%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU526^1 : 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 : n006.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 09:35:05 AM UTC 2026
% Result : Theorem 1.90s 1.39s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 961 ( 270 equ; 0 cnn)
% Maximal formula atoms : 45 ( 35 avg)
% Number of connectives : 501 ( 30 ~; 16 |; 143 &; 89 @)
% ( 2 <=>; 221 =>; 0 <=; 0 <~>)
% Maximal formula depth : 50 ( 17 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 108 usr; 46 con; 0-3 aty)
% Number of variables : 45 ( 0 ^; 27 !; 18 ?; 45 :)
% 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_66,type,
sP0: $i > $i > $o ).
thf(func_def_67,type,
sP1: $i > $o ).
thf(func_def_68,type,
sP2: $i > $i > $o ).
thf(func_def_69,type,
sP3: $i > $i > $o ).
thf(func_def_74,type,
sK8: $i > $i ).
thf(func_def_75,type,
sK9: $i > $i > $i ).
thf(func_def_76,type,
sK10: $i > $i > $i ).
thf(func_def_77,type,
sK11: $i > $i > $i ).
thf(func_def_78,type,
sK12: $i > $i > $i ).
thf(func_def_79,type,
sK13: $i > $i > $i > $i ).
thf(func_def_80,type,
sK14: $i > $i ).
thf(func_def_81,type,
sK15: $i > $i ).
thf(func_def_82,type,
sK16: $i > $i ).
thf(func_def_83,type,
sK17: $i > $i ).
thf(func_def_84,type,
sK18: $i > $i > $i > $i ).
thf(func_def_85,type,
sK19: $i > $i > $i > $i ).
thf(func_def_86,type,
sK20: $i > $i > $i ).
thf(func_def_87,type,
sK21: $i > $i > $i ).
thf(func_def_88,type,
sK22: $i > $i > $i ).
thf(func_def_89,type,
sK23: $i > $i ).
thf(func_def_90,type,
sK24: $i > $i > $i ).
thf(func_def_92,type,
sK26: $i > $i ).
thf(func_def_93,type,
sK27: $i > $i ).
thf(func_def_96,type,
sK30: $i > $i ).
thf(func_def_98,type,
sK32: $i > $i > $i ).
thf(func_def_104,type,
sK38: $i > $o ).
thf(func_def_112,type,
sK46: $o > $i > $i > $i ).
thf(func_def_124,type,
sK58: $i > $o ).
thf(func_def_128,type,
sK62: $i > $o ).
thf(func_def_132,type,
sK66: $i > $i ).
thf(func_def_134,type,
sK68: $i > $i ).
thf(func_def_136,type,
sK70: $i > $i > $o ).
thf(func_def_137,type,
sK71: $i > $i ).
thf(func_def_138,type,
sK72: $i > $i ).
thf(func_def_139,type,
sK73: ( $i > $i > $o ) > $i > $i ).
thf(func_def_140,type,
sK74: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_141,type,
sK75: ( $i > $i > $o ) > $i > $i ).
thf(func_def_149,type,
sK83: $i > $i > $i ).
thf(func_def_152,type,
sK86: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK87: $i > $o ).
thf(func_def_154,type,
sK88: $i > $i ).
thf(func_def_155,type,
sK89: $i > $o ).
thf(func_def_156,type,
sK90: $i > $i ).
thf(func_def_157,type,
sK91: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK93: $i > $o ).
thf(func_def_161,type,
sK95: $i > $i ).
thf(func_def_163,type,
sK97: $i > $i ).
thf(func_def_170,type,
sK104: $i > $i > $i ).
thf(func_def_171,type,
sK105: $i > $i > $i ).
thf(func_def_172,type,
sK106: $i > $i > $i ).
thf(func_def_175,type,
sK109: $i > $o ).
thf(func_def_181,type,
sK115: $i > $o ).
thf(func_def_182,type,
sK116: ( $i > $o ) > $i ).
thf(func_def_188,type,
sK122: $i > $i > $i ).
thf(func_def_193,type,
ph127:
!>[X0: $tType] : X0 ).
thf(f1112,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1110,f425]) ).
thf(f425,plain,
( $true
= ( nonempty @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
thf(f197,plain,
( ( noeltsimpempty = $true )
& ( emptysetAx = $true )
& ( setextAx = $true )
& ( powersetAx = $true )
& ( emptyI = $true )
& ( setadjoinAx = $true )
& ( exuE1 = $true )
& ( emptyinunitempty = $true )
& ( nonemptyI1 = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( setbeta = $true )
& ( emptysetE = $true )
& ( exuE3e = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( setadjoinIR = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( powersetE = $true )
& ( emptyinPowerset = $true )
& ( exuE2 = $true )
& ( setadjoinIL = $true )
& ( dsetconstrI = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( replAx = $true )
& ( omega0Ax = $true )
& ( notinemptyset = $true )
& ( subPowSU = $true )
& ( $true
= ( nonempty @ sK5 ) )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ sK5 ) )
& ( setadjoinE = $true )
& ( dsetconstrER = $true )
& ( setadjoinOr = $true )
& ( setunionI = $true )
& ( dsetconstrEL = $true )
& ( setext = $true )
& ( prop2setE = $true )
& ( setunionE = $true )
& ( omegaIndAx = $true )
& ( wellorderingAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f168,f196]) ).
thf(f196,plain,
( ? [X0: $i] :
( ( $true
= ( nonempty @ X0 ) )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) ) )
=> ( ( $true
= ( nonempty @ sK5 ) )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f168,plain,
( ( noeltsimpempty = $true )
& ( emptysetAx = $true )
& ( setextAx = $true )
& ( powersetAx = $true )
& ( emptyI = $true )
& ( setadjoinAx = $true )
& ( exuE1 = $true )
& ( emptyinunitempty = $true )
& ( nonemptyI1 = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( setbeta = $true )
& ( emptysetE = $true )
& ( exuE3e = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( setadjoinIR = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( powersetE = $true )
& ( emptyinPowerset = $true )
& ( exuE2 = $true )
& ( setadjoinIL = $true )
& ( dsetconstrI = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( replAx = $true )
& ( omega0Ax = $true )
& ( notinemptyset = $true )
& ( subPowSU = $true )
& ? [X0: $i] :
( ( $true
= ( nonempty @ X0 ) )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) ) )
& ( setadjoinE = $true )
& ( dsetconstrER = $true )
& ( setadjoinOr = $true )
& ( setunionI = $true )
& ( dsetconstrEL = $true )
& ( setext = $true )
& ( prop2setE = $true )
& ( setunionE = $true )
& ( omegaIndAx = $true )
& ( wellorderingAx = $true ) ),
inference(flattening,[status(thm)],[f167]) ).
thf(f167,plain,
( ? [X0: $i] :
( ( $true
= ( nonempty @ X0 ) )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) ) )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f136]) ).
thf(f136,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ! [X0: $i] :
( ( $true
= ( nonempty @ X0 ) )
=> ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(true_and_false_elimination,[status(thm)],[f135]) ).
thf(f135,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ! [X0: $i] :
( ( $true
= ( nonempty @ X0 ) )
=> ? [X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f134]) ).
thf(f134,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( ( in @ X1 @ X0 )
& $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ! [X3: $i] :
( ( nonempty @ X3 )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
thf(f46,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ! [X3: $i] :
( ( nonempty @ X3 )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.N8AcFdfOIF/DTF2THF_20249.p',nonemptyImpWitness) ).
thf(f1110,plain,
( $true
!= ( nonempty @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1108]) ).
thf(f1108,plain,
( ( $true != $true )
| ( $true
!= ( nonempty @ sK5 ) ) ),
inference(superposition,[status(thm)],[f424,f850]) ).
thf(f850,plain,
! [X2: $i] :
( ( $true
= ( in @ ( sK8 @ X2 ) @ X2 ) )
| ( $true
!= ( nonempty @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f657]) ).
thf(f657,plain,
! [X2: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( sK8 @ X2 ) @ X2 ) )
| ( $true
!= ( nonempty @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f462,f438]) ).
thf(f438,plain,
nonemptyE1 = $true,
inference(cnf_transformation,[status(thm)],[f197]) ).
thf(f462,plain,
! [X2: $i] :
( ( $true
= ( in @ ( sK8 @ X2 ) @ X2 ) )
| ( $true
!= ( nonempty @ X2 ) )
| ( nonemptyE1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
thf(f206,plain,
( ( ( nonemptyE1 = $true )
| ( ! [X1: $i] :
( $true
!= ( in @ X1 @ sK7 ) )
& ( $true
= ( nonempty @ sK7 ) ) ) )
& ( ! [X2: $i] :
( ( $true
= ( in @ ( sK8 @ X2 ) @ X2 ) )
| ( $true
!= ( nonempty @ X2 ) ) )
| ( nonemptyE1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f203,f205,f204]) ).
thf(f204,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( nonempty @ X0 ) ) )
=> ( ! [X1: $i] :
( $true
!= ( in @ X1 @ sK7 ) )
& ( $true
= ( nonempty @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f205,plain,
! [X2: $i] :
( ? [X3: $i] :
( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( sK8 @ X2 ) @ X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f203,plain,
( ( ( nonemptyE1 = $true )
| ? [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( nonempty @ X0 ) ) ) )
& ( ! [X2: $i] :
( ? [X3: $i] :
( $true
= ( in @ X3 @ X2 ) )
| ( $true
!= ( nonempty @ X2 ) ) )
| ( nonemptyE1 != $true ) ) ),
inference(rectify,[status(thm)],[f202]) ).
