%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU519^1 : 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 : n011.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 2.04s 1.58s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 853 ( 232 equ; 0 cnn)
% Maximal formula atoms : 37 ( 21 avg)
% Number of connectives : 543 ( 45 ~; 29 |; 122 &; 189 @)
% ( 5 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 99 usr; 42 con; 0-3 aty)
% Number of variables : 63 ( 0 ^; 47 !; 16 ?; 63 :)
% 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_60,type,
sP1: $i > $i > $o ).
thf(func_def_61,type,
sP2: $i > $o ).
thf(func_def_62,type,
sP3: $i > $i > $o ).
thf(func_def_63,type,
sP4: $i > $i > $o ).
thf(func_def_64,type,
sK5: $i > $o ).
thf(func_def_69,type,
sK10: $i > $i > $o ).
thf(func_def_70,type,
sK11: $i > $i ).
thf(func_def_71,type,
sK12: $i > $i ).
thf(func_def_72,type,
sK13: ( $i > $i > $o ) > $i > $i ).
thf(func_def_73,type,
sK14: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_74,type,
sK15: ( $i > $i > $o ) > $i > $i ).
thf(func_def_77,type,
sK18: $i > $o ).
thf(func_def_78,type,
sK19: $i > $i ).
thf(func_def_79,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_82,type,
sK23: $i > $o ).
thf(func_def_90,type,
sK31: $i > $i ).
thf(func_def_100,type,
sK41: $i > $o ).
thf(func_def_105,type,
sK46: $i > $i ).
thf(func_def_106,type,
sK47: $i > $o ).
thf(func_def_107,type,
sK48: ( $i > $o ) > $i ).
thf(func_def_108,type,
sK49: $i > $i ).
thf(func_def_114,type,
sK55: $i > $o ).
thf(func_def_117,type,
sK58: $i > $i > $i ).
thf(func_def_125,type,
sK66: $i > $i > $i ).
thf(func_def_128,type,
sK69: $i > $i > $i ).
thf(func_def_129,type,
sK70: $i > $i > $i ).
thf(func_def_133,type,
sK74: $i > $i > $i ).
thf(func_def_134,type,
sK75: $i > $i ).
thf(func_def_140,type,
sK81: $i > $i ).
thf(func_def_141,type,
sK82: $i > $i ).
thf(func_def_144,type,
sK85: $i > $o ).
thf(func_def_145,type,
sK86: $i > $i > $i ).
thf(func_def_146,type,
sK87: $i > $i > $i ).
thf(func_def_147,type,
sK88: $i > $i > $i ).
thf(func_def_148,type,
sK89: $i > $i > $i ).
thf(func_def_149,type,
sK90: $i > $i > $i > $i ).
thf(func_def_150,type,
sK91: $i > $i ).
thf(func_def_151,type,
sK92: $i > $i ).
thf(func_def_152,type,
sK93: $i > $i ).
thf(func_def_153,type,
sK94: $i > $i ).
thf(func_def_154,type,
sK95: $i > $i > $i > $i ).
thf(func_def_155,type,
sK96: $i > $i > $i > $i ).
thf(func_def_156,type,
sK97: $i > $i > $i ).
thf(func_def_157,type,
sK98: $i > $i > $i ).
thf(func_def_158,type,
sK99: $i > $i > $i ).
thf(func_def_159,type,
sK100: $i > $i ).
thf(func_def_160,type,
sK101: $i > $i > $i ).
thf(func_def_162,type,
sK103: $i > $i ).
thf(func_def_163,type,
sK104: $i > $i ).
thf(func_def_165,type,
ph106:
!>[X0: $tType] : X0 ).
thf(f1099,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1096]) ).
thf(f1096,plain,
$true != $true,
inference(superposition,[status(thm)],[f407,f1093]) ).
thf(f1093,plain,
! [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1089]) ).
thf(f1089,plain,
! [X0: $i] :
( ( ( in @ emptyset @ ( powerset @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f713,f691]) ).
thf(f691,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK74 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( in @ X3 @ ( powerset @ X4 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f635]) ).
thf(f635,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ ( sK74 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( in @ X3 @ ( powerset @ X4 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f481,f415]) ).
thf(f415,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f230]) ).
thf(f230,plain,
( ( emptysetE = $true )
& ( notinemptyset = $true )
& ( dsetconstrI = $true )
& ( powersetAx = $true )
& ( nonemptyI1 = $true )
& ( noeltsimpempty = $true )
& ( emptysetimpfalse = $true )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( foundationAx = $true )
& ( setadjoinIL = $true )
& ( setext = $true )
& ( emptyinunitempty = $true )
& ( setunionAx = $true )
& ( emptysetAx = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( dsetconstrER = $true )
& ( omegaSAx = $true )
& ( ( in @ emptyset @ ( powerset @ sK38 ) )
!= $true )
& ( setbeta = $true )
& ( setextAx = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ( replAx = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( setoftrueEq = $true )
& ( setadjoinAx = $true )
& ( wellorderingAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f153,f229]) ).
thf(f229,plain,
( ? [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
!= $true )
=> ( ( in @ emptyset @ ( powerset @ sK38 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f153,plain,
( ( emptysetE = $true )
& ( notinemptyset = $true )
& ( dsetconstrI = $true )
& ( powersetAx = $true )
& ( nonemptyI1 = $true )
& ( noeltsimpempty = $true )
& ( emptysetimpfalse = $true )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( foundationAx = $true )
& ( setadjoinIL = $true )
& ( setext = $true )
& ( emptyinunitempty = $true )
& ( setunionAx = $true )
& ( emptysetAx = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( dsetconstrER = $true )
& ( omegaSAx = $true )
& ? [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
!= $true )
& ( setbeta = $true )
& ( setextAx = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ( replAx = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( setoftrueEq = $true )
& ( setadjoinAx = $true )
& ( wellorderingAx = $true ) ),
inference(flattening,[status(thm)],[f152]) ).
thf(f152,plain,
( ? [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
!= $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)],[f112]) ).
thf(f112,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 )
=> ! [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f111]) ).
thf(f111,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
=> ! [X0: $i] : ( in @ emptyset @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,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
=> ! [X3: $i] : ( in @ emptyset @ ( powerset @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
thf(f39,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
=> ! [X3: $i] : ( in @ emptyset @ ( powerset @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oqPmhAEHHv/DTF2THF_30490.p',emptyinPowerset) ).
thf(f481,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK74 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( in @ X3 @ ( powerset @ X4 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
thf(f292,plain,
( ( ( powersetI = $true )
| ( ! [X2: $i] :
( ( ( in @ X2 @ sK73 )
= $true )
| ( ( in @ X2 @ sK72 )
!= $true ) )
& ( ( in @ sK72 @ ( powerset @ sK73 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( ( in @ ( sK74 @ X4 @ X3 ) @ X4 )
!= $true )
& ( ( in @ ( sK74 @ X4 @ X3 ) @ X3 )
= $true ) )
| ( ( in @ X3 @ ( powerset @ X4 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73,sK74])],[f289,f291,f290]) ).
thf(f290,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK73 )
= $true )
| ( ( in @ X2 @ sK72 )
!= $true ) )
& ( ( in @ sK72 @ ( powerset @ sK73 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f291,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true ) )
=> ( ( ( in @ ( sK74 @ X4 @ X3 ) @ X4 )
!= $true )
& ( ( in @ ( sK74 @ X4 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f289,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true ) )
| ( ( in @ X3 @ ( powerset @ X4 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(rectify,[status(thm)],[f288]) ).
thf(f288,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f132]) ).
thf(f132,plain,
( ( powersetI = $true )
<=> ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f86]) ).
thf(f86,plain,
( ( powersetI = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f85]) ).
thf(f85,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,axiom,
! [X4: $i,X3: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
=> ( in @ X4 @ ( powerset @ X3 ) ) )
= powersetI ),
file('/export/starexec/sandbox/tmp/tmp.oqPmhAEHHv/DTF2THF_30490.p',powersetI) ).
thf(f713,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f546]) ).
thf(f546,plain,
! [X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ emptyset )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f348,f425]) ).
thf(f425,plain,
emptysetimpfalse = $true,
inference(cnf_transformation,[status(thm)],[f230]) ).
thf(f348,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
thf(f172,plain,
( ( ( emptysetimpfalse = $true )
| ( ( in @ sK8 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f170,f171]) ).
thf(f171,plain,
( ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true )
=> ( ( in @ sK8 @ emptyset )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f170,plain,
( ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(rectify,[status(thm)],[f169]) ).
thf(f169,plain,
( ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f119]) ).
thf(f119,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(flattening,[status(thm)],[f118]) ).
thf(f118,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(true_and_false_elimination,[status(thm)],[f110]) ).
thf(f110,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> $false ) ),
inference(fool_elimination,[status(thm)],[f109]) ).
thf(f109,plain,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
( emptysetimpfalse
= ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oqPmhAEHHv/DTF2THF_30490.p',emptysetimpfalse) ).
