%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU543^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 09:35:11 AM UTC 2026
% Result : Theorem 2.13s 1.44s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 1192 ( 334 equ; 0 cnn)
% Maximal formula atoms : 63 ( 74 avg)
% Number of connectives : 611 ( 29 ~; 7 |; 194 &; 74 @)
% ( 0 <=>; 307 =>; 0 <=; 0 <~>)
% Maximal formula depth : 69 ( 34 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 143 ( 140 usr; 63 con; 0-3 aty)
% Number of variables : 37 ( 0 ^; 21 !; 16 ?; 37 :)
% 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_85,type,
sP1: $i > $i > $o ).
thf(func_def_86,type,
sP2: $i > $o ).
thf(func_def_87,type,
sP3: $i > $i > $o ).
thf(func_def_88,type,
sP4: $i > $i > $o ).
thf(func_def_92,type,
sK8: $i > $i ).
thf(func_def_100,type,
sK16: $i > $i > $i ).
thf(func_def_101,type,
sK17: $i > $i > $i ).
thf(func_def_103,type,
sK19: $i > $i ).
thf(func_def_105,type,
sK21: $i > $o ).
thf(func_def_107,type,
sK23: ( $i > $o ) > $i > $i ).
thf(func_def_113,type,
sK29: $i > $o ).
thf(func_def_118,type,
sK34: $i > $i > $i ).
thf(func_def_122,type,
sK38: $i > $o ).
thf(func_def_123,type,
sK39: $i > $i ).
thf(func_def_124,type,
sK40: ( $i > $o ) > $i ).
thf(func_def_126,type,
sK42: $i > $o ).
thf(func_def_127,type,
sK43: $i > $i ).
thf(func_def_128,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_129,type,
sK45: $i > $i ).
thf(func_def_131,type,
sK47: $i > $i ).
thf(func_def_135,type,
sK51: $i > $i > $i ).
thf(func_def_139,type,
sK55: $i > $i > $o ).
thf(func_def_141,type,
sK57: $i > $i ).
thf(func_def_142,type,
sK58: $i > $i ).
thf(func_def_143,type,
sK59: $i > ( $i > $i > $o ) > $i ).
thf(func_def_144,type,
sK60: $i > ( $i > $i > $o ) > $i ).
thf(func_def_145,type,
sK61: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_147,type,
sK63: $i > $o ).
thf(func_def_149,type,
sK65: ( $i > $o ) > $i > $i ).
thf(func_def_152,type,
sK68: $i > $o ).
thf(func_def_158,type,
sK74: $i > $i > $i ).
thf(func_def_167,type,
sK83: $i > $i ).
thf(func_def_172,type,
sK88: $i > $o ).
thf(func_def_175,type,
sK91: $i > $i > $i ).
thf(func_def_176,type,
sK92: $i > $o ).
thf(func_def_179,type,
sK95: $i > $i ).
thf(func_def_187,type,
sK103: $i > ( $i > $o ) > $i ).
thf(func_def_188,type,
sK104: $i > $o ).
thf(func_def_197,type,
sK113: $o > $i > $i > $i ).
thf(func_def_199,type,
sK115: $i > $o ).
thf(func_def_201,type,
sK117: ( $i > $o ) > $i ).
thf(func_def_202,type,
sK118: $i > $o ).
thf(func_def_203,type,
sK119: ( $i > $o ) > $i > $i ).
thf(func_def_205,type,
sK121: $i > $o ).
thf(func_def_208,type,
sK124: $i > $o ).
thf(func_def_210,type,
sK126: ( $i > $o ) > $i > $i ).
thf(func_def_213,type,
sK129: $i > $o ).
thf(func_def_221,type,
sK137: $i > $i ).
thf(func_def_231,type,
sK147: $i > $o ).
thf(func_def_235,type,
sK151: $i > $o ).
thf(func_def_236,type,
sK152: $i > $i > $i ).
thf(func_def_237,type,
sK153: $i > $i > $i ).
thf(func_def_238,type,
sK154: $i > $i > $i ).
thf(func_def_239,type,
sK155: $i > $i > $i ).
thf(func_def_240,type,
sK156: $i > $i > $i > $i ).
thf(func_def_241,type,
sK157: $i > $i ).
thf(func_def_242,type,
sK158: $i > $i ).
thf(func_def_243,type,
sK159: $i > $i ).
thf(func_def_244,type,
sK160: $i > $i ).
thf(func_def_245,type,
sK161: $i > $i > $i > $i ).
thf(func_def_246,type,
sK162: $i > $i > $i > $i ).
thf(func_def_247,type,
sK163: $i > $i > $i ).
thf(func_def_248,type,
sK164: $i > $i > $i ).
thf(func_def_249,type,
sK165: $i > $i > $i ).
thf(func_def_250,type,
sK166: $i > $i ).
thf(func_def_251,type,
sK167: $i > $i > $i ).
thf(func_def_253,type,
sK169: $i > $i ).
thf(func_def_254,type,
sK170: $i > $i ).
thf(func_def_256,type,
ph172:
!>[X0: $tType] : X0 ).
thf(f1299,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1271,f623]) ).
thf(f623,plain,
( $true
!= ( sK29 @ sK31 ) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
thf(f314,plain,
( ( setoftrueEq = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIL = $true )
& ( emptysetimpfalse = $true )
& ( vacuousDall = $true )
& ( upairsetE = $true )
& ( powersetE = $true )
& ( dsetconstrEL = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( exuE1 = $true )
& ( setunionI = $true )
& ( setadjoinIR = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( foundationAx = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( upairsetIL = $true )
& ( setunionAx = $true )
& ( setadjoinOr = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( emptyinPowerset = $true )
& ( quantDeMorgan4 = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyImpWitness = $true )
& ( descrp = $true )
& ( omega0Ax = $true )
& ( noeltsimpempty = $true )
& ( quantDeMorgan1 = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ( $true
= ( in @ sK31 @ sK30 ) )
& ( $true
!= ( sK29 @ sK31 ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK30 ) )
| ( $true
= ( sK29 @ X3 ) ) )
& ( nonemptyI1 = $true )
& ( prop2setI = $true )
& ( setbeta = $true )
& ( notdexE = $true )
& ( setunionE = $true )
& ( omegaSAx = $true )
& ( emptysetE = $true )
& ( dsetconstrI = $true )
& ( omegaIndAx = $true )
& ( subPowSU = $true )
& ( powersetAx = $true )
& ( powersetI = $true )
& ( emptyInPowerset = $true )
& ( exuE3e = $true )
& ( singletonsswitch = $true )
& ( uniqinunit = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( upairsetIR = $true )
& ( notinsingleton = $true )
& ( prop2set2propI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f222,f313,f312]) ).
thf(f312,plain,
( ? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( ( X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( X0 @ X3 ) ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK30 ) )
& ( $true
!= ( sK29 @ X2 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK30 ) )
| ( $true
= ( sK29 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f313,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK30 ) )
& ( $true
!= ( sK29 @ X2 ) ) )
=> ( ( $true
= ( in @ sK31 @ sK30 ) )
& ( $true
!= ( sK29 @ sK31 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f222,plain,
( ( setoftrueEq = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIL = $true )
& ( emptysetimpfalse = $true )
& ( vacuousDall = $true )
& ( upairsetE = $true )
& ( powersetE = $true )
& ( dsetconstrEL = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( exuE1 = $true )
& ( setunionI = $true )
& ( setadjoinIR = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( foundationAx = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( upairsetIL = $true )
& ( setunionAx = $true )
& ( setadjoinOr = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( emptyinPowerset = $true )
& ( quantDeMorgan4 = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyImpWitness = $true )
& ( descrp = $true )
& ( omega0Ax = $true )
& ( noeltsimpempty = $true )
& ( quantDeMorgan1 = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( ( X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( X0 @ X3 ) ) ) )
& ( nonemptyI1 = $true )
& ( prop2setI = $true )
& ( setbeta = $true )
& ( notdexE = $true )
& ( setunionE = $true )
& ( omegaSAx = $true )
& ( emptysetE = $true )
& ( dsetconstrI = $true )
& ( omegaIndAx = $true )
& ( subPowSU = $true )
& ( powersetAx = $true )
& ( powersetI = $true )
& ( emptyInPowerset = $true )
& ( exuE3e = $true )
& ( singletonsswitch = $true )
& ( uniqinunit = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( upairsetIR = $true )
& ( notinsingleton = $true )
& ( prop2set2propI = $true ) ),
inference(flattening,[status(thm)],[f221]) ).
thf(f221,plain,
( ? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( ( X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( X0 @ X3 ) ) ) )
& ( 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)],[f185]) ).
thf(f185,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 )
=> ! [X0: $i > $o,X1: $i] :
( ~ ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( X0 @ X2 )
= $true ) )
=> ? [X3: $i] :
( ( $true
!= ( X0 @ X3 ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f110]) ).
thf(f110,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 )
=> ! [X0: $i > $o,X1: $i] :
( ~ ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( X0 @ X2 )
= $true ) )
=> ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( X0 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f109]) ).
thf(f109,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
=> ! [X0: $i > $o,X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X0 @ X2 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ~ ( X0 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f63]) ).
thf(f63,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
=> ! [X0: $i > $o,X3: $i] :
( ~ ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( X0 @ X1 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ~ ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f62]) ).
thf(f62,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
=> ! [X0: $i > $o,X3: $i] :
( ~ ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( X0 @ X1 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ~ ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lFFNRSEeHn/DTF2THF_17621.p',notdallE) ).
thf(f1271,plain,
( $true
= ( sK29 @ sK31 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1260]) ).
