%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU521^1 : 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 09:35:03 AM UTC 2026
% Result : Theorem 2.03s 1.50s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 965 ( 262 equ; 0 cnn)
% Maximal formula atoms : 40 ( 31 avg)
% Number of connectives : 673 ( 56 ~; 43 |; 144 &; 261 @)
% ( 6 <=>; 163 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 107 ( 104 usr; 45 con; 0-3 aty)
% Number of variables : 70 ( 0 ^; 47 !; 23 ?; 70 :)
% 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_62,type,
sP1: $i > $i > $o ).
thf(func_def_63,type,
sP2: $i > $o ).
thf(func_def_64,type,
sP3: $i > $i > $o ).
thf(func_def_65,type,
sP4: $i > $i > $o ).
thf(func_def_68,type,
sK7: $i > $i ).
thf(func_def_69,type,
sK8: $i > $i > $i ).
thf(func_def_79,type,
sK18: $i > $i ).
thf(func_def_82,type,
sK21: $i > $o ).
thf(func_def_86,type,
sK25: $i > $o ).
thf(func_def_87,type,
sK26: $i > $o ).
thf(func_def_90,type,
sK29: $i > $i ).
thf(func_def_92,type,
sK31: $i > $i ).
thf(func_def_95,type,
sK34: $i > $i ).
thf(func_def_96,type,
sK35: $i > $i > $i ).
thf(func_def_99,type,
sK38: $i > $i > $i ).
thf(func_def_100,type,
sK39: $i > $i > $i ).
thf(func_def_104,type,
sK43: $i > $i > $o ).
thf(func_def_105,type,
sK44: $i > $i ).
thf(func_def_106,type,
sK45: $i > $i ).
thf(func_def_107,type,
sK46: ( $i > $i > $o ) > $i > $i ).
thf(func_def_108,type,
sK47: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_109,type,
sK48: ( $i > $i > $o ) > $i > $i ).
thf(func_def_110,type,
sK49: $i > $i ).
thf(func_def_113,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_114,type,
sK53: $i > $o ).
thf(func_def_115,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_116,type,
sK55: $i > $o ).
thf(func_def_117,type,
sK56: $i > $i ).
thf(func_def_134,type,
sK73: $i > $i > $i ).
thf(func_def_135,type,
sK74: $i > $i > $i ).
thf(func_def_136,type,
sK75: $i > $i > $i ).
thf(func_def_137,type,
sK76: $i > $i > $i ).
thf(func_def_138,type,
sK77: $i > $i > $i ).
thf(func_def_139,type,
sK78: $i > $i > $i > $i ).
thf(func_def_140,type,
sK79: $i > $i ).
thf(func_def_141,type,
sK80: $i > $i ).
thf(func_def_142,type,
sK81: $i > $i ).
thf(func_def_143,type,
sK82: $i > $i ).
thf(func_def_144,type,
sK83: $i > $i > $i > $i ).
thf(func_def_145,type,
sK84: $i > $i > $i > $i ).
thf(func_def_146,type,
sK85: $i > $i > $i ).
thf(func_def_147,type,
sK86: $i > $i > $i ).
thf(func_def_148,type,
sK87: $i > $i > $i ).
thf(func_def_149,type,
sK88: $i > $i ).
thf(func_def_151,type,
sK90: $i > $i ).
thf(func_def_152,type,
sK91: $i > $i ).
thf(func_def_155,type,
sK94: $i > $o ).
thf(func_def_160,type,
sK99: $i > $i > $i ).
thf(func_def_164,type,
sK103: $i > $o ).
thf(func_def_173,type,
sK112: $i > $i > $i ).
thf(func_def_174,type,
sK113: $i > $o ).
thf(func_def_176,type,
ph115:
!>[X0: $tType] : X0 ).
thf(f685,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f682]) ).
thf(f682,plain,
$true != $true,
inference(superposition,[status(thm)],[f642,f472]) ).
thf(f472,plain,
( $true
= ( in @ sK59 @ sK60 ) ),
inference(cnf_transformation,[status(thm)],[f271]) ).
thf(f271,plain,
( ( emptysetAx = $true )
& ( emptyinunitempty = $true )
& ( setunionAx = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI1 = $true )
& ( prop2setE = $true )
& ( emptyinPowerset = $true )
& ( setext = $true )
& ( omega0Ax = $true )
& ( wellorderingAx = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( exuE1 = $true )
& ( powersetI = $true )
& ( emptyInPowerset = $true )
& ( notinemptyset = $true )
& ( exuE3e = $true )
& ( replAx = $true )
& ( emptysetimpfalse = $true )
& ( $true
= ( in @ sK59 @ sK60 ) )
& ( $true
= ( in @ sK60 @ ( powerset @ sK58 ) ) )
& ( ( in @ sK59 @ sK58 )
!= $true )
& ( setadjoinE = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( setextAx = $true )
& ( descrp = $true )
& ( omegaIndAx = $true )
& ( setadjoinAx = $true )
& ( dsetconstrI = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( dsetconstrER = $true )
& ( setadjoinIL = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( setoftrueEq = $true )
& ( omegaSAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60])],[f163,f270]) ).
thf(f270,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
=> ( ( $true
= ( in @ sK59 @ sK60 ) )
& ( $true
= ( in @ sK60 @ ( powerset @ sK58 ) ) )
& ( ( in @ sK59 @ sK58 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f163,plain,
( ( emptysetAx = $true )
& ( emptyinunitempty = $true )
& ( setunionAx = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI1 = $true )
& ( prop2setE = $true )
& ( emptyinPowerset = $true )
& ( setext = $true )
& ( omega0Ax = $true )
& ( wellorderingAx = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( exuE1 = $true )
& ( powersetI = $true )
& ( emptyInPowerset = $true )
& ( notinemptyset = $true )
& ( exuE3e = $true )
& ( replAx = $true )
& ( emptysetimpfalse = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
& ( setadjoinE = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( setextAx = $true )
& ( descrp = $true )
& ( omegaIndAx = $true )
& ( setadjoinAx = $true )
& ( dsetconstrI = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( dsetconstrER = $true )
& ( setadjoinIL = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( setoftrueEq = $true )
& ( omegaSAx = $true ) ),
inference(flattening,[status(thm)],[f162]) ).
thf(f162,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $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)],[f75]) ).
thf(f75,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f74]) ).
thf(f74,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,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
=> ! [X3: $i,X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f41,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
=> ! [X3: $i,X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tJKBZQcyjw/DTF2THF_14826.p',powersetE) ).
thf(f642,plain,
( $true
!= ( in @ sK59 @ sK60 ) ),
inference(trivial_inequality_removal,[status(thm)],[f638]) ).
thf(f638,plain,
( ( $true
!= ( in @ sK59 @ sK60 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f470,f623]) ).
thf(f623,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK58 ) )
| ( ( in @ X0 @ sK60 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f622]) ).
thf(f622,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ sK60 )
!= $true )
| ( $true
= ( in @ X0 @ sK58 ) ) ),
inference(forward_demodulation,[status(thm)],[f621,f459]) ).
thf(f459,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f271]) ).
thf(f621,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK60 )
!= $true )
| ( powersetAx != $true )
| ( $true
= ( in @ X0 @ sK58 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f618]) ).
thf(f618,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK60 )
!= $true )
| ( powersetAx != $true )
| ( $true != $true )
| ( $true
= ( in @ X0 @ sK58 ) ) ),
inference(superposition,[status(thm)],[f569,f471]) ).
thf(f471,plain,
( $true
= ( in @ sK60 @ ( powerset @ sK58 ) ) ),
inference(cnf_transformation,[status(thm)],[f271]) ).
thf(f569,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( powersetAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f347]) ).
thf(f347,plain,
( ( ! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
& ( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( $true
!= ( in @ ( sK99 @ X1 @ X0 ) @ X0 ) )
& ( ( in @ ( sK99 @ X1 @ X0 ) @ X1 )
= $true ) ) ) )
| ( powersetAx != $true ) )
& ( ( powersetAx = $true )
| ( ( ( $true
!= ( in @ sK101 @ ( powerset @ sK100 ) ) )
| ( ( $true
!= ( in @ sK102 @ sK100 ) )
& ( ( in @ sK102 @ sK101 )
= $true ) ) )
& ( ( $true
= ( in @ sK101 @ ( powerset @ sK100 ) ) )
| ! [X7: $i] :
( ( ( in @ X7 @ sK100 )
= $true )
| ( ( in @ X7 @ sK101 )
!= $true ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK99,sK100,sK101,sK102])],[f343,f346,f345,f344]) ).
