%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU515^1 : 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 : n022.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 09:35:01 AM UTC 2026
% Result : Theorem 2.04s 1.53s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 925 ( 278 equ; 0 cnn)
% Maximal formula atoms : 37 ( 23 avg)
% Number of connectives : 668 ( 72 ~; 76 |; 136 &; 230 @)
% ( 7 <=>; 147 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 99 usr; 43 con; 0-3 aty)
% Number of variables : 72 ( 0 ^; 46 !; 26 ?; 72 :)
% 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_56,type,
sP1: $i > $i > $o ).
thf(func_def_57,type,
sP2: $i > $o ).
thf(func_def_58,type,
sP3: $i > $i > $o ).
thf(func_def_59,type,
sP4: $i > $i > $o ).
thf(func_def_60,type,
sK5: $i > $o ).
thf(func_def_65,type,
sK10: $i > $i > $i ).
thf(func_def_66,type,
sK11: $i > $i > $i ).
thf(func_def_75,type,
sK20: $i > $i > $o ).
thf(func_def_77,type,
sK22: $i > $i ).
thf(func_def_78,type,
sK23: $i > $i ).
thf(func_def_79,type,
sK24: $i > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK25: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_81,type,
sK26: $i > ( $i > $i > $o ) > $i ).
thf(func_def_87,type,
sK32: $i > $o ).
thf(func_def_89,type,
sK34: $i > $i > $i ).
thf(func_def_90,type,
sK35: $i > $i > $i ).
thf(func_def_91,type,
sK36: $i > $i > $i ).
thf(func_def_92,type,
sK37: $i > $i > $i ).
thf(func_def_93,type,
sK38: $i > $i > $i > $i ).
thf(func_def_94,type,
sK39: $i > $i ).
thf(func_def_95,type,
sK40: $i > $i ).
thf(func_def_96,type,
sK41: $i > $i ).
thf(func_def_97,type,
sK42: $i > $i ).
thf(func_def_98,type,
sK43: $i > $i > $i ).
thf(func_def_99,type,
sK44: $i > $i > $i > $i ).
thf(func_def_100,type,
sK45: $i > $i > $i > $i ).
thf(func_def_101,type,
sK46: $i > $i > $i ).
thf(func_def_102,type,
sK47: $i > $i > $i ).
thf(func_def_104,type,
sK49: $i > $i ).
thf(func_def_105,type,
sK50: $i > $i ).
thf(func_def_106,type,
sK51: $i > $i ).
thf(func_def_107,type,
sK52: $i > $i > $i ).
thf(func_def_108,type,
sK53: $i > $o ).
thf(func_def_109,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_113,type,
sK58: $i > $o ).
thf(func_def_119,type,
sK64: $i > $i ).
thf(func_def_120,type,
sK65: $i > $i ).
thf(func_def_122,type,
sK67: $i > $i ).
thf(func_def_125,type,
sK70: $i > $o ).
thf(func_def_127,type,
sK72: $i > $i ).
thf(func_def_130,type,
sK75: $i > $i ).
thf(func_def_133,type,
sK78: $i > $i > $i ).
thf(func_def_138,type,
sK83: $i > $i > $i ).
thf(func_def_144,type,
sK89: $i > $o ).
thf(func_def_145,type,
sK90: $i > $i ).
thf(func_def_149,type,
sK94: $i > $o ).
thf(func_def_150,type,
sK95: $i > $i ).
thf(func_def_151,type,
sK96: ( $i > $o ) > $i ).
thf(func_def_153,type,
ph98:
!>[X0: $tType] : X0 ).
thf(f1016,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f660,f665,f666,f1009]) ).
thf(f1009,plain,
( spl97_1
| spl97_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f1008]) ).
thf(f1008,plain,
( $false
| spl97_1
| spl97_3 ),
inference(subsumption_resolution,[status(thm)],[f1007,f664]) ).
thf(f664,plain,
( ( ( in @ sK29 @ sK28 )
!= $true )
| spl97_3 ),
inference(avatar_component_clause,[status(thm)],[f662]) ).
thf(f662,definition,
( spl97_3
<=> ( ( in @ sK29 @ sK28 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl97_3])],[avatar_definition]) ).
