx
% 0.22/1.52 @ ( dsetconstr @ A
% 0.22/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.22/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstrER_type,type,
% 0.22/1.52 dsetconstrER: $o ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstrER,definition,
% 0.22/1.52 ( dsetconstrER
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx
% 0.22/1.52 @ ( dsetconstr @ A
% 0.22/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.22/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exuE1_type,type,
% 0.22/1.52 exuE1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exuE1,definition,
% 0.22/1.52 ( exuE1
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 => ? [Xx: $i] :
% 0.22/1.52 ( ( Xphi @ Xx )
% 0.22/1.52 & ! [Xy: $i] :
% 0.22/1.52 ( ( Xphi @ Xy )
% 0.22/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(prop2set_type,type,
% 0.22/1.52 prop2set: $o > $i ).
% 0.22/1.52
% 0.22/1.52 thf(prop2setE_type,type,
% 0.22/1.52 prop2setE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(prop2setE,definition,
% 0.22/1.52 ( prop2setE
% 0.22/1.52 = ( ! [Xphi: $o,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.22/1.52 => Xphi ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptysetE_type,type,
% 0.22/1.52 emptysetE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptysetE,definition,
% 0.22/1.52 ( emptysetE
% 0.22/1.52 = ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ emptyset )
% 0.22/1.52 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptysetimpfalse_type,type,
% 0.22/1.52 emptysetimpfalse: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptysetimpfalse,definition,
% 0.22/1.52 ( emptysetimpfalse
% 0.22/1.52 = ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ emptyset )
% 0.22/1.52 => $false ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(notinemptyset_type,type,
% 0.22/1.52 notinemptyset: $o ).
% 0.22/1.52
% 0.22/1.52 thf(notinemptyset,definition,
% 0.22/1.52 ( notinemptyset
% 0.22/1.52 = ( ! [Xx: $i] :
% 0.22/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exuE3e_type,type,
% 0.22/1.52 exuE3e: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exuE3e,definition,
% 0.22/1.52 ( exuE3e
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setext_type,type,
% 0.22/1.52 setext: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setext,definition,
% 0.22/1.52 ( setext
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( in @ Xx @ B ) )
% 0.22/1.52 => ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ B )
% 0.22/1.52 => ( in @ Xx @ A ) )
% 0.22/1.52 => ( A = B ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptyI_type,type,
% 0.22/1.52 emptyI: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptyI,definition,
% 0.22/1.52 ( emptyI
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ~ ( in @ Xx @ A )
% 0.22/1.52 => ( A = emptyset ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(noeltsimpempty_type,type,
% 0.22/1.52 noeltsimpempty: $o ).
% 0.22/1.52
% 0.22/1.52 thf(noeltsimpempty,definition,
% 0.22/1.52 ( noeltsimpempty
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ~ ( in @ Xx @ A )
% 0.22/1.52 => ( A = emptyset ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setbeta_type,type,
% 0.22/1.52 setbeta: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setbeta,definition,
% 0.22/1.52 ( setbeta
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( ( in @ Xx
% 0.22/1.52 @ ( dsetconstr @ A
% 0.22/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.22/1.52 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(nonempty_type,type,
% 0.22/1.52 nonempty: $i > $o ).
% 0.22/1.52
% 0.22/1.52 thf(nonempty,definition,
% 0.22/1.52 ( nonempty
% 0.22/1.52 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(nonemptyE1_type,type,
% 0.22/1.52 nonemptyE1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(nonemptyE1,definition,
% 0.22/1.52 ( nonemptyE1
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ( ( nonempty @ A )
% 0.22/1.52 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(nonemptyI_type,type,
% 0.22/1.52 nonemptyI: $o ).
% 0.22/1.52
% 0.22/1.52 thf(nonemptyI,definition,
% 0.22/1.52 ( nonemptyI
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( ( Xphi @ Xx )
% 0.22/1.52 => ( nonempty
% 0.22/1.52 @ ( dsetconstr @ A
% 0.22/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(nonemptyI1_type,type,
% 0.22/1.52 nonemptyI1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(nonemptyI1,definition,
% 0.22/1.52 ( nonemptyI1
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.22/1.52 => ( nonempty @ A ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinIL_type,type,
% 0.22/1.52 setadjoinIL: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinIL,definition,
% 0.22/1.52 ( setadjoinIL
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptyinunitempty_type,type,
% 0.22/1.52 emptyinunitempty: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptyinunitempty,definition,
% 0.22/1.52 ( emptyinunitempty
% 0.22/1.52 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinIR_type,type,
% 0.22/1.52 setadjoinIR: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinIR,definition,
% 0.22/1.52 ( setadjoinIR
% 0.22/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.22/1.52 ( ( in @ Xy @ A )
% 0.22/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinE_type,type,
% 0.22/1.52 setadjoinE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinE,definition,
% 0.22/1.52 ( setadjoinE
% 0.22/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.22/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.22/1.52 => ! [Xphi: $o] :
% 0.22/1.52 ( ( ( Xy = Xx )
% 0.22/1.52 => Xphi )
% 0.22/1.52 => ( ( ( in @ Xy @ A )
% 0.22/1.52 => Xphi )
% 0.22/1.52 => Xphi ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinOr_type,type,
% 0.22/1.52 setadjoinOr: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoinOr,definition,
% 0.22/1.52 ( setadjoinOr
% 0.22/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.22/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.22/1.52 => ( ( Xy = Xx )
% 0.22/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setoftrueEq_type,type,
% 0.22/1.52 setoftrueEq: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setoftrueEq,definition,
% 0.22/1.52 ( setoftrueEq
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ( ( dsetconstr @ A
% 0.22/1.52 @ ^ [Xx: $i] : $true )
% 0.22/1.52 = A ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(powersetI_type,type,
% 0.22/1.52 powersetI: $o ).