thf(f344,plain,
! [X0: $i,X1: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
=> ( ( $true
!= ( in @ ( sK99 @ X1 @ X0 ) @ X0 ) )
& ( ( in @ ( sK99 @ X1 @ X0 ) @ X1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f345,plain,
( ? [X4: $i,X5: $i] :
( ( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ? [X6: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
& ( ( in @ X6 @ X5 )
= $true ) ) )
& ( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ X5 )
!= $true ) ) ) )
=> ( ( ( $true
!= ( in @ sK101 @ ( powerset @ sK100 ) ) )
| ? [X6: $i] :
( ( ( in @ X6 @ sK100 )
!= $true )
& ( ( in @ X6 @ sK101 )
= $true ) ) )
& ( ( $true
= ( in @ sK101 @ ( powerset @ sK100 ) ) )
| ! [X7: $i] :
( ( ( in @ X7 @ sK100 )
= $true )
| ( ( in @ X7 @ sK101 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f346,plain,
( ? [X6: $i] :
( ( ( in @ X6 @ sK100 )
!= $true )
& ( ( in @ X6 @ sK101 )
= $true ) )
=> ( ( $true
!= ( in @ sK102 @ sK100 ) )
& ( ( in @ sK102 @ sK101 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f343,plain,
( ( ! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
& ( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) ) )
| ( powersetAx != $true ) )
& ( ( powersetAx = $true )
| ? [X4: $i,X5: $i] :
( ( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ? [X6: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
& ( ( in @ X6 @ X5 )
= $true ) ) )
& ( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ X5 )
!= $true ) ) ) ) ) ),
inference(rectify,[status(thm)],[f342]) ).
thf(f342,plain,
( ( ! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
& ( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) ) )
| ( powersetAx != $true ) )
& ( ( powersetAx = $true )
| ? [X0: $i,X1: $i] :
( ( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f156]) ).
thf(f156,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f89]) ).
thf(f89,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
<=> ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( powersetAx = $true ) ),
inference(fool_elimination,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
<=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetAx ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X3: $i,X4: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
<=> ( in @ X4 @ ( powerset @ X3 ) ) )
= powersetAx ),
file('/export/starexec/sandbox2/tmp/tmp.tJKBZQcyjw/DTF2THF_14826.p',powersetAx) ).
thf(f470,plain,
( ( in @ sK59 @ sK58 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU521^1 : 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 12:25:42 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
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU521^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Preliminary Notions - Power Sets and Unions
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : (! A:i.! B:i.! x:i.in B (powerset A) -> in x B -> in x A)
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC023g [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.40 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 89 ( 40 unt; 48 typ; 40 def)
% 0.31/0.47 % Number of atoms : 225 ( 52 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 40 ( 5 avg)
% 0.31/0.47 % Number of connectives : 373 ( 7 ~; 4 |; 18 &; 245 @)
% 0.31/0.47 % ( 7 <=>; 92 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 45 ( 2 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 51 ( 48 usr; 41 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 123 ( 15 ^; 92 !; 16 ?; 123 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=86
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu_type,type,
% 0.31/0.47 exu: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu,definition,
% 0.31/0.47 ( exu
% 0.31/0.47 = ( ^ [Xphi: $i > $o] :
% 0.31/0.47 ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx_type,type,
% 0.31/0.47 setextAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx,definition,
% 0.31/0.47 ( setextAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xx @ B ) )
% 0.31/0.47 => ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset_type,type,
% 0.31/0.47 emptyset: $i ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx_type,type,
% 0.31/0.47 emptysetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx,definition,
% 0.31/0.47 ( emptysetAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin_type,type,
% 0.31/0.47 setadjoin: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx_type,type,
% 0.31/0.47 setadjoinAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx,definition,
% 0.31/0.47 ( setadjoinAx
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 <=> ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset_type,type,
% 0.31/0.47 powerset: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx_type,type,
% 0.31/0.47 powersetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx,definition,
% 0.31/0.47 ( powersetAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 <=> ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion_type,type,
% 0.31/0.47 setunion: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx_type,type,
% 0.31/0.47 setunionAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx,definition,
% 0.31/0.47 ( setunionAx
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 <=> ? [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega_type,type,
% 0.31/0.47 omega: $i ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax_type,type,
% 0.31/0.47 omega0Ax: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax,definition,
% 0.31/0.47 ( omega0Ax
% 0.31/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx_type,type,
% 0.31/0.47 omegaSAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx,definition,
% 0.31/0.47 ( omegaSAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx_type,type,
% 0.31/0.47 omegaIndAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx,definition,
% 0.31/0.47 ( omegaIndAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( ( in @ emptyset @ A )
% 0.31/0.47 & ! [Xx: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ omega )
% 0.31/0.47 & ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(replAx_type,type,
% 0.31/0.47 replAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(replAx,definition,
% 0.31/0.47 ( replAx
% 0.31/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 <=> ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx_type,type,
% 0.31/0.47 foundationAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx,definition,
% 0.31/0.47 ( foundationAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ( ( in @ B @ A )
% 0.31/0.47 & ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx_type,type,
% 0.31/0.47 wellorderingAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx,definition,
% 0.31/0.47 ( wellorderingAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ? [B: $i] :
% 0.31/0.47 ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) ) )
% 0.31/0.47 & ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ A )
% 0.31/0.47 & ( in @ Xy @ A ) )
% 0.31/0.47 => ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ( ( in @ Xx @ C )
% 0.31/0.47 <=> ( in @ Xy @ C ) ) )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 & ! [C: $i,D: $i] :
% 0.31/0.47 ( ( ( in @ C @ B )
% 0.31/0.47 & ( in @ D @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ D ) )
% 0.31/0.47 | ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ D )
% 0.31/0.47 => ( in @ Xx @ C ) ) ) )
% 0.31/0.47 & ! [C: $i] :
% 0.31/0.47 ( ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/0.47 => ? [D: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ D @ B )
% 0.31/0.47 & ( in @ Xx @ C )
% 0.31/0.47 & ~ ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ D )
% 0.31/0.47 & ( in @ Xy @ C ) )
% 0.31/0.47 & ! [E: $i] :
% 0.31/0.47 ( ( in @ E @ B )
% 0.31/0.47 => ( ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ E )
% 0.31/0.47 => ( in @ Xy @ D ) )
% 0.31/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr_type,type,
% 0.31/0.47 descr: ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(descrp_type,type,
% 0.31/0.47 descrp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descrp,definition,
% 0.31/0.47 ( descrp
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 @ ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr_type,type,
% 0.31/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI_type,type,
% 0.31/0.47 dsetconstrI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI,definition,
% 0.31/0.47 ( dsetconstrI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL_type,type,
% 0.31/0.47 dsetconstrEL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL,definition,
% 0.31/0.47 ( dsetconstrEL
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER_type,type,
% 0.31/0.47 dsetconstrER: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER,definition,
% 0.31/0.47 ( dsetconstrER
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1_type,type,
% 0.31/0.47 exuE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1,definition,
% 0.31/0.47 ( exuE1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set_type,type,
% 0.31/0.47 prop2set: $o > $i ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set,definition,
% 0.31/0.47 ( prop2set
% 0.31/0.47 = ( ^ [Xphi: $o] :
% 0.31/0.47 ( dsetconstr @ ( powerset @ emptyset )
% 0.31/0.47 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE_type,type,
% 0.31/0.47 prop2setE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE,definition,
% 0.31/0.47 ( prop2setE
% 0.31/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE_type,type,
% 0.31/0.47 emptysetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE,definition,
% 0.31/0.47 ( emptysetE
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse_type,type,
% 0.31/0.47 emptysetimpfalse: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse,definition,
% 0.31/0.47 ( emptysetimpfalse
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => $false ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset_type,type,
% 0.31/0.47 notinemptyset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset,definition,
% 0.31/0.47 ( notinemptyset
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e_type,type,
% 0.31/0.47 exuE3e: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e,definition,
% 0.31/0.47 ( exuE3e
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setext_type,type,
% 0.31/0.47 setext: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setext,definition,
% 0.31/0.47 ( setext
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( A = B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI_type,type,
% 0.31/0.47 emptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI,definition,
% 0.31/0.47 ( emptyI
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty_type,type,
% 0.31/0.47 noeltsimpempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty,definition,
% 0.31/0.47 ( noeltsimpempty
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta_type,type,
% 0.31/0.47 setbeta: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta,definition,
% 0.31/0.47 ( setbeta
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty_type,type,
% 0.31/0.47 nonempty: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty,definition,
% 0.31/0.47 ( nonempty
% 0.31/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1_type,type,
% 0.31/0.47 nonemptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1,definition,
% 0.31/0.47 ( nonemptyE1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI_type,type,
% 0.31/0.47 nonemptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI,definition,
% 0.31/0.47 ( nonemptyI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( nonempty
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1_type,type,
% 0.31/0.47 nonemptyI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1,definition,
% 0.31/0.47 ( nonemptyI1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL_type,type,
% 0.31/0.47 setadjoinIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL,definition,
% 0.31/0.47 ( setadjoinIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty_type,type,
% 0.31/0.47 emptyinunitempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty,definition,
% 0.31/0.47 ( emptyinunitempty
% 0.31/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR_type,type,
% 0.31/0.47 setadjoinIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR,definition,
% 0.31/0.47 ( setadjoinIR
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE_type,type,
% 0.31/0.47 setadjoinE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE,definition,
% 0.31/0.47 ( setadjoinE
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ( ( Xy = Xx )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xy @ A )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr_type,type,
% 0.31/0.47 setadjoinOr: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr,definition,
% 0.31/0.47 ( setadjoinOr
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq_type,type,
% 0.31/0.47 setoftrueEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq,definition,
% 0.31/0.47 ( setoftrueEq
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : $true )
% 0.31/0.47 = A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI_type,type,
% 0.31/0.47 powersetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI,definition,
% 0.31/0.47 ( powersetI
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset_type,type,
% 0.31/0.47 emptyinPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset,definition,
% 0.31/0.47 ( emptyinPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset_type,type,
% 0.31/0.47 emptyInPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset,definition,
% 0.31/0.47 ( emptyInPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE,conjecture,
% 0.31/0.47 ( setextAx
% 0.31/0.47 => ( emptysetAx
% 0.31/0.47 => ( setadjoinAx
% 0.31/0.47 => ( powersetAx
% 0.31/0.47 => ( setunionAx
% 0.31/0.47 => ( omega0Ax
% 0.31/0.47 => ( omegaSAx
% 0.31/0.47 => ( omegaIndAx
% 0.31/0.47 => ( replAx
% 0.31/0.47 => ( foundationAx
% 0.31/0.47 => ( wellorderingAx
% 0.31/0.47 => ( descrp
% 0.31/0.47 => ( dsetconstrI
% 0.31/0.47 => ( dsetconstrEL
% 0.31/0.47 => ( dsetconstrER
% 0.31/0.47 => ( exuE1
% 0.31/0.47 => ( prop2setE
% 0.31/0.47 => ( emptysetE
% 0.31/0.47 => ( emptysetimpfalse
% 0.31/0.47 => ( notinemptyset
% 0.31/0.47 => ( exuE3e
% 0.31/0.47 => ( setext
% 0.31/0.47 => ( emptyI
% 0.31/0.47 => ( noeltsimpempty
% 0.31/0.47 => ( setbeta
% 0.31/0.47 => ( nonemptyE1
% 0.31/0.47 => ( nonemptyI
% 0.31/0.47 => ( nonemptyI1
% 0.31/0.47 => ( setadjoinIL
% 0.31/0.47 => ( emptyinunitempty
% 0.31/0.47 => ( setadjoinIR
% 0.31/0.47 => ( setadjoinE
% 0.31/0.47 => ( setadjoinOr
% 0.31/0.47 => ( setoftrueEq
% 0.31/0.47 => ( powersetI
% 0.31/0.47 => ( emptyinPowerset
% 0.31/0.47 => ( emptyInPowerset
% 0.31/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 => ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.87/1.37 ---- Embedded in THF ---
% 1.87/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.87/1.37 %%% Generated on Tue Feb 24 12:25:43 EST 2026
% 1.87/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.87/1.37 %%% Logic specification used:
% 1.87/1.37 %%% thf(spec, logic, $$dhol).
