%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU527^1 : 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 : n009.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 2.13s 1.51s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 1102 ( 314 equ; 0 cnn)
% Maximal formula atoms : 46 ( 22 avg)
% Number of connectives : 715 ( 76 ~; 69 |; 161 &; 222 @)
% ( 8 <=>; 179 =>; 0 <=; 0 <~>)
% Maximal formula depth : 51 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 121 ( 118 usr; 54 con; 0-3 aty)
% Number of variables : 61 ( 0 ^; 40 !; 21 ?; 61 :)
% 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_68,type,
sP1: $i > $i > $o ).
thf(func_def_69,type,
sP2: $i > $o ).
thf(func_def_70,type,
sP3: $i > $i > $o ).
thf(func_def_71,type,
sP4: $i > $i > $o ).
thf(func_def_72,type,
sK5: $i > $i > $i ).
thf(func_def_75,type,
sK8: $i > $o ).
thf(func_def_76,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_81,type,
sK14: $i > $o ).
thf(func_def_82,type,
sK15: $i > $i ).
thf(func_def_83,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_84,type,
sK17: $i > $i ).
thf(func_def_90,type,
sK23: $i > $i > $i ).
thf(func_def_93,type,
sK26: $i > $i > $i ).
thf(func_def_94,type,
sK27: $i > $i > $i ).
thf(func_def_100,type,
sK33: $i > $i ).
thf(func_def_102,type,
sK35: $i > $i ).
thf(func_def_107,type,
sK40: $i > $i > $i ).
thf(func_def_108,type,
sK41: $i > $i ).
thf(func_def_119,type,
sK52: $i > $o ).
thf(func_def_121,type,
sK54: $i > $i ).
thf(func_def_124,type,
sK57: $i > $i ).
thf(func_def_128,type,
sK61: $i > $i > $o ).
thf(func_def_129,type,
sK62: $i > $i ).
thf(func_def_130,type,
sK63: $i > $i ).
thf(func_def_131,type,
sK64: ( $i > $i > $o ) > $i > $i ).
thf(func_def_132,type,
sK65: ( $i > $i > $o ) > $i > $i ).
thf(func_def_133,type,
sK66: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_137,type,
sK70: $i > $o ).
thf(func_def_144,type,
sK77: $o > $i > $i > $i ).
thf(func_def_148,type,
sK81: $i > $i > $i ).
thf(func_def_149,type,
sK82: $i > $i > $i ).
thf(func_def_150,type,
sK83: $i > $i > $i ).
thf(func_def_151,type,
sK84: $i > $i > $i ).
thf(func_def_152,type,
sK85: $i > $i > $i > $i ).
thf(func_def_153,type,
sK86: $i > $i ).
thf(func_def_154,type,
sK87: $i > $i ).
thf(func_def_155,type,
sK88: $i > $i ).
thf(func_def_156,type,
sK89: $i > $i ).
thf(func_def_157,type,
sK90: $i > $i > $i ).
thf(func_def_158,type,
sK91: $i > $i > $i > $i ).
thf(func_def_159,type,
sK92: $i > $i > $i > $i ).
thf(func_def_160,type,
sK93: $i > $i > $i ).
thf(func_def_161,type,
sK94: $i > $i > $i ).
thf(func_def_163,type,
sK96: $i > $i ).
thf(func_def_164,type,
sK97: $i > $i ).
thf(func_def_165,type,
sK98: $i > $i ).
thf(func_def_166,type,
sK99: $i > $i > $i ).
thf(func_def_168,type,
sK101: ( $i > $o ) > $i ).
thf(func_def_169,type,
sK102: $i > $o ).
thf(func_def_170,type,
sK103: $i > $i ).
thf(func_def_172,type,
sK105: $i > $i > $i ).
thf(func_def_178,type,
sK111: $i > $o ).
thf(func_def_183,type,
sK116: $i > $o ).
thf(func_def_185,type,
sK118: $i > $i ).
thf(func_def_191,type,
sK124: $i > $o ).
thf(func_def_194,type,
sK127: $i > $o ).
thf(func_def_198,type,
ph131:
!>[X0: $tType] : X0 ).
thf(f759,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f726,f754,f758]) ).
thf(f758,plain,
~ spl130_1,
inference(avatar_contradiction_clause,[status(thm)],[f757]) ).
thf(f757,plain,
( $false
| ~ spl130_1 ),
inference(trivial_inequality_removal,[status(thm)],[f756]) ).
thf(f756,plain,
( ( sK11 != sK11 )
| ~ spl130_1 ),
inference(superposition,[status(thm)],[f458,f718]) ).
thf(f718,plain,
( ( sK12 = sK11 )
| ~ spl130_1 ),
inference(avatar_component_clause,[status(thm)],[f716]) ).
thf(f716,definition,
( spl130_1
<=> ( sK12 = sK11 ) ),
introduced(definition,[new_symbols(naming,[spl130_1])],[avatar_definition]) ).
thf(f458,plain,
sK12 != sK11,
inference(cnf_transformation,[status(thm)],[f216]) ).
thf(f216,plain,
( ( powersetI = $true )
& ( exuE3e = $true )
& ( emptyinunitempty = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrER = $true )
& ( emptysetE = $true )
& ( setoftrueEq = $true )
& ( subPowSU = $true )
& ( emptyinPowerset = $true )
& ( setunionAx = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( wellorderingAx = $true )
& ( notinemptyset = $true )
& ( replAx = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinOr = $true )
& ( nonemptyI = $true )
& ( emptysetAx = $true )
& ( sK12 != sK11 )
& ( ( in @ sK12 @ ( setadjoin @ sK11 @ emptyset ) )
= $true )
& ( omegaIndAx = $true )
& ( descrp = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( dsetconstrEL = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( setunionE = $true )
& ( nonemptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( setadjoinIL = $true )
& ( emptyInPowerset = $true )
& ( powersetE = $true )
& ( setbeta = $true )
& ( omegaSAx = $true )
& ( setadjoinIR = $true )
& ( setunionI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f185,f215]) ).
thf(f215,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) )
=> ( ( sK12 != sK11 )
& ( ( in @ sK12 @ ( setadjoin @ sK11 @ emptyset ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f185,plain,
( ( powersetI = $true )
& ( exuE3e = $true )
& ( emptyinunitempty = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrER = $true )
& ( emptysetE = $true )
& ( setoftrueEq = $true )
& ( subPowSU = $true )
& ( emptyinPowerset = $true )
& ( setunionAx = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( wellorderingAx = $true )
& ( notinemptyset = $true )
& ( replAx = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinOr = $true )
& ( nonemptyI = $true )
& ( emptysetAx = $true )
& ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) )
& ( omegaIndAx = $true )
& ( descrp = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( dsetconstrEL = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( setunionE = $true )
& ( nonemptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( setadjoinIL = $true )
& ( emptyInPowerset = $true )
& ( powersetE = $true )
& ( setbeta = $true )
& ( omegaSAx = $true )
& ( setadjoinIR = $true )
& ( setunionI = $true ) ),
inference(flattening,[status(thm)],[f184]) ).
thf(f184,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) )
& ( nonemptyImpWitness = $true )
& ( 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)],[f124]) ).
thf(f124,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 )
=> ( ( nonemptyImpWitness = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f123]) ).
thf(f123,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
=> ( nonemptyImpWitness
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f48]) ).
thf(f48,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
=> ( nonemptyImpWitness
=> ! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
thf(f47,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
=> ( nonemptyImpWitness
=> ! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.p9jyL4yqSG/DTF2THF_5545.p',uniqinunit) ).
thf(f754,plain,
~ spl130_2,
inference(avatar_contradiction_clause,[status(thm)],[f753]) ).
thf(f753,plain,
( $false
| ~ spl130_2 ),
inference(trivial_inequality_removal,[status(thm)],[f752]) ).
thf(f752,plain,
( ( $true != $true )
| ~ spl130_2 ),
inference(superposition,[status(thm)],[f740,f464]) ).
thf(f464,plain,
notinemptyset = $true,
inference(cnf_transformation,[status(thm)],[f216]) ).
thf(f740,plain,
( ( notinemptyset != $true )
| ~ spl130_2 ),
inference(trivial_inequality_removal,[status(thm)],[f737]) ).
thf(f737,plain,
( ( notinemptyset != $true )
| ( $true != $true )
| ~ spl130_2 ),
inference(superposition,[status(thm)],[f485,f722]) ).
thf(f722,plain,
( ( ( in @ sK12 @ emptyset )
= $true )
| ~ spl130_2 ),
inference(avatar_component_clause,[status(thm)],[f720]) ).
thf(f720,definition,
( spl130_2
<=> ( ( in @ sK12 @ emptyset )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl130_2])],[avatar_definition]) ).
thf(f485,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ),
inference(cnf_transformation,[status(thm)],[f220]) ).
thf(f220,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( notinemptyset != $true ) )
& ( ( notinemptyset = $true )
| ( ( in @ sK13 @ emptyset )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f218,f219]) ).
thf(f219,plain,
( ? [X1: $i] :
( ( in @ X1 @ emptyset )
= $true )
=> ( ( in @ sK13 @ emptyset )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f218,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( notinemptyset != $true ) )
& ( ( notinemptyset = $true )
| ? [X1: $i] :
( ( in @ X1 @ emptyset )
= $true ) ) ),
inference(rectify,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( notinemptyset != $true ) )
& ( ( notinemptyset = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( notinemptyset = $true ) ),
inference(flattening,[status(thm)],[f100]) ).
thf(f100,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( notinemptyset = $true ) ),
inference(fool_elimination,[status(thm)],[f99]) ).
thf(f99,plain,
! [X0: $i] :
( ( ~ ( in @ X0 @ emptyset ) )
= notinemptyset ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,axiom,
! [X1: $i] :
( ( ~ ( in @ X1 @ emptyset ) )
= notinemptyset ),
file('/export/starexec/sandbox/tmp/tmp.p9jyL4yqSG/DTF2THF_5545.p',notinemptyset) ).
thf(f726,plain,
( spl130_1
| spl130_2 ),
inference(avatar_split_clause,[status(thm)],[f725,f720,f716]) ).
thf(f725,plain,
( ( ( in @ sK12 @ emptyset )
= $true )
| ( sK12 = sK11 ) ),
inference(trivial_inequality_removal,[status(thm)],[f724]) ).
thf(f724,plain,
( ( $true != $true )
| ( ( in @ sK12 @ emptyset )
= $true )
| ( sK12 = sK11 ) ),
inference(forward_demodulation,[status(thm)],[f711,f450]) ).
thf(f450,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f216]) ).
thf(f711,plain,
( ( setadjoinAx != $true )
| ( sK12 = sK11 )
| ( ( in @ sK12 @ emptyset )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f706]) ).
thf(f706,plain,
( ( $true != $true )
| ( sK12 = sK11 )
| ( setadjoinAx != $true )
| ( ( in @ sK12 @ emptyset )
= $true ) ),
inference(superposition,[status(thm)],[f659,f457]) ).
thf(f457,plain,
( ( in @ sK12 @ ( setadjoin @ sK11 @ emptyset ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f216]) ).
thf(f659,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f407]) ).
thf(f407,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( X1 != X2 )
& ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ( X1 = X2 )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( ( sK120 != sK121 )
& ( ( in @ sK120 @ sK119 )
!= $true ) )
| ( ( in @ sK120 @ ( setadjoin @ sK121 @ sK119 ) )
!= $true ) )
& ( ( sK120 = sK121 )
| ( ( in @ sK120 @ sK119 )
= $true )
| ( ( in @ sK120 @ ( setadjoin @ sK121 @ sK119 ) )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK119,sK120,sK121])],[f405,f406]) ).
thf(f406,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( X4 != X5 )
& ( ( in @ X4 @ X3 )
!= $true ) )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true ) )
& ( ( X4 = X5 )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true ) ) )
=> ( ( ( ( sK120 != sK121 )
& ( ( in @ sK120 @ sK119 )
!= $true ) )
| ( ( in @ sK120 @ ( setadjoin @ sK121 @ sK119 ) )
!= $true ) )
& ( ( sK120 = sK121 )
| ( ( in @ sK120 @ sK119 )
= $true )
| ( ( in @ sK120 @ ( setadjoin @ sK121 @ sK119 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f405,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( X1 != X2 )
& ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ( X1 = X2 )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( X4 != X5 )
& ( ( in @ X4 @ X3 )
!= $true ) )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true ) )
& ( ( X4 = X5 )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f404]) ).
thf(f404,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( X1 != X2 )
& ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ( X1 = X2 )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( X1 != X2 )
& ( ( in @ X1 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) )
& ( ( X1 = X2 )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f403]) ).
thf(f403,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( X1 != X2 )
& ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ( X1 = X2 )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( X1 != X2 )
& ( ( in @ X1 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) )
& ( ( X1 = X2 )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
thf(f64,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
<=> ( ( X1 = X2 )
| ( ( in @ X1 @ X0 )
= $true ) ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
<=> ( ( in @ X1 @ X0 )
| ( X1 = X2 ) ) )
= setadjoinAx ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
<=> ( ( in @ X2 @ X3 )
| ( X1 = X2 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox/tmp/tmp.p9jyL4yqSG/DTF2THF_5545.p',setadjoinAx) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU527^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n009.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:25:40 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.46 ---- Original DTF file ---
% 0.32/0.46 thf(spec,logic,$$dhol).
