%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU522^1 : 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 : n010.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 09:35:04 AM UTC 2026
% Result : Theorem 2.20s 1.74s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 968 ( 262 equ; 0 cnn)
% Maximal formula atoms : 41 ( 32 avg)
% Number of connectives : 669 ( 55 ~; 42 |; 150 &; 254 @)
% ( 4 <=>; 164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 108 ( 105 usr; 46 con; 0-3 aty)
% Number of variables : 67 ( 0 ^; 41 !; 26 ?; 67 :)
% 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_63,type,
sP1: $i > $i > $o ).
thf(func_def_64,type,
sP2: $i > $o ).
thf(func_def_65,type,
sP3: $i > $i > $o ).
thf(func_def_66,type,
sP4: $i > $i > $o ).
thf(func_def_68,type,
sK6: $i > $i ).
thf(func_def_70,type,
sK8: $i > $i ).
thf(func_def_71,type,
sK9: $i > $i > $i ).
thf(func_def_85,type,
sK23: $i > $o ).
thf(func_def_90,type,
sK28: $i > $o ).
thf(func_def_91,type,
sK29: $i > $o ).
thf(func_def_101,type,
sK39: $i > $i ).
thf(func_def_103,type,
sK41: $i > $o ).
thf(func_def_111,type,
sK49: $i > $i ).
thf(func_def_114,type,
sK52: $i > $o ).
thf(func_def_118,type,
sK56: $i > $i > $o ).
thf(func_def_119,type,
sK57: $i > $i ).
thf(func_def_120,type,
sK58: $i > $i ).
thf(func_def_121,type,
sK59: ( $i > $i > $o ) > $i > $i ).
thf(func_def_122,type,
sK60: ( $i > $i > $o ) > $i > $i ).
thf(func_def_123,type,
sK61: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_127,type,
sK65: $i > $i > $i ).
thf(func_def_130,type,
sK68: $i > $i ).
thf(func_def_134,type,
sK72: $i > $i > $i ).
thf(func_def_135,type,
sK73: $i > $i ).
thf(func_def_139,type,
sK77: $i > $i > $i ).
thf(func_def_140,type,
sK78: $i > $i > $i ).
thf(func_def_141,type,
sK79: $i > $i > $i ).
thf(func_def_142,type,
sK80: $i > $i > $i ).
thf(func_def_143,type,
sK81: $i > $i > $i > $i ).
thf(func_def_144,type,
sK82: $i > $i ).
thf(func_def_145,type,
sK83: $i > $i ).
thf(func_def_146,type,
sK84: $i > $i ).
thf(func_def_147,type,
sK85: $i > $i ).
thf(func_def_148,type,
sK86: $i > $i > $i > $i ).
thf(func_def_149,type,
sK87: $i > $i > $i > $i ).
thf(func_def_150,type,
sK88: $i > $i > $i ).
thf(func_def_151,type,
sK89: $i > $i > $i ).
thf(func_def_152,type,
sK90: $i > $i > $i ).
thf(func_def_153,type,
sK91: $i > $i ).
thf(func_def_154,type,
sK92: $i > $i > $i ).
thf(func_def_156,type,
sK94: $i > $i ).
thf(func_def_157,type,
sK95: $i > $i ).
thf(func_def_160,type,
sK98: $i > $i > $i ).
thf(func_def_161,type,
sK99: $i > $i > $i ).
thf(func_def_165,type,
sK103: ( $i > $o ) > $i ).
thf(func_def_166,type,
sK104: $i > $o ).
thf(func_def_167,type,
sK105: $i > $i ).
thf(func_def_170,type,
sK108: $i > $i > $i ).
thf(func_def_174,type,
sK112: ( $i > $o ) > $i ).
thf(func_def_175,type,
sK113: $i > $o ).
thf(func_def_176,type,
sK114: $i > $o ).
thf(func_def_180,type,
ph118:
!>[X0: $tType] : X0 ).
thf(f835,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f831]) ).
thf(f831,plain,
$true != $true,
inference(superposition,[status(thm)],[f667,f541]) ).
thf(f541,plain,
( $true
= ( in @ sK101 @ sK102 ) ),
inference(cnf_transformation,[status(thm)],[f353]) ).
thf(f353,plain,
( ( exuE3e = $true )
& ( setext = $true )
& ( setadjoinOr = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( setunionAx = $true )
& ( emptyI = $true )
& ( powersetI = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( nonemptyI1 = $true )
& ( wellorderingAx = $true )
& ( omega0Ax = $true )
& ( emptysetAx = $true )
& ( powersetAx = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( setbeta = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIR = $true )
& ( prop2setE = $true )
& ( powersetE = $true )
& ( notinemptyset = $true )
& ( setadjoinE = $true )
& ( emptyInPowerset = $true )
& ( setextAx = $true )
& ( omegaSAx = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( noeltsimpempty = $true )
& ( replAx = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrI = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ( $true
= ( in @ sK101 @ sK102 ) )
& ( ( in @ sK100 @ ( setunion @ sK102 ) )
!= $true )
& ( $true
= ( in @ sK100 @ sK101 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK100,sK101,sK102])],[f144,f352]) ).
thf(f352,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X0 @ ( setunion @ X2 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
=> ( ( $true
= ( in @ sK101 @ sK102 ) )
& ( ( in @ sK100 @ ( setunion @ sK102 ) )
!= $true )
& ( $true
= ( in @ sK100 @ sK101 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f144,plain,
( ( exuE3e = $true )
& ( setext = $true )
& ( setadjoinOr = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( setunionAx = $true )
& ( emptyI = $true )
& ( powersetI = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( nonemptyI1 = $true )
& ( wellorderingAx = $true )
& ( omega0Ax = $true )
& ( emptysetAx = $true )
& ( powersetAx = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( setbeta = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIR = $true )
& ( prop2setE = $true )
& ( powersetE = $true )
& ( notinemptyset = $true )
& ( setadjoinE = $true )
& ( emptyInPowerset = $true )
& ( setextAx = $true )
& ( omegaSAx = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( noeltsimpempty = $true )
& ( replAx = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrI = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X0 @ ( setunion @ X2 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f143]) ).
thf(f143,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setunion @ X2 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
= $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)],[f103]) ).
thf(f103,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X0 @ ( setunion @ X2 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f102]) ).
thf(f102,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X0 @ ( setunion @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,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
=> ! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ X4 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X1 @ ( setunion @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
thf(f42,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
=> ! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ X4 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X1 @ ( setunion @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aBJSbpOuWU/DTF2THF_23191.p',setunionI) ).
thf(f667,plain,
( $true
!= ( in @ sK101 @ sK102 ) ),
inference(trivial_inequality_removal,[status(thm)],[f656]) ).
thf(f656,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK101 @ sK102 ) ) ),
inference(superposition,[status(thm)],[f641,f539]) ).
thf(f539,plain,
( $true
= ( in @ sK100 @ sK101 ) ),
inference(cnf_transformation,[status(thm)],[f353]) ).
thf(f641,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK100 @ X0 ) )
| ( ( in @ X0 @ sK102 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f640]) ).
thf(f640,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK102 )
!= $true )
| ( $true
!= ( in @ sK100 @ X0 ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f637,f574]) ).
thf(f574,plain,
setunionAx = $true,
inference(cnf_transformation,[status(thm)],[f353]) ).
thf(f637,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK102 )
!= $true )
| ( $true
!= ( in @ sK100 @ X0 ) )
| ( setunionAx != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f634]) ).
thf(f634,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ sK100 @ X0 ) )
| ( ( in @ X0 @ sK102 )
!= $true )
| ( setunionAx != $true ) ),
inference(superposition,[status(thm)],[f540,f593]) ).
thf(f593,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( setunionAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f369]) ).
thf(f369,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ) )
& ( ( ( $true
= ( in @ ( sK108 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ X0 @ ( sK108 @ X1 @ X0 ) )
= $true ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) ) )
| ( setunionAx != $true ) )
& ( ( setunionAx = $true )
| ( ( ! [X6: $i] :
( ( ( in @ X6 @ sK110 )
!= $true )
| ( ( in @ sK109 @ X6 )
!= $true ) )
| ( ( in @ sK109 @ ( setunion @ sK110 ) )
!= $true ) )
& ( ( ( ( in @ sK111 @ sK110 )
= $true )
& ( $true
= ( in @ sK109 @ sK111 ) ) )
| ( ( in @ sK109 @ ( setunion @ sK110 ) )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108,sK109,sK110,sK111])],[f365,f368,f367,f366]) ).
thf(f366,plain,
! [X0: $i,X1: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X0 @ X3 )
= $true ) )
=> ( ( $true
= ( in @ ( sK108 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ X0 @ ( sK108 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f367,plain,
( ? [X4: $i,X5: $i] :
( ( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ X5 ) )
| ( ( in @ X4 @ X6 )
!= $true ) )
| ( ( in @ X4 @ ( setunion @ X5 ) )
!= $true ) )
& ( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( ( in @ X4 @ X7 )
= $true ) )
| ( ( in @ X4 @ ( setunion @ X5 ) )
= $true ) ) )
=> ( ( ! [X6: $i] :
( ( ( in @ X6 @ sK110 )
!= $true )
| ( ( in @ sK109 @ X6 )
!= $true ) )
| ( ( in @ sK109 @ ( setunion @ sK110 ) )
!= $true ) )
& ( ? [X7: $i] :
( ( ( in @ X7 @ sK110 )
= $true )
& ( $true
= ( in @ sK109 @ X7 ) ) )
| ( ( in @ sK109 @ ( setunion @ sK110 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f368,plain,
( ? [X7: $i] :
( ( ( in @ X7 @ sK110 )
= $true )
& ( $true
= ( in @ sK109 @ X7 ) ) )
=> ( ( ( in @ sK111 @ sK110 )
= $true )
& ( $true
= ( in @ sK109 @ sK111 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f365,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ) )
& ( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X0 @ X3 )
= $true ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) ) )
| ( setunionAx != $true ) )
& ( ( setunionAx = $true )
| ? [X4: $i,X5: $i] :
( ( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ X5 ) )
| ( ( in @ X4 @ X6 )
!= $true ) )
| ( ( in @ X4 @ ( setunion @ X5 ) )
!= $true ) )
& ( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( ( in @ X4 @ X7 )
= $true ) )
| ( ( in @ X4 @ ( setunion @ X5 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f364]) ).
thf(f364,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ) )
& ( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) ) )
| ( setunionAx != $true ) )
& ( ( setunionAx = $true )
| ? [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) )
& ( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f113]) ).
thf(f113,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
<=> ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
= $true ) ) )
<=> ( setunionAx = $true ) ),
inference(fool_elimination,[status(thm)],[f112]) ).
thf(f112,plain,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X0 @ X2 ) )
<=> ( in @ X0 @ ( setunion @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( setunionAx
= ( ! [X1: $i,X3: $i] :
( ? [X4: $i] :
( ( in @ X4 @ X3 )
& ( in @ X1 @ X4 ) )
<=> ( in @ X1 @ ( setunion @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aBJSbpOuWU/DTF2THF_23191.p',setunionAx) ).
thf(f540,plain,
( ( in @ sK100 @ ( setunion @ sK102 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f353]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU522^1 : 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
% 0.16/0.34 % Computer : n010.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:25:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.34/0.50 ---- Original DTF file ---
% 0.34/0.50 thf(spec,logic,$$dhol).