% 1.87/1.37
% 1.87/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.tJKBZQcyjw/DTF2DTF14826.p
% See solution above
% 1.87/1.37 ------------------------
% 1.87/1.39 ---- Cleaned THF ---
% 1.87/1.39 thf(in_type,type,
% 1.87/1.39 in: $i > $i > $o ).
% 1.87/1.39
% 1.87/1.39 thf(exu_type,type,
% 1.87/1.39 exu: ( $i > $o ) > $o ).
% 1.87/1.39
% 1.87/1.39 thf(exu,definition,
% 1.87/1.39 ( exu
% 1.87/1.39 = ( ^ [Xphi: $i > $o] :
% 1.87/1.39 ? [Xx: $i] :
% 1.87/1.39 ( ( Xphi @ Xx )
% 1.87/1.39 & ! [Xy: $i] :
% 1.87/1.39 ( ( Xphi @ Xy )
% 1.87/1.39 => ( Xx = Xy ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setextAx_type,type,
% 1.87/1.39 setextAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setextAx,definition,
% 1.87/1.39 ( setextAx
% 1.87/1.39 = ( ! [A: $i,B: $i] :
% 1.87/1.39 ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ A )
% 1.87/1.39 <=> ( in @ Xx @ B ) )
% 1.87/1.39 => ( A = B ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(emptyset_type,type,
% 1.87/1.39 emptyset: $i ).
% 1.87/1.39
% 1.87/1.39 thf(emptysetAx_type,type,
% 1.87/1.39 emptysetAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(emptysetAx,definition,
% 1.87/1.39 ( emptysetAx
% 1.87/1.39 = ( ! [Xx: $i] :
% 1.87/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoin_type,type,
% 1.87/1.39 setadjoin: $i > $i > $i ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinAx_type,type,
% 1.87/1.39 setadjoinAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinAx,definition,
% 1.87/1.39 ( setadjoinAx
% 1.87/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.87/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.87/1.39 <=> ( ( Xy = Xx )
% 1.87/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(powerset_type,type,
% 1.87/1.39 powerset: $i > $i ).
% 1.87/1.39
% 1.87/1.39 thf(powersetAx_type,type,
% 1.87/1.39 powersetAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(powersetAx,definition,
% 1.87/1.39 ( powersetAx
% 1.87/1.39 = ( ! [A: $i,B: $i] :
% 1.87/1.39 ( ( in @ B @ ( powerset @ A ) )
% 1.87/1.39 <=> ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ B )
% 1.87/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setunion_type,type,
% 1.87/1.39 setunion: $i > $i ).
% 1.87/1.39
% 1.87/1.39 thf(setunionAx_type,type,
% 1.87/1.39 setunionAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setunionAx,definition,
% 1.87/1.39 ( setunionAx
% 1.87/1.39 = ( ! [A: $i,Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 1.87/1.39 <=> ? [B: $i] :
% 1.87/1.39 ( ( in @ Xx @ B )
% 1.87/1.39 & ( in @ B @ A ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(omega_type,type,
% 1.87/1.39 omega: $i ).
% 1.87/1.39
% 1.87/1.39 thf(omega0Ax_type,type,
% 1.87/1.39 omega0Ax: $o ).
% 1.87/1.39
% 1.87/1.39 thf(omega0Ax,definition,
% 1.87/1.39 ( omega0Ax
% 1.87/1.39 = ( in @ emptyset @ omega ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(omegaSAx_type,type,
% 1.87/1.39 omegaSAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(omegaSAx,definition,
% 1.87/1.39 ( omegaSAx
% 1.87/1.39 = ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ omega )
% 1.87/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(omegaIndAx_type,type,
% 1.87/1.39 omegaIndAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(omegaIndAx,definition,
% 1.87/1.39 ( omegaIndAx
% 1.87/1.39 = ( ! [A: $i] :
% 1.87/1.39 ( ( ( in @ emptyset @ A )
% 1.87/1.39 & ! [Xx: $i] :
% 1.87/1.39 ( ( ( in @ Xx @ omega )
% 1.87/1.39 & ( in @ Xx @ A ) )
% 1.87/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.87/1.39 => ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ omega )
% 1.87/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(replAx_type,type,
% 1.87/1.39 replAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(replAx,definition,
% 1.87/1.39 ( replAx
% 1.87/1.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.87/1.39 ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ A )
% 1.87/1.39 => ( exu
% 1.87/1.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.87/1.39 => ? [B: $i] :
% 1.87/1.39 ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ B )
% 1.87/1.39 <=> ? [Xy: $i] :
% 1.87/1.39 ( ( in @ Xy @ A )
% 1.87/1.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(foundationAx_type,type,
% 1.87/1.39 foundationAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(foundationAx,definition,
% 1.87/1.39 ( foundationAx
% 1.87/1.39 = ( ! [A: $i] :
% 1.87/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.87/1.39 => ? [B: $i] :
% 1.87/1.39 ( ( in @ B @ A )
% 1.87/1.39 & ~ ? [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ B )
% 1.87/1.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(wellorderingAx_type,type,
% 1.87/1.39 wellorderingAx: $o ).
% 1.87/1.39
% 1.87/1.39 thf(wellorderingAx,definition,
% 1.87/1.39 ( wellorderingAx
% 1.87/1.39 = ( ! [A: $i] :
% 1.87/1.39 ? [B: $i] :
% 1.87/1.39 ( ! [C: $i] :
% 1.87/1.39 ( ( in @ C @ B )
% 1.87/1.39 => ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ C )
% 1.87/1.39 => ( in @ Xx @ A ) ) )
% 1.87/1.39 & ! [Xx: $i,Xy: $i] :
% 1.87/1.39 ( ( ( in @ Xx @ A )
% 1.87/1.39 & ( in @ Xy @ A ) )
% 1.87/1.39 => ( ! [C: $i] :
% 1.87/1.39 ( ( in @ C @ B )
% 1.87/1.39 => ( ( in @ Xx @ C )
% 1.87/1.39 <=> ( in @ Xy @ C ) ) )
% 1.87/1.39 => ( Xx = Xy ) ) )
% 1.87/1.39 & ! [C: $i,D: $i] :
% 1.87/1.39 ( ( ( in @ C @ B )
% 1.87/1.39 & ( in @ D @ B ) )
% 1.87/1.39 => ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ C )
% 1.87/1.39 => ( in @ Xx @ D ) )
% 1.87/1.39 | ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ D )
% 1.87/1.39 => ( in @ Xx @ C ) ) ) )
% 1.87/1.39 & ! [C: $i] :
% 1.87/1.39 ( ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ C )
% 1.87/1.39 => ( in @ Xx @ A ) )
% 1.87/1.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.87/1.39 => ? [D: $i,Xx: $i] :
% 1.87/1.39 ( ( in @ D @ B )
% 1.87/1.39 & ( in @ Xx @ C )
% 1.87/1.39 & ~ ? [Xy: $i] :
% 1.87/1.39 ( ( in @ Xy @ D )
% 1.87/1.39 & ( in @ Xy @ C ) )
% 1.87/1.39 & ! [E: $i] :
% 1.87/1.39 ( ( in @ E @ B )
% 1.87/1.39 => ( ! [Xy: $i] :
% 1.87/1.39 ( ( in @ Xy @ E )
% 1.87/1.39 => ( in @ Xy @ D ) )
% 1.87/1.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(descr_type,type,
% 1.87/1.39 descr: ( $i > $o ) > $i ).