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 % File : SEU527^1 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.46 % Domain : Set Theory
% 0.32/0.46 % Problem : Preliminary Notions - Equality Laws
% 0.32/0.46 % Version : Especial.
% 0.32/0.46 % English : (! x:i.! y:i.in x (setadjoin y emptyset) -> x = y)
% 0.32/0.46
% 0.32/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.46 % Source : [Bro08]
% 0.32/0.46 % Names : ZFC029g [Bro08]
% 0.32/0.46
% 0.32/0.46 % Status : Theorem
% 0.32/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.32/0.46 % Syntax : Number of formulae : 101 ( 46 unt; 54 typ; 46 def)
% 0.32/0.46 % Number of atoms : 258 ( 60 equ; 0 cnn)
% 0.32/0.46 % Maximal formula atoms : 45 ( 5 avg)
% 0.32/0.46 % Number of connectives : 421 ( 7 ~; 4 |; 19 &; 275 @)
% 0.32/0.46 % ( 8 <=>; 108 =>; 0 <=; 0 <~>)
% 0.32/0.46 % Maximal formula depth : 50 ( 2 avg)
% 0.32/0.46 % Number of types : 2 ( 0 usr)
% 0.32/0.46 % Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% 0.32/0.46 % Number of symbols : 57 ( 54 usr; 47 con; 0-2 aty)
% 0.32/0.46 % Number of variables : 140 ( 16 ^; 106 !; 18 ?; 140 :)
% 0.32/0.46 % SPC : TH0_THM_EQU_NAR
% 0.32/0.46
% 0.32/0.46 % Comments : http://mathgate.info/detsetitem.php?id=93
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 thf(in_type,type,
% 0.32/0.46 in: $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(exu_type,type,
% 0.32/0.46 exu: ( $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(exu,definition,
% 0.32/0.46 ( exu
% 0.32/0.46 = ( ^ [Xphi: $i > $o] :
% 0.32/0.46 ? [Xx: $i] :
% 0.32/0.46 ( ( Xphi @ Xx )
% 0.32/0.46 & ! [Xy: $i] :
% 0.32/0.46 ( ( Xphi @ Xy )
% 0.32/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setextAx_type,type,
% 0.32/0.46 setextAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setextAx,definition,
% 0.32/0.46 ( setextAx
% 0.32/0.46 = ( ! [A: $i,B: $i] :
% 0.32/0.46 ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ A )
% 0.32/0.46 <=> ( in @ Xx @ B ) )
% 0.32/0.46 => ( A = B ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(emptyset_type,type,
% 0.32/0.46 emptyset: $i ).
% 0.32/0.46
% 0.32/0.46 thf(emptysetAx_type,type,
% 0.32/0.46 emptysetAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(emptysetAx,definition,
% 0.32/0.46 ( emptysetAx
% 0.32/0.46 = ( ! [Xx: $i] :
% 0.32/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoin_type,type,
% 0.32/0.46 setadjoin: $i > $i > $i ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinAx_type,type,
% 0.32/0.46 setadjoinAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinAx,definition,
% 0.32/0.46 ( setadjoinAx
% 0.32/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/0.46 <=> ( ( Xy = Xx )
% 0.32/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(powerset_type,type,
% 0.32/0.46 powerset: $i > $i ).
% 0.32/0.46
% 0.32/0.46 thf(powersetAx_type,type,
% 0.32/0.46 powersetAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(powersetAx,definition,
% 0.32/0.46 ( powersetAx
% 0.32/0.46 = ( ! [A: $i,B: $i] :
% 0.32/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.32/0.46 <=> ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ B )
% 0.32/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setunion_type,type,
% 0.32/0.46 setunion: $i > $i ).
% 0.32/0.46
% 0.32/0.46 thf(setunionAx_type,type,
% 0.32/0.46 setunionAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setunionAx,definition,
% 0.32/0.46 ( setunionAx
% 0.32/0.46 = ( ! [A: $i,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/0.46 <=> ? [B: $i] :
% 0.32/0.46 ( ( in @ Xx @ B )
% 0.32/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(omega_type,type,
% 0.32/0.46 omega: $i ).
% 0.32/0.46
% 0.32/0.46 thf(omega0Ax_type,type,
% 0.32/0.46 omega0Ax: $o ).
% 0.32/0.46
% 0.32/0.46 thf(omega0Ax,definition,
% 0.32/0.46 ( omega0Ax
% 0.32/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(omegaSAx_type,type,
% 0.32/0.46 omegaSAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(omegaSAx,definition,
% 0.32/0.46 ( omegaSAx
% 0.32/0.46 = ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ omega )
% 0.32/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(omegaIndAx_type,type,
% 0.32/0.46 omegaIndAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(omegaIndAx,definition,
% 0.32/0.46 ( omegaIndAx
% 0.32/0.46 = ( ! [A: $i] :
% 0.32/0.46 ( ( ( in @ emptyset @ A )
% 0.32/0.46 & ! [Xx: $i] :
% 0.32/0.46 ( ( ( in @ Xx @ omega )
% 0.32/0.46 & ( in @ Xx @ A ) )
% 0.32/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.32/0.46 => ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ omega )
% 0.32/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(replAx_type,type,
% 0.32/0.46 replAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(replAx,definition,
% 0.32/0.46 ( replAx
% 0.32/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.32/0.46 ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ A )
% 0.32/0.46 => ( exu
% 0.32/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.32/0.46 => ? [B: $i] :
% 0.32/0.46 ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ B )
% 0.32/0.46 <=> ? [Xy: $i] :
% 0.32/0.46 ( ( in @ Xy @ A )
% 0.32/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(foundationAx_type,type,
% 0.32/0.46 foundationAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(foundationAx,definition,
% 0.32/0.46 ( foundationAx
% 0.32/0.46 = ( ! [A: $i] :
% 0.32/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/0.46 => ? [B: $i] :
% 0.32/0.46 ( ( in @ B @ A )
% 0.32/0.46 & ~ ? [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ B )
% 0.32/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(wellorderingAx_type,type,
% 0.32/0.46 wellorderingAx: $o ).
% 0.32/0.46
% 0.32/0.46 thf(wellorderingAx,definition,
% 0.32/0.46 ( wellorderingAx
% 0.32/0.46 = ( ! [A: $i] :
% 0.32/0.46 ? [B: $i] :
% 0.32/0.46 ( ! [C: $i] :
% 0.32/0.46 ( ( in @ C @ B )
% 0.32/0.46 => ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ C )
% 0.32/0.46 => ( in @ Xx @ A ) ) )
% 0.32/0.46 & ! [Xx: $i,Xy: $i] :
% 0.32/0.46 ( ( ( in @ Xx @ A )
% 0.32/0.46 & ( in @ Xy @ A ) )
% 0.32/0.46 => ( ! [C: $i] :
% 0.32/0.46 ( ( in @ C @ B )
% 0.32/0.46 => ( ( in @ Xx @ C )
% 0.32/0.46 <=> ( in @ Xy @ C ) ) )
% 0.32/0.46 => ( Xx = Xy ) ) )
% 0.32/0.46 & ! [C: $i,D: $i] :
% 0.32/0.46 ( ( ( in @ C @ B )
% 0.32/0.46 & ( in @ D @ B ) )
% 0.32/0.46 => ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ C )
% 0.32/0.46 => ( in @ Xx @ D ) )
% 0.32/0.46 | ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ D )
% 0.32/0.46 => ( in @ Xx @ C ) ) ) )
% 0.32/0.46 & ! [C: $i] :
% 0.32/0.46 ( ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ C )
% 0.32/0.46 => ( in @ Xx @ A ) )
% 0.32/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.32/0.46 => ? [D: $i,Xx: $i] :
% 0.32/0.46 ( ( in @ D @ B )
% 0.32/0.46 & ( in @ Xx @ C )
% 0.32/0.46 & ~ ? [Xy: $i] :
% 0.32/0.46 ( ( in @ Xy @ D )
% 0.32/0.46 & ( in @ Xy @ C ) )
% 0.32/0.46 & ! [E: $i] :
% 0.32/0.46 ( ( in @ E @ B )
% 0.32/0.46 => ( ! [Xy: $i] :
% 0.32/0.46 ( ( in @ Xy @ E )
% 0.32/0.46 => ( in @ Xy @ D ) )
% 0.32/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(descr_type,type,
% 0.32/0.46 descr: ( $i > $o ) > $i ).
% 0.32/0.46
% 0.32/0.46 thf(descrp_type,type,
% 0.32/0.46 descrp: $o ).
% 0.32/0.46
% 0.32/0.46 thf(descrp,definition,
% 0.32/0.46 ( descrp
% 0.32/0.46 = ( ! [Xphi: $i > $o] :
% 0.32/0.46 ( ( exu
% 0.32/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.46 => ( Xphi
% 0.32/0.46 @ ( descr
% 0.32/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(dsetconstr_type,type,
% 0.32/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.32/0.46
% 0.32/0.46 thf(dsetconstrI_type,type,
% 0.32/0.46 dsetconstrI: $o ).
% 0.32/0.46
% 0.32/0.46 thf(dsetconstrI,definition,
% 0.32/0.46 ( dsetconstrI
% 0.32/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ A )
% 0.32/0.46 => ( ( Xphi @ Xx )
% 0.32/0.46 => ( in @ Xx
% 0.32/0.46 @ ( dsetconstr @ A
% 0.32/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(dsetconstrEL_type,type,
% 0.32/0.46 dsetconstrEL: $o ).
% 0.32/0.46
% 0.32/0.46 thf(dsetconstrEL,definition,
% 0.32/0.46 ( dsetconstrEL
% 0.32/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx
% 0.32/0.46 @ ( dsetconstr @ A
% 0.32/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(dsetconstrER_type,type,
% 0.32/0.46 dsetconstrER: $o ).
% 0.32/0.46
% 0.32/0.46 thf(dsetconstrER,definition,
% 0.32/0.46 ( dsetconstrER
% 0.32/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx
% 0.32/0.46 @ ( dsetconstr @ A
% 0.32/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(exuE1_type,type,
% 0.32/0.46 exuE1: $o ).
% 0.32/0.46
% 0.32/0.46 thf(exuE1,definition,
% 0.32/0.46 ( exuE1
% 0.32/0.46 = ( ! [Xphi: $i > $o] :
% 0.32/0.46 ( ( exu
% 0.32/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.46 => ? [Xx: $i] :
% 0.32/0.46 ( ( Xphi @ Xx )
% 0.32/0.46 & ! [Xy: $i] :
% 0.32/0.46 ( ( Xphi @ Xy )
% 0.32/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(prop2set_type,type,
% 0.32/0.46 prop2set: $o > $i ).