thf(f407,plain,
( ( in @ emptyset @ ( powerset @ sK38 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU519^1 : 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
% 0.17/0.34 % Computer : n011.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 12:25:02 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEU519^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.45 % Domain : Set Theory
% 0.20/0.45 % Problem : Preliminary Notions - Power Sets and Unions
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English : (! A:i.in emptyset (powerset A))
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.45 % Source : [Bro08]
% 0.20/0.45 % Names : ZFC021g [Bro08]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % 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, 0.11 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 v3.7.0
% 0.20/0.45 % Syntax : Number of formulae : 85 ( 38 unt; 46 typ; 38 def)
% 0.20/0.45 % Number of atoms : 215 ( 50 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 36 ( 5 avg)
% 0.20/0.45 % Number of connectives : 359 ( 7 ~; 4 |; 18 &; 235 @)
% 0.20/0.45 % ( 7 <=>; 88 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 39 ( 2 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 49 ( 46 usr; 39 con; 0-2 aty)
% 0.20/0.45 % Number of variables : 119 ( 15 ^; 88 !; 16 ?; 119 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : http://mathgate.info/detsetitem.php?id=389
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(in_type,type,
% 0.20/0.45 in: $i > $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(exu_type,type,
% 0.20/0.45 exu: ( $i > $o ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(exu,definition,
% 0.20/0.45 ( exu
% 0.20/0.45 = ( ^ [Xphi: $i > $o] :
% 0.20/0.45 ? [Xx: $i] :
% 0.20/0.45 ( ( Xphi @ Xx )
% 0.20/0.45 & ! [Xy: $i] :
% 0.20/0.45 ( ( Xphi @ Xy )
% 0.20/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setextAx_type,type,
% 0.20/0.45 setextAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setextAx,definition,
% 0.20/0.45 ( setextAx
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 <=> ( in @ Xx @ B ) )
% 0.20/0.45 => ( A = B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyset_type,type,
% 0.20/0.45 emptyset: $i ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetAx_type,type,
% 0.20/0.45 emptysetAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetAx,definition,
% 0.20/0.45 ( emptysetAx
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoin_type,type,
% 0.20/0.45 setadjoin: $i > $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinAx_type,type,
% 0.20/0.45 setadjoinAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinAx,definition,
% 0.20/0.45 ( setadjoinAx
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 <=> ( ( Xy = Xx )
% 0.20/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(powerset_type,type,
% 0.20/0.45 powerset: $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(powersetAx_type,type,
% 0.20/0.45 powersetAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(powersetAx,definition,
% 0.20/0.45 ( powersetAx
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.45 <=> ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setunion_type,type,
% 0.20/0.45 setunion: $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(setunionAx_type,type,
% 0.20/0.45 setunionAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setunionAx,definition,
% 0.20/0.45 ( setunionAx
% 0.20/0.45 = ( ! [A: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.45 <=> ? [B: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omega_type,type,
% 0.20/0.45 omega: $i ).
% 0.20/0.45
% 0.20/0.45 thf(omega0Ax_type,type,
% 0.20/0.45 omega0Ax: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omega0Ax,definition,
% 0.20/0.45 ( omega0Ax
% 0.20/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omegaSAx_type,type,
% 0.20/0.45 omegaSAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omegaSAx,definition,
% 0.20/0.45 ( omegaSAx
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ omega )
% 0.20/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omegaIndAx_type,type,
% 0.20/0.45 omegaIndAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omegaIndAx,definition,
% 0.20/0.45 ( omegaIndAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ( ( in @ emptyset @ A )
% 0.20/0.45 & ! [Xx: $i] :
% 0.20/0.45 ( ( ( in @ Xx @ omega )
% 0.20/0.45 & ( in @ Xx @ A ) )
% 0.20/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.45 => ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ omega )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(replAx_type,type,
% 0.20/0.45 replAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(replAx,definition,
% 0.20/0.45 ( replAx
% 0.20/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( exu
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.45 => ? [B: $i] :
% 0.20/0.45 ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 <=> ? [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ A )
% 0.20/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(foundationAx_type,type,
% 0.20/0.45 foundationAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(foundationAx,definition,
% 0.20/0.45 ( foundationAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.45 => ? [B: $i] :
% 0.20/0.45 ( ( in @ B @ A )
% 0.20/0.45 & ~ ? [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(wellorderingAx_type,type,
% 0.20/0.45 wellorderingAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(wellorderingAx,definition,
% 0.20/0.45 ( wellorderingAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ? [B: $i] :
% 0.20/0.45 ( ! [C: $i] :
% 0.20/0.45 ( ( in @ C @ B )
% 0.20/0.45 => ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ A ) ) )
% 0.20/0.45 & ! [Xx: $i,Xy: $i] :
% 0.20/0.45 ( ( ( in @ Xx @ A )
% 0.20/0.45 & ( in @ Xy @ A ) )
% 0.20/0.45 => ( ! [C: $i] :
% 0.20/0.45 ( ( in @ C @ B )
% 0.20/0.45 => ( ( in @ Xx @ C )
% 0.20/0.45 <=> ( in @ Xy @ C ) ) )
% 0.20/0.45 => ( Xx = Xy ) ) )
% 0.20/0.45 & ! [C: $i,D: $i] :
% 0.20/0.45 ( ( ( in @ C @ B )
% 0.20/0.45 & ( in @ D @ B ) )
% 0.20/0.45 => ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ D ) )
% 0.20/0.45 | ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ D )
% 0.20/0.45 => ( in @ Xx @ C ) ) ) )
% 0.20/0.45 & ! [C: $i] :
% 0.20/0.45 ( ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ A ) )
% 0.20/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.45 => ? [D: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ D @ B )
% 0.20/0.45 & ( in @ Xx @ C )
% 0.20/0.45 & ~ ? [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ D )
% 0.20/0.45 & ( in @ Xy @ C ) )
% 0.20/0.45 & ! [E: $i] :
% 0.20/0.45 ( ( in @ E @ B )
% 0.20/0.45 => ( ! [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ E )
% 0.20/0.45 => ( in @ Xy @ D ) )
% 0.20/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(descr_type,type,
% 0.20/0.45 descr: ( $i > $o ) > $i ).
% 0.20/0.45
% 0.20/0.45 thf(descrp_type,type,
% 0.20/0.45 descrp: $o ).
% 0.20/0.45
% 0.20/0.45 thf(descrp,definition,
% 0.20/0.45 ( descrp
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ( Xphi
% 0.20/0.45 @ ( descr
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstr_type,type,
% 0.20/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrI_type,type,
% 0.20/0.45 dsetconstrI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrI,definition,
% 0.20/0.45 ( dsetconstrI
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( ( Xphi @ Xx )
% 0.20/0.45 => ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrEL_type,type,
% 0.20/0.45 dsetconstrEL: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrEL,definition,
% 0.20/0.45 ( dsetconstrEL
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrER_type,type,
% 0.20/0.45 dsetconstrER: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrER,definition,
% 0.20/0.45 ( dsetconstrER
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(exuE1_type,type,
% 0.20/0.45 exuE1: $o ).
% 0.20/0.45
% 0.20/0.45 thf(exuE1,definition,
% 0.20/0.45 ( exuE1
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ? [Xx: $i] :
% 0.20/0.45 ( ( Xphi @ Xx )
% 0.20/0.45 & ! [Xy: $i] :
% 0.20/0.45 ( ( Xphi @ Xy )
% 0.20/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(prop2set_type,type,
% 0.20/0.45 prop2set: $o > $i ).
% 0.20/0.45
% 0.20/0.45 thf(prop2set,definition,
% 0.20/0.45 ( prop2set
% 0.20/0.45 = ( ^ [Xphi: $o] :
% 0.20/0.45 ( dsetconstr @ ( powerset @ emptyset )
% 0.20/0.45 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(prop2setE_type,type,
% 0.20/0.45 prop2setE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(prop2setE,definition,
% 0.20/0.45 ( prop2setE
% 0.20/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.45 => Xphi ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetE_type,type,
% 0.20/0.45 emptysetE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetE,definition,
% 0.20/0.45 ( emptysetE
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ emptyset )
% 0.20/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetimpfalse_type,type,
% 0.20/0.45 emptysetimpfalse: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetimpfalse,definition,
% 0.20/0.45 ( emptysetimpfalse
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ emptyset )
% 0.20/0.45 => $false ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(notinemptyset_type,type,
% 0.20/0.45 notinemptyset: $o ).
% 0.20/0.45
% 0.20/0.45 thf(notinemptyset,definition,
% 0.20/0.45 ( notinemptyset
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(exuE3e_type,type,
% 0.20/0.45 exuE3e: $o ).
% 0.20/0.45
% 0.20/0.45 thf(exuE3e,definition,
% 0.20/0.45 ( exuE3e
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setext_type,type,
% 0.20/0.45 setext: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setext,definition,
% 0.20/0.45 ( setext
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( in @ Xx @ B ) )
% 0.20/0.45 => ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( in @ Xx @ A ) )
% 0.20/0.45 => ( A = B ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyI_type,type,
% 0.20/0.45 emptyI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptyI,definition,
% 0.20/0.45 ( emptyI
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ A )
% 0.20/0.45 => ( A = emptyset ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(noeltsimpempty_type,type,
% 0.20/0.45 noeltsimpempty: $o ).