% 1.87/1.39
% 1.87/1.39 thf(descrp_type,type,
% 1.87/1.39 descrp: $o ).
% 1.87/1.39
% 1.87/1.39 thf(descrp,definition,
% 1.87/1.39 ( descrp
% 1.87/1.39 = ( ! [Xphi: $i > $o] :
% 1.87/1.39 ( ( exu
% 1.87/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.87/1.39 => ( Xphi
% 1.87/1.39 @ ( descr
% 1.87/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(dsetconstr_type,type,
% 1.87/1.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.87/1.39
% 1.87/1.39 thf(dsetconstrI_type,type,
% 1.87/1.39 dsetconstrI: $o ).
% 1.87/1.39
% 1.87/1.39 thf(dsetconstrI,definition,
% 1.87/1.39 ( dsetconstrI
% 1.87/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ A )
% 1.87/1.39 => ( ( Xphi @ Xx )
% 1.87/1.39 => ( in @ Xx
% 1.87/1.39 @ ( dsetconstr @ A
% 1.87/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(dsetconstrEL_type,type,
% 1.87/1.39 dsetconstrEL: $o ).
% 1.87/1.39
% 1.87/1.39 thf(dsetconstrEL,definition,
% 1.87/1.39 ( dsetconstrEL
% 1.87/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.87/1.39 ( ( in @ Xx
% 1.87/1.39 @ ( dsetconstr @ A
% 1.87/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.87/1.39 => ( in @ Xx @ A ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(dsetconstrER_type,type,
% 1.87/1.39 dsetconstrER: $o ).
% 1.87/1.39
% 1.87/1.39 thf(dsetconstrER,definition,
% 1.87/1.39 ( dsetconstrER
% 1.87/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.87/1.39 ( ( in @ Xx
% 1.87/1.39 @ ( dsetconstr @ A
% 1.87/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.87/1.39 => ( Xphi @ Xx ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(exuE1_type,type,
% 1.87/1.39 exuE1: $o ).
% 1.87/1.39
% 1.87/1.39 thf(exuE1,definition,
% 1.87/1.39 ( exuE1
% 1.87/1.39 = ( ! [Xphi: $i > $o] :
% 1.87/1.39 ( ( exu
% 1.87/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.87/1.39 => ? [Xx: $i] :
% 1.87/1.39 ( ( Xphi @ Xx )
% 1.87/1.39 & ! [Xy: $i] :
% 1.87/1.39 ( ( Xphi @ Xy )
% 1.87/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(prop2set_type,type,
% 1.87/1.39 prop2set: $o > $i ).
% 1.87/1.39
% 1.87/1.39 thf(prop2set,definition,
% 1.87/1.39 ( prop2set
% 1.87/1.39 = ( ^ [Xphi: $o] :
% 1.87/1.39 ( dsetconstr @ ( powerset @ emptyset )
% 1.87/1.39 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(prop2setE_type,type,
% 1.87/1.39 prop2setE: $o ).
% 1.87/1.39
% 1.87/1.39 thf(prop2setE,definition,
% 1.87/1.39 ( prop2setE
% 1.87/1.39 = ( ! [Xphi: $o,Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.87/1.39 => Xphi ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(emptysetE_type,type,
% 1.87/1.39 emptysetE: $o ).
% 1.87/1.39
% 1.87/1.39 thf(emptysetE,definition,
% 1.87/1.39 ( emptysetE
% 1.87/1.39 = ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ emptyset )
% 1.87/1.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(emptysetimpfalse_type,type,
% 1.87/1.39 emptysetimpfalse: $o ).
% 1.87/1.39
% 1.87/1.39 thf(emptysetimpfalse,definition,
% 1.87/1.39 ( emptysetimpfalse
% 1.87/1.39 = ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ emptyset )
% 1.87/1.39 => $false ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(notinemptyset_type,type,
% 1.87/1.39 notinemptyset: $o ).
% 1.87/1.39
% 1.87/1.39 thf(notinemptyset,definition,
% 1.87/1.39 ( notinemptyset
% 1.87/1.39 = ( ! [Xx: $i] :
% 1.87/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(exuE3e_type,type,
% 1.87/1.39 exuE3e: $o ).
% 1.87/1.39
% 1.87/1.39 thf(exuE3e,definition,
% 1.87/1.39 ( exuE3e
% 1.87/1.39 = ( ! [Xphi: $i > $o] :
% 1.87/1.39 ( ( exu
% 1.87/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.87/1.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setext_type,type,
% 1.87/1.39 setext: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setext,definition,
% 1.87/1.39 ( setext
% 1.87/1.39 = ( ! [A: $i,B: $i] :
% 1.87/1.39 ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ A )
% 1.87/1.39 => ( in @ Xx @ B ) )
% 1.87/1.39 => ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ B )
% 1.87/1.39 => ( in @ Xx @ A ) )
% 1.87/1.39 => ( A = B ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(emptyI_type,type,
% 1.87/1.39 emptyI: $o ).
% 1.87/1.39
% 1.87/1.39 thf(emptyI,definition,
% 1.87/1.39 ( emptyI
% 1.87/1.39 = ( ! [A: $i] :
% 1.87/1.39 ( ! [Xx: $i] :
% 1.87/1.39 ~ ( in @ Xx @ A )
% 1.87/1.39 => ( A = emptyset ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(noeltsimpempty_type,type,
% 1.87/1.39 noeltsimpempty: $o ).
% 1.87/1.39
% 1.87/1.39 thf(noeltsimpempty,definition,
% 1.87/1.39 ( noeltsimpempty
% 1.87/1.39 = ( ! [A: $i] :
% 1.87/1.39 ( ! [Xx: $i] :
% 1.87/1.39 ~ ( in @ Xx @ A )
% 1.87/1.39 => ( A = emptyset ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setbeta_type,type,
% 1.87/1.39 setbeta: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setbeta,definition,
% 1.87/1.39 ( setbeta
% 1.87/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ A )
% 1.87/1.39 => ( ( in @ Xx
% 1.87/1.39 @ ( dsetconstr @ A
% 1.87/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.87/1.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(nonempty_type,type,
% 1.87/1.39 nonempty: $i > $o ).
% 1.87/1.39
% 1.87/1.39 thf(nonempty,definition,
% 1.87/1.39 ( nonempty
% 1.87/1.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(nonemptyE1_type,type,
% 1.87/1.39 nonemptyE1: $o ).
% 1.87/1.39
% 1.87/1.39 thf(nonemptyE1,definition,
% 1.87/1.39 ( nonemptyE1
% 1.87/1.39 = ( ! [A: $i] :
% 1.87/1.39 ( ( nonempty @ A )
% 1.87/1.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(nonemptyI_type,type,
% 1.87/1.39 nonemptyI: $o ).
% 1.87/1.39
% 1.87/1.39 thf(nonemptyI,definition,
% 1.87/1.39 ( nonemptyI
% 1.87/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ A )
% 1.87/1.39 => ( ( Xphi @ Xx )
% 1.87/1.39 => ( nonempty
% 1.87/1.39 @ ( dsetconstr @ A
% 1.87/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(nonemptyI1_type,type,
% 1.87/1.39 nonemptyI1: $o ).
% 1.87/1.39
% 1.87/1.39 thf(nonemptyI1,definition,
% 1.87/1.39 ( nonemptyI1
% 1.87/1.39 = ( ! [A: $i] :
% 1.87/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.87/1.39 => ( nonempty @ A ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinIL_type,type,
% 1.87/1.39 setadjoinIL: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinIL,definition,
% 1.87/1.39 ( setadjoinIL
% 1.87/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(emptyinunitempty_type,type,
% 1.87/1.39 emptyinunitempty: $o ).
% 1.87/1.39
% 1.87/1.39 thf(emptyinunitempty,definition,
% 1.87/1.39 ( emptyinunitempty
% 1.87/1.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinIR_type,type,
% 1.87/1.39 setadjoinIR: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinIR,definition,
% 1.87/1.39 ( setadjoinIR
% 1.87/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.87/1.39 ( ( in @ Xy @ A )
% 1.87/1.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinE_type,type,
% 1.87/1.39 setadjoinE: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinE,definition,
% 1.87/1.39 ( setadjoinE
% 1.87/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.87/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.87/1.39 => ! [Xphi: $o] :
% 1.87/1.39 ( ( ( Xy = Xx )
% 1.87/1.39 => Xphi )
% 1.87/1.39 => ( ( ( in @ Xy @ A )
% 1.87/1.39 => Xphi )
% 1.87/1.39 => Xphi ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinOr_type,type,
% 1.87/1.39 setadjoinOr: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setadjoinOr,definition,
% 1.87/1.39 ( setadjoinOr
% 1.87/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.87/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.87/1.39 => ( ( Xy = Xx )
% 1.87/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(setoftrueEq_type,type,
% 1.87/1.39 setoftrueEq: $o ).