thf(f202,plain,
( ( ( nonemptyE1 = $true )
| ? [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( nonempty @ X0 ) ) ) )
& ( ! [X0: $i] :
( ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( nonempty @ X0 ) ) )
| ( nonemptyE1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f166]) ).
thf(f166,plain,
( ( nonemptyE1 = $true )
<=> ! [X0: $i] :
( ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( nonempty @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f64]) ).
thf(f64,plain,
( ! [X0: $i] :
( ( $true
= ( nonempty @ X0 ) )
=> ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) ) )
<=> ( nonemptyE1 = $true ) ),
inference(fool_elimination,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $i] :
( ( ( nonempty @ X0 )
=> ? [X1: $i] : ( in @ X1 @ X0 ) )
= nonemptyE1 ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,axiom,
! [X3: $i] :
( ( ( nonempty @ X3 )
=> ? [X1: $i] : ( in @ X1 @ X3 ) )
= nonemptyE1 ),
file('/export/starexec/sandbox/tmp/tmp.N8AcFdfOIF/DTF2THF_20249.p',nonemptyE1) ).
thf(f424,plain,
! [X1: $i] :
( $true
!= ( in @ X1 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU526^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:25:45 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SEU526^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.45 % Domain : Set Theory
% 0.30/0.45 % Problem : Preliminary Notions - Equality Laws
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English : (! A:i.nonempty A -> (? x:i.in x A & true))
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.45 % Source : [Bro08]
% 0.30/0.45 % Names : ZFC028g [Bro08]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.30/0.45 % Syntax : Number of formulae : 99 ( 45 unt; 53 typ; 45 def)
% 0.30/0.45 % Number of atoms : 253 ( 58 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 45 ( 5 avg)
% 0.30/0.45 % Number of connectives : 415 ( 7 ~; 4 |; 19 &; 271 @)
% 0.30/0.45 % ( 8 <=>; 106 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 49 ( 2 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 56 ( 53 usr; 46 con; 0-2 aty)
% 0.30/0.45 % Number of variables : 138 ( 16 ^; 104 !; 18 ?; 138 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : http://mathgate.info/detsetitem.php?id=467
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(in_type,type,
% 0.30/0.45 in: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(exu_type,type,
% 0.30/0.45 exu: ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(exu,definition,
% 0.30/0.45 ( exu
% 0.30/0.45 = ( ^ [Xphi: $i > $o] :
% 0.30/0.45 ? [Xx: $i] :
% 0.30/0.45 ( ( Xphi @ Xx )
% 0.30/0.45 & ! [Xy: $i] :
% 0.30/0.45 ( ( Xphi @ Xy )
% 0.30/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setextAx_type,type,
% 0.30/0.45 setextAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setextAx,definition,
% 0.30/0.45 ( setextAx
% 0.30/0.45 = ( ! [A: $i,B: $i] :
% 0.30/0.45 ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 <=> ( in @ Xx @ B ) )
% 0.30/0.45 => ( A = B ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(emptyset_type,type,
% 0.30/0.45 emptyset: $i ).
% 0.30/0.45
% 0.30/0.45 thf(emptysetAx_type,type,
% 0.30/0.45 emptysetAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(emptysetAx,definition,
% 0.30/0.45 ( emptysetAx
% 0.30/0.45 = ( ! [Xx: $i] :
% 0.30/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoin_type,type,
% 0.30/0.45 setadjoin: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinAx_type,type,
% 0.30/0.45 setadjoinAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinAx,definition,
% 0.30/0.45 ( setadjoinAx
% 0.30/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.45 <=> ( ( Xy = Xx )
% 0.30/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(powerset_type,type,
% 0.30/0.45 powerset: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(powersetAx_type,type,
% 0.30/0.45 powersetAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(powersetAx,definition,
% 0.30/0.45 ( powersetAx
% 0.30/0.45 = ( ! [A: $i,B: $i] :
% 0.30/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.45 <=> ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ B )
% 0.30/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setunion_type,type,
% 0.30/0.45 setunion: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(setunionAx_type,type,
% 0.30/0.45 setunionAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setunionAx,definition,
% 0.30/0.45 ( setunionAx
% 0.30/0.45 = ( ! [A: $i,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.45 <=> ? [B: $i] :
% 0.30/0.45 ( ( in @ Xx @ B )
% 0.30/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(omega_type,type,
% 0.30/0.45 omega: $i ).
% 0.30/0.45
% 0.30/0.45 thf(omega0Ax_type,type,
% 0.30/0.45 omega0Ax: $o ).
% 0.30/0.45
% 0.30/0.45 thf(omega0Ax,definition,
% 0.30/0.45 ( omega0Ax
% 0.30/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(omegaSAx_type,type,
% 0.30/0.45 omegaSAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(omegaSAx,definition,
% 0.30/0.45 ( omegaSAx
% 0.30/0.45 = ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ omega )
% 0.30/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(omegaIndAx_type,type,
% 0.30/0.45 omegaIndAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(omegaIndAx,definition,
% 0.30/0.45 ( omegaIndAx
% 0.30/0.45 = ( ! [A: $i] :
% 0.30/0.45 ( ( ( in @ emptyset @ A )
% 0.30/0.45 & ! [Xx: $i] :
% 0.30/0.45 ( ( ( in @ Xx @ omega )
% 0.30/0.45 & ( in @ Xx @ A ) )
% 0.30/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.45 => ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ omega )
% 0.30/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(replAx_type,type,
% 0.30/0.45 replAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(replAx,definition,
% 0.30/0.45 ( replAx
% 0.30/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.45 ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 => ( exu
% 0.30/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.45 => ? [B: $i] :
% 0.30/0.45 ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ B )
% 0.30/0.45 <=> ? [Xy: $i] :
% 0.30/0.45 ( ( in @ Xy @ A )
% 0.30/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(foundationAx_type,type,
% 0.30/0.45 foundationAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(foundationAx,definition,
% 0.30/0.45 ( foundationAx
% 0.30/0.45 = ( ! [A: $i] :
% 0.30/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.45 => ? [B: $i] :
% 0.30/0.45 ( ( in @ B @ A )
% 0.30/0.45 & ~ ? [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ B )
% 0.30/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(wellorderingAx_type,type,
% 0.30/0.45 wellorderingAx: $o ).
% 0.30/0.45
% 0.30/0.45 thf(wellorderingAx,definition,
% 0.30/0.45 ( wellorderingAx
% 0.30/0.45 = ( ! [A: $i] :
% 0.30/0.45 ? [B: $i] :
% 0.30/0.45 ( ! [C: $i] :
% 0.30/0.45 ( ( in @ C @ B )
% 0.30/0.45 => ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ C )
% 0.30/0.45 => ( in @ Xx @ A ) ) )
% 0.30/0.45 & ! [Xx: $i,Xy: $i] :
% 0.30/0.45 ( ( ( in @ Xx @ A )
% 0.30/0.45 & ( in @ Xy @ A ) )
% 0.30/0.45 => ( ! [C: $i] :
% 0.30/0.45 ( ( in @ C @ B )
% 0.30/0.45 => ( ( in @ Xx @ C )
% 0.30/0.45 <=> ( in @ Xy @ C ) ) )
% 0.30/0.45 => ( Xx = Xy ) ) )
% 0.30/0.45 & ! [C: $i,D: $i] :
% 0.30/0.45 ( ( ( in @ C @ B )
% 0.30/0.45 & ( in @ D @ B ) )
% 0.30/0.45 => ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ C )
% 0.30/0.45 => ( in @ Xx @ D ) )
% 0.30/0.45 | ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ D )
% 0.30/0.45 => ( in @ Xx @ C ) ) ) )
% 0.30/0.45 & ! [C: $i] :
% 0.30/0.45 ( ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ C )
% 0.30/0.45 => ( in @ Xx @ A ) )
% 0.30/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.45 => ? [D: $i,Xx: $i] :
% 0.30/0.45 ( ( in @ D @ B )
% 0.30/0.45 & ( in @ Xx @ C )
% 0.30/0.45 & ~ ? [Xy: $i] :
% 0.30/0.45 ( ( in @ Xy @ D )
% 0.30/0.45 & ( in @ Xy @ C ) )
% 0.30/0.45 & ! [E: $i] :
% 0.30/0.45 ( ( in @ E @ B )
% 0.30/0.45 => ( ! [Xy: $i] :
% 0.30/0.45 ( ( in @ Xy @ E )
% 0.30/0.45 => ( in @ Xy @ D ) )
% 0.30/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(descr_type,type,
% 0.30/0.45 descr: ( $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(descrp_type,type,
% 0.30/0.45 descrp: $o ).
% 0.30/0.45
% 0.30/0.45 thf(descrp,definition,
% 0.30/0.45 ( descrp
% 0.30/0.45 = ( ! [Xphi: $i > $o] :
% 0.30/0.45 ( ( exu
% 0.30/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.45 => ( Xphi
% 0.30/0.45 @ ( descr
% 0.30/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstr_type,type,
% 0.30/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstrI_type,type,
% 0.30/0.45 dsetconstrI: $o ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstrI,definition,
% 0.30/0.45 ( dsetconstrI
% 0.30/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 => ( ( Xphi @ Xx )
% 0.30/0.45 => ( in @ Xx
% 0.30/0.45 @ ( dsetconstr @ A
% 0.30/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstrEL_type,type,
% 0.30/0.45 dsetconstrEL: $o ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstrEL,definition,
% 0.30/0.45 ( dsetconstrEL
% 0.30/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx
% 0.30/0.45 @ ( dsetconstr @ A
% 0.30/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstrER_type,type,
% 0.30/0.45 dsetconstrER: $o ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstrER,definition,
% 0.30/0.45 ( dsetconstrER
% 0.30/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx
% 0.30/0.45 @ ( dsetconstr @ A
% 0.30/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(exuE1_type,type,
% 0.30/0.45 exuE1: $o ).