thf(f1007,plain,
( ( ( in @ sK29 @ sK28 )
= $true )
| spl97_1 ),
inference(subsumption_resolution,[status(thm)],[f1002,f655]) ).
thf(f655,plain,
( ( sK29 != sK27 )
| spl97_1 ),
inference(avatar_component_clause,[status(thm)],[f653]) ).
thf(f653,definition,
( spl97_1
<=> ( sK29 = sK27 ) ),
introduced(definition,[new_symbols(naming,[spl97_1])],[avatar_definition]) ).
thf(f1002,plain,
( ( sK29 = sK27 )
| ( ( in @ sK29 @ sK28 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f981]) ).
thf(f981,plain,
( ( sK29 = sK27 )
| ( $true != $true )
| ( ( in @ sK29 @ sK28 )
= $true ) ),
inference(superposition,[status(thm)],[f600,f380]) ).
thf(f380,plain,
( $true
= ( in @ sK29 @ ( setadjoin @ sK27 @ sK28 ) ) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
thf(f189,plain,
( ( setext = $true )
& ( setextAx = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI1 = $true )
& ( $true
= ( in @ sK29 @ ( setadjoin @ sK27 @ sK28 ) ) )
& ( sK30 != $true )
& ( ( sK30 = $true )
| ( ( in @ sK29 @ sK28 )
!= $true ) )
& ( ( sK29 != sK27 )
| ( sK30 = $true ) )
& ( setadjoinAx = $true )
& ( emptysetE = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( replAx = $true )
& ( foundationAx = $true )
& ( dsetconstrER = $true )
& ( emptyinunitempty = $true )
& ( emptyI = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( emptysetimpfalse = $true )
& ( omegaSAx = $true )
& ( nonemptyI = $true )
& ( omega0Ax = $true )
& ( powersetAx = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( setbeta = $true )
& ( dsetconstrI = $true )
& ( exuE1 = $true )
& ( descrp = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30])],[f136,f188,f187]) ).
thf(f187,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X2 @ X1 ) ) )
& ( ( X0 != X2 )
| ( $true = X3 ) ) ) )
=> ( ( $true
= ( in @ sK29 @ ( setadjoin @ sK27 @ sK28 ) ) )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ sK29 @ sK28 )
!= $true ) )
& ( ( sK29 != sK27 )
| ( $true = X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f188,plain,
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ sK29 @ sK28 )
!= $true ) )
& ( ( sK29 != sK27 )
| ( $true = X3 ) ) )
=> ( ( sK30 != $true )
& ( ( sK30 = $true )
| ( ( in @ sK29 @ sK28 )
!= $true ) )
& ( ( sK29 != sK27 )
| ( sK30 = $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f136,plain,
( ( setext = $true )
& ( setextAx = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X2 @ X1 ) ) )
& ( ( X0 != X2 )
| ( $true = X3 ) ) ) )
& ( setadjoinAx = $true )
& ( emptysetE = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( replAx = $true )
& ( foundationAx = $true )
& ( dsetconstrER = $true )
& ( emptyinunitempty = $true )
& ( emptyI = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( emptysetimpfalse = $true )
& ( omegaSAx = $true )
& ( nonemptyI = $true )
& ( omega0Ax = $true )
& ( powersetAx = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( setbeta = $true )
& ( dsetconstrI = $true )
& ( exuE1 = $true )
& ( descrp = $true ) ),
inference(flattening,[status(thm)],[f135]) ).
thf(f135,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X2 @ X1 ) ) )
& ( ( X0 != X2 )
| ( $true = X3 ) ) )
& ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $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)],[f96]) ).
thf(f96,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> ( $true = X3 ) )
=> ( ( ( $true
= ( in @ X2 @ X1 ) )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f95]) ).
thf(f95,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,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
=> ! [X1: $i,X3: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
=> ! [X0: $o] :
( ( ( X1 = X2 )
=> X0 )
=> ( ( ( in @ X2 @ X3 )
=> X0 )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f35,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
=> ! [X1: $i,X3: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
=> ! [X0: $o] :
( ( ( X1 = X2 )
=> X0 )
=> ( ( ( in @ X2 @ X3 )
=> X0 )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WdysWW27tQ/DTF2THF_29721.p',setadjoinE) ).