% 1.87/1.39
% 1.87/1.39 thf(setoftrueEq,definition,
% 1.87/1.39 ( setoftrueEq
% 1.87/1.39 = ( ! [A: $i] :
% 1.87/1.39 ( ( dsetconstr @ A
% 1.87/1.39 @ ^ [Xx: $i] : $true )
% 1.87/1.39 = A ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(powersetI_type,type,
% 1.87/1.39 powersetI: $o ).
% 1.87/1.39
% 1.87/1.39 thf(powersetI,definition,
% 1.87/1.39 ( powersetI
% 1.87/1.39 = ( ! [A: $i,B: $i] :
% 1.87/1.39 ( ! [Xx: $i] :
% 1.87/1.39 ( ( in @ Xx @ B )
% 1.87/1.39 => ( in @ Xx @ A ) )
% 1.87/1.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(emptyinPowerset_type,type,
% 1.87/1.39 emptyinPowerset: $o ).
% 1.87/1.39
% 1.87/1.39 thf(emptyinPowerset,definition,
% 1.87/1.39 ( emptyinPowerset
% 1.87/1.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(emptyInPowerset_type,type,
% 1.87/1.39 emptyInPowerset: $o ).
% 1.87/1.39
% 1.87/1.39 thf(emptyInPowerset,definition,
% 1.87/1.39 ( emptyInPowerset
% 1.87/1.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.87/1.39
% 1.87/1.39 thf(powersetE,conjecture,
% 1.87/1.39 ( setextAx
% 1.87/1.39 => ( emptysetAx
% 1.87/1.39 => ( setadjoinAx
% 1.87/1.39 => ( powersetAx
% 1.87/1.39 => ( setunionAx
% 1.87/1.39 => ( omega0Ax
% 1.87/1.39 => ( omegaSAx
% 1.87/1.39 => ( omegaIndAx
% 1.87/1.39 => ( replAx
% 1.87/1.39 => ( foundationAx
% 1.87/1.39 => ( wellorderingAx
% 1.87/1.39 => ( descrp
% 1.87/1.39 => ( dsetconstrI
% 1.87/1.39 => ( dsetconstrEL
% 1.87/1.39 => ( dsetconstrER
% 1.87/1.39 => ( exuE1
% 1.87/1.39 => ( prop2setE
% 1.87/1.39 => ( emptysetE
% 1.87/1.39 => ( emptysetimpfalse
% 1.87/1.39 => ( notinemptyset
% 1.87/1.39 => ( exuE3e
% 1.87/1.39 => ( setext
% 1.87/1.39 => ( emptyI
% 1.87/1.39 => ( noeltsimpempty
% 1.87/1.39 => ( setbeta
% 1.87/1.39 => ( nonemptyE1
% 1.87/1.39 => ( nonemptyI
% 1.87/1.39 => ( nonemptyI1
% 1.87/1.39 => ( setadjoinIL
% 1.87/1.39 => ( emptyinunitempty
% 1.87/1.39 => ( setadjoinIR
% 1.87/1.39 => ( setadjoinE
% 1.87/1.39 => ( setadjoinOr
% 1.87/1.39 => ( setoftrueEq
% 1.87/1.39 => ( powersetI
% 1.87/1.39 => ( emptyinPowerset
% 1.87/1.39 => ( emptyInPowerset
% 1.87/1.39 => ! [A: $i,B: $i,Xx: $i] :
% 1.87/1.39 ( ( in @ B @ ( powerset @ A ) )
% 1.87/1.39 => ( ( in @ Xx @ B )
% 1.87/1.39 => ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.87/1.39 ------------------------
% 2.03/1.40 % (14946)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_14826 for (2999ds/275Mi)
% 2.03/1.40 % (14945)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_14826 for (2999ds/2Mi)
% 2.03/1.41 % (14945)Instruction limit reached!
% 2.03/1.41 % (14945)------------------------------
% 2.03/1.41 % (14945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.41 % (14945)Termination reason: Unknown
% 2.03/1.41 % (14945)Termination phase: shuffling
% 2.03/1.41
% 2.03/1.41 % (14945)Memory used [KB]: 1023
% 2.03/1.41 % (14945)Time elapsed: 0.002 s
% 2.03/1.41 % (14945)Instructions burned: 3 (million)
% 2.03/1.41 % (14945)------------------------------
% 2.03/1.41 % (14945)------------------------------
% 2.03/1.41 % (14941)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/183Mi)
% 2.03/1.41 % (14944)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/2Mi)
% 2.03/1.41 % (14943)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_14826 for (2999ds/27Mi)
% 2.03/1.41 % (14947)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/18Mi)
% 2.03/1.41 % (14942)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_14826 for (2999ds/4Mi)
% 2.03/1.41 % (14944)Instruction limit reached!
% 2.03/1.41 % (14944)------------------------------
% 2.03/1.41 % (14944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.41 % (14944)Termination reason: Unknown
% 2.03/1.41 % (14944)Termination phase: shuffling
% 2.03/1.41
% 2.03/1.41 % (14944)Memory used [KB]: 1023
% 2.03/1.41 % (14944)Time elapsed: 0.004 s
% 2.03/1.41 % (14944)Instructions burned: 3 (million)
% 2.03/1.41 % (14944)------------------------------
% 2.03/1.41 % (14944)------------------------------
% 2.03/1.41 % (14942)Instruction limit reached!
% 2.03/1.41 % (14942)------------------------------
% 2.03/1.41 % (14942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.41 % (14942)Termination reason: Unknown
% 2.03/1.41 % (14942)Termination phase: shuffling
% 2.03/1.41
% 2.03/1.41 % (14942)Memory used [KB]: 1151
% 2.03/1.41 % (14942)Time elapsed: 0.004 s
% 2.03/1.41 % (14942)Instructions burned: 4 (million)
% 2.03/1.41 % (14942)------------------------------
% 2.03/1.41 % (14942)------------------------------
% 2.03/1.42 % (14948)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/3Mi)
% 2.03/1.42 % (14948)Instruction limit reached!
% 2.03/1.42 % (14948)------------------------------
% 2.03/1.42 % (14948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.42 % (14948)Termination reason: Unknown
% 2.03/1.42 % (14948)Termination phase: shuffling
% 2.03/1.42
% 2.03/1.42 % (14948)Memory used [KB]: 1023
% 2.03/1.42 % (14948)Time elapsed: 0.002 s
% 2.03/1.42 % (14948)Instructions burned: 3 (million)
% 2.03/1.42 % (14948)------------------------------
% 2.03/1.42 % (14948)------------------------------
% 2.03/1.42 % (14947)Instruction limit reached!
% 2.03/1.42 % (14947)------------------------------
% 2.03/1.42 % (14947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.42 % (14947)Termination reason: Unknown
% 2.03/1.42 % (14947)Termination phase: Property scanning
% 2.03/1.42
% 2.03/1.42 % (14947)Memory used [KB]: 1535
% 2.03/1.42 % (14947)Time elapsed: 0.012 s
% 2.03/1.42 % (14947)Instructions burned: 18 (million)
% 2.03/1.42 % (14947)------------------------------
% 2.03/1.42 % (14947)------------------------------
% 2.03/1.43 % (14943)Instruction limit reached!
% 2.03/1.43 % (14943)------------------------------
% 2.03/1.43 % (14943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.43 % (14943)Termination reason: Unknown
% 2.03/1.43 % (14943)Termination phase: Saturation
% 2.03/1.43
% 2.03/1.43 % (14943)Memory used [KB]: 5756
% 2.03/1.43 % (14943)Time elapsed: 0.017 s
% 2.03/1.43 % (14943)Instructions burned: 29 (million)
% 2.03/1.43 % (14943)------------------------------
% 2.03/1.43 % (14943)------------------------------
% 2.03/1.43 % (14951)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_14826 for (2999ds/3Mi)
% 2.03/1.43 % (14951)Instruction limit reached!
% 2.03/1.43 % (14951)------------------------------
% 2.03/1.43 % (14951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.43 % (14951)Termination reason: Unknown
% 2.03/1.43 % (14951)Termination phase: shuffling
% 2.03/1.43
% 2.03/1.43 % (14951)Memory used [KB]: 1151
% 2.03/1.43 % (14951)Time elapsed: 0.003 s
% 2.03/1.43 % (14951)Instructions burned: 4 (million)
% 2.03/1.43 % (14951)------------------------------
% 2.03/1.43 % (14951)------------------------------
% 2.03/1.43 % (14949)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_14826 for (2999ds/37Mi)
% 2.03/1.43 % (14950)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_14826 for (2999ds/15Mi)
% 2.03/1.44 % (14954)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/16Mi)
% 2.03/1.44 % (14952)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_14826 for (2999ds/1041Mi)
% 2.03/1.44 % (14950)Instruction limit reached!