% 0.20/0.45
% 0.20/0.45 thf(noeltsimpempty,definition,
% 0.20/0.45 ( noeltsimpempty
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ A )
% 0.20/0.45 => ( A = emptyset ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setbeta_type,type,
% 0.20/0.45 setbeta: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setbeta,definition,
% 0.20/0.45 ( setbeta
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonempty_type,type,
% 0.20/0.45 nonempty: $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonempty,definition,
% 0.20/0.45 ( nonempty
% 0.20/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyE1_type,type,
% 0.20/0.45 nonemptyE1: $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyE1,definition,
% 0.20/0.45 ( nonemptyE1
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ( nonempty @ A )
% 0.20/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyI_type,type,
% 0.20/0.45 nonemptyI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyI,definition,
% 0.20/0.45 ( nonemptyI
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( ( Xphi @ Xx )
% 0.20/0.45 => ( nonempty
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyI1_type,type,
% 0.20/0.45 nonemptyI1: $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyI1,definition,
% 0.20/0.45 ( nonemptyI1
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.45 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinIL_type,type,
% 0.20/0.45 setadjoinIL: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinIL,definition,
% 0.20/0.45 ( setadjoinIL
% 0.20/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyinunitempty_type,type,
% 0.20/0.45 emptyinunitempty: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptyinunitempty,definition,
% 0.20/0.45 ( emptyinunitempty
% 0.20/0.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinIR_type,type,
% 0.20/0.45 setadjoinIR: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinIR,definition,
% 0.20/0.45 ( setadjoinIR
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ A )
% 0.20/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinE_type,type,
% 0.20/0.45 setadjoinE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinE,definition,
% 0.20/0.45 ( setadjoinE
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 => ! [Xphi: $o] :
% 0.20/0.45 ( ( ( Xy = Xx )
% 0.20/0.45 => Xphi )
% 0.20/0.45 => ( ( ( in @ Xy @ A )
% 0.20/0.45 => Xphi )
% 0.20/0.45 => Xphi ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinOr_type,type,
% 0.20/0.45 setadjoinOr: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinOr,definition,
% 0.20/0.45 ( setadjoinOr
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 => ( ( Xy = Xx )
% 0.20/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setoftrueEq_type,type,
% 0.20/0.45 setoftrueEq: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setoftrueEq,definition,
% 0.20/0.45 ( setoftrueEq
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xx: $i] : $true )
% 0.20/0.45 = A ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(powersetI_type,type,
% 0.20/0.45 powersetI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(powersetI,definition,
% 0.20/0.45 ( powersetI
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( in @ Xx @ A ) )
% 0.20/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyinPowerset,conjecture,
% 0.20/0.45 ( setextAx
% 0.20/0.45 => ( emptysetAx
% 0.20/0.45 => ( setadjoinAx
% 0.20/0.45 => ( powersetAx
% 0.20/0.45 => ( setunionAx
% 0.20/0.45 => ( omega0Ax
% 0.20/0.45 => ( omegaSAx
% 0.20/0.45 => ( omegaIndAx
% 0.20/0.45 => ( replAx
% 0.20/0.45 => ( foundationAx
% 0.20/0.45 => ( wellorderingAx
% 0.20/0.45 => ( descrp
% 0.20/0.45 => ( dsetconstrI
% 0.20/0.45 => ( dsetconstrEL
% 0.20/0.45 => ( dsetconstrER
% 0.20/0.45 => ( exuE1
% 0.20/0.45 => ( prop2setE
% 0.20/0.45 => ( emptysetE
% 0.20/0.45 => ( emptysetimpfalse
% 0.20/0.45 => ( notinemptyset
% 0.20/0.45 => ( exuE3e
% 0.20/0.45 => ( setext
% 0.20/0.45 => ( emptyI
% 0.20/0.45 => ( noeltsimpempty
% 0.20/0.45 => ( setbeta
% 0.20/0.45 => ( nonemptyE1
% 0.20/0.45 => ( nonemptyI
% 0.20/0.45 => ( nonemptyI1
% 0.20/0.45 => ( setadjoinIL
% 0.20/0.45 => ( emptyinunitempty
% 0.20/0.45 => ( setadjoinIR
% 0.20/0.45 => ( setadjoinE
% 0.20/0.45 => ( setadjoinOr
% 0.20/0.45 => ( setoftrueEq
% 0.20/0.45 => ( powersetI
% 0.20/0.45 => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.88/1.46 ---- Embedded in THF ---
% 1.88/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.88/1.46 %%% Generated on Tue Feb 24 12:25:03 EST 2026
% 1.88/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.88/1.46 %%% Logic specification used:
% 1.88/1.46 %%% thf(spec, logic, $$dhol).
% 1.88/1.46
% 1.88/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oqPmhAEHHv/DTF2DTF30490.p
% See solution above
% 1.88/1.46 ------------------------
% 1.88/1.47 ---- Cleaned THF ---
% 1.88/1.48 thf(in_type,type,
% 1.88/1.48 in: $i > $i > $o ).
% 1.88/1.48
% 1.88/1.48 thf(exu_type,type,
% 1.88/1.48 exu: ( $i > $o ) > $o ).
% 1.88/1.48
% 1.88/1.48 thf(exu,definition,
% 1.88/1.48 ( exu
% 1.88/1.48 = ( ^ [Xphi: $i > $o] :
% 1.88/1.48 ? [Xx: $i] :
% 1.88/1.48 ( ( Xphi @ Xx )
% 1.88/1.48 & ! [Xy: $i] :
% 1.88/1.48 ( ( Xphi @ Xy )
% 1.88/1.48 => ( Xx = Xy ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setextAx_type,type,
% 1.88/1.48 setextAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setextAx,definition,
% 1.88/1.48 ( setextAx
% 1.88/1.48 = ( ! [A: $i,B: $i] :
% 1.88/1.48 ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ A )
% 1.88/1.48 <=> ( in @ Xx @ B ) )
% 1.88/1.48 => ( A = B ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(emptyset_type,type,
% 1.88/1.48 emptyset: $i ).
% 1.88/1.48
% 1.88/1.48 thf(emptysetAx_type,type,
% 1.88/1.48 emptysetAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(emptysetAx,definition,
% 1.88/1.48 ( emptysetAx
% 1.88/1.48 = ( ! [Xx: $i] :
% 1.88/1.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoin_type,type,
% 1.88/1.48 setadjoin: $i > $i > $i ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinAx_type,type,
% 1.88/1.48 setadjoinAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinAx,definition,
% 1.88/1.48 ( setadjoinAx
% 1.88/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.88/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.88/1.48 <=> ( ( Xy = Xx )
% 1.88/1.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(powerset_type,type,
% 1.88/1.48 powerset: $i > $i ).
% 1.88/1.48
% 1.88/1.48 thf(powersetAx_type,type,
% 1.88/1.48 powersetAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(powersetAx,definition,
% 1.88/1.48 ( powersetAx
% 1.88/1.48 = ( ! [A: $i,B: $i] :
% 1.88/1.48 ( ( in @ B @ ( powerset @ A ) )
% 1.88/1.48 <=> ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ B )
% 1.88/1.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setunion_type,type,
% 1.88/1.48 setunion: $i > $i ).
% 1.88/1.48
% 1.88/1.48 thf(setunionAx_type,type,
% 1.88/1.48 setunionAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setunionAx,definition,
% 1.88/1.48 ( setunionAx
% 1.88/1.48 = ( ! [A: $i,Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ ( setunion @ A ) )
% 1.88/1.48 <=> ? [B: $i] :
% 1.88/1.48 ( ( in @ Xx @ B )
% 1.88/1.48 & ( in @ B @ A ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(omega_type,type,
% 1.88/1.48 omega: $i ).
% 1.88/1.48
% 1.88/1.48 thf(omega0Ax_type,type,
% 1.88/1.48 omega0Ax: $o ).
% 1.88/1.48
% 1.88/1.48 thf(omega0Ax,definition,
% 1.88/1.48 ( omega0Ax
% 1.88/1.48 = ( in @ emptyset @ omega ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(omegaSAx_type,type,
% 1.88/1.48 omegaSAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(omegaSAx,definition,
% 1.88/1.48 ( omegaSAx
% 1.88/1.48 = ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ omega )
% 1.88/1.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(omegaIndAx_type,type,
% 1.88/1.48 omegaIndAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(omegaIndAx,definition,
% 1.88/1.48 ( omegaIndAx
% 1.88/1.48 = ( ! [A: $i] :
% 1.88/1.48 ( ( ( in @ emptyset @ A )
% 1.88/1.48 & ! [Xx: $i] :
% 1.88/1.48 ( ( ( in @ Xx @ omega )
% 1.88/1.48 & ( in @ Xx @ A ) )
% 1.88/1.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.88/1.48 => ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ omega )
% 1.88/1.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(replAx_type,type,
% 1.88/1.48 replAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(replAx,definition,
% 1.88/1.48 ( replAx
% 1.88/1.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.88/1.48 ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ A )
% 1.88/1.48 => ( exu
% 1.88/1.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.88/1.48 => ? [B: $i] :
% 1.88/1.48 ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ B )
% 1.88/1.48 <=> ? [Xy: $i] :
% 1.88/1.48 ( ( in @ Xy @ A )
% 1.88/1.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(foundationAx_type,type,
% 1.88/1.48 foundationAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(foundationAx,definition,
% 1.88/1.48 ( foundationAx
% 1.88/1.48 = ( ! [A: $i] :
% 1.88/1.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.88/1.48 => ? [B: $i] :
% 1.88/1.48 ( ( in @ B @ A )
% 1.88/1.48 & ~ ? [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ B )
% 1.88/1.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(wellorderingAx_type,type,
% 1.88/1.48 wellorderingAx: $o ).