% 0.30/0.45
% 0.30/0.45 thf(exuE1,definition,
% 0.30/0.45 ( exuE1
% 0.30/0.45 = ( ! [Xphi: $i > $o] :
% 0.30/0.45 ( ( exu
% 0.30/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.45 => ? [Xx: $i] :
% 0.30/0.45 ( ( Xphi @ Xx )
% 0.30/0.45 & ! [Xy: $i] :
% 0.30/0.45 ( ( Xphi @ Xy )
% 0.30/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(prop2set_type,type,
% 0.30/0.45 prop2set: $o > $i ).
% 0.30/0.45
% 0.30/0.45 thf(prop2set,definition,
% 0.30/0.45 ( prop2set
% 0.30/0.45 = ( ^ [Xphi: $o] :
% 0.30/0.45 ( dsetconstr @ ( powerset @ emptyset )
% 0.30/0.45 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(prop2setE_type,type,
% 0.30/0.45 prop2setE: $o ).
% 0.30/0.45
% 0.30/0.45 thf(prop2setE,definition,
% 0.30/0.45 ( prop2setE
% 0.30/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.45 => Xphi ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(emptysetE_type,type,
% 0.30/0.45 emptysetE: $o ).
% 0.30/0.45
% 0.30/0.45 thf(emptysetE,definition,
% 0.30/0.45 ( emptysetE
% 0.30/0.45 = ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ emptyset )
% 0.30/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(emptysetimpfalse_type,type,
% 0.30/0.45 emptysetimpfalse: $o ).
% 0.30/0.45
% 0.30/0.45 thf(emptysetimpfalse,definition,
% 0.30/0.45 ( emptysetimpfalse
% 0.30/0.45 = ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ emptyset )
% 0.30/0.45 => $false ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(notinemptyset_type,type,
% 0.30/0.45 notinemptyset: $o ).
% 0.30/0.45
% 0.30/0.45 thf(notinemptyset,definition,
% 0.30/0.45 ( notinemptyset
% 0.30/0.45 = ( ! [Xx: $i] :
% 0.30/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(exuE3e_type,type,
% 0.30/0.45 exuE3e: $o ).
% 0.30/0.45
% 0.30/0.45 thf(exuE3e,definition,
% 0.30/0.45 ( exuE3e
% 0.30/0.45 = ( ! [Xphi: $i > $o] :
% 0.30/0.45 ( ( exu
% 0.30/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setext_type,type,
% 0.30/0.45 setext: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setext,definition,
% 0.30/0.45 ( setext
% 0.30/0.45 = ( ! [A: $i,B: $i] :
% 0.30/0.45 ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 => ( in @ Xx @ B ) )
% 0.30/0.45 => ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ B )
% 0.30/0.45 => ( in @ Xx @ A ) )
% 0.30/0.45 => ( A = B ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(emptyI_type,type,
% 0.30/0.45 emptyI: $o ).
% 0.30/0.45
% 0.30/0.45 thf(emptyI,definition,
% 0.30/0.45 ( emptyI
% 0.30/0.45 = ( ! [A: $i] :
% 0.30/0.45 ( ! [Xx: $i] :
% 0.30/0.45 ~ ( in @ Xx @ A )
% 0.30/0.45 => ( A = emptyset ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(noeltsimpempty_type,type,
% 0.30/0.45 noeltsimpempty: $o ).
% 0.30/0.45
% 0.30/0.45 thf(noeltsimpempty,definition,
% 0.30/0.45 ( noeltsimpempty
% 0.30/0.45 = ( ! [A: $i] :
% 0.30/0.45 ( ! [Xx: $i] :
% 0.30/0.45 ~ ( in @ Xx @ A )
% 0.30/0.45 => ( A = emptyset ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setbeta_type,type,
% 0.30/0.45 setbeta: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setbeta,definition,
% 0.30/0.45 ( setbeta
% 0.30/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 => ( ( in @ Xx
% 0.30/0.45 @ ( dsetconstr @ A
% 0.30/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(nonempty_type,type,
% 0.30/0.45 nonempty: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(nonempty,definition,
% 0.30/0.45 ( nonempty
% 0.30/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(nonemptyE1_type,type,
% 0.30/0.45 nonemptyE1: $o ).
% 0.30/0.45
% 0.30/0.45 thf(nonemptyE1,definition,
% 0.30/0.45 ( nonemptyE1
% 0.30/0.45 = ( ! [A: $i] :
% 0.30/0.45 ( ( nonempty @ A )
% 0.30/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(nonemptyI_type,type,
% 0.30/0.45 nonemptyI: $o ).
% 0.30/0.45
% 0.30/0.45 thf(nonemptyI,definition,
% 0.30/0.45 ( nonemptyI
% 0.30/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 => ( ( Xphi @ Xx )
% 0.30/0.45 => ( nonempty
% 0.30/0.45 @ ( dsetconstr @ A
% 0.30/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(nonemptyI1_type,type,
% 0.30/0.45 nonemptyI1: $o ).
% 0.30/0.45
% 0.30/0.45 thf(nonemptyI1,definition,
% 0.30/0.45 ( nonemptyI1
% 0.30/0.45 = ( ! [A: $i] :
% 0.30/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.45 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinIL_type,type,
% 0.30/0.45 setadjoinIL: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinIL,definition,
% 0.30/0.45 ( setadjoinIL
% 0.30/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(emptyinunitempty_type,type,
% 0.30/0.45 emptyinunitempty: $o ).
% 0.30/0.45
% 0.30/0.45 thf(emptyinunitempty,definition,
% 0.30/0.45 ( emptyinunitempty
% 0.30/0.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinIR_type,type,
% 0.30/0.45 setadjoinIR: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinIR,definition,
% 0.30/0.45 ( setadjoinIR
% 0.30/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.45 ( ( in @ Xy @ A )
% 0.30/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinE_type,type,
% 0.30/0.45 setadjoinE: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinE,definition,
% 0.30/0.45 ( setadjoinE
% 0.30/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.45 => ! [Xphi: $o] :
% 0.30/0.45 ( ( ( Xy = Xx )
% 0.30/0.45 => Xphi )
% 0.30/0.45 => ( ( ( in @ Xy @ A )
% 0.30/0.45 => Xphi )
% 0.30/0.45 => Xphi ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinOr_type,type,
% 0.30/0.45 setadjoinOr: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setadjoinOr,definition,
% 0.30/0.45 ( setadjoinOr
% 0.30/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.45 => ( ( Xy = Xx )
% 0.30/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setoftrueEq_type,type,
% 0.30/0.45 setoftrueEq: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setoftrueEq,definition,
% 0.30/0.45 ( setoftrueEq
% 0.30/0.45 = ( ! [A: $i] :
% 0.30/0.45 ( ( dsetconstr @ A
% 0.30/0.45 @ ^ [Xx: $i] : $true )
% 0.30/0.45 = A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(powersetI_type,type,
% 0.30/0.45 powersetI: $o ).
% 0.30/0.45
% 0.30/0.45 thf(powersetI,definition,
% 0.30/0.45 ( powersetI
% 0.30/0.45 = ( ! [A: $i,B: $i] :
% 0.30/0.45 ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ B )
% 0.30/0.45 => ( in @ Xx @ A ) )
% 0.30/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(emptyinPowerset_type,type,
% 0.30/0.45 emptyinPowerset: $o ).
% 0.30/0.45
% 0.30/0.45 thf(emptyinPowerset,definition,
% 0.30/0.45 ( emptyinPowerset
% 0.30/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(emptyInPowerset_type,type,
% 0.30/0.45 emptyInPowerset: $o ).
% 0.30/0.45
% 0.30/0.45 thf(emptyInPowerset,definition,
% 0.30/0.45 ( emptyInPowerset
% 0.30/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(powersetE_type,type,
% 0.30/0.45 powersetE: $o ).
% 0.30/0.45
% 0.30/0.45 thf(powersetE,definition,
% 0.30/0.45 ( powersetE
% 0.30/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.45 => ( ( in @ Xx @ B )
% 0.30/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setunionI_type,type,
% 0.30/0.45 setunionI: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setunionI,definition,
% 0.30/0.45 ( setunionI
% 0.30/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.45 ( ( in @ Xx @ B )
% 0.30/0.45 => ( ( in @ B @ A )
% 0.30/0.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(setunionE_type,type,
% 0.30/0.45 setunionE: $o ).
% 0.30/0.45
% 0.30/0.45 thf(setunionE,definition,
% 0.30/0.45 ( setunionE
% 0.30/0.45 = ( ! [A: $i,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.45 => ! [Xphi: $o] :
% 0.30/0.45 ( ! [B: $i] :
% 0.30/0.45 ( ( in @ Xx @ B )
% 0.30/0.45 => ( ( in @ B @ A )
% 0.30/0.45 => Xphi ) )
% 0.30/0.45 => Xphi ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(subPowSU_type,type,
% 0.30/0.45 subPowSU: $o ).