% 2.03/1.44 % (14950)------------------------------
% 2.03/1.44 % (14950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.44 % (14950)Termination reason: Unknown
% 2.03/1.44 % (14950)Termination phase: Preprocessing 3
% 2.03/1.44
% 2.03/1.44 % (14950)Memory used [KB]: 1535
% 2.03/1.44 % (14950)Time elapsed: 0.011 s
% 2.03/1.44 % (14950)Instructions burned: 16 (million)
% 2.03/1.44 % (14950)------------------------------
% 2.03/1.44 % (14950)------------------------------
% 2.03/1.44 % (14953)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/7Mi)
% 2.03/1.44 % (14954)Instruction limit reached!
% 2.03/1.44 % (14954)------------------------------
% 2.03/1.44 % (14954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.44 % (14954)Termination reason: Unknown
% 2.03/1.44 % (14954)Termination phase: Twee Goal Transformation
% 2.03/1.44
% 2.03/1.44 % (14954)Memory used [KB]: 1151
% 2.03/1.44 % (14954)Time elapsed: 0.007 s
% 2.03/1.44 % (14954)Instructions burned: 17 (million)
% 2.03/1.44 % (14954)------------------------------
% 2.03/1.44 % (14954)------------------------------
% 2.03/1.45 % (14953)Instruction limit reached!
% 2.03/1.45 % (14953)------------------------------
% 2.03/1.45 % (14953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.45 % (14953)Termination reason: Unknown
% 2.03/1.45 % (14953)Termination phase: Property scanning
% 2.03/1.45
% 2.03/1.45 % (14953)Memory used [KB]: 1151
% 2.03/1.45 % (14953)Time elapsed: 0.005 s
% 2.03/1.45 % (14953)Instructions burned: 9 (million)
% 2.03/1.45 % (14953)------------------------------
% 2.03/1.45 % (14953)------------------------------
% 2.03/1.45 % (14949)Instruction limit reached!
% 2.03/1.45 % (14949)------------------------------
% 2.03/1.45 % (14949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.45 % (14949)Termination reason: Unknown
% 2.03/1.45 % (14949)Termination phase: Saturation
% 2.03/1.45
% 2.03/1.45 % (14949)Memory used [KB]: 6012
% 2.03/1.45 % (14949)Time elapsed: 0.020 s
% 2.03/1.45 % (14949)Instructions burned: 37 (million)
% 2.03/1.45 % (14949)------------------------------
% 2.03/1.45 % (14949)------------------------------
% 2.03/1.46 % (14960)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/7Mi)
% 2.03/1.46 % (14960)Instruction limit reached!
% 2.03/1.46 % (14960)------------------------------
% 2.03/1.46 % (14960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.46 % (14960)Termination reason: Unknown
% 2.03/1.46 % (14960)Termination phase: Property scanning
% 2.03/1.46
% 2.03/1.46 % (14960)Memory used [KB]: 1151
% 2.03/1.46 % (14960)Time elapsed: 0.005 s
% 2.03/1.46 % (14960)Instructions burned: 8 (million)
% 2.03/1.46 % (14960)------------------------------
% 2.03/1.46 % (14960)------------------------------
% 2.03/1.46 % (14959)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_14826 for (2999ds/3Mi)
% 2.03/1.46 % (14959)Instruction limit reached!
% 2.03/1.46 % (14959)------------------------------
% 2.03/1.46 % (14959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.46 % (14959)Termination reason: Unknown
% 2.03/1.46 % (14959)Termination phase: shuffling
% 2.03/1.46
% 2.03/1.46 % (14959)Memory used [KB]: 1023
% 2.03/1.46 % (14959)Time elapsed: 0.004 s
% 2.03/1.46 % (14959)Instructions burned: 4 (million)
% 2.03/1.46 % (14959)------------------------------
% 2.03/1.46 % (14959)------------------------------
% 2.03/1.47 % (14961)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/3Mi)
% 2.03/1.47 % (14961)Instruction limit reached!
% 2.03/1.47 % (14961)------------------------------
% 2.03/1.47 % (14961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.47 % (14961)Termination reason: Unknown
% 2.03/1.47 % (14961)Termination phase: shuffling
% 2.03/1.47
% 2.03/1.47 % (14961)Memory used [KB]: 1023
% 2.03/1.47 % (14961)Time elapsed: 0.003 s
% 2.03/1.47 % (14961)Instructions burned: 3 (million)
% 2.03/1.47 % (14961)------------------------------
% 2.03/1.47 % (14961)------------------------------
% 2.03/1.47 % (14955)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_14826 for (2999ds/3Mi)
% 2.03/1.47 % (14970)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/4Mi)
% 2.03/1.47 % (14970)Instruction limit reached!
% 2.03/1.47 % (14970)------------------------------
% 2.03/1.47 % (14970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.47 % (14970)Termination reason: Unknown
% 2.03/1.47 % (14970)Termination phase: shuffling
% 2.03/1.47
% 2.03/1.47 % (14970)Memory used [KB]: 1151
% 2.03/1.47 % (14970)Time elapsed: 0.003 s
% 2.03/1.47 % (14970)Instructions burned: 5 (million)
% 2.03/1.47 % (14970)------------------------------
% 2.03/1.47 % (14970)------------------------------
% 2.03/1.47 % (14955)Instruction limit reached!
% 2.03/1.47 % (14955)------------------------------
% 2.03/1.47 % (14955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.47 % (14955)Termination reason: Unknown
% 2.03/1.47 % (14955)Termination phase: shuffling
% 2.03/1.47
% 2.03/1.47 % (14955)Memory used [KB]: 1023
% 2.03/1.47 % (14955)Time elapsed: 0.005 s
% 2.03/1.47 % (14955)Instructions burned: 3 (million)
% 2.03/1.47 % (14955)------------------------------
% 2.03/1.47 % (14955)------------------------------
% 2.03/1.48 % (14975)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/18Mi)
% 2.03/1.48 % (14979)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/6Mi)
% 2.03/1.48 % (14980)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_14826 for (2999ds/902Mi)
% 2.03/1.48 % (14979)Instruction limit reached!
% 2.03/1.48 % (14979)------------------------------
% 2.03/1.48 % (14979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.48 % (14979)Termination reason: Unknown
% 2.03/1.48 % (14979)Termination phase: Property scanning
% 2.03/1.48
% 2.03/1.48 % (14979)Memory used [KB]: 1151
% 2.03/1.48 % (14979)Time elapsed: 0.004 s
% 2.03/1.48 % (14979)Instructions burned: 7 (million)
% 2.03/1.48 % (14979)------------------------------
% 2.03/1.48 % (14979)------------------------------
% 2.03/1.48 % (14941)Instruction limit reached!
% 2.03/1.48 % (14941)------------------------------
% 2.03/1.48 % (14941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.48 % (14941)Termination reason: Unknown
% 2.03/1.48 % (14941)Termination phase: Saturation
% 2.03/1.48
% 2.03/1.48 % (14941)Memory used [KB]: 6780
% 2.03/1.48 % (14941)Time elapsed: 0.076 s
% 2.03/1.48 % (14941)Instructions burned: 185 (million)
% 2.03/1.48 % (14941)------------------------------
% 2.03/1.48 % (14941)------------------------------
% 2.03/1.49 % (14978)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/710Mi)
% 2.03/1.49 % (14975)Instruction limit reached!
% 2.03/1.49 % (14975)------------------------------
% 2.03/1.49 % (14975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.49 % (14975)Termination reason: Unknown
% 2.03/1.49 % (14975)Termination phase: Saturation
% 2.03/1.49
% 2.03/1.49 % (14975)Memory used [KB]: 5756
% 2.03/1.49 % (14975)Time elapsed: 0.011 s
% 2.03/1.49 % (14975)Instructions burned: 19 (million)
% 2.03/1.49 % (14975)------------------------------
% 2.03/1.49 % (14975)------------------------------
% 2.03/1.49 % (14946)Instruction limit reached!
% 2.03/1.49 % (14946)------------------------------
% 2.03/1.49 % (14946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.49 % (14946)Termination reason: Unknown
% 2.03/1.49 % (14946)Termination phase: Saturation
% 2.03/1.49
% 2.03/1.49 % (14946)Memory used [KB]: 6908
% 2.03/1.49 % (14946)Time elapsed: 0.088 s
% 2.03/1.49 % (14946)Instructions burned: 276 (million)
% 2.03/1.49 % (14946)------------------------------
% 2.03/1.49 % (14946)------------------------------
% 2.03/1.49 % (14981)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_14826 for (2999ds/21Mi)
% 2.03/1.50 % (14982)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14826 for (2999ds/5Mi)
% 2.03/1.50 % (14982)Instruction limit reached!
% 2.03/1.50 % (14982)------------------------------
% 2.03/1.50 % (14982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.50 % (14982)Termination reason: Unknown
% 2.03/1.50 % (14982)Termination phase: Property scanning
% 2.03/1.50
% 2.03/1.50 % (14982)Memory used [KB]: 1151
% 2.03/1.50 % (14982)Time elapsed: 0.003 s
% 2.03/1.50 % (14982)Instructions burned: 7 (million)
% 2.03/1.50 % (14982)------------------------------
% 2.03/1.50 % (14982)------------------------------
% 2.03/1.50 % (14980)First to succeed.