% 1.88/1.48
% 1.88/1.48 thf(wellorderingAx,definition,
% 1.88/1.48 ( wellorderingAx
% 1.88/1.48 = ( ! [A: $i] :
% 1.88/1.48 ? [B: $i] :
% 1.88/1.48 ( ! [C: $i] :
% 1.88/1.48 ( ( in @ C @ B )
% 1.88/1.48 => ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ C )
% 1.88/1.48 => ( in @ Xx @ A ) ) )
% 1.88/1.48 & ! [Xx: $i,Xy: $i] :
% 1.88/1.48 ( ( ( in @ Xx @ A )
% 1.88/1.48 & ( in @ Xy @ A ) )
% 1.88/1.48 => ( ! [C: $i] :
% 1.88/1.48 ( ( in @ C @ B )
% 1.88/1.48 => ( ( in @ Xx @ C )
% 1.88/1.48 <=> ( in @ Xy @ C ) ) )
% 1.88/1.48 => ( Xx = Xy ) ) )
% 1.88/1.48 & ! [C: $i,D: $i] :
% 1.88/1.48 ( ( ( in @ C @ B )
% 1.88/1.48 & ( in @ D @ B ) )
% 1.88/1.48 => ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ C )
% 1.88/1.48 => ( in @ Xx @ D ) )
% 1.88/1.48 | ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ D )
% 1.88/1.48 => ( in @ Xx @ C ) ) ) )
% 1.88/1.48 & ! [C: $i] :
% 1.88/1.48 ( ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ C )
% 1.88/1.48 => ( in @ Xx @ A ) )
% 1.88/1.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.88/1.48 => ? [D: $i,Xx: $i] :
% 1.88/1.48 ( ( in @ D @ B )
% 1.88/1.48 & ( in @ Xx @ C )
% 1.88/1.48 & ~ ? [Xy: $i] :
% 1.88/1.48 ( ( in @ Xy @ D )
% 1.88/1.48 & ( in @ Xy @ C ) )
% 1.88/1.48 & ! [E: $i] :
% 1.88/1.48 ( ( in @ E @ B )
% 1.88/1.48 => ( ! [Xy: $i] :
% 1.88/1.48 ( ( in @ Xy @ E )
% 1.88/1.48 => ( in @ Xy @ D ) )
% 1.88/1.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(descr_type,type,
% 1.88/1.48 descr: ( $i > $o ) > $i ).
% 1.88/1.48
% 1.88/1.48 thf(descrp_type,type,
% 1.88/1.48 descrp: $o ).
% 1.88/1.48
% 1.88/1.48 thf(descrp,definition,
% 1.88/1.48 ( descrp
% 1.88/1.48 = ( ! [Xphi: $i > $o] :
% 1.88/1.48 ( ( exu
% 1.88/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.88/1.48 => ( Xphi
% 1.88/1.48 @ ( descr
% 1.88/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(dsetconstr_type,type,
% 1.88/1.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.88/1.48
% 1.88/1.48 thf(dsetconstrI_type,type,
% 1.88/1.48 dsetconstrI: $o ).
% 1.88/1.48
% 1.88/1.48 thf(dsetconstrI,definition,
% 1.88/1.48 ( dsetconstrI
% 1.88/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ A )
% 1.88/1.48 => ( ( Xphi @ Xx )
% 1.88/1.48 => ( in @ Xx
% 1.88/1.48 @ ( dsetconstr @ A
% 1.88/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(dsetconstrEL_type,type,
% 1.88/1.48 dsetconstrEL: $o ).
% 1.88/1.48
% 1.88/1.48 thf(dsetconstrEL,definition,
% 1.88/1.48 ( dsetconstrEL
% 1.88/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.88/1.48 ( ( in @ Xx
% 1.88/1.48 @ ( dsetconstr @ A
% 1.88/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.88/1.48 => ( in @ Xx @ A ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(dsetconstrER_type,type,
% 1.88/1.48 dsetconstrER: $o ).
% 1.88/1.48
% 1.88/1.48 thf(dsetconstrER,definition,
% 1.88/1.48 ( dsetconstrER
% 1.88/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.88/1.48 ( ( in @ Xx
% 1.88/1.48 @ ( dsetconstr @ A
% 1.88/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.88/1.48 => ( Xphi @ Xx ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(exuE1_type,type,
% 1.88/1.48 exuE1: $o ).
% 1.88/1.48
% 1.88/1.48 thf(exuE1,definition,
% 1.88/1.48 ( exuE1
% 1.88/1.48 = ( ! [Xphi: $i > $o] :
% 1.88/1.48 ( ( exu
% 1.88/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.88/1.48 => ? [Xx: $i] :
% 1.88/1.48 ( ( Xphi @ Xx )
% 1.88/1.48 & ! [Xy: $i] :
% 1.88/1.48 ( ( Xphi @ Xy )
% 1.88/1.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(prop2set_type,type,
% 1.88/1.48 prop2set: $o > $i ).
% 1.88/1.48
% 1.88/1.48 thf(prop2set,definition,
% 1.88/1.48 ( prop2set
% 1.88/1.48 = ( ^ [Xphi: $o] :
% 1.88/1.48 ( dsetconstr @ ( powerset @ emptyset )
% 1.88/1.48 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(prop2setE_type,type,
% 1.88/1.48 prop2setE: $o ).
% 1.88/1.48
% 1.88/1.48 thf(prop2setE,definition,
% 1.88/1.48 ( prop2setE
% 1.88/1.48 = ( ! [Xphi: $o,Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.88/1.48 => Xphi ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(emptysetE_type,type,
% 1.88/1.48 emptysetE: $o ).
% 1.88/1.48
% 1.88/1.48 thf(emptysetE,definition,
% 1.88/1.48 ( emptysetE
% 1.88/1.48 = ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ emptyset )
% 1.88/1.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(emptysetimpfalse_type,type,
% 1.88/1.48 emptysetimpfalse: $o ).
% 1.88/1.48
% 1.88/1.48 thf(emptysetimpfalse,definition,
% 1.88/1.48 ( emptysetimpfalse
% 1.88/1.48 = ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ emptyset )
% 1.88/1.48 => $false ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(notinemptyset_type,type,
% 1.88/1.48 notinemptyset: $o ).
% 1.88/1.48
% 1.88/1.48 thf(notinemptyset,definition,
% 1.88/1.48 ( notinemptyset
% 1.88/1.48 = ( ! [Xx: $i] :
% 1.88/1.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(exuE3e_type,type,
% 1.88/1.48 exuE3e: $o ).
% 1.88/1.48
% 1.88/1.48 thf(exuE3e,definition,
% 1.88/1.48 ( exuE3e
% 1.88/1.48 = ( ! [Xphi: $i > $o] :
% 1.88/1.48 ( ( exu
% 1.88/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.88/1.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setext_type,type,
% 1.88/1.48 setext: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setext,definition,
% 1.88/1.48 ( setext
% 1.88/1.48 = ( ! [A: $i,B: $i] :
% 1.88/1.48 ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ A )
% 1.88/1.48 => ( in @ Xx @ B ) )
% 1.88/1.48 => ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ B )
% 1.88/1.48 => ( in @ Xx @ A ) )
% 1.88/1.48 => ( A = B ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(emptyI_type,type,
% 1.88/1.48 emptyI: $o ).
% 1.88/1.48
% 1.88/1.48 thf(emptyI,definition,
% 1.88/1.48 ( emptyI
% 1.88/1.48 = ( ! [A: $i] :
% 1.88/1.48 ( ! [Xx: $i] :
% 1.88/1.48 ~ ( in @ Xx @ A )
% 1.88/1.48 => ( A = emptyset ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(noeltsimpempty_type,type,
% 1.88/1.48 noeltsimpempty: $o ).
% 1.88/1.48
% 1.88/1.48 thf(noeltsimpempty,definition,
% 1.88/1.48 ( noeltsimpempty
% 1.88/1.48 = ( ! [A: $i] :
% 1.88/1.48 ( ! [Xx: $i] :
% 1.88/1.48 ~ ( in @ Xx @ A )
% 1.88/1.48 => ( A = emptyset ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setbeta_type,type,
% 1.88/1.48 setbeta: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setbeta,definition,
% 1.88/1.48 ( setbeta
% 1.88/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ A )
% 1.88/1.48 => ( ( in @ Xx
% 1.88/1.48 @ ( dsetconstr @ A
% 1.88/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.88/1.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(nonempty_type,type,
% 1.88/1.48 nonempty: $i > $o ).