% 0.34/0.50 %------------------------------------------------------------------------------
% 0.34/0.50 % File : SEU522^1 : TPTP v9.2.1. Released v3.7.0.
% 0.34/0.50 % Domain : Set Theory
% 0.34/0.50 % Problem : Preliminary Notions - Power Sets and Unions
% 0.34/0.50 % Version : Especial.
% 0.34/0.50 % English : (! A:i.! x:i.! B:i.in x B -> in B A -> in x (setunion A))
% 0.34/0.50
% 0.34/0.50 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.34/0.50 % Source : [Bro08]
% 0.34/0.50 % Names : ZFC024g [Bro08]
% 0.34/0.50
% 0.34/0.50 % Status : Theorem
% 0.34/0.50 % 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, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 1.00 v3.7.0
% 0.34/0.50 % Syntax : Number of formulae : 91 ( 41 unt; 49 typ; 41 def)
% 0.34/0.50 % Number of atoms : 231 ( 53 equ; 0 cnn)
% 0.34/0.50 % Maximal formula atoms : 41 ( 5 avg)
% 0.34/0.50 % Number of connectives : 383 ( 7 ~; 4 |; 18 &; 252 @)
% 0.34/0.50 % ( 7 <=>; 95 =>; 0 <=; 0 <~>)
% 0.34/0.50 % Maximal formula depth : 46 ( 2 avg)
% 0.34/0.50 % Number of types : 2 ( 0 usr)
% 0.34/0.50 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.34/0.50 % Number of symbols : 52 ( 49 usr; 42 con; 0-2 aty)
% 0.34/0.50 % Number of variables : 126 ( 15 ^; 95 !; 16 ?; 126 :)
% 0.34/0.50 % SPC : TH0_THM_EQU_NAR
% 0.34/0.50
% 0.34/0.50 % Comments : http://mathgate.info/detsetitem.php?id=87
% 0.34/0.50 %------------------------------------------------------------------------------
% 0.34/0.50 thf(in_type,type,
% 0.34/0.50 in: $i > $i > $o ).
% 0.34/0.50
% 0.34/0.50 thf(exu_type,type,
% 0.34/0.50 exu: ( $i > $o ) > $o ).
% 0.34/0.50
% 0.34/0.50 thf(exu,definition,
% 0.34/0.50 ( exu
% 0.34/0.50 = ( ^ [Xphi: $i > $o] :
% 0.34/0.50 ? [Xx: $i] :
% 0.34/0.50 ( ( Xphi @ Xx )
% 0.34/0.50 & ! [Xy: $i] :
% 0.34/0.50 ( ( Xphi @ Xy )
% 0.34/0.50 => ( Xx = Xy ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setextAx_type,type,
% 0.34/0.50 setextAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setextAx,definition,
% 0.34/0.50 ( setextAx
% 0.34/0.50 = ( ! [A: $i,B: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 <=> ( in @ Xx @ B ) )
% 0.34/0.50 => ( A = B ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyset_type,type,
% 0.34/0.50 emptyset: $i ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetAx_type,type,
% 0.34/0.50 emptysetAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetAx,definition,
% 0.34/0.50 ( emptysetAx
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoin_type,type,
% 0.34/0.50 setadjoin: $i > $i > $i ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinAx_type,type,
% 0.34/0.50 setadjoinAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinAx,definition,
% 0.34/0.50 ( setadjoinAx
% 0.34/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.50 <=> ( ( Xy = Xx )
% 0.34/0.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(powerset_type,type,
% 0.34/0.50 powerset: $i > $i ).
% 0.34/0.50
% 0.34/0.50 thf(powersetAx_type,type,
% 0.34/0.50 powersetAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(powersetAx,definition,
% 0.34/0.50 ( powersetAx
% 0.34/0.50 = ( ! [A: $i,B: $i] :
% 0.34/0.50 ( ( in @ B @ ( powerset @ A ) )
% 0.34/0.50 <=> ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setunion_type,type,
% 0.34/0.50 setunion: $i > $i ).
% 0.34/0.50
% 0.34/0.50 thf(setunionAx_type,type,
% 0.34/0.50 setunionAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setunionAx,definition,
% 0.34/0.50 ( setunionAx
% 0.34/0.50 = ( ! [A: $i,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ ( setunion @ A ) )
% 0.34/0.50 <=> ? [B: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 & ( in @ B @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(omega_type,type,
% 0.34/0.50 omega: $i ).
% 0.34/0.50
% 0.34/0.50 thf(omega0Ax_type,type,
% 0.34/0.50 omega0Ax: $o ).
% 0.34/0.50
% 0.34/0.50 thf(omega0Ax,definition,
% 0.34/0.50 ( omega0Ax
% 0.34/0.50 = ( in @ emptyset @ omega ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(omegaSAx_type,type,
% 0.34/0.50 omegaSAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(omegaSAx,definition,
% 0.34/0.50 ( omegaSAx
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ omega )
% 0.34/0.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(omegaIndAx_type,type,
% 0.34/0.50 omegaIndAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(omegaIndAx,definition,
% 0.34/0.50 ( omegaIndAx
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ( ( in @ emptyset @ A )
% 0.34/0.50 & ! [Xx: $i] :
% 0.34/0.50 ( ( ( in @ Xx @ omega )
% 0.34/0.50 & ( in @ Xx @ A ) )
% 0.34/0.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.34/0.50 => ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ omega )
% 0.34/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(replAx_type,type,
% 0.34/0.50 replAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(replAx,definition,
% 0.34/0.50 ( replAx
% 0.34/0.50 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( exu
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.34/0.50 => ? [B: $i] :
% 0.34/0.50 ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 <=> ? [Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ A )
% 0.34/0.50 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(foundationAx_type,type,
% 0.34/0.50 foundationAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(foundationAx,definition,
% 0.34/0.50 ( foundationAx
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.34/0.50 => ? [B: $i] :
% 0.34/0.50 ( ( in @ B @ A )
% 0.34/0.50 & ~ ? [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(wellorderingAx_type,type,
% 0.34/0.50 wellorderingAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(wellorderingAx,definition,
% 0.34/0.50 ( wellorderingAx
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ? [B: $i] :
% 0.34/0.50 ( ! [C: $i] :
% 0.34/0.50 ( ( in @ C @ B )
% 0.34/0.50 => ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ C )
% 0.34/0.50 => ( in @ Xx @ A ) ) )
% 0.34/0.50 & ! [Xx: $i,Xy: $i] :
% 0.34/0.50 ( ( ( in @ Xx @ A )
% 0.34/0.50 & ( in @ Xy @ A ) )
% 0.34/0.50 => ( ! [C: $i] :
% 0.34/0.50 ( ( in @ C @ B )
% 0.34/0.50 => ( ( in @ Xx @ C )
% 0.34/0.50 <=> ( in @ Xy @ C ) ) )
% 0.34/0.50 => ( Xx = Xy ) ) )
% 0.34/0.50 & ! [C: $i,D: $i] :
% 0.34/0.50 ( ( ( in @ C @ B )
% 0.34/0.50 & ( in @ D @ B ) )
% 0.34/0.50 => ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ C )
% 0.34/0.50 => ( in @ Xx @ D ) )
% 0.34/0.50 | ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ D )
% 0.34/0.50 => ( in @ Xx @ C ) ) ) )
% 0.34/0.50 & ! [C: $i] :
% 0.34/0.50 ( ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ C )
% 0.34/0.50 => ( in @ Xx @ A ) )
% 0.34/0.50 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.34/0.50 => ? [D: $i,Xx: $i] :
% 0.34/0.50 ( ( in @ D @ B )
% 0.34/0.50 & ( in @ Xx @ C )
% 0.34/0.50 & ~ ? [Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ D )
% 0.34/0.50 & ( in @ Xy @ C ) )
% 0.34/0.50 & ! [E: $i] :
% 0.34/0.50 ( ( in @ E @ B )
% 0.34/0.50 => ( ! [Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ E )
% 0.34/0.50 => ( in @ Xy @ D ) )
% 0.34/0.50 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(descr_type,type,
% 0.34/0.50 descr: ( $i > $o ) > $i ).
% 0.34/0.50
% 0.34/0.50 thf(descrp_type,type,
% 0.34/0.50 descrp: $o ).
% 0.34/0.50
% 0.34/0.50 thf(descrp,definition,
% 0.34/0.50 ( descrp
% 0.34/0.50 = ( ! [Xphi: $i > $o] :
% 0.34/0.50 ( ( exu
% 0.34/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.50 => ( Xphi
% 0.34/0.50 @ ( descr
% 0.34/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstr_type,type,
% 0.34/0.50 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrI_type,type,
% 0.34/0.50 dsetconstrI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrI,definition,
% 0.34/0.50 ( dsetconstrI
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( ( Xphi @ Xx )
% 0.34/0.50 => ( in @ Xx
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrEL_type,type,
% 0.34/0.50 dsetconstrEL: $o ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrEL,definition,
% 0.34/0.50 ( dsetconstrEL
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.50 => ( in @ Xx @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrER_type,type,
% 0.34/0.50 dsetconstrER: $o ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrER,definition,
% 0.34/0.50 ( dsetconstrER
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.50 => ( Xphi @ Xx ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(exuE1_type,type,
% 0.34/0.50 exuE1: $o ).
% 0.34/0.50
% 0.34/0.50 thf(exuE1,definition,
% 0.34/0.50 ( exuE1
% 0.34/0.50 = ( ! [Xphi: $i > $o] :
% 0.34/0.50 ( ( exu
% 0.34/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.50 => ? [Xx: $i] :
% 0.34/0.50 ( ( Xphi @ Xx )
% 0.34/0.50 & ! [Xy: $i] :
% 0.34/0.50 ( ( Xphi @ Xy )
% 0.34/0.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(prop2set_type,type,
% 0.34/0.50 prop2set: $o > $i ).