% 0.30/0.45
% 0.30/0.45 thf(subPowSU,definition,
% 0.30/0.45 ( subPowSU
% 0.30/0.45 = ( ! [A: $i,Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(exuE2_type,type,
% 0.30/0.45 exuE2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(exuE2,definition,
% 0.30/0.45 ( exuE2
% 0.30/0.45 = ( ! [Xphi: $i > $o] :
% 0.30/0.45 ( ( exu
% 0.30/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.45 => ? [Xx: $i] :
% 0.30/0.45 ! [Xy: $i] :
% 0.30/0.45 ( ( Xphi @ Xy )
% 0.30/0.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(nonemptyImpWitness,conjecture,
% 0.30/0.45 ( setextAx
% 0.30/0.45 => ( emptysetAx
% 0.30/0.45 => ( setadjoinAx
% 0.30/0.45 => ( powersetAx
% 0.30/0.45 => ( setunionAx
% 0.30/0.45 => ( omega0Ax
% 0.30/0.45 => ( omegaSAx
% 0.30/0.45 => ( omegaIndAx
% 0.30/0.45 => ( replAx
% 0.30/0.45 => ( foundationAx
% 0.30/0.45 => ( wellorderingAx
% 0.30/0.45 => ( descrp
% 0.30/0.45 => ( dsetconstrI
% 0.30/0.45 => ( dsetconstrEL
% 0.30/0.45 => ( dsetconstrER
% 0.30/0.45 => ( exuE1
% 0.30/0.45 => ( prop2setE
% 0.30/0.45 => ( emptysetE
% 0.30/0.45 => ( emptysetimpfalse
% 0.30/0.45 => ( notinemptyset
% 0.30/0.45 => ( exuE3e
% 0.30/0.45 => ( setext
% 0.30/0.45 => ( emptyI
% 0.30/0.45 => ( noeltsimpempty
% 0.30/0.45 => ( setbeta
% 0.30/0.45 => ( nonemptyE1
% 0.30/0.45 => ( nonemptyI
% 0.30/0.45 => ( nonemptyI1
% 0.30/0.45 => ( setadjoinIL
% 0.30/0.45 => ( emptyinunitempty
% 0.30/0.45 => ( setadjoinIR
% 0.30/0.45 => ( setadjoinE
% 0.30/0.45 => ( setadjoinOr
% 0.30/0.45 => ( setoftrueEq
% 0.30/0.45 => ( powersetI
% 0.30/0.45 => ( emptyinPowerset
% 0.30/0.45 => ( emptyInPowerset
% 0.30/0.45 => ( powersetE
% 0.30/0.45 => ( setunionI
% 0.30/0.45 => ( setunionE
% 0.30/0.45 => ( subPowSU
% 0.30/0.45 => ( exuE2
% 0.30/0.45 => ! [A: $i] :
% 0.30/0.45 ( ( nonempty @ A )
% 0.30/0.45 => ? [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 & $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.90/1.32 ---- Embedded in THF ---
% 1.90/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.90/1.33 %%% Generated on Tue Feb 24 12:25:46 EST 2026
% 1.90/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.90/1.33 %%% Logic specification used:
% 1.90/1.33 %%% thf(spec, logic, $$dhol).
% 1.90/1.33
% 1.90/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.N8AcFdfOIF/DTF2DTF20249.p
% See solution above
% 1.90/1.33 ------------------------
% 1.90/1.34 ---- Cleaned THF ---
% 1.90/1.34 thf(in_type,type,
% 1.90/1.34 in: $i > $i > $o ).
% 1.90/1.34
% 1.90/1.34 thf(exu_type,type,
% 1.90/1.34 exu: ( $i > $o ) > $o ).
% 1.90/1.34
% 1.90/1.34 thf(exu,definition,
% 1.90/1.34 ( exu
% 1.90/1.34 = ( ^ [Xphi: $i > $o] :
% 1.90/1.34 ? [Xx: $i] :
% 1.90/1.34 ( ( Xphi @ Xx )
% 1.90/1.34 & ! [Xy: $i] :
% 1.90/1.34 ( ( Xphi @ Xy )
% 1.90/1.34 => ( Xx = Xy ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setextAx_type,type,
% 1.90/1.34 setextAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setextAx,definition,
% 1.90/1.34 ( setextAx
% 1.90/1.34 = ( ! [A: $i,B: $i] :
% 1.90/1.34 ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ A )
% 1.90/1.34 <=> ( in @ Xx @ B ) )
% 1.90/1.34 => ( A = B ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(emptyset_type,type,
% 1.90/1.34 emptyset: $i ).
% 1.90/1.34
% 1.90/1.34 thf(emptysetAx_type,type,
% 1.90/1.34 emptysetAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(emptysetAx,definition,
% 1.90/1.34 ( emptysetAx
% 1.90/1.34 = ( ! [Xx: $i] :
% 1.90/1.34 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoin_type,type,
% 1.90/1.34 setadjoin: $i > $i > $i ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinAx_type,type,
% 1.90/1.34 setadjoinAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinAx,definition,
% 1.90/1.34 ( setadjoinAx
% 1.90/1.34 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.90/1.34 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.90/1.34 <=> ( ( Xy = Xx )
% 1.90/1.34 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(powerset_type,type,
% 1.90/1.34 powerset: $i > $i ).
% 1.90/1.34
% 1.90/1.34 thf(powersetAx_type,type,
% 1.90/1.34 powersetAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(powersetAx,definition,
% 1.90/1.34 ( powersetAx
% 1.90/1.34 = ( ! [A: $i,B: $i] :
% 1.90/1.34 ( ( in @ B @ ( powerset @ A ) )
% 1.90/1.34 <=> ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ B )
% 1.90/1.34 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setunion_type,type,
% 1.90/1.34 setunion: $i > $i ).
% 1.90/1.34
% 1.90/1.34 thf(setunionAx_type,type,
% 1.90/1.34 setunionAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setunionAx,definition,
% 1.90/1.34 ( setunionAx
% 1.90/1.34 = ( ! [A: $i,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ ( setunion @ A ) )
% 1.90/1.34 <=> ? [B: $i] :
% 1.90/1.34 ( ( in @ Xx @ B )
% 1.90/1.34 & ( in @ B @ A ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(omega_type,type,
% 1.90/1.34 omega: $i ).
% 1.90/1.34
% 1.90/1.34 thf(omega0Ax_type,type,
% 1.90/1.34 omega0Ax: $o ).
% 1.90/1.34
% 1.90/1.34 thf(omega0Ax,definition,
% 1.90/1.34 ( omega0Ax
% 1.90/1.34 = ( in @ emptyset @ omega ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(omegaSAx_type,type,
% 1.90/1.34 omegaSAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(omegaSAx,definition,
% 1.90/1.34 ( omegaSAx
% 1.90/1.34 = ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ omega )
% 1.90/1.34 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(omegaIndAx_type,type,
% 1.90/1.34 omegaIndAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(omegaIndAx,definition,
% 1.90/1.34 ( omegaIndAx
% 1.90/1.34 = ( ! [A: $i] :
% 1.90/1.34 ( ( ( in @ emptyset @ A )
% 1.90/1.34 & ! [Xx: $i] :
% 1.90/1.34 ( ( ( in @ Xx @ omega )
% 1.90/1.34 & ( in @ Xx @ A ) )
% 1.90/1.34 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.90/1.34 => ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ omega )
% 1.90/1.34 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(replAx_type,type,
% 1.90/1.34 replAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(replAx,definition,
% 1.90/1.34 ( replAx
% 1.90/1.34 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.90/1.34 ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ A )
% 1.90/1.34 => ( exu
% 1.90/1.34 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.90/1.34 => ? [B: $i] :
% 1.90/1.34 ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ B )
% 1.90/1.34 <=> ? [Xy: $i] :
% 1.90/1.34 ( ( in @ Xy @ A )
% 1.90/1.34 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(foundationAx_type,type,
% 1.90/1.34 foundationAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(foundationAx,definition,
% 1.90/1.34 ( foundationAx
% 1.90/1.34 = ( ! [A: $i] :
% 1.90/1.34 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.90/1.34 => ? [B: $i] :
% 1.90/1.34 ( ( in @ B @ A )
% 1.90/1.34 & ~ ? [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ B )
% 1.90/1.34 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(wellorderingAx_type,type,
% 1.90/1.34 wellorderingAx: $o ).
% 1.90/1.34
% 1.90/1.34 thf(wellorderingAx,definition,
% 1.90/1.34 ( wellorderingAx
% 1.90/1.34 = ( ! [A: $i] :
% 1.90/1.34 ? [B: $i] :
% 1.90/1.34 ( ! [C: $i] :
% 1.90/1.34 ( ( in @ C @ B )
% 1.90/1.34 => ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ C )
% 1.90/1.34 => ( in @ Xx @ A ) ) )
% 1.90/1.34 & ! [Xx: $i,Xy: $i] :
% 1.90/1.34 ( ( ( in @ Xx @ A )
% 1.90/1.34 & ( in @ Xy @ A ) )
% 1.90/1.34 => ( ! [C: $i] :
% 1.90/1.34 ( ( in @ C @ B )
% 1.90/1.34 => ( ( in @ Xx @ C )
% 1.90/1.34 <=> ( in @ Xy @ C ) ) )
% 1.90/1.34 => ( Xx = Xy ) ) )
% 1.90/1.34 & ! [C: $i,D: $i] :
% 1.90/1.34 ( ( ( in @ C @ B )
% 1.90/1.34 & ( in @ D @ B ) )
% 1.90/1.34 => ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ C )
% 1.90/1.34 => ( in @ Xx @ D ) )
% 1.90/1.34 | ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ D )
% 1.90/1.34 => ( in @ Xx @ C ) ) ) )
% 1.90/1.34 & ! [C: $i] :
% 1.90/1.34 ( ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ C )
% 1.90/1.34 => ( in @ Xx @ A ) )
% 1.90/1.34 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.90/1.34 => ? [D: $i,Xx: $i] :
% 1.90/1.34 ( ( in @ D @ B )
% 1.90/1.34 & ( in @ Xx @ C )
% 1.90/1.34 & ~ ? [Xy: $i] :
% 1.90/1.34 ( ( in @ Xy @ D )
% 1.90/1.34 & ( in @ Xy @ C ) )
% 1.90/1.34 & ! [E: $i] :
% 1.90/1.34 ( ( in @ E @ B )
% 1.90/1.34 => ( ! [Xy: $i] :
% 1.90/1.34 ( ( in @ Xy @ E )
% 1.90/1.34 => ( in @ Xy @ D ) )
% 1.90/1.34 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(descr_type,type,
% 1.90/1.34 descr: ( $i > $o ) > $i ).