% 1.88/1.48
% 1.88/1.48 thf(nonempty,definition,
% 1.88/1.48 ( nonempty
% 1.88/1.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(nonemptyE1_type,type,
% 1.88/1.48 nonemptyE1: $o ).
% 1.88/1.48
% 1.88/1.48 thf(nonemptyE1,definition,
% 1.88/1.48 ( nonemptyE1
% 1.88/1.48 = ( ! [A: $i] :
% 1.88/1.48 ( ( nonempty @ A )
% 1.88/1.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(nonemptyI_type,type,
% 1.88/1.48 nonemptyI: $o ).
% 1.88/1.48
% 1.88/1.48 thf(nonemptyI,definition,
% 1.88/1.48 ( nonemptyI
% 1.88/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ A )
% 1.88/1.48 => ( ( Xphi @ Xx )
% 1.88/1.48 => ( nonempty
% 1.88/1.48 @ ( dsetconstr @ A
% 1.88/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(nonemptyI1_type,type,
% 1.88/1.48 nonemptyI1: $o ).
% 1.88/1.48
% 1.88/1.48 thf(nonemptyI1,definition,
% 1.88/1.48 ( nonemptyI1
% 1.88/1.48 = ( ! [A: $i] :
% 1.88/1.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.88/1.48 => ( nonempty @ A ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinIL_type,type,
% 1.88/1.48 setadjoinIL: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinIL,definition,
% 1.88/1.48 ( setadjoinIL
% 1.88/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(emptyinunitempty_type,type,
% 1.88/1.48 emptyinunitempty: $o ).
% 1.88/1.48
% 1.88/1.48 thf(emptyinunitempty,definition,
% 1.88/1.48 ( emptyinunitempty
% 1.88/1.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinIR_type,type,
% 1.88/1.48 setadjoinIR: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinIR,definition,
% 1.88/1.48 ( setadjoinIR
% 1.88/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.88/1.48 ( ( in @ Xy @ A )
% 1.88/1.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinE_type,type,
% 1.88/1.48 setadjoinE: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinE,definition,
% 1.88/1.48 ( setadjoinE
% 1.88/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.88/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.88/1.48 => ! [Xphi: $o] :
% 1.88/1.48 ( ( ( Xy = Xx )
% 1.88/1.48 => Xphi )
% 1.88/1.48 => ( ( ( in @ Xy @ A )
% 1.88/1.48 => Xphi )
% 1.88/1.48 => Xphi ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinOr_type,type,
% 1.88/1.48 setadjoinOr: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setadjoinOr,definition,
% 1.88/1.48 ( setadjoinOr
% 1.88/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.88/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.88/1.48 => ( ( Xy = Xx )
% 1.88/1.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(setoftrueEq_type,type,
% 1.88/1.48 setoftrueEq: $o ).
% 1.88/1.48
% 1.88/1.48 thf(setoftrueEq,definition,
% 1.88/1.48 ( setoftrueEq
% 1.88/1.48 = ( ! [A: $i] :
% 1.88/1.48 ( ( dsetconstr @ A
% 1.88/1.48 @ ^ [Xx: $i] : $true )
% 1.88/1.48 = A ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(powersetI_type,type,
% 1.88/1.48 powersetI: $o ).
% 1.88/1.48
% 1.88/1.48 thf(powersetI,definition,
% 1.88/1.48 ( powersetI
% 1.88/1.48 = ( ! [A: $i,B: $i] :
% 1.88/1.48 ( ! [Xx: $i] :
% 1.88/1.48 ( ( in @ Xx @ B )
% 1.88/1.48 => ( in @ Xx @ A ) )
% 1.88/1.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.88/1.48
% 1.88/1.48 thf(emptyinPowerset,conjecture,
% 1.88/1.48 ( setextAx
% 1.88/1.48 => ( emptysetAx
% 1.88/1.48 => ( setadjoinAx
% 1.88/1.48 => ( powersetAx
% 1.88/1.48 => ( setunionAx
% 1.88/1.48 => ( omega0Ax
% 1.88/1.48 => ( omegaSAx
% 1.88/1.48 => ( omegaIndAx
% 1.88/1.48 => ( replAx
% 1.88/1.48 => ( foundationAx
% 1.88/1.48 => ( wellorderingAx
% 1.88/1.48 => ( descrp
% 1.88/1.48 => ( dsetconstrI
% 1.88/1.48 => ( dsetconstrEL
% 1.88/1.48 => ( dsetconstrER
% 1.88/1.48 => ( exuE1
% 1.88/1.48 => ( prop2setE
% 1.88/1.48 => ( emptysetE
% 1.88/1.48 => ( emptysetimpfalse
% 1.88/1.48 => ( notinemptyset
% 1.88/1.48 => ( exuE3e
% 1.88/1.48 => ( setext
% 1.88/1.48 => ( emptyI
% 1.88/1.48 => ( noeltsimpempty
% 1.88/1.48 => ( setbeta
% 1.88/1.48 => ( nonemptyE1
% 1.88/1.48 => ( nonemptyI
% 1.88/1.48 => ( nonemptyI1
% 1.88/1.48 => ( setadjoinIL
% 1.88/1.48 => ( emptyinunitempty
% 1.88/1.48 => ( setadjoinIR
% 1.88/1.48 => ( setadjoinE
% 1.88/1.48 => ( setadjoinOr
% 1.88/1.48 => ( setoftrueEq
% 1.88/1.48 => ( powersetI
% 1.88/1.48 => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.88/1.48 ------------------------
% 2.04/1.50 % (30591)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_30490 for (2999ds/4Mi)
% 2.04/1.50 % (30596)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/18Mi)
% 2.04/1.50 % (30593)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/2Mi)
% 2.04/1.50 % (30590)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/183Mi)
% 2.04/1.50 % (30592)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_30490 for (2999ds/27Mi)
% 2.04/1.50 % (30594)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_30490 for (2999ds/2Mi)
% 2.04/1.50 % (30595)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_30490 for (2999ds/275Mi)
% 2.04/1.50 % (30593)Instruction limit reached!
% 2.04/1.50 % (30593)------------------------------
% 2.04/1.50 % (30593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.50 % (30593)Termination reason: Unknown
% 2.04/1.50 % (30593)Termination phase: shuffling
% 2.04/1.50
% 2.04/1.50 % (30593)Memory used [KB]: 1023
% 2.04/1.50 % (30593)Time elapsed: 0.003 s
% 2.04/1.50 % (30593)Instructions burned: 2 (million)
% 2.04/1.50 % (30593)------------------------------
% 2.04/1.50 % (30593)------------------------------
% 2.04/1.50 % (30591)Instruction limit reached!
% 2.04/1.50 % (30591)------------------------------
% 2.04/1.50 % (30591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.50 % (30591)Termination reason: Unknown
% 2.04/1.50 % (30591)Termination phase: shuffling
% 2.04/1.50
% 2.04/1.50 % (30591)Memory used [KB]: 1151
% 2.04/1.50 % (30591)Time elapsed: 0.004 s
% 2.04/1.50 % (30591)Instructions burned: 4 (million)
% 2.04/1.50 % (30591)------------------------------
% 2.04/1.50 % (30591)------------------------------
% 2.04/1.50 % (30594)Instruction limit reached!
% 2.04/1.50 % (30594)------------------------------
% 2.04/1.50 % (30594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.50 % (30594)Termination reason: Unknown
% 2.04/1.50 % (30594)Termination phase: shuffling
% 2.04/1.50
% 2.04/1.50 % (30594)Memory used [KB]: 1023
% 2.04/1.50 % (30594)Time elapsed: 0.004 s
% 2.04/1.50 % (30594)Instructions burned: 3 (million)
% 2.04/1.50 % (30594)------------------------------
% 2.04/1.50 % (30594)------------------------------
% 2.04/1.51 % (30596)Instruction limit reached!
% 2.04/1.51 % (30596)------------------------------
% 2.04/1.51 % (30596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.51 % (30596)Termination reason: Unknown
% 2.04/1.51 % (30596)Termination phase: Property scanning
% 2.04/1.51
% 2.04/1.51 % (30596)Memory used [KB]: 1535
% 2.04/1.51 % (30596)Time elapsed: 0.011 s
% 2.04/1.51 % (30596)Instructions burned: 20 (million)
% 2.04/1.51 % (30596)------------------------------
% 2.04/1.51 % (30596)------------------------------
% 2.04/1.51 % (30592)Instruction limit reached!