% 0.34/0.50
% 0.34/0.50 thf(prop2set,definition,
% 0.34/0.50 ( prop2set
% 0.34/0.50 = ( ^ [Xphi: $o] :
% 0.34/0.50 ( dsetconstr @ ( powerset @ emptyset )
% 0.34/0.50 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(prop2setE_type,type,
% 0.34/0.50 prop2setE: $o ).
% 0.34/0.50
% 0.34/0.50 thf(prop2setE,definition,
% 0.34/0.50 ( prop2setE
% 0.34/0.50 = ( ! [Xphi: $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.34/0.50 => Xphi ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetE_type,type,
% 0.34/0.50 emptysetE: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetE,definition,
% 0.34/0.50 ( emptysetE
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ emptyset )
% 0.34/0.50 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetimpfalse_type,type,
% 0.34/0.50 emptysetimpfalse: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetimpfalse,definition,
% 0.34/0.50 ( emptysetimpfalse
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ emptyset )
% 0.34/0.50 => $false ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(notinemptyset_type,type,
% 0.34/0.50 notinemptyset: $o ).
% 0.34/0.50
% 0.34/0.50 thf(notinemptyset,definition,
% 0.34/0.50 ( notinemptyset
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(exuE3e_type,type,
% 0.34/0.50 exuE3e: $o ).
% 0.34/0.50
% 0.34/0.50 thf(exuE3e,definition,
% 0.34/0.50 ( exuE3e
% 0.34/0.50 = ( ! [Xphi: $i > $o] :
% 0.34/0.50 ( ( exu
% 0.34/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.50 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setext_type,type,
% 0.34/0.50 setext: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setext,definition,
% 0.34/0.50 ( setext
% 0.34/0.50 = ( ! [A: $i,B: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( in @ Xx @ B ) )
% 0.34/0.50 => ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 => ( in @ Xx @ A ) )
% 0.34/0.50 => ( A = B ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyI_type,type,
% 0.34/0.50 emptyI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptyI,definition,
% 0.34/0.50 ( emptyI
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ~ ( in @ Xx @ A )
% 0.34/0.50 => ( A = emptyset ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(noeltsimpempty_type,type,
% 0.34/0.50 noeltsimpempty: $o ).
% 0.34/0.50
% 0.34/0.50 thf(noeltsimpempty,definition,
% 0.34/0.50 ( noeltsimpempty
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ~ ( in @ Xx @ A )
% 0.34/0.50 => ( A = emptyset ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setbeta_type,type,
% 0.34/0.50 setbeta: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setbeta,definition,
% 0.34/0.50 ( setbeta
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( ( in @ Xx
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.50 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(nonempty_type,type,
% 0.34/0.50 nonempty: $i > $o ).
% 0.34/0.50
% 0.34/0.50 thf(nonempty,definition,
% 0.34/0.50 ( nonempty
% 0.34/0.50 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyE1_type,type,
% 0.34/0.50 nonemptyE1: $o ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyE1,definition,
% 0.34/0.50 ( nonemptyE1
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ( nonempty @ A )
% 0.34/0.50 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyI_type,type,
% 0.34/0.50 nonemptyI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyI,definition,
% 0.34/0.50 ( nonemptyI
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( ( Xphi @ Xx )
% 0.34/0.50 => ( nonempty
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyI1_type,type,
% 0.34/0.50 nonemptyI1: $o ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyI1,definition,
% 0.34/0.50 ( nonemptyI1
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.34/0.50 => ( nonempty @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinIL_type,type,
% 0.34/0.50 setadjoinIL: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinIL,definition,
% 0.34/0.50 ( setadjoinIL
% 0.34/0.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyinunitempty_type,type,
% 0.34/0.50 emptyinunitempty: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptyinunitempty,definition,
% 0.34/0.50 ( emptyinunitempty
% 0.34/0.50 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinIR_type,type,
% 0.34/0.50 setadjoinIR: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinIR,definition,
% 0.34/0.50 ( setadjoinIR
% 0.34/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ A )
% 0.34/0.50 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinE_type,type,
% 0.34/0.50 setadjoinE: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinE,definition,
% 0.34/0.50 ( setadjoinE
% 0.34/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.50 => ! [Xphi: $o] :
% 0.34/0.50 ( ( ( Xy = Xx )
% 0.34/0.50 => Xphi )
% 0.34/0.50 => ( ( ( in @ Xy @ A )
% 0.34/0.50 => Xphi )
% 0.34/0.50 => Xphi ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinOr_type,type,
% 0.34/0.50 setadjoinOr: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinOr,definition,
% 0.34/0.50 ( setadjoinOr
% 0.34/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.50 => ( ( Xy = Xx )
% 0.34/0.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setoftrueEq_type,type,
% 0.34/0.50 setoftrueEq: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setoftrueEq,definition,
% 0.34/0.50 ( setoftrueEq
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xx: $i] : $true )
% 0.34/0.50 = A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(powersetI_type,type,
% 0.34/0.50 powersetI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(powersetI,definition,
% 0.34/0.50 ( powersetI
% 0.34/0.50 = ( ! [A: $i,B: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 => ( in @ Xx @ A ) )
% 0.34/0.50 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyinPowerset_type,type,
% 0.34/0.50 emptyinPowerset: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptyinPowerset,definition,
% 0.34/0.50 ( emptyinPowerset
% 0.34/0.50 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyInPowerset_type,type,
% 0.34/0.50 emptyInPowerset: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptyInPowerset,definition,
% 0.34/0.50 ( emptyInPowerset
% 0.34/0.50 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(powersetE_type,type,
% 0.34/0.50 powersetE: $o ).
% 0.34/0.50
% 0.34/0.50 thf(powersetE,definition,
% 0.34/0.50 ( powersetE
% 0.34/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.50 ( ( in @ B @ ( powerset @ A ) )
% 0.34/0.50 => ( ( in @ Xx @ B )
% 0.34/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setunionI,conjecture,
% 0.34/0.50 ( setextAx
% 0.34/0.50 => ( emptysetAx
% 0.34/0.50 => ( setadjoinAx
% 0.34/0.50 => ( powersetAx
% 0.34/0.50 => ( setunionAx
% 0.34/0.50 => ( omega0Ax
% 0.34/0.50 => ( omegaSAx
% 0.34/0.50 => ( omegaIndAx
% 0.34/0.50 => ( replAx
% 0.34/0.50 => ( foundationAx
% 0.34/0.50 => ( wellorderingAx
% 0.34/0.50 => ( descrp
% 0.34/0.50 => ( dsetconstrI
% 0.34/0.50 => ( dsetconstrEL
% 0.34/0.50 => ( dsetconstrER
% 0.34/0.50 => ( exuE1
% 0.34/0.50 => ( prop2setE
% 0.34/0.50 => ( emptysetE
% 0.34/0.50 => ( emptysetimpfalse
% 0.34/0.50 => ( notinemptyset
% 0.34/0.50 => ( exuE3e
% 0.34/0.50 => ( setext
% 0.34/0.50 => ( emptyI
% 0.34/0.50 => ( noeltsimpempty
% 0.34/0.50 => ( setbeta
% 0.34/0.50 => ( nonemptyE1
% 0.34/0.50 => ( nonemptyI
% 0.34/0.50 => ( nonemptyI1
% 0.34/0.50 => ( setadjoinIL
% 0.34/0.50 => ( emptyinunitempty
% 0.34/0.50 => ( setadjoinIR
% 0.34/0.50 => ( setadjoinE
% 0.34/0.50 => ( setadjoinOr
% 0.34/0.50 => ( setoftrueEq
% 0.34/0.50 => ( powersetI
% 0.34/0.50 => ( emptyinPowerset
% 0.34/0.50 => ( emptyInPowerset
% 0.34/0.50 => ( powersetE
% 0.34/0.50 => ! [A: $i,Xx: $i,B: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 => ( ( in @ B @ A )
% 0.34/0.50 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 %------------------------------------------------------------------------------
% 0.34/0.50 ------------------------
% 2.02/1.58 ---- Embedded in THF ---
% 2.02/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.02/1.58 %%% Generated on Tue Feb 24 12:25:19 EST 2026
% 2.02/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.02/1.58 %%% Logic specification used:
% 2.02/1.58 %%% thf(spec, logic, $$dhol).
% 2.02/1.58
% 2.02/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aBJSbpOuWU/DTF2DTF23191.p
% See solution above
% 2.02/1.58 ------------------------
% 2.02/1.59 ---- Cleaned THF ---
% 2.02/1.60 thf(in_type,type,
% 2.02/1.60 in: $i > $i > $o ).
% 2.02/1.60
% 2.02/1.60 thf(exu_type,type,
% 2.02/1.60 exu: ( $i > $o ) > $o ).
% 2.02/1.60
% 2.02/1.60 thf(exu,definition,
% 2.02/1.60 ( exu
% 2.02/1.60 = ( ^ [Xphi: $i > $o] :
% 2.02/1.60 ? [Xx: $i] :
% 2.02/1.60 ( ( Xphi @ Xx )
% 2.02/1.60 & ! [Xy: $i] :
% 2.02/1.60 ( ( Xphi @ Xy )
% 2.02/1.60 => ( Xx = Xy ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(setextAx_type,type,
% 2.02/1.60 setextAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(setextAx,definition,
% 2.02/1.60 ( setextAx
% 2.02/1.60 = ( ! [A: $i,B: $i] :
% 2.02/1.60 ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ A )
% 2.02/1.60 <=> ( in @ Xx @ B ) )
% 2.02/1.60 => ( A = B ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(emptyset_type,type,
% 2.02/1.60 emptyset: $i ).
% 2.02/1.60
% 2.02/1.60 thf(emptysetAx_type,type,
% 2.02/1.60 emptysetAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(emptysetAx,definition,
% 2.02/1.60 ( emptysetAx
% 2.02/1.60 = ( ! [Xx: $i] :
% 2.02/1.60 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoin_type,type,
% 2.02/1.60 setadjoin: $i > $i > $i ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoinAx_type,type,
% 2.02/1.60 setadjoinAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoinAx,definition,
% 2.02/1.60 ( setadjoinAx
% 2.02/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.02/1.60 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.02/1.60 <=> ( ( Xy = Xx )
% 2.02/1.60 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(powerset_type,type,
% 2.02/1.60 powerset: $i > $i ).