thf(f600,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true )
| ( X4 = X5 )
| ( ( in @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f505]) ).
thf(f505,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
= $true )
| ( X4 = X5 )
| ( $true != $true )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f323,f376]) ).
thf(f376,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f189]) ).
thf(f323,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
thf(f162,plain,
( ( ( setadjoinAx = $true )
| ( ( ( ( sK14 != sK13 )
& ( ( in @ sK13 @ sK12 )
!= $true ) )
| ( $true
!= ( in @ sK13 @ ( setadjoin @ sK14 @ sK12 ) ) ) )
& ( ( sK14 = sK13 )
| ( ( in @ sK13 @ sK12 )
= $true )
| ( $true
= ( in @ sK13 @ ( setadjoin @ sK14 @ sK12 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true )
| ( ( X4 != X5 )
& ( ( in @ X4 @ X3 )
!= $true ) ) )
& ( ( X4 = X5 )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f160,f161]) ).
thf(f161,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( X1 != X2 )
& ( $true
!= ( in @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) )
& ( ( X1 = X2 )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) )
=> ( ( ( ( sK14 != sK13 )
& ( ( in @ sK13 @ sK12 )
!= $true ) )
| ( $true
!= ( in @ sK13 @ ( setadjoin @ sK14 @ sK12 ) ) ) )
& ( ( sK14 = sK13 )
| ( ( in @ sK13 @ sK12 )
= $true )
| ( $true
= ( in @ sK13 @ ( setadjoin @ sK14 @ sK12 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f160,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( X1 != X2 )
& ( $true
!= ( in @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) )
& ( ( X1 = X2 )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true )
| ( ( X4 != X5 )
& ( ( in @ X4 @ X3 )
!= $true ) ) )
& ( ( X4 = X5 )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) ) ),
inference(rectify,[status(thm)],[f159]) ).
thf(f159,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( X1 != X2 )
& ( $true
!= ( in @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) )
& ( ( X1 = X2 )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
| ( ( X1 != X2 )
& ( $true
!= ( in @ X1 @ X0 ) ) ) )
& ( ( X1 = X2 )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(flattening,[status(thm)],[f158]) ).
thf(f158,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( X1 != X2 )
& ( $true
!= ( in @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) )
& ( ( X1 = X2 )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
| ( ( X1 != X2 )
& ( $true
!= ( in @ X1 @ X0 ) ) ) )
& ( ( X1 = X2 )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f102]) ).
thf(f102,plain,
( ( setadjoinAx = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
<=> ( ( X1 = X2 )
| ( $true
= ( in @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f101]) ).
thf(f101,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( X1 = X2 )
| ( in @ X1 @ X0 ) )
<=> ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( setadjoinAx
= ( ! [X3: $i,X2: $i,X1: $i] :
( ( ( X1 = X2 )
| ( in @ X2 @ X3 ) )
<=> ( in @ X2 @ ( setadjoin @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WdysWW27tQ/DTF2THF_29721.p',setadjoinAx) ).
thf(f666,plain,
~ spl97_2,
inference(avatar_split_clause,[status(thm)],[f379,f657]) ).
thf(f657,definition,
( spl97_2
<=> ( sK30 = $true ) ),
introduced(definition,[new_symbols(naming,[spl97_2])],[avatar_definition]) ).
thf(f379,plain,
sK30 != $true,
inference(cnf_transformation,[status(thm)],[f189]) ).
thf(f665,plain,
( spl97_2
| ~ spl97_3 ),
inference(avatar_split_clause,[status(thm)],[f378,f662,f657]) ).
thf(f378,plain,
( ( ( in @ sK29 @ sK28 )
!= $true )
| ( sK30 = $true ) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
thf(f660,plain,
( ~ spl97_1
| spl97_2 ),
inference(avatar_split_clause,[status(thm)],[f377,f657,f653]) ).
thf(f377,plain,
( ( sK30 = $true )
| ( sK29 != sK27 ) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU515^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:25:21 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : SEU515^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.49 % Domain : Set Theory
% 0.27/0.49 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.27/0.49 % Version : Especial.