% 0.22/1.52
% 0.22/1.52 thf(powersetI,definition,
% 0.22/1.52 ( powersetI
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ B )
% 0.22/1.52 => ( in @ Xx @ A ) )
% 0.22/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptyinPowerset_type,type,
% 0.22/1.52 emptyinPowerset: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptyinPowerset,definition,
% 0.22/1.52 ( emptyinPowerset
% 0.22/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptyInPowerset_type,type,
% 0.22/1.52 emptyInPowerset: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptyInPowerset,definition,
% 0.22/1.52 ( emptyInPowerset
% 0.22/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(powersetE_type,type,
% 0.22/1.52 powersetE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(powersetE,definition,
% 0.22/1.52 ( powersetE
% 0.22/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.22/1.52 ( ( in @ B @ ( powerset @ A ) )
% 0.22/1.52 => ( ( in @ Xx @ B )
% 0.22/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setunionI_type,type,
% 0.22/1.52 setunionI: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setunionI,definition,
% 0.22/1.52 ( setunionI
% 0.22/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.22/1.52 ( ( in @ Xx @ B )
% 0.22/1.52 => ( ( in @ B @ A )
% 0.22/1.52 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setunionE_type,type,
% 0.22/1.52 setunionE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setunionE,definition,
% 0.22/1.52 ( setunionE
% 0.22/1.52 = ( ! [A: $i,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 0.22/1.52 => ! [Xphi: $o] :
% 0.22/1.52 ( ! [B: $i] :
% 0.22/1.52 ( ( in @ Xx @ B )
% 0.22/1.52 => ( ( in @ B @ A )
% 0.22/1.52 => Xphi ) )
% 0.22/1.52 => Xphi ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(subPowSU_type,type,
% 0.22/1.52 subPowSU: $o ).
% 0.22/1.52
% 0.22/1.52 thf(subPowSU,definition,
% 0.22/1.52 ( subPowSU
% 0.22/1.52 = ( ! [A: $i,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exuE2_type,type,
% 0.22/1.52 exuE2: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exuE2,definition,
% 0.22/1.52 ( exuE2
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 => ? [Xx: $i] :
% 0.22/1.52 ! [Xy: $i] :
% 0.22/1.52 ( ( Xphi @ Xy )
% 0.22/1.52 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(nonemptyImpWitness_type,type,
% 0.22/1.52 nonemptyImpWitness: $o ).
% 0.22/1.52
% 0.22/1.52 thf(nonemptyImpWitness,definition,
% 0.22/1.52 ( nonemptyImpWitness
% 0.22/1.52 = ( ! [A: $i] :
% 0.22/1.52 ( ( nonempty @ A )
% 0.22/1.52 => ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 & $true ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(uniqinunit_type,type,
% 0.22/1.52 uniqinunit: $o ).
% 0.22/1.52
% 0.22/1.52 thf(uniqinunit,definition,
% 0.22/1.52 ( uniqinunit
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.22/1.52 => ( Xx = Xy ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(notinsingleton_type,type,
% 0.22/1.52 notinsingleton: $o ).
% 0.22/1.52
% 0.22/1.52 thf(notinsingleton,definition,
% 0.22/1.52 ( notinsingleton
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xx != Xy )
% 0.22/1.52 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(eqinunit_type,type,
% 0.22/1.52 eqinunit: $o ).
% 0.22/1.52
% 0.22/1.52 thf(eqinunit,definition,
% 0.22/1.52 ( eqinunit
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xx = Xy )
% 0.22/1.52 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(singletonsswitch_type,type,
% 0.22/1.52 singletonsswitch: $o ).
% 0.22/1.52
% 0.22/1.52 thf(singletonsswitch,definition,
% 0.22/1.52 ( singletonsswitch
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.22/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(upairsetE_type,type,
% 0.22/1.52 upairsetE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(upairsetE,definition,
% 0.22/1.52 ( upairsetE
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.22/1.52 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.22/1.52 => ( ( Xz = Xx )
% 0.22/1.52 | ( Xz = Xy ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(upairsetIL_type,type,
% 0.22/1.52 upairsetIL: $o ).
% 0.22/1.52
% 0.22/1.52 thf(upairsetIL,definition,
% 0.22/1.52 ( upairsetIL
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(upairsetIR_type,type,
% 0.22/1.52 upairsetIR: $o ).
% 0.22/1.52
% 0.22/1.52 thf(upairsetIR,definition,
% 0.22/1.52 ( upairsetIR
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptyE1_type,type,
% 0.22/1.52 emptyE1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptyE1,definition,
% 0.22/1.52 ( emptyE1
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 0.22/1.52 ( ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 & ( Xphi @ Xx ) )
% 0.22/1.52 => ( ( ( dsetconstr @ A
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 = emptyset )
% 0.22/1.52 => $false ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(vacuousDall_type,type,
% 0.22/1.52 vacuousDall: $o ).
% 0.22/1.52
% 0.22/1.52 thf(vacuousDall,definition,
% 0.22/1.52 ( vacuousDall
% 0.22/1.52 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ emptyset )
% 0.22/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(quantDeMorgan1_type,type,
% 0.22/1.52 quantDeMorgan1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(quantDeMorgan1,definition,
% 0.22/1.52 ( quantDeMorgan1
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 0.22/1.52 ( ~ ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( Xphi @ Xx ) )
% 0.22/1.52 => ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(quantDeMorgan2_type,type,
% 0.22/1.52 quantDeMorgan2: $o ).
% 0.22/1.52
% 0.22/1.52 thf(quantDeMorgan2,definition,
% 0.22/1.52 ( quantDeMorgan2
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ~ ( Xphi @ Xx ) )
% 0.22/1.52 => ~ ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(quantDeMorgan3_type,type,
% 0.22/1.52 quantDeMorgan3: $o ).
% 0.22/1.52
% 0.22/1.52 thf(quantDeMorgan3,definition,
% 0.22/1.52 ( quantDeMorgan3
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 0.22/1.52 ( ~ ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 & ( Xphi @ Xx ) )
% 0.22/1.52 => ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(quantDeMorgan4_type,type,
% 0.22/1.52 quantDeMorgan4: $o ).
% 0.22/1.52
% 0.22/1.52 thf(quantDeMorgan4,definition,
% 0.22/1.52 ( quantDeMorgan4
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 0.22/1.52 ( ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 & ~ ( Xphi @ Xx ) )
% 0.22/1.52 => ~ ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(prop2setI_type,type,
% 0.22/1.52 prop2setI: $o ).
% 0.22/1.52
% 0.22/1.52 thf(prop2setI,definition,
% 0.22/1.52 ( prop2setI
% 0.22/1.52 = ( ! [Xphi: $o] :
% 0.22/1.52 ( Xphi
% 0.22/1.52 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(set2prop_type,type,
% 0.22/1.52 set2prop: $i > $o ).
% 0.22/1.52
% 0.22/1.52 thf(prop2set2propI_type,type,
% 0.22/1.52 prop2set2propI: $o ).