% 2.02/1.60
% 2.02/1.60 thf(powersetAx_type,type,
% 2.02/1.60 powersetAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(powersetAx,definition,
% 2.02/1.60 ( powersetAx
% 2.02/1.60 = ( ! [A: $i,B: $i] :
% 2.02/1.60 ( ( in @ B @ ( powerset @ A ) )
% 2.02/1.60 <=> ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ B )
% 2.02/1.60 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(setunion_type,type,
% 2.02/1.60 setunion: $i > $i ).
% 2.02/1.60
% 2.02/1.60 thf(setunionAx_type,type,
% 2.02/1.60 setunionAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(setunionAx,definition,
% 2.02/1.60 ( setunionAx
% 2.02/1.60 = ( ! [A: $i,Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ ( setunion @ A ) )
% 2.02/1.60 <=> ? [B: $i] :
% 2.02/1.60 ( ( in @ Xx @ B )
% 2.02/1.60 & ( in @ B @ A ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(omega_type,type,
% 2.02/1.60 omega: $i ).
% 2.02/1.60
% 2.02/1.60 thf(omega0Ax_type,type,
% 2.02/1.60 omega0Ax: $o ).
% 2.02/1.60
% 2.02/1.60 thf(omega0Ax,definition,
% 2.02/1.60 ( omega0Ax
% 2.02/1.60 = ( in @ emptyset @ omega ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(omegaSAx_type,type,
% 2.02/1.60 omegaSAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(omegaSAx,definition,
% 2.02/1.60 ( omegaSAx
% 2.02/1.60 = ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ omega )
% 2.02/1.60 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(omegaIndAx_type,type,
% 2.02/1.60 omegaIndAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(omegaIndAx,definition,
% 2.02/1.60 ( omegaIndAx
% 2.02/1.60 = ( ! [A: $i] :
% 2.02/1.60 ( ( ( in @ emptyset @ A )
% 2.02/1.60 & ! [Xx: $i] :
% 2.02/1.60 ( ( ( in @ Xx @ omega )
% 2.02/1.60 & ( in @ Xx @ A ) )
% 2.02/1.60 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.02/1.60 => ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ omega )
% 2.02/1.60 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(replAx_type,type,
% 2.02/1.60 replAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(replAx,definition,
% 2.02/1.60 ( replAx
% 2.02/1.60 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.02/1.60 ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ A )
% 2.02/1.60 => ( exu
% 2.02/1.60 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.02/1.60 => ? [B: $i] :
% 2.02/1.60 ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ B )
% 2.02/1.60 <=> ? [Xy: $i] :
% 2.02/1.60 ( ( in @ Xy @ A )
% 2.02/1.60 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(foundationAx_type,type,
% 2.02/1.60 foundationAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(foundationAx,definition,
% 2.02/1.60 ( foundationAx
% 2.02/1.60 = ( ! [A: $i] :
% 2.02/1.60 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.02/1.60 => ? [B: $i] :
% 2.02/1.60 ( ( in @ B @ A )
% 2.02/1.60 & ~ ? [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ B )
% 2.02/1.60 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(wellorderingAx_type,type,
% 2.02/1.60 wellorderingAx: $o ).
% 2.02/1.60
% 2.02/1.60 thf(wellorderingAx,definition,
% 2.02/1.60 ( wellorderingAx
% 2.02/1.60 = ( ! [A: $i] :
% 2.02/1.60 ? [B: $i] :
% 2.02/1.60 ( ! [C: $i] :
% 2.02/1.60 ( ( in @ C @ B )
% 2.02/1.60 => ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ C )
% 2.02/1.60 => ( in @ Xx @ A ) ) )
% 2.02/1.60 & ! [Xx: $i,Xy: $i] :
% 2.02/1.60 ( ( ( in @ Xx @ A )
% 2.02/1.60 & ( in @ Xy @ A ) )
% 2.02/1.60 => ( ! [C: $i] :
% 2.02/1.60 ( ( in @ C @ B )
% 2.02/1.60 => ( ( in @ Xx @ C )
% 2.02/1.60 <=> ( in @ Xy @ C ) ) )
% 2.02/1.60 => ( Xx = Xy ) ) )
% 2.02/1.60 & ! [C: $i,D: $i] :
% 2.02/1.60 ( ( ( in @ C @ B )
% 2.02/1.60 & ( in @ D @ B ) )
% 2.02/1.60 => ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ C )
% 2.02/1.60 => ( in @ Xx @ D ) )
% 2.02/1.60 | ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ D )
% 2.02/1.60 => ( in @ Xx @ C ) ) ) )
% 2.02/1.60 & ! [C: $i] :
% 2.02/1.60 ( ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ C )
% 2.02/1.60 => ( in @ Xx @ A ) )
% 2.02/1.60 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.02/1.60 => ? [D: $i,Xx: $i] :
% 2.02/1.60 ( ( in @ D @ B )
% 2.02/1.60 & ( in @ Xx @ C )
% 2.02/1.60 & ~ ? [Xy: $i] :
% 2.02/1.60 ( ( in @ Xy @ D )
% 2.02/1.60 & ( in @ Xy @ C ) )
% 2.02/1.60 & ! [E: $i] :
% 2.02/1.60 ( ( in @ E @ B )
% 2.02/1.60 => ( ! [Xy: $i] :
% 2.02/1.60 ( ( in @ Xy @ E )
% 2.02/1.60 => ( in @ Xy @ D ) )
% 2.02/1.60 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(descr_type,type,
% 2.02/1.60 descr: ( $i > $o ) > $i ).
% 2.02/1.60
% 2.02/1.60 thf(descrp_type,type,
% 2.02/1.60 descrp: $o ).
% 2.02/1.60
% 2.02/1.60 thf(descrp,definition,
% 2.02/1.60 ( descrp
% 2.02/1.60 = ( ! [Xphi: $i > $o] :
% 2.02/1.60 ( ( exu
% 2.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.02/1.60 => ( Xphi
% 2.02/1.60 @ ( descr
% 2.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(dsetconstr_type,type,
% 2.02/1.60 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.02/1.60
% 2.02/1.60 thf(dsetconstrI_type,type,
% 2.02/1.60 dsetconstrI: $o ).
% 2.02/1.60
% 2.02/1.60 thf(dsetconstrI,definition,
% 2.02/1.60 ( dsetconstrI
% 2.02/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ A )
% 2.02/1.60 => ( ( Xphi @ Xx )
% 2.02/1.60 => ( in @ Xx
% 2.02/1.60 @ ( dsetconstr @ A
% 2.02/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(dsetconstrEL_type,type,
% 2.02/1.60 dsetconstrEL: $o ).
% 2.02/1.60
% 2.02/1.60 thf(dsetconstrEL,definition,
% 2.02/1.60 ( dsetconstrEL
% 2.02/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.02/1.60 ( ( in @ Xx
% 2.02/1.60 @ ( dsetconstr @ A
% 2.02/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.02/1.60 => ( in @ Xx @ A ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(dsetconstrER_type,type,
% 2.02/1.60 dsetconstrER: $o ).
% 2.02/1.60
% 2.02/1.60 thf(dsetconstrER,definition,
% 2.02/1.60 ( dsetconstrER
% 2.02/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.02/1.60 ( ( in @ Xx
% 2.02/1.60 @ ( dsetconstr @ A
% 2.02/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.02/1.60 => ( Xphi @ Xx ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(exuE1_type,type,
% 2.02/1.60 exuE1: $o ).
% 2.02/1.60
% 2.02/1.60 thf(exuE1,definition,
% 2.02/1.60 ( exuE1
% 2.02/1.60 = ( ! [Xphi: $i > $o] :
% 2.02/1.60 ( ( exu
% 2.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.02/1.60 => ? [Xx: $i] :
% 2.02/1.60 ( ( Xphi @ Xx )
% 2.02/1.60 & ! [Xy: $i] :
% 2.02/1.60 ( ( Xphi @ Xy )
% 2.02/1.60 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(prop2set_type,type,
% 2.02/1.60 prop2set: $o > $i ).
% 2.02/1.60
% 2.02/1.60 thf(prop2set,definition,
% 2.02/1.60 ( prop2set
% 2.02/1.60 = ( ^ [Xphi: $o] :
% 2.02/1.60 ( dsetconstr @ ( powerset @ emptyset )
% 2.02/1.60 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(prop2setE_type,type,
% 2.02/1.60 prop2setE: $o ).
% 2.02/1.60
% 2.02/1.60 thf(prop2setE,definition,
% 2.02/1.60 ( prop2setE
% 2.02/1.60 = ( ! [Xphi: $o,Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.02/1.60 => Xphi ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(emptysetE_type,type,
% 2.02/1.60 emptysetE: $o ).
% 2.02/1.60
% 2.02/1.60 thf(emptysetE,definition,
% 2.02/1.60 ( emptysetE
% 2.02/1.60 = ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ emptyset )
% 2.02/1.60 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(emptysetimpfalse_type,type,
% 2.02/1.60 emptysetimpfalse: $o ).
% 2.02/1.60
% 2.02/1.60 thf(emptysetimpfalse,definition,
% 2.02/1.60 ( emptysetimpfalse
% 2.02/1.60 = ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ emptyset )
% 2.02/1.60 => $false ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(notinemptyset_type,type,
% 2.02/1.60 notinemptyset: $o ).
% 2.02/1.60
% 2.02/1.60 thf(notinemptyset,definition,
% 2.02/1.60 ( notinemptyset
% 2.02/1.60 = ( ! [Xx: $i] :
% 2.02/1.60 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(exuE3e_type,type,
% 2.02/1.60 exuE3e: $o ).
% 2.02/1.60
% 2.02/1.60 thf(exuE3e,definition,
% 2.02/1.60 ( exuE3e
% 2.02/1.60 = ( ! [Xphi: $i > $o] :
% 2.02/1.60 ( ( exu
% 2.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.02/1.60 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(setext_type,type,
% 2.02/1.60 setext: $o ).
% 2.02/1.60
% 2.02/1.60 thf(setext,definition,
% 2.02/1.60 ( setext
% 2.02/1.60 = ( ! [A: $i,B: $i] :
% 2.02/1.60 ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ A )
% 2.02/1.60 => ( in @ Xx @ B ) )
% 2.02/1.60 => ( ! [Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ B )
% 2.02/1.60 => ( in @ Xx @ A ) )
% 2.02/1.60 => ( A = B ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(emptyI_type,type,
% 2.02/1.60 emptyI: $o ).