% 2.04/1.51 % (30592)------------------------------
% 2.04/1.51 % (30592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.51 % (30592)Termination reason: Unknown
% 2.04/1.51 % (30592)Termination phase: Saturation
% 2.04/1.51
% 2.04/1.51 % (30592)Memory used [KB]: 5756
% 2.04/1.51 % (30592)Time elapsed: 0.015 s
% 2.04/1.51 % (30592)Instructions burned: 29 (million)
% 2.04/1.51 % (30592)------------------------------
% 2.04/1.51 % (30592)------------------------------
% 2.04/1.52 % (30597)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/3Mi)
% 2.04/1.52 % (30598)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_30490 for (2999ds/37Mi)
% 2.04/1.52 % (30599)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_30490 for (2999ds/15Mi)
% 2.04/1.52 % (30597)Instruction limit reached!
% 2.04/1.52 % (30597)------------------------------
% 2.04/1.52 % (30597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.52 % (30597)Termination reason: Unknown
% 2.04/1.52 % (30597)Termination phase: shuffling
% 2.04/1.52
% 2.04/1.52 % (30597)Memory used [KB]: 1023
% 2.04/1.52 % (30597)Time elapsed: 0.003 s
% 2.04/1.52 % (30597)Instructions burned: 3 (million)
% 2.04/1.52 % (30597)------------------------------
% 2.04/1.52 % (30597)------------------------------
% 2.04/1.52 % (30600)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_30490 for (2999ds/3Mi)
% 2.04/1.52 % (30599)Instruction limit reached!
% 2.04/1.52 % (30599)------------------------------
% 2.04/1.52 % (30599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.52 % (30599)Termination reason: Unknown
% 2.04/1.52 % (30599)Termination phase: Preprocessing 3
% 2.04/1.52
% 2.04/1.52 % (30599)Memory used [KB]: 1407
% 2.04/1.52 % (30599)Time elapsed: 0.009 s
% 2.04/1.52 % (30599)Instructions burned: 15 (million)
% 2.04/1.52 % (30599)------------------------------
% 2.04/1.52 % (30599)------------------------------
% 2.04/1.52 % (30600)Instruction limit reached!
% 2.04/1.52 % (30600)------------------------------
% 2.04/1.52 % (30600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.52 % (30600)Termination reason: Unknown
% 2.04/1.52 % (30600)Termination phase: shuffling
% 2.04/1.52
% 2.04/1.52 % (30600)Memory used [KB]: 1023
% 2.04/1.52 % (30600)Time elapsed: 0.003 s
% 2.04/1.52 % (30600)Instructions burned: 4 (million)
% 2.04/1.52 % (30600)------------------------------
% 2.04/1.52 % (30600)------------------------------
% 2.04/1.53 % (30601)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_30490 for (2999ds/1041Mi)
% 2.04/1.53 % (30598)Instruction limit reached!
% 2.04/1.53 % (30598)------------------------------
% 2.04/1.53 % (30598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.53 % (30598)Termination reason: Unknown
% 2.04/1.53 % (30598)Termination phase: Saturation
% 2.04/1.53
% 2.04/1.53 % (30598)Memory used [KB]: 6012
% 2.04/1.53 % (30598)Time elapsed: 0.017 s
% 2.04/1.53 % (30598)Instructions burned: 37 (million)
% 2.04/1.53 % (30598)------------------------------
% 2.04/1.53 % (30598)------------------------------
% 2.04/1.53 % (30602)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/7Mi)
% 2.04/1.54 % (30602)Instruction limit reached!
% 2.04/1.54 % (30602)------------------------------
% 2.04/1.54 % (30602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.54 % (30602)Termination reason: Unknown
% 2.04/1.54 % (30602)Termination phase: Property scanning
% 2.04/1.54
% 2.04/1.54 % (30602)Memory used [KB]: 1151
% 2.04/1.54 % (30602)Time elapsed: 0.005 s
% 2.04/1.54 % (30602)Instructions burned: 8 (million)
% 2.04/1.54 % (30602)------------------------------
% 2.04/1.54 % (30602)------------------------------
% 2.04/1.54 % (30603)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/16Mi)
% 2.04/1.54 % (30604)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_30490 for (2999ds/3Mi)
% 2.04/1.54 % (30604)Instruction limit reached!
% 2.04/1.54 % (30604)------------------------------
% 2.04/1.54 % (30604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.54 % (30604)Termination reason: Unknown
% 2.04/1.54 % (30604)Termination phase: shuffling
% 2.04/1.54
% 2.04/1.54 % (30604)Memory used [KB]: 1023
% 2.04/1.54 % (30604)Time elapsed: 0.003 s
% 2.04/1.54 % (30604)Instructions burned: 4 (million)
% 2.04/1.54 % (30604)------------------------------
% 2.04/1.54 % (30604)------------------------------
% 2.04/1.55 % (30603)Instruction limit reached!
% 2.04/1.55 % (30603)------------------------------
% 2.04/1.55 % (30603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.55 % (30603)Termination reason: Unknown
% 2.04/1.55 % (30603)Termination phase: Twee Goal Transformation
% 2.04/1.55
% 2.04/1.55 % (30603)Memory used [KB]: 1151
% 2.04/1.55 % (30603)Time elapsed: 0.009 s
% 2.04/1.55 % (30603)Instructions burned: 17 (million)
% 2.04/1.55 % (30603)------------------------------
% 2.04/1.55 % (30603)------------------------------
% 2.04/1.55 % (30605)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_30490 for (2999ds/3Mi)
% 2.04/1.55 % (30605)Instruction limit reached!
% 2.04/1.55 % (30605)------------------------------
% 2.04/1.55 % (30605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.55 % (30605)Termination reason: Unknown
% 2.04/1.55 % (30605)Termination phase: shuffling
% 2.04/1.55
% 2.04/1.55 % (30605)Memory used [KB]: 1023
% 2.04/1.55 % (30605)Time elapsed: 0.003 s
% 2.04/1.55 % (30605)Instructions burned: 4 (million)
% 2.04/1.55 % (30605)------------------------------
% 2.04/1.55 % (30605)------------------------------
% 2.04/1.55 % (30606)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/7Mi)
% 2.04/1.56 % (30606)Instruction limit reached!
% 2.04/1.56 % (30606)------------------------------
% 2.04/1.56 % (30606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.56 % (30606)Termination reason: Unknown
% 2.04/1.56 % (30606)Termination phase: Property scanning
% 2.04/1.56
% 2.04/1.56 % (30606)Memory used [KB]: 1151
% 2.04/1.56 % (30606)Time elapsed: 0.005 s
% 2.04/1.56 % (30606)Instructions burned: 8 (million)
% 2.04/1.56 % (30606)------------------------------
% 2.04/1.56 % (30606)------------------------------
% 2.04/1.56 % (30607)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/3Mi)
% 2.04/1.56 % (30607)Instruction limit reached!
% 2.04/1.56 % (30607)------------------------------
% 2.04/1.56 % (30607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.56 % (30607)Termination reason: Unknown
% 2.04/1.56 % (30607)Termination phase: shuffling
% 2.04/1.56
% 2.04/1.56 % (30607)Memory used [KB]: 1151
% 2.04/1.56 % (30607)Time elapsed: 0.003 s
% 2.04/1.56 % (30607)Instructions burned: 4 (million)
% 2.04/1.56 % (30607)------------------------------
% 2.04/1.56 % (30607)------------------------------
% 2.04/1.56 % (30608)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/4Mi)
% 2.04/1.56 % (30608)Instruction limit reached!
% 2.04/1.56 % (30608)------------------------------
% 2.04/1.56 % (30608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.56 % (30608)Termination reason: Unknown
% 2.04/1.56 % (30608)Termination phase: shuffling
% 2.04/1.56
% 2.04/1.56 % (30608)Memory used [KB]: 1023
% 2.04/1.56 % (30608)Time elapsed: 0.003 s
% 2.04/1.56 % (30608)Instructions burned: 4 (million)
% 2.04/1.56 % (30608)------------------------------
% 2.04/1.56 % (30608)------------------------------
% 2.04/1.56 % (30609)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/18Mi)
% 2.04/1.57 % (30610)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/710Mi)
% 2.04/1.57 % (30609)Instruction limit reached!
% 2.04/1.57 % (30609)------------------------------
% 2.04/1.57 % (30609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.57 % (30609)Termination reason: Unknown
% 2.04/1.57 % (30609)Termination phase: Saturation
% 2.04/1.57
% 2.04/1.57 % (30609)Memory used [KB]: 5756
% 2.04/1.57 % (30609)Time elapsed: 0.010 s
% 2.04/1.57 % (30609)Instructions burned: 19 (million)
% 2.04/1.57 % (30609)------------------------------
% 2.04/1.57 % (30609)------------------------------
% 2.04/1.58 % (30611)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30490 for (2999ds/6Mi)
% 2.04/1.58 % (30611)Instruction limit reached!
% 2.04/1.58 % (30611)------------------------------
% 2.04/1.58 % (30611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.58 % (30611)Termination reason: Unknown
% 2.04/1.58 % (30611)Termination phase: shuffling
% 2.04/1.58
% 2.04/1.58 % (30611)Memory used [KB]: 1151
% 2.04/1.58 % (30611)Time elapsed: 0.004 s
% 2.04/1.58 % (30611)Instructions burned: 6 (million)
% 2.04/1.58 % (30611)------------------------------
% 2.04/1.58 % (30611)------------------------------
% 2.04/1.58 % (30612)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_30490 for (2999ds/902Mi)
% 2.04/1.58 % (30595)First to succeed.