% 0.22/1.52
% 0.22/1.52 thf(prop2set2propI,definition,
% 0.22/1.52 ( prop2set2propI
% 0.22/1.52 = ( ! [Xphi: $o] :
% 0.22/1.52 ( Xphi
% 0.22/1.52 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(notdexE_type,type,
% 0.22/1.52 notdexE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(notdexE,definition,
% 0.22/1.52 ( notdexE
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 0.22/1.52 ( ~ ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 & ( Xphi @ Xx ) )
% 0.22/1.52 => ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(notdallE_type,type,
% 0.22/1.52 notdallE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(notdallE,definition,
% 0.22/1.52 ( notdallE
% 0.22/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 0.22/1.52 ( ~ ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( Xphi @ Xx ) )
% 0.22/1.52 => ? [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exuI1_type,type,
% 0.22/1.52 exuI1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exuI1,definition,
% 0.22/1.52 ( exuI1
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ? [Xx: $i] :
% 0.22/1.52 ( ( Xphi @ Xx )
% 0.22/1.52 & ! [Xy: $i] :
% 0.22/1.52 ( ( Xphi @ Xy )
% 0.22/1.52 => ( Xx = Xy ) ) )
% 0.22/1.52 => ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exuI3_type,type,
% 0.22/1.52 exuI3: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exuI3,definition,
% 0.22/1.52 ( exuI3
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.22/1.52 => ( ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xphi @ Xx )
% 0.22/1.52 => ( ( Xphi @ Xy )
% 0.22/1.52 => ( Xx = Xy ) ) )
% 0.22/1.52 => ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exuI2_type,type,
% 0.22/1.52 exuI2: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exuI2,definition,
% 0.22/1.52 ( exuI2
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ? [Xx: $i] :
% 0.22/1.52 ! [Xy: $i] :
% 0.22/1.52 ( ( Xphi @ Xy )
% 0.22/1.52 <=> ( Xy = Xx ) )
% 0.22/1.52 => ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(inCongP_type,type,
% 0.22/1.52 inCongP: $o ).
% 0.22/1.52
% 0.22/1.52 thf(inCongP,definition,
% 0.22/1.52 ( inCongP
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ( A = B )
% 0.22/1.52 => ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xx = Xy )
% 0.22/1.52 => ( ( in @ Xx @ A )
% 0.22/1.52 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(in__Cong_type,type,
% 0.22/1.52 in__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(in__Cong,definition,
% 0.22/1.52 ( in__Cong
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ( A = B )
% 0.22/1.52 => ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xx = Xy )
% 0.22/1.52 => ( ( in @ Xx @ A )
% 0.22/1.52 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exuE3u_type,type,
% 0.22/1.52 exuE3u: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exuE3u,definition,
% 0.22/1.52 ( exuE3u
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 => ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xphi @ Xx )
% 0.22/1.52 => ( ( Xphi @ Xy )
% 0.22/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exu__Cong_type,type,
% 0.22/1.52 exu__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exu__Cong,definition,
% 0.22/1.52 ( exu__Cong
% 0.22/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.22/1.52 ( ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xx = Xy )
% 0.22/1.52 => ( ( Xphi @ Xx )
% 0.22/1.52 <=> ( Xpsi @ Xy ) ) )
% 0.22/1.52 => ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 <=> ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptyset__Cong_type,type,
% 0.22/1.52 emptyset__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptyset__Cong,definition,
% 0.22/1.52 ( emptyset__Cong
% 0.22/1.52 = ( emptyset = emptyset ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoin__Cong_type,type,
% 0.22/1.52 setadjoin__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setadjoin__Cong,definition,
% 0.22/1.52 ( setadjoin__Cong
% 0.22/1.52 = ( ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xx = Xy )
% 0.22/1.52 => ! [Xz: $i,Xu: $i] :
% 0.22/1.52 ( ( Xz = Xu )
% 0.22/1.52 => ( ( setadjoin @ Xx @ Xz )
% 0.22/1.52 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(powerset__Cong_type,type,
% 0.22/1.52 powerset__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(powerset__Cong,definition,
% 0.22/1.52 ( powerset__Cong
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ( A = B )
% 0.22/1.52 => ( ( powerset @ A )
% 0.22/1.52 = ( powerset @ B ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(setunion__Cong_type,type,
% 0.22/1.52 setunion__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(setunion__Cong,definition,
% 0.22/1.52 ( setunion__Cong
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ( A = B )
% 0.22/1.52 => ( ( setunion @ A )
% 0.22/1.52 = ( setunion @ B ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(omega__Cong_type,type,
% 0.22/1.52 omega__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(omega__Cong,definition,
% 0.22/1.52 ( omega__Cong
% 0.22/1.52 = ( omega = omega ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(exuEu_type,type,
% 0.22/1.52 exuEu: $o ).
% 0.22/1.52
% 0.22/1.52 thf(exuEu,definition,
% 0.22/1.52 ( exuEu
% 0.22/1.52 = ( ! [Xphi: $i > $o] :
% 0.22/1.52 ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 => ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xphi @ Xx )
% 0.22/1.52 => ( ( Xphi @ Xy )
% 0.22/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(descr__Cong_type,type,
% 0.22/1.52 descr__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(descr__Cong,definition,
% 0.22/1.52 ( descr__Cong
% 0.22/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.22/1.52 ( ! [Xx: $i,Xy: $i] :
% 0.22/1.52 ( ( Xx = Xy )
% 0.22/1.52 => ( ( Xphi @ Xx )
% 0.22/1.52 <=> ( Xpsi @ Xy ) ) )
% 0.22/1.52 => ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 => ( ( exu
% 0.22/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.22/1.52 => ( ( descr
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 = ( descr
% 0.22/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstr__Cong_type,type,
% 0.22/1.52 dsetconstr__Cong: $o ).
% 0.22/1.52
% 0.22/1.52 thf(dsetconstr__Cong,definition,
% 0.22/1.52 ( dsetconstr__Cong
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ( A = B )
% 0.22/1.52 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ! [Xy: $i] :
% 0.22/1.52 ( ( in @ Xy @ B )
% 0.22/1.52 => ( ( Xx = Xy )
% 0.22/1.52 => ( ( Xphi @ Xx )
% 0.22/1.52 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.22/1.52 => ( ( dsetconstr @ A
% 0.22/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.22/1.52 = ( dsetconstr @ B
% 0.22/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(subset_type,type,
% 0.22/1.52 subset: $i > $i > $o ).
% 0.22/1.52
% 0.22/1.52 thf(disjoint_type,type,
% 0.22/1.52 disjoint: $i > $i > $o ).
% 0.22/1.52
% 0.22/1.52 thf(setsmeet_type,type,
% 0.22/1.52 setsmeet: $i > $i > $o ).