thf(f1260,plain,
( ( $true != $true )
| ( $true
= ( sK29 @ sK31 ) ) ),
inference(superposition,[status(thm)],[f622,f624]) ).
thf(f624,plain,
( $true
= ( in @ sK31 @ sK30 ) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
thf(f622,plain,
! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK30 ) )
| ( $true
= ( sK29 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU543^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:26:27 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SEU543^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.47 % Domain : Set Theory
% 0.30/0.47 % Problem : Preliminary Notions - Negated Quantifiers
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English : (! A:i.! phi:i>o.~(! x:i.in x A -> phi x) ->
% 0.30/0.47 % (? x:i.in x A & ~(phi x)))
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.47 % Source : [Bro08]
% 0.30/0.47 % Names : ZFC045g [Bro08]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.11 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, 0.00 v3.7.0
% 0.30/0.47 % Syntax : Number of formulae : 133 ( 61 unt; 71 typ; 61 def)
% 0.30/0.47 % Number of atoms : 334 ( 80 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 61 ( 5 avg)
% 0.30/0.47 % Number of connectives : 561 ( 21 ~; 5 |; 26 &; 356 @)
% 0.30/0.47 % ( 8 <=>; 145 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 68 ( 2 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 74 ( 71 usr; 63 con; 0-2 aty)
% 0.30/0.47 % Number of variables : 183 ( 15 ^; 143 !; 25 ?; 183 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : http://mathgate.info/detsetitem.php?id=120
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(in_type,type,
% 0.30/0.47 in: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(exu_type,type,
% 0.30/0.47 exu: ( $i > $o ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(exu,definition,
% 0.30/0.47 ( exu
% 0.30/0.47 = ( ^ [Xphi: $i > $o] :
% 0.30/0.47 ? [Xx: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 & ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setextAx_type,type,
% 0.30/0.47 setextAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setextAx,definition,
% 0.30/0.47 ( setextAx
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 <=> ( in @ Xx @ B ) )
% 0.30/0.47 => ( A = B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyset_type,type,
% 0.30/0.47 emptyset: $i ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetAx_type,type,
% 0.30/0.47 emptysetAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetAx,definition,
% 0.30/0.47 ( emptysetAx
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoin_type,type,
% 0.30/0.47 setadjoin: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinAx_type,type,
% 0.30/0.47 setadjoinAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinAx,definition,
% 0.30/0.47 ( setadjoinAx
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.47 <=> ( ( Xy = Xx )
% 0.30/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powerset_type,type,
% 0.30/0.47 powerset: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(powersetAx_type,type,
% 0.30/0.47 powersetAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetAx,definition,
% 0.30/0.47 ( powersetAx
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.47 <=> ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunion_type,type,
% 0.30/0.47 setunion: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(setunionAx_type,type,
% 0.30/0.47 setunionAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionAx,definition,
% 0.30/0.47 ( setunionAx
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.47 <=> ? [B: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omega_type,type,
% 0.30/0.47 omega: $i ).
% 0.30/0.47
% 0.30/0.47 thf(omega0Ax_type,type,
% 0.30/0.47 omega0Ax: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omega0Ax,definition,
% 0.30/0.47 ( omega0Ax
% 0.30/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omegaSAx_type,type,
% 0.30/0.47 omegaSAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omegaSAx,definition,
% 0.30/0.47 ( omegaSAx
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ omega )
% 0.30/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omegaIndAx_type,type,
% 0.30/0.47 omegaIndAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omegaIndAx,definition,
% 0.30/0.47 ( omegaIndAx
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( ( in @ emptyset @ A )
% 0.30/0.47 & ! [Xx: $i] :
% 0.30/0.47 ( ( ( in @ Xx @ omega )
% 0.30/0.47 & ( in @ Xx @ A ) )
% 0.30/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ omega )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(replAx_type,type,
% 0.30/0.47 replAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(replAx,definition,
% 0.30/0.47 ( replAx
% 0.30/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( exu
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.47 => ? [B: $i] :
% 0.30/0.47 ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 <=> ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(foundationAx_type,type,
% 0.30/0.47 foundationAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(foundationAx,definition,
% 0.30/0.47 ( foundationAx
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.47 => ? [B: $i] :
% 0.30/0.47 ( ( in @ B @ A )
% 0.30/0.47 & ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(wellorderingAx_type,type,
% 0.30/0.47 wellorderingAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(wellorderingAx,definition,
% 0.30/0.47 ( wellorderingAx
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ? [B: $i] :
% 0.30/0.47 ( ! [C: $i] :
% 0.30/0.47 ( ( in @ C @ B )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ C )
% 0.30/0.47 => ( in @ Xx @ A ) ) )
% 0.30/0.47 & ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( ( in @ Xx @ A )
% 0.30/0.47 & ( in @ Xy @ A ) )
% 0.30/0.47 => ( ! [C: $i] :
% 0.30/0.47 ( ( in @ C @ B )
% 0.30/0.47 => ( ( in @ Xx @ C )
% 0.30/0.47 <=> ( in @ Xy @ C ) ) )
% 0.30/0.47 => ( Xx = Xy ) ) )
% 0.30/0.47 & ! [C: $i,D: $i] :
% 0.30/0.47 ( ( ( in @ C @ B )
% 0.30/0.47 & ( in @ D @ B ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ C )
% 0.30/0.47 => ( in @ Xx @ D ) )
% 0.30/0.47 | ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ D )
% 0.30/0.47 => ( in @ Xx @ C ) ) ) )
% 0.30/0.47 & ! [C: $i] :
% 0.30/0.47 ( ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ C )
% 0.30/0.47 => ( in @ Xx @ A ) )
% 0.30/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.47 => ? [D: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ D @ B )
% 0.30/0.47 & ( in @ Xx @ C )
% 0.30/0.47 & ~ ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ D )
% 0.30/0.47 & ( in @ Xy @ C ) )
% 0.30/0.47 & ! [E: $i] :
% 0.30/0.47 ( ( in @ E @ B )
% 0.30/0.47 => ( ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ E )
% 0.30/0.47 => ( in @ Xy @ D ) )
% 0.30/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(descr_type,type,
% 0.30/0.47 descr: ( $i > $o ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(descrp_type,type,
% 0.30/0.47 descrp: $o ).
% 0.30/0.47
% 0.30/0.47 thf(descrp,definition,
% 0.30/0.47 ( descrp
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ( Xphi
% 0.30/0.47 @ ( descr
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstr_type,type,
% 0.30/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrI_type,type,
% 0.30/0.47 dsetconstrI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrI,definition,
% 0.30/0.47 ( dsetconstrI
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrEL_type,type,
% 0.30/0.47 dsetconstrEL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrEL,definition,
% 0.30/0.47 ( dsetconstrEL
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrER_type,type,
% 0.30/0.47 dsetconstrER: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrER,definition,
% 0.30/0.47 ( dsetconstrER
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE1_type,type,
% 0.30/0.47 exuE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE1,definition,
% 0.30/0.47 ( exuE1
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 & ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(prop2set_type,type,
% 0.30/0.47 prop2set: $o > $i ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setE_type,type,
% 0.30/0.47 prop2setE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setE,definition,
% 0.30/0.47 ( prop2setE
% 0.30/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.47 => Xphi ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetE_type,type,
% 0.30/0.47 emptysetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetE,definition,
% 0.30/0.47 ( emptysetE
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ emptyset )
% 0.30/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetimpfalse_type,type,
% 0.30/0.47 emptysetimpfalse: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetimpfalse,definition,
% 0.30/0.47 ( emptysetimpfalse
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ emptyset )
% 0.30/0.47 => $false ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notinemptyset_type,type,
% 0.30/0.47 notinemptyset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notinemptyset,definition,
% 0.30/0.47 ( notinemptyset
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE3e_type,type,
% 0.30/0.47 exuE3e: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE3e,definition,
% 0.30/0.47 ( exuE3e
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setext_type,type,
% 0.30/0.47 setext: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setext,definition,
% 0.30/0.47 ( setext
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ B ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) )
% 0.30/0.47 => ( A = B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyI_type,type,
% 0.30/0.47 emptyI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyI,definition,
% 0.30/0.47 ( emptyI
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ~ ( in @ Xx @ A )
% 0.30/0.47 => ( A = emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(noeltsimpempty_type,type,
% 0.30/0.47 noeltsimpempty: $o ).