% 2.04/1.58 % (30595)Refutation found. Thanks to Tanya!
% 2.04/1.58 % SZS status Theorem for DTF2THF_30490
% 2.04/1.58 % SZS output start Proof for DTF2THF_30490
% 2.04/1.58 thf(func_def_0, type, in: $i > $i > $o).
% 2.04/1.58 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.04/1.58 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.04/1.58 thf(func_def_8, type, powerset: $i > $i).
% 2.04/1.58 thf(func_def_10, type, setunion: $i > $i).
% 2.04/1.58 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.04/1.58 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.04/1.58 thf(func_def_26, type, prop2set: $o > $i).
% 2.04/1.58 thf(func_def_36, type, nonempty: $i > $o).
% 2.04/1.58 thf(func_def_60, type, sP1: $i > $i > $o).
% 2.04/1.58 thf(func_def_61, type, sP2: $i > $o).
% 2.04/1.58 thf(func_def_62, type, sP3: $i > $i > $o).
% 2.04/1.58 thf(func_def_63, type, sP4: $i > $i > $o).
% 2.04/1.58 thf(func_def_64, type, sK5: $i > $o).
% 2.04/1.58 thf(func_def_69, type, sK10: $i > $i > $o).
% 2.04/1.58 thf(func_def_70, type, sK11: $i > $i).
% 2.04/1.58 thf(func_def_71, type, sK12: $i > $i).
% 2.04/1.58 thf(func_def_72, type, sK13: ($i > $i > $o) > $i > $i).
% 2.04/1.58 thf(func_def_73, type, sK14: $i > ($i > $i > $o) > $i > $i).
% 2.04/1.58 thf(func_def_74, type, sK15: ($i > $i > $o) > $i > $i).
% 2.04/1.58 thf(func_def_77, type, sK18: $i > $o).
% 2.04/1.58 thf(func_def_78, type, sK19: $i > $i).
% 2.04/1.58 thf(func_def_79, type, sK20: ($i > $o) > $i).
% 2.04/1.58 thf(func_def_82, type, sK23: $i > $o).
% 2.04/1.58 thf(func_def_90, type, sK31: $i > $i).
% 2.04/1.58 thf(func_def_100, type, sK41: $i > $o).
% 2.04/1.58 thf(func_def_105, type, sK46: $i > $i).
% 2.04/1.58 thf(func_def_106, type, sK47: $i > $o).
% 2.04/1.58 thf(func_def_107, type, sK48: ($i > $o) > $i).
% 2.04/1.58 thf(func_def_108, type, sK49: $i > $i).
% 2.04/1.58 thf(func_def_114, type, sK55: $i > $o).
% 2.04/1.58 thf(func_def_117, type, sK58: $i > $i > $i).
% 2.04/1.58 thf(func_def_125, type, sK66: $i > $i > $i).
% 2.04/1.58 thf(func_def_128, type, sK69: $i > $i > $i).
% 2.04/1.58 thf(func_def_129, type, sK70: $i > $i > $i).
% 2.04/1.58 thf(func_def_133, type, sK74: $i > $i > $i).
% 2.04/1.58 thf(func_def_134, type, sK75: $i > $i).
% 2.04/1.58 thf(func_def_140, type, sK81: $i > $i).
% 2.04/1.58 thf(func_def_141, type, sK82: $i > $i).
% 2.04/1.58 thf(func_def_144, type, sK85: $i > $o).
% 2.04/1.58 thf(func_def_145, type, sK86: $i > $i > $i).
% 2.04/1.58 thf(func_def_146, type, sK87: $i > $i > $i).
% 2.04/1.58 thf(func_def_147, type, sK88: $i > $i > $i).
% 2.04/1.58 thf(func_def_148, type, sK89: $i > $i > $i).
% 2.04/1.58 thf(func_def_149, type, sK90: $i > $i > $i > $i).
% 2.04/1.58 thf(func_def_150, type, sK91: $i > $i).
% 2.04/1.58 thf(func_def_151, type, sK92: $i > $i).
% 2.04/1.58 thf(func_def_152, type, sK93: $i > $i).
% 2.04/1.58 thf(func_def_153, type, sK94: $i > $i).
% 2.04/1.58 thf(func_def_154, type, sK95: $i > $i > $i > $i).
% 2.04/1.58 thf(func_def_155, type, sK96: $i > $i > $i > $i).
% 2.04/1.58 thf(func_def_156, type, sK97: $i > $i > $i).
% 2.04/1.58 thf(func_def_157, type, sK98: $i > $i > $i).
% 2.04/1.58 thf(func_def_158, type, sK99: $i > $i > $i).
% 2.04/1.58 thf(func_def_159, type, sK100: $i > $i).
% 2.04/1.58 thf(func_def_160, type, sK101: $i > $i > $i).
% 2.04/1.58 thf(func_def_162, type, sK103: $i > $i).
% 2.04/1.58 thf(func_def_163, type, sK104: $i > $i).
% 2.04/1.58 thf(func_def_165, type, ph106: !>[X0: $tType]:(X0)).
% 2.04/1.58 thf(f1099,plain,(
% 2.04/1.58 $false),
% 2.04/1.58 inference(trivial_inequality_removal,[status(thm)],[f1096])).
% 2.04/1.58 thf(f1096,plain,(
% 2.04/1.58 ($true != $true)),
% 2.04/1.58 inference(superposition,[status(thm)],[f407,f1093])).
% 2.04/1.58 thf(f1093,plain,(
% 2.04/1.58 ( ! [X0 : $i] : (((in @ emptyset @ (powerset @ X0)) = $true)) )),
% 2.04/1.58 inference(trivial_inequality_removal,[status(thm)],[f1089])).
% 2.04/1.58 thf(f1089,plain,(
% 2.04/1.58 ( ! [X0 : $i] : (((in @ emptyset @ (powerset @ X0)) = $true) | ($true != $true)) )),
% 2.04/1.58 inference(superposition,[status(thm)],[f713,f691])).
% 2.04/1.58 thf(f691,plain,(
% 2.04/1.58 ( ! [X3 : $i,X4 : $i] : (((in @ (sK74 @ X4 @ X3) @ X3) = $true) | ((in @ X3 @ (powerset @ X4)) = $true)) )),
% 2.04/1.58 inference(trivial_inequality_removal,[status(thm)],[f635])).
% 2.04/1.58 thf(f635,plain,(
% 2.04/1.58 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ (sK74 @ X4 @ X3) @ X3) = $true) | ((in @ X3 @ (powerset @ X4)) = $true)) )),
% 2.04/1.58 inference(definition_unfolding,[status(thm)],[f481,f415])).
% 2.04/1.58 thf(f415,plain,(
% 2.04/1.58 (powersetI = $true)),
% 2.04/1.58 inference(cnf_transformation,[status(thm)],[f230])).
% 2.04/1.58 thf(f230,plain,(
% 2.04/1.58 (emptysetE = $true) & (notinemptyset = $true) & (dsetconstrI = $true) & (powersetAx = $true) & (nonemptyI1 = $true) & (noeltsimpempty = $true) & (emptysetimpfalse = $true) & (omegaIndAx = $true) & (exuE3e = $true) & (nonemptyE1 = $true) & (foundationAx = $true) & (setadjoinIL = $true) & (setext = $true) & (emptyinunitempty = $true) & (setunionAx = $true) & (emptysetAx = $true) & (powersetI = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (descrp = $true) & (dsetconstrER = $true) & (omegaSAx = $true) & ((in @ emptyset @ (powerset @ sK38)) != $true) & (setbeta = $true) & (setextAx = $true) & (setadjoinOr = $true) & (emptyI = $true) & (nonemptyI = $true) & (replAx = $true) & (exuE1 = $true) & (omega0Ax = $true) & (setoftrueEq = $true) & (setadjoinAx = $true) & (wellorderingAx = $true)),
% 2.04/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f153,f229])).
% 2.04/1.58 thf(f229,plain,(
% 2.04/1.58 ? [X0 : $i] : ((in @ emptyset @ (powerset @ X0)) != $true) => ((in @ emptyset @ (powerset @ sK38)) != $true)),
% 2.04/1.58 introduced(definition,[],[choice_axiom])).
% 2.04/1.58 thf(f153,plain,(
% 2.04/1.58 (emptysetE = $true) & (notinemptyset = $true) & (dsetconstrI = $true) & (powersetAx = $true) & (nonemptyI1 = $true) & (noeltsimpempty = $true) & (emptysetimpfalse = $true) & (omegaIndAx = $true) & (exuE3e = $true) & (nonemptyE1 = $true) & (foundationAx = $true) & (setadjoinIL = $true) & (setext = $true) & (emptyinunitempty = $true) & (setunionAx = $true) & (emptysetAx = $true) & (powersetI = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (descrp = $true) & (dsetconstrER = $true) & (omegaSAx = $true) & ? [X0 : $i] : ((in @ emptyset @ (powerset @ X0)) != $true) & (setbeta = $true) & (setextAx = $true) & (setadjoinOr = $true) & (emptyI = $true) & (nonemptyI = $true) & (replAx = $true) & (exuE1 = $true) & (omega0Ax = $true) & (setoftrueEq = $true) & (setadjoinAx = $true) & (wellorderingAx = $true)),
% 2.04/1.58 inference(flattening,[status(thm)],[f152])).