% 0.22/1.52
% 0.22/1.52 thf(subsetI1_type,type,
% 0.22/1.52 subsetI1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(subsetI1,definition,
% 0.22/1.52 ( subsetI1
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( in @ Xx @ B ) )
% 0.22/1.52 => ( subset @ A @ B ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(eqimpsubset2_type,type,
% 0.22/1.52 eqimpsubset2: $o ).
% 0.22/1.52
% 0.22/1.52 thf(eqimpsubset2,definition,
% 0.22/1.52 ( eqimpsubset2
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ( A = B )
% 0.22/1.52 => ( subset @ B @ A ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(eqimpsubset1_type,type,
% 0.22/1.52 eqimpsubset1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(eqimpsubset1,definition,
% 0.22/1.52 ( eqimpsubset1
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ( A = B )
% 0.22/1.52 => ( subset @ A @ B ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(subsetI2_type,type,
% 0.22/1.52 subsetI2: $o ).
% 0.22/1.52
% 0.22/1.52 thf(subsetI2,definition,
% 0.22/1.52 ( subsetI2
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ! [Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( in @ Xx @ B ) )
% 0.22/1.52 => ( subset @ A @ B ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(emptysetsubset_type,type,
% 0.22/1.52 emptysetsubset: $o ).
% 0.22/1.52
% 0.22/1.52 thf(emptysetsubset,definition,
% 0.22/1.52 ( emptysetsubset
% 0.22/1.52 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(subsetE_type,type,
% 0.22/1.52 subsetE: $o ).
% 0.22/1.52
% 0.22/1.52 thf(subsetE,definition,
% 0.22/1.52 ( subsetE
% 0.22/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.22/1.52 ( ( subset @ A @ B )
% 0.22/1.52 => ( ( in @ Xx @ A )
% 0.22/1.52 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(subsetE2_type,type,
% 0.22/1.52 subsetE2: $o ).
% 0.22/1.52
% 0.22/1.52 thf(subsetE2,definition,
% 0.22/1.52 ( subsetE2
% 0.22/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.22/1.52 ( ( subset @ A @ B )
% 0.22/1.52 => ( ~ ( in @ Xx @ B )
% 0.22/1.52 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(notsubsetI_type,type,
% 0.22/1.52 notsubsetI: $o ).
% 0.22/1.52
% 0.22/1.52 thf(notsubsetI,definition,
% 0.22/1.52 ( notsubsetI
% 0.22/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( ~ ( in @ Xx @ B )
% 0.22/1.52 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(notequalI1_type,type,
% 0.22/1.52 notequalI1: $o ).
% 0.22/1.52
% 0.22/1.52 thf(notequalI1,definition,
% 0.22/1.52 ( notequalI1
% 0.22/1.52 = ( ! [A: $i,B: $i] :
% 0.22/1.52 ( ~ ( subset @ A @ B )
% 0.22/1.52 => ( A != B ) ) ) ) ).
% 0.22/1.52
% 0.22/1.52 thf(notequalI2,conjecture,
% 0.22/1.52 ( setextAx
% 0.22/1.52 => ( emptysetAx
% 0.22/1.52 => ( setadjoinAx
% 0.22/1.52 => ( powersetAx
% 0.22/1.52 => ( setunionAx
% 0.22/1.52 => ( omega0Ax
% 0.22/1.52 => ( omegaSAx
% 0.22/1.52 => ( omegaIndAx
% 0.22/1.52 => ( replAx
% 0.22/1.52 => ( foundationAx
% 0.22/1.52 => ( wellorderingAx
% 0.22/1.52 => ( descrp
% 0.22/1.52 => ( dsetconstrI
% 0.22/1.52 => ( dsetconstrEL
% 0.22/1.52 => ( dsetconstrER
% 0.22/1.52 => ( exuE1
% 0.22/1.52 => ( prop2setE
% 0.22/1.52 => ( emptysetE
% 0.22/1.52 => ( emptysetimpfalse
% 0.22/1.52 => ( notinemptyset
% 0.22/1.52 => ( exuE3e
% 0.22/1.52 => ( setext
% 0.22/1.52 => ( emptyI
% 0.22/1.52 => ( noeltsimpempty
% 0.22/1.52 => ( setbeta
% 0.22/1.52 => ( nonemptyE1
% 0.22/1.52 => ( nonemptyI
% 0.22/1.52 => ( nonemptyI1
% 0.22/1.52 => ( setadjoinIL
% 0.22/1.52 => ( emptyinunitempty
% 0.22/1.52 => ( setadjoinIR
% 0.22/1.52 => ( setadjoinE
% 0.22/1.52 => ( setadjoinOr
% 0.22/1.52 => ( setoftrueEq
% 0.22/1.52 => ( powersetI
% 0.22/1.52 => ( emptyinPowerset
% 0.22/1.52 => ( emptyInPowerset
% 0.22/1.52 => ( powersetE
% 0.22/1.52 => ( setunionI
% 0.22/1.52 => ( setunionE
% 0.22/1.52 => ( subPowSU
% 0.22/1.52 => ( exuE2
% 0.22/1.52 => ( nonemptyImpWitness
% 0.22/1.52 => ( uniqinunit
% 0.22/1.52 => ( notinsingleton
% 0.22/1.52 => ( eqinunit
% 0.22/1.52 => ( singletonsswitch
% 0.22/1.52 => ( upairsetE
% 0.22/1.52 => ( upairsetIL
% 0.22/1.52 => ( upairsetIR
% 0.22/1.52 => ( emptyE1
% 0.22/1.52 => ( vacuousDall
% 0.22/1.52 => ( quantDeMorgan1
% 0.22/1.52 => ( quantDeMorgan2
% 0.22/1.52 => ( quantDeMorgan3
% 0.22/1.52 => ( quantDeMorgan4
% 0.22/1.52 => ( prop2setI
% 0.22/1.52 => ( prop2set2propI
% 0.22/1.52 => ( notdexE
% 0.22/1.52 => ( notdallE
% 0.22/1.52 => ( exuI1
% 0.22/1.52 => ( exuI3
% 0.22/1.52 => ( exuI2
% 0.22/1.52 => ( inCongP
% 0.22/1.52 => ( in__Cong
% 0.22/1.52 => ( exuE3u
% 0.22/1.52 => ( exu__Cong
% 0.22/1.52 => ( emptyset__Cong
% 0.22/1.52 => ( setadjoin__Cong
% 0.22/1.52 => ( powerset__Cong
% 0.22/1.52 => ( setunion__Cong
% 0.22/1.52 => ( omega__Cong
% 0.22/1.52 => ( exuEu
% 0.22/1.52 => ( descr__Cong
% 0.22/1.52 => ( dsetconstr__Cong
% 0.22/1.52 => ( subsetI1
% 0.22/1.52 => ( eqimpsubset2
% 0.22/1.52 => ( eqimpsubset1
% 0.22/1.52 => ( subsetI2
% 0.22/1.52 => ( emptysetsubset
% 0.22/1.52 => ( subsetE
% 0.22/1.52 => ( subsetE2
% 0.22/1.52 => ( notsubsetI
% 0.22/1.52 => ( notequalI1
% 0.22/1.52 => ! [A: $i,B: $i,Xx: $i] :
% 0.22/1.52 ( ( in @ Xx @ A )
% 0.22/1.52 => ( ~ ( in @ Xx @ B )
% 0.22/1.52 => ( A != B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/1.52 ------------------------
% 0.22/1.55 % (8049)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_7946 for (2999ds/2Mi)
% 0.22/1.55 % (8045)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7946 for (2999ds/183Mi)
% 0.22/1.55 % (8048)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7946 for (2999ds/2Mi)
% 0.22/1.55 % (8051)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7946 for (2999ds/18Mi)
% 0.22/1.55 % (8050)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_7946 for (2999ds/275Mi)
% 0.22/1.55 % (8046)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_7946 for (2999ds/4Mi)
% 0.22/1.55 % (8047)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_7946 for (2999ds/27Mi)
% 0.22/1.55 % (8048)Instruction limit reached!