% 0.32/0.46
% 0.32/0.46 thf(prop2set,definition,
% 0.32/0.46 ( prop2set
% 0.32/0.46 = ( ^ [Xphi: $o] :
% 0.32/0.46 ( dsetconstr @ ( powerset @ emptyset )
% 0.32/0.46 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(prop2setE_type,type,
% 0.32/0.46 prop2setE: $o ).
% 0.32/0.46
% 0.32/0.46 thf(prop2setE,definition,
% 0.32/0.46 ( prop2setE
% 0.32/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.32/0.46 => Xphi ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(emptysetE_type,type,
% 0.32/0.46 emptysetE: $o ).
% 0.32/0.46
% 0.32/0.46 thf(emptysetE,definition,
% 0.32/0.46 ( emptysetE
% 0.32/0.46 = ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ emptyset )
% 0.32/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(emptysetimpfalse_type,type,
% 0.32/0.46 emptysetimpfalse: $o ).
% 0.32/0.46
% 0.32/0.46 thf(emptysetimpfalse,definition,
% 0.32/0.46 ( emptysetimpfalse
% 0.32/0.46 = ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ emptyset )
% 0.32/0.46 => $false ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(notinemptyset_type,type,
% 0.32/0.46 notinemptyset: $o ).
% 0.32/0.46
% 0.32/0.46 thf(notinemptyset,definition,
% 0.32/0.46 ( notinemptyset
% 0.32/0.46 = ( ! [Xx: $i] :
% 0.32/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(exuE3e_type,type,
% 0.32/0.46 exuE3e: $o ).
% 0.32/0.46
% 0.32/0.46 thf(exuE3e,definition,
% 0.32/0.46 ( exuE3e
% 0.32/0.46 = ( ! [Xphi: $i > $o] :
% 0.32/0.46 ( ( exu
% 0.32/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setext_type,type,
% 0.32/0.46 setext: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setext,definition,
% 0.32/0.46 ( setext
% 0.32/0.46 = ( ! [A: $i,B: $i] :
% 0.32/0.46 ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ A )
% 0.32/0.46 => ( in @ Xx @ B ) )
% 0.32/0.46 => ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ B )
% 0.32/0.46 => ( in @ Xx @ A ) )
% 0.32/0.46 => ( A = B ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(emptyI_type,type,
% 0.32/0.46 emptyI: $o ).
% 0.32/0.46
% 0.32/0.46 thf(emptyI,definition,
% 0.32/0.46 ( emptyI
% 0.32/0.46 = ( ! [A: $i] :
% 0.32/0.46 ( ! [Xx: $i] :
% 0.32/0.46 ~ ( in @ Xx @ A )
% 0.32/0.46 => ( A = emptyset ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(noeltsimpempty_type,type,
% 0.32/0.46 noeltsimpempty: $o ).
% 0.32/0.46
% 0.32/0.46 thf(noeltsimpempty,definition,
% 0.32/0.46 ( noeltsimpempty
% 0.32/0.46 = ( ! [A: $i] :
% 0.32/0.46 ( ! [Xx: $i] :
% 0.32/0.46 ~ ( in @ Xx @ A )
% 0.32/0.46 => ( A = emptyset ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setbeta_type,type,
% 0.32/0.46 setbeta: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setbeta,definition,
% 0.32/0.46 ( setbeta
% 0.32/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ A )
% 0.32/0.46 => ( ( in @ Xx
% 0.32/0.46 @ ( dsetconstr @ A
% 0.32/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(nonempty_type,type,
% 0.32/0.46 nonempty: $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(nonempty,definition,
% 0.32/0.46 ( nonempty
% 0.32/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(nonemptyE1_type,type,
% 0.32/0.46 nonemptyE1: $o ).
% 0.32/0.46
% 0.32/0.46 thf(nonemptyE1,definition,
% 0.32/0.46 ( nonemptyE1
% 0.32/0.46 = ( ! [A: $i] :
% 0.32/0.46 ( ( nonempty @ A )
% 0.32/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(nonemptyI_type,type,
% 0.32/0.46 nonemptyI: $o ).
% 0.32/0.46
% 0.32/0.46 thf(nonemptyI,definition,
% 0.32/0.46 ( nonemptyI
% 0.32/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ A )
% 0.32/0.46 => ( ( Xphi @ Xx )
% 0.32/0.46 => ( nonempty
% 0.32/0.46 @ ( dsetconstr @ A
% 0.32/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(nonemptyI1_type,type,
% 0.32/0.46 nonemptyI1: $o ).
% 0.32/0.46
% 0.32/0.46 thf(nonemptyI1,definition,
% 0.32/0.46 ( nonemptyI1
% 0.32/0.46 = ( ! [A: $i] :
% 0.32/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinIL_type,type,
% 0.32/0.46 setadjoinIL: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinIL,definition,
% 0.32/0.46 ( setadjoinIL
% 0.32/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(emptyinunitempty_type,type,
% 0.32/0.46 emptyinunitempty: $o ).
% 0.32/0.46
% 0.32/0.46 thf(emptyinunitempty,definition,
% 0.32/0.46 ( emptyinunitempty
% 0.32/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinIR_type,type,
% 0.32/0.46 setadjoinIR: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinIR,definition,
% 0.32/0.46 ( setadjoinIR
% 0.32/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/0.46 ( ( in @ Xy @ A )
% 0.32/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinE_type,type,
% 0.32/0.46 setadjoinE: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinE,definition,
% 0.32/0.46 ( setadjoinE
% 0.32/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/0.46 => ! [Xphi: $o] :
% 0.32/0.46 ( ( ( Xy = Xx )
% 0.32/0.46 => Xphi )
% 0.32/0.46 => ( ( ( in @ Xy @ A )
% 0.32/0.46 => Xphi )
% 0.32/0.46 => Xphi ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinOr_type,type,
% 0.32/0.46 setadjoinOr: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setadjoinOr,definition,
% 0.32/0.46 ( setadjoinOr
% 0.32/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/0.46 => ( ( Xy = Xx )
% 0.32/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setoftrueEq_type,type,
% 0.32/0.46 setoftrueEq: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setoftrueEq,definition,
% 0.32/0.46 ( setoftrueEq
% 0.32/0.46 = ( ! [A: $i] :
% 0.32/0.46 ( ( dsetconstr @ A
% 0.32/0.46 @ ^ [Xx: $i] : $true )
% 0.32/0.46 = A ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(powersetI_type,type,
% 0.32/0.46 powersetI: $o ).
% 0.32/0.46
% 0.32/0.46 thf(powersetI,definition,
% 0.32/0.46 ( powersetI
% 0.32/0.46 = ( ! [A: $i,B: $i] :
% 0.32/0.46 ( ! [Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ B )
% 0.32/0.46 => ( in @ Xx @ A ) )
% 0.32/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(emptyinPowerset_type,type,
% 0.32/0.46 emptyinPowerset: $o ).
% 0.32/0.46
% 0.32/0.46 thf(emptyinPowerset,definition,
% 0.32/0.46 ( emptyinPowerset
% 0.32/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(emptyInPowerset_type,type,
% 0.32/0.46 emptyInPowerset: $o ).
% 0.32/0.46
% 0.32/0.46 thf(emptyInPowerset,definition,
% 0.32/0.46 ( emptyInPowerset
% 0.32/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(powersetE_type,type,
% 0.32/0.46 powersetE: $o ).
% 0.32/0.46
% 0.32/0.46 thf(powersetE,definition,
% 0.32/0.46 ( powersetE
% 0.32/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.32/0.46 => ( ( in @ Xx @ B )
% 0.32/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setunionI_type,type,
% 0.32/0.46 setunionI: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setunionI,definition,
% 0.32/0.46 ( setunionI
% 0.32/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.32/0.46 ( ( in @ Xx @ B )
% 0.32/0.46 => ( ( in @ B @ A )
% 0.32/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(setunionE_type,type,
% 0.32/0.46 setunionE: $o ).
% 0.32/0.46
% 0.32/0.46 thf(setunionE,definition,
% 0.32/0.46 ( setunionE
% 0.32/0.46 = ( ! [A: $i,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/0.46 => ! [Xphi: $o] :
% 0.32/0.46 ( ! [B: $i] :
% 0.32/0.46 ( ( in @ Xx @ B )
% 0.32/0.46 => ( ( in @ B @ A )
% 0.32/0.46 => Xphi ) )
% 0.32/0.46 => Xphi ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(subPowSU_type,type,
% 0.32/0.46 subPowSU: $o ).
% 0.32/0.46
% 0.32/0.46 thf(subPowSU,definition,
% 0.32/0.46 ( subPowSU
% 0.32/0.46 = ( ! [A: $i,Xx: $i] :
% 0.32/0.46 ( ( in @ Xx @ A )
% 0.32/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(exuE2_type,type,
% 0.32/0.46 exuE2: $o ).
% 0.32/0.46
% 0.32/0.46 thf(exuE2,definition,
% 0.32/0.46 ( exuE2
% 0.32/0.46 = ( ! [Xphi: $i > $o] :
% 0.32/0.46 ( ( exu
% 0.32/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.46 => ? [Xx: $i] :
% 0.32/0.46 ! [Xy: $i] :
% 0.32/0.46 ( ( Xphi @ Xy )
% 0.32/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(nonemptyImpWitness_type,type,
% 0.32/0.46 nonemptyImpWitness: $o ).
% 0.32/0.47
% 0.32/0.47 thf(nonemptyImpWitness,definition,
% 0.32/0.47 ( nonemptyImpWitness
% 0.32/0.47 = ( ! [A: $i] :
% 0.32/0.47 ( ( nonempty @ A )
% 0.32/0.47 => ? [Xx: $i] :
% 0.32/0.47 ( ( in @ Xx @ A )
% 0.32/0.47 & $true ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(uniqinunit,conjecture,
% 0.32/0.47 ( setextAx
% 0.32/0.47 => ( emptysetAx
% 0.32/0.47 => ( setadjoinAx
% 0.32/0.47 => ( powersetAx
% 0.32/0.47 => ( setunionAx
% 0.32/0.47 => ( omega0Ax
% 0.32/0.47 => ( omegaSAx
% 0.32/0.47 => ( omegaIndAx
% 0.32/0.47 => ( replAx
% 0.32/0.47 => ( foundationAx
% 0.32/0.47 => ( wellorderingAx
% 0.32/0.47 => ( descrp
% 0.32/0.47 => ( dsetconstrI
% 0.32/0.47 => ( dsetconstrEL
% 0.32/0.47 => ( dsetconstrER
% 0.32/0.47 => ( exuE1
% 0.32/0.47 => ( prop2setE
% 0.32/0.47 => ( emptysetE
% 0.32/0.47 => ( emptysetimpfalse
% 0.32/0.47 => ( notinemptyset
% 0.32/0.47 => ( exuE3e
% 0.32/0.47 => ( setext
% 0.32/0.47 => ( emptyI
% 0.32/0.47 => ( noeltsimpempty
% 0.32/0.47 => ( setbeta
% 0.32/0.47 => ( nonemptyE1
% 0.32/0.47 => ( nonemptyI
% 0.32/0.47 => ( nonemptyI1
% 0.32/0.47 => ( setadjoinIL
% 0.32/0.47 => ( emptyinunitempty
% 0.32/0.47 => ( setadjoinIR
% 0.32/0.47 => ( setadjoinE
% 0.32/0.47 => ( setadjoinOr
% 0.32/0.47 => ( setoftrueEq
% 0.32/0.47 => ( powersetI
% 0.32/0.47 => ( emptyinPowerset
% 0.32/0.47 => ( emptyInPowerset
% 0.32/0.47 => ( powersetE
% 0.32/0.47 => ( setunionI
% 0.32/0.47 => ( setunionE
% 0.32/0.47 => ( subPowSU
% 0.32/0.47 => ( exuE2
% 0.32/0.47 => ( nonemptyImpWitness
% 0.32/0.47 => ! [Xx: $i,Xy: $i] :
% 0.32/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 1.89/1.39 ---- Embedded in THF ---
% 1.89/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.89/1.39 %%% Generated on Tue Feb 24 12:25:41 EST 2026
% 1.89/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.89/1.39 %%% Logic specification used:
% 1.89/1.39 %%% thf(spec, logic, $$dhol).
