%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU518^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 09:35:02 AM UTC 2026
% Result : Theorem 2.10s 1.70s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 959 ( 261 equ; 0 cnn)
% Maximal formula atoms : 37 ( 28 avg)
% Number of connectives : 702 ( 65 ~; 56 |; 130 &; 294 @)
% ( 6 <=>; 151 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 99 usr; 41 con; 0-3 aty)
% Number of variables : 74 ( 0 ^; 54 !; 20 ?; 74 :)
% 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_58,type,
sP0: $i > $i > $o ).
thf(func_def_59,type,
sP1: $i > $o ).
thf(func_def_60,type,
sP2: $i > $i > $o ).
thf(func_def_61,type,
sP3: $i > $i > $o ).
thf(func_def_64,type,
sK6: $i > $i ).
thf(func_def_65,type,
sK7: $i > $i ).
thf(func_def_68,type,
sK10: $i > $i ).
thf(func_def_79,type,
sK21: $i > $i ).
thf(func_def_82,type,
sK24: $i > $i ).
thf(func_def_83,type,
sK25: $i > $i > $i ).
thf(func_def_84,type,
sK26: $i > $i > $i ).
thf(func_def_87,type,
sK29: $i > $i > $i ).
thf(func_def_92,type,
sK34: $i > $i > $i ).
thf(func_def_93,type,
sK35: $i > $i > $i ).
thf(func_def_94,type,
sK36: $i > $i > $i ).
thf(func_def_95,type,
sK37: $i > $i > $i ).
thf(func_def_96,type,
sK38: $i > $i > $i > $i ).
thf(func_def_97,type,
sK39: $i > $i ).
thf(func_def_98,type,
sK40: $i > $i ).
thf(func_def_99,type,
sK41: $i > $i ).
thf(func_def_100,type,
sK42: $i > $i ).
thf(func_def_101,type,
sK43: $i > $i > $i > $i ).
thf(func_def_102,type,
sK44: $i > $i > $i > $i ).
thf(func_def_103,type,
sK45: $i > $i > $i ).
thf(func_def_104,type,
sK46: $i > $i > $i ).
thf(func_def_105,type,
sK47: $i > $i > $i ).
thf(func_def_106,type,
sK48: $i > $i ).
thf(func_def_107,type,
sK49: $i > $i > $i ).
thf(func_def_109,type,
sK51: $i > $i ).
thf(func_def_110,type,
sK52: $i > $i ).
thf(func_def_111,type,
sK53: $i > $i > $i ).
thf(func_def_114,type,
sK56: $i > $o ).
thf(func_def_121,type,
sK63: ( $i > $o ) > $i ).
thf(func_def_122,type,
sK64: $i > $o ).
thf(func_def_127,type,
sK69: $i > $o ).
thf(func_def_130,type,
sK72: $i > $o ).
thf(func_def_133,type,
sK75: $i > $i > $o ).
thf(func_def_134,type,
sK76: $i > $i ).
thf(func_def_135,type,
sK77: $i > $i ).
thf(func_def_136,type,
sK78: ( $i > $i > $o ) > $i > $i ).
thf(func_def_137,type,
sK79: ( $i > $i > $o ) > $i > $i ).
thf(func_def_138,type,
sK80: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_144,type,
sK86: $i > $o ).
thf(func_def_145,type,
sK87: ( $i > $o ) > $i ).
thf(func_def_146,type,
sK88: $i > $o ).
thf(func_def_147,type,
sK89: $i > $i ).
thf(func_def_148,type,
sK90: $i > $i ).
thf(func_def_152,type,
sK94: $i > $o ).
thf(func_def_153,type,
sK95: $i > $o ).
thf(func_def_159,type,
sK101: $i > $i > $i ).
thf(func_def_167,type,
ph109:
!>[X0: $tType] : X0 ).
thf(f1248,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1244]) ).
thf(f1244,plain,
$true != $true,
inference(superposition,[status(thm)],[f461,f653]) ).
thf(f653,plain,
( ( in @ sK61 @ ( powerset @ sK62 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f652]) ).
thf(f652,plain,
( ( $true != $true )
| ( ( in @ sK61 @ ( powerset @ sK62 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f649,f463]) ).
thf(f463,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f264]) ).
thf(f264,plain,
( ( dsetconstrER = $true )
& ( wellorderingAx = $true )
& ( setadjoinIR = $true )
& ( prop2setE = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( omega0Ax = $true )
& ( notinemptyset = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( setoftrueEq = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( powersetAx = $true )
& ( nonemptyI = $true )
& ( ( in @ sK61 @ ( powerset @ sK62 ) )
!= $true )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK62 ) )
| ( $true
!= ( in @ X2 @ sK61 ) ) )
& ( omegaSAx = $true )
& ( setadjoinOr = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( setadjoinE = $true )
& ( emptyinunitempty = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( exuE1 = $true )
& ( setadjoinAx = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( dsetconstrEL = $true )
& ( omegaIndAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62])],[f147,f263]) ).
thf(f263,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
=> ( ( ( in @ sK61 @ ( powerset @ sK62 ) )
!= $true )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK62 ) )
| ( $true
!= ( in @ X2 @ sK61 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f147,plain,
( ( dsetconstrER = $true )
& ( wellorderingAx = $true )
& ( setadjoinIR = $true )
& ( prop2setE = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( omega0Ax = $true )
& ( notinemptyset = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( setoftrueEq = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( powersetAx = $true )
& ( nonemptyI = $true )
& ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( omegaSAx = $true )
& ( setadjoinOr = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( setadjoinE = $true )
& ( emptyinunitempty = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( exuE1 = $true )
& ( setadjoinAx = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( dsetconstrEL = $true )
& ( omegaIndAx = $true ) ),
inference(flattening,[status(thm)],[f146]) ).
thf(f146,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $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)],[f61]) ).
thf(f61,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 )
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f60]) ).
thf(f60,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
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,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
=> ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
=> ( in @ X4 @ ( powerset @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
thf(f38,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
=> ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
=> ( in @ X4 @ ( powerset @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gkmIHVRPeB/DTF2THF_4213.p',powersetI) ).
thf(f649,plain,
( ( powersetAx != $true )
| ( ( in @ sK61 @ ( powerset @ sK62 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f648]) ).
thf(f648,plain,
( ( $true != $true )
| ( ( in @ sK61 @ ( powerset @ sK62 ) )
= $true )
| ( powersetAx != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f645]) ).
thf(f645,plain,
( ( ( in @ sK61 @ ( powerset @ sK62 ) )
= $true )
| ( powersetAx != $true )
| ( ( in @ sK61 @ ( powerset @ sK62 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f634,f390]) ).
thf(f390,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK29 @ X1 @ X0 ) @ X0 ) )
| ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( powersetAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
thf(f213,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( ( in @ ( sK29 @ X1 @ X0 ) @ X1 )
!= $true )
& ( $true
= ( in @ ( sK29 @ X1 @ X0 ) @ X0 ) ) ) )
& ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
| ( powersetAx != $true ) )
& ( ( powersetAx = $true )
| ( ( ( ( ( in @ sK32 @ sK31 )
!= $true )
& ( ( in @ sK32 @ sK30 )
= $true ) )
| ( ( in @ sK30 @ ( powerset @ sK31 ) )
!= $true ) )
& ( ! [X7: $i] :
( ( ( in @ X7 @ sK31 )
= $true )
| ( $true
!= ( in @ X7 @ sK30 ) ) )
| ( ( in @ sK30 @ ( powerset @ sK31 ) )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32])],[f209,f212,f211,f210]) ).
thf(f210,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( ( in @ ( sK29 @ X1 @ X0 ) @ X1 )
!= $true )
& ( $true
= ( in @ ( sK29 @ X1 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f211,plain,
( ? [X4: $i,X5: $i] :
( ( ? [X6: $i] :
( ( $true
!= ( in @ X6 @ X5 ) )
& ( ( in @ X6 @ X4 )
= $true ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
& ( ! [X7: $i] :
( ( ( in @ X7 @ X5 )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) )
| ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) ) ) )
=> ( ( ? [X6: $i] :
( ( ( in @ X6 @ sK31 )
!= $true )
& ( ( in @ X6 @ sK30 )
= $true ) )
| ( ( in @ sK30 @ ( powerset @ sK31 ) )
!= $true ) )
& ( ! [X7: $i] :
( ( ( in @ X7 @ sK31 )
= $true )
| ( $true
!= ( in @ X7 @ sK30 ) ) )
| ( ( in @ sK30 @ ( powerset @ sK31 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f212,plain,
( ? [X6: $i] :
( ( ( in @ X6 @ sK31 )
!= $true )
& ( ( in @ X6 @ sK30 )
= $true ) )
=> ( ( ( in @ sK32 @ sK31 )
!= $true )
& ( ( in @ sK32 @ sK30 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f209,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
| ( powersetAx != $true ) )
& ( ( powersetAx = $true )
| ? [X4: $i,X5: $i] :
( ( ? [X6: $i] :
( ( $true
!= ( in @ X6 @ X5 ) )
& ( ( in @ X6 @ X4 )
= $true ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
& ( ! [X7: $i] :
( ( ( in @ X7 @ X5 )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) )
| ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f208]) ).
thf(f208,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
| ( powersetAx != $true ) )
& ( ( powersetAx = $true )
| ? [X0: $i,X1: $i] :
( ( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f139]) ).
thf(f139,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
<=> ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( powersetAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
<=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) )
<=> ( powersetAx = $true ) ),
inference(fool_elimination,[status(thm)],[f47]) ).
thf(f47,plain,
( powersetAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
<=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( powersetAx
= ( ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
<=> ( in @ X4 @ ( powerset @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gkmIHVRPeB/DTF2THF_4213.p',powersetAx) ).
thf(f634,plain,
! [X0: $i] :
( ( ( in @ ( sK29 @ sK62 @ X0 ) @ sK61 )
!= $true )
| ( $true
= ( in @ X0 @ ( powerset @ sK62 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f633]) ).
thf(f633,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ sK62 ) ) )
| ( $true != $true )
| ( ( in @ ( sK29 @ sK62 @ X0 ) @ sK61 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f593,f463]) ).
thf(f593,plain,
! [X0: $i] :
( ( ( in @ ( sK29 @ sK62 @ X0 ) @ sK61 )
!= $true )
| ( $true
= ( in @ X0 @ ( powerset @ sK62 ) ) )
| ( powersetAx != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f582]) ).
thf(f582,plain,
! [X0: $i] :
( ( $true != $true )
| ( powersetAx != $true )
| ( $true
= ( in @ X0 @ ( powerset @ sK62 ) ) )
| ( ( in @ ( sK29 @ sK62 @ X0 ) @ sK61 )
!= $true ) ),
inference(superposition,[status(thm)],[f391,f460]) ).
thf(f460,plain,
! [X2: $i] :
( ( $true
= ( in @ X2 @ sK62 ) )
| ( $true
!= ( in @ X2 @ sK61 ) ) ),
inference(cnf_transformation,[status(thm)],[f264]) ).
thf(f391,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK29 @ X1 @ X0 ) @ X1 )
!= $true )
| ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( powersetAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
thf(f461,plain,
( ( in @ sK61 @ ( powerset @ sK62 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU518^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:23:56 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.50 ---- Original DTF file ---
% 0.29/0.50 thf(spec,logic,$$dhol).