% 0.30/0.47
% 0.30/0.47 thf(noeltsimpempty,definition,
% 0.30/0.47 ( noeltsimpempty
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ~ ( in @ Xx @ A )
% 0.30/0.47 => ( A = emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setbeta_type,type,
% 0.30/0.47 setbeta: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setbeta,definition,
% 0.30/0.47 ( setbeta
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonempty_type,type,
% 0.30/0.47 nonempty: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonempty,definition,
% 0.30/0.47 ( nonempty
% 0.30/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyE1_type,type,
% 0.30/0.47 nonemptyE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyE1,definition,
% 0.30/0.47 ( nonemptyE1
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( nonempty @ A )
% 0.30/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyI_type,type,
% 0.30/0.47 nonemptyI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyI,definition,
% 0.30/0.47 ( nonemptyI
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( nonempty
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyI1_type,type,
% 0.30/0.47 nonemptyI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyI1,definition,
% 0.30/0.47 ( nonemptyI1
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIL_type,type,
% 0.30/0.47 setadjoinIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIL,definition,
% 0.30/0.47 ( setadjoinIL
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinunitempty_type,type,
% 0.30/0.47 emptyinunitempty: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinunitempty,definition,
% 0.30/0.47 ( emptyinunitempty
% 0.30/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIR_type,type,
% 0.30/0.47 setadjoinIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIR,definition,
% 0.30/0.47 ( setadjoinIR
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinE_type,type,
% 0.30/0.47 setadjoinE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinE,definition,
% 0.30/0.47 ( setadjoinE
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ( ( Xy = Xx )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => ( ( ( in @ Xy @ A )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinOr_type,type,
% 0.30/0.47 setadjoinOr: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinOr,definition,
% 0.30/0.47 ( setadjoinOr
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.47 => ( ( Xy = Xx )
% 0.30/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setoftrueEq_type,type,
% 0.30/0.47 setoftrueEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setoftrueEq,definition,
% 0.30/0.47 ( setoftrueEq
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : $true )
% 0.30/0.47 = A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetI_type,type,
% 0.30/0.47 powersetI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetI,definition,
% 0.30/0.47 ( powersetI
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) )
% 0.30/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinPowerset_type,type,
% 0.30/0.47 emptyinPowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinPowerset,definition,
% 0.30/0.47 ( emptyinPowerset
% 0.30/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyInPowerset_type,type,
% 0.30/0.47 emptyInPowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyInPowerset,definition,
% 0.30/0.47 ( emptyInPowerset
% 0.30/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetE_type,type,
% 0.30/0.47 powersetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetE,definition,
% 0.30/0.47 ( powersetE
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.47 => ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionI_type,type,
% 0.30/0.47 setunionI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionI,definition,
% 0.30/0.47 ( setunionI
% 0.30/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( ( in @ B @ A )
% 0.30/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionE_type,type,
% 0.30/0.47 setunionE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionE,definition,
% 0.30/0.47 ( setunionE
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ! [B: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( ( in @ B @ A )
% 0.30/0.47 => Xphi ) )
% 0.30/0.47 => Xphi ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subPowSU_type,type,
% 0.30/0.47 subPowSU: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subPowSU,definition,
% 0.30/0.47 ( subPowSU
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE2_type,type,
% 0.30/0.47 exuE2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE2,definition,
% 0.30/0.47 ( exuE2
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyImpWitness_type,type,
% 0.30/0.47 nonemptyImpWitness: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyImpWitness,definition,
% 0.30/0.47 ( nonemptyImpWitness
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( nonempty @ A )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & $true ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(uniqinunit_type,type,
% 0.30/0.47 uniqinunit: $o ).
% 0.30/0.47
% 0.30/0.47 thf(uniqinunit,definition,
% 0.30/0.47 ( uniqinunit
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notinsingleton_type,type,
% 0.30/0.47 notinsingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notinsingleton,definition,
% 0.30/0.47 ( notinsingleton
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx != Xy )
% 0.30/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eqinunit_type,type,
% 0.30/0.47 eqinunit: $o ).
% 0.30/0.47
% 0.30/0.47 thf(eqinunit,definition,
% 0.30/0.47 ( eqinunit
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsswitch_type,type,
% 0.30/0.47 singletonsswitch: $o ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsswitch,definition,
% 0.30/0.47 ( singletonsswitch
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetE_type,type,
% 0.30/0.47 upairsetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetE,definition,
% 0.30/0.47 ( upairsetE
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.47 => ( ( Xz = Xx )
% 0.30/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIL_type,type,
% 0.30/0.47 upairsetIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIL,definition,
% 0.30/0.47 ( upairsetIL
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIR_type,type,
% 0.30/0.47 upairsetIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIR,definition,
% 0.30/0.47 ( upairsetIR
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyE1_type,type,
% 0.30/0.47 emptyE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyE1,definition,
% 0.30/0.47 ( emptyE1
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ( ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 = emptyset )
% 0.30/0.47 => $false ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(vacuousDall_type,type,
% 0.30/0.47 vacuousDall: $o ).
% 0.30/0.47
% 0.30/0.47 thf(vacuousDall,definition,
% 0.30/0.47 ( vacuousDall
% 0.30/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ emptyset )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan1_type,type,
% 0.30/0.47 quantDeMorgan1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan1,definition,
% 0.30/0.47 ( quantDeMorgan1
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan2_type,type,
% 0.30/0.47 quantDeMorgan2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan2,definition,
% 0.30/0.47 ( quantDeMorgan2
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) )
% 0.30/0.47 => ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan3_type,type,
% 0.30/0.47 quantDeMorgan3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan3,definition,
% 0.30/0.47 ( quantDeMorgan3
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan4_type,type,
% 0.30/0.47 quantDeMorgan4: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan4,definition,
% 0.30/0.47 ( quantDeMorgan4
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) )
% 0.30/0.47 => ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setI_type,type,
% 0.30/0.47 prop2setI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setI,definition,
% 0.30/0.47 ( prop2setI
% 0.30/0.47 = ( ! [Xphi: $o] :
% 0.30/0.47 ( Xphi
% 0.30/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(set2prop_type,type,
% 0.30/0.47 set2prop: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2set2propI_type,type,
% 0.30/0.47 prop2set2propI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2set2propI,definition,
% 0.30/0.47 ( prop2set2propI
% 0.30/0.47 = ( ! [Xphi: $o] :
% 0.30/0.47 ( Xphi
% 0.30/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notdexE_type,type,
% 0.30/0.47 notdexE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notdexE,definition,
% 0.30/0.47 ( notdexE
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notdallE,conjecture,
% 0.30/0.47 ( setextAx
% 0.30/0.47 => ( emptysetAx
% 0.30/0.47 => ( setadjoinAx
% 0.30/0.47 => ( powersetAx
% 0.30/0.47 => ( setunionAx
% 0.30/0.47 => ( omega0Ax
% 0.30/0.47 => ( omegaSAx
% 0.30/0.47 => ( omegaIndAx
% 0.30/0.47 => ( replAx
% 0.30/0.47 => ( foundationAx
% 0.30/0.47 => ( wellorderingAx
% 0.30/0.47 => ( descrp
% 0.30/0.47 => ( dsetconstrI
% 0.30/0.47 => ( dsetconstrEL
% 0.30/0.47 => ( dsetconstrER
% 0.30/0.47 => ( exuE1
% 0.30/0.47 => ( prop2setE
% 0.30/0.47 => ( emptysetE
% 0.30/0.47 => ( emptysetimpfalse
% 0.30/0.47 => ( notinemptyset
% 0.30/0.47 => ( exuE3e
% 0.30/0.47 => ( setext
% 0.30/0.47 => ( emptyI
% 0.30/0.47 => ( noeltsimpempty
% 0.30/0.47 => ( setbeta
% 0.30/0.47 => ( nonemptyE1
% 0.30/0.47 => ( nonemptyI
% 0.30/0.47 => ( nonemptyI1
% 0.30/0.47 => ( setadjoinIL
% 0.30/0.47 => ( emptyinunitempty
% 0.30/0.47 => ( setadjoinIR
% 0.30/0.47 => ( setadjoinE
% 0.30/0.47 => ( setadjoinOr
% 0.30/0.47 => ( setoftrueEq
% 0.30/0.47 => ( powersetI
% 0.30/0.47 => ( emptyinPowerset
% 0.30/0.47 => ( emptyInPowerset
% 0.30/0.47 => ( powersetE
% 0.30/0.47 => ( setunionI
% 0.30/0.47 => ( setunionE
% 0.30/0.47 => ( subPowSU
% 0.30/0.47 => ( exuE2
% 0.30/0.47 => ( nonemptyImpWitness
% 0.30/0.47 => ( uniqinunit
% 0.30/0.47 => ( notinsingleton
% 0.30/0.47 => ( eqinunit
% 0.30/0.47 => ( singletonsswitch
% 0.30/0.47 => ( upairsetE
% 0.30/0.47 => ( upairsetIL
% 0.30/0.47 => ( upairsetIR
% 0.30/0.47 => ( emptyE1
% 0.30/0.47 => ( vacuousDall
% 0.30/0.47 => ( quantDeMorgan1
% 0.30/0.47 => ( quantDeMorgan2
% 0.30/0.47 => ( quantDeMorgan3
% 0.30/0.47 => ( quantDeMorgan4
% 0.30/0.47 => ( prop2setI
% 0.30/0.47 => ( prop2set2propI
% 0.30/0.47 => ( notdexE
% 0.30/0.47 => ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.91/1.38 ---- Embedded in THF ---
% 1.91/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.91/1.38 %%% Generated on Tue Feb 24 12:26:28 EST 2026
% 1.91/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.91/1.38 %%% Logic specification used:
% 1.91/1.38 %%% thf(spec, logic, $$dhol).
% 1.91/1.38
% 1.91/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lFFNRSEeHn/DTF2DTF17621.p
% See solution above
% 1.91/1.38 ------------------------
% 1.91/1.39 ---- Cleaned THF ---
% 1.91/1.39 thf(in_type,type,
% 1.91/1.39 in: $i > $i > $o ).
% 1.91/1.39
% 1.91/1.39 thf(exu_type,type,
% 1.91/1.39 exu: ( $i > $o ) > $o ).
% 1.91/1.39
% 1.91/1.39 thf(exu,definition,
% 1.91/1.39 ( exu
% 1.91/1.39 = ( ^ [Xphi: $i > $o] :
% 1.91/1.39 ? [Xx: $i] :
% 1.91/1.39 ( ( Xphi @ Xx )
% 1.91/1.39 & ! [Xy: $i] :
% 1.91/1.39 ( ( Xphi @ Xy )
% 1.91/1.39 => ( Xx = Xy ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setextAx_type,type,
% 1.91/1.39 setextAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setextAx,definition,
% 1.91/1.39 ( setextAx
% 1.91/1.39 = ( ! [A: $i,B: $i] :
% 1.91/1.39 ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 <=> ( in @ Xx @ B ) )
% 1.91/1.39 => ( A = B ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(emptyset_type,type,
% 1.91/1.39 emptyset: $i ).