% 1.89/1.39
% 1.89/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.p9jyL4yqSG/DTF2DTF5545.p
% See solution above
% 1.89/1.39 ------------------------
% 2.11/1.40 ---- Cleaned THF ---
% 2.11/1.40 thf(in_type,type,
% 2.11/1.40 in: $i > $i > $o ).
% 2.11/1.40
% 2.11/1.40 thf(exu_type,type,
% 2.11/1.40 exu: ( $i > $o ) > $o ).
% 2.11/1.40
% 2.11/1.40 thf(exu,definition,
% 2.11/1.40 ( exu
% 2.11/1.40 = ( ^ [Xphi: $i > $o] :
% 2.11/1.40 ? [Xx: $i] :
% 2.11/1.40 ( ( Xphi @ Xx )
% 2.11/1.40 & ! [Xy: $i] :
% 2.11/1.40 ( ( Xphi @ Xy )
% 2.11/1.40 => ( Xx = Xy ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(setextAx_type,type,
% 2.11/1.40 setextAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(setextAx,definition,
% 2.11/1.40 ( setextAx
% 2.11/1.40 = ( ! [A: $i,B: $i] :
% 2.11/1.40 ( ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ A )
% 2.11/1.40 <=> ( in @ Xx @ B ) )
% 2.11/1.40 => ( A = B ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(emptyset_type,type,
% 2.11/1.40 emptyset: $i ).
% 2.11/1.40
% 2.11/1.40 thf(emptysetAx_type,type,
% 2.11/1.40 emptysetAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(emptysetAx,definition,
% 2.11/1.40 ( emptysetAx
% 2.11/1.40 = ( ! [Xx: $i] :
% 2.11/1.40 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(setadjoin_type,type,
% 2.11/1.40 setadjoin: $i > $i > $i ).
% 2.11/1.40
% 2.11/1.40 thf(setadjoinAx_type,type,
% 2.11/1.40 setadjoinAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(setadjoinAx,definition,
% 2.11/1.40 ( setadjoinAx
% 2.11/1.40 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.11/1.40 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.11/1.40 <=> ( ( Xy = Xx )
% 2.11/1.40 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(powerset_type,type,
% 2.11/1.40 powerset: $i > $i ).
% 2.11/1.40
% 2.11/1.40 thf(powersetAx_type,type,
% 2.11/1.40 powersetAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(powersetAx,definition,
% 2.11/1.40 ( powersetAx
% 2.11/1.40 = ( ! [A: $i,B: $i] :
% 2.11/1.40 ( ( in @ B @ ( powerset @ A ) )
% 2.11/1.40 <=> ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ B )
% 2.11/1.40 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(setunion_type,type,
% 2.11/1.40 setunion: $i > $i ).
% 2.11/1.40
% 2.11/1.40 thf(setunionAx_type,type,
% 2.11/1.40 setunionAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(setunionAx,definition,
% 2.11/1.40 ( setunionAx
% 2.11/1.40 = ( ! [A: $i,Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ ( setunion @ A ) )
% 2.11/1.40 <=> ? [B: $i] :
% 2.11/1.40 ( ( in @ Xx @ B )
% 2.11/1.40 & ( in @ B @ A ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(omega_type,type,
% 2.11/1.40 omega: $i ).
% 2.11/1.40
% 2.11/1.40 thf(omega0Ax_type,type,
% 2.11/1.40 omega0Ax: $o ).
% 2.11/1.40
% 2.11/1.40 thf(omega0Ax,definition,
% 2.11/1.40 ( omega0Ax
% 2.11/1.40 = ( in @ emptyset @ omega ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(omegaSAx_type,type,
% 2.11/1.40 omegaSAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(omegaSAx,definition,
% 2.11/1.40 ( omegaSAx
% 2.11/1.40 = ( ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ omega )
% 2.11/1.40 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(omegaIndAx_type,type,
% 2.11/1.40 omegaIndAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(omegaIndAx,definition,
% 2.11/1.40 ( omegaIndAx
% 2.11/1.40 = ( ! [A: $i] :
% 2.11/1.40 ( ( ( in @ emptyset @ A )
% 2.11/1.40 & ! [Xx: $i] :
% 2.11/1.40 ( ( ( in @ Xx @ omega )
% 2.11/1.40 & ( in @ Xx @ A ) )
% 2.11/1.40 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.11/1.40 => ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ omega )
% 2.11/1.40 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(replAx_type,type,
% 2.11/1.40 replAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(replAx,definition,
% 2.11/1.40 ( replAx
% 2.11/1.40 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.11/1.40 ( ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ A )
% 2.11/1.40 => ( exu
% 2.11/1.40 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.11/1.40 => ? [B: $i] :
% 2.11/1.40 ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ B )
% 2.11/1.40 <=> ? [Xy: $i] :
% 2.11/1.40 ( ( in @ Xy @ A )
% 2.11/1.40 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(foundationAx_type,type,
% 2.11/1.40 foundationAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(foundationAx,definition,
% 2.11/1.40 ( foundationAx
% 2.11/1.40 = ( ! [A: $i] :
% 2.11/1.40 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.11/1.40 => ? [B: $i] :
% 2.11/1.40 ( ( in @ B @ A )
% 2.11/1.40 & ~ ? [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ B )
% 2.11/1.40 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(wellorderingAx_type,type,
% 2.11/1.40 wellorderingAx: $o ).
% 2.11/1.40
% 2.11/1.40 thf(wellorderingAx,definition,
% 2.11/1.40 ( wellorderingAx
% 2.11/1.40 = ( ! [A: $i] :
% 2.11/1.40 ? [B: $i] :
% 2.11/1.40 ( ! [C: $i] :
% 2.11/1.40 ( ( in @ C @ B )
% 2.11/1.40 => ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ C )
% 2.11/1.40 => ( in @ Xx @ A ) ) )
% 2.11/1.40 & ! [Xx: $i,Xy: $i] :
% 2.11/1.40 ( ( ( in @ Xx @ A )
% 2.11/1.40 & ( in @ Xy @ A ) )
% 2.11/1.40 => ( ! [C: $i] :
% 2.11/1.40 ( ( in @ C @ B )
% 2.11/1.40 => ( ( in @ Xx @ C )
% 2.11/1.40 <=> ( in @ Xy @ C ) ) )
% 2.11/1.40 => ( Xx = Xy ) ) )
% 2.11/1.40 & ! [C: $i,D: $i] :
% 2.11/1.40 ( ( ( in @ C @ B )
% 2.11/1.40 & ( in @ D @ B ) )
% 2.11/1.40 => ( ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ C )
% 2.11/1.40 => ( in @ Xx @ D ) )
% 2.11/1.40 | ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ D )
% 2.11/1.40 => ( in @ Xx @ C ) ) ) )
% 2.11/1.40 & ! [C: $i] :
% 2.11/1.40 ( ( ! [Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ C )
% 2.11/1.40 => ( in @ Xx @ A ) )
% 2.11/1.40 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.11/1.40 => ? [D: $i,Xx: $i] :
% 2.11/1.40 ( ( in @ D @ B )
% 2.11/1.40 & ( in @ Xx @ C )
% 2.11/1.40 & ~ ? [Xy: $i] :
% 2.11/1.40 ( ( in @ Xy @ D )
% 2.11/1.40 & ( in @ Xy @ C ) )
% 2.11/1.40 & ! [E: $i] :
% 2.11/1.40 ( ( in @ E @ B )
% 2.11/1.40 => ( ! [Xy: $i] :
% 2.11/1.40 ( ( in @ Xy @ E )
% 2.11/1.40 => ( in @ Xy @ D ) )
% 2.11/1.40 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(descr_type,type,
% 2.11/1.40 descr: ( $i > $o ) > $i ).
% 2.11/1.40
% 2.11/1.40 thf(descrp_type,type,
% 2.11/1.40 descrp: $o ).
% 2.11/1.40
% 2.11/1.40 thf(descrp,definition,
% 2.11/1.40 ( descrp
% 2.11/1.40 = ( ! [Xphi: $i > $o] :
% 2.11/1.40 ( ( exu
% 2.11/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.40 => ( Xphi
% 2.11/1.40 @ ( descr
% 2.11/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(dsetconstr_type,type,
% 2.11/1.40 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.11/1.40
% 2.11/1.40 thf(dsetconstrI_type,type,
% 2.11/1.40 dsetconstrI: $o ).
% 2.11/1.40
% 2.11/1.40 thf(dsetconstrI,definition,
% 2.11/1.40 ( dsetconstrI
% 2.11/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.40 ( ( in @ Xx @ A )
% 2.11/1.40 => ( ( Xphi @ Xx )
% 2.11/1.40 => ( in @ Xx
% 2.11/1.40 @ ( dsetconstr @ A
% 2.11/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(dsetconstrEL_type,type,
% 2.11/1.40 dsetconstrEL: $o ).
% 2.11/1.40
% 2.11/1.40 thf(dsetconstrEL,definition,
% 2.11/1.40 ( dsetconstrEL
% 2.11/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.40 ( ( in @ Xx
% 2.11/1.40 @ ( dsetconstr @ A
% 2.11/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.11/1.40 => ( in @ Xx @ A ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(dsetconstrER_type,type,
% 2.11/1.40 dsetconstrER: $o ).
% 2.11/1.40
% 2.11/1.40 thf(dsetconstrER,definition,
% 2.11/1.40 ( dsetconstrER
% 2.11/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.40 ( ( in @ Xx
% 2.11/1.40 @ ( dsetconstr @ A
% 2.11/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.11/1.40 => ( Xphi @ Xx ) ) ) ) ).
% 2.11/1.40
% 2.11/1.40 thf(exuE1_type,type,
% 2.11/1.40 exuE1: $o ).
% 2.11/1.40
% 2.11/1.40 thf(exuE1,definition,
% 2.11/1.40 ( exuE1
% 2.11/1.40 = ( ! [Xphi: $i > $o] :
% 2.11/1.41 ( ( exu
% 2.11/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.41 => ? [Xx: $i] :
% 2.11/1.41 ( ( Xphi @ Xx )
% 2.11/1.41 & ! [Xy: $i] :
% 2.11/1.41 ( ( Xphi @ Xy )
% 2.11/1.41 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(prop2set_type,type,
% 2.11/1.41 prop2set: $o > $i ).
% 2.11/1.41
% 2.11/1.41 thf(prop2set,definition,
% 2.11/1.41 ( prop2set
% 2.11/1.41 = ( ^ [Xphi: $o] :
% 2.11/1.41 ( dsetconstr @ ( powerset @ emptyset )
% 2.11/1.41 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(prop2setE_type,type,
% 2.11/1.41 prop2setE: $o ).
% 2.11/1.41
% 2.11/1.41 thf(prop2setE,definition,
% 2.11/1.41 ( prop2setE
% 2.11/1.41 = ( ! [Xphi: $o,Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.11/1.41 => Xphi ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(emptysetE_type,type,
% 2.11/1.41 emptysetE: $o ).
% 2.11/1.41
% 2.11/1.41 thf(emptysetE,definition,
% 2.11/1.41 ( emptysetE
% 2.11/1.41 = ( ! [Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ emptyset )
% 2.11/1.41 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(emptysetimpfalse_type,type,
% 2.11/1.41 emptysetimpfalse: $o ).