% 2.02/1.60
% 2.02/1.60 thf(emptyI,definition,
% 2.02/1.60 ( emptyI
% 2.02/1.60 = ( ! [A: $i] :
% 2.02/1.60 ( ! [Xx: $i] :
% 2.02/1.60 ~ ( in @ Xx @ A )
% 2.02/1.60 => ( A = emptyset ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(noeltsimpempty_type,type,
% 2.02/1.60 noeltsimpempty: $o ).
% 2.02/1.60
% 2.02/1.60 thf(noeltsimpempty,definition,
% 2.02/1.60 ( noeltsimpempty
% 2.02/1.60 = ( ! [A: $i] :
% 2.02/1.60 ( ! [Xx: $i] :
% 2.02/1.60 ~ ( in @ Xx @ A )
% 2.02/1.60 => ( A = emptyset ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(setbeta_type,type,
% 2.02/1.60 setbeta: $o ).
% 2.02/1.60
% 2.02/1.60 thf(setbeta,definition,
% 2.02/1.60 ( setbeta
% 2.02/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ A )
% 2.02/1.60 => ( ( in @ Xx
% 2.02/1.60 @ ( dsetconstr @ A
% 2.02/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.02/1.60 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(nonempty_type,type,
% 2.02/1.60 nonempty: $i > $o ).
% 2.02/1.60
% 2.02/1.60 thf(nonempty,definition,
% 2.02/1.60 ( nonempty
% 2.02/1.60 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(nonemptyE1_type,type,
% 2.02/1.60 nonemptyE1: $o ).
% 2.02/1.60
% 2.02/1.60 thf(nonemptyE1,definition,
% 2.02/1.60 ( nonemptyE1
% 2.02/1.60 = ( ! [A: $i] :
% 2.02/1.60 ( ( nonempty @ A )
% 2.02/1.60 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(nonemptyI_type,type,
% 2.02/1.60 nonemptyI: $o ).
% 2.02/1.60
% 2.02/1.60 thf(nonemptyI,definition,
% 2.02/1.60 ( nonemptyI
% 2.02/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.02/1.60 ( ( in @ Xx @ A )
% 2.02/1.60 => ( ( Xphi @ Xx )
% 2.02/1.60 => ( nonempty
% 2.02/1.60 @ ( dsetconstr @ A
% 2.02/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(nonemptyI1_type,type,
% 2.02/1.60 nonemptyI1: $o ).
% 2.02/1.60
% 2.02/1.60 thf(nonemptyI1,definition,
% 2.02/1.60 ( nonemptyI1
% 2.02/1.60 = ( ! [A: $i] :
% 2.02/1.60 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.02/1.60 => ( nonempty @ A ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoinIL_type,type,
% 2.02/1.60 setadjoinIL: $o ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoinIL,definition,
% 2.02/1.60 ( setadjoinIL
% 2.02/1.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(emptyinunitempty_type,type,
% 2.02/1.60 emptyinunitempty: $o ).
% 2.02/1.60
% 2.02/1.60 thf(emptyinunitempty,definition,
% 2.02/1.60 ( emptyinunitempty
% 2.02/1.60 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoinIR_type,type,
% 2.02/1.60 setadjoinIR: $o ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoinIR,definition,
% 2.02/1.60 ( setadjoinIR
% 2.02/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.02/1.60 ( ( in @ Xy @ A )
% 2.02/1.60 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoinE_type,type,
% 2.02/1.60 setadjoinE: $o ).
% 2.02/1.60
% 2.02/1.60 thf(setadjoinE,definition,
% 2.02/1.60 ( setadjoinE
% 2.02/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.02/1.60 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.02/1.60 => ! [Xphi: $o] :
% 2.02/1.60 ( ( ( Xy = Xx )
% 2.02/1.60 => Xphi )
% 2.20/1.60 => ( ( ( in @ Xy @ A )
% 2.20/1.60 => Xphi )
% 2.20/1.60 => Xphi ) ) ) ) ) ).
% 2.20/1.60
% 2.20/1.60 thf(setadjoinOr_type,type,
% 2.20/1.60 setadjoinOr: $o ).
% 2.20/1.60
% 2.20/1.60 thf(setadjoinOr,definition,
% 2.20/1.60 ( setadjoinOr
% 2.20/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.20/1.60 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.20/1.60 => ( ( Xy = Xx )
% 2.20/1.60 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.20/1.60
% 2.20/1.60 thf(setoftrueEq_type,type,
% 2.20/1.60 setoftrueEq: $o ).
% 2.20/1.60
% 2.20/1.60 thf(setoftrueEq,definition,
% 2.20/1.60 ( setoftrueEq
% 2.20/1.60 = ( ! [A: $i] :
% 2.20/1.60 ( ( dsetconstr @ A
% 2.20/1.60 @ ^ [Xx: $i] : $true )
% 2.20/1.60 = A ) ) ) ).
% 2.20/1.60
% 2.20/1.60 thf(powersetI_type,type,
% 2.20/1.60 powersetI: $o ).
% 2.20/1.60
% 2.20/1.60 thf(powersetI,definition,
% 2.20/1.60 ( powersetI
% 2.20/1.60 = ( ! [A: $i,B: $i] :
% 2.20/1.60 ( ! [Xx: $i] :
% 2.20/1.60 ( ( in @ Xx @ B )
% 2.20/1.60 => ( in @ Xx @ A ) )
% 2.20/1.60 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.20/1.60
% 2.20/1.60 thf(emptyinPowerset_type,type,
% 2.20/1.60 emptyinPowerset: $o ).
% 2.20/1.60
% 2.20/1.60 thf(emptyinPowerset,definition,
% 2.20/1.60 ( emptyinPowerset
% 2.20/1.60 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.20/1.60
% 2.20/1.60 thf(emptyInPowerset_type,type,
% 2.20/1.60 emptyInPowerset: $o ).
% 2.20/1.60
% 2.20/1.60 thf(emptyInPowerset,definition,
% 2.20/1.60 ( emptyInPowerset
% 2.20/1.60 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.20/1.60
% 2.20/1.60 thf(powersetE_type,type,
% 2.20/1.60 powersetE: $o ).
% 2.20/1.60
% 2.20/1.60 thf(powersetE,definition,
% 2.20/1.60 ( powersetE
% 2.20/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.20/1.60 ( ( in @ B @ ( powerset @ A ) )
% 2.20/1.60 => ( ( in @ Xx @ B )
% 2.20/1.60 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.20/1.60
% 2.20/1.60 thf(setunionI,conjecture,
% 2.20/1.60 ( setextAx
% 2.20/1.60 => ( emptysetAx
% 2.20/1.60 => ( setadjoinAx
% 2.20/1.60 => ( powersetAx
% 2.20/1.60 => ( setunionAx
% 2.20/1.60 => ( omega0Ax
% 2.20/1.60 => ( omegaSAx
% 2.20/1.60 => ( omegaIndAx
% 2.20/1.60 => ( replAx
% 2.20/1.60 => ( foundationAx
% 2.20/1.60 => ( wellorderingAx
% 2.20/1.60 => ( descrp
% 2.20/1.60 => ( dsetconstrI
% 2.20/1.60 => ( dsetconstrEL
% 2.20/1.60 => ( dsetconstrER
% 2.20/1.60 => ( exuE1
% 2.20/1.60 => ( prop2setE
% 2.20/1.60 => ( emptysetE
% 2.20/1.60 => ( emptysetimpfalse
% 2.20/1.60 => ( notinemptyset
% 2.20/1.60 => ( exuE3e
% 2.20/1.60 => ( setext
% 2.20/1.60 => ( emptyI
% 2.20/1.60 => ( noeltsimpempty
% 2.20/1.60 => ( setbeta
% 2.20/1.60 => ( nonemptyE1
% 2.20/1.60 => ( nonemptyI
% 2.20/1.60 => ( nonemptyI1
% 2.20/1.60 => ( setadjoinIL
% 2.20/1.60 => ( emptyinunitempty
% 2.20/1.60 => ( setadjoinIR
% 2.20/1.60 => ( setadjoinE
% 2.20/1.60 => ( setadjoinOr
% 2.20/1.60 => ( setoftrueEq
% 2.20/1.60 => ( powersetI
% 2.20/1.60 => ( emptyinPowerset
% 2.20/1.60 => ( emptyInPowerset
% 2.20/1.60 => ( powersetE
% 2.20/1.60 => ! [A: $i,Xx: $i,B: $i] :
% 2.20/1.60 ( ( in @ Xx @ B )
% 2.20/1.60 => ( ( in @ B @ A )
% 2.20/1.60 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.20/1.60 ------------------------
% 2.20/1.62 % (23304)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/183Mi)
% 2.20/1.62 % (23305)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_23191 for (2999ds/4Mi)
% 2.20/1.62 % (23308)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_23191 for (2999ds/2Mi)
% 2.20/1.62 % (23310)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/18Mi)
% 2.20/1.62 % (23307)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/2Mi)
% 2.20/1.62 % (23306)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_23191 for (2999ds/27Mi)
% 2.20/1.62 % (23309)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_23191 for (2999ds/275Mi)
% 2.20/1.62 % (23307)Instruction limit reached!
% 2.20/1.62 % (23307)------------------------------
% 2.20/1.62 % (23307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.62 % (23307)Termination reason: Unknown
% 2.20/1.62 % (23307)Termination phase: shuffling
% 2.20/1.62 % (23308)Instruction limit reached!
% 2.20/1.62 % (23308)------------------------------
% 2.20/1.62 % (23308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.62 % (23308)Termination reason: Unknown
% 2.20/1.62 % (23308)Termination phase: shuffling
% 2.20/1.62
% 2.20/1.62 % (23308)Memory used [KB]: 1023
% 2.20/1.62 % (23308)Time elapsed: 0.003 s
% 2.20/1.62 % (23308)Instructions burned: 3 (million)
% 2.20/1.62 % (23308)------------------------------
% 2.20/1.62 % (23308)------------------------------
% 2.20/1.62
% 2.20/1.62 % (23307)Memory used [KB]: 1023
% 2.20/1.62 % (23307)Time elapsed: 0.003 s
% 2.20/1.62 % (23307)Instructions burned: 3 (million)
% 2.20/1.62 % (23307)------------------------------
% 2.20/1.62 % (23307)------------------------------
% 2.20/1.62 % (23305)Instruction limit reached!