% 1.91/1.39
% 1.91/1.39 thf(emptysetAx_type,type,
% 1.91/1.39 emptysetAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(emptysetAx,definition,
% 1.91/1.39 ( emptysetAx
% 1.91/1.39 = ( ! [Xx: $i] :
% 1.91/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoin_type,type,
% 1.91/1.39 setadjoin: $i > $i > $i ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinAx_type,type,
% 1.91/1.39 setadjoinAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinAx,definition,
% 1.91/1.39 ( setadjoinAx
% 1.91/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.91/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.91/1.39 <=> ( ( Xy = Xx )
% 1.91/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(powerset_type,type,
% 1.91/1.39 powerset: $i > $i ).
% 1.91/1.39
% 1.91/1.39 thf(powersetAx_type,type,
% 1.91/1.39 powersetAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(powersetAx,definition,
% 1.91/1.39 ( powersetAx
% 1.91/1.39 = ( ! [A: $i,B: $i] :
% 1.91/1.39 ( ( in @ B @ ( powerset @ A ) )
% 1.91/1.39 <=> ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ B )
% 1.91/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setunion_type,type,
% 1.91/1.39 setunion: $i > $i ).
% 1.91/1.39
% 1.91/1.39 thf(setunionAx_type,type,
% 1.91/1.39 setunionAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setunionAx,definition,
% 1.91/1.39 ( setunionAx
% 1.91/1.39 = ( ! [A: $i,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 1.91/1.39 <=> ? [B: $i] :
% 1.91/1.39 ( ( in @ Xx @ B )
% 1.91/1.39 & ( in @ B @ A ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(omega_type,type,
% 1.91/1.39 omega: $i ).
% 1.91/1.39
% 1.91/1.39 thf(omega0Ax_type,type,
% 1.91/1.39 omega0Ax: $o ).
% 1.91/1.39
% 1.91/1.39 thf(omega0Ax,definition,
% 1.91/1.39 ( omega0Ax
% 1.91/1.39 = ( in @ emptyset @ omega ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(omegaSAx_type,type,
% 1.91/1.39 omegaSAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(omegaSAx,definition,
% 1.91/1.39 ( omegaSAx
% 1.91/1.39 = ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ omega )
% 1.91/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(omegaIndAx_type,type,
% 1.91/1.39 omegaIndAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(omegaIndAx,definition,
% 1.91/1.39 ( omegaIndAx
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ( ( ( in @ emptyset @ A )
% 1.91/1.39 & ! [Xx: $i] :
% 1.91/1.39 ( ( ( in @ Xx @ omega )
% 1.91/1.39 & ( in @ Xx @ A ) )
% 1.91/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.91/1.39 => ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ omega )
% 1.91/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(replAx_type,type,
% 1.91/1.39 replAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(replAx,definition,
% 1.91/1.39 ( replAx
% 1.91/1.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.91/1.39 ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( exu
% 1.91/1.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.91/1.39 => ? [B: $i] :
% 1.91/1.39 ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ B )
% 1.91/1.39 <=> ? [Xy: $i] :
% 1.91/1.39 ( ( in @ Xy @ A )
% 1.91/1.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(foundationAx_type,type,
% 1.91/1.39 foundationAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(foundationAx,definition,
% 1.91/1.39 ( foundationAx
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.91/1.39 => ? [B: $i] :
% 1.91/1.39 ( ( in @ B @ A )
% 1.91/1.39 & ~ ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ B )
% 1.91/1.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(wellorderingAx_type,type,
% 1.91/1.39 wellorderingAx: $o ).
% 1.91/1.39
% 1.91/1.39 thf(wellorderingAx,definition,
% 1.91/1.39 ( wellorderingAx
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ? [B: $i] :
% 1.91/1.39 ( ! [C: $i] :
% 1.91/1.39 ( ( in @ C @ B )
% 1.91/1.39 => ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ C )
% 1.91/1.39 => ( in @ Xx @ A ) ) )
% 1.91/1.39 & ! [Xx: $i,Xy: $i] :
% 1.91/1.39 ( ( ( in @ Xx @ A )
% 1.91/1.39 & ( in @ Xy @ A ) )
% 1.91/1.39 => ( ! [C: $i] :
% 1.91/1.39 ( ( in @ C @ B )
% 1.91/1.39 => ( ( in @ Xx @ C )
% 1.91/1.39 <=> ( in @ Xy @ C ) ) )
% 1.91/1.39 => ( Xx = Xy ) ) )
% 1.91/1.39 & ! [C: $i,D: $i] :
% 1.91/1.39 ( ( ( in @ C @ B )
% 1.91/1.39 & ( in @ D @ B ) )
% 1.91/1.39 => ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ C )
% 1.91/1.39 => ( in @ Xx @ D ) )
% 1.91/1.39 | ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ D )
% 1.91/1.39 => ( in @ Xx @ C ) ) ) )
% 1.91/1.39 & ! [C: $i] :
% 1.91/1.39 ( ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ C )
% 1.91/1.39 => ( in @ Xx @ A ) )
% 1.91/1.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.91/1.39 => ? [D: $i,Xx: $i] :
% 1.91/1.39 ( ( in @ D @ B )
% 1.91/1.39 & ( in @ Xx @ C )
% 1.91/1.39 & ~ ? [Xy: $i] :
% 1.91/1.39 ( ( in @ Xy @ D )
% 1.91/1.39 & ( in @ Xy @ C ) )
% 1.91/1.39 & ! [E: $i] :
% 1.91/1.39 ( ( in @ E @ B )
% 1.91/1.39 => ( ! [Xy: $i] :
% 1.91/1.39 ( ( in @ Xy @ E )
% 1.91/1.39 => ( in @ Xy @ D ) )
% 1.91/1.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(descr_type,type,
% 1.91/1.39 descr: ( $i > $o ) > $i ).
% 1.91/1.39
% 1.91/1.39 thf(descrp_type,type,
% 1.91/1.39 descrp: $o ).
% 1.91/1.39
% 1.91/1.39 thf(descrp,definition,
% 1.91/1.39 ( descrp
% 1.91/1.39 = ( ! [Xphi: $i > $o] :
% 1.91/1.39 ( ( exu
% 1.91/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.39 => ( Xphi
% 1.91/1.39 @ ( descr
% 1.91/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(dsetconstr_type,type,
% 1.91/1.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.91/1.39
% 1.91/1.39 thf(dsetconstrI_type,type,
% 1.91/1.39 dsetconstrI: $o ).
% 1.91/1.39
% 1.91/1.39 thf(dsetconstrI,definition,
% 1.91/1.39 ( dsetconstrI
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( ( Xphi @ Xx )
% 1.91/1.39 => ( in @ Xx
% 1.91/1.39 @ ( dsetconstr @ A
% 1.91/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(dsetconstrEL_type,type,
% 1.91/1.39 dsetconstrEL: $o ).
% 1.91/1.39
% 1.91/1.39 thf(dsetconstrEL,definition,
% 1.91/1.39 ( dsetconstrEL
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx
% 1.91/1.39 @ ( dsetconstr @ A
% 1.91/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.91/1.39 => ( in @ Xx @ A ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(dsetconstrER_type,type,
% 1.91/1.39 dsetconstrER: $o ).
% 1.91/1.39
% 1.91/1.39 thf(dsetconstrER,definition,
% 1.91/1.39 ( dsetconstrER
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx
% 1.91/1.39 @ ( dsetconstr @ A
% 1.91/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.91/1.39 => ( Xphi @ Xx ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(exuE1_type,type,
% 1.91/1.39 exuE1: $o ).
% 1.91/1.39
% 1.91/1.39 thf(exuE1,definition,
% 1.91/1.39 ( exuE1
% 1.91/1.39 = ( ! [Xphi: $i > $o] :
% 1.91/1.39 ( ( exu
% 1.91/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.39 => ? [Xx: $i] :
% 1.91/1.39 ( ( Xphi @ Xx )
% 1.91/1.39 & ! [Xy: $i] :
% 1.91/1.39 ( ( Xphi @ Xy )
% 1.91/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(prop2set_type,type,
% 1.91/1.39 prop2set: $o > $i ).
% 1.91/1.39
% 1.91/1.39 thf(prop2setE_type,type,
% 1.91/1.39 prop2setE: $o ).
% 1.91/1.39
% 1.91/1.39 thf(prop2setE,definition,
% 1.91/1.39 ( prop2setE
% 1.91/1.39 = ( ! [Xphi: $o,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.91/1.39 => Xphi ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(emptysetE_type,type,
% 1.91/1.39 emptysetE: $o ).
% 1.91/1.39
% 1.91/1.39 thf(emptysetE,definition,
% 1.91/1.39 ( emptysetE
% 1.91/1.39 = ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ emptyset )
% 1.91/1.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(emptysetimpfalse_type,type,
% 1.91/1.39 emptysetimpfalse: $o ).
% 1.91/1.39
% 1.91/1.39 thf(emptysetimpfalse,definition,
% 1.91/1.39 ( emptysetimpfalse
% 1.91/1.39 = ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ emptyset )
% 1.91/1.39 => $false ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(notinemptyset_type,type,
% 1.91/1.39 notinemptyset: $o ).
% 1.91/1.39
% 1.91/1.39 thf(notinemptyset,definition,
% 1.91/1.39 ( notinemptyset
% 1.91/1.39 = ( ! [Xx: $i] :
% 1.91/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(exuE3e_type,type,
% 1.91/1.39 exuE3e: $o ).