% 0.22/1.55 % (8048)------------------------------
% 0.22/1.55 % (8048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.55 % (8048)Termination reason: Unknown
% 0.22/1.55 % (8048)Termination phase: shuffling
% 0.22/1.55 % (8049)Instruction limit reached!
% 0.22/1.55 % (8049)------------------------------
% 0.22/1.55 % (8049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.55 % (8049)Termination reason: Unknown
% 0.22/1.55 % (8049)Termination phase: shuffling
% 0.22/1.55
% 0.22/1.55 % (8049)Memory used [KB]: 1151
% 0.22/1.55 % (8049)Time elapsed: 0.003 s
% 0.22/1.55 % (8049)Instructions burned: 3 (million)
% 0.22/1.55 % (8049)------------------------------
% 0.22/1.55 % (8049)------------------------------
% 0.22/1.55
% 0.22/1.55 % (8048)Memory used [KB]: 1151
% 0.22/1.55 % (8048)Time elapsed: 0.003 s
% 0.22/1.55 % (8048)Instructions burned: 3 (million)
% 0.22/1.55 % (8048)------------------------------
% 0.22/1.55 % (8048)------------------------------
% 0.22/1.55 % (8046)Instruction limit reached!
% 0.22/1.55 % (8046)------------------------------
% 0.22/1.55 % (8046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.55 % (8046)Termination reason: Unknown
% 0.22/1.55 % (8046)Termination phase: shuffling
% 0.22/1.55
% 0.22/1.55 % (8046)Memory used [KB]: 1151
% 0.22/1.55 % (8046)Time elapsed: 0.004 s
% 0.22/1.55 % (8046)Instructions burned: 5 (million)
% 0.22/1.55 % (8046)------------------------------
% 0.22/1.55 % (8046)------------------------------
% 0.22/1.55 % (8051)Instruction limit reached!
% 0.22/1.55 % (8051)------------------------------
% 0.22/1.55 % (8051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.55 % (8051)Termination reason: Unknown
% 0.22/1.55 % (8051)Termination phase: Preprocessing 3
% 0.22/1.55
% 0.22/1.55 % (8051)Memory used [KB]: 1663
% 0.22/1.55 % (8051)Time elapsed: 0.011 s
% 0.22/1.55 % (8051)Instructions burned: 19 (million)
% 0.22/1.55 % (8051)------------------------------
% 0.22/1.55 % (8051)------------------------------
% 0.22/1.56 % (8047)Instruction limit reached!
% 0.22/1.56 % (8047)------------------------------
% 0.22/1.56 % (8047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.56 % (8047)Termination reason: Unknown
% 0.22/1.56 % (8047)Termination phase: Property scanning
% 0.22/1.56
% 0.22/1.56 % (8047)Memory used [KB]: 1407
% 0.22/1.56 % (8047)Time elapsed: 0.014 s
% 0.22/1.56 % (8047)Instructions burned: 27 (million)
% 0.22/1.56 % (8047)------------------------------
% 0.22/1.56 % (8047)------------------------------
% 0.22/1.56 % (8052)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7946 for (2999ds/3Mi)
% 0.22/1.56 % (8053)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_7946 for (2999ds/37Mi)
% 0.22/1.56 % (8054)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_7946 for (2999ds/15Mi)
% 0.22/1.56 % (8052)Instruction limit reached!
% 0.22/1.56 % (8052)------------------------------
% 0.22/1.56 % (8052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.56 % (8052)Termination reason: Unknown
% 0.22/1.56 % (8052)Termination phase: shuffling
% 0.22/1.56
% 0.22/1.56 % (8052)Memory used [KB]: 1151
% 0.22/1.56 % (8052)Time elapsed: 0.003 s
% 0.22/1.56 % (8052)Instructions burned: 4 (million)
% 0.22/1.56 % (8052)------------------------------
% 0.22/1.56 % (8052)------------------------------
% 0.22/1.57 % (8055)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_7946 for (2999ds/3Mi)
% 0.22/1.57 % (8054)Instruction limit reached!
% 0.22/1.57 % (8054)------------------------------
% 0.22/1.57 % (8054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.57 % (8054)Termination reason: Unknown
% 0.22/1.57 % (8054)Termination phase: Preprocessing 3
% 0.22/1.57
% 0.22/1.57 % (8054)Memory used [KB]: 1535
% 0.22/1.57 % (8054)Time elapsed: 0.009 s
% 0.22/1.57 % (8054)Instructions burned: 16 (million)
% 0.22/1.57 % (8054)------------------------------
% 0.22/1.57 % (8054)------------------------------
% 0.22/1.57 % (8055)Instruction limit reached!
% 0.22/1.57 % (8055)------------------------------
% 0.22/1.57 % (8055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.57 % (8055)Termination reason: Unknown
% 0.22/1.57 % (8055)Termination phase: shuffling
% 0.22/1.57
% 0.22/1.57 % (8055)Memory used [KB]: 1151
% 0.22/1.57 % (8055)Time elapsed: 0.003 s
% 0.22/1.57 % (8055)Instructions burned: 3 (million)
% 0.22/1.57 % (8055)------------------------------
% 0.22/1.57 % (8055)------------------------------
% 0.22/1.57 % (8056)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_7946 for (2999ds/1041Mi)
% 0.22/1.58 % (8053)Instruction limit reached!