% 2.20/1.62 % (23305)------------------------------
% 2.20/1.62 % (23305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.62 % (23305)Termination reason: Unknown
% 2.20/1.62 % (23305)Termination phase: shuffling
% 2.20/1.62
% 2.20/1.62 % (23305)Memory used [KB]: 1151
% 2.20/1.62 % (23305)Time elapsed: 0.004 s
% 2.20/1.62 % (23305)Instructions burned: 4 (million)
% 2.20/1.62 % (23305)------------------------------
% 2.20/1.62 % (23305)------------------------------
% 2.20/1.63 % (23310)Instruction limit reached!
% 2.20/1.63 % (23310)------------------------------
% 2.20/1.63 % (23310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.63 % (23310)Termination reason: Unknown
% 2.20/1.63 % (23310)Termination phase: Property scanning
% 2.20/1.63
% 2.20/1.63 % (23310)Memory used [KB]: 1535
% 2.20/1.63 % (23310)Time elapsed: 0.011 s
% 2.20/1.63 % (23310)Instructions burned: 19 (million)
% 2.20/1.63 % (23310)------------------------------
% 2.20/1.63 % (23310)------------------------------
% 2.20/1.63 % (23306)Instruction limit reached!
% 2.20/1.63 % (23306)------------------------------
% 2.20/1.63 % (23306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.63 % (23306)Termination reason: Unknown
% 2.20/1.63 % (23306)Termination phase: Saturation
% 2.20/1.63
% 2.20/1.63 % (23306)Memory used [KB]: 5756
% 2.20/1.63 % (23306)Time elapsed: 0.014 s
% 2.20/1.63 % (23306)Instructions burned: 27 (million)
% 2.20/1.63 % (23306)------------------------------
% 2.20/1.63 % (23306)------------------------------
% 2.20/1.64 % (23311)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/3Mi)
% 2.20/1.64 % (23312)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_23191 for (2999ds/37Mi)
% 2.20/1.64 % (23313)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_23191 for (2999ds/15Mi)
% 2.20/1.64 % (23311)Instruction limit reached!
% 2.20/1.64 % (23311)------------------------------
% 2.20/1.64 % (23311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.64 % (23311)Termination reason: Unknown
% 2.20/1.64 % (23311)Termination phase: shuffling
% 2.20/1.64
% 2.20/1.64 % (23311)Memory used [KB]: 1023
% 2.20/1.64 % (23311)Time elapsed: 0.003 s
% 2.20/1.64 % (23311)Instructions burned: 3 (million)
% 2.20/1.64 % (23311)------------------------------
% 2.20/1.64 % (23311)------------------------------
% 2.20/1.64 % (23313)Instruction limit reached!
% 2.20/1.64 % (23313)------------------------------
% 2.20/1.64 % (23313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.64 % (23313)Termination reason: Unknown
% 2.20/1.64 % (23313)Termination phase: Preprocessing 3
% 2.20/1.64
% 2.20/1.64 % (23314)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_23191 for (2999ds/3Mi)
% 2.20/1.64 % (23313)Memory used [KB]: 1407
% 2.20/1.64 % (23313)Time elapsed: 0.009 s
% 2.20/1.64 % (23313)Instructions burned: 15 (million)
% 2.20/1.64 % (23313)------------------------------
% 2.20/1.64 % (23313)------------------------------
% 2.20/1.64 % (23314)Instruction limit reached!
% 2.20/1.64 % (23314)------------------------------
% 2.20/1.64 % (23314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.64 % (23314)Termination reason: Unknown
% 2.20/1.64 % (23314)Termination phase: shuffling
% 2.20/1.64
% 2.20/1.64 % (23314)Memory used [KB]: 1023
% 2.20/1.64 % (23314)Time elapsed: 0.003 s
% 2.20/1.64 % (23314)Instructions burned: 3 (million)
% 2.20/1.64 % (23314)------------------------------
% 2.20/1.64 % (23314)------------------------------
% 2.20/1.65 % (23315)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_23191 for (2999ds/1041Mi)
% 2.20/1.65 % (23312)Instruction limit reached!
% 2.20/1.65 % (23312)------------------------------
% 2.20/1.65 % (23312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.65 % (23312)Termination reason: Unknown
% 2.20/1.65 % (23312)Termination phase: Saturation
% 2.20/1.65
% 2.20/1.65 % (23312)Memory used [KB]: 6012
% 2.20/1.65 % (23312)Time elapsed: 0.018 s
% 2.20/1.65 % (23312)Instructions burned: 39 (million)
% 2.20/1.65 % (23312)------------------------------
% 2.20/1.65 % (23312)------------------------------
% 2.20/1.65 % (23316)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/7Mi)
% 2.20/1.66 % (23316)Instruction limit reached!
% 2.20/1.66 % (23316)------------------------------
% 2.20/1.66 % (23316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.66 % (23316)Termination reason: Unknown
% 2.20/1.66 % (23316)Termination phase: Property scanning
% 2.20/1.66
% 2.20/1.66 % (23316)Memory used [KB]: 1151
% 2.20/1.66 % (23316)Time elapsed: 0.005 s
% 2.20/1.66 % (23316)Instructions burned: 8 (million)
% 2.20/1.66 % (23316)------------------------------
% 2.20/1.66 % (23316)------------------------------
% 2.20/1.66 % (23317)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/16Mi)
% 2.20/1.66 % (23318)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_23191 for (2999ds/3Mi)
% 2.20/1.67 % (23318)Instruction limit reached!
% 2.20/1.67 % (23318)------------------------------
% 2.20/1.67 % (23318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.67 % (23318)Termination reason: Unknown
% 2.20/1.67 % (23318)Termination phase: shuffling
% 2.20/1.67
% 2.20/1.67 % (23318)Memory used [KB]: 1023
% 2.20/1.67 % (23318)Time elapsed: 0.003 s
% 2.20/1.67 % (23318)Instructions burned: 3 (million)
% 2.20/1.67 % (23318)------------------------------
% 2.20/1.67 % (23318)------------------------------
% 2.20/1.67 % (23317)Instruction limit reached!
% 2.20/1.67 % (23317)------------------------------
% 2.20/1.67 % (23317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.67 % (23317)Termination reason: Unknown
% 2.20/1.67 % (23317)Termination phase: Twee Goal Transformation
% 2.20/1.67
% 2.20/1.67 % (23317)Memory used [KB]: 1279
% 2.20/1.67 % (23317)Time elapsed: 0.009 s
% 2.20/1.67 % (23317)Instructions burned: 17 (million)
% 2.20/1.67 % (23317)------------------------------
% 2.20/1.67 % (23317)------------------------------
% 2.20/1.67 % (23320)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/7Mi)
% 2.20/1.68 % (23320)Instruction limit reached!
% 2.20/1.68 % (23320)------------------------------
% 2.20/1.68 % (23320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.68 % (23320)Termination reason: Unknown
% 2.20/1.68 % (23320)Termination phase: Property scanning
% 2.20/1.68
% 2.20/1.68 % (23320)Memory used [KB]: 1151
% 2.20/1.68 % (23320)Time elapsed: 0.005 s
% 2.20/1.68 % (23320)Instructions burned: 8 (million)
% 2.20/1.68 % (23320)------------------------------
% 2.20/1.68 % (23320)------------------------------
% 2.20/1.68 % (23319)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_23191 for (2999ds/3Mi)
% 2.20/1.68 % (23321)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/3Mi)
% 2.20/1.68 % (23319)Instruction limit reached!
% 2.20/1.68 % (23319)------------------------------
% 2.20/1.68 % (23319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.68 % (23319)Termination reason: Unknown
% 2.20/1.68 % (23319)Termination phase: shuffling
% 2.20/1.68
% 2.20/1.68 % (23319)Memory used [KB]: 1023
% 2.20/1.68 % (23319)Time elapsed: 0.002 s
% 2.20/1.68 % (23319)Instructions burned: 4 (million)
% 2.20/1.68 % (23319)------------------------------
% 2.20/1.68 % (23319)------------------------------
% 2.20/1.68 % (23321)Instruction limit reached!
% 2.20/1.68 % (23321)------------------------------
% 2.20/1.68 % (23321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.68 % (23321)Termination reason: Unknown
% 2.20/1.68 % (23321)Termination phase: shuffling
% 2.20/1.68
% 2.20/1.68 % (23321)Memory used [KB]: 1151
% 2.20/1.68 % (23321)Time elapsed: 0.003 s
% 2.20/1.68 % (23321)Instructions burned: 4 (million)
% 2.20/1.68 % (23321)------------------------------
% 2.20/1.68 % (23321)------------------------------
% 2.20/1.68 % (23322)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/4Mi)
% 2.20/1.68 % (23322)Instruction limit reached!
% 2.20/1.68 % (23322)------------------------------
% 2.20/1.68 % (23322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.68 % (23322)Termination reason: Unknown
% 2.20/1.68 % (23322)Termination phase: shuffling
% 2.20/1.68
% 2.20/1.68 % (23322)Memory used [KB]: 1023
% 2.20/1.68 % (23322)Time elapsed: 0.003 s
% 2.20/1.68 % (23322)Instructions burned: 4 (million)
% 2.20/1.68 % (23322)------------------------------
% 2.20/1.68 % (23322)------------------------------
% 2.20/1.69 % (23324)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/710Mi)
% 2.20/1.69 % (23323)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/18Mi)
% 2.20/1.70 % (23325)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/6Mi)
% 2.20/1.70 % (23325)Instruction limit reached!
% 2.20/1.70 % (23325)------------------------------
% 2.20/1.70 % (23325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.70 % (23325)Termination reason: Unknown
% 2.20/1.70 % (23325)Termination phase: shuffling
% 2.20/1.70
% 2.20/1.70 % (23325)Memory used [KB]: 1151
% 2.20/1.70 % (23325)Time elapsed: 0.004 s
% 2.20/1.70 % (23325)Instructions burned: 6 (million)
% 2.20/1.70 % (23325)------------------------------
% 2.20/1.70 % (23325)------------------------------
% 2.20/1.70 % (23323)Instruction limit reached!
% 2.20/1.70 % (23323)------------------------------
% 2.20/1.70 % (23323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.70 % (23323)Termination reason: Unknown
% 2.20/1.70 % (23323)Termination phase: Saturation
% 2.20/1.70
% 2.20/1.70 % (23323)Memory used [KB]: 5628
% 2.20/1.70 % (23323)Time elapsed: 0.010 s
% 2.20/1.70 % (23323)Instructions burned: 18 (million)
% 2.20/1.70 % (23323)------------------------------
% 2.20/1.70 % (23323)------------------------------
% 2.20/1.70 % (23326)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_23191 for (2999ds/902Mi)
% 2.20/1.71 % (23304)Instruction limit reached!