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 % File : SEU518^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.50 % Domain : Set Theory
% 0.29/0.50 % Problem : Preliminary Notions - Power Sets and Unions
% 0.29/0.50 % Version : Especial.
% 0.29/0.50 % English : (! A:i.! B:i.(! x:i.in x B -> in x A) -> in B (powerset A))
% 0.29/0.50
% 0.29/0.50 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.50 % Source : [Bro08]
% 0.29/0.50 % Names : ZFC020g [Bro08]
% 0.29/0.50
% 0.29/0.50 % Status : Theorem
% 0.29/0.50 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.29/0.50 % Syntax : Number of formulae : 83 ( 37 unt; 45 typ; 37 def)
% 0.29/0.50 % Number of atoms : 211 ( 49 equ; 0 cnn)
% 0.29/0.50 % Maximal formula atoms : 37 ( 5 avg)
% 0.29/0.50 % Number of connectives : 355 ( 7 ~; 4 |; 18 &; 232 @)
% 0.29/0.50 % ( 7 <=>; 87 =>; 0 <=; 0 <~>)
% 0.29/0.50 % Maximal formula depth : 42 ( 2 avg)
% 0.29/0.50 % Number of types : 2 ( 0 usr)
% 0.29/0.50 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.29/0.50 % Number of symbols : 48 ( 45 usr; 38 con; 0-2 aty)
% 0.29/0.50 % Number of variables : 118 ( 15 ^; 87 !; 16 ?; 118 :)
% 0.29/0.50 % SPC : TH0_THM_EQU_NAR
% 0.29/0.50
% 0.29/0.50 % Comments : http://mathgate.info/detsetitem.php?id=85
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 thf(in_type,type,
% 0.29/0.50 in: $i > $i > $o ).
% 0.29/0.50
% 0.29/0.50 thf(exu_type,type,
% 0.29/0.50 exu: ( $i > $o ) > $o ).
% 0.29/0.50
% 0.29/0.50 thf(exu,definition,
% 0.29/0.50 ( exu
% 0.29/0.50 = ( ^ [Xphi: $i > $o] :
% 0.29/0.50 ? [Xx: $i] :
% 0.29/0.50 ( ( Xphi @ Xx )
% 0.29/0.50 & ! [Xy: $i] :
% 0.29/0.50 ( ( Xphi @ Xy )
% 0.29/0.50 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setextAx_type,type,
% 0.29/0.50 setextAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setextAx,definition,
% 0.29/0.50 ( setextAx
% 0.29/0.50 = ( ! [A: $i,B: $i] :
% 0.29/0.50 ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ A )
% 0.29/0.50 <=> ( in @ Xx @ B ) )
% 0.29/0.50 => ( A = B ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(emptyset_type,type,
% 0.29/0.50 emptyset: $i ).
% 0.29/0.50
% 0.29/0.50 thf(emptysetAx_type,type,
% 0.29/0.50 emptysetAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(emptysetAx,definition,
% 0.29/0.50 ( emptysetAx
% 0.29/0.50 = ( ! [Xx: $i] :
% 0.29/0.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoin_type,type,
% 0.29/0.50 setadjoin: $i > $i > $i ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinAx_type,type,
% 0.29/0.50 setadjoinAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinAx,definition,
% 0.29/0.50 ( setadjoinAx
% 0.29/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.50 <=> ( ( Xy = Xx )
% 0.29/0.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(powerset_type,type,
% 0.29/0.50 powerset: $i > $i ).
% 0.29/0.50
% 0.29/0.50 thf(powersetAx_type,type,
% 0.29/0.50 powersetAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(powersetAx,definition,
% 0.29/0.50 ( powersetAx
% 0.29/0.50 = ( ! [A: $i,B: $i] :
% 0.29/0.50 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.50 <=> ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ B )
% 0.29/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setunion_type,type,
% 0.29/0.50 setunion: $i > $i ).
% 0.29/0.50
% 0.29/0.50 thf(setunionAx_type,type,
% 0.29/0.50 setunionAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setunionAx,definition,
% 0.29/0.50 ( setunionAx
% 0.29/0.50 = ( ! [A: $i,Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.50 <=> ? [B: $i] :
% 0.29/0.50 ( ( in @ Xx @ B )
% 0.29/0.50 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(omega_type,type,
% 0.29/0.50 omega: $i ).
% 0.29/0.50
% 0.29/0.50 thf(omega0Ax_type,type,
% 0.29/0.50 omega0Ax: $o ).
% 0.29/0.50
% 0.29/0.50 thf(omega0Ax,definition,
% 0.29/0.50 ( omega0Ax
% 0.29/0.50 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(omegaSAx_type,type,
% 0.29/0.50 omegaSAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(omegaSAx,definition,
% 0.29/0.50 ( omegaSAx
% 0.29/0.50 = ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ omega )
% 0.29/0.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(omegaIndAx_type,type,
% 0.29/0.50 omegaIndAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(omegaIndAx,definition,
% 0.29/0.50 ( omegaIndAx
% 0.29/0.50 = ( ! [A: $i] :
% 0.29/0.50 ( ( ( in @ emptyset @ A )
% 0.29/0.50 & ! [Xx: $i] :
% 0.29/0.50 ( ( ( in @ Xx @ omega )
% 0.29/0.50 & ( in @ Xx @ A ) )
% 0.29/0.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.50 => ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ omega )
% 0.29/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(replAx_type,type,
% 0.29/0.50 replAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(replAx,definition,
% 0.29/0.50 ( replAx
% 0.29/0.50 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.50 ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ A )
% 0.29/0.50 => ( exu
% 0.29/0.50 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.50 => ? [B: $i] :
% 0.29/0.50 ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ B )
% 0.29/0.50 <=> ? [Xy: $i] :
% 0.29/0.50 ( ( in @ Xy @ A )
% 0.29/0.50 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(foundationAx_type,type,
% 0.29/0.50 foundationAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(foundationAx,definition,
% 0.29/0.50 ( foundationAx
% 0.29/0.50 = ( ! [A: $i] :
% 0.29/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.50 => ? [B: $i] :
% 0.29/0.50 ( ( in @ B @ A )
% 0.29/0.50 & ~ ? [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ B )
% 0.29/0.50 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(wellorderingAx_type,type,
% 0.29/0.50 wellorderingAx: $o ).
% 0.29/0.50
% 0.29/0.50 thf(wellorderingAx,definition,
% 0.29/0.50 ( wellorderingAx
% 0.29/0.50 = ( ! [A: $i] :
% 0.29/0.50 ? [B: $i] :
% 0.29/0.50 ( ! [C: $i] :
% 0.29/0.50 ( ( in @ C @ B )
% 0.29/0.50 => ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ C )
% 0.29/0.50 => ( in @ Xx @ A ) ) )
% 0.29/0.50 & ! [Xx: $i,Xy: $i] :
% 0.29/0.50 ( ( ( in @ Xx @ A )
% 0.29/0.50 & ( in @ Xy @ A ) )
% 0.29/0.50 => ( ! [C: $i] :
% 0.29/0.50 ( ( in @ C @ B )
% 0.29/0.50 => ( ( in @ Xx @ C )
% 0.29/0.50 <=> ( in @ Xy @ C ) ) )
% 0.29/0.50 => ( Xx = Xy ) ) )
% 0.29/0.50 & ! [C: $i,D: $i] :
% 0.29/0.50 ( ( ( in @ C @ B )
% 0.29/0.50 & ( in @ D @ B ) )
% 0.29/0.50 => ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ C )
% 0.29/0.50 => ( in @ Xx @ D ) )
% 0.29/0.50 | ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ D )
% 0.29/0.50 => ( in @ Xx @ C ) ) ) )
% 0.29/0.50 & ! [C: $i] :
% 0.29/0.50 ( ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ C )
% 0.29/0.50 => ( in @ Xx @ A ) )
% 0.29/0.50 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.50 => ? [D: $i,Xx: $i] :
% 0.29/0.50 ( ( in @ D @ B )
% 0.29/0.50 & ( in @ Xx @ C )
% 0.29/0.50 & ~ ? [Xy: $i] :
% 0.29/0.50 ( ( in @ Xy @ D )
% 0.29/0.50 & ( in @ Xy @ C ) )
% 0.29/0.50 & ! [E: $i] :
% 0.29/0.50 ( ( in @ E @ B )
% 0.29/0.50 => ( ! [Xy: $i] :
% 0.29/0.50 ( ( in @ Xy @ E )
% 0.29/0.50 => ( in @ Xy @ D ) )
% 0.29/0.50 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(descr_type,type,
% 0.29/0.50 descr: ( $i > $o ) > $i ).
% 0.29/0.50
% 0.29/0.50 thf(descrp_type,type,
% 0.29/0.50 descrp: $o ).
% 0.29/0.50
% 0.29/0.50 thf(descrp,definition,
% 0.29/0.50 ( descrp
% 0.29/0.50 = ( ! [Xphi: $i > $o] :
% 0.29/0.50 ( ( exu
% 0.29/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.50 => ( Xphi
% 0.29/0.50 @ ( descr
% 0.29/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(dsetconstr_type,type,
% 0.29/0.50 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.50
% 0.29/0.50 thf(dsetconstrI_type,type,
% 0.29/0.50 dsetconstrI: $o ).
% 0.29/0.50
% 0.29/0.50 thf(dsetconstrI,definition,
% 0.29/0.50 ( dsetconstrI
% 0.29/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ A )
% 0.29/0.50 => ( ( Xphi @ Xx )
% 0.29/0.50 => ( in @ Xx
% 0.29/0.50 @ ( dsetconstr @ A
% 0.29/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(dsetconstrEL_type,type,
% 0.29/0.50 dsetconstrEL: $o ).
% 0.29/0.50
% 0.29/0.50 thf(dsetconstrEL,definition,
% 0.29/0.50 ( dsetconstrEL
% 0.29/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.50 ( ( in @ Xx
% 0.29/0.50 @ ( dsetconstr @ A
% 0.29/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.50 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(dsetconstrER_type,type,
% 0.29/0.50 dsetconstrER: $o ).