% 2.11/1.41
% 2.11/1.41 thf(emptysetimpfalse,definition,
% 2.11/1.41 ( emptysetimpfalse
% 2.11/1.41 = ( ! [Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ emptyset )
% 2.11/1.41 => $false ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(notinemptyset_type,type,
% 2.11/1.41 notinemptyset: $o ).
% 2.11/1.41
% 2.11/1.41 thf(notinemptyset,definition,
% 2.11/1.41 ( notinemptyset
% 2.11/1.41 = ( ! [Xx: $i] :
% 2.11/1.41 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(exuE3e_type,type,
% 2.11/1.41 exuE3e: $o ).
% 2.11/1.41
% 2.11/1.41 thf(exuE3e,definition,
% 2.11/1.41 ( exuE3e
% 2.11/1.41 = ( ! [Xphi: $i > $o] :
% 2.11/1.41 ( ( exu
% 2.11/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.41 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setext_type,type,
% 2.11/1.41 setext: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setext,definition,
% 2.11/1.41 ( setext
% 2.11/1.41 = ( ! [A: $i,B: $i] :
% 2.11/1.41 ( ! [Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ A )
% 2.11/1.41 => ( in @ Xx @ B ) )
% 2.11/1.41 => ( ! [Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ B )
% 2.11/1.41 => ( in @ Xx @ A ) )
% 2.11/1.41 => ( A = B ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(emptyI_type,type,
% 2.11/1.41 emptyI: $o ).
% 2.11/1.41
% 2.11/1.41 thf(emptyI,definition,
% 2.11/1.41 ( emptyI
% 2.11/1.41 = ( ! [A: $i] :
% 2.11/1.41 ( ! [Xx: $i] :
% 2.11/1.41 ~ ( in @ Xx @ A )
% 2.11/1.41 => ( A = emptyset ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(noeltsimpempty_type,type,
% 2.11/1.41 noeltsimpempty: $o ).
% 2.11/1.41
% 2.11/1.41 thf(noeltsimpempty,definition,
% 2.11/1.41 ( noeltsimpempty
% 2.11/1.41 = ( ! [A: $i] :
% 2.11/1.41 ( ! [Xx: $i] :
% 2.11/1.41 ~ ( in @ Xx @ A )
% 2.11/1.41 => ( A = emptyset ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setbeta_type,type,
% 2.11/1.41 setbeta: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setbeta,definition,
% 2.11/1.41 ( setbeta
% 2.11/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ A )
% 2.11/1.41 => ( ( in @ Xx
% 2.11/1.41 @ ( dsetconstr @ A
% 2.11/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.11/1.41 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(nonempty_type,type,
% 2.11/1.41 nonempty: $i > $o ).
% 2.11/1.41
% 2.11/1.41 thf(nonempty,definition,
% 2.11/1.41 ( nonempty
% 2.11/1.41 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(nonemptyE1_type,type,
% 2.11/1.41 nonemptyE1: $o ).
% 2.11/1.41
% 2.11/1.41 thf(nonemptyE1,definition,
% 2.11/1.41 ( nonemptyE1
% 2.11/1.41 = ( ! [A: $i] :
% 2.11/1.41 ( ( nonempty @ A )
% 2.11/1.41 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(nonemptyI_type,type,
% 2.11/1.41 nonemptyI: $o ).
% 2.11/1.41
% 2.11/1.41 thf(nonemptyI,definition,
% 2.11/1.41 ( nonemptyI
% 2.11/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ A )
% 2.11/1.41 => ( ( Xphi @ Xx )
% 2.11/1.41 => ( nonempty
% 2.11/1.41 @ ( dsetconstr @ A
% 2.11/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(nonemptyI1_type,type,
% 2.11/1.41 nonemptyI1: $o ).
% 2.11/1.41
% 2.11/1.41 thf(nonemptyI1,definition,
% 2.11/1.41 ( nonemptyI1
% 2.11/1.41 = ( ! [A: $i] :
% 2.11/1.41 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.11/1.41 => ( nonempty @ A ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setadjoinIL_type,type,
% 2.11/1.41 setadjoinIL: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setadjoinIL,definition,
% 2.11/1.41 ( setadjoinIL
% 2.11/1.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(emptyinunitempty_type,type,
% 2.11/1.41 emptyinunitempty: $o ).
% 2.11/1.41
% 2.11/1.41 thf(emptyinunitempty,definition,
% 2.11/1.41 ( emptyinunitempty
% 2.11/1.41 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setadjoinIR_type,type,
% 2.11/1.41 setadjoinIR: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setadjoinIR,definition,
% 2.11/1.41 ( setadjoinIR
% 2.11/1.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.11/1.41 ( ( in @ Xy @ A )
% 2.11/1.41 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setadjoinE_type,type,
% 2.11/1.41 setadjoinE: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setadjoinE,definition,
% 2.11/1.41 ( setadjoinE
% 2.11/1.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.11/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.11/1.41 => ! [Xphi: $o] :
% 2.11/1.41 ( ( ( Xy = Xx )
% 2.11/1.41 => Xphi )
% 2.11/1.41 => ( ( ( in @ Xy @ A )
% 2.11/1.41 => Xphi )
% 2.11/1.41 => Xphi ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setadjoinOr_type,type,
% 2.11/1.41 setadjoinOr: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setadjoinOr,definition,
% 2.11/1.41 ( setadjoinOr
% 2.11/1.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.11/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.11/1.41 => ( ( Xy = Xx )
% 2.11/1.41 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setoftrueEq_type,type,
% 2.11/1.41 setoftrueEq: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setoftrueEq,definition,
% 2.11/1.41 ( setoftrueEq
% 2.11/1.41 = ( ! [A: $i] :
% 2.11/1.41 ( ( dsetconstr @ A
% 2.11/1.41 @ ^ [Xx: $i] : $true )
% 2.11/1.41 = A ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(powersetI_type,type,
% 2.11/1.41 powersetI: $o ).
% 2.11/1.41
% 2.11/1.41 thf(powersetI,definition,
% 2.11/1.41 ( powersetI
% 2.11/1.41 = ( ! [A: $i,B: $i] :
% 2.11/1.41 ( ! [Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ B )
% 2.11/1.41 => ( in @ Xx @ A ) )
% 2.11/1.41 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(emptyinPowerset_type,type,
% 2.11/1.41 emptyinPowerset: $o ).
% 2.11/1.41
% 2.11/1.41 thf(emptyinPowerset,definition,
% 2.11/1.41 ( emptyinPowerset
% 2.11/1.41 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(emptyInPowerset_type,type,
% 2.11/1.41 emptyInPowerset: $o ).
% 2.11/1.41
% 2.11/1.41 thf(emptyInPowerset,definition,
% 2.11/1.41 ( emptyInPowerset
% 2.11/1.41 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(powersetE_type,type,
% 2.11/1.41 powersetE: $o ).
% 2.11/1.41
% 2.11/1.41 thf(powersetE,definition,
% 2.11/1.41 ( powersetE
% 2.11/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.41 ( ( in @ B @ ( powerset @ A ) )
% 2.11/1.41 => ( ( in @ Xx @ B )
% 2.11/1.41 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setunionI_type,type,
% 2.11/1.41 setunionI: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setunionI,definition,
% 2.11/1.41 ( setunionI
% 2.11/1.41 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.11/1.41 ( ( in @ Xx @ B )
% 2.11/1.41 => ( ( in @ B @ A )
% 2.11/1.41 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(setunionE_type,type,
% 2.11/1.41 setunionE: $o ).
% 2.11/1.41
% 2.11/1.41 thf(setunionE,definition,
% 2.11/1.41 ( setunionE
% 2.11/1.41 = ( ! [A: $i,Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ ( setunion @ A ) )
% 2.11/1.41 => ! [Xphi: $o] :
% 2.11/1.41 ( ! [B: $i] :
% 2.11/1.41 ( ( in @ Xx @ B )
% 2.11/1.41 => ( ( in @ B @ A )
% 2.11/1.41 => Xphi ) )
% 2.11/1.41 => Xphi ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(subPowSU_type,type,
% 2.11/1.41 subPowSU: $o ).
% 2.11/1.41
% 2.11/1.41 thf(subPowSU,definition,
% 2.11/1.41 ( subPowSU
% 2.11/1.41 = ( ! [A: $i,Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ A )
% 2.11/1.41 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(exuE2_type,type,
% 2.11/1.41 exuE2: $o ).
% 2.11/1.41
% 2.11/1.41 thf(exuE2,definition,
% 2.11/1.41 ( exuE2
% 2.11/1.41 = ( ! [Xphi: $i > $o] :
% 2.11/1.41 ( ( exu
% 2.11/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.41 => ? [Xx: $i] :
% 2.11/1.41 ! [Xy: $i] :
% 2.11/1.41 ( ( Xphi @ Xy )
% 2.11/1.41 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(nonemptyImpWitness_type,type,
% 2.11/1.41 nonemptyImpWitness: $o ).
% 2.11/1.41
% 2.11/1.41 thf(nonemptyImpWitness,definition,
% 2.11/1.41 ( nonemptyImpWitness
% 2.11/1.41 = ( ! [A: $i] :
% 2.11/1.41 ( ( nonempty @ A )
% 2.11/1.41 => ? [Xx: $i] :
% 2.11/1.41 ( ( in @ Xx @ A )
% 2.11/1.41 & $true ) ) ) ) ).
% 2.11/1.41
% 2.11/1.41 thf(uniqinunit,conjecture,
% 2.11/1.41 ( setextAx
% 2.11/1.41 => ( emptysetAx
% 2.11/1.41 => ( setadjoinAx
% 2.11/1.41 => ( powersetAx
% 2.11/1.41 => ( setunionAx
% 2.11/1.41 => ( omega0Ax
% 2.11/1.41 => ( omegaSAx
% 2.11/1.41 => ( omegaIndAx
% 2.11/1.41 => ( replAx
% 2.11/1.41 => ( foundationAx
% 2.11/1.41 => ( wellorderingAx
% 2.11/1.41 => ( descrp
% 2.11/1.41 => ( dsetconstrI
% 2.11/1.41 => ( dsetconstrEL
% 2.11/1.41 => ( dsetconstrER
% 2.11/1.41 => ( exuE1
% 2.11/1.41 => ( prop2setE
% 2.11/1.41 => ( emptysetE
% 2.11/1.41 => ( emptysetimpfalse
% 2.11/1.41 => ( notinemptyset
% 2.11/1.41 => ( exuE3e
% 2.11/1.41 => ( setext
% 2.11/1.41 => ( emptyI
% 2.11/1.41 => ( noeltsimpempty
% 2.11/1.41 => ( setbeta
% 2.11/1.41 => ( nonemptyE1
% 2.11/1.41 => ( nonemptyI
% 2.11/1.41 => ( nonemptyI1
% 2.11/1.41 => ( setadjoinIL
% 2.11/1.41 => ( emptyinunitempty
% 2.11/1.41 => ( setadjoinIR
% 2.11/1.41 => ( setadjoinE
% 2.11/1.41 => ( setadjoinOr
% 2.11/1.41 => ( setoftrueEq
% 2.11/1.41 => ( powersetI
% 2.11/1.41 => ( emptyinPowerset
% 2.11/1.41 => ( emptyInPowerset
% 2.11/1.41 => ( powersetE
% 2.11/1.41 => ( setunionI
% 2.11/1.41 => ( setunionE
% 2.11/1.41 => ( subPowSU
% 2.11/1.41 => ( exuE2
% 2.11/1.41 => ( nonemptyImpWitness
% 2.11/1.41 => ! [Xx: $i,Xy: $i] :
% 2.11/1.41 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.11/1.41 => ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.11/1.41 ------------------------
% 2.11/1.42 % (5668)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/18Mi)
% 2.11/1.42 % (5666)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_5545 for (2999ds/2Mi)
% 2.11/1.42 % (5666)Instruction limit reached!