% 2.20/1.71 % (23304)------------------------------
% 2.20/1.71 % (23304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.71 % (23304)Termination reason: Unknown
% 2.20/1.71 % (23304)Termination phase: Saturation
% 2.20/1.71
% 2.20/1.71 % (23304)Memory used [KB]: 6908
% 2.20/1.71 % (23304)Time elapsed: 0.093 s
% 2.20/1.71 % (23304)Instructions burned: 184 (million)
% 2.20/1.71 % (23304)------------------------------
% 2.20/1.71 % (23304)------------------------------
% 2.20/1.72 % (23327)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/21Mi)
% 2.20/1.72 % (23328)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23191 for (2999ds/5Mi)
% 2.20/1.72 % (23328)Instruction limit reached!
% 2.20/1.72 % (23328)------------------------------
% 2.20/1.72 % (23328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.72 % (23328)Termination reason: Unknown
% 2.20/1.72 % (23328)Termination phase: shuffling
% 2.20/1.72
% 2.20/1.72 % (23328)Memory used [KB]: 1151
% 2.20/1.72 % (23328)Time elapsed: 0.004 s
% 2.20/1.72 % (23328)Instructions burned: 6 (million)
% 2.20/1.72 % (23328)------------------------------
% 2.20/1.72 % (23328)------------------------------
% 2.20/1.73 % (23329)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23191 for (2998ds/6Mi)
% 2.20/1.73 % (23327)Instruction limit reached!
% 2.20/1.73 % (23327)------------------------------
% 2.20/1.73 % (23327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.73 % (23327)Termination reason: Unknown
% 2.20/1.73 % (23327)Termination phase: Property scanning
% 2.20/1.73
% 2.20/1.73 % (23327)Memory used [KB]: 1151
% 2.20/1.73 % (23327)Time elapsed: 0.011 s
% 2.20/1.73 % (23327)Instructions burned: 21 (million)
% 2.20/1.73 % (23327)------------------------------
% 2.20/1.73 % (23327)------------------------------
% 2.20/1.73 % (23329)Instruction limit reached!
% 2.20/1.73 % (23329)------------------------------
% 2.20/1.73 % (23329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.73 % (23329)Termination reason: Unknown
% 2.20/1.73 % (23329)Termination phase: Property scanning
% 2.20/1.73
% 2.20/1.73 % (23329)Memory used [KB]: 1151
% 2.20/1.73 % (23329)Time elapsed: 0.005 s
% 2.20/1.73 % (23329)Instructions burned: 7 (million)
% 2.20/1.73 % (23329)------------------------------
% 2.20/1.73 % (23329)------------------------------
% 2.20/1.73 % (23326)First to succeed.
% 2.20/1.74 % (23326)Refutation found. Thanks to Tanya!
% 2.20/1.74 % SZS status Theorem for DTF2THF_23191
% 2.20/1.74 % SZS output start Proof for DTF2THF_23191
% 2.20/1.74 thf(func_def_0, type, in: $i > $i > $o).
% 2.20/1.74 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.20/1.74 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.20/1.74 thf(func_def_8, type, powerset: $i > $i).
% 2.20/1.74 thf(func_def_10, type, setunion: $i > $i).
% 2.20/1.74 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.20/1.74 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.20/1.74 thf(func_def_26, type, prop2set: $o > $i).
% 2.20/1.74 thf(func_def_36, type, nonempty: $i > $o).
% 2.20/1.74 thf(func_def_63, type, sP1: $i > $i > $o).
% 2.20/1.74 thf(func_def_64, type, sP2: $i > $o).
% 2.20/1.74 thf(func_def_65, type, sP3: $i > $i > $o).
% 2.20/1.74 thf(func_def_66, type, sP4: $i > $i > $o).
% 2.20/1.74 thf(func_def_68, type, sK6: $i > $i).
% 2.20/1.74 thf(func_def_70, type, sK8: $i > $i).
% 2.20/1.74 thf(func_def_71, type, sK9: $i > $i > $i).
% 2.20/1.74 thf(func_def_85, type, sK23: $i > $o).
% 2.20/1.74 thf(func_def_90, type, sK28: $i > $o).
% 2.20/1.74 thf(func_def_91, type, sK29: $i > $o).
% 2.20/1.74 thf(func_def_101, type, sK39: $i > $i).
% 2.20/1.74 thf(func_def_103, type, sK41: $i > $o).
% 2.20/1.74 thf(func_def_111, type, sK49: $i > $i).
% 2.20/1.74 thf(func_def_114, type, sK52: $i > $o).
% 2.20/1.74 thf(func_def_118, type, sK56: $i > $i > $o).
% 2.20/1.74 thf(func_def_119, type, sK57: $i > $i).
% 2.20/1.74 thf(func_def_120, type, sK58: $i > $i).
% 2.20/1.74 thf(func_def_121, type, sK59: ($i > $i > $o) > $i > $i).
% 2.20/1.74 thf(func_def_122, type, sK60: ($i > $i > $o) > $i > $i).
% 2.20/1.74 thf(func_def_123, type, sK61: $i > ($i > $i > $o) > $i > $i).
% 2.20/1.74 thf(func_def_127, type, sK65: $i > $i > $i).
% 2.20/1.74 thf(func_def_130, type, sK68: $i > $i).
% 2.20/1.74 thf(func_def_134, type, sK72: $i > $i > $i).
% 2.20/1.74 thf(func_def_135, type, sK73: $i > $i).
% 2.20/1.74 thf(func_def_139, type, sK77: $i > $i > $i).
% 2.20/1.74 thf(func_def_140, type, sK78: $i > $i > $i).
% 2.20/1.74 thf(func_def_141, type, sK79: $i > $i > $i).
% 2.20/1.74 thf(func_def_142, type, sK80: $i > $i > $i).
% 2.20/1.74 thf(func_def_143, type, sK81: $i > $i > $i > $i).
% 2.20/1.74 thf(func_def_144, type, sK82: $i > $i).
% 2.20/1.74 thf(func_def_145, type, sK83: $i > $i).
% 2.20/1.74 thf(func_def_146, type, sK84: $i > $i).
% 2.20/1.74 thf(func_def_147, type, sK85: $i > $i).
% 2.20/1.74 thf(func_def_148, type, sK86: $i > $i > $i > $i).
% 2.20/1.74 thf(func_def_149, type, sK87: $i > $i > $i > $i).
% 2.20/1.74 thf(func_def_150, type, sK88: $i > $i > $i).
% 2.20/1.74 thf(func_def_151, type, sK89: $i > $i > $i).
% 2.20/1.74 thf(func_def_152, type, sK90: $i > $i > $i).
% 2.20/1.74 thf(func_def_153, type, sK91: $i > $i).
% 2.20/1.74 thf(func_def_154, type, sK92: $i > $i > $i).
% 2.20/1.74 thf(func_def_156, type, sK94: $i > $i).
% 2.20/1.74 thf(func_def_157, type, sK95: $i > $i).
% 2.20/1.74 thf(func_def_160, type, sK98: $i > $i > $i).
% 2.20/1.74 thf(func_def_161, type, sK99: $i > $i > $i).
% 2.20/1.74 thf(func_def_165, type, sK103: ($i > $o) > $i).
% 2.20/1.74 thf(func_def_166, type, sK104: $i > $o).
% 2.20/1.74 thf(func_def_167, type, sK105: $i > $i).
% 2.20/1.74 thf(func_def_170, type, sK108: $i > $i > $i).
% 2.20/1.74 thf(func_def_174, type, sK112: ($i > $o) > $i).
% 2.20/1.74 thf(func_def_175, type, sK113: $i > $o).
% 2.20/1.74 thf(func_def_176, type, sK114: $i > $o).
% 2.20/1.74 thf(func_def_180, type, ph118: !>[X0: $tType]:(X0)).
% 2.20/1.74 thf(f835,plain,(
% 2.20/1.74 $false),
% 2.20/1.74 inference(trivial_inequality_removal,[status(thm)],[f831])).
% 2.20/1.74 thf(f831,plain,(
% 2.20/1.74 ($true != $true)),
% 2.20/1.74 inference(superposition,[status(thm)],[f667,f541])).
% 2.20/1.74 thf(f541,plain,(
% 2.20/1.74 ($true = (in @ sK101 @ sK102))),
% 2.20/1.74 inference(cnf_transformation,[status(thm)],[f353])).
% 2.20/1.74 thf(f353,plain,(
% 2.20/1.74 (exuE3e = $true) & (setext = $true) & (setadjoinOr = $true) & (omegaIndAx = $true) & (nonemptyE1 = $true) & (setunionAx = $true) & (emptyI = $true) & (powersetI = $true) & (setadjoinIL = $true) & (emptysetE = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (wellorderingAx = $true) & (omega0Ax = $true) & (emptysetAx = $true) & (powersetAx = $true) & (dsetconstrEL = $true) & (nonemptyI = $true) & (descrp = $true) & (setbeta = $true) & (emptysetimpfalse = $true) & (setadjoinIR = $true) & (prop2setE = $true) & (powersetE = $true) & (notinemptyset = $true) & (setadjoinE = $true) & (emptyInPowerset = $true) & (setextAx = $true) & (omegaSAx = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (noeltsimpempty = $true) & (replAx = $true) & (emptyinPowerset = $true) & (dsetconstrI = $true) & (setoftrueEq = $true) & (foundationAx = $true) & (($true = (in @ sK101 @ sK102)) & ((in @ sK100 @ (setunion @ sK102)) != $true) & ($true = (in @ sK100 @ sK101)))),
% 2.20/1.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK100,sK101,sK102])],[f144,f352])).
% 2.20/1.74 thf(f352,plain,(
% 2.20/1.74 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X0 @ (setunion @ X2)) != $true) & ((in @ X0 @ X1) = $true)) => (($true = (in @ sK101 @ sK102)) & ((in @ sK100 @ (setunion @ sK102)) != $true) & ($true = (in @ sK100 @ sK101)))),
% 2.20/1.74 introduced(definition,[],[choice_axiom])).