% 0.27/0.49 % English : (! x:i.! A:i.! y:i.in y (setadjoin x A) -> (! phi:o.(y = x -> phi)
% 0.27/0.49 % -> (in y A -> phi) -> phi))
% 0.27/0.49
% 0.27/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.49 % Source : [Bro08]
% 0.27/0.49 % Names : ZFC017g [Bro08]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.27/0.49 % Syntax : Number of formulae : 77 ( 34 unt; 42 typ; 34 def)
% 0.27/0.49 % Number of atoms : 194 ( 44 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 34 ( 5 avg)
% 0.27/0.49 % Number of connectives : 333 ( 7 ~; 3 |; 18 &; 217 @)
% 0.27/0.49 % ( 7 <=>; 81 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 42 ( 2 avg)
% 0.27/0.49 % Number of types : 2 ( 0 usr)
% 0.27/0.49 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 44 ( 42 usr; 34 con; 0-2 aty)
% 0.27/0.49 % Number of variables : 110 ( 14 ^; 80 !; 16 ?; 110 :)
% 0.27/0.49 % SPC : TH0_THM_EQU_NAR
% 0.27/0.49
% 0.27/0.49 % Comments : http://mathgate.info/detsetitem.php?id=82
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf(in_type,type,
% 0.27/0.49 in: $i > $i > $o ).
% 0.27/0.49
% 0.27/0.49 thf(exu_type,type,
% 0.27/0.49 exu: ( $i > $o ) > $o ).
% 0.27/0.49
% 0.27/0.49 thf(exu,definition,
% 0.27/0.49 ( exu
% 0.27/0.49 = ( ^ [Xphi: $i > $o] :
% 0.27/0.49 ? [Xx: $i] :
% 0.27/0.49 ( ( Xphi @ Xx )
% 0.27/0.49 & ! [Xy: $i] :
% 0.27/0.49 ( ( Xphi @ Xy )
% 0.27/0.49 => ( Xx = Xy ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(setextAx_type,type,
% 0.27/0.49 setextAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(setextAx,definition,
% 0.27/0.49 ( setextAx
% 0.27/0.49 = ( ! [A: $i,B: $i] :
% 0.27/0.49 ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ A )
% 0.27/0.49 <=> ( in @ Xx @ B ) )
% 0.27/0.49 => ( A = B ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(emptyset_type,type,
% 0.27/0.49 emptyset: $i ).
% 0.27/0.49
% 0.27/0.49 thf(emptysetAx_type,type,
% 0.27/0.49 emptysetAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(emptysetAx,definition,
% 0.27/0.49 ( emptysetAx
% 0.27/0.49 = ( ! [Xx: $i] :
% 0.27/0.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(setadjoin_type,type,
% 0.27/0.49 setadjoin: $i > $i > $i ).
% 0.27/0.49
% 0.27/0.49 thf(setadjoinAx_type,type,
% 0.27/0.49 setadjoinAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(setadjoinAx,definition,
% 0.27/0.49 ( setadjoinAx
% 0.27/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.49 <=> ( ( Xy = Xx )
% 0.27/0.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(powerset_type,type,
% 0.27/0.49 powerset: $i > $i ).
% 0.27/0.49
% 0.27/0.49 thf(powersetAx_type,type,
% 0.27/0.49 powersetAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(powersetAx,definition,
% 0.27/0.49 ( powersetAx
% 0.27/0.49 = ( ! [A: $i,B: $i] :
% 0.27/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.49 <=> ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ B )
% 0.27/0.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(setunion_type,type,
% 0.27/0.49 setunion: $i > $i ).
% 0.27/0.49
% 0.27/0.49 thf(setunionAx_type,type,
% 0.27/0.49 setunionAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(setunionAx,definition,
% 0.27/0.49 ( setunionAx
% 0.27/0.49 = ( ! [A: $i,Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.49 <=> ? [B: $i] :
% 0.27/0.49 ( ( in @ Xx @ B )
% 0.27/0.49 & ( in @ B @ A ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(omega_type,type,
% 0.27/0.49 omega: $i ).