% 0.29/0.50
% 0.29/0.50 thf(dsetconstrER,definition,
% 0.29/0.50 ( dsetconstrER
% 0.29/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.50 ( ( in @ Xx
% 0.29/0.50 @ ( dsetconstr @ A
% 0.29/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.50 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(exuE1_type,type,
% 0.29/0.50 exuE1: $o ).
% 0.29/0.50
% 0.29/0.50 thf(exuE1,definition,
% 0.29/0.50 ( exuE1
% 0.29/0.50 = ( ! [Xphi: $i > $o] :
% 0.29/0.50 ( ( exu
% 0.29/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.50 => ? [Xx: $i] :
% 0.29/0.50 ( ( Xphi @ Xx )
% 0.29/0.50 & ! [Xy: $i] :
% 0.29/0.50 ( ( Xphi @ Xy )
% 0.29/0.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(prop2set_type,type,
% 0.29/0.50 prop2set: $o > $i ).
% 0.29/0.50
% 0.29/0.50 thf(prop2set,definition,
% 0.29/0.50 ( prop2set
% 0.29/0.50 = ( ^ [Xphi: $o] :
% 0.29/0.50 ( dsetconstr @ ( powerset @ emptyset )
% 0.29/0.50 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(prop2setE_type,type,
% 0.29/0.50 prop2setE: $o ).
% 0.29/0.50
% 0.29/0.50 thf(prop2setE,definition,
% 0.29/0.50 ( prop2setE
% 0.29/0.50 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.50 => Xphi ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(emptysetE_type,type,
% 0.29/0.50 emptysetE: $o ).
% 0.29/0.50
% 0.29/0.50 thf(emptysetE,definition,
% 0.29/0.50 ( emptysetE
% 0.29/0.50 = ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ emptyset )
% 0.29/0.50 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(emptysetimpfalse_type,type,
% 0.29/0.50 emptysetimpfalse: $o ).
% 0.29/0.50
% 0.29/0.50 thf(emptysetimpfalse,definition,
% 0.29/0.50 ( emptysetimpfalse
% 0.29/0.50 = ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ emptyset )
% 0.29/0.50 => $false ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(notinemptyset_type,type,
% 0.29/0.50 notinemptyset: $o ).
% 0.29/0.50
% 0.29/0.50 thf(notinemptyset,definition,
% 0.29/0.50 ( notinemptyset
% 0.29/0.50 = ( ! [Xx: $i] :
% 0.29/0.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(exuE3e_type,type,
% 0.29/0.50 exuE3e: $o ).
% 0.29/0.50
% 0.29/0.50 thf(exuE3e,definition,
% 0.29/0.50 ( exuE3e
% 0.29/0.50 = ( ! [Xphi: $i > $o] :
% 0.29/0.50 ( ( exu
% 0.29/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.50 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setext_type,type,
% 0.29/0.50 setext: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setext,definition,
% 0.29/0.50 ( setext
% 0.29/0.50 = ( ! [A: $i,B: $i] :
% 0.29/0.50 ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ A )
% 0.29/0.50 => ( in @ Xx @ B ) )
% 0.29/0.50 => ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ B )
% 0.29/0.50 => ( in @ Xx @ A ) )
% 0.29/0.50 => ( A = B ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(emptyI_type,type,
% 0.29/0.50 emptyI: $o ).
% 0.29/0.50
% 0.29/0.50 thf(emptyI,definition,
% 0.29/0.50 ( emptyI
% 0.29/0.50 = ( ! [A: $i] :
% 0.29/0.50 ( ! [Xx: $i] :
% 0.29/0.50 ~ ( in @ Xx @ A )
% 0.29/0.50 => ( A = emptyset ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(noeltsimpempty_type,type,
% 0.29/0.50 noeltsimpempty: $o ).
% 0.29/0.50
% 0.29/0.50 thf(noeltsimpempty,definition,
% 0.29/0.50 ( noeltsimpempty
% 0.29/0.50 = ( ! [A: $i] :
% 0.29/0.50 ( ! [Xx: $i] :
% 0.29/0.50 ~ ( in @ Xx @ A )
% 0.29/0.50 => ( A = emptyset ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setbeta_type,type,
% 0.29/0.50 setbeta: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setbeta,definition,
% 0.29/0.50 ( setbeta
% 0.29/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ A )
% 0.29/0.50 => ( ( in @ Xx
% 0.29/0.50 @ ( dsetconstr @ A
% 0.29/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.50 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(nonempty_type,type,
% 0.29/0.50 nonempty: $i > $o ).
% 0.29/0.50
% 0.29/0.50 thf(nonempty,definition,
% 0.29/0.50 ( nonempty
% 0.29/0.50 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(nonemptyE1_type,type,
% 0.29/0.50 nonemptyE1: $o ).
% 0.29/0.50
% 0.29/0.50 thf(nonemptyE1,definition,
% 0.29/0.50 ( nonemptyE1
% 0.29/0.50 = ( ! [A: $i] :
% 0.29/0.50 ( ( nonempty @ A )
% 0.29/0.50 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(nonemptyI_type,type,
% 0.29/0.50 nonemptyI: $o ).
% 0.29/0.50
% 0.29/0.50 thf(nonemptyI,definition,
% 0.29/0.50 ( nonemptyI
% 0.29/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ A )
% 0.29/0.50 => ( ( Xphi @ Xx )
% 0.29/0.50 => ( nonempty
% 0.29/0.50 @ ( dsetconstr @ A
% 0.29/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(nonemptyI1_type,type,
% 0.29/0.50 nonemptyI1: $o ).
% 0.29/0.50
% 0.29/0.50 thf(nonemptyI1,definition,
% 0.29/0.50 ( nonemptyI1
% 0.29/0.50 = ( ! [A: $i] :
% 0.29/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.50 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinIL_type,type,
% 0.29/0.50 setadjoinIL: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinIL,definition,
% 0.29/0.50 ( setadjoinIL
% 0.29/0.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(emptyinunitempty_type,type,
% 0.29/0.50 emptyinunitempty: $o ).
% 0.29/0.50
% 0.29/0.50 thf(emptyinunitempty,definition,
% 0.29/0.50 ( emptyinunitempty
% 0.29/0.50 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinIR_type,type,
% 0.29/0.50 setadjoinIR: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinIR,definition,
% 0.29/0.50 ( setadjoinIR
% 0.29/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.50 ( ( in @ Xy @ A )
% 0.29/0.50 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinE_type,type,
% 0.29/0.50 setadjoinE: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinE,definition,
% 0.29/0.50 ( setadjoinE
% 0.29/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.50 => ! [Xphi: $o] :
% 0.29/0.50 ( ( ( Xy = Xx )
% 0.29/0.50 => Xphi )
% 0.29/0.50 => ( ( ( in @ Xy @ A )
% 0.29/0.50 => Xphi )
% 0.29/0.50 => Xphi ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinOr_type,type,
% 0.29/0.50 setadjoinOr: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setadjoinOr,definition,
% 0.29/0.50 ( setadjoinOr
% 0.29/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.50 => ( ( Xy = Xx )
% 0.29/0.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setoftrueEq_type,type,
% 0.29/0.50 setoftrueEq: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setoftrueEq,definition,
% 0.29/0.50 ( setoftrueEq
% 0.29/0.50 = ( ! [A: $i] :
% 0.29/0.50 ( ( dsetconstr @ A
% 0.29/0.50 @ ^ [Xx: $i] : $true )
% 0.29/0.50 = A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(powersetI,conjecture,
% 0.29/0.50 ( setextAx
% 0.29/0.50 => ( emptysetAx
% 0.29/0.50 => ( setadjoinAx
% 0.29/0.50 => ( powersetAx
% 0.29/0.50 => ( setunionAx
% 0.29/0.50 => ( omega0Ax
% 0.29/0.50 => ( omegaSAx
% 0.29/0.50 => ( omegaIndAx
% 0.29/0.50 => ( replAx
% 0.29/0.50 => ( foundationAx
% 0.29/0.50 => ( wellorderingAx
% 0.29/0.50 => ( descrp
% 0.29/0.50 => ( dsetconstrI
% 0.29/0.50 => ( dsetconstrEL
% 0.29/0.50 => ( dsetconstrER
% 0.29/0.50 => ( exuE1
% 0.29/0.50 => ( prop2setE
% 0.29/0.50 => ( emptysetE
% 0.29/0.50 => ( emptysetimpfalse
% 0.29/0.50 => ( notinemptyset
% 0.29/0.50 => ( exuE3e
% 0.29/0.50 => ( setext
% 0.29/0.50 => ( emptyI
% 0.29/0.50 => ( noeltsimpempty
% 0.29/0.50 => ( setbeta
% 0.29/0.50 => ( nonemptyE1
% 0.29/0.50 => ( nonemptyI
% 0.29/0.50 => ( nonemptyI1
% 0.29/0.50 => ( setadjoinIL
% 0.29/0.50 => ( emptyinunitempty
% 0.29/0.50 => ( setadjoinIR
% 0.29/0.50 => ( setadjoinE
% 0.29/0.50 => ( setadjoinOr
% 0.29/0.50 => ( setoftrueEq
% 0.29/0.50 => ! [A: $i,B: $i] :
% 0.29/0.50 ( ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ B )
% 0.29/0.50 => ( in @ Xx @ A ) )
% 0.29/0.50 => ( in @ B @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 ------------------------
% 2.03/1.52 ---- Embedded in THF ---
% 2.03/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.03/1.53 %%% Generated on Tue Feb 24 12:23:57 EST 2026
% 2.03/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.03/1.53 %%% Logic specification used:
% 2.03/1.53 %%% thf(spec, logic, $$dhol).
% 2.03/1.53
% 2.03/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gkmIHVRPeB/DTF2DTF4213.p
% See solution above
% 2.03/1.53 ------------------------
% 2.03/1.54 ---- Cleaned THF ---
% 2.03/1.54 thf(in_type,type,
% 2.03/1.54 in: $i > $i > $o ).
% 2.03/1.54
% 2.03/1.54 thf(exu_type,type,
% 2.03/1.54 exu: ( $i > $o ) > $o ).
% 2.03/1.54
% 2.03/1.54 thf(exu,definition,
% 2.03/1.54 ( exu
% 2.03/1.54 = ( ^ [Xphi: $i > $o] :
% 2.03/1.54 ? [Xx: $i] :
% 2.03/1.54 ( ( Xphi @ Xx )
% 2.03/1.54 & ! [Xy: $i] :
% 2.03/1.54 ( ( Xphi @ Xy )
% 2.03/1.54 => ( Xx = Xy ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setextAx_type,type,
% 2.03/1.54 setextAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setextAx,definition,
% 2.03/1.54 ( setextAx
% 2.03/1.54 = ( ! [A: $i,B: $i] :
% 2.03/1.54 ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ A )
% 2.03/1.54 <=> ( in @ Xx @ B ) )
% 2.03/1.54 => ( A = B ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(emptyset_type,type,
% 2.03/1.54 emptyset: $i ).