% 0.22/1.58 % (8053)------------------------------
% 0.22/1.58 % (8053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.58 % (8053)Termination reason: Unknown
% 0.22/1.58 % (8053)Termination phase: Property scanning
% 0.22/1.58
% 0.22/1.58 % (8053)Memory used [KB]: 1407
% 0.22/1.58 % (8053)Time elapsed: 0.018 s
% 0.22/1.58 % (8053)Instructions burned: 39 (million)
% 0.22/1.58 % (8053)------------------------------
% 0.22/1.58 % (8053)------------------------------
% 0.22/1.58 % (8057)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7946 for (2999ds/7Mi)
% 0.22/1.58 % (8057)Instruction limit reached!
% 0.22/1.58 % (8057)------------------------------
% 0.22/1.58 % (8057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.58 % (8057)Termination reason: Unknown
% 0.22/1.58 % (8057)Termination phase: shuffling
% 0.22/1.58
% 0.22/1.58 % (8057)Memory used [KB]: 1279
% 0.22/1.58 % (8057)Time elapsed: 0.005 s
% 0.22/1.58 % (8057)Instructions burned: 8 (million)
% 0.22/1.58 % (8057)------------------------------
% 0.22/1.58 % (8057)------------------------------
% 0.22/1.59 % (8059)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_7946 for (2999ds/3Mi)
% 0.22/1.59 % (8058)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7946 for (2999ds/16Mi)
% 0.22/1.59 % (8059)Instruction limit reached!
% 0.22/1.59 % (8059)------------------------------
% 0.22/1.59 % (8059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.59 % (8059)Termination reason: Unknown
% 0.22/1.59 % (8059)Termination phase: shuffling
% 0.22/1.59
% 0.22/1.59 % (8059)Memory used [KB]: 1151
% 0.22/1.59 % (8059)Time elapsed: 0.003 s
% 0.22/1.59 % (8059)Instructions burned: 4 (million)
% 0.22/1.59 % (8059)------------------------------
% 0.22/1.59 % (8059)------------------------------
% 0.22/1.59 % (8050)First to succeed.
% 0.22/1.59 % (8050)Refutation found. Thanks to Tanya!
% 0.22/1.59 % SZS status Theorem for DTF2THF_7946
% 0.22/1.59 % SZS output start Proof for DTF2THF_7946
% 0.22/1.59 thf(func_def_0, type, in: $i > $i > $o).
% 0.22/1.59 thf(func_def_1, type, exu: ($i > $o) > $o).
% 0.22/1.59 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 0.22/1.59 thf(func_def_8, type, powerset: $i > $i).
% 0.22/1.59 thf(func_def_10, type, setunion: $i > $i).
% 0.22/1.59 thf(func_def_19, type, descr: ($i > $o) > $i).
% 0.22/1.59 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_26, type, prop2set: $o > $i).
% 0.22/1.59 thf(func_def_36, type, nonempty: $i > $o).
% 0.22/1.59 thf(func_def_69, type, set2prop: $i > $o).
% 0.22/1.59 thf(func_def_88, type, subset: $i > $i > $o).
% 0.22/1.59 thf(func_def_89, type, disjoint: $i > $i > $o).
% 0.22/1.59 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 0.22/1.59 thf(func_def_113, type, sP1: $i > $i > $o).
% 0.22/1.59 thf(func_def_114, type, sP2: $i > $o).
% 0.22/1.59 thf(func_def_115, type, sP3: $i > $i > $o).
% 0.22/1.59 thf(func_def_116, type, sP4: $i > $i > $o).
% 0.22/1.59 thf(func_def_117, type, sK5: ($i > $o) > $i > $i).
% 0.22/1.59 thf(func_def_119, type, sK7: $i > $o).
% 0.22/1.59 thf(func_def_121, type, sK9: $i > $o).
% 0.22/1.59 thf(func_def_122, type, sK10: $i > $i).
% 0.22/1.59 thf(func_def_126, type, sK14: $i > $i > $i).
% 0.22/1.59 thf(func_def_131, type, sK19: $i > $i > $i).
% 0.22/1.59 thf(func_def_136, type, sK24: $i > $o).
% 0.22/1.59 thf(func_def_137, type, sK25: $i > $o).
% 0.22/1.59 thf(func_def_139, type, sK27: $i > $o).
% 0.22/1.59 thf(func_def_140, type, sK28: $i > $o).
% 0.22/1.59 thf(func_def_141, type, sK29: ($i > $o) > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_142, type, sK30: ($i > $o) > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_143, type, sK31: $i > $o).
% 0.22/1.59 thf(func_def_144, type, sK32: $i > $o).
% 0.22/1.59 thf(func_def_145, type, sK33: ($i > $o) > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_146, type, sK34: ($i > $o) > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_148, type, sK36: $i > $o).
% 0.22/1.59 thf(func_def_149, type, sK37: ($i > $o) > $i).
% 0.22/1.59 thf(func_def_153, type, sK41: ($i > $o) > $i).
% 0.22/1.59 thf(func_def_154, type, sK42: $i > $o).
% 0.22/1.59 thf(func_def_155, type, sK43: $i > $i).
% 0.22/1.59 thf(func_def_160, type, sK48: ($i > $o) > ($i > $o) > $i > $i > $i).
% 0.22/1.59 thf(func_def_161, type, sK49: ($i > $o) > ($i > $o) > $i > $i > $i).
% 0.22/1.59 thf(func_def_164, type, sK52: $i > $o).
% 0.22/1.59 thf(func_def_165, type, sK53: $i > $o).
% 0.22/1.59 thf(func_def_181, type, sK69: $i > $o).
% 0.22/1.59 thf(func_def_187, type, sK75: $i > $o).
% 0.22/1.59 thf(func_def_194, type, sK82: $i > $o).
% 0.22/1.59 thf(func_def_197, type, sK85: $i > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_206, type, sK94: $i > $o).
% 0.22/1.59 thf(func_def_208, type, sK96: $i > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_209, type, sK97: $i > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_210, type, sK98: $i > $o).
% 0.22/1.59 thf(func_def_213, type, sK101: $i > $i > $o).
% 0.22/1.59 thf(func_def_215, type, sK103: $i > $i).
% 0.22/1.59 thf(func_def_216, type, sK104: $i > $i).
% 0.22/1.59 thf(func_def_217, type, sK105: $i > ($i > $i > $o) > $i).
% 0.22/1.59 thf(func_def_218, type, sK106: $i > ($i > $i > $o) > $i).