% 0.27/0.49
% 0.27/0.49 thf(omega0Ax_type,type,
% 0.27/0.49 omega0Ax: $o ).
% 0.27/0.49
% 0.27/0.49 thf(omega0Ax,definition,
% 0.27/0.49 ( omega0Ax
% 0.27/0.49 = ( in @ emptyset @ omega ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(omegaSAx_type,type,
% 0.27/0.49 omegaSAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(omegaSAx,definition,
% 0.27/0.49 ( omegaSAx
% 0.27/0.49 = ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ omega )
% 0.27/0.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(omegaIndAx_type,type,
% 0.27/0.49 omegaIndAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(omegaIndAx,definition,
% 0.27/0.49 ( omegaIndAx
% 0.27/0.49 = ( ! [A: $i] :
% 0.27/0.49 ( ( ( in @ emptyset @ A )
% 0.27/0.49 & ! [Xx: $i] :
% 0.27/0.49 ( ( ( in @ Xx @ omega )
% 0.27/0.49 & ( in @ Xx @ A ) )
% 0.27/0.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.27/0.49 => ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ omega )
% 0.27/0.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(replAx_type,type,
% 0.27/0.49 replAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(replAx,definition,
% 0.27/0.49 ( replAx
% 0.27/0.49 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.27/0.49 ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ A )
% 0.27/0.49 => ( exu
% 0.27/0.49 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.27/0.49 => ? [B: $i] :
% 0.27/0.49 ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ B )
% 0.27/0.49 <=> ? [Xy: $i] :
% 0.27/0.49 ( ( in @ Xy @ A )
% 0.27/0.49 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(foundationAx_type,type,
% 0.27/0.49 foundationAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(foundationAx,definition,
% 0.27/0.49 ( foundationAx
% 0.27/0.49 = ( ! [A: $i] :
% 0.27/0.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.49 => ? [B: $i] :
% 0.27/0.49 ( ( in @ B @ A )
% 0.27/0.49 & ~ ? [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ B )
% 0.27/0.49 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(wellorderingAx_type,type,
% 0.27/0.49 wellorderingAx: $o ).
% 0.27/0.49
% 0.27/0.49 thf(wellorderingAx,definition,
% 0.27/0.49 ( wellorderingAx
% 0.27/0.49 = ( ! [A: $i] :
% 0.27/0.49 ? [B: $i] :
% 0.27/0.49 ( ! [C: $i] :
% 0.27/0.49 ( ( in @ C @ B )
% 0.27/0.49 => ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ C )
% 0.27/0.49 => ( in @ Xx @ A ) ) )
% 0.27/0.49 & ! [Xx: $i,Xy: $i] :
% 0.27/0.49 ( ( ( in @ Xx @ A )
% 0.27/0.49 & ( in @ Xy @ A ) )
% 0.27/0.49 => ( ! [C: $i] :
% 0.27/0.49 ( ( in @ C @ B )
% 0.27/0.49 => ( ( in @ Xx @ C )
% 0.27/0.49 <=> ( in @ Xy @ C ) ) )
% 0.27/0.49 => ( Xx = Xy ) ) )
% 0.27/0.49 & ! [C: $i,D: $i] :
% 0.27/0.49 ( ( ( in @ C @ B )
% 0.27/0.49 & ( in @ D @ B ) )
% 0.27/0.49 => ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ C )
% 0.27/0.49 => ( in @ Xx @ D ) )
% 0.27/0.49 | ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ D )
% 0.27/0.49 => ( in @ Xx @ C ) ) ) )
% 0.27/0.49 & ! [C: $i] :
% 0.27/0.49 ( ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ C )
% 0.27/0.49 => ( in @ Xx @ A ) )
% 0.27/0.49 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.27/0.49 => ? [D: $i,Xx: $i] :
% 0.27/0.49 ( ( in @ D @ B )
% 0.27/0.49 & ( in @ Xx @ C )
% 0.27/0.49 & ~ ? [Xy: $i] :
% 0.27/0.49 ( ( in @ Xy @ D )
% 0.27/0.49 & ( in @ Xy @ C ) )
% 0.27/0.49 & ! [E: $i] :
% 0.27/0.49 ( ( in @ E @ B )
% 0.27/0.49 => ( ! [Xy: $i] :
% 0.27/0.49 ( ( in @ Xy @ E )
% 0.27/0.49 => ( in @ Xy @ D ) )
% 0.27/0.49 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(descr_type,type,
% 0.27/0.49 descr: ( $i > $o ) > $i ).