% 1.91/1.39
% 1.91/1.39 thf(exuE3e,definition,
% 1.91/1.39 ( exuE3e
% 1.91/1.39 = ( ! [Xphi: $i > $o] :
% 1.91/1.39 ( ( exu
% 1.91/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setext_type,type,
% 1.91/1.39 setext: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setext,definition,
% 1.91/1.39 ( setext
% 1.91/1.39 = ( ! [A: $i,B: $i] :
% 1.91/1.39 ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( in @ Xx @ B ) )
% 1.91/1.39 => ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ B )
% 1.91/1.39 => ( in @ Xx @ A ) )
% 1.91/1.39 => ( A = B ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(emptyI_type,type,
% 1.91/1.39 emptyI: $o ).
% 1.91/1.39
% 1.91/1.39 thf(emptyI,definition,
% 1.91/1.39 ( emptyI
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ( ! [Xx: $i] :
% 1.91/1.39 ~ ( in @ Xx @ A )
% 1.91/1.39 => ( A = emptyset ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(noeltsimpempty_type,type,
% 1.91/1.39 noeltsimpempty: $o ).
% 1.91/1.39
% 1.91/1.39 thf(noeltsimpempty,definition,
% 1.91/1.39 ( noeltsimpempty
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ( ! [Xx: $i] :
% 1.91/1.39 ~ ( in @ Xx @ A )
% 1.91/1.39 => ( A = emptyset ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setbeta_type,type,
% 1.91/1.39 setbeta: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setbeta,definition,
% 1.91/1.39 ( setbeta
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( ( in @ Xx
% 1.91/1.39 @ ( dsetconstr @ A
% 1.91/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.91/1.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(nonempty_type,type,
% 1.91/1.39 nonempty: $i > $o ).
% 1.91/1.39
% 1.91/1.39 thf(nonempty,definition,
% 1.91/1.39 ( nonempty
% 1.91/1.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(nonemptyE1_type,type,
% 1.91/1.39 nonemptyE1: $o ).
% 1.91/1.39
% 1.91/1.39 thf(nonemptyE1,definition,
% 1.91/1.39 ( nonemptyE1
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ( ( nonempty @ A )
% 1.91/1.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(nonemptyI_type,type,
% 1.91/1.39 nonemptyI: $o ).
% 1.91/1.39
% 1.91/1.39 thf(nonemptyI,definition,
% 1.91/1.39 ( nonemptyI
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( ( Xphi @ Xx )
% 1.91/1.39 => ( nonempty
% 1.91/1.39 @ ( dsetconstr @ A
% 1.91/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(nonemptyI1_type,type,
% 1.91/1.39 nonemptyI1: $o ).
% 1.91/1.39
% 1.91/1.39 thf(nonemptyI1,definition,
% 1.91/1.39 ( nonemptyI1
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.91/1.39 => ( nonempty @ A ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinIL_type,type,
% 1.91/1.39 setadjoinIL: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinIL,definition,
% 1.91/1.39 ( setadjoinIL
% 1.91/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(emptyinunitempty_type,type,
% 1.91/1.39 emptyinunitempty: $o ).
% 1.91/1.39
% 1.91/1.39 thf(emptyinunitempty,definition,
% 1.91/1.39 ( emptyinunitempty
% 1.91/1.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinIR_type,type,
% 1.91/1.39 setadjoinIR: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinIR,definition,
% 1.91/1.39 ( setadjoinIR
% 1.91/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.91/1.39 ( ( in @ Xy @ A )
% 1.91/1.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinE_type,type,
% 1.91/1.39 setadjoinE: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinE,definition,
% 1.91/1.39 ( setadjoinE
% 1.91/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.91/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.91/1.39 => ! [Xphi: $o] :
% 1.91/1.39 ( ( ( Xy = Xx )
% 1.91/1.39 => Xphi )
% 1.91/1.39 => ( ( ( in @ Xy @ A )
% 1.91/1.39 => Xphi )
% 1.91/1.39 => Xphi ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinOr_type,type,
% 1.91/1.39 setadjoinOr: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setadjoinOr,definition,
% 1.91/1.39 ( setadjoinOr
% 1.91/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.91/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.91/1.39 => ( ( Xy = Xx )
% 1.91/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setoftrueEq_type,type,
% 1.91/1.39 setoftrueEq: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setoftrueEq,definition,
% 1.91/1.39 ( setoftrueEq
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ( ( dsetconstr @ A
% 1.91/1.39 @ ^ [Xx: $i] : $true )
% 1.91/1.39 = A ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(powersetI_type,type,
% 1.91/1.39 powersetI: $o ).
% 1.91/1.39
% 1.91/1.39 thf(powersetI,definition,
% 1.91/1.39 ( powersetI
% 1.91/1.39 = ( ! [A: $i,B: $i] :
% 1.91/1.39 ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ B )
% 1.91/1.39 => ( in @ Xx @ A ) )
% 1.91/1.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(emptyinPowerset_type,type,
% 1.91/1.39 emptyinPowerset: $o ).
% 1.91/1.39
% 1.91/1.39 thf(emptyinPowerset,definition,
% 1.91/1.39 ( emptyinPowerset
% 1.91/1.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(emptyInPowerset_type,type,
% 1.91/1.39 emptyInPowerset: $o ).
% 1.91/1.39
% 1.91/1.39 thf(emptyInPowerset,definition,
% 1.91/1.39 ( emptyInPowerset
% 1.91/1.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(powersetE_type,type,
% 1.91/1.39 powersetE: $o ).
% 1.91/1.39
% 1.91/1.39 thf(powersetE,definition,
% 1.91/1.39 ( powersetE
% 1.91/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.91/1.39 ( ( in @ B @ ( powerset @ A ) )
% 1.91/1.39 => ( ( in @ Xx @ B )
% 1.91/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setunionI_type,type,
% 1.91/1.39 setunionI: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setunionI,definition,
% 1.91/1.39 ( setunionI
% 1.91/1.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.91/1.39 ( ( in @ Xx @ B )
% 1.91/1.39 => ( ( in @ B @ A )
% 1.91/1.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(setunionE_type,type,
% 1.91/1.39 setunionE: $o ).
% 1.91/1.39
% 1.91/1.39 thf(setunionE,definition,
% 1.91/1.39 ( setunionE
% 1.91/1.39 = ( ! [A: $i,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 1.91/1.39 => ! [Xphi: $o] :
% 1.91/1.39 ( ! [B: $i] :
% 1.91/1.39 ( ( in @ Xx @ B )
% 1.91/1.39 => ( ( in @ B @ A )
% 1.91/1.39 => Xphi ) )
% 1.91/1.39 => Xphi ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(subPowSU_type,type,
% 1.91/1.39 subPowSU: $o ).
% 1.91/1.39
% 1.91/1.39 thf(subPowSU,definition,
% 1.91/1.39 ( subPowSU
% 1.91/1.39 = ( ! [A: $i,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(exuE2_type,type,
% 1.91/1.39 exuE2: $o ).
% 1.91/1.39
% 1.91/1.39 thf(exuE2,definition,
% 1.91/1.39 ( exuE2
% 1.91/1.39 = ( ! [Xphi: $i > $o] :
% 1.91/1.39 ( ( exu
% 1.91/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.39 => ? [Xx: $i] :
% 1.91/1.39 ! [Xy: $i] :
% 1.91/1.39 ( ( Xphi @ Xy )
% 1.91/1.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(nonemptyImpWitness_type,type,
% 1.91/1.39 nonemptyImpWitness: $o ).
% 1.91/1.39
% 1.91/1.39 thf(nonemptyImpWitness,definition,
% 1.91/1.39 ( nonemptyImpWitness
% 1.91/1.39 = ( ! [A: $i] :
% 1.91/1.39 ( ( nonempty @ A )
% 1.91/1.39 => ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 & $true ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(uniqinunit_type,type,
% 1.91/1.39 uniqinunit: $o ).
% 1.91/1.39
% 1.91/1.39 thf(uniqinunit,definition,
% 1.91/1.39 ( uniqinunit
% 1.91/1.39 = ( ! [Xx: $i,Xy: $i] :
% 1.91/1.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.91/1.39 => ( Xx = Xy ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(notinsingleton_type,type,
% 1.91/1.39 notinsingleton: $o ).
% 1.91/1.39
% 1.91/1.39 thf(notinsingleton,definition,
% 1.91/1.39 ( notinsingleton
% 1.91/1.39 = ( ! [Xx: $i,Xy: $i] :
% 1.91/1.39 ( ( Xx != Xy )
% 1.91/1.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(eqinunit_type,type,
% 1.91/1.39 eqinunit: $o ).
% 1.91/1.39
% 1.91/1.39 thf(eqinunit,definition,
% 1.91/1.39 ( eqinunit
% 1.91/1.39 = ( ! [Xx: $i,Xy: $i] :
% 1.91/1.39 ( ( Xx = Xy )
% 1.91/1.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(singletonsswitch_type,type,
% 1.91/1.39 singletonsswitch: $o ).
% 1.91/1.39
% 1.91/1.39 thf(singletonsswitch,definition,
% 1.91/1.39 ( singletonsswitch
% 1.91/1.39 = ( ! [Xx: $i,Xy: $i] :
% 1.91/1.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.91/1.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(upairsetE_type,type,
% 1.91/1.39 upairsetE: $o ).