% 0.22/1.59 thf(func_def_219, type, sK107: $i > $i > ($i > $i > $o) > $i).
% 0.22/1.59 thf(func_def_229, type, sK117: $i > $o).
% 0.22/1.59 thf(func_def_232, type, sK120: $i > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_234, type, sK122: $i > $i).
% 0.22/1.59 thf(func_def_237, type, sK125: $i > $i > $i).
% 0.22/1.59 thf(func_def_245, type, sK133: $i > $o).
% 0.22/1.59 thf(func_def_248, type, sK136: $i > $i).
% 0.22/1.59 thf(func_def_249, type, sK137: $i > $o).
% 0.22/1.59 thf(func_def_251, type, sK139: ($i > $o) > $i).
% 0.22/1.59 thf(func_def_252, type, sK140: ($i > $o) > $i).
% 0.22/1.59 thf(func_def_253, type, sK141: $i > $i > $i).
% 0.22/1.59 thf(func_def_259, type, sK147: $i > $i > $i).
% 0.22/1.59 thf(func_def_265, type, sK153: $i > $i > $i).
% 0.22/1.59 thf(func_def_266, type, sK154: $i > $i > $i).
% 0.22/1.59 thf(func_def_269, type, sK157: $o > $i > $i > $i).
% 0.22/1.59 thf(func_def_276, type, sK164: $i > $o).
% 0.22/1.59 thf(func_def_278, type, sK166: $i > $i).
% 0.22/1.59 thf(func_def_280, type, sK168: $i > $o).
% 0.22/1.59 thf(func_def_288, type, sK176: ($i > $o) > $i > $i).
% 0.22/1.59 thf(func_def_290, type, sK178: $i > $o).
% 0.22/1.59 thf(func_def_294, type, sK182: $i > $i > $i).
% 0.22/1.59 thf(func_def_300, type, sK188: $i > ($i > $o) > $i).
% 0.22/1.59 thf(func_def_301, type, sK189: $i > $o).
% 0.22/1.59 thf(func_def_307, type, sK195: $i > $o).
% 0.22/1.59 thf(func_def_309, type, sK197: ($i > $o) > $i > $i).
% 0.22/1.59 thf(func_def_318, type, sK206: $i > $o).
% 0.22/1.59 thf(func_def_324, type, sK212: $i > $o).
% 0.22/1.59 thf(func_def_327, type, sK215: $i > $i).
% 0.22/1.59 thf(func_def_330, type, sK218: $i > $i).
% 0.22/1.59 thf(func_def_332, type, sK220: $i > $i).
% 0.22/1.59 thf(func_def_333, type, sK221: $i > $o).
% 0.22/1.59 thf(func_def_334, type, sK222: $i > $i).
% 0.22/1.59 thf(func_def_335, type, sK223: ($i > $o) > $i).
% 0.22/1.59 thf(func_def_336, type, sK224: $i > $i > $i).
% 0.22/1.59 thf(func_def_337, type, sK225: $i > $i > $i).
% 0.22/1.59 thf(func_def_338, type, sK226: $i > $i > $i).
% 0.22/1.59 thf(func_def_339, type, sK227: $i > $i > $i).
% 0.22/1.59 thf(func_def_340, type, sK228: $i > $i > $i).
% 0.22/1.59 thf(func_def_341, type, sK229: $i > $i > $i > $i).
% 0.22/1.59 thf(func_def_342, type, sK230: $i > $i).
% 0.22/1.59 thf(func_def_343, type, sK231: $i > $i).
% 0.22/1.59 thf(func_def_344, type, sK232: $i > $i).
% 0.22/1.59 thf(func_def_345, type, sK233: $i > $i).
% 0.22/1.59 thf(func_def_346, type, sK234: $i > $i > $i > $i).
% 0.22/1.59 thf(func_def_347, type, sK235: $i > $i > $i > $i).
% 0.22/1.59 thf(func_def_348, type, sK236: $i > $i > $i).
% 0.22/1.59 thf(func_def_349, type, sK237: $i > $i > $i).
% 0.22/1.59 thf(func_def_350, type, sK238: $i > $i > $i).
% 0.22/1.59 thf(func_def_351, type, sK239: $i > $i).
% 0.22/1.59 thf(func_def_353, type, sK241: $i > $i).
% 0.22/1.59 thf(func_def_354, type, sK242: $i > $i).
% 0.22/1.59 thf(func_def_357, type, ph245: !>[X0: $tType]:(X0)).
% 0.22/1.59 thf(f1747,plain,(
% 0.22/1.59 $false),
% 0.22/1.59 inference(subsumption_resolution,[status(thm)],[f1368,f954])).
% 0.22/1.59 thf(f954,plain,(
% 0.22/1.59 ((in @ sK110 @ sK109) = $true)),
% 0.22/1.59 inference(cnf_transformation,[status(thm)],[f555])).
% 0.22/1.59 thf(f555,plain,(
% 0.22/1.59 (wellorderingAx = $true) & (nonemptyI = $true) & (powerset__Cong = $true) & (setunion__Cong = $true) & (setadjoinE = $true) & (eqinunit = $true) & (quantDeMorgan2 = $true) & (dsetconstrEL = $true) & (prop2setI = $true) & (dsetconstr__Cong = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (eqimpsubset2 = $true) & (emptyInPowerset = $true) & (subsetI2 = $true) & (exuEu = $true) & (subsetI1 = $true) & (setadjoinOr = $true) & (setadjoinIL = $true) & (exu__Cong = $true) & (upairsetIL = $true) & (emptyI = $true) & (setunionE = $true) & (nonemptyImpWitness = $true) & (powersetAx = $true) & (notdallE = $true) & (notsubsetI = $true) & (setextAx = $true) & (setunionI = $true) & (omegaIndAx = $true) & (emptysetAx = $true) & (dsetconstrI = $true) & (upairsetIR = $true) & (setunionAx = $true) & (replAx = $true) & (quantDeMorgan3 = $true) & (subsetE2 = $true) & (vacuousDall = $true) & (exuE3e = $true) & (powersetE = $true) & (emptyinPowerset = $true) & (prop2setE = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (emptyinunitempty = $true) & (emptyset__Cong = $true) & (exuE2 = $true) & (in__Cong = $true) & (setoftrueEq = $true) & (notinsingleton = $true) & (nonemptyE1 = $true) & (descr__Cong = $true) & (notinemptyset = $true) & (omega0Ax = $true) & (prop2set2propI = $true) & (emptysetimpfalse = $true) & (subsetE = $true) & (upairsetE = $true) & (emptysetE = $true) & (setadjoin__Cong = $true) & (omega__Cong = $true) & (exuI1 = $true) & (quantDeMorgan1 = $true) & (eqimpsubset1 = $true) & (setbeta = $true) & (foundationAx = $true) & (($true != (in @ sK110 @ sK108)) & (sK108 = sK109) & ((in @ sK110 @ sK109) = $true)) & (dsetconstrER = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (descrp = $true) & (emptysetsubset = $true) & (powersetI = $true) & (quantDeMorgan4 = $true) & (nonemptyI1 = $true) & (emptyE1 = $true) & (uniqinunit = $true) & (setext = $true) & (notequalI1 = $true) & (exuE3u = $true) & (exuI2 = $true) & (inCongP = $true) & (notdexE = $true) & (singletonsswitch = $true) & (subPowSU = $true)),
% 0.22/1.59 inference(skolemisation,[status(esa),new_symbols(skolem,[sK108,sK109,sK110])],[f306,f554])).