% 2.03/1.50 % (14980)Refutation found. Thanks to Tanya!
% 2.03/1.50 % SZS status Theorem for DTF2THF_14826
% 2.03/1.50 % SZS output start Proof for DTF2THF_14826
% 2.03/1.50 thf(func_def_0, type, in: $i > $i > $o).
% 2.03/1.50 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.03/1.50 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.03/1.50 thf(func_def_8, type, powerset: $i > $i).
% 2.03/1.50 thf(func_def_10, type, setunion: $i > $i).
% 2.03/1.50 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.03/1.50 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.03/1.50 thf(func_def_26, type, prop2set: $o > $i).
% 2.03/1.50 thf(func_def_36, type, nonempty: $i > $o).
% 2.03/1.50 thf(func_def_62, type, sP1: $i > $i > $o).
% 2.03/1.50 thf(func_def_63, type, sP2: $i > $o).
% 2.03/1.50 thf(func_def_64, type, sP3: $i > $i > $o).
% 2.03/1.50 thf(func_def_65, type, sP4: $i > $i > $o).
% 2.03/1.50 thf(func_def_68, type, sK7: $i > $i).
% 2.03/1.50 thf(func_def_69, type, sK8: $i > $i > $i).
% 2.03/1.50 thf(func_def_79, type, sK18: $i > $i).
% 2.03/1.50 thf(func_def_82, type, sK21: $i > $o).
% 2.03/1.50 thf(func_def_86, type, sK25: $i > $o).
% 2.03/1.50 thf(func_def_87, type, sK26: $i > $o).
% 2.03/1.50 thf(func_def_90, type, sK29: $i > $i).
% 2.03/1.50 thf(func_def_92, type, sK31: $i > $i).
% 2.03/1.50 thf(func_def_95, type, sK34: $i > $i).
% 2.03/1.50 thf(func_def_96, type, sK35: $i > $i > $i).
% 2.03/1.50 thf(func_def_99, type, sK38: $i > $i > $i).
% 2.03/1.50 thf(func_def_100, type, sK39: $i > $i > $i).
% 2.03/1.50 thf(func_def_104, type, sK43: $i > $i > $o).
% 2.03/1.50 thf(func_def_105, type, sK44: $i > $i).
% 2.03/1.50 thf(func_def_106, type, sK45: $i > $i).
% 2.03/1.50 thf(func_def_107, type, sK46: ($i > $i > $o) > $i > $i).
% 2.03/1.50 thf(func_def_108, type, sK47: $i > ($i > $i > $o) > $i > $i).
% 2.03/1.50 thf(func_def_109, type, sK48: ($i > $i > $o) > $i > $i).
% 2.03/1.50 thf(func_def_110, type, sK49: $i > $i).
% 2.03/1.50 thf(func_def_113, type, sK52: ($i > $o) > $i).
% 2.03/1.50 thf(func_def_114, type, sK53: $i > $o).
% 2.03/1.50 thf(func_def_115, type, sK54: ($i > $o) > $i).
% 2.03/1.50 thf(func_def_116, type, sK55: $i > $o).
% 2.03/1.50 thf(func_def_117, type, sK56: $i > $i).
% 2.03/1.50 thf(func_def_134, type, sK73: $i > $i > $i).
% 2.03/1.50 thf(func_def_135, type, sK74: $i > $i > $i).
% 2.03/1.50 thf(func_def_136, type, sK75: $i > $i > $i).
% 2.03/1.50 thf(func_def_137, type, sK76: $i > $i > $i).
% 2.03/1.50 thf(func_def_138, type, sK77: $i > $i > $i).
% 2.03/1.50 thf(func_def_139, type, sK78: $i > $i > $i > $i).
% 2.03/1.50 thf(func_def_140, type, sK79: $i > $i).
% 2.03/1.50 thf(func_def_141, type, sK80: $i > $i).
% 2.03/1.50 thf(func_def_142, type, sK81: $i > $i).
% 2.03/1.50 thf(func_def_143, type, sK82: $i > $i).
% 2.03/1.50 thf(func_def_144, type, sK83: $i > $i > $i > $i).
% 2.03/1.50 thf(func_def_145, type, sK84: $i > $i > $i > $i).
% 2.03/1.50 thf(func_def_146, type, sK85: $i > $i > $i).
% 2.03/1.50 thf(func_def_147, type, sK86: $i > $i > $i).
% 2.03/1.50 thf(func_def_148, type, sK87: $i > $i > $i).
% 2.03/1.50 thf(func_def_149, type, sK88: $i > $i).
% 2.03/1.50 thf(func_def_151, type, sK90: $i > $i).
% 2.03/1.50 thf(func_def_152, type, sK91: $i > $i).
% 2.03/1.50 thf(func_def_155, type, sK94: $i > $o).
% 2.03/1.50 thf(func_def_160, type, sK99: $i > $i > $i).
% 2.03/1.50 thf(func_def_164, type, sK103: $i > $o).
% 2.03/1.50 thf(func_def_173, type, sK112: $i > $i > $i).
% 2.03/1.50 thf(func_def_174, type, sK113: $i > $o).
% 2.03/1.50 thf(func_def_176, type, ph115: !>[X0: $tType]:(X0)).
% 2.03/1.50 thf(f685,plain,(
% 2.03/1.50 $false),
% 2.03/1.50 inference(trivial_inequality_removal,[status(thm)],[f682])).
% 2.03/1.50 thf(f682,plain,(
% 2.03/1.50 ($true != $true)),
% 2.03/1.50 inference(superposition,[status(thm)],[f642,f472])).
% 2.03/1.50 thf(f472,plain,(
% 2.03/1.50 ($true = (in @ sK59 @ sK60))),
% 2.03/1.50 inference(cnf_transformation,[status(thm)],[f271])).
% 2.03/1.50 thf(f271,plain,(
% 2.03/1.50 (emptysetAx = $true) & (emptyinunitempty = $true) & (setunionAx = $true) & (nonemptyE1 = $true) & (nonemptyI1 = $true) & (prop2setE = $true) & (emptyinPowerset = $true) & (setext = $true) & (omega0Ax = $true) & (wellorderingAx = $true) & (emptyI = $true) & (setbeta = $true) & (exuE1 = $true) & (powersetI = $true) & (emptyInPowerset = $true) & (notinemptyset = $true) & (exuE3e = $true) & (replAx = $true) & (emptysetimpfalse = $true) & (($true = (in @ sK59 @ sK60)) & ($true = (in @ sK60 @ (powerset @ sK58))) & ((in @ sK59 @ sK58) != $true)) & (setadjoinE = $true) & (noeltsimpempty = $true) & (setadjoinOr = $true) & (setextAx = $true) & (descrp = $true) & (omegaIndAx = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (dsetconstrEL = $true) & (nonemptyI = $true) & (powersetAx = $true) & (emptysetE = $true) & (dsetconstrER = $true) & (setadjoinIL = $true) & (setadjoinIR = $true) & (foundationAx = $true) & (setoftrueEq = $true) & (omegaSAx = $true)),
% 2.03/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60])],[f163,f270])).
% 2.03/1.50 thf(f270,plain,(
% 2.03/1.50 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X2 @ (powerset @ X0)) = $true) & ((in @ X1 @ X0) != $true)) => (($true = (in @ sK59 @ sK60)) & ($true = (in @ sK60 @ (powerset @ sK58))) & ((in @ sK59 @ sK58) != $true))),
% 2.03/1.50 introduced(definition,[],[choice_axiom])).
% 2.03/1.50 thf(f163,plain,(
% 2.03/1.50 (emptysetAx = $true) & (emptyinunitempty = $true) & (setunionAx = $true) & (nonemptyE1 = $true) & (nonemptyI1 = $true) & (prop2setE = $true) & (emptyinPowerset = $true) & (setext = $true) & (omega0Ax = $true) & (wellorderingAx = $true) & (emptyI = $true) & (setbeta = $true) & (exuE1 = $true) & (powersetI = $true) & (emptyInPowerset = $true) & (notinemptyset = $true) & (exuE3e = $true) & (replAx = $true) & (emptysetimpfalse = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X2 @ (powerset @ X0)) = $true) & ((in @ X1 @ X0) != $true)) & (setadjoinE = $true) & (noeltsimpempty = $true) & (setadjoinOr = $true) & (setextAx = $true) & (descrp = $true) & (omegaIndAx = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (dsetconstrEL = $true) & (nonemptyI = $true) & (powersetAx = $true) & (emptysetE = $true) & (dsetconstrER = $true) & (setadjoinIL = $true) & (setadjoinIR = $true) & (foundationAx = $true) & (setoftrueEq = $true) & (omegaSAx = $true)),
% 2.03/1.50 inference(flattening,[status(thm)],[f162])).
% 2.03/1.50 thf(f162,plain,(
% 2.03/1.50 ((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0) != $true) & ((in @ X1 @ X2) = $true)) & ((in @ X2 @ (powerset @ X0)) = $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)),
% 2.03/1.50 inference(ennf_transformation,[status(thm)],[f75])).