% 1.91/1.39
% 1.91/1.39 thf(upairsetE,definition,
% 1.91/1.39 ( upairsetE
% 1.91/1.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.91/1.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.91/1.39 => ( ( Xz = Xx )
% 1.91/1.39 | ( Xz = Xy ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(upairsetIL_type,type,
% 1.91/1.39 upairsetIL: $o ).
% 1.91/1.39
% 1.91/1.39 thf(upairsetIL,definition,
% 1.91/1.39 ( upairsetIL
% 1.91/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(upairsetIR_type,type,
% 1.91/1.39 upairsetIR: $o ).
% 1.91/1.39
% 1.91/1.39 thf(upairsetIR,definition,
% 1.91/1.39 ( upairsetIR
% 1.91/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(emptyE1_type,type,
% 1.91/1.39 emptyE1: $o ).
% 1.91/1.39
% 1.91/1.39 thf(emptyE1,definition,
% 1.91/1.39 ( emptyE1
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 1.91/1.39 ( ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 & ( Xphi @ Xx ) )
% 1.91/1.39 => ( ( ( dsetconstr @ A
% 1.91/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.39 = emptyset )
% 1.91/1.39 => $false ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(vacuousDall_type,type,
% 1.91/1.39 vacuousDall: $o ).
% 1.91/1.39
% 1.91/1.39 thf(vacuousDall,definition,
% 1.91/1.39 ( vacuousDall
% 1.91/1.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ emptyset )
% 1.91/1.39 => ( Xphi @ Xx ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(quantDeMorgan1_type,type,
% 1.91/1.39 quantDeMorgan1: $o ).
% 1.91/1.39
% 1.91/1.39 thf(quantDeMorgan1,definition,
% 1.91/1.39 ( quantDeMorgan1
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 1.91/1.39 ( ~ ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( Xphi @ Xx ) )
% 1.91/1.39 => ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(quantDeMorgan2_type,type,
% 1.91/1.39 quantDeMorgan2: $o ).
% 1.91/1.39
% 1.91/1.39 thf(quantDeMorgan2,definition,
% 1.91/1.39 ( quantDeMorgan2
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 1.91/1.39 ( ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ~ ( Xphi @ Xx ) )
% 1.91/1.39 => ~ ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(quantDeMorgan3_type,type,
% 1.91/1.39 quantDeMorgan3: $o ).
% 1.91/1.39
% 1.91/1.39 thf(quantDeMorgan3,definition,
% 1.91/1.39 ( quantDeMorgan3
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 1.91/1.39 ( ~ ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 & ( Xphi @ Xx ) )
% 1.91/1.39 => ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(quantDeMorgan4_type,type,
% 1.91/1.39 quantDeMorgan4: $o ).
% 1.91/1.39
% 1.91/1.39 thf(quantDeMorgan4,definition,
% 1.91/1.39 ( quantDeMorgan4
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 1.91/1.39 ( ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 & ~ ( Xphi @ Xx ) )
% 1.91/1.39 => ~ ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(prop2setI_type,type,
% 1.91/1.39 prop2setI: $o ).
% 1.91/1.39
% 1.91/1.39 thf(prop2setI,definition,
% 1.91/1.39 ( prop2setI
% 1.91/1.39 = ( ! [Xphi: $o] :
% 1.91/1.39 ( Xphi
% 1.91/1.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(set2prop_type,type,
% 1.91/1.39 set2prop: $i > $o ).
% 1.91/1.39
% 1.91/1.39 thf(prop2set2propI_type,type,
% 1.91/1.39 prop2set2propI: $o ).
% 1.91/1.39
% 1.91/1.39 thf(prop2set2propI,definition,
% 1.91/1.39 ( prop2set2propI
% 1.91/1.39 = ( ! [Xphi: $o] :
% 1.91/1.39 ( Xphi
% 1.91/1.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(notdexE_type,type,
% 1.91/1.39 notdexE: $o ).
% 1.91/1.39
% 1.91/1.39 thf(notdexE,definition,
% 1.91/1.39 ( notdexE
% 1.91/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 1.91/1.39 ( ~ ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 & ( Xphi @ Xx ) )
% 1.91/1.39 => ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 1.91/1.39
% 1.91/1.39 thf(notdallE,conjecture,
% 1.91/1.39 ( setextAx
% 1.91/1.39 => ( emptysetAx
% 1.91/1.39 => ( setadjoinAx
% 1.91/1.39 => ( powersetAx
% 1.91/1.39 => ( setunionAx
% 1.91/1.39 => ( omega0Ax
% 1.91/1.39 => ( omegaSAx
% 1.91/1.39 => ( omegaIndAx
% 1.91/1.39 => ( replAx
% 1.91/1.39 => ( foundationAx
% 1.91/1.39 => ( wellorderingAx
% 1.91/1.39 => ( descrp
% 1.91/1.39 => ( dsetconstrI
% 1.91/1.39 => ( dsetconstrEL
% 1.91/1.39 => ( dsetconstrER
% 1.91/1.39 => ( exuE1
% 1.91/1.39 => ( prop2setE
% 1.91/1.39 => ( emptysetE
% 1.91/1.39 => ( emptysetimpfalse
% 1.91/1.39 => ( notinemptyset
% 1.91/1.39 => ( exuE3e
% 1.91/1.39 => ( setext
% 1.91/1.39 => ( emptyI
% 1.91/1.39 => ( noeltsimpempty
% 1.91/1.39 => ( setbeta
% 1.91/1.39 => ( nonemptyE1
% 1.91/1.39 => ( nonemptyI
% 1.91/1.39 => ( nonemptyI1
% 1.91/1.39 => ( setadjoinIL
% 1.91/1.39 => ( emptyinunitempty
% 1.91/1.39 => ( setadjoinIR
% 1.91/1.39 => ( setadjoinE
% 1.91/1.39 => ( setadjoinOr
% 1.91/1.39 => ( setoftrueEq
% 1.91/1.39 => ( powersetI
% 1.91/1.39 => ( emptyinPowerset
% 1.91/1.39 => ( emptyInPowerset
% 1.91/1.39 => ( powersetE
% 1.91/1.39 => ( setunionI
% 1.91/1.39 => ( setunionE
% 1.91/1.39 => ( subPowSU
% 1.91/1.39 => ( exuE2
% 1.91/1.39 => ( nonemptyImpWitness
% 1.91/1.39 => ( uniqinunit
% 1.91/1.39 => ( notinsingleton
% 1.91/1.39 => ( eqinunit
% 1.91/1.39 => ( singletonsswitch
% 1.91/1.39 => ( upairsetE
% 1.91/1.39 => ( upairsetIL
% 1.91/1.39 => ( upairsetIR
% 1.91/1.39 => ( emptyE1
% 1.91/1.39 => ( vacuousDall
% 1.91/1.39 => ( quantDeMorgan1
% 1.91/1.39 => ( quantDeMorgan2
% 1.91/1.39 => ( quantDeMorgan3
% 1.91/1.39 => ( quantDeMorgan4
% 1.91/1.39 => ( prop2setI
% 1.91/1.39 => ( prop2set2propI
% 1.91/1.39 => ( notdexE
% 1.91/1.39 => ! [A: $i,Xphi: $i > $o] :
% 1.91/1.39 ( ~ ! [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 => ( Xphi @ Xx ) )
% 1.91/1.39 => ? [Xx: $i] :
% 1.91/1.39 ( ( in @ Xx @ A )
% 1.91/1.39 & ~ ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.91/1.39 ------------------------
% 2.13/1.41 % (17742)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_17621 for (2999ds/2Mi)
% 2.13/1.41 % (17744)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17621 for (2999ds/18Mi)
% 2.13/1.41 % (17742)Instruction limit reached!
% 2.13/1.41 % (17742)------------------------------
% 2.13/1.41 % (17742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.41 % (17742)Termination reason: Unknown
% 2.13/1.41 % (17742)Termination phase: shuffling
% 2.13/1.41
% 2.13/1.41 % (17742)Memory used [KB]: 1151
% 2.13/1.41 % (17742)Time elapsed: 0.002 s
% 2.13/1.41 % (17742)Instructions burned: 2 (million)
% 2.13/1.41 % (17742)------------------------------
% 2.13/1.41 % (17742)------------------------------
% 2.13/1.41 % (17743)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_17621 for (2999ds/275Mi)
% 2.13/1.41 % (17744)Instruction limit reached!
% 2.13/1.41 % (17744)------------------------------
% 2.13/1.41 % (17744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.41 % (17744)Termination reason: Unknown
% 2.13/1.41 % (17744)Termination phase: Preprocessing 3
% 2.13/1.41
% 2.13/1.41 % (17744)Memory used [KB]: 1663
% 2.13/1.41 % (17744)Time elapsed: 0.007 s
% 2.13/1.41 % (17744)Instructions burned: 20 (million)
% 2.13/1.41 % (17744)------------------------------
% 2.13/1.41 % (17744)------------------------------
% 2.13/1.42 % (17739)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_17621 for (2999ds/4Mi)
% 2.13/1.42 % (17741)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17621 for (2999ds/2Mi)
% 2.13/1.42 % (17738)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17621 for (2999ds/183Mi)
% 2.13/1.42 % (17740)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_17621 for (2999ds/27Mi)
% 2.13/1.42 % (17741)Instruction limit reached!
% 2.13/1.42 % (17741)------------------------------
% 2.13/1.42 % (17741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.42 % (17741)Termination reason: Unknown
% 2.13/1.42 % (17741)Termination phase: shuffling
% 2.13/1.42
% 2.13/1.42 % (17741)Memory used [KB]: 1151
% 2.13/1.42 % (17741)Time elapsed: 0.004 s
% 2.13/1.42 % (17741)Instructions burned: 3 (million)
% 2.13/1.42 % (17741)------------------------------
% 2.13/1.42 % (17741)------------------------------
% 2.13/1.42 % (17739)Instruction limit reached!