% 1.90/1.34
% 1.90/1.34 thf(descrp_type,type,
% 1.90/1.34 descrp: $o ).
% 1.90/1.34
% 1.90/1.34 thf(descrp,definition,
% 1.90/1.34 ( descrp
% 1.90/1.34 = ( ! [Xphi: $i > $o] :
% 1.90/1.34 ( ( exu
% 1.90/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.90/1.34 => ( Xphi
% 1.90/1.34 @ ( descr
% 1.90/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(dsetconstr_type,type,
% 1.90/1.34 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.90/1.34
% 1.90/1.34 thf(dsetconstrI_type,type,
% 1.90/1.34 dsetconstrI: $o ).
% 1.90/1.34
% 1.90/1.34 thf(dsetconstrI,definition,
% 1.90/1.34 ( dsetconstrI
% 1.90/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ A )
% 1.90/1.34 => ( ( Xphi @ Xx )
% 1.90/1.34 => ( in @ Xx
% 1.90/1.34 @ ( dsetconstr @ A
% 1.90/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(dsetconstrEL_type,type,
% 1.90/1.34 dsetconstrEL: $o ).
% 1.90/1.34
% 1.90/1.34 thf(dsetconstrEL,definition,
% 1.90/1.34 ( dsetconstrEL
% 1.90/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx
% 1.90/1.34 @ ( dsetconstr @ A
% 1.90/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.90/1.34 => ( in @ Xx @ A ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(dsetconstrER_type,type,
% 1.90/1.34 dsetconstrER: $o ).
% 1.90/1.34
% 1.90/1.34 thf(dsetconstrER,definition,
% 1.90/1.34 ( dsetconstrER
% 1.90/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx
% 1.90/1.34 @ ( dsetconstr @ A
% 1.90/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.90/1.34 => ( Xphi @ Xx ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(exuE1_type,type,
% 1.90/1.34 exuE1: $o ).
% 1.90/1.34
% 1.90/1.34 thf(exuE1,definition,
% 1.90/1.34 ( exuE1
% 1.90/1.34 = ( ! [Xphi: $i > $o] :
% 1.90/1.34 ( ( exu
% 1.90/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.90/1.34 => ? [Xx: $i] :
% 1.90/1.34 ( ( Xphi @ Xx )
% 1.90/1.34 & ! [Xy: $i] :
% 1.90/1.34 ( ( Xphi @ Xy )
% 1.90/1.34 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(prop2set_type,type,
% 1.90/1.34 prop2set: $o > $i ).
% 1.90/1.34
% 1.90/1.34 thf(prop2set,definition,
% 1.90/1.34 ( prop2set
% 1.90/1.34 = ( ^ [Xphi: $o] :
% 1.90/1.34 ( dsetconstr @ ( powerset @ emptyset )
% 1.90/1.34 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(prop2setE_type,type,
% 1.90/1.34 prop2setE: $o ).
% 1.90/1.34
% 1.90/1.34 thf(prop2setE,definition,
% 1.90/1.34 ( prop2setE
% 1.90/1.34 = ( ! [Xphi: $o,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.90/1.34 => Xphi ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(emptysetE_type,type,
% 1.90/1.34 emptysetE: $o ).
% 1.90/1.34
% 1.90/1.34 thf(emptysetE,definition,
% 1.90/1.34 ( emptysetE
% 1.90/1.34 = ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ emptyset )
% 1.90/1.34 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(emptysetimpfalse_type,type,
% 1.90/1.34 emptysetimpfalse: $o ).
% 1.90/1.34
% 1.90/1.34 thf(emptysetimpfalse,definition,
% 1.90/1.34 ( emptysetimpfalse
% 1.90/1.34 = ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ emptyset )
% 1.90/1.34 => $false ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(notinemptyset_type,type,
% 1.90/1.34 notinemptyset: $o ).
% 1.90/1.34
% 1.90/1.34 thf(notinemptyset,definition,
% 1.90/1.34 ( notinemptyset
% 1.90/1.34 = ( ! [Xx: $i] :
% 1.90/1.34 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(exuE3e_type,type,
% 1.90/1.34 exuE3e: $o ).
% 1.90/1.34
% 1.90/1.34 thf(exuE3e,definition,
% 1.90/1.34 ( exuE3e
% 1.90/1.34 = ( ! [Xphi: $i > $o] :
% 1.90/1.34 ( ( exu
% 1.90/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.90/1.34 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setext_type,type,
% 1.90/1.34 setext: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setext,definition,
% 1.90/1.34 ( setext
% 1.90/1.34 = ( ! [A: $i,B: $i] :
% 1.90/1.34 ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ A )
% 1.90/1.34 => ( in @ Xx @ B ) )
% 1.90/1.34 => ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ B )
% 1.90/1.34 => ( in @ Xx @ A ) )
% 1.90/1.34 => ( A = B ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(emptyI_type,type,
% 1.90/1.34 emptyI: $o ).
% 1.90/1.34
% 1.90/1.34 thf(emptyI,definition,
% 1.90/1.34 ( emptyI
% 1.90/1.34 = ( ! [A: $i] :
% 1.90/1.34 ( ! [Xx: $i] :
% 1.90/1.34 ~ ( in @ Xx @ A )
% 1.90/1.34 => ( A = emptyset ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(noeltsimpempty_type,type,
% 1.90/1.34 noeltsimpempty: $o ).
% 1.90/1.34
% 1.90/1.34 thf(noeltsimpempty,definition,
% 1.90/1.34 ( noeltsimpempty
% 1.90/1.34 = ( ! [A: $i] :
% 1.90/1.34 ( ! [Xx: $i] :
% 1.90/1.34 ~ ( in @ Xx @ A )
% 1.90/1.34 => ( A = emptyset ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setbeta_type,type,
% 1.90/1.34 setbeta: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setbeta,definition,
% 1.90/1.34 ( setbeta
% 1.90/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ A )
% 1.90/1.34 => ( ( in @ Xx
% 1.90/1.34 @ ( dsetconstr @ A
% 1.90/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.90/1.34 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(nonempty_type,type,
% 1.90/1.34 nonempty: $i > $o ).
% 1.90/1.34
% 1.90/1.34 thf(nonempty,definition,
% 1.90/1.34 ( nonempty
% 1.90/1.34 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(nonemptyE1_type,type,
% 1.90/1.34 nonemptyE1: $o ).
% 1.90/1.34
% 1.90/1.34 thf(nonemptyE1,definition,
% 1.90/1.34 ( nonemptyE1
% 1.90/1.34 = ( ! [A: $i] :
% 1.90/1.34 ( ( nonempty @ A )
% 1.90/1.34 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(nonemptyI_type,type,
% 1.90/1.34 nonemptyI: $o ).
% 1.90/1.34
% 1.90/1.34 thf(nonemptyI,definition,
% 1.90/1.34 ( nonemptyI
% 1.90/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ A )
% 1.90/1.34 => ( ( Xphi @ Xx )
% 1.90/1.34 => ( nonempty
% 1.90/1.34 @ ( dsetconstr @ A
% 1.90/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(nonemptyI1_type,type,
% 1.90/1.34 nonemptyI1: $o ).
% 1.90/1.34
% 1.90/1.34 thf(nonemptyI1,definition,
% 1.90/1.34 ( nonemptyI1
% 1.90/1.34 = ( ! [A: $i] :
% 1.90/1.34 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.90/1.34 => ( nonempty @ A ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinIL_type,type,
% 1.90/1.34 setadjoinIL: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinIL,definition,
% 1.90/1.34 ( setadjoinIL
% 1.90/1.34 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(emptyinunitempty_type,type,
% 1.90/1.34 emptyinunitempty: $o ).
% 1.90/1.34
% 1.90/1.34 thf(emptyinunitempty,definition,
% 1.90/1.34 ( emptyinunitempty
% 1.90/1.34 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinIR_type,type,
% 1.90/1.34 setadjoinIR: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinIR,definition,
% 1.90/1.34 ( setadjoinIR
% 1.90/1.34 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.90/1.34 ( ( in @ Xy @ A )
% 1.90/1.34 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinE_type,type,
% 1.90/1.34 setadjoinE: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinE,definition,
% 1.90/1.34 ( setadjoinE
% 1.90/1.34 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.90/1.34 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.90/1.34 => ! [Xphi: $o] :
% 1.90/1.34 ( ( ( Xy = Xx )
% 1.90/1.34 => Xphi )
% 1.90/1.34 => ( ( ( in @ Xy @ A )
% 1.90/1.34 => Xphi )
% 1.90/1.34 => Xphi ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinOr_type,type,
% 1.90/1.34 setadjoinOr: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setadjoinOr,definition,
% 1.90/1.34 ( setadjoinOr
% 1.90/1.34 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.90/1.34 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.90/1.34 => ( ( Xy = Xx )
% 1.90/1.34 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setoftrueEq_type,type,
% 1.90/1.34 setoftrueEq: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setoftrueEq,definition,
% 1.90/1.34 ( setoftrueEq
% 1.90/1.34 = ( ! [A: $i] :
% 1.90/1.34 ( ( dsetconstr @ A
% 1.90/1.34 @ ^ [Xx: $i] : $true )
% 1.90/1.34 = A ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(powersetI_type,type,
% 1.90/1.34 powersetI: $o ).