% 2.11/1.42 % (5666)------------------------------
% 2.11/1.42 % (5666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.42 % (5666)Termination reason: Unknown
% 2.11/1.42 % (5666)Termination phase: shuffling
% 2.11/1.42
% 2.11/1.42 % (5666)Memory used [KB]: 1023
% 2.11/1.42 % (5666)Time elapsed: 0.002 s
% 2.11/1.42 % (5666)Instructions burned: 3 (million)
% 2.11/1.42 % (5666)------------------------------
% 2.11/1.42 % (5666)------------------------------
% 2.11/1.42 % (5668)Instruction limit reached!
% 2.11/1.42 % (5668)------------------------------
% 2.11/1.42 % (5668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.42 % (5668)Termination reason: Unknown
% 2.11/1.42 % (5668)Termination phase: Property scanning
% 2.11/1.42
% 2.11/1.42 % (5668)Memory used [KB]: 1535
% 2.11/1.42 % (5668)Time elapsed: 0.007 s
% 2.11/1.42 % (5668)Instructions burned: 18 (million)
% 2.11/1.42 % (5668)------------------------------
% 2.11/1.42 % (5668)------------------------------
% 2.11/1.43 % (5663)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_5545 for (2999ds/4Mi)
% 2.11/1.43 % (5662)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/183Mi)
% 2.11/1.43 % (5664)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_5545 for (2999ds/27Mi)
% 2.11/1.43 % (5665)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/2Mi)
% 2.11/1.43 % (5667)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_5545 for (2999ds/275Mi)
% 2.11/1.43 % (5663)Instruction limit reached!
% 2.11/1.43 % (5663)------------------------------
% 2.11/1.43 % (5663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.43 % (5663)Termination reason: Unknown
% 2.11/1.43 % (5663)Termination phase: shuffling
% 2.11/1.43
% 2.11/1.43 % (5663)Memory used [KB]: 1151
% 2.11/1.43 % (5663)Time elapsed: 0.004 s
% 2.11/1.43 % (5663)Instructions burned: 5 (million)
% 2.11/1.43 % (5665)Instruction limit reached!
% 2.11/1.43 % (5665)------------------------------
% 2.11/1.43 % (5665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.43 % (5665)Termination reason: Unknown
% 2.11/1.43 % (5665)Termination phase: shuffling
% 2.11/1.43
% 2.11/1.43 % (5665)Memory used [KB]: 1023
% 2.11/1.43 % (5665)Time elapsed: 0.004 s
% 2.11/1.43 % (5665)Instructions burned: 3 (million)
% 2.11/1.43 % (5665)------------------------------
% 2.11/1.43 % (5665)------------------------------
% 2.11/1.43 % (5663)------------------------------
% 2.11/1.43 % (5663)------------------------------
% 2.11/1.43 % (5669)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/3Mi)
% 2.11/1.43 % (5669)Instruction limit reached!
% 2.11/1.43 % (5669)------------------------------
% 2.11/1.43 % (5669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.43 % (5669)Termination reason: Unknown
% 2.11/1.43 % (5669)Termination phase: shuffling
% 2.11/1.43
% 2.11/1.43 % (5669)Memory used [KB]: 1151
% 2.11/1.43 % (5669)Time elapsed: 0.003 s
% 2.11/1.43 % (5669)Instructions burned: 4 (million)
% 2.11/1.43 % (5669)------------------------------
% 2.11/1.43 % (5669)------------------------------
% 2.11/1.43 % (5670)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_5545 for (2999ds/37Mi)
% 2.11/1.44 % (5664)Instruction limit reached!
% 2.11/1.44 % (5664)------------------------------
% 2.11/1.44 % (5664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.44 % (5664)Termination reason: Unknown
% 2.11/1.44 % (5664)Termination phase: Saturation
% 2.11/1.44
% 2.11/1.44 % (5664)Memory used [KB]: 5756
% 2.11/1.44 % (5664)Time elapsed: 0.016 s
% 2.11/1.44 % (5664)Instructions burned: 27 (million)
% 2.11/1.44 % (5664)------------------------------
% 2.11/1.44 % (5664)------------------------------
% 2.11/1.44 % (5671)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_5545 for (2999ds/15Mi)
% 2.11/1.44 % (5673)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_5545 for (2999ds/1041Mi)
% 2.11/1.44 % (5670)Instruction limit reached!
% 2.11/1.44 % (5670)------------------------------
% 2.11/1.44 % (5670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.44 % (5670)Termination reason: Unknown
% 2.11/1.44 % (5670)Termination phase: Saturation
% 2.11/1.44
% 2.11/1.44 % (5670)Memory used [KB]: 6012
% 2.11/1.44 % (5670)Time elapsed: 0.011 s
% 2.11/1.44 % (5670)Instructions burned: 40 (million)
% 2.11/1.44 % (5670)------------------------------
% 2.11/1.44 % (5670)------------------------------
% 2.11/1.45 % (5671)Instruction limit reached!
% 2.11/1.45 % (5671)------------------------------
% 2.11/1.45 % (5671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.45 % (5671)Termination reason: Unknown
% 2.11/1.45 % (5671)Termination phase: Preprocessing 3
% 2.11/1.45
% 2.11/1.45 % (5671)Memory used [KB]: 1407
% 2.11/1.45 % (5671)Time elapsed: 0.006 s
% 2.11/1.45 % (5671)Instructions burned: 15 (million)
% 2.11/1.45 % (5671)------------------------------
% 2.11/1.45 % (5671)------------------------------
% 2.11/1.45 % (5672)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_5545 for (2999ds/3Mi)
% 2.11/1.45 % (5672)Instruction limit reached!
% 2.11/1.45 % (5672)------------------------------
% 2.11/1.45 % (5672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.45 % (5672)Termination reason: Unknown
% 2.11/1.45 % (5672)Termination phase: shuffling
% 2.11/1.45
% 2.11/1.45 % (5672)Memory used [KB]: 1023
% 2.11/1.45 % (5672)Time elapsed: 0.004 s
% 2.11/1.45 % (5672)Instructions burned: 4 (million)
% 2.11/1.45 % (5672)------------------------------
% 2.11/1.45 % (5672)------------------------------
% 2.11/1.45 % (5675)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/16Mi)
% 2.11/1.46 % (5676)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_5545 for (2999ds/3Mi)
% 2.11/1.46 % (5676)Instruction limit reached!
% 2.11/1.46 % (5676)------------------------------
% 2.11/1.46 % (5676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.46 % (5676)Termination reason: Unknown
% 2.11/1.46 % (5676)Termination phase: shuffling
% 2.11/1.46
% 2.11/1.46 % (5676)Memory used [KB]: 1151
% 2.11/1.46 % (5676)Time elapsed: 0.003 s
% 2.11/1.46 % (5676)Instructions burned: 4 (million)
% 2.11/1.46 % (5676)------------------------------
% 2.11/1.46 % (5676)------------------------------
% 2.11/1.46 % (5674)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/7Mi)
% 2.11/1.46 % (5675)Instruction limit reached!
% 2.11/1.46 % (5675)------------------------------
% 2.11/1.46 % (5675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.46 % (5675)Termination reason: Unknown
% 2.11/1.46 % (5675)Termination phase: Twee Goal Transformation
% 2.11/1.46
% 2.11/1.46 % (5675)Memory used [KB]: 1279
% 2.11/1.46 % (5675)Time elapsed: 0.006 s
% 2.11/1.46 % (5675)Instructions burned: 18 (million)
% 2.11/1.46 % (5675)------------------------------
% 2.11/1.46 % (5675)------------------------------
% 2.11/1.46 % (5674)Instruction limit reached!
% 2.11/1.46 % (5674)------------------------------
% 2.11/1.46 % (5674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.46 % (5674)Termination reason: Unknown
% 2.11/1.46 % (5674)Termination phase: shuffling
% 2.11/1.46
% 2.11/1.46 % (5674)Memory used [KB]: 1151
% 2.11/1.46 % (5674)Time elapsed: 0.006 s
% 2.11/1.46 % (5674)Instructions burned: 8 (million)
% 2.11/1.46 % (5674)------------------------------
% 2.11/1.46 % (5674)------------------------------
% 2.11/1.46 % (5677)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_5545 for (2999ds/3Mi)
% 2.11/1.46 % (5677)Instruction limit reached!
% 2.11/1.46 % (5677)------------------------------
% 2.11/1.46 % (5677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.46 % (5677)Termination reason: Unknown
% 2.11/1.46 % (5677)Termination phase: shuffling
% 2.11/1.46
% 2.11/1.46 % (5677)Memory used [KB]: 1151
% 2.11/1.46 % (5677)Time elapsed: 0.003 s
% 2.11/1.46 % (5677)Instructions burned: 4 (million)
% 2.11/1.46 % (5677)------------------------------
% 2.11/1.46 % (5677)------------------------------
% 2.11/1.47 % (5678)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/7Mi)
% 2.11/1.47 % (5679)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/3Mi)
% 2.11/1.47 % (5679)Instruction limit reached!
% 2.11/1.47 % (5679)------------------------------
% 2.11/1.47 % (5679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.47 % (5679)Termination reason: Unknown
% 2.11/1.47 % (5679)Termination phase: shuffling
% 2.11/1.47
% 2.11/1.47 % (5679)Memory used [KB]: 1151
% 2.11/1.47 % (5679)Time elapsed: 0.002 s
% 2.11/1.47 % (5679)Instructions burned: 4 (million)
% 2.11/1.47 % (5679)------------------------------
% 2.11/1.47 % (5679)------------------------------
% 2.11/1.47 % (5678)Instruction limit reached!
% 2.11/1.47 % (5678)------------------------------
% 2.11/1.47 % (5678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.47 % (5678)Termination reason: Unknown
% 2.11/1.47 % (5678)Termination phase: shuffling
% 2.11/1.47
% 2.11/1.47 % (5678)Memory used [KB]: 1151
% 2.11/1.47 % (5678)Time elapsed: 0.003 s
% 2.11/1.47 % (5678)Instructions burned: 7 (million)
% 2.11/1.47 % (5678)------------------------------
% 2.11/1.47 % (5678)------------------------------
% 2.11/1.47 % (5680)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/4Mi)
% 2.11/1.47 % (5681)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/18Mi)
% 2.11/1.48 % (5680)Instruction limit reached!
% 2.11/1.48 % (5680)------------------------------
% 2.11/1.48 % (5680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.48 % (5680)Termination reason: Unknown
% 2.11/1.48 % (5680)Termination phase: shuffling
% 2.11/1.48
% 2.11/1.48 % (5680)Memory used [KB]: 1151
% 2.11/1.48 % (5680)Time elapsed: 0.003 s
% 2.11/1.48 % (5680)Instructions burned: 7 (million)
% 2.11/1.48 % (5680)------------------------------
% 2.11/1.48 % (5680)------------------------------
% 2.11/1.48 % (5682)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/710Mi)
% 2.11/1.48 % (5681)Instruction limit reached!
% 2.11/1.48 % (5681)------------------------------
% 2.11/1.48 % (5681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.48 % (5681)Termination reason: Unknown
% 2.11/1.48 % (5681)Termination phase: Saturation
% 2.11/1.48 % (5683)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/6Mi)
% 2.11/1.48
% 2.11/1.48 % (5681)Memory used [KB]: 5756
% 2.11/1.48 % (5681)Time elapsed: 0.007 s
% 2.11/1.48 % (5681)Instructions burned: 18 (million)
% 2.11/1.48 % (5681)------------------------------
% 2.11/1.48 % (5681)------------------------------
% 2.11/1.48 % (5683)Instruction limit reached!