% 0.27/0.49
% 0.27/0.49 thf(descrp_type,type,
% 0.27/0.49 descrp: $o ).
% 0.27/0.49
% 0.27/0.49 thf(descrp,definition,
% 0.27/0.49 ( descrp
% 0.27/0.49 = ( ! [Xphi: $i > $o] :
% 0.27/0.49 ( ( exu
% 0.27/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.49 => ( Xphi
% 0.27/0.49 @ ( descr
% 0.27/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(dsetconstr_type,type,
% 0.27/0.49 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.27/0.49
% 0.27/0.49 thf(dsetconstrI_type,type,
% 0.27/0.49 dsetconstrI: $o ).
% 0.27/0.49
% 0.27/0.49 thf(dsetconstrI,definition,
% 0.27/0.49 ( dsetconstrI
% 0.27/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ A )
% 0.27/0.49 => ( ( Xphi @ Xx )
% 0.27/0.49 => ( in @ Xx
% 0.27/0.49 @ ( dsetconstr @ A
% 0.27/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(dsetconstrEL_type,type,
% 0.27/0.49 dsetconstrEL: $o ).
% 0.27/0.49
% 0.27/0.49 thf(dsetconstrEL,definition,
% 0.27/0.49 ( dsetconstrEL
% 0.27/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.49 ( ( in @ Xx
% 0.27/0.49 @ ( dsetconstr @ A
% 0.27/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(dsetconstrER_type,type,
% 0.27/0.49 dsetconstrER: $o ).
% 0.27/0.49
% 0.27/0.49 thf(dsetconstrER,definition,
% 0.27/0.49 ( dsetconstrER
% 0.27/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.49 ( ( in @ Xx
% 0.27/0.49 @ ( dsetconstr @ A
% 0.27/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.49 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(exuE1_type,type,
% 0.27/0.49 exuE1: $o ).
% 0.27/0.49
% 0.27/0.49 thf(exuE1,definition,
% 0.27/0.49 ( exuE1
% 0.27/0.49 = ( ! [Xphi: $i > $o] :
% 0.27/0.49 ( ( exu
% 0.27/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.49 => ? [Xx: $i] :
% 0.27/0.49 ( ( Xphi @ Xx )
% 0.27/0.49 & ! [Xy: $i] :
% 0.27/0.49 ( ( Xphi @ Xy )
% 0.27/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(prop2set_type,type,
% 0.27/0.49 prop2set: $o > $i ).
% 0.27/0.49
% 0.27/0.49 thf(prop2set,definition,
% 0.27/0.49 ( prop2set
% 0.27/0.49 = ( ^ [Xphi: $o] :
% 0.27/0.49 ( dsetconstr @ ( powerset @ emptyset )
% 0.27/0.49 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(prop2setE_type,type,
% 0.27/0.49 prop2setE: $o ).
% 0.27/0.49
% 0.27/0.49 thf(prop2setE,definition,
% 0.27/0.49 ( prop2setE
% 0.27/0.49 = ( ! [Xphi: $o,Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.27/0.49 => Xphi ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(emptysetE_type,type,
% 0.27/0.49 emptysetE: $o ).
% 0.27/0.49
% 0.27/0.49 thf(emptysetE,definition,
% 0.27/0.49 ( emptysetE
% 0.27/0.49 = ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ emptyset )
% 0.27/0.49 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(emptysetimpfalse_type,type,
% 0.27/0.49 emptysetimpfalse: $o ).
% 0.27/0.49
% 0.27/0.49 thf(emptysetimpfalse,definition,
% 0.27/0.49 ( emptysetimpfalse
% 0.27/0.49 = ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ emptyset )
% 0.27/0.49 => $false ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(notinemptyset_type,type,
% 0.27/0.49 notinemptyset: $o ).