% 2.13/1.42 % (17739)------------------------------
% 2.13/1.42 % (17739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.42 % (17739)Termination reason: Unknown
% 2.13/1.42 % (17739)Termination phase: shuffling
% 2.13/1.42
% 2.13/1.42 % (17739)Memory used [KB]: 1151
% 2.13/1.42 % (17739)Time elapsed: 0.005 s
% 2.13/1.42 % (17739)Instructions burned: 5 (million)
% 2.13/1.42 % (17739)------------------------------
% 2.13/1.42 % (17739)------------------------------
% 2.13/1.42 % (17745)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17621 for (2999ds/3Mi)
% 2.13/1.42 % (17745)Instruction limit reached!
% 2.13/1.42 % (17745)------------------------------
% 2.13/1.42 % (17745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.42 % (17745)Termination reason: Unknown
% 2.13/1.42 % (17745)Termination phase: shuffling
% 2.13/1.42
% 2.13/1.42 % (17745)Memory used [KB]: 1151
% 2.13/1.42 % (17745)Time elapsed: 0.002 s
% 2.13/1.42 % (17745)Instructions burned: 3 (million)
% 2.13/1.42 % (17745)------------------------------
% 2.13/1.42 % (17745)------------------------------
% 2.13/1.42 % (17746)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_17621 for (2999ds/37Mi)
% 2.13/1.43 % (17740)Instruction limit reached!
% 2.13/1.43 % (17740)------------------------------
% 2.13/1.43 % (17740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.43 % (17740)Termination reason: Unknown
% 2.13/1.43 % (17740)Termination phase: Property scanning
% 2.13/1.43
% 2.13/1.43 % (17740)Memory used [KB]: 1407
% 2.13/1.43 % (17740)Time elapsed: 0.016 s
% 2.13/1.43 % (17740)Instructions burned: 28 (million)
% 2.13/1.43 % (17740)------------------------------
% 2.13/1.43 % (17740)------------------------------
% 2.13/1.43 % (17749)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_17621 for (2999ds/1041Mi)
% 2.13/1.43 % (17746)Instruction limit reached!
% 2.13/1.43 % (17746)------------------------------
% 2.13/1.43 % (17746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.43 % (17746)Termination reason: Unknown
% 2.13/1.43 % (17746)Termination phase: Saturation
% 2.13/1.43
% 2.13/1.43 % (17746)Memory used [KB]: 5884
% 2.13/1.43 % (17746)Time elapsed: 0.011 s
% 2.13/1.43 % (17746)Instructions burned: 39 (million)
% 2.13/1.43 % (17746)------------------------------
% 2.13/1.43 % (17746)------------------------------
% 2.13/1.43 % (17747)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_17621 for (2999ds/15Mi)
% 2.13/1.44 % (17748)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_17621 for (2999ds/3Mi)
% 2.13/1.44 % (17748)Instruction limit reached!
% 2.13/1.44 % (17748)------------------------------
% 2.13/1.44 % (17748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.44 % (17748)Termination reason: Unknown
% 2.13/1.44 % (17748)Termination phase: shuffling
% 2.13/1.44
% 2.13/1.44 % (17748)Memory used [KB]: 1151
% 2.13/1.44 % (17748)Time elapsed: 0.004 s
% 2.13/1.44 % (17748)Instructions burned: 4 (million)
% 2.13/1.44 % (17748)------------------------------
% 2.13/1.44 % (17748)------------------------------
% 2.13/1.44 % (17743)First to succeed.
% 2.13/1.44 % (17743)Refutation found. Thanks to Tanya!
% 2.13/1.44 % SZS status Theorem for DTF2THF_17621
% 2.13/1.44 % SZS output start Proof for DTF2THF_17621
% 2.13/1.44 thf(func_def_0, type, in: $i > $i > $o).
% 2.13/1.44 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.13/1.44 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.13/1.44 thf(func_def_8, type, powerset: $i > $i).
% 2.13/1.44 thf(func_def_10, type, setunion: $i > $i).
% 2.13/1.44 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.13/1.44 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.13/1.44 thf(func_def_26, type, prop2set: $o > $i).
% 2.13/1.44 thf(func_def_36, type, nonempty: $i > $o).
% 2.13/1.44 thf(func_def_69, type, set2prop: $i > $o).
% 2.13/1.44 thf(func_def_85, type, sP1: $i > $i > $o).
% 2.13/1.44 thf(func_def_86, type, sP2: $i > $o).
% 2.13/1.44 thf(func_def_87, type, sP3: $i > $i > $o).
% 2.13/1.44 thf(func_def_88, type, sP4: $i > $i > $o).
% 2.13/1.44 thf(func_def_92, type, sK8: $i > $i).
% 2.13/1.44 thf(func_def_100, type, sK16: $i > $i > $i).
% 2.13/1.44 thf(func_def_101, type, sK17: $i > $i > $i).
% 2.13/1.44 thf(func_def_103, type, sK19: $i > $i).
% 2.13/1.44 thf(func_def_105, type, sK21: $i > $o).
% 2.13/1.44 thf(func_def_107, type, sK23: ($i > $o) > $i > $i).
% 2.13/1.44 thf(func_def_113, type, sK29: $i > $o).
% 2.13/1.44 thf(func_def_118, type, sK34: $i > $i > $i).
% 2.13/1.44 thf(func_def_122, type, sK38: $i > $o).
% 2.13/1.44 thf(func_def_123, type, sK39: $i > $i).
% 2.13/1.44 thf(func_def_124, type, sK40: ($i > $o) > $i).
% 2.13/1.44 thf(func_def_126, type, sK42: $i > $o).
% 2.13/1.44 thf(func_def_127, type, sK43: $i > $i).
% 2.13/1.44 thf(func_def_128, type, sK44: ($i > $o) > $i).
% 2.13/1.44 thf(func_def_129, type, sK45: $i > $i).
% 2.13/1.44 thf(func_def_131, type, sK47: $i > $i).
% 2.13/1.44 thf(func_def_135, type, sK51: $i > $i > $i).
% 2.13/1.44 thf(func_def_139, type, sK55: $i > $i > $o).
% 2.13/1.44 thf(func_def_141, type, sK57: $i > $i).
% 2.13/1.44 thf(func_def_142, type, sK58: $i > $i).
% 2.13/1.44 thf(func_def_143, type, sK59: $i > ($i > $i > $o) > $i).
% 2.13/1.44 thf(func_def_144, type, sK60: $i > ($i > $i > $o) > $i).
% 2.13/1.44 thf(func_def_145, type, sK61: $i > $i > ($i > $i > $o) > $i).
% 2.13/1.44 thf(func_def_147, type, sK63: $i > $o).
% 2.13/1.44 thf(func_def_149, type, sK65: ($i > $o) > $i > $i).
% 2.13/1.44 thf(func_def_152, type, sK68: $i > $o).
% 2.13/1.44 thf(func_def_158, type, sK74: $i > $i > $i).
% 2.13/1.44 thf(func_def_167, type, sK83: $i > $i).
% 2.13/1.44 thf(func_def_172, type, sK88: $i > $o).
% 2.13/1.44 thf(func_def_175, type, sK91: $i > $i > $i).
% 2.13/1.44 thf(func_def_176, type, sK92: $i > $o).
% 2.13/1.44 thf(func_def_179, type, sK95: $i > $i).
% 2.13/1.44 thf(func_def_187, type, sK103: $i > ($i > $o) > $i).
% 2.13/1.44 thf(func_def_188, type, sK104: $i > $o).
% 2.13/1.44 thf(func_def_197, type, sK113: $o > $i > $i > $i).
% 2.13/1.44 thf(func_def_199, type, sK115: $i > $o).
% 2.13/1.44 thf(func_def_201, type, sK117: ($i > $o) > $i).
% 2.13/1.44 thf(func_def_202, type, sK118: $i > $o).
% 2.13/1.44 thf(func_def_203, type, sK119: ($i > $o) > $i > $i).
% 2.13/1.44 thf(func_def_205, type, sK121: $i > $o).
% 2.13/1.44 thf(func_def_208, type, sK124: $i > $o).
% 2.13/1.44 thf(func_def_210, type, sK126: ($i > $o) > $i > $i).
% 2.13/1.44 thf(func_def_213, type, sK129: $i > $o).
% 2.13/1.44 thf(func_def_221, type, sK137: $i > $i).
% 2.13/1.44 thf(func_def_231, type, sK147: $i > $o).
% 2.13/1.44 thf(func_def_235, type, sK151: $i > $o).
% 2.13/1.44 thf(func_def_236, type, sK152: $i > $i > $i).
% 2.13/1.44 thf(func_def_237, type, sK153: $i > $i > $i).
% 2.13/1.44 thf(func_def_238, type, sK154: $i > $i > $i).
% 2.13/1.44 thf(func_def_239, type, sK155: $i > $i > $i).
% 2.13/1.44 thf(func_def_240, type, sK156: $i > $i > $i > $i).
% 2.13/1.44 thf(func_def_241, type, sK157: $i > $i).
% 2.13/1.44 thf(func_def_242, type, sK158: $i > $i).
% 2.13/1.44 thf(func_def_243, type, sK159: $i > $i).
% 2.13/1.44 thf(func_def_244, type, sK160: $i > $i).
% 2.13/1.44 thf(func_def_245, type, sK161: $i > $i > $i > $i).
% 2.13/1.44 thf(func_def_246, type, sK162: $i > $i > $i > $i).