% 2.03/1.54
% 2.03/1.54 thf(emptysetAx_type,type,
% 2.03/1.54 emptysetAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(emptysetAx,definition,
% 2.03/1.54 ( emptysetAx
% 2.03/1.54 = ( ! [Xx: $i] :
% 2.03/1.54 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoin_type,type,
% 2.03/1.54 setadjoin: $i > $i > $i ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinAx_type,type,
% 2.03/1.54 setadjoinAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinAx,definition,
% 2.03/1.54 ( setadjoinAx
% 2.03/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.03/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.03/1.54 <=> ( ( Xy = Xx )
% 2.03/1.54 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(powerset_type,type,
% 2.03/1.54 powerset: $i > $i ).
% 2.03/1.54
% 2.03/1.54 thf(powersetAx_type,type,
% 2.03/1.54 powersetAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(powersetAx,definition,
% 2.03/1.54 ( powersetAx
% 2.03/1.54 = ( ! [A: $i,B: $i] :
% 2.03/1.54 ( ( in @ B @ ( powerset @ A ) )
% 2.03/1.54 <=> ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ B )
% 2.03/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setunion_type,type,
% 2.03/1.54 setunion: $i > $i ).
% 2.03/1.54
% 2.03/1.54 thf(setunionAx_type,type,
% 2.03/1.54 setunionAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setunionAx,definition,
% 2.03/1.54 ( setunionAx
% 2.03/1.54 = ( ! [A: $i,Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 2.03/1.54 <=> ? [B: $i] :
% 2.03/1.54 ( ( in @ Xx @ B )
% 2.03/1.54 & ( in @ B @ A ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(omega_type,type,
% 2.03/1.54 omega: $i ).
% 2.03/1.54
% 2.03/1.54 thf(omega0Ax_type,type,
% 2.03/1.54 omega0Ax: $o ).
% 2.03/1.54
% 2.03/1.54 thf(omega0Ax,definition,
% 2.03/1.54 ( omega0Ax
% 2.03/1.54 = ( in @ emptyset @ omega ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(omegaSAx_type,type,
% 2.03/1.54 omegaSAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(omegaSAx,definition,
% 2.03/1.54 ( omegaSAx
% 2.03/1.54 = ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ omega )
% 2.03/1.54 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(omegaIndAx_type,type,
% 2.03/1.54 omegaIndAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(omegaIndAx,definition,
% 2.03/1.54 ( omegaIndAx
% 2.03/1.54 = ( ! [A: $i] :
% 2.03/1.54 ( ( ( in @ emptyset @ A )
% 2.03/1.54 & ! [Xx: $i] :
% 2.03/1.54 ( ( ( in @ Xx @ omega )
% 2.03/1.54 & ( in @ Xx @ A ) )
% 2.03/1.54 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.03/1.54 => ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ omega )
% 2.03/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(replAx_type,type,
% 2.03/1.54 replAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(replAx,definition,
% 2.03/1.54 ( replAx
% 2.03/1.54 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.03/1.54 ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ A )
% 2.03/1.54 => ( exu
% 2.03/1.54 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.03/1.54 => ? [B: $i] :
% 2.03/1.54 ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ B )
% 2.03/1.54 <=> ? [Xy: $i] :
% 2.03/1.54 ( ( in @ Xy @ A )
% 2.03/1.54 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(foundationAx_type,type,
% 2.03/1.54 foundationAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(foundationAx,definition,
% 2.03/1.54 ( foundationAx
% 2.03/1.54 = ( ! [A: $i] :
% 2.03/1.54 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.03/1.54 => ? [B: $i] :
% 2.03/1.54 ( ( in @ B @ A )
% 2.03/1.54 & ~ ? [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ B )
% 2.03/1.54 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(wellorderingAx_type,type,
% 2.03/1.54 wellorderingAx: $o ).
% 2.03/1.54
% 2.03/1.54 thf(wellorderingAx,definition,
% 2.03/1.54 ( wellorderingAx
% 2.03/1.54 = ( ! [A: $i] :
% 2.03/1.54 ? [B: $i] :
% 2.03/1.54 ( ! [C: $i] :
% 2.03/1.54 ( ( in @ C @ B )
% 2.03/1.54 => ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ C )
% 2.03/1.54 => ( in @ Xx @ A ) ) )
% 2.03/1.54 & ! [Xx: $i,Xy: $i] :
% 2.03/1.54 ( ( ( in @ Xx @ A )
% 2.03/1.54 & ( in @ Xy @ A ) )
% 2.03/1.54 => ( ! [C: $i] :
% 2.03/1.54 ( ( in @ C @ B )
% 2.03/1.54 => ( ( in @ Xx @ C )
% 2.03/1.54 <=> ( in @ Xy @ C ) ) )
% 2.03/1.54 => ( Xx = Xy ) ) )
% 2.03/1.54 & ! [C: $i,D: $i] :
% 2.03/1.54 ( ( ( in @ C @ B )
% 2.03/1.54 & ( in @ D @ B ) )
% 2.03/1.54 => ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ C )
% 2.03/1.54 => ( in @ Xx @ D ) )
% 2.03/1.54 | ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ D )
% 2.03/1.54 => ( in @ Xx @ C ) ) ) )
% 2.03/1.54 & ! [C: $i] :
% 2.03/1.54 ( ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ C )
% 2.03/1.54 => ( in @ Xx @ A ) )
% 2.03/1.54 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.03/1.54 => ? [D: $i,Xx: $i] :
% 2.03/1.54 ( ( in @ D @ B )
% 2.03/1.54 & ( in @ Xx @ C )
% 2.03/1.54 & ~ ? [Xy: $i] :
% 2.03/1.54 ( ( in @ Xy @ D )
% 2.03/1.54 & ( in @ Xy @ C ) )
% 2.03/1.54 & ! [E: $i] :
% 2.03/1.54 ( ( in @ E @ B )
% 2.03/1.54 => ( ! [Xy: $i] :
% 2.03/1.54 ( ( in @ Xy @ E )
% 2.03/1.54 => ( in @ Xy @ D ) )
% 2.03/1.54 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(descr_type,type,
% 2.03/1.54 descr: ( $i > $o ) > $i ).
% 2.03/1.54
% 2.03/1.54 thf(descrp_type,type,
% 2.03/1.54 descrp: $o ).
% 2.03/1.54
% 2.03/1.54 thf(descrp,definition,
% 2.03/1.54 ( descrp
% 2.03/1.54 = ( ! [Xphi: $i > $o] :
% 2.03/1.54 ( ( exu
% 2.03/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.03/1.54 => ( Xphi
% 2.03/1.54 @ ( descr
% 2.03/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(dsetconstr_type,type,
% 2.03/1.54 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.03/1.54
% 2.03/1.54 thf(dsetconstrI_type,type,
% 2.03/1.54 dsetconstrI: $o ).
% 2.03/1.54
% 2.03/1.54 thf(dsetconstrI,definition,
% 2.03/1.54 ( dsetconstrI
% 2.03/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ A )
% 2.03/1.54 => ( ( Xphi @ Xx )
% 2.03/1.54 => ( in @ Xx
% 2.03/1.54 @ ( dsetconstr @ A
% 2.03/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(dsetconstrEL_type,type,
% 2.03/1.54 dsetconstrEL: $o ).
% 2.03/1.54
% 2.03/1.54 thf(dsetconstrEL,definition,
% 2.03/1.54 ( dsetconstrEL
% 2.03/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.03/1.54 ( ( in @ Xx
% 2.03/1.54 @ ( dsetconstr @ A
% 2.03/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.03/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(dsetconstrER_type,type,
% 2.03/1.54 dsetconstrER: $o ).
% 2.03/1.54
% 2.03/1.54 thf(dsetconstrER,definition,
% 2.03/1.54 ( dsetconstrER
% 2.03/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.03/1.54 ( ( in @ Xx
% 2.03/1.54 @ ( dsetconstr @ A
% 2.03/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.03/1.54 => ( Xphi @ Xx ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(exuE1_type,type,
% 2.03/1.54 exuE1: $o ).
% 2.03/1.54
% 2.03/1.54 thf(exuE1,definition,
% 2.03/1.54 ( exuE1
% 2.03/1.54 = ( ! [Xphi: $i > $o] :
% 2.03/1.54 ( ( exu
% 2.03/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.03/1.54 => ? [Xx: $i] :
% 2.03/1.54 ( ( Xphi @ Xx )
% 2.03/1.54 & ! [Xy: $i] :
% 2.03/1.54 ( ( Xphi @ Xy )
% 2.03/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(prop2set_type,type,
% 2.03/1.54 prop2set: $o > $i ).
% 2.03/1.54
% 2.03/1.54 thf(prop2set,definition,
% 2.03/1.54 ( prop2set
% 2.03/1.54 = ( ^ [Xphi: $o] :
% 2.03/1.54 ( dsetconstr @ ( powerset @ emptyset )
% 2.03/1.54 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(prop2setE_type,type,
% 2.03/1.54 prop2setE: $o ).
% 2.03/1.54
% 2.03/1.54 thf(prop2setE,definition,
% 2.03/1.54 ( prop2setE
% 2.03/1.54 = ( ! [Xphi: $o,Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.03/1.54 => Xphi ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(emptysetE_type,type,
% 2.03/1.54 emptysetE: $o ).
% 2.03/1.54
% 2.03/1.54 thf(emptysetE,definition,
% 2.03/1.54 ( emptysetE
% 2.03/1.54 = ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ emptyset )
% 2.03/1.54 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(emptysetimpfalse_type,type,
% 2.03/1.54 emptysetimpfalse: $o ).
% 2.03/1.54
% 2.03/1.54 thf(emptysetimpfalse,definition,
% 2.03/1.54 ( emptysetimpfalse
% 2.03/1.54 = ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ emptyset )
% 2.03/1.54 => $false ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(notinemptyset_type,type,
% 2.03/1.54 notinemptyset: $o ).
% 2.03/1.54
% 2.03/1.54 thf(notinemptyset,definition,
% 2.03/1.54 ( notinemptyset
% 2.03/1.54 = ( ! [Xx: $i] :
% 2.03/1.54 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(exuE3e_type,type,
% 2.03/1.54 exuE3e: $o ).