% 1.90/1.34
% 1.90/1.34 thf(powersetI,definition,
% 1.90/1.34 ( powersetI
% 1.90/1.34 = ( ! [A: $i,B: $i] :
% 1.90/1.34 ( ! [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ B )
% 1.90/1.34 => ( in @ Xx @ A ) )
% 1.90/1.34 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(emptyinPowerset_type,type,
% 1.90/1.34 emptyinPowerset: $o ).
% 1.90/1.34
% 1.90/1.34 thf(emptyinPowerset,definition,
% 1.90/1.34 ( emptyinPowerset
% 1.90/1.34 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(emptyInPowerset_type,type,
% 1.90/1.34 emptyInPowerset: $o ).
% 1.90/1.34
% 1.90/1.34 thf(emptyInPowerset,definition,
% 1.90/1.34 ( emptyInPowerset
% 1.90/1.34 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(powersetE_type,type,
% 1.90/1.34 powersetE: $o ).
% 1.90/1.34
% 1.90/1.34 thf(powersetE,definition,
% 1.90/1.34 ( powersetE
% 1.90/1.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.90/1.34 ( ( in @ B @ ( powerset @ A ) )
% 1.90/1.34 => ( ( in @ Xx @ B )
% 1.90/1.34 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setunionI_type,type,
% 1.90/1.34 setunionI: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setunionI,definition,
% 1.90/1.34 ( setunionI
% 1.90/1.34 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.90/1.34 ( ( in @ Xx @ B )
% 1.90/1.34 => ( ( in @ B @ A )
% 1.90/1.34 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(setunionE_type,type,
% 1.90/1.34 setunionE: $o ).
% 1.90/1.34
% 1.90/1.34 thf(setunionE,definition,
% 1.90/1.34 ( setunionE
% 1.90/1.34 = ( ! [A: $i,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ ( setunion @ A ) )
% 1.90/1.34 => ! [Xphi: $o] :
% 1.90/1.34 ( ! [B: $i] :
% 1.90/1.34 ( ( in @ Xx @ B )
% 1.90/1.34 => ( ( in @ B @ A )
% 1.90/1.34 => Xphi ) )
% 1.90/1.34 => Xphi ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(subPowSU_type,type,
% 1.90/1.34 subPowSU: $o ).
% 1.90/1.34
% 1.90/1.34 thf(subPowSU,definition,
% 1.90/1.34 ( subPowSU
% 1.90/1.34 = ( ! [A: $i,Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ A )
% 1.90/1.34 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(exuE2_type,type,
% 1.90/1.34 exuE2: $o ).
% 1.90/1.34
% 1.90/1.34 thf(exuE2,definition,
% 1.90/1.34 ( exuE2
% 1.90/1.34 = ( ! [Xphi: $i > $o] :
% 1.90/1.34 ( ( exu
% 1.90/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.90/1.34 => ? [Xx: $i] :
% 1.90/1.34 ! [Xy: $i] :
% 1.90/1.34 ( ( Xphi @ Xy )
% 1.90/1.34 <=> ( Xy = Xx ) ) ) ) ) ).
% 1.90/1.34
% 1.90/1.34 thf(nonemptyImpWitness,conjecture,
% 1.90/1.34 ( setextAx
% 1.90/1.34 => ( emptysetAx
% 1.90/1.34 => ( setadjoinAx
% 1.90/1.34 => ( powersetAx
% 1.90/1.34 => ( setunionAx
% 1.90/1.34 => ( omega0Ax
% 1.90/1.34 => ( omegaSAx
% 1.90/1.34 => ( omegaIndAx
% 1.90/1.34 => ( replAx
% 1.90/1.34 => ( foundationAx
% 1.90/1.34 => ( wellorderingAx
% 1.90/1.34 => ( descrp
% 1.90/1.34 => ( dsetconstrI
% 1.90/1.34 => ( dsetconstrEL
% 1.90/1.34 => ( dsetconstrER
% 1.90/1.34 => ( exuE1
% 1.90/1.34 => ( prop2setE
% 1.90/1.34 => ( emptysetE
% 1.90/1.34 => ( emptysetimpfalse
% 1.90/1.34 => ( notinemptyset
% 1.90/1.34 => ( exuE3e
% 1.90/1.34 => ( setext
% 1.90/1.34 => ( emptyI
% 1.90/1.34 => ( noeltsimpempty
% 1.90/1.34 => ( setbeta
% 1.90/1.34 => ( nonemptyE1
% 1.90/1.34 => ( nonemptyI
% 1.90/1.34 => ( nonemptyI1
% 1.90/1.34 => ( setadjoinIL
% 1.90/1.34 => ( emptyinunitempty
% 1.90/1.34 => ( setadjoinIR
% 1.90/1.34 => ( setadjoinE
% 1.90/1.34 => ( setadjoinOr
% 1.90/1.34 => ( setoftrueEq
% 1.90/1.34 => ( powersetI
% 1.90/1.34 => ( emptyinPowerset
% 1.90/1.34 => ( emptyInPowerset
% 1.90/1.34 => ( powersetE
% 1.90/1.34 => ( setunionI
% 1.90/1.34 => ( setunionE
% 1.90/1.34 => ( subPowSU
% 1.90/1.34 => ( exuE2
% 1.90/1.34 => ! [A: $i] :
% 1.90/1.34 ( ( nonempty @ A )
% 1.90/1.34 => ? [Xx: $i] :
% 1.90/1.34 ( ( in @ Xx @ A )
% 1.90/1.34 & $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.90/1.34 ------------------------
% 1.90/1.36 % (20354)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_20249 for (2999ds/275Mi)
% 1.90/1.36 % (20352)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20249 for (2999ds/2Mi)
% 1.90/1.36 % (20352)Instruction limit reached!
% 1.90/1.36 % (20352)------------------------------
% 1.90/1.36 % (20352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.36 % (20352)Termination reason: Unknown
% 1.90/1.36 % (20352)Termination phase: shuffling
% 1.90/1.36
% 1.90/1.36 % (20352)Memory used [KB]: 1023
% 1.90/1.36 % (20352)Time elapsed: 0.002 s
% 1.90/1.36 % (20352)Instructions burned: 3 (million)
% 1.90/1.36 % (20352)------------------------------
% 1.90/1.36 % (20352)------------------------------
% 1.90/1.37 % (20349)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20249 for (2999ds/183Mi)
% 1.90/1.37 % (20350)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_20249 for (2999ds/4Mi)
% 1.90/1.37 % (20351)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_20249 for (2999ds/27Mi)
% 1.90/1.37 % (20353)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_20249 for (2999ds/2Mi)
% 1.90/1.37 % (20355)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20249 for (2999ds/18Mi)
% 1.90/1.37 % (20353)Instruction limit reached!
% 1.90/1.37 % (20353)------------------------------
% 1.90/1.37 % (20353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.37 % (20353)Termination reason: Unknown
% 1.90/1.37 % (20353)Termination phase: shuffling
% 1.90/1.37
% 1.90/1.37 % (20353)Memory used [KB]: 1023
% 1.90/1.37 % (20353)Time elapsed: 0.003 s
% 1.90/1.37 % (20353)Instructions burned: 2 (million)
% 1.90/1.37 % (20353)------------------------------
% 1.90/1.37 % (20353)------------------------------
% 1.90/1.37 % (20350)Instruction limit reached!
% 1.90/1.37 % (20350)------------------------------
% 1.90/1.37 % (20350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.37 % (20350)Termination reason: Unknown
% 1.90/1.37 % (20350)Termination phase: shuffling
% 1.90/1.37
% 1.90/1.37 % (20350)Memory used [KB]: 1151
% 1.90/1.37 % (20350)Time elapsed: 0.004 s
% 1.90/1.37 % (20350)Instructions burned: 4 (million)
% 1.90/1.37 % (20350)------------------------------
% 1.90/1.37 % (20350)------------------------------
% 1.90/1.37 % (20356)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20249 for (2999ds/3Mi)
% 1.90/1.37 % (20356)Instruction limit reached!
% 1.90/1.37 % (20356)------------------------------
% 1.90/1.37 % (20356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.37 % (20356)Termination reason: Unknown
% 1.90/1.37 % (20356)Termination phase: shuffling
% 1.90/1.37
% 1.90/1.37 % (20356)Memory used [KB]: 1151
% 1.90/1.37 % (20356)Time elapsed: 0.003 s
% 1.90/1.37 % (20356)Instructions burned: 4 (million)
% 1.90/1.37 % (20356)------------------------------
% 1.90/1.37 % (20356)------------------------------
% 1.90/1.38 % (20355)Instruction limit reached!
% 1.90/1.38 % (20355)------------------------------
% 1.90/1.38 % (20355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.38 % (20355)Termination reason: Unknown
% 1.90/1.38 % (20355)Termination phase: Property scanning
% 1.90/1.38
% 1.90/1.38 % (20355)Memory used [KB]: 1535
% 1.90/1.38 % (20355)Time elapsed: 0.012 s
% 1.90/1.38 % (20355)Instructions burned: 18 (million)
% 1.90/1.38 % (20355)------------------------------
% 1.90/1.38 % (20355)------------------------------
% 1.90/1.38 % (20351)Instruction limit reached!