% 2.20/1.74 thf(f144,plain,(
% 2.20/1.74 (exuE3e = $true) & (setext = $true) & (setadjoinOr = $true) & (omegaIndAx = $true) & (nonemptyE1 = $true) & (setunionAx = $true) & (emptyI = $true) & (powersetI = $true) & (setadjoinIL = $true) & (emptysetE = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (wellorderingAx = $true) & (omega0Ax = $true) & (emptysetAx = $true) & (powersetAx = $true) & (dsetconstrEL = $true) & (nonemptyI = $true) & (descrp = $true) & (setbeta = $true) & (emptysetimpfalse = $true) & (setadjoinIR = $true) & (prop2setE = $true) & (powersetE = $true) & (notinemptyset = $true) & (setadjoinE = $true) & (emptyInPowerset = $true) & (setextAx = $true) & (omegaSAx = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (noeltsimpempty = $true) & (replAx = $true) & (emptyinPowerset = $true) & (dsetconstrI = $true) & (setoftrueEq = $true) & (foundationAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X0 @ (setunion @ X2)) != $true) & ((in @ X0 @ X1) = $true))),
% 2.20/1.74 inference(flattening,[status(thm)],[f143])).
% 2.20/1.74 thf(f143,plain,(
% 2.20/1.74 (((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setunion @ X2)) != $true) & ((in @ X1 @ X2) = $true)) & ((in @ X0 @ X1) = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.20/1.74 inference(ennf_transformation,[status(thm)],[f103])).
% 2.20/1.74 thf(f103,plain,(
% 2.20/1.74 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => (((in @ X1 @ X2) = $true) => ((in @ X0 @ (setunion @ X2)) = $true)))))))))))))))))))))))))))))))))))))))))),
% 2.20/1.74 inference(fool_elimination,[status(thm)],[f102])).
% 2.20/1.74 thf(f102,plain,(
% 2.20/1.74 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ((in @ X1 @ X2) => (in @ X0 @ (setunion @ X2))))))))))))))))))))))))))))))))))))))))))),
% 2.20/1.74 inference(rectify,[status(thm)],[f43])).
% 2.20/1.74 thf(f43,negated_conjecture,(
% 2.20/1.74 ~(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 => ! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => (in @ X1 @ (setunion @ X3))))))))))))))))))))))))))))))))))))))))))),
% 2.20/1.74 inference(negated_conjecture,[status(cth)],[f42])).
% 2.20/1.74 thf(f42,conjecture,(
% 2.20/1.74 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 => ! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => (in @ X1 @ (setunion @ X3)))))))))))))))))))))))))))))))))))))))))),
% 2.20/1.74 file('/export/starexec/sandbox/tmp/tmp.aBJSbpOuWU/DTF2THF_23191.p',setunionI)).
% 2.20/1.74 thf(f667,plain,(
% 2.20/1.74 ($true != (in @ sK101 @ sK102))),
% 2.20/1.74 inference(trivial_inequality_removal,[status(thm)],[f656])).
% 2.20/1.74 thf(f656,plain,(
% 2.20/1.74 ($true != $true) | ($true != (in @ sK101 @ sK102))),
% 2.20/1.74 inference(superposition,[status(thm)],[f641,f539])).
% 2.20/1.74 thf(f539,plain,(
% 2.20/1.74 ($true = (in @ sK100 @ sK101))),
% 2.20/1.74 inference(cnf_transformation,[status(thm)],[f353])).
% 2.20/1.74 thf(f641,plain,(
% 2.20/1.74 ( ! [X0 : $i] : (($true != (in @ sK100 @ X0)) | ((in @ X0 @ sK102) != $true)) )),
% 2.20/1.74 inference(trivial_inequality_removal,[status(thm)],[f640])).
% 2.20/1.74 thf(f640,plain,(
% 2.20/1.74 ( ! [X0 : $i] : (((in @ X0 @ sK102) != $true) | ($true != (in @ sK100 @ X0)) | ($true != $true)) )),
% 2.20/1.74 inference(forward_demodulation,[status(thm)],[f637,f574])).
% 2.20/1.74 thf(f574,plain,(
% 2.20/1.74 (setunionAx = $true)),
% 2.20/1.74 inference(cnf_transformation,[status(thm)],[f353])).
% 2.20/1.74 thf(f637,plain,(
% 2.20/1.74 ( ! [X0 : $i] : (((in @ X0 @ sK102) != $true) | ($true != (in @ sK100 @ X0)) | (setunionAx != $true)) )),
% 2.20/1.74 inference(trivial_inequality_removal,[status(thm)],[f634])).
% 2.20/1.74 thf(f634,plain,(
% 2.20/1.74 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ sK100 @ X0)) | ((in @ X0 @ sK102) != $true) | (setunionAx != $true)) )),
% 2.20/1.74 inference(superposition,[status(thm)],[f540,f593])).
% 2.20/1.74 thf(f593,plain,(
% 2.20/1.74 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X2 @ X1) != $true) | (setunionAx != $true)) )),
% 2.20/1.74 inference(cnf_transformation,[status(thm)],[f369])).
% 2.20/1.74 thf(f369,plain,(
% 2.20/1.74 (! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setunion @ X1)) = $true) | ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true))) & ((($true = (in @ (sK108 @ X1 @ X0) @ X1)) & ((in @ X0 @ (sK108 @ X1 @ X0)) = $true)) | ((in @ X0 @ (setunion @ X1)) != $true))) | (setunionAx != $true)) & ((setunionAx = $true) | ((! [X6 : $i] : (((in @ X6 @ sK110) != $true) | ((in @ sK109 @ X6) != $true)) | ((in @ sK109 @ (setunion @ sK110)) != $true)) & ((((in @ sK111 @ sK110) = $true) & ($true = (in @ sK109 @ sK111))) | ((in @ sK109 @ (setunion @ sK110)) = $true))))),
% 2.20/1.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK108,sK109,sK110,sK111])],[f365,f368,f367,f366])).
% 2.20/1.74 thf(f366,plain,(
% 2.20/1.74 ! [X0 : $i,X1 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X0 @ X3) = $true)) => (($true = (in @ (sK108 @ X1 @ X0) @ X1)) & ((in @ X0 @ (sK108 @ X1 @ X0)) = $true)))),
% 2.20/1.74 introduced(definition,[],[choice_axiom])).
% 2.20/1.74 thf(f367,plain,(
% 2.20/1.74 ? [X4 : $i,X5 : $i] : ((! [X6 : $i] : (($true != (in @ X6 @ X5)) | ((in @ X4 @ X6) != $true)) | ((in @ X4 @ (setunion @ X5)) != $true)) & (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ((in @ X4 @ X7) = $true)) | ((in @ X4 @ (setunion @ X5)) = $true))) => ((! [X6 : $i] : (((in @ X6 @ sK110) != $true) | ((in @ sK109 @ X6) != $true)) | ((in @ sK109 @ (setunion @ sK110)) != $true)) & (? [X7 : $i] : (((in @ X7 @ sK110) = $true) & ($true = (in @ sK109 @ X7))) | ((in @ sK109 @ (setunion @ sK110)) = $true)))),
% 2.20/1.74 introduced(definition,[],[choice_axiom])).
% 2.20/1.74 thf(f368,plain,(
% 2.20/1.74 ? [X7 : $i] : (((in @ X7 @ sK110) = $true) & ($true = (in @ sK109 @ X7))) => (((in @ sK111 @ sK110) = $true) & ($true = (in @ sK109 @ sK111)))),
% 2.20/1.74 introduced(definition,[],[choice_axiom])).
% 2.20/1.74 thf(f365,plain,(
% 2.20/1.74 (! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setunion @ X1)) = $true) | ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true))) & (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X0 @ X3) = $true)) | ((in @ X0 @ (setunion @ X1)) != $true))) | (setunionAx != $true)) & ((setunionAx = $true) | ? [X4 : $i,X5 : $i] : ((! [X6 : $i] : (($true != (in @ X6 @ X5)) | ((in @ X4 @ X6) != $true)) | ((in @ X4 @ (setunion @ X5)) != $true)) & (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ((in @ X4 @ X7) = $true)) | ((in @ X4 @ (setunion @ X5)) = $true))))),
% 2.20/1.74 inference(rectify,[status(thm)],[f364])).
% 2.20/1.74 thf(f364,plain,(
% 2.20/1.74 (! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setunion @ X1)) = $true) | ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true))) & (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X0 @ X2) = $true)) | ((in @ X0 @ (setunion @ X1)) != $true))) | (setunionAx != $true)) & ((setunionAx = $true) | ? [X0 : $i,X1 : $i] : ((! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true)) | ((in @ X0 @ (setunion @ X1)) != $true)) & (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X0 @ X2) = $true)) | ((in @ X0 @ (setunion @ X1)) = $true))))),
% 2.20/1.74 inference(nnf_transformation,[status(thm)],[f113])).
% 2.20/1.74 thf(f113,plain,(
% 2.20/1.74 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) = $true) <=> ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X0 @ X2) = $true))) <=> (setunionAx = $true)),
% 2.20/1.74 inference(fool_elimination,[status(thm)],[f112])).
% 2.20/1.74 thf(f112,plain,(
% 2.20/1.74 (setunionAx = ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X1) & (in @ X0 @ X2)) <=> (in @ X0 @ (setunion @ X1))))),
% 2.20/1.74 inference(rectify,[status(thm)],[f6])).
% 2.20/1.74 thf(f6,axiom,(
% 2.20/1.74 (setunionAx = ! [X1 : $i,X3 : $i] : (? [X4 : $i] : ((in @ X4 @ X3) & (in @ X1 @ X4)) <=> (in @ X1 @ (setunion @ X3))))),
% 2.20/1.74 file('/export/starexec/sandbox/tmp/tmp.aBJSbpOuWU/DTF2THF_23191.p',setunionAx)).
% 2.20/1.74 thf(f540,plain,(
% 2.20/1.74 ((in @ sK100 @ (setunion @ sK102)) != $true)),
% 2.20/1.74 inference(cnf_transformation,[status(thm)],[f353])).
% 2.20/1.74 % SZS output end Proof for DTF2THF_23191
% 2.20/1.74 % (23326)------------------------------
% 2.20/1.74 % (23326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.20/1.74 % (23326)Termination reason: Refutation
% 2.20/1.74
% 2.20/1.74 % (23326)Memory used [KB]: 6268
% 2.20/1.74 % (23326)Time elapsed: 0.031 s
% 2.20/1.74 % (23326)Instructions burned: 56 (million)
% 2.20/1.74 % (23326)------------------------------
% 2.20/1.74 % (23326)------------------------------
% 2.20/1.74 % (23303)Success in time 0.125 s
%------------------------------------------------------------------------------