% 0.27/0.49
% 0.27/0.49 thf(notinemptyset,definition,
% 0.27/0.49 ( notinemptyset
% 0.27/0.49 = ( ! [Xx: $i] :
% 0.27/0.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(exuE3e_type,type,
% 0.27/0.49 exuE3e: $o ).
% 0.27/0.49
% 0.27/0.49 thf(exuE3e,definition,
% 0.27/0.49 ( exuE3e
% 0.27/0.49 = ( ! [Xphi: $i > $o] :
% 0.27/0.49 ( ( exu
% 0.27/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.49 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(setext_type,type,
% 0.27/0.49 setext: $o ).
% 0.27/0.49
% 0.27/0.49 thf(setext,definition,
% 0.27/0.49 ( setext
% 0.27/0.49 = ( ! [A: $i,B: $i] :
% 0.27/0.49 ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ A )
% 0.27/0.49 => ( in @ Xx @ B ) )
% 0.27/0.49 => ( ! [Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ B )
% 0.27/0.49 => ( in @ Xx @ A ) )
% 0.27/0.49 => ( A = B ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(emptyI_type,type,
% 0.27/0.49 emptyI: $o ).
% 0.27/0.49
% 0.27/0.49 thf(emptyI,definition,
% 0.27/0.49 ( emptyI
% 0.27/0.49 = ( ! [A: $i] :
% 0.27/0.49 ( ! [Xx: $i] :
% 0.27/0.49 ~ ( in @ Xx @ A )
% 0.27/0.49 => ( A = emptyset ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(noeltsimpempty_type,type,
% 0.27/0.49 noeltsimpempty: $o ).
% 0.27/0.49
% 0.27/0.49 thf(noeltsimpempty,definition,
% 0.27/0.49 ( noeltsimpempty
% 0.27/0.49 = ( ! [A: $i] :
% 0.27/0.49 ( ! [Xx: $i] :
% 0.27/0.49 ~ ( in @ Xx @ A )
% 0.27/0.49 => ( A = emptyset ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(setbeta_type,type,
% 0.27/0.49 setbeta: $o ).
% 0.27/0.49
% 0.27/0.49 thf(setbeta,definition,
% 0.27/0.49 ( setbeta
% 0.27/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ A )
% 0.27/0.49 => ( ( in @ Xx
% 0.27/0.49 @ ( dsetconstr @ A
% 0.27/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.49 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(nonempty_type,type,
% 0.27/0.49 nonempty: $i > $o ).
% 0.27/0.49
% 0.27/0.49 thf(nonempty,definition,
% 0.27/0.49 ( nonempty
% 0.27/0.49 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(nonemptyE1_type,type,
% 0.27/0.49 nonemptyE1: $o ).
% 0.27/0.49
% 0.27/0.49 thf(nonemptyE1,definition,
% 0.27/0.49 ( nonemptyE1
% 0.27/0.49 = ( ! [A: $i] :
% 0.27/0.49 ( ( nonempty @ A )
% 0.27/0.49 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(nonemptyI_type,type,
% 0.27/0.49 nonemptyI: $o ).
% 0.27/0.49
% 0.27/0.49 thf(nonemptyI,definition,
% 0.27/0.49 ( nonemptyI
% 0.27/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ A )
% 0.27/0.49 => ( ( Xphi @ Xx )
% 0.27/0.49 => ( nonempty
% 0.27/0.49 @ ( dsetconstr @ A
% 0.27/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(nonemptyI1_type,type,
% 0.27/0.49 nonemptyI1: $o ).
% 0.27/0.49
% 0.27/0.49 thf(nonemptyI1,definition,
% 0.27/0.49 ( nonemptyI1
% 0.27/0.49 = ( ! [A: $i] :
% 0.27/0.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.49 => ( nonempty @ A ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(setadjoinIL_type,type,
% 0.27/0.49 setadjoinIL: $o ).
% 0.27/0.49
% 0.27/0.49 thf(setadjoinIL,definition,
% 0.27/0.49 ( setadjoinIL
% 0.27/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(emptyinunitempty_type,type,
% 0.27/0.49 emptyinunitempty: $o ).