% 1.90/1.38 % (20351)------------------------------
% 1.90/1.38 % (20351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.38 % (20351)Termination reason: Unknown
% 1.90/1.38 % (20351)Termination phase: Saturation
% 1.90/1.38
% 1.90/1.38 % (20351)Memory used [KB]: 5756
% 1.90/1.38 % (20351)Time elapsed: 0.016 s
% 1.90/1.38 % (20351)Instructions burned: 27 (million)
% 1.90/1.38 % (20351)------------------------------
% 1.90/1.38 % (20351)------------------------------
% 1.90/1.38 % (20359)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_20249 for (2999ds/3Mi)
% 1.90/1.38 % (20358)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_20249 for (2999ds/15Mi)
% 1.90/1.38 % (20359)Instruction limit reached!
% 1.90/1.38 % (20359)------------------------------
% 1.90/1.38 % (20359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.38 % (20359)Termination reason: Unknown
% 1.90/1.38 % (20359)Termination phase: shuffling
% 1.90/1.38
% 1.90/1.38 % (20359)Memory used [KB]: 1151
% 1.90/1.38 % (20359)Time elapsed: 0.003 s
% 1.90/1.38 % (20359)Instructions burned: 4 (million)
% 1.90/1.38 % (20359)------------------------------
% 1.90/1.38 % (20359)------------------------------
% 1.90/1.39 % (20357)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_20249 for (2999ds/37Mi)
% 1.90/1.39 % (20358)Instruction limit reached!
% 1.90/1.39 % (20358)------------------------------
% 1.90/1.39 % (20358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.39 % (20358)Termination reason: Unknown
% 1.90/1.39 % (20358)Termination phase: Preprocessing 3
% 1.90/1.39
% 1.90/1.39 % (20358)Memory used [KB]: 1535
% 1.90/1.39 % (20354)First to succeed.
% 1.90/1.39 % (20358)Time elapsed: 0.008 s
% 1.90/1.39 % (20358)Instructions burned: 16 (million)
% 1.90/1.39 % (20358)------------------------------
% 1.90/1.39 % (20358)------------------------------
% 1.90/1.39 % (20354)Refutation found. Thanks to Tanya!
% 1.90/1.39 % SZS status Theorem for DTF2THF_20249
% 1.90/1.39 % SZS output start Proof for DTF2THF_20249
% 1.90/1.39 thf(func_def_0, type, in: $i > $i > $o).
% 1.90/1.39 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.90/1.39 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.90/1.39 thf(func_def_8, type, powerset: $i > $i).
% 1.90/1.39 thf(func_def_10, type, setunion: $i > $i).
% 1.90/1.39 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.90/1.39 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.90/1.39 thf(func_def_26, type, prop2set: $o > $i).
% 1.90/1.39 thf(func_def_36, type, nonempty: $i > $o).
% 1.90/1.39 thf(func_def_66, type, sP0: $i > $i > $o).
% 1.90/1.39 thf(func_def_67, type, sP1: $i > $o).
% 1.90/1.39 thf(func_def_68, type, sP2: $i > $i > $o).
% 1.90/1.39 thf(func_def_69, type, sP3: $i > $i > $o).
% 1.90/1.39 thf(func_def_74, type, sK8: $i > $i).
% 1.90/1.39 thf(func_def_75, type, sK9: $i > $i > $i).
% 1.90/1.39 thf(func_def_76, type, sK10: $i > $i > $i).
% 1.90/1.39 thf(func_def_77, type, sK11: $i > $i > $i).
% 1.90/1.39 thf(func_def_78, type, sK12: $i > $i > $i).
% 1.90/1.39 thf(func_def_79, type, sK13: $i > $i > $i > $i).
% 1.90/1.39 thf(func_def_80, type, sK14: $i > $i).
% 1.90/1.39 thf(func_def_81, type, sK15: $i > $i).
% 1.90/1.39 thf(func_def_82, type, sK16: $i > $i).
% 1.90/1.39 thf(func_def_83, type, sK17: $i > $i).
% 1.90/1.39 thf(func_def_84, type, sK18: $i > $i > $i > $i).
% 1.90/1.39 thf(func_def_85, type, sK19: $i > $i > $i > $i).
% 1.90/1.39 thf(func_def_86, type, sK20: $i > $i > $i).
% 1.90/1.39 thf(func_def_87, type, sK21: $i > $i > $i).
% 1.90/1.39 thf(func_def_88, type, sK22: $i > $i > $i).
% 1.90/1.39 thf(func_def_89, type, sK23: $i > $i).
% 1.90/1.39 thf(func_def_90, type, sK24: $i > $i > $i).
% 1.90/1.39 thf(func_def_92, type, sK26: $i > $i).
% 1.90/1.39 thf(func_def_93, type, sK27: $i > $i).
% 1.90/1.39 thf(func_def_96, type, sK30: $i > $i).
% 1.90/1.39 thf(func_def_98, type, sK32: $i > $i > $i).
% 1.90/1.39 thf(func_def_104, type, sK38: $i > $o).
% 1.90/1.39 thf(func_def_112, type, sK46: $o > $i > $i > $i).
% 1.90/1.39 thf(func_def_124, type, sK58: $i > $o).
% 1.90/1.39 thf(func_def_128, type, sK62: $i > $o).
% 1.90/1.39 thf(func_def_132, type, sK66: $i > $i).
% 1.90/1.39 thf(func_def_134, type, sK68: $i > $i).
% 1.90/1.39 thf(func_def_136, type, sK70: $i > $i > $o).
% 1.90/1.39 thf(func_def_137, type, sK71: $i > $i).
% 1.90/1.39 thf(func_def_138, type, sK72: $i > $i).
% 1.90/1.39 thf(func_def_139, type, sK73: ($i > $i > $o) > $i > $i).
% 1.90/1.39 thf(func_def_140, type, sK74: $i > ($i > $i > $o) > $i > $i).
% 1.90/1.39 thf(func_def_141, type, sK75: ($i > $i > $o) > $i > $i).
% 1.90/1.39 thf(func_def_149, type, sK83: $i > $i > $i).
% 1.90/1.39 thf(func_def_152, type, sK86: ($i > $o) > $i).
% 1.90/1.39 thf(func_def_153, type, sK87: $i > $o).
% 1.90/1.39 thf(func_def_154, type, sK88: $i > $i).
% 1.90/1.39 thf(func_def_155, type, sK89: $i > $o).
% 1.90/1.39 thf(func_def_156, type, sK90: $i > $i).
% 1.90/1.39 thf(func_def_157, type, sK91: ($i > $o) > $i).
% 1.90/1.39 thf(func_def_159, type, sK93: $i > $o).
% 1.90/1.39 thf(func_def_161, type, sK95: $i > $i).
% 1.90/1.39 thf(func_def_163, type, sK97: $i > $i).
% 1.90/1.39 thf(func_def_170, type, sK104: $i > $i > $i).
% 1.90/1.39 thf(func_def_171, type, sK105: $i > $i > $i).
% 1.90/1.39 thf(func_def_172, type, sK106: $i > $i > $i).
% 1.90/1.39 thf(func_def_175, type, sK109: $i > $o).
% 1.90/1.39 thf(func_def_181, type, sK115: $i > $o).
% 1.90/1.39 thf(func_def_182, type, sK116: ($i > $o) > $i).
% 1.90/1.39 thf(func_def_188, type, sK122: $i > $i > $i).
% 1.90/1.39 thf(func_def_193, type, ph127: !>[X0: $tType]:(X0)).
% 1.90/1.39 thf(f1112,plain,(
% 1.90/1.39 $false),
% 1.90/1.39 inference(subsumption_resolution,[status(thm)],[f1110,f425])).
% 1.90/1.39 thf(f425,plain,(
% 1.90/1.39 ($true = (nonempty @ sK5))),
% 1.90/1.39 inference(cnf_transformation,[status(thm)],[f197])).
% 1.90/1.39 thf(f197,plain,(
% 1.90/1.39 (noeltsimpempty = $true) & (emptysetAx = $true) & (setextAx = $true) & (powersetAx = $true) & (emptyI = $true) & (setadjoinAx = $true) & (exuE1 = $true) & (emptyinunitempty = $true) & (nonemptyI1 = $true) & (setoftrueEq = $true) & (emptysetimpfalse = $true) & (setbeta = $true) & (emptysetE = $true) & (exuE3e = $true) & (descrp = $true) & (setunionAx = $true) & (foundationAx = $true) & (setadjoinIR = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (powersetE = $true) & (emptyinPowerset = $true) & (exuE2 = $true) & (setadjoinIL = $true) & (dsetconstrI = $true) & (powersetI = $true) & (omegaSAx = $true) & (emptyInPowerset = $true) & (replAx = $true) & (omega0Ax = $true) & (notinemptyset = $true) & (subPowSU = $true) & (($true = (nonempty @ sK5)) & ! [X1 : $i] : ($true != (in @ X1 @ sK5))) & (setadjoinE = $true) & (dsetconstrER = $true) & (setadjoinOr = $true) & (setunionI = $true) & (dsetconstrEL = $true) & (setext = $true) & (prop2setE = $true) & (setunionE = $true) & (omegaIndAx = $true) & (wellorderingAx = $true)),
% 1.90/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f168,f196])).