% 2.03/1.50 thf(f75,plain,(
% 2.03/1.50 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => (((in @ X1 @ X2) = $true) => ((in @ X1 @ X0) = $true))))))))))))))))))))))))))))))))))))))))),
% 2.03/1.50 inference(fool_elimination,[status(thm)],[f74])).
% 2.03/1.50 thf(f74,plain,(
% 2.03/1.50 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((in @ X1 @ X2) => (in @ X1 @ X0))))))))))))))))))))))))))))))))))))))))),
% 2.03/1.50 inference(rectify,[status(thm)],[f42])).
% 2.03/1.50 thf(f42,negated_conjecture,(
% 2.03/1.50 ~(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 => ! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X4 @ (powerset @ X3)) => ((in @ X1 @ X4) => (in @ X1 @ X3))))))))))))))))))))))))))))))))))))))))),
% 2.03/1.50 inference(negated_conjecture,[status(cth)],[f41])).
% 2.03/1.50 thf(f41,conjecture,(
% 2.03/1.50 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 => ! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X4 @ (powerset @ X3)) => ((in @ X1 @ X4) => (in @ X1 @ X3)))))))))))))))))))))))))))))))))))))))),
% 2.03/1.50 file('/export/starexec/sandbox2/tmp/tmp.tJKBZQcyjw/DTF2THF_14826.p',powersetE)).
% 2.03/1.50 thf(f642,plain,(
% 2.03/1.50 ($true != (in @ sK59 @ sK60))),
% 2.03/1.50 inference(trivial_inequality_removal,[status(thm)],[f638])).
% 2.03/1.50 thf(f638,plain,(
% 2.03/1.50 ($true != (in @ sK59 @ sK60)) | ($true != $true)),
% 2.03/1.50 inference(superposition,[status(thm)],[f470,f623])).
% 2.03/1.50 thf(f623,plain,(
% 2.03/1.50 ( ! [X0 : $i] : (($true = (in @ X0 @ sK58)) | ((in @ X0 @ sK60) != $true)) )),
% 2.03/1.50 inference(trivial_inequality_removal,[status(thm)],[f622])).
% 2.03/1.50 thf(f622,plain,(
% 2.03/1.50 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK60) != $true) | ($true = (in @ X0 @ sK58))) )),
% 2.03/1.50 inference(forward_demodulation,[status(thm)],[f621,f459])).
% 2.03/1.50 thf(f459,plain,(
% 2.03/1.50 (powersetAx = $true)),
% 2.03/1.50 inference(cnf_transformation,[status(thm)],[f271])).
% 2.03/1.50 thf(f621,plain,(
% 2.03/1.50 ( ! [X0 : $i] : (((in @ X0 @ sK60) != $true) | (powersetAx != $true) | ($true = (in @ X0 @ sK58))) )),
% 2.03/1.50 inference(trivial_inequality_removal,[status(thm)],[f618])).
% 2.03/1.50 thf(f618,plain,(
% 2.03/1.50 ( ! [X0 : $i] : (((in @ X0 @ sK60) != $true) | (powersetAx != $true) | ($true != $true) | ($true = (in @ X0 @ sK58))) )),
% 2.03/1.50 inference(superposition,[status(thm)],[f569,f471])).
% 2.03/1.50 thf(f471,plain,(
% 2.03/1.50 ($true = (in @ sK60 @ (powerset @ sK58)))),
% 2.03/1.50 inference(cnf_transformation,[status(thm)],[f271])).
% 2.03/1.50 thf(f569,plain,(
% 2.03/1.50 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true) | (powersetAx != $true)) )),
% 2.03/1.50 inference(cnf_transformation,[status(thm)],[f347])).
% 2.03/1.50 thf(f347,plain,(
% 2.03/1.50 (! [X0 : $i,X1 : $i] : ((! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) & (((in @ X1 @ (powerset @ X0)) = $true) | (($true != (in @ (sK99 @ X1 @ X0) @ X0)) & ((in @ (sK99 @ X1 @ X0) @ X1) = $true)))) | (powersetAx != $true)) & ((powersetAx = $true) | ((($true != (in @ sK101 @ (powerset @ sK100))) | (($true != (in @ sK102 @ sK100)) & ((in @ sK102 @ sK101) = $true))) & (($true = (in @ sK101 @ (powerset @ sK100))) | ! [X7 : $i] : (((in @ X7 @ sK100) = $true) | ((in @ X7 @ sK101) != $true)))))),
% 2.03/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK99,sK100,sK101,sK102])],[f343,f346,f345,f344])).
% 2.03/1.50 thf(f344,plain,(
% 2.03/1.50 ! [X0 : $i,X1 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true)) => (($true != (in @ (sK99 @ X1 @ X0) @ X0)) & ((in @ (sK99 @ X1 @ X0) @ X1) = $true)))),
% 2.03/1.50 introduced(definition,[],[choice_axiom])).
% 2.03/1.50 thf(f345,plain,(
% 2.03/1.50 ? [X4 : $i,X5 : $i] : ((((in @ X5 @ (powerset @ X4)) != $true) | ? [X6 : $i] : (((in @ X6 @ X4) != $true) & ((in @ X6 @ X5) = $true))) & (((in @ X5 @ (powerset @ X4)) = $true) | ! [X7 : $i] : (((in @ X7 @ X4) = $true) | ((in @ X7 @ X5) != $true)))) => ((($true != (in @ sK101 @ (powerset @ sK100))) | ? [X6 : $i] : (((in @ X6 @ sK100) != $true) & ((in @ X6 @ sK101) = $true))) & (($true = (in @ sK101 @ (powerset @ sK100))) | ! [X7 : $i] : (((in @ X7 @ sK100) = $true) | ((in @ X7 @ sK101) != $true))))),
% 2.03/1.50 introduced(definition,[],[choice_axiom])).
% 2.03/1.50 thf(f346,plain,(
% 2.03/1.50 ? [X6 : $i] : (((in @ X6 @ sK100) != $true) & ((in @ X6 @ sK101) = $true)) => (($true != (in @ sK102 @ sK100)) & ((in @ sK102 @ sK101) = $true))),
% 2.03/1.50 introduced(definition,[],[choice_axiom])).
% 2.03/1.50 thf(f343,plain,(
% 2.03/1.50 (! [X0 : $i,X1 : $i] : ((! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) & (((in @ X1 @ (powerset @ X0)) = $true) | ? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true)))) | (powersetAx != $true)) & ((powersetAx = $true) | ? [X4 : $i,X5 : $i] : ((((in @ X5 @ (powerset @ X4)) != $true) | ? [X6 : $i] : (((in @ X6 @ X4) != $true) & ((in @ X6 @ X5) = $true))) & (((in @ X5 @ (powerset @ X4)) = $true) | ! [X7 : $i] : (((in @ X7 @ X4) = $true) | ((in @ X7 @ X5) != $true)))))),
% 2.03/1.50 inference(rectify,[status(thm)],[f342])).
% 2.03/1.50 thf(f342,plain,(
% 2.03/1.50 (! [X0 : $i,X1 : $i] : ((! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) & (((in @ X1 @ (powerset @ X0)) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)))) | (powersetAx != $true)) & ((powersetAx = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0)) != $true) | ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) & (((in @ X1 @ (powerset @ X0)) = $true) | ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)))))),
% 2.03/1.50 inference(nnf_transformation,[status(thm)],[f156])).
% 2.03/1.50 thf(f156,plain,(
% 2.03/1.50 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) <=> ((in @ X1 @ (powerset @ X0)) = $true)) <=> (powersetAx = $true)),
% 2.03/1.50 inference(ennf_transformation,[status(thm)],[f89])).
% 2.03/1.50 thf(f89,plain,(
% 2.03/1.50 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) <=> ! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true))) <=> (powersetAx = $true)),
% 2.03/1.50 inference(fool_elimination,[status(thm)],[f88])).
% 2.03/1.50 thf(f88,plain,(
% 2.03/1.50 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))) = powersetAx)),
% 2.03/1.50 inference(rectify,[status(thm)],[f5])).
% 2.03/1.50 thf(f5,axiom,(
% 2.03/1.50 (! [X3 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) <=> (in @ X4 @ (powerset @ X3))) = powersetAx)),
% 2.03/1.50 file('/export/starexec/sandbox2/tmp/tmp.tJKBZQcyjw/DTF2THF_14826.p',powersetAx)).
% 2.03/1.50 thf(f470,plain,(
% 2.03/1.50 ((in @ sK59 @ sK58) != $true)),
% 2.03/1.50 inference(cnf_transformation,[status(thm)],[f271])).
% 2.03/1.50 % SZS output end Proof for DTF2THF_14826
% 2.03/1.50 % (14980)------------------------------
% 2.03/1.50 % (14980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.03/1.50 % (14980)Termination reason: Refutation
% 2.03/1.50
% 2.03/1.50 % (14980)Memory used [KB]: 6268
% 2.03/1.50 % (14980)Time elapsed: 0.042 s
% 2.03/1.50 % (14980)Instructions burned: 50 (million)
% 2.03/1.50 % (14980)------------------------------
% 2.03/1.50 % (14980)------------------------------
% 2.03/1.50 % (14940)Success in time 0.108 s
%------------------------------------------------------------------------------