% 2.03/1.54
% 2.03/1.54 thf(exuE3e,definition,
% 2.03/1.54 ( exuE3e
% 2.03/1.54 = ( ! [Xphi: $i > $o] :
% 2.03/1.54 ( ( exu
% 2.03/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.03/1.54 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setext_type,type,
% 2.03/1.54 setext: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setext,definition,
% 2.03/1.54 ( setext
% 2.03/1.54 = ( ! [A: $i,B: $i] :
% 2.03/1.54 ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ A )
% 2.03/1.54 => ( in @ Xx @ B ) )
% 2.03/1.54 => ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ B )
% 2.03/1.54 => ( in @ Xx @ A ) )
% 2.03/1.54 => ( A = B ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(emptyI_type,type,
% 2.03/1.54 emptyI: $o ).
% 2.03/1.54
% 2.03/1.54 thf(emptyI,definition,
% 2.03/1.54 ( emptyI
% 2.03/1.54 = ( ! [A: $i] :
% 2.03/1.54 ( ! [Xx: $i] :
% 2.03/1.54 ~ ( in @ Xx @ A )
% 2.03/1.54 => ( A = emptyset ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(noeltsimpempty_type,type,
% 2.03/1.54 noeltsimpempty: $o ).
% 2.03/1.54
% 2.03/1.54 thf(noeltsimpempty,definition,
% 2.03/1.54 ( noeltsimpempty
% 2.03/1.54 = ( ! [A: $i] :
% 2.03/1.54 ( ! [Xx: $i] :
% 2.03/1.54 ~ ( in @ Xx @ A )
% 2.03/1.54 => ( A = emptyset ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setbeta_type,type,
% 2.03/1.54 setbeta: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setbeta,definition,
% 2.03/1.54 ( setbeta
% 2.03/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ A )
% 2.03/1.54 => ( ( in @ Xx
% 2.03/1.54 @ ( dsetconstr @ A
% 2.03/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.03/1.54 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(nonempty_type,type,
% 2.03/1.54 nonempty: $i > $o ).
% 2.03/1.54
% 2.03/1.54 thf(nonempty,definition,
% 2.03/1.54 ( nonempty
% 2.03/1.54 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(nonemptyE1_type,type,
% 2.03/1.54 nonemptyE1: $o ).
% 2.03/1.54
% 2.03/1.54 thf(nonemptyE1,definition,
% 2.03/1.54 ( nonemptyE1
% 2.03/1.54 = ( ! [A: $i] :
% 2.03/1.54 ( ( nonempty @ A )
% 2.03/1.54 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(nonemptyI_type,type,
% 2.03/1.54 nonemptyI: $o ).
% 2.03/1.54
% 2.03/1.54 thf(nonemptyI,definition,
% 2.03/1.54 ( nonemptyI
% 2.03/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ A )
% 2.03/1.54 => ( ( Xphi @ Xx )
% 2.03/1.54 => ( nonempty
% 2.03/1.54 @ ( dsetconstr @ A
% 2.03/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(nonemptyI1_type,type,
% 2.03/1.54 nonemptyI1: $o ).
% 2.03/1.54
% 2.03/1.54 thf(nonemptyI1,definition,
% 2.03/1.54 ( nonemptyI1
% 2.03/1.54 = ( ! [A: $i] :
% 2.03/1.54 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.03/1.54 => ( nonempty @ A ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinIL_type,type,
% 2.03/1.54 setadjoinIL: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinIL,definition,
% 2.03/1.54 ( setadjoinIL
% 2.03/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(emptyinunitempty_type,type,
% 2.03/1.54 emptyinunitempty: $o ).
% 2.03/1.54
% 2.03/1.54 thf(emptyinunitempty,definition,
% 2.03/1.54 ( emptyinunitempty
% 2.03/1.54 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinIR_type,type,
% 2.03/1.54 setadjoinIR: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinIR,definition,
% 2.03/1.54 ( setadjoinIR
% 2.03/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.03/1.54 ( ( in @ Xy @ A )
% 2.03/1.54 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinE_type,type,
% 2.03/1.54 setadjoinE: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinE,definition,
% 2.03/1.54 ( setadjoinE
% 2.03/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.03/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.03/1.54 => ! [Xphi: $o] :
% 2.03/1.54 ( ( ( Xy = Xx )
% 2.03/1.54 => Xphi )
% 2.03/1.54 => ( ( ( in @ Xy @ A )
% 2.03/1.54 => Xphi )
% 2.03/1.54 => Xphi ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinOr_type,type,
% 2.03/1.54 setadjoinOr: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setadjoinOr,definition,
% 2.03/1.54 ( setadjoinOr
% 2.03/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.03/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.03/1.54 => ( ( Xy = Xx )
% 2.03/1.54 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(setoftrueEq_type,type,
% 2.03/1.54 setoftrueEq: $o ).
% 2.03/1.54
% 2.03/1.54 thf(setoftrueEq,definition,
% 2.03/1.54 ( setoftrueEq
% 2.03/1.54 = ( ! [A: $i] :
% 2.03/1.54 ( ( dsetconstr @ A
% 2.03/1.54 @ ^ [Xx: $i] : $true )
% 2.03/1.54 = A ) ) ) ).
% 2.03/1.54
% 2.03/1.54 thf(powersetI,conjecture,
% 2.03/1.54 ( setextAx
% 2.03/1.54 => ( emptysetAx
% 2.03/1.54 => ( setadjoinAx
% 2.03/1.54 => ( powersetAx
% 2.03/1.54 => ( setunionAx
% 2.03/1.54 => ( omega0Ax
% 2.03/1.54 => ( omegaSAx
% 2.03/1.54 => ( omegaIndAx
% 2.03/1.54 => ( replAx
% 2.03/1.54 => ( foundationAx
% 2.03/1.54 => ( wellorderingAx
% 2.03/1.54 => ( descrp
% 2.03/1.54 => ( dsetconstrI
% 2.03/1.54 => ( dsetconstrEL
% 2.03/1.54 => ( dsetconstrER
% 2.03/1.54 => ( exuE1
% 2.03/1.54 => ( prop2setE
% 2.03/1.54 => ( emptysetE
% 2.03/1.54 => ( emptysetimpfalse
% 2.03/1.54 => ( notinemptyset
% 2.03/1.54 => ( exuE3e
% 2.03/1.54 => ( setext
% 2.03/1.54 => ( emptyI
% 2.03/1.54 => ( noeltsimpempty
% 2.03/1.54 => ( setbeta
% 2.03/1.54 => ( nonemptyE1
% 2.03/1.54 => ( nonemptyI
% 2.03/1.54 => ( nonemptyI1
% 2.03/1.54 => ( setadjoinIL
% 2.03/1.54 => ( emptyinunitempty
% 2.03/1.54 => ( setadjoinIR
% 2.03/1.54 => ( setadjoinE
% 2.03/1.54 => ( setadjoinOr
% 2.03/1.54 => ( setoftrueEq
% 2.03/1.54 => ! [A: $i,B: $i] :
% 2.03/1.54 ( ! [Xx: $i] :
% 2.03/1.54 ( ( in @ Xx @ B )
% 2.03/1.54 => ( in @ Xx @ A ) )
% 2.03/1.54 => ( in @ B @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.03/1.54 ------------------------
% 2.03/1.56 % (4320)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/183Mi)
% 2.03/1.56 % (4322)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_4213 for (2999ds/27Mi)
% 2.03/1.56 % (4321)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_4213 for (2999ds/4Mi)
% 2.03/1.56 % (4323)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/2Mi)
% 2.03/1.56 % (4324)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_4213 for (2999ds/2Mi)
% 2.03/1.56 % (4326)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/18Mi)
% 2.03/1.56 % (4325)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_4213 for (2999ds/275Mi)
% 2.03/1.56 % (4323)Instruction limit reached!
% 2.03/1.56 % (4323)------------------------------
% 2.03/1.56 % (4323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.56 % (4323)Termination reason: Unknown
% 2.03/1.56 % (4324)Instruction limit reached!
% 2.03/1.56 % (4324)------------------------------
% 2.03/1.56 % (4324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.56 % (4323)Termination phase: shuffling
% 2.03/1.56
% 2.03/1.56 % (4323)Memory used [KB]: 1023
% 2.03/1.56 % (4323)Time elapsed: 0.003 s
% 2.03/1.56 % (4323)Instructions burned: 3 (million)
% 2.03/1.56 % (4323)------------------------------
% 2.03/1.56 % (4323)------------------------------
% 2.03/1.56 % (4324)Termination reason: Unknown
% 2.03/1.56 % (4324)Termination phase: shuffling
% 2.03/1.56
% 2.03/1.56 % (4324)Memory used [KB]: 1023
% 2.03/1.56 % (4324)Time elapsed: 0.003 s
% 2.03/1.56 % (4324)Instructions burned: 3 (million)
% 2.03/1.56 % (4324)------------------------------
% 2.03/1.56 % (4324)------------------------------
% 2.03/1.56 % (4321)Instruction limit reached!
% 2.03/1.56 % (4321)------------------------------
% 2.03/1.56 % (4321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.56 % (4321)Termination reason: Unknown
% 2.03/1.56 % (4321)Termination phase: shuffling
% 2.03/1.56
% 2.03/1.56 % (4321)Memory used [KB]: 1151
% 2.03/1.56 % (4321)Time elapsed: 0.004 s
% 2.03/1.56 % (4321)Instructions burned: 5 (million)
% 2.03/1.56 % (4321)------------------------------
% 2.03/1.56 % (4321)------------------------------
% 2.03/1.57 % (4326)Instruction limit reached!
% 2.03/1.57 % (4326)------------------------------
% 2.03/1.57 % (4326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.57 % (4326)Termination reason: Unknown
% 2.03/1.57 % (4326)Termination phase: Property scanning
% 2.03/1.57
% 2.03/1.57 % (4326)Memory used [KB]: 1535
% 2.03/1.57 % (4326)Time elapsed: 0.011 s
% 2.03/1.57 % (4326)Instructions burned: 20 (million)
% 2.03/1.57 % (4326)------------------------------
% 2.03/1.57 % (4326)------------------------------
% 2.03/1.57 % (4322)Instruction limit reached!
% 2.03/1.57 % (4322)------------------------------
% 2.03/1.57 % (4322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.57 % (4322)Termination reason: Unknown
% 2.03/1.57 % (4322)Termination phase: Saturation
% 2.03/1.57
% 2.03/1.57 % (4322)Memory used [KB]: 5756
% 2.03/1.57 % (4322)Time elapsed: 0.014 s
% 2.03/1.57 % (4322)Instructions burned: 27 (million)
% 2.03/1.57 % (4322)------------------------------
% 2.03/1.57 % (4322)------------------------------
% 2.03/1.58 % (4327)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/3Mi)
% 2.03/1.58 % (4328)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_4213 for (2999ds/37Mi)
% 2.03/1.58 % (4329)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_4213 for (2999ds/15Mi)
% 2.03/1.58 % (4327)Instruction limit reached!