% 2.04/1.58 thf(f152,plain,(
% 2.04/1.58 ((((((((((((((((((((((((((((((((((? [X0 : $i] : ((in @ emptyset @ (powerset @ X0)) != $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)),
% 2.04/1.58 inference(ennf_transformation,[status(thm)],[f112])).
% 2.04/1.58 thf(f112,plain,(
% 2.04/1.58 ~((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) => ! [X0 : $i] : ((in @ emptyset @ (powerset @ X0)) = $true))))))))))))))))))))))))))))))))))))),
% 2.04/1.58 inference(fool_elimination,[status(thm)],[f111])).
% 2.04/1.58 thf(f111,plain,(
% 2.04/1.58 ~(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 => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))))))))))))))))))))))))))))))))))))),
% 2.04/1.58 inference(rectify,[status(thm)],[f40])).
% 2.04/1.58 thf(f40,negated_conjecture,(
% 2.04/1.58 ~(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 => ! [X3 : $i] : (in @ emptyset @ (powerset @ X3)))))))))))))))))))))))))))))))))))))),
% 2.04/1.58 inference(negated_conjecture,[status(cth)],[f39])).
% 2.04/1.58 thf(f39,conjecture,(
% 2.04/1.58 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 => ! [X3 : $i] : (in @ emptyset @ (powerset @ X3))))))))))))))))))))))))))))))))))))),
% 2.04/1.58 file('/export/starexec/sandbox/tmp/tmp.oqPmhAEHHv/DTF2THF_30490.p',emptyinPowerset)).
% 2.04/1.58 thf(f481,plain,(
% 2.04/1.58 ( ! [X3 : $i,X4 : $i] : (((in @ (sK74 @ X4 @ X3) @ X3) = $true) | ((in @ X3 @ (powerset @ X4)) = $true) | (powersetI != $true)) )),
% 2.04/1.58 inference(cnf_transformation,[status(thm)],[f292])).
% 2.04/1.58 thf(f292,plain,(
% 2.04/1.58 ((powersetI = $true) | (! [X2 : $i] : (((in @ X2 @ sK73) = $true) | ((in @ X2 @ sK72) != $true)) & ((in @ sK72 @ (powerset @ sK73)) != $true))) & (! [X3 : $i,X4 : $i] : ((((in @ (sK74 @ X4 @ X3) @ X4) != $true) & ((in @ (sK74 @ X4 @ X3) @ X3) = $true)) | ((in @ X3 @ (powerset @ X4)) = $true)) | (powersetI != $true))),
% 2.04/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73,sK74])],[f289,f291,f290])).
% 2.04/1.58 thf(f290,plain,(
% 2.04/1.58 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) & ((in @ X0 @ (powerset @ X1)) != $true)) => (! [X2 : $i] : (((in @ X2 @ sK73) = $true) | ((in @ X2 @ sK72) != $true)) & ((in @ sK72 @ (powerset @ sK73)) != $true))),
% 2.04/1.58 introduced(definition,[],[choice_axiom])).
% 2.04/1.58 thf(f291,plain,(
% 2.04/1.58 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) != $true) & ((in @ X5 @ X3) = $true)) => (((in @ (sK74 @ X4 @ X3) @ X4) != $true) & ((in @ (sK74 @ X4 @ X3) @ X3) = $true)))),
% 2.04/1.58 introduced(definition,[],[choice_axiom])).
% 2.04/1.58 thf(f289,plain,(
% 2.04/1.58 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) & ((in @ X0 @ (powerset @ X1)) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) != $true) & ((in @ X5 @ X3) = $true)) | ((in @ X3 @ (powerset @ X4)) = $true)) | (powersetI != $true))),
% 2.04/1.58 inference(rectify,[status(thm)],[f288])).
% 2.04/1.58 thf(f288,plain,(
% 2.04/1.58 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) & ((in @ X0 @ (powerset @ X1)) != $true))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI != $true))),
% 2.04/1.58 inference(nnf_transformation,[status(thm)],[f132])).
% 2.04/1.58 thf(f132,plain,(
% 2.04/1.58 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((in @ X0 @ (powerset @ X1)) = $true))),
% 2.04/1.58 inference(ennf_transformation,[status(thm)],[f86])).
% 2.04/1.58 thf(f86,plain,(
% 2.04/1.58 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((in @ X0 @ (powerset @ X1)) = $true))),
% 2.04/1.58 inference(fool_elimination,[status(thm)],[f85])).
% 2.04/1.58 thf(f85,plain,(
% 2.04/1.58 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))) = powersetI)),
% 2.04/1.58 inference(rectify,[status(thm)],[f38])).
% 2.04/1.58 thf(f38,axiom,(
% 2.04/1.58 (! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (in @ X4 @ (powerset @ X3))) = powersetI)),
% 2.04/1.58 file('/export/starexec/sandbox/tmp/tmp.oqPmhAEHHv/DTF2THF_30490.p',powersetI)).
% 2.04/1.58 thf(f713,plain,(
% 2.04/1.58 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true)) )),
% 2.04/1.58 inference(trivial_inequality_removal,[status(thm)],[f546])).
% 2.04/1.58 thf(f546,plain,(
% 2.04/1.58 ( ! [X1 : $i] : (($true != $true) | ((in @ X1 @ emptyset) != $true)) )),
% 2.04/1.58 inference(definition_unfolding,[status(thm)],[f348,f425])).
% 2.04/1.58 thf(f425,plain,(
% 2.04/1.58 (emptysetimpfalse = $true)),
% 2.04/1.58 inference(cnf_transformation,[status(thm)],[f230])).
% 2.04/1.58 thf(f348,plain,(
% 2.04/1.58 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true)) )),
% 2.04/1.58 inference(cnf_transformation,[status(thm)],[f172])).
% 2.04/1.58 thf(f172,plain,(
% 2.04/1.58 ((emptysetimpfalse = $true) | ((in @ sK8 @ emptyset) = $true)) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 2.04/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f170,f171])).
% 2.04/1.58 thf(f171,plain,(
% 2.04/1.58 ? [X0 : $i] : ((in @ X0 @ emptyset) = $true) => ((in @ sK8 @ emptyset) = $true)),
% 2.04/1.58 introduced(definition,[],[choice_axiom])).
% 2.04/1.58 thf(f170,plain,(
% 2.04/1.58 ((emptysetimpfalse = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 2.04/1.58 inference(rectify,[status(thm)],[f169])).
% 2.04/1.58 thf(f169,plain,(
% 2.04/1.58 ((emptysetimpfalse = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)) & (! [X0 : $i] : ((in @ X0 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 2.04/1.58 inference(nnf_transformation,[status(thm)],[f119])).
% 2.04/1.58 thf(f119,plain,(
% 2.04/1.58 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ((in @ X0 @ emptyset) != $true)),
% 2.04/1.58 inference(flattening,[status(thm)],[f118])).
% 2.04/1.58 thf(f118,plain,(
% 2.04/1.58 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ~((in @ X0 @ emptyset) = $true)),
% 2.04/1.58 inference(true_and_false_elimination,[status(thm)],[f110])).
% 2.04/1.58 thf(f110,plain,(
% 2.04/1.58 (emptysetimpfalse = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => $false)),
% 2.04/1.58 inference(fool_elimination,[status(thm)],[f109])).
% 2.04/1.58 thf(f109,plain,(
% 2.04/1.58 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 2.04/1.58 inference(rectify,[status(thm)],[f21])).
% 2.04/1.58 thf(f21,axiom,(
% 2.04/1.58 (emptysetimpfalse = ! [X1 : $i] : ((in @ X1 @ emptyset) => $false))),
% 2.04/1.58 file('/export/starexec/sandbox/tmp/tmp.oqPmhAEHHv/DTF2THF_30490.p',emptysetimpfalse)).
% 2.04/1.58 thf(f407,plain,(
% 2.04/1.58 ((in @ emptyset @ (powerset @ sK38)) != $true)),
% 2.04/1.58 inference(cnf_transformation,[status(thm)],[f230])).
% 2.04/1.58 % SZS output end Proof for DTF2THF_30490
% 2.04/1.58 % (30595)------------------------------
% 2.04/1.58 % (30595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.58 % (30595)Termination reason: Refutation
% 2.04/1.58
% 2.04/1.58 % (30595)Memory used [KB]: 6524
% 2.04/1.58 % (30595)Time elapsed: 0.087 s
% 2.04/1.58 % (30595)Instructions burned: 170 (million)
% 2.04/1.58 % (30595)------------------------------
% 2.04/1.58 % (30595)------------------------------
% 2.04/1.58 % (30589)Success in time 0.108 s
%------------------------------------------------------------------------------