% 2.11/1.48 % (5683)------------------------------
% 2.11/1.48 % (5683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.48 % (5683)Termination reason: Unknown
% 2.11/1.48 % (5683)Termination phase: shuffling
% 2.11/1.48
% 2.11/1.48 % (5683)Memory used [KB]: 1151
% 2.11/1.48 % (5683)Time elapsed: 0.004 s
% 2.11/1.48 % (5683)Instructions burned: 8 (million)
% 2.11/1.48 % (5683)------------------------------
% 2.11/1.48 % (5683)------------------------------
% 2.11/1.49 % (5684)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_5545 for (2999ds/902Mi)
% 2.11/1.49 % (5685)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_5545 for (2999ds/21Mi)
% 2.11/1.49 % (5686)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5545 for (2999ds/5Mi)
% 2.11/1.49 % (5686)Instruction limit reached!
% 2.11/1.49 % (5686)------------------------------
% 2.11/1.49 % (5686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.49 % (5686)Termination reason: Unknown
% 2.11/1.49 % (5686)Termination phase: shuffling
% 2.11/1.49
% 2.11/1.49 % (5686)Memory used [KB]: 1151
% 2.11/1.49 % (5686)Time elapsed: 0.004 s
% 2.11/1.49 % (5686)Instructions burned: 8 (million)
% 2.11/1.49 % (5686)------------------------------
% 2.11/1.49 % (5686)------------------------------
% 2.11/1.50 % (5685)Instruction limit reached!
% 2.11/1.50 % (5685)------------------------------
% 2.11/1.50 % (5685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.50 % (5685)Termination reason: Unknown
% 2.11/1.50 % (5685)Termination phase: Property scanning
% 2.11/1.50
% 2.11/1.50 % (5685)Memory used [KB]: 1279
% 2.11/1.50 % (5685)Time elapsed: 0.008 s
% 2.11/1.50 % (5685)Instructions burned: 22 (million)
% 2.11/1.50 % (5685)------------------------------
% 2.11/1.50 % (5685)------------------------------
% 2.13/1.50 % (5684)First to succeed.
% 2.13/1.50 % (5687)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_5545 for (2999ds/6Mi)
% 2.13/1.51 % (5684)Refutation found. Thanks to Tanya!
% 2.13/1.51 % SZS status Theorem for DTF2THF_5545
% 2.13/1.51 % SZS output start Proof for DTF2THF_5545
% 2.13/1.51 thf(func_def_0, type, in: $i > $i > $o).
% 2.13/1.51 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.13/1.51 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.13/1.51 thf(func_def_8, type, powerset: $i > $i).
% 2.13/1.51 thf(func_def_10, type, setunion: $i > $i).
% 2.13/1.51 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.13/1.51 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.13/1.51 thf(func_def_26, type, prop2set: $o > $i).
% 2.13/1.51 thf(func_def_36, type, nonempty: $i > $o).
% 2.13/1.51 thf(func_def_68, type, sP1: $i > $i > $o).
% 2.13/1.51 thf(func_def_69, type, sP2: $i > $o).
% 2.13/1.51 thf(func_def_70, type, sP3: $i > $i > $o).
% 2.13/1.51 thf(func_def_71, type, sP4: $i > $i > $o).
% 2.13/1.51 thf(func_def_72, type, sK5: $i > $i > $i).
% 2.13/1.51 thf(func_def_75, type, sK8: $i > $o).
% 2.13/1.51 thf(func_def_76, type, sK9: ($i > $o) > $i).
% 2.13/1.51 thf(func_def_81, type, sK14: $i > $o).
% 2.13/1.51 thf(func_def_82, type, sK15: $i > $i).
% 2.13/1.51 thf(func_def_83, type, sK16: ($i > $o) > $i).
% 2.13/1.51 thf(func_def_84, type, sK17: $i > $i).
% 2.13/1.51 thf(func_def_90, type, sK23: $i > $i > $i).
% 2.13/1.51 thf(func_def_93, type, sK26: $i > $i > $i).
% 2.13/1.51 thf(func_def_94, type, sK27: $i > $i > $i).
% 2.13/1.51 thf(func_def_100, type, sK33: $i > $i).
% 2.13/1.51 thf(func_def_102, type, sK35: $i > $i).
% 2.13/1.51 thf(func_def_107, type, sK40: $i > $i > $i).
% 2.13/1.51 thf(func_def_108, type, sK41: $i > $i).
% 2.13/1.51 thf(func_def_119, type, sK52: $i > $o).
% 2.13/1.51 thf(func_def_121, type, sK54: $i > $i).
% 2.13/1.51 thf(func_def_124, type, sK57: $i > $i).
% 2.13/1.51 thf(func_def_128, type, sK61: $i > $i > $o).
% 2.13/1.51 thf(func_def_129, type, sK62: $i > $i).
% 2.13/1.51 thf(func_def_130, type, sK63: $i > $i).
% 2.13/1.51 thf(func_def_131, type, sK64: ($i > $i > $o) > $i > $i).
% 2.13/1.51 thf(func_def_132, type, sK65: ($i > $i > $o) > $i > $i).
% 2.13/1.51 thf(func_def_133, type, sK66: $i > ($i > $i > $o) > $i > $i).
% 2.13/1.51 thf(func_def_137, type, sK70: $i > $o).
% 2.13/1.51 thf(func_def_144, type, sK77: $o > $i > $i > $i).
% 2.13/1.51 thf(func_def_148, type, sK81: $i > $i > $i).
% 2.13/1.51 thf(func_def_149, type, sK82: $i > $i > $i).
% 2.13/1.51 thf(func_def_150, type, sK83: $i > $i > $i).
% 2.13/1.51 thf(func_def_151, type, sK84: $i > $i > $i).
% 2.13/1.51 thf(func_def_152, type, sK85: $i > $i > $i > $i).
% 2.13/1.51 thf(func_def_153, type, sK86: $i > $i).
% 2.13/1.51 thf(func_def_154, type, sK87: $i > $i).
% 2.13/1.51 thf(func_def_155, type, sK88: $i > $i).
% 2.13/1.51 thf(func_def_156, type, sK89: $i > $i).
% 2.13/1.51 thf(func_def_157, type, sK90: $i > $i > $i).
% 2.13/1.51 thf(func_def_158, type, sK91: $i > $i > $i > $i).
% 2.13/1.51 thf(func_def_159, type, sK92: $i > $i > $i > $i).
% 2.13/1.51 thf(func_def_160, type, sK93: $i > $i > $i).
% 2.13/1.51 thf(func_def_161, type, sK94: $i > $i > $i).
% 2.13/1.51 thf(func_def_163, type, sK96: $i > $i).
% 2.13/1.51 thf(func_def_164, type, sK97: $i > $i).
% 2.13/1.51 thf(func_def_165, type, sK98: $i > $i).
% 2.13/1.51 thf(func_def_166, type, sK99: $i > $i > $i).
% 2.13/1.51 thf(func_def_168, type, sK101: ($i > $o) > $i).
% 2.13/1.51 thf(func_def_169, type, sK102: $i > $o).
% 2.13/1.51 thf(func_def_170, type, sK103: $i > $i).
% 2.13/1.51 thf(func_def_172, type, sK105: $i > $i > $i).
% 2.13/1.51 thf(func_def_178, type, sK111: $i > $o).
% 2.13/1.51 thf(func_def_183, type, sK116: $i > $o).
% 2.13/1.51 thf(func_def_185, type, sK118: $i > $i).
% 2.13/1.51 thf(func_def_191, type, sK124: $i > $o).
% 2.13/1.51 thf(func_def_194, type, sK127: $i > $o).
% 2.13/1.51 thf(func_def_198, type, ph131: !>[X0: $tType]:(X0)).
% 2.13/1.51 thf(f759,plain,(
% 2.13/1.51 $false),
% 2.13/1.51 inference(avatar_sat_refutation,[status(thm)],[f726,f754,f758])).
% 2.13/1.51 thf(f758,plain,(
% 2.13/1.51 ~spl130_1),
% 2.13/1.51 inference(avatar_contradiction_clause,[status(thm)],[f757])).
% 2.13/1.51 thf(f757,plain,(
% 2.13/1.51 $false | ~spl130_1),
% 2.13/1.51 inference(trivial_inequality_removal,[status(thm)],[f756])).
% 2.13/1.51 thf(f756,plain,(
% 2.13/1.51 (sK11 != sK11) | ~spl130_1),
% 2.13/1.51 inference(superposition,[status(thm)],[f458,f718])).
% 2.13/1.51 thf(f718,plain,(
% 2.13/1.51 (sK12 = sK11) | ~spl130_1),
% 2.13/1.51 inference(avatar_component_clause,[status(thm)],[f716])).
% 2.13/1.51 thf(f716,definition,(
% 2.13/1.51 spl130_1 <=> (sK12 = sK11)),
% 2.13/1.51 introduced(definition,[new_symbols(naming,[spl130_1])],[avatar_definition])).
% 2.13/1.51 thf(f458,plain,(
% 2.13/1.51 (sK12 != sK11)),
% 2.13/1.51 inference(cnf_transformation,[status(thm)],[f216])).
% 2.13/1.51 thf(f216,plain,(
% 2.13/1.51 (powersetI = $true) & (exuE3e = $true) & (emptyinunitempty = $true) & (setextAx = $true) & (dsetconstrI = $true) & (setadjoinE = $true) & (foundationAx = $true) & (prop2setE = $true) & (nonemptyI1 = $true) & (dsetconstrER = $true) & (emptysetE = $true) & (setoftrueEq = $true) & (subPowSU = $true) & (emptyinPowerset = $true) & (setunionAx = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (wellorderingAx = $true) & (notinemptyset = $true) & (replAx = $true) & (emptysetimpfalse = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (emptysetAx = $true) & ((sK12 != sK11) & ((in @ sK12 @ (setadjoin @ sK11 @ emptyset)) = $true)) & (omegaIndAx = $true) & (descrp = $true) & (omega0Ax = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (setunionE = $true) & (nonemptyE1 = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (setadjoinIL = $true) & (emptyInPowerset = $true) & (powersetE = $true) & (setbeta = $true) & (omegaSAx = $true) & (setadjoinIR = $true) & (setunionI = $true)),
% 2.13/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f185,f215])).
% 2.13/1.51 thf(f215,plain,(
% 2.13/1.51 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true)) => ((sK12 != sK11) & ((in @ sK12 @ (setadjoin @ sK11 @ emptyset)) = $true))),
% 2.13/1.51 introduced(definition,[],[choice_axiom])).
% 2.13/1.51 thf(f185,plain,(
% 2.13/1.51 (powersetI = $true) & (exuE3e = $true) & (emptyinunitempty = $true) & (setextAx = $true) & (dsetconstrI = $true) & (setadjoinE = $true) & (foundationAx = $true) & (prop2setE = $true) & (nonemptyI1 = $true) & (dsetconstrER = $true) & (emptysetE = $true) & (setoftrueEq = $true) & (subPowSU = $true) & (emptyinPowerset = $true) & (setunionAx = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (wellorderingAx = $true) & (notinemptyset = $true) & (replAx = $true) & (emptysetimpfalse = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (emptysetAx = $true) & ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true)) & (omegaIndAx = $true) & (descrp = $true) & (omega0Ax = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (setunionE = $true) & (nonemptyE1 = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (setadjoinIL = $true) & (emptyInPowerset = $true) & (powersetE = $true) & (setbeta = $true) & (omegaSAx = $true) & (setadjoinIR = $true) & (setunionI = $true)),
% 2.13/1.51 inference(flattening,[status(thm)],[f184])).
% 2.13/1.51 thf(f184,plain,(
% 2.13/1.51 ((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((X0 != X1) & ((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true)) & (nonemptyImpWitness = $true)) & (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)),
% 2.13/1.51 inference(ennf_transformation,[status(thm)],[f124])).
% 2.13/1.51 thf(f124,plain,(
% 2.13/1.51 ~((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) => ((nonemptyImpWitness = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) => (X0 = X1)))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.51 inference(fool_elimination,[status(thm)],[f123])).