% 2.03/1.58 % (4327)------------------------------
% 2.03/1.58 % (4327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.58 % (4327)Termination reason: Unknown
% 2.03/1.58 % (4327)Termination phase: shuffling
% 2.03/1.58
% 2.03/1.58 % (4327)Memory used [KB]: 1023
% 2.03/1.58 % (4327)Time elapsed: 0.003 s
% 2.03/1.58 % (4327)Instructions burned: 3 (million)
% 2.03/1.58 % (4327)------------------------------
% 2.03/1.58 % (4327)------------------------------
% 2.03/1.59 % (4329)Instruction limit reached!
% 2.03/1.59 % (4329)------------------------------
% 2.03/1.59 % (4329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.59 % (4329)Termination reason: Unknown
% 2.03/1.59 % (4329)Termination phase: Property scanning
% 2.03/1.59
% 2.03/1.59 % (4329)Memory used [KB]: 1535
% 2.03/1.59 % (4329)Time elapsed: 0.010 s
% 2.03/1.59 % (4329)Instructions burned: 16 (million)
% 2.03/1.59 % (4329)------------------------------
% 2.03/1.59 % (4329)------------------------------
% 2.03/1.59 % (4330)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_4213 for (2999ds/3Mi)
% 2.03/1.59 % (4330)Instruction limit reached!
% 2.03/1.59 % (4330)------------------------------
% 2.03/1.59 % (4330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.59 % (4330)Termination reason: Unknown
% 2.03/1.59 % (4330)Termination phase: shuffling
% 2.03/1.59
% 2.03/1.59 % (4330)Memory used [KB]: 1023
% 2.03/1.59 % (4330)Time elapsed: 0.003 s
% 2.03/1.59 % (4330)Instructions burned: 3 (million)
% 2.03/1.59 % (4330)------------------------------
% 2.03/1.59 % (4330)------------------------------
% 2.03/1.59 % (4331)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_4213 for (2999ds/1041Mi)
% 2.03/1.60 % (4328)Instruction limit reached!
% 2.03/1.60 % (4328)------------------------------
% 2.03/1.60 % (4328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.60 % (4328)Termination reason: Unknown
% 2.03/1.60 % (4328)Termination phase: Saturation
% 2.03/1.60
% 2.03/1.60 % (4328)Memory used [KB]: 6012
% 2.03/1.60 % (4328)Time elapsed: 0.017 s
% 2.03/1.60 % (4328)Instructions burned: 37 (million)
% 2.03/1.60 % (4328)------------------------------
% 2.03/1.60 % (4328)------------------------------
% 2.10/1.60 % (4332)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/7Mi)
% 2.10/1.60 % (4332)Instruction limit reached!
% 2.10/1.60 % (4332)------------------------------
% 2.10/1.60 % (4332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.60 % (4332)Termination reason: Unknown
% 2.10/1.60 % (4332)Termination phase: Property scanning
% 2.10/1.60
% 2.10/1.60 % (4332)Memory used [KB]: 1151
% 2.10/1.60 % (4332)Time elapsed: 0.005 s
% 2.10/1.60 % (4332)Instructions burned: 7 (million)
% 2.10/1.60 % (4332)------------------------------
% 2.10/1.60 % (4332)------------------------------
% 2.10/1.60 % (4333)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/16Mi)
% 2.10/1.61 % (4334)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/3Mi)
% 2.10/1.61 % (4334)Instruction limit reached!
% 2.10/1.61 % (4334)------------------------------
% 2.10/1.61 % (4334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.61 % (4334)Termination reason: Unknown
% 2.10/1.61 % (4334)Termination phase: shuffling
% 2.10/1.61
% 2.10/1.61 % (4334)Memory used [KB]: 1023
% 2.10/1.61 % (4334)Time elapsed: 0.003 s
% 2.10/1.61 % (4334)Instructions burned: 4 (million)
% 2.10/1.61 % (4334)------------------------------
% 2.10/1.61 % (4334)------------------------------
% 2.10/1.61 % (4333)Instruction limit reached!
% 2.10/1.61 % (4333)------------------------------
% 2.10/1.61 % (4333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.61 % (4333)Termination reason: Unknown
% 2.10/1.61 % (4333)Termination phase: Twee Goal Transformation
% 2.10/1.61
% 2.10/1.61 % (4333)Memory used [KB]: 1151
% 2.10/1.61 % (4333)Time elapsed: 0.009 s
% 2.10/1.61 % (4333)Instructions burned: 16 (million)
% 2.10/1.61 % (4333)------------------------------
% 2.10/1.61 % (4333)------------------------------
% 2.10/1.61 % (4335)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/3Mi)
% 2.10/1.61 % (4335)Instruction limit reached!
% 2.10/1.61 % (4335)------------------------------
% 2.10/1.61 % (4335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.61 % (4335)Termination reason: Unknown
% 2.10/1.61 % (4335)Termination phase: shuffling
% 2.10/1.61
% 2.10/1.61 % (4335)Memory used [KB]: 1023
% 2.10/1.61 % (4335)Time elapsed: 0.003 s
% 2.10/1.61 % (4335)Instructions burned: 3 (million)
% 2.10/1.61 % (4335)------------------------------
% 2.10/1.61 % (4335)------------------------------
% 2.10/1.62 % (4336)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/7Mi)
% 2.10/1.62 % (4336)Instruction limit reached!
% 2.10/1.62 % (4336)------------------------------
% 2.10/1.62 % (4336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.62 % (4336)Termination reason: Unknown
% 2.10/1.62 % (4336)Termination phase: Property scanning
% 2.10/1.62
% 2.10/1.62 % (4336)Memory used [KB]: 1151
% 2.10/1.62 % (4336)Time elapsed: 0.005 s
% 2.10/1.62 % (4336)Instructions burned: 7 (million)
% 2.10/1.62 % (4336)------------------------------
% 2.10/1.62 % (4336)------------------------------
% 2.10/1.62 % (4337)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/3Mi)
% 2.10/1.62 % (4337)Instruction limit reached!
% 2.10/1.62 % (4337)------------------------------
% 2.10/1.62 % (4337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.62 % (4337)Termination reason: Unknown
% 2.10/1.62 % (4337)Termination phase: shuffling
% 2.10/1.62
% 2.10/1.62 % (4337)Memory used [KB]: 1023
% 2.10/1.62 % (4337)Time elapsed: 0.003 s
% 2.10/1.62 % (4337)Instructions burned: 3 (million)
% 2.10/1.62 % (4337)------------------------------
% 2.10/1.62 % (4337)------------------------------
% 2.10/1.63 % (4338)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/4Mi)
% 2.10/1.63 % (4338)Instruction limit reached!
% 2.10/1.63 % (4338)------------------------------
% 2.10/1.63 % (4338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.63 % (4338)Termination reason: Unknown
% 2.10/1.63 % (4338)Termination phase: shuffling
% 2.10/1.63
% 2.10/1.63 % (4338)Memory used [KB]: 1151
% 2.10/1.63 % (4338)Time elapsed: 0.003 s
% 2.10/1.63 % (4338)Instructions burned: 4 (million)
% 2.10/1.63 % (4338)------------------------------
% 2.10/1.63 % (4338)------------------------------
% 2.10/1.63 % (4339)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/18Mi)
% 2.10/1.64 % (4340)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/710Mi)
% 2.10/1.64 % (4339)Instruction limit reached!
% 2.10/1.64 % (4339)------------------------------
% 2.10/1.64 % (4339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.64 % (4339)Termination reason: Unknown
% 2.10/1.64 % (4339)Termination phase: Saturation
% 2.10/1.64
% 2.10/1.64 % (4339)Memory used [KB]: 5756
% 2.10/1.64 % (4339)Time elapsed: 0.011 s
% 2.10/1.64 % (4339)Instructions burned: 19 (million)
% 2.10/1.64 % (4339)------------------------------
% 2.10/1.64 % (4339)------------------------------
% 2.10/1.64 % (4341)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/6Mi)
% 2.10/1.64 % (4341)Instruction limit reached!
% 2.10/1.64 % (4341)------------------------------
% 2.10/1.64 % (4341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.64 % (4341)Termination reason: Unknown
% 2.10/1.64 % (4341)Termination phase: Property scanning
% 2.10/1.64
% 2.10/1.64 % (4341)Memory used [KB]: 1151
% 2.10/1.64 % (4341)Time elapsed: 0.005 s
% 2.10/1.64 % (4341)Instructions burned: 8 (million)
% 2.10/1.64 % (4341)------------------------------
% 2.10/1.64 % (4341)------------------------------
% 2.10/1.64 % (4342)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/902Mi)
% 2.10/1.65 % (4320)Instruction limit reached!
% 2.10/1.65 % (4320)------------------------------
% 2.10/1.65 % (4320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.65 % (4320)Termination reason: Unknown
% 2.10/1.65 % (4320)Termination phase: Saturation
% 2.10/1.65
% 2.10/1.65 % (4320)Memory used [KB]: 6780
% 2.10/1.65 % (4320)Time elapsed: 0.090 s
% 2.10/1.65 % (4320)Instructions burned: 184 (million)
% 2.10/1.65 % (4320)------------------------------
% 2.10/1.65 % (4320)------------------------------
% 2.10/1.65 % (4343)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/21Mi)
% 2.10/1.66 % (4344)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/5Mi)
% 2.10/1.66 % (4344)Instruction limit reached!
% 2.10/1.66 % (4344)------------------------------
% 2.10/1.66 % (4344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.66 % (4344)Termination reason: Unknown
% 2.10/1.66 % (4344)Termination phase: shuffling
% 2.10/1.66
% 2.10/1.66 % (4344)Memory used [KB]: 1151
% 2.10/1.66 % (4344)Time elapsed: 0.004 s
% 2.10/1.66 % (4344)Instructions burned: 5 (million)
% 2.10/1.66 % (4344)------------------------------
% 2.10/1.66 % (4344)------------------------------
% 2.10/1.66 % (4343)Instruction limit reached!
% 2.10/1.66 % (4343)------------------------------
% 2.10/1.66 % (4343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.66 % (4343)Termination reason: Unknown
% 2.10/1.66 % (4343)Termination phase: Property scanning
% 2.10/1.66
% 2.10/1.66 % (4343)Memory used [KB]: 1151
% 2.10/1.66 % (4343)Time elapsed: 0.011 s
% 2.10/1.66 % (4343)Instructions burned: 22 (million)
% 2.10/1.66 % (4343)------------------------------
% 2.10/1.66 % (4343)------------------------------
% 2.10/1.67 % (4345)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_4213 for (2999ds/6Mi)
% 2.10/1.67 % (4345)Instruction limit reached!