% 2.13/1.44 thf(func_def_247, type, sK163: $i > $i > $i).
% 2.13/1.44 thf(func_def_248, type, sK164: $i > $i > $i).
% 2.13/1.44 thf(func_def_249, type, sK165: $i > $i > $i).
% 2.13/1.44 thf(func_def_250, type, sK166: $i > $i).
% 2.13/1.44 thf(func_def_251, type, sK167: $i > $i > $i).
% 2.13/1.44 thf(func_def_253, type, sK169: $i > $i).
% 2.13/1.44 thf(func_def_254, type, sK170: $i > $i).
% 2.13/1.44 thf(func_def_256, type, ph172: !>[X0: $tType]:(X0)).
% 2.13/1.44 thf(f1299,plain,(
% 2.13/1.44 $false),
% 2.13/1.44 inference(subsumption_resolution,[status(thm)],[f1271,f623])).
% 2.13/1.44 thf(f623,plain,(
% 2.13/1.44 ($true != (sK29 @ sK31))),
% 2.13/1.44 inference(cnf_transformation,[status(thm)],[f314])).
% 2.13/1.44 thf(f314,plain,(
% 2.13/1.44 (setoftrueEq = $true) & (quantDeMorgan2 = $true) & (setadjoinIL = $true) & (emptysetimpfalse = $true) & (vacuousDall = $true) & (upairsetE = $true) & (powersetE = $true) & (dsetconstrEL = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (nonemptyE1 = $true) & (exuE1 = $true) & (setunionI = $true) & (setadjoinIR = $true) & (prop2setE = $true) & (setadjoinE = $true) & (foundationAx = $true) & (emptysetAx = $true) & (emptyE1 = $true) & (upairsetIL = $true) & (setunionAx = $true) & (setadjoinOr = $true) & (setext = $true) & (exuE2 = $true) & (emptyinPowerset = $true) & (quantDeMorgan4 = $true) & (dsetconstrER = $true) & (eqinunit = $true) & (quantDeMorgan3 = $true) & (nonemptyImpWitness = $true) & (descrp = $true) & (omega0Ax = $true) & (noeltsimpempty = $true) & (quantDeMorgan1 = $true) & (replAx = $true) & (setextAx = $true) & (emptyI = $true) & (nonemptyI = $true) & ((($true = (in @ sK31 @ sK30)) & ($true != (sK29 @ sK31))) & ! [X3 : $i] : (($true != (in @ X3 @ sK30)) | ($true = (sK29 @ X3)))) & (nonemptyI1 = $true) & (prop2setI = $true) & (setbeta = $true) & (notdexE = $true) & (setunionE = $true) & (omegaSAx = $true) & (emptysetE = $true) & (dsetconstrI = $true) & (omegaIndAx = $true) & (subPowSU = $true) & (powersetAx = $true) & (powersetI = $true) & (emptyInPowerset = $true) & (exuE3e = $true) & (singletonsswitch = $true) & (uniqinunit = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (upairsetIR = $true) & (notinsingleton = $true) & (prop2set2propI = $true)),
% 2.13/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f222,f313,f312])).
% 2.13/1.44 thf(f312,plain,(
% 2.13/1.44 ? [X0 : $i > $o,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ((X0 @ X2) != $true)) & ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (X0 @ X3)))) => (? [X2 : $i] : (($true = (in @ X2 @ sK30)) & ($true != (sK29 @ X2))) & ! [X3 : $i] : (($true != (in @ X3 @ sK30)) | ($true = (sK29 @ X3))))),
% 2.13/1.44 introduced(definition,[],[choice_axiom])).
% 2.13/1.44 thf(f313,plain,(
% 2.13/1.44 ? [X2 : $i] : (($true = (in @ X2 @ sK30)) & ($true != (sK29 @ X2))) => (($true = (in @ sK31 @ sK30)) & ($true != (sK29 @ sK31)))),
% 2.13/1.44 introduced(definition,[],[choice_axiom])).
% 2.13/1.44 thf(f222,plain,(
% 2.13/1.44 (setoftrueEq = $true) & (quantDeMorgan2 = $true) & (setadjoinIL = $true) & (emptysetimpfalse = $true) & (vacuousDall = $true) & (upairsetE = $true) & (powersetE = $true) & (dsetconstrEL = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (nonemptyE1 = $true) & (exuE1 = $true) & (setunionI = $true) & (setadjoinIR = $true) & (prop2setE = $true) & (setadjoinE = $true) & (foundationAx = $true) & (emptysetAx = $true) & (emptyE1 = $true) & (upairsetIL = $true) & (setunionAx = $true) & (setadjoinOr = $true) & (setext = $true) & (exuE2 = $true) & (emptyinPowerset = $true) & (quantDeMorgan4 = $true) & (dsetconstrER = $true) & (eqinunit = $true) & (quantDeMorgan3 = $true) & (nonemptyImpWitness = $true) & (descrp = $true) & (omega0Ax = $true) & (noeltsimpempty = $true) & (quantDeMorgan1 = $true) & (replAx = $true) & (setextAx = $true) & (emptyI = $true) & (nonemptyI = $true) & ? [X0 : $i > $o,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ((X0 @ X2) != $true)) & ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (X0 @ X3)))) & (nonemptyI1 = $true) & (prop2setI = $true) & (setbeta = $true) & (notdexE = $true) & (setunionE = $true) & (omegaSAx = $true) & (emptysetE = $true) & (dsetconstrI = $true) & (omegaIndAx = $true) & (subPowSU = $true) & (powersetAx = $true) & (powersetI = $true) & (emptyInPowerset = $true) & (exuE3e = $true) & (singletonsswitch = $true) & (uniqinunit = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (upairsetIR = $true) & (notinsingleton = $true) & (prop2set2propI = $true)),
% 2.13/1.44 inference(flattening,[status(thm)],[f221])).
% 2.13/1.44 thf(f221,plain,(
% 2.13/1.44 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i > $o,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ((X0 @ X2) != $true)) & ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (X0 @ X3)))) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.13/1.44 inference(ennf_transformation,[status(thm)],[f185])).
% 2.13/1.44 thf(f185,plain,(
% 2.13/1.44 ~((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) => ! [X0 : $i > $o,X1 : $i] : (~! [X2 : $i] : (($true = (in @ X2 @ X1)) => ((X0 @ X2) = $true)) => ? [X3 : $i] : (($true != (X0 @ X3)) & ($true = (in @ X3 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.44 inference(flattening,[status(thm)],[f110])).
% 2.13/1.44 thf(f110,plain,(
% 2.13/1.44 ~((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) => ! [X0 : $i > $o,X1 : $i] : (~! [X2 : $i] : (($true = (in @ X2 @ X1)) => ((X0 @ X2) = $true)) => ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ~($true = (X0 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.44 inference(fool_elimination,[status(thm)],[f109])).
% 2.13/1.44 thf(f109,plain,(
% 2.13/1.44 ~(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 => ! [X0 : $i > $o,X1 : $i] : (~! [X2 : $i] : ((in @ X2 @ X1) => (X0 @ X2)) => ? [X3 : $i] : ((in @ X3 @ X1) & ~(X0 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.44 inference(rectify,[status(thm)],[f63])).
% 2.13/1.44 thf(f63,negated_conjecture,(
% 2.13/1.44 ~(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 => ! [X0 : $i > $o,X3 : $i] : (~! [X1 : $i] : ((in @ X1 @ X3) => (X0 @ X1)) => ? [X1 : $i] : ((in @ X1 @ X3) & ~(X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.44 inference(negated_conjecture,[status(cth)],[f62])).
% 2.13/1.44 thf(f62,conjecture,(
% 2.13/1.44 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 => ! [X0 : $i > $o,X3 : $i] : (~! [X1 : $i] : ((in @ X1 @ X3) => (X0 @ X1)) => ? [X1 : $i] : ((in @ X1 @ X3) & ~(X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.44 file('/export/starexec/sandbox2/tmp/tmp.lFFNRSEeHn/DTF2THF_17621.p',notdallE)).
% 2.13/1.44 thf(f1271,plain,(
% 2.13/1.44 ($true = (sK29 @ sK31))),
% 2.13/1.44 inference(trivial_inequality_removal,[status(thm)],[f1260])).
% 2.13/1.44 thf(f1260,plain,(
% 2.13/1.44 ($true != $true) | ($true = (sK29 @ sK31))),
% 2.13/1.44 inference(superposition,[status(thm)],[f622,f624])).
% 2.13/1.44 thf(f624,plain,(
% 2.13/1.44 ($true = (in @ sK31 @ sK30))),
% 2.13/1.44 inference(cnf_transformation,[status(thm)],[f314])).
% 2.13/1.44 thf(f622,plain,(
% 2.13/1.44 ( ! [X3 : $i] : (($true != (in @ X3 @ sK30)) | ($true = (sK29 @ X3))) )),
% 2.13/1.44 inference(cnf_transformation,[status(thm)],[f314])).
% 2.13/1.44 % SZS output end Proof for DTF2THF_17621
% 2.13/1.44 % (17743)------------------------------
% 2.13/1.44 % (17743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.44 % (17743)Termination reason: Refutation
% 2.13/1.44
% 2.13/1.44 % (17743)Memory used [KB]: 6652
% 2.13/1.44 % (17743)Time elapsed: 0.032 s
% 2.13/1.44 % (17743)Instructions burned: 89 (million)
% 2.13/1.44 % (17743)------------------------------
% 2.13/1.44 % (17743)------------------------------
% 2.13/1.44 % (17737)Success in time 0.036 s
%------------------------------------------------------------------------------