% 0.22/1.59 thf(f554,plain,(
% 0.22/1.59 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & (X0 = X1) & ((in @ X2 @ X1) = $true)) => (($true != (in @ sK110 @ sK108)) & (sK108 = sK109) & ((in @ sK110 @ sK109) = $true))),
% 0.22/1.59 introduced(definition,[],[choice_axiom])).
% 0.22/1.59 thf(f306,plain,(
% 0.22/1.59 (wellorderingAx = $true) & (nonemptyI = $true) & (powerset__Cong = $true) & (setunion__Cong = $true) & (setadjoinE = $true) & (eqinunit = $true) & (quantDeMorgan2 = $true) & (dsetconstrEL = $true) & (prop2setI = $true) & (dsetconstr__Cong = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (eqimpsubset2 = $true) & (emptyInPowerset = $true) & (subsetI2 = $true) & (exuEu = $true) & (subsetI1 = $true) & (setadjoinOr = $true) & (setadjoinIL = $true) & (exu__Cong = $true) & (upairsetIL = $true) & (emptyI = $true) & (setunionE = $true) & (nonemptyImpWitness = $true) & (powersetAx = $true) & (notdallE = $true) & (notsubsetI = $true) & (setextAx = $true) & (setunionI = $true) & (omegaIndAx = $true) & (emptysetAx = $true) & (dsetconstrI = $true) & (upairsetIR = $true) & (setunionAx = $true) & (replAx = $true) & (quantDeMorgan3 = $true) & (subsetE2 = $true) & (vacuousDall = $true) & (exuE3e = $true) & (powersetE = $true) & (emptyinPowerset = $true) & (prop2setE = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (emptyinunitempty = $true) & (emptyset__Cong = $true) & (exuE2 = $true) & (in__Cong = $true) & (setoftrueEq = $true) & (notinsingleton = $true) & (nonemptyE1 = $true) & (descr__Cong = $true) & (notinemptyset = $true) & (omega0Ax = $true) & (prop2set2propI = $true) & (emptysetimpfalse = $true) & (subsetE = $true) & (upairsetE = $true) & (emptysetE = $true) & (setadjoin__Cong = $true) & (omega__Cong = $true) & (exuI1 = $true) & (quantDeMorgan1 = $true) & (eqimpsubset1 = $true) & (setbeta = $true) & (foundationAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & (X0 = X1) & ((in @ X2 @ X1) = $true)) & (dsetconstrER = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (descrp = $true) & (emptysetsubset = $true) & (powersetI = $true) & (quantDeMorgan4 = $true) & (nonemptyI1 = $true) & (emptyE1 = $true) & (uniqinunit = $true) & (setext = $true) & (notequalI1 = $true) & (exuE3u = $true) & (exuI2 = $true) & (inCongP = $true) & (notdexE = $true) & (singletonsswitch = $true) & (subPowSU = $true)),
% 0.22/1.59 inference(flattening,[status(thm)],[f305])).
% 0.22/1.59 thf(f305,plain,(
% 0.22/1.59 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((X0 = X1) & ((in @ X2 @ X0) != $true)) & ((in @ X2 @ X1) = $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)),
% 0.22/1.59 inference(ennf_transformation,[status(thm)],[f258])).
% 0.22/1.59 thf(f258,plain,(
% 0.22/1.59 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) => (((in @ X2 @ X0) != $true) => (X0 != X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/1.59 inference(flattening,[status(thm)],[f138])).
% 0.22/1.59 thf(f138,plain,(
% 0.22/1.59 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) => (~((in @ X2 @ X0) = $true) => (X0 != X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/1.59 inference(fool_elimination,[status(thm)],[f137])).
% 0.22/1.59 thf(f137,plain,(
% 0.22/1.59 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (~(in @ X2 @ X0) => (X0 != X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/1.59 inference(rectify,[status(thm)],[f88])).
% 0.22/1.59 thf(f88,negated_conjecture,(
% 0.22/1.59 ~(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 => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (X3 != X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/1.59 inference(negated_conjecture,[status(cth)],[f87])).
% 0.22/1.59 thf(f87,conjecture,(
% 0.22/1.59 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 => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (X3 != X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/1.59 file('/export/starexec/sandbox/tmp/tmp.F3Lz7gYs5d/DTF2THF_7946.p',notequalI2)).
% 0.22/1.59 thf(f1368,plain,(
% 0.22/1.59 ((in @ sK110 @ sK109) != $true)),
% 0.22/1.59 inference(definition_unfolding,[status(thm)],[f956,f955])).
% 0.22/1.59 thf(f955,plain,(
% 0.22/1.59 (sK108 = sK109)),
% 0.22/1.59 inference(cnf_transformation,[status(thm)],[f555])).
% 0.22/1.59 thf(f956,plain,(
% 0.22/1.59 ($true != (in @ sK110 @ sK108))),
% 0.22/1.59 inference(cnf_transformation,[status(thm)],[f555])).
% 0.22/1.59 % SZS output end Proof for DTF2THF_7946
% 0.22/1.59 % (8050)------------------------------
% 0.22/1.59 % (8050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.59 % (8050)Termination reason: Refutation
% 0.22/1.59
% 0.22/1.59 % (8050)Memory used [KB]: 6908
% 0.22/1.59 % (8050)Time elapsed: 0.046 s
% 0.22/1.59 % (8050)Instructions burned: 85 (million)
% 0.22/1.59 % (8050)------------------------------
% 0.22/1.59 % (8050)------------------------------
% 0.22/1.59 % (8044)Success in time 0.061 s
%------------------------------------------------------------------------------