% 2.10/1.67 % (4345)------------------------------
% 2.10/1.67 % (4345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.67 % (4345)Termination reason: Unknown
% 2.10/1.67 % (4345)Termination phase: Property scanning
% 2.10/1.67
% 2.10/1.67 % (4345)Memory used [KB]: 1151
% 2.10/1.67 % (4345)Time elapsed: 0.005 s
% 2.10/1.67 % (4345)Instructions burned: 7 (million)
% 2.10/1.67 % (4345)------------------------------
% 2.10/1.67 % (4345)------------------------------
% 2.10/1.68 % (4347)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4213 for (2998ds/377Mi)
% 2.10/1.68 % (4348)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_4213 for (2998ds/779Mi)
% 2.10/1.69 % (4349)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_4213 for (2998ds/19Mi)
% 2.10/1.69 % (4349)Instruction limit reached!
% 2.10/1.69 % (4349)------------------------------
% 2.10/1.69 % (4349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.69 % (4349)Termination reason: Unknown
% 2.10/1.69 % (4349)Termination phase: Property scanning
% 2.10/1.69
% 2.10/1.69 % (4349)Memory used [KB]: 1151
% 2.10/1.69 % (4349)Time elapsed: 0.010 s
% 2.10/1.69 % (4349)Instructions burned: 19 (million)
% 2.10/1.69 % (4349)------------------------------
% 2.10/1.69 % (4349)------------------------------
% 2.10/1.70 % (4342)First to succeed.
% 2.10/1.70 % (4325)Instruction limit reached!
% 2.10/1.70 % (4325)------------------------------
% 2.10/1.70 % (4325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.70 % (4325)Termination reason: Unknown
% 2.10/1.70 % (4325)Termination phase: Saturation
% 2.10/1.70
% 2.10/1.70 % (4325)Memory used [KB]: 6908
% 2.10/1.70 % (4325)Time elapsed: 0.140 s
% 2.10/1.70 % (4325)Instructions burned: 275 (million)
% 2.10/1.70 % (4325)------------------------------
% 2.10/1.70 % (4325)------------------------------
% 2.10/1.70 % (4342)Refutation found. Thanks to Tanya!
% 2.10/1.70 % SZS status Theorem for DTF2THF_4213
% 2.10/1.70 % SZS output start Proof for DTF2THF_4213
% 2.10/1.70 thf(func_def_0, type, in: $i > $i > $o).
% 2.10/1.70 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.10/1.70 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.10/1.70 thf(func_def_8, type, powerset: $i > $i).
% 2.10/1.70 thf(func_def_10, type, setunion: $i > $i).
% 2.10/1.70 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.10/1.70 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.10/1.70 thf(func_def_26, type, prop2set: $o > $i).
% 2.10/1.70 thf(func_def_36, type, nonempty: $i > $o).
% 2.10/1.70 thf(func_def_58, type, sP0: $i > $i > $o).
% 2.10/1.70 thf(func_def_59, type, sP1: $i > $o).
% 2.10/1.70 thf(func_def_60, type, sP2: $i > $i > $o).
% 2.10/1.70 thf(func_def_61, type, sP3: $i > $i > $o).
% 2.10/1.70 thf(func_def_64, type, sK6: $i > $i).
% 2.10/1.70 thf(func_def_65, type, sK7: $i > $i).
% 2.10/1.70 thf(func_def_68, type, sK10: $i > $i).
% 2.10/1.70 thf(func_def_79, type, sK21: $i > $i).
% 2.10/1.70 thf(func_def_82, type, sK24: $i > $i).
% 2.10/1.70 thf(func_def_83, type, sK25: $i > $i > $i).
% 2.10/1.70 thf(func_def_84, type, sK26: $i > $i > $i).
% 2.10/1.70 thf(func_def_87, type, sK29: $i > $i > $i).
% 2.10/1.70 thf(func_def_92, type, sK34: $i > $i > $i).
% 2.10/1.70 thf(func_def_93, type, sK35: $i > $i > $i).
% 2.10/1.70 thf(func_def_94, type, sK36: $i > $i > $i).
% 2.10/1.70 thf(func_def_95, type, sK37: $i > $i > $i).
% 2.10/1.70 thf(func_def_96, type, sK38: $i > $i > $i > $i).
% 2.10/1.70 thf(func_def_97, type, sK39: $i > $i).
% 2.10/1.70 thf(func_def_98, type, sK40: $i > $i).
% 2.10/1.70 thf(func_def_99, type, sK41: $i > $i).
% 2.10/1.70 thf(func_def_100, type, sK42: $i > $i).
% 2.10/1.70 thf(func_def_101, type, sK43: $i > $i > $i > $i).
% 2.10/1.70 thf(func_def_102, type, sK44: $i > $i > $i > $i).
% 2.10/1.70 thf(func_def_103, type, sK45: $i > $i > $i).
% 2.10/1.70 thf(func_def_104, type, sK46: $i > $i > $i).
% 2.10/1.70 thf(func_def_105, type, sK47: $i > $i > $i).
% 2.10/1.70 thf(func_def_106, type, sK48: $i > $i).
% 2.10/1.70 thf(func_def_107, type, sK49: $i > $i > $i).
% 2.10/1.70 thf(func_def_109, type, sK51: $i > $i).
% 2.10/1.70 thf(func_def_110, type, sK52: $i > $i).
% 2.10/1.70 thf(func_def_111, type, sK53: $i > $i > $i).
% 2.10/1.70 thf(func_def_114, type, sK56: $i > $o).
% 2.10/1.70 thf(func_def_121, type, sK63: ($i > $o) > $i).
% 2.10/1.70 thf(func_def_122, type, sK64: $i > $o).
% 2.10/1.70 thf(func_def_127, type, sK69: $i > $o).
% 2.10/1.70 thf(func_def_130, type, sK72: $i > $o).
% 2.10/1.70 thf(func_def_133, type, sK75: $i > $i > $o).
% 2.10/1.70 thf(func_def_134, type, sK76: $i > $i).
% 2.10/1.70 thf(func_def_135, type, sK77: $i > $i).
% 2.10/1.70 thf(func_def_136, type, sK78: ($i > $i > $o) > $i > $i).
% 2.10/1.70 thf(func_def_137, type, sK79: ($i > $i > $o) > $i > $i).
% 2.10/1.70 thf(func_def_138, type, sK80: $i > ($i > $i > $o) > $i > $i).
% 2.10/1.70 thf(func_def_144, type, sK86: $i > $o).
% 2.10/1.70 thf(func_def_145, type, sK87: ($i > $o) > $i).
% 2.10/1.70 thf(func_def_146, type, sK88: $i > $o).
% 2.10/1.70 thf(func_def_147, type, sK89: $i > $i).
% 2.10/1.70 thf(func_def_148, type, sK90: $i > $i).
% 2.10/1.70 thf(func_def_152, type, sK94: $i > $o).
% 2.10/1.70 thf(func_def_153, type, sK95: $i > $o).
% 2.10/1.70 thf(func_def_159, type, sK101: $i > $i > $i).
% 2.10/1.70 thf(func_def_167, type, ph109: !>[X0: $tType]:(X0)).
% 2.10/1.70 thf(f1248,plain,(
% 2.10/1.70 $false),
% 2.10/1.70 inference(trivial_inequality_removal,[status(thm)],[f1244])).
% 2.10/1.70 thf(f1244,plain,(
% 2.10/1.70 ($true != $true)),
% 2.10/1.70 inference(superposition,[status(thm)],[f461,f653])).
% 2.10/1.70 thf(f653,plain,(
% 2.10/1.70 ((in @ sK61 @ (powerset @ sK62)) = $true)),
% 2.10/1.70 inference(trivial_inequality_removal,[status(thm)],[f652])).
% 2.10/1.70 thf(f652,plain,(
% 2.10/1.70 ($true != $true) | ((in @ sK61 @ (powerset @ sK62)) = $true)),
% 2.10/1.70 inference(forward_demodulation,[status(thm)],[f649,f463])).
% 2.10/1.70 thf(f463,plain,(
% 2.10/1.70 (powersetAx = $true)),
% 2.10/1.70 inference(cnf_transformation,[status(thm)],[f264])).
% 2.10/1.70 thf(f264,plain,(
% 2.10/1.70 (dsetconstrER = $true) & (wellorderingAx = $true) & (setadjoinIR = $true) & (prop2setE = $true) & (emptysetimpfalse = $true) & (replAx = $true) & (omega0Ax = $true) & (notinemptyset = $true) & (setadjoinIL = $true) & (emptysetE = $true) & (setoftrueEq = $true) & (nonemptyI1 = $true) & (emptysetAx = $true) & (powersetAx = $true) & (nonemptyI = $true) & (((in @ sK61 @ (powerset @ sK62)) != $true) & ! [X2 : $i] : (($true = (in @ X2 @ sK62)) | ($true != (in @ X2 @ sK61)))) & (omegaSAx = $true) & (setadjoinOr = $true) & (exuE3e = $true) & (setext = $true) & (setadjoinE = $true) & (emptyinunitempty = $true) & (emptyI = $true) & (setbeta = $true) & (foundationAx = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (setextAx = $true) & (descrp = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (omegaIndAx = $true)),
% 2.10/1.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62])],[f147,f263])).
% 2.10/1.70 thf(f263,plain,(
% 2.10/1.70 ? [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))) => (((in @ sK61 @ (powerset @ sK62)) != $true) & ! [X2 : $i] : (($true = (in @ X2 @ sK62)) | ($true != (in @ X2 @ sK61))))),
% 2.10/1.70 introduced(definition,[],[choice_axiom])).
% 2.10/1.70 thf(f147,plain,(
% 2.10/1.70 (dsetconstrER = $true) & (wellorderingAx = $true) & (setadjoinIR = $true) & (prop2setE = $true) & (emptysetimpfalse = $true) & (replAx = $true) & (omega0Ax = $true) & (notinemptyset = $true) & (setadjoinIL = $true) & (emptysetE = $true) & (setoftrueEq = $true) & (nonemptyI1 = $true) & (emptysetAx = $true) & (powersetAx = $true) & (nonemptyI = $true) & ? [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))) & (omegaSAx = $true) & (setadjoinOr = $true) & (exuE3e = $true) & (setext = $true) & (setadjoinE = $true) & (emptyinunitempty = $true) & (emptyI = $true) & (setbeta = $true) & (foundationAx = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (exuE1 = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (setextAx = $true) & (descrp = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (omegaIndAx = $true)),
% 2.10/1.70 inference(flattening,[status(thm)],[f146])).