% 1.90/1.39 thf(f196,plain,(
% 1.90/1.39 ? [X0 : $i] : (($true = (nonempty @ X0)) & ! [X1 : $i] : ($true != (in @ X1 @ X0))) => (($true = (nonempty @ sK5)) & ! [X1 : $i] : ($true != (in @ X1 @ sK5)))),
% 1.90/1.39 introduced(definition,[],[choice_axiom])).
% 1.90/1.39 thf(f168,plain,(
% 1.90/1.39 (noeltsimpempty = $true) & (emptysetAx = $true) & (setextAx = $true) & (powersetAx = $true) & (emptyI = $true) & (setadjoinAx = $true) & (exuE1 = $true) & (emptyinunitempty = $true) & (nonemptyI1 = $true) & (setoftrueEq = $true) & (emptysetimpfalse = $true) & (setbeta = $true) & (emptysetE = $true) & (exuE3e = $true) & (descrp = $true) & (setunionAx = $true) & (foundationAx = $true) & (setadjoinIR = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (powersetE = $true) & (emptyinPowerset = $true) & (exuE2 = $true) & (setadjoinIL = $true) & (dsetconstrI = $true) & (powersetI = $true) & (omegaSAx = $true) & (emptyInPowerset = $true) & (replAx = $true) & (omega0Ax = $true) & (notinemptyset = $true) & (subPowSU = $true) & ? [X0 : $i] : (($true = (nonempty @ X0)) & ! [X1 : $i] : ($true != (in @ X1 @ X0))) & (setadjoinE = $true) & (dsetconstrER = $true) & (setadjoinOr = $true) & (setunionI = $true) & (dsetconstrEL = $true) & (setext = $true) & (prop2setE = $true) & (setunionE = $true) & (omegaIndAx = $true) & (wellorderingAx = $true)),
% 1.90/1.39 inference(flattening,[status(thm)],[f167])).
% 1.90/1.39 thf(f167,plain,(
% 1.90/1.39 (((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (($true = (nonempty @ X0)) & ! [X1 : $i] : ($true != (in @ X1 @ X0))) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 1.90/1.39 inference(ennf_transformation,[status(thm)],[f136])).
% 1.90/1.39 thf(f136,plain,(
% 1.90/1.39 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ! [X0 : $i] : (($true = (nonempty @ X0)) => ? [X1 : $i] : ($true = (in @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))),
% 1.90/1.39 inference(true_and_false_elimination,[status(thm)],[f135])).
% 1.90/1.39 thf(f135,plain,(
% 1.90/1.39 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ! [X0 : $i] : (($true = (nonempty @ X0)) => ? [X1 : $i] : (($true = (in @ X1 @ X0)) & $true))))))))))))))))))))))))))))))))))))))))))))),
% 1.90/1.39 inference(fool_elimination,[status(thm)],[f134])).
% 1.90/1.39 thf(f134,plain,(
% 1.90/1.39 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & $true))))))))))))))))))))))))))))))))))))))))))))),
% 1.90/1.39 inference(rectify,[status(thm)],[f47])).
% 1.90/1.39 thf(f47,negated_conjecture,(
% 1.90/1.39 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => ! [X3 : $i] : ((nonempty @ X3) => ? [X1 : $i] : ((in @ X1 @ X3) & $true))))))))))))))))))))))))))))))))))))))))))))),
% 1.90/1.39 inference(negated_conjecture,[status(cth)],[f46])).
% 1.90/1.39 thf(f46,conjecture,(
% 1.90/1.39 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => ! [X3 : $i] : ((nonempty @ X3) => ? [X1 : $i] : ((in @ X1 @ X3) & $true)))))))))))))))))))))))))))))))))))))))))))),
% 1.90/1.39 file('/export/starexec/sandbox/tmp/tmp.N8AcFdfOIF/DTF2THF_20249.p',nonemptyImpWitness)).
% 1.90/1.39 thf(f1110,plain,(
% 1.90/1.39 ($true != (nonempty @ sK5))),
% 1.90/1.39 inference(trivial_inequality_removal,[status(thm)],[f1108])).
% 1.90/1.39 thf(f1108,plain,(
% 1.90/1.39 ($true != $true) | ($true != (nonempty @ sK5))),
% 1.90/1.39 inference(superposition,[status(thm)],[f424,f850])).
% 1.90/1.39 thf(f850,plain,(
% 1.90/1.39 ( ! [X2 : $i] : (($true = (in @ (sK8 @ X2) @ X2)) | ($true != (nonempty @ X2))) )),
% 1.90/1.39 inference(trivial_inequality_removal,[status(thm)],[f657])).
% 1.90/1.39 thf(f657,plain,(
% 1.90/1.39 ( ! [X2 : $i] : (($true != $true) | ($true = (in @ (sK8 @ X2) @ X2)) | ($true != (nonempty @ X2))) )),
% 1.90/1.39 inference(definition_unfolding,[status(thm)],[f462,f438])).
% 1.90/1.39 thf(f438,plain,(
% 1.90/1.39 (nonemptyE1 = $true)),
% 1.90/1.39 inference(cnf_transformation,[status(thm)],[f197])).
% 1.90/1.39 thf(f462,plain,(
% 1.90/1.39 ( ! [X2 : $i] : (($true = (in @ (sK8 @ X2) @ X2)) | ($true != (nonempty @ X2)) | (nonemptyE1 != $true)) )),
% 1.90/1.39 inference(cnf_transformation,[status(thm)],[f206])).
% 1.90/1.39 thf(f206,plain,(
% 1.90/1.39 ((nonemptyE1 = $true) | (! [X1 : $i] : ($true != (in @ X1 @ sK7)) & ($true = (nonempty @ sK7)))) & (! [X2 : $i] : (($true = (in @ (sK8 @ X2) @ X2)) | ($true != (nonempty @ X2))) | (nonemptyE1 != $true))),
% 1.90/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f203,f205,f204])).
% 1.90/1.39 thf(f204,plain,(
% 1.90/1.39 ? [X0 : $i] : (! [X1 : $i] : ($true != (in @ X1 @ X0)) & ($true = (nonempty @ X0))) => (! [X1 : $i] : ($true != (in @ X1 @ sK7)) & ($true = (nonempty @ sK7)))),
% 1.90/1.39 introduced(definition,[],[choice_axiom])).
% 1.90/1.39 thf(f205,plain,(
% 1.90/1.39 ! [X2 : $i] : (? [X3 : $i] : ($true = (in @ X3 @ X2)) => ($true = (in @ (sK8 @ X2) @ X2)))),
% 1.90/1.39 introduced(definition,[],[choice_axiom])).
% 1.90/1.39 thf(f203,plain,(
% 1.90/1.39 ((nonemptyE1 = $true) | ? [X0 : $i] : (! [X1 : $i] : ($true != (in @ X1 @ X0)) & ($true = (nonempty @ X0)))) & (! [X2 : $i] : (? [X3 : $i] : ($true = (in @ X3 @ X2)) | ($true != (nonempty @ X2))) | (nonemptyE1 != $true))),
% 1.90/1.39 inference(rectify,[status(thm)],[f202])).
% 1.90/1.39 thf(f202,plain,(
% 1.90/1.39 ((nonemptyE1 = $true) | ? [X0 : $i] : (! [X1 : $i] : ($true != (in @ X1 @ X0)) & ($true = (nonempty @ X0)))) & (! [X0 : $i] : (? [X1 : $i] : ($true = (in @ X1 @ X0)) | ($true != (nonempty @ X0))) | (nonemptyE1 != $true))),
% 1.90/1.39 inference(nnf_transformation,[status(thm)],[f166])).
% 1.90/1.39 thf(f166,plain,(
% 1.90/1.39 (nonemptyE1 = $true) <=> ! [X0 : $i] : (? [X1 : $i] : ($true = (in @ X1 @ X0)) | ($true != (nonempty @ X0)))),
% 1.90/1.39 inference(ennf_transformation,[status(thm)],[f64])).
% 1.90/1.39 thf(f64,plain,(
% 1.90/1.39 ! [X0 : $i] : (($true = (nonempty @ X0)) => ? [X1 : $i] : ($true = (in @ X1 @ X0))) <=> (nonemptyE1 = $true)),
% 1.90/1.39 inference(fool_elimination,[status(thm)],[f63])).
% 1.90/1.39 thf(f63,plain,(
% 1.90/1.39 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 1.90/1.39 inference(rectify,[status(thm)],[f29])).
% 1.90/1.39 thf(f29,axiom,(
% 1.90/1.39 (! [X3 : $i] : ((nonempty @ X3) => ? [X1 : $i] : (in @ X1 @ X3)) = nonemptyE1)),
% 1.90/1.39 file('/export/starexec/sandbox/tmp/tmp.N8AcFdfOIF/DTF2THF_20249.p',nonemptyE1)).
% 1.90/1.39 thf(f424,plain,(
% 1.90/1.39 ( ! [X1 : $i] : (($true != (in @ X1 @ sK5))) )),
% 1.90/1.39 inference(cnf_transformation,[status(thm)],[f197])).
% 1.90/1.39 % SZS output end Proof for DTF2THF_20249
% 1.90/1.39 % (20354)------------------------------
% 1.90/1.39 % (20354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.39 % (20354)Termination reason: Refutation
% 1.90/1.39
% 1.90/1.39 % (20354)Memory used [KB]: 6524
% 1.90/1.39 % (20354)Time elapsed: 0.033 s
% 1.90/1.39 % (20354)Instructions burned: 101 (million)
% 1.90/1.39 % (20354)------------------------------
% 1.90/1.39 % (20354)------------------------------
% 1.90/1.39 % (20348)Success in time 0.033 s
%------------------------------------------------------------------------------