% 2.13/1.51 thf(f123,plain,(
% 2.13/1.51 ~(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 => (nonemptyImpWitness => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.51 inference(rectify,[status(thm)],[f48])).
% 2.13/1.51 thf(f48,negated_conjecture,(
% 2.13/1.51 ~(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 => (nonemptyImpWitness => ! [X2 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X1 = X2)))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.51 inference(negated_conjecture,[status(cth)],[f47])).
% 2.13/1.51 thf(f47,conjecture,(
% 2.13/1.51 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 => (nonemptyImpWitness => ! [X2 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X1 = X2))))))))))))))))))))))))))))))))))))))))))))),
% 2.13/1.51 file('/export/starexec/sandbox/tmp/tmp.p9jyL4yqSG/DTF2THF_5545.p',uniqinunit)).
% 2.13/1.51 thf(f754,plain,(
% 2.13/1.51 ~spl130_2),
% 2.13/1.51 inference(avatar_contradiction_clause,[status(thm)],[f753])).
% 2.13/1.51 thf(f753,plain,(
% 2.13/1.51 $false | ~spl130_2),
% 2.13/1.51 inference(trivial_inequality_removal,[status(thm)],[f752])).
% 2.13/1.51 thf(f752,plain,(
% 2.13/1.51 ($true != $true) | ~spl130_2),
% 2.13/1.51 inference(superposition,[status(thm)],[f740,f464])).
% 2.13/1.51 thf(f464,plain,(
% 2.13/1.51 (notinemptyset = $true)),
% 2.13/1.51 inference(cnf_transformation,[status(thm)],[f216])).
% 2.13/1.51 thf(f740,plain,(
% 2.13/1.51 (notinemptyset != $true) | ~spl130_2),
% 2.13/1.51 inference(trivial_inequality_removal,[status(thm)],[f737])).
% 2.13/1.51 thf(f737,plain,(
% 2.13/1.51 (notinemptyset != $true) | ($true != $true) | ~spl130_2),
% 2.13/1.51 inference(superposition,[status(thm)],[f485,f722])).
% 2.13/1.51 thf(f722,plain,(
% 2.13/1.51 ((in @ sK12 @ emptyset) = $true) | ~spl130_2),
% 2.13/1.51 inference(avatar_component_clause,[status(thm)],[f720])).
% 2.13/1.51 thf(f720,definition,(
% 2.13/1.51 spl130_2 <=> ((in @ sK12 @ emptyset) = $true)),
% 2.13/1.51 introduced(definition,[new_symbols(naming,[spl130_2])],[avatar_definition])).
% 2.13/1.51 thf(f485,plain,(
% 2.13/1.51 ( ! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | (notinemptyset != $true)) )),
% 2.13/1.51 inference(cnf_transformation,[status(thm)],[f220])).
% 2.13/1.51 thf(f220,plain,(
% 2.13/1.51 (! [X0 : $i] : ((in @ X0 @ emptyset) != $true) | (notinemptyset != $true)) & ((notinemptyset = $true) | ((in @ sK13 @ emptyset) = $true))),
% 2.13/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f218,f219])).
% 2.13/1.51 thf(f219,plain,(
% 2.13/1.51 ? [X1 : $i] : ((in @ X1 @ emptyset) = $true) => ((in @ sK13 @ emptyset) = $true)),
% 2.13/1.51 introduced(definition,[],[choice_axiom])).
% 2.13/1.51 thf(f218,plain,(
% 2.13/1.51 (! [X0 : $i] : ((in @ X0 @ emptyset) != $true) | (notinemptyset != $true)) & ((notinemptyset = $true) | ? [X1 : $i] : ((in @ X1 @ emptyset) = $true))),
% 2.13/1.51 inference(rectify,[status(thm)],[f217])).
% 2.13/1.51 thf(f217,plain,(
% 2.13/1.51 (! [X0 : $i] : ((in @ X0 @ emptyset) != $true) | (notinemptyset != $true)) & ((notinemptyset = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true))),
% 2.13/1.51 inference(nnf_transformation,[status(thm)],[f144])).
% 2.13/1.51 thf(f144,plain,(
% 2.13/1.51 ! [X0 : $i] : ((in @ X0 @ emptyset) != $true) <=> (notinemptyset = $true)),
% 2.13/1.51 inference(flattening,[status(thm)],[f100])).
% 2.13/1.51 thf(f100,plain,(
% 2.13/1.51 ! [X0 : $i] : ~((in @ X0 @ emptyset) = $true) <=> (notinemptyset = $true)),
% 2.13/1.51 inference(fool_elimination,[status(thm)],[f99])).
% 2.13/1.51 thf(f99,plain,(
% 2.13/1.51 (! [X0 : $i] : ~(in @ X0 @ emptyset) = notinemptyset)),
% 2.13/1.51 inference(rectify,[status(thm)],[f22])).
% 2.13/1.51 thf(f22,axiom,(
% 2.13/1.51 (! [X1 : $i] : ~(in @ X1 @ emptyset) = notinemptyset)),
% 2.13/1.51 file('/export/starexec/sandbox/tmp/tmp.p9jyL4yqSG/DTF2THF_5545.p',notinemptyset)).
% 2.13/1.51 thf(f726,plain,(
% 2.13/1.51 spl130_1 | spl130_2),
% 2.13/1.51 inference(avatar_split_clause,[status(thm)],[f725,f720,f716])).
% 2.13/1.51 thf(f725,plain,(
% 2.13/1.51 ((in @ sK12 @ emptyset) = $true) | (sK12 = sK11)),
% 2.13/1.51 inference(trivial_inequality_removal,[status(thm)],[f724])).
% 2.13/1.51 thf(f724,plain,(
% 2.13/1.51 ($true != $true) | ((in @ sK12 @ emptyset) = $true) | (sK12 = sK11)),
% 2.13/1.51 inference(forward_demodulation,[status(thm)],[f711,f450])).
% 2.13/1.51 thf(f450,plain,(
% 2.13/1.51 (setadjoinAx = $true)),
% 2.13/1.51 inference(cnf_transformation,[status(thm)],[f216])).
% 2.13/1.51 thf(f711,plain,(
% 2.13/1.51 (setadjoinAx != $true) | (sK12 = sK11) | ((in @ sK12 @ emptyset) = $true)),
% 2.13/1.51 inference(trivial_inequality_removal,[status(thm)],[f706])).
% 2.13/1.51 thf(f706,plain,(
% 2.13/1.51 ($true != $true) | (sK12 = sK11) | (setadjoinAx != $true) | ((in @ sK12 @ emptyset) = $true)),
% 2.13/1.51 inference(superposition,[status(thm)],[f659,f457])).
% 2.13/1.51 thf(f457,plain,(
% 2.13/1.51 ((in @ sK12 @ (setadjoin @ sK11 @ emptyset)) = $true)),
% 2.13/1.51 inference(cnf_transformation,[status(thm)],[f216])).
% 2.13/1.51 thf(f659,plain,(
% 2.13/1.51 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X2 @ X0)) != $true) | ((in @ X1 @ X0) = $true) | (X1 = X2) | (setadjoinAx != $true)) )),
% 2.13/1.51 inference(cnf_transformation,[status(thm)],[f407])).
% 2.13/1.51 thf(f407,plain,(
% 2.13/1.51 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ X0)) = $true) | ((X1 != X2) & ((in @ X1 @ X0) != $true))) & ((X1 = X2) | ((in @ X1 @ X0) = $true) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ((((sK120 != sK121) & ((in @ sK120 @ sK119) != $true)) | ((in @ sK120 @ (setadjoin @ sK121 @ sK119)) != $true)) & ((sK120 = sK121) | ((in @ sK120 @ sK119) = $true) | ((in @ sK120 @ (setadjoin @ sK121 @ sK119)) = $true))))),
% 2.13/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK119,sK120,sK121])],[f405,f406])).
% 2.13/1.51 thf(f406,plain,(
% 2.13/1.51 ? [X3 : $i,X4 : $i,X5 : $i] : ((((X4 != X5) & ((in @ X4 @ X3) != $true)) | ((in @ X4 @ (setadjoin @ X5 @ X3)) != $true)) & ((X4 = X5) | ((in @ X4 @ X3) = $true) | ((in @ X4 @ (setadjoin @ X5 @ X3)) = $true))) => ((((sK120 != sK121) & ((in @ sK120 @ sK119) != $true)) | ((in @ sK120 @ (setadjoin @ sK121 @ sK119)) != $true)) & ((sK120 = sK121) | ((in @ sK120 @ sK119) = $true) | ((in @ sK120 @ (setadjoin @ sK121 @ sK119)) = $true)))),
% 2.13/1.51 introduced(definition,[],[choice_axiom])).
% 2.13/1.51 thf(f405,plain,(
% 2.13/1.51 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ X0)) = $true) | ((X1 != X2) & ((in @ X1 @ X0) != $true))) & ((X1 = X2) | ((in @ X1 @ X0) = $true) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((X4 != X5) & ((in @ X4 @ X3) != $true)) | ((in @ X4 @ (setadjoin @ X5 @ X3)) != $true)) & ((X4 = X5) | ((in @ X4 @ X3) = $true) | ((in @ X4 @ (setadjoin @ X5 @ X3)) = $true))))),
% 2.13/1.51 inference(rectify,[status(thm)],[f404])).
% 2.13/1.51 thf(f404,plain,(
% 2.13/1.51 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ X0)) = $true) | ((X1 != X2) & ((in @ X1 @ X0) != $true))) & ((X1 = X2) | ((in @ X1 @ X0) = $true) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((X1 != X2) & ((in @ X1 @ X0) != $true)) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true)) & ((X1 = X2) | ((in @ X1 @ X0) = $true) | ((in @ X1 @ (setadjoin @ X2 @ X0)) = $true))))),
% 2.13/1.51 inference(flattening,[status(thm)],[f403])).
% 2.13/1.51 thf(f403,plain,(
% 2.13/1.51 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ X0)) = $true) | ((X1 != X2) & ((in @ X1 @ X0) != $true))) & (((X1 = X2) | ((in @ X1 @ X0) = $true)) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((X1 != X2) & ((in @ X1 @ X0) != $true)) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true)) & (((X1 = X2) | ((in @ X1 @ X0) = $true)) | ((in @ X1 @ (setadjoin @ X2 @ X0)) = $true))))),
% 2.13/1.51 inference(nnf_transformation,[status(thm)],[f64])).
% 2.13/1.51 thf(f64,plain,(
% 2.13/1.51 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setadjoin @ X2 @ X0)) = $true) <=> ((X1 = X2) | ((in @ X1 @ X0) = $true))) <=> (setadjoinAx = $true)),
% 2.13/1.51 inference(fool_elimination,[status(thm)],[f63])).
% 2.13/1.51 thf(f63,plain,(
% 2.13/1.51 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ X0)) <=> ((in @ X1 @ X0) | (X1 = X2))) = setadjoinAx)),
% 2.13/1.51 inference(rectify,[status(thm)],[f4])).
% 2.13/1.51 thf(f4,axiom,(
% 2.13/1.51 (! [X3 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) <=> ((in @ X2 @ X3) | (X1 = X2))) = setadjoinAx)),
% 2.13/1.51 file('/export/starexec/sandbox/tmp/tmp.p9jyL4yqSG/DTF2THF_5545.p',setadjoinAx)).
% 2.13/1.51 % SZS output end Proof for DTF2THF_5545
% 2.13/1.51 % (5684)------------------------------
% 2.13/1.51 % (5684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.13/1.51 % (5684)Termination reason: Refutation
% 2.13/1.51
% 2.13/1.51 % (5684)Memory used [KB]: 6268
% 2.13/1.51 % (5684)Time elapsed: 0.019 s
% 2.13/1.51 % (5684)Instructions burned: 50 (million)
% 2.13/1.51 % (5684)------------------------------
% 2.13/1.51 % (5684)------------------------------
% 2.13/1.51 % (5661)Success in time 0.102 s
%------------------------------------------------------------------------------