% 2.10/1.70 thf(f146,plain,(
% 2.10/1.70 (((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $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)),
% 2.10/1.70 inference(ennf_transformation,[status(thm)],[f61])).
% 2.10/1.70 thf(f61,plain,(
% 2.10/1.70 ~((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) => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ($true = (in @ X0 @ (powerset @ X1))))))))))))))))))))))))))))))))))))))),
% 2.10/1.70 inference(fool_elimination,[status(thm)],[f60])).
% 2.10/1.70 thf(f60,plain,(
% 2.10/1.70 ~(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 => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1)))))))))))))))))))))))))))))))))))))),
% 2.10/1.70 inference(rectify,[status(thm)],[f39])).
% 2.10/1.70 thf(f39,negated_conjecture,(
% 2.10/1.70 ~(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 => ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (in @ X4 @ (powerset @ X3)))))))))))))))))))))))))))))))))))))),
% 2.10/1.70 inference(negated_conjecture,[status(cth)],[f38])).
% 2.10/1.70 thf(f38,conjecture,(
% 2.10/1.70 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 => ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (in @ X4 @ (powerset @ X3))))))))))))))))))))))))))))))))))))),
% 2.10/1.70 file('/export/starexec/sandbox/tmp/tmp.gkmIHVRPeB/DTF2THF_4213.p',powersetI)).
% 2.10/1.70 thf(f649,plain,(
% 2.10/1.70 (powersetAx != $true) | ((in @ sK61 @ (powerset @ sK62)) = $true)),
% 2.10/1.70 inference(trivial_inequality_removal,[status(thm)],[f648])).
% 2.10/1.70 thf(f648,plain,(
% 2.10/1.70 ($true != $true) | ((in @ sK61 @ (powerset @ sK62)) = $true) | (powersetAx != $true)),
% 2.10/1.70 inference(duplicate_literal_removal,[status(thm)],[f645])).
% 2.10/1.70 thf(f645,plain,(
% 2.10/1.70 ((in @ sK61 @ (powerset @ sK62)) = $true) | (powersetAx != $true) | ((in @ sK61 @ (powerset @ sK62)) = $true) | ($true != $true)),
% 2.10/1.70 inference(superposition,[status(thm)],[f634,f390])).
% 2.10/1.70 thf(f390,plain,(
% 2.10/1.70 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK29 @ X1 @ X0) @ X0)) | ($true = (in @ X0 @ (powerset @ X1))) | (powersetAx != $true)) )),
% 2.10/1.70 inference(cnf_transformation,[status(thm)],[f213])).
% 2.10/1.70 thf(f213,plain,(
% 2.10/1.70 (! [X0 : $i,X1 : $i] : ((($true = (in @ X0 @ (powerset @ X1))) | (((in @ (sK29 @ X1 @ X0) @ X1) != $true) & ($true = (in @ (sK29 @ X1 @ X0) @ X0)))) & (! [X3 : $i] : (((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) | ($true != (in @ X0 @ (powerset @ X1))))) | (powersetAx != $true)) & ((powersetAx = $true) | (((((in @ sK32 @ sK31) != $true) & ((in @ sK32 @ sK30) = $true)) | ((in @ sK30 @ (powerset @ sK31)) != $true)) & (! [X7 : $i] : (((in @ X7 @ sK31) = $true) | ($true != (in @ X7 @ sK30))) | ((in @ sK30 @ (powerset @ sK31)) = $true))))),
% 2.10/1.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32])],[f209,f212,f211,f210])).
% 2.10/1.70 thf(f210,plain,(
% 2.10/1.70 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) => (((in @ (sK29 @ X1 @ X0) @ X1) != $true) & ($true = (in @ (sK29 @ X1 @ X0) @ X0))))),
% 2.10/1.70 introduced(definition,[],[choice_axiom])).
% 2.10/1.70 thf(f211,plain,(
% 2.10/1.70 ? [X4 : $i,X5 : $i] : ((? [X6 : $i] : (($true != (in @ X6 @ X5)) & ((in @ X6 @ X4) = $true)) | ($true != (in @ X4 @ (powerset @ X5)))) & (! [X7 : $i] : (((in @ X7 @ X5) = $true) | ((in @ X7 @ X4) != $true)) | ($true = (in @ X4 @ (powerset @ X5))))) => ((? [X6 : $i] : (((in @ X6 @ sK31) != $true) & ((in @ X6 @ sK30) = $true)) | ((in @ sK30 @ (powerset @ sK31)) != $true)) & (! [X7 : $i] : (((in @ X7 @ sK31) = $true) | ($true != (in @ X7 @ sK30))) | ((in @ sK30 @ (powerset @ sK31)) = $true)))),
% 2.10/1.70 introduced(definition,[],[choice_axiom])).
% 2.10/1.70 thf(f212,plain,(
% 2.10/1.70 ? [X6 : $i] : (((in @ X6 @ sK31) != $true) & ((in @ X6 @ sK30) = $true)) => (((in @ sK32 @ sK31) != $true) & ((in @ sK32 @ sK30) = $true))),
% 2.10/1.70 introduced(definition,[],[choice_axiom])).
% 2.10/1.70 thf(f209,plain,(
% 2.10/1.70 (! [X0 : $i,X1 : $i] : ((($true = (in @ X0 @ (powerset @ X1))) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) & (! [X3 : $i] : (((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) | ($true != (in @ X0 @ (powerset @ X1))))) | (powersetAx != $true)) & ((powersetAx = $true) | ? [X4 : $i,X5 : $i] : ((? [X6 : $i] : (($true != (in @ X6 @ X5)) & ((in @ X6 @ X4) = $true)) | ($true != (in @ X4 @ (powerset @ X5)))) & (! [X7 : $i] : (((in @ X7 @ X5) = $true) | ((in @ X7 @ X4) != $true)) | ($true = (in @ X4 @ (powerset @ X5))))))),
% 2.10/1.70 inference(rectify,[status(thm)],[f208])).
% 2.10/1.70 thf(f208,plain,(
% 2.10/1.70 (! [X0 : $i,X1 : $i] : ((($true = (in @ X0 @ (powerset @ X1))) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) & (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | ($true != (in @ X0 @ (powerset @ X1))))) | (powersetAx != $true)) & ((powersetAx = $true) | ? [X0 : $i,X1 : $i] : ((? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ($true != (in @ X0 @ (powerset @ X1)))) & (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | ($true = (in @ X0 @ (powerset @ X1))))))),
% 2.10/1.70 inference(nnf_transformation,[status(thm)],[f139])).
% 2.10/1.70 thf(f139,plain,(
% 2.10/1.70 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) <=> ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))) <=> (powersetAx = $true)),
% 2.10/1.70 inference(ennf_transformation,[status(thm)],[f48])).
% 2.10/1.70 thf(f48,plain,(
% 2.10/1.70 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) <=> ! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true))) <=> (powersetAx = $true)),
% 2.10/1.70 inference(fool_elimination,[status(thm)],[f47])).
% 2.10/1.70 thf(f47,plain,(
% 2.10/1.70 (powersetAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) <=> (in @ X0 @ (powerset @ X1))))),
% 2.10/1.70 inference(rectify,[status(thm)],[f5])).
% 2.10/1.70 thf(f5,axiom,(
% 2.10/1.70 (powersetAx = ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) <=> (in @ X4 @ (powerset @ X3))))),
% 2.10/1.70 file('/export/starexec/sandbox/tmp/tmp.gkmIHVRPeB/DTF2THF_4213.p',powersetAx)).
% 2.10/1.70 thf(f634,plain,(
% 2.10/1.70 ( ! [X0 : $i] : (((in @ (sK29 @ sK62 @ X0) @ sK61) != $true) | ($true = (in @ X0 @ (powerset @ sK62)))) )),
% 2.10/1.70 inference(trivial_inequality_removal,[status(thm)],[f633])).
% 2.10/1.70 thf(f633,plain,(
% 2.10/1.70 ( ! [X0 : $i] : (($true = (in @ X0 @ (powerset @ sK62))) | ($true != $true) | ((in @ (sK29 @ sK62 @ X0) @ sK61) != $true)) )),
% 2.10/1.70 inference(forward_demodulation,[status(thm)],[f593,f463])).
% 2.10/1.70 thf(f593,plain,(
% 2.10/1.70 ( ! [X0 : $i] : (((in @ (sK29 @ sK62 @ X0) @ sK61) != $true) | ($true = (in @ X0 @ (powerset @ sK62))) | (powersetAx != $true)) )),
% 2.10/1.70 inference(trivial_inequality_removal,[status(thm)],[f582])).
% 2.10/1.70 thf(f582,plain,(
% 2.10/1.70 ( ! [X0 : $i] : (($true != $true) | (powersetAx != $true) | ($true = (in @ X0 @ (powerset @ sK62))) | ((in @ (sK29 @ sK62 @ X0) @ sK61) != $true)) )),
% 2.10/1.70 inference(superposition,[status(thm)],[f391,f460])).
% 2.10/1.70 thf(f460,plain,(
% 2.10/1.70 ( ! [X2 : $i] : (($true = (in @ X2 @ sK62)) | ($true != (in @ X2 @ sK61))) )),
% 2.10/1.70 inference(cnf_transformation,[status(thm)],[f264])).
% 2.10/1.70 thf(f391,plain,(
% 2.10/1.70 ( ! [X0 : $i,X1 : $i] : (((in @ (sK29 @ X1 @ X0) @ X1) != $true) | ($true = (in @ X0 @ (powerset @ X1))) | (powersetAx != $true)) )),
% 2.10/1.70 inference(cnf_transformation,[status(thm)],[f213])).
% 2.10/1.70 thf(f461,plain,(
% 2.10/1.70 ((in @ sK61 @ (powerset @ sK62)) != $true)),
% 2.10/1.70 inference(cnf_transformation,[status(thm)],[f264])).
% 2.10/1.70 % SZS output end Proof for DTF2THF_4213
% 2.10/1.70 % (4342)------------------------------
% 2.10/1.70 % (4342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.10/1.70 % (4342)Termination reason: Refutation
% 2.10/1.70
% 2.10/1.70 % (4342)Memory used [KB]: 6524
% 2.10/1.70 % (4342)Time elapsed: 0.057 s
% 2.10/1.70 % (4342)Instructions burned: 105 (million)
% 2.10/1.70 % (4342)------------------------------
% 2.10/1.70 % (4342)------------------------------
% 2.10/1.70 % (4319)Success in time 0.146 s
%------------------------------------------------------------------------------