% 0.27/0.49
% 0.27/0.49 thf(emptyinunitempty,definition,
% 0.27/0.49 ( emptyinunitempty
% 0.27/0.49 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(setadjoinIR_type,type,
% 0.27/0.49 setadjoinIR: $o ).
% 0.27/0.49
% 0.27/0.49 thf(setadjoinIR,definition,
% 0.27/0.49 ( setadjoinIR
% 0.27/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.49 ( ( in @ Xy @ A )
% 0.27/0.49 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(setadjoinE,conjecture,
% 0.27/0.49 ( setextAx
% 0.27/0.49 => ( emptysetAx
% 0.27/0.49 => ( setadjoinAx
% 0.27/0.49 => ( powersetAx
% 0.27/0.49 => ( setunionAx
% 0.27/0.49 => ( omega0Ax
% 0.27/0.49 => ( omegaSAx
% 0.27/0.49 => ( omegaIndAx
% 0.27/0.49 => ( replAx
% 0.27/0.49 => ( foundationAx
% 0.27/0.49 => ( wellorderingAx
% 0.27/0.49 => ( descrp
% 0.27/0.49 => ( dsetconstrI
% 0.27/0.49 => ( dsetconstrEL
% 0.27/0.49 => ( dsetconstrER
% 0.27/0.49 => ( exuE1
% 0.27/0.49 => ( prop2setE
% 0.27/0.49 => ( emptysetE
% 0.27/0.49 => ( emptysetimpfalse
% 0.27/0.49 => ( notinemptyset
% 0.27/0.49 => ( exuE3e
% 0.27/0.49 => ( setext
% 0.27/0.49 => ( emptyI
% 0.27/0.49 => ( noeltsimpempty
% 0.27/0.49 => ( setbeta
% 0.27/0.49 => ( nonemptyE1
% 0.27/0.49 => ( nonemptyI
% 0.27/0.49 => ( nonemptyI1
% 0.27/0.49 => ( setadjoinIL
% 0.27/0.49 => ( emptyinunitempty
% 0.27/0.49 => ( setadjoinIR
% 0.27/0.49 => ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.49 => ! [Xphi: $o] :
% 0.27/0.49 ( ( ( Xy = Xx )
% 0.27/0.49 => Xphi )
% 0.27/0.49 => ( ( ( in @ Xy @ A )
% 0.27/0.49 => Xphi )
% 0.27/0.49 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 0.32/1.40 ---- Embedded in THF ---
% 0.32/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.40 %%% Generated on Tue Feb 24 12:25:22 EST 2026
% 0.32/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.40 %%% Logic specification used:
% 0.32/1.40 %%% thf(spec, logic, $$dhol).
% 0.32/1.40
% 0.32/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WdysWW27tQ/DTF2DTF29721.p
% See solution above
% 0.32/1.40 ------------------------
% 0.32/1.42 ---- Cleaned THF ---
% 0.32/1.42 thf(in_type,type,
% 0.32/1.42 in: $i > $i > $o ).
% 0.32/1.42
% 0.32/1.42 thf(exu_type,type,
% 0.32/1.42 exu: ( $i > $o ) > $o ).
% 0.32/1.42
% 0.32/1.42 thf(exu,definition,
% 0.32/1.42 ( exu
% 0.32/1.42 = ( ^ [Xphi: $i > $o] :
% 0.32/1.42 ? [Xx: $i] :
% 0.32/1.42 ( ( Xphi @ Xx )
% 0.32/1.42 & ! [Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xy )
% 0.32/1.42 => ( Xx = Xy ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setextAx_type,type,
% 0.32/1.42 setextAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setextAx,definition,
% 0.32/1.42 ( setextAx
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 <=> ( in @ Xx @ B ) )
% 0.32/1.42 => ( A = B ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyset_type,type,
% 0.32/1.42 emptyset: $i ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetAx_type,type,
% 0.32/1.42 emptysetAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetAx,definition,
% 0.32/1.42 ( emptysetAx
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoin_type,type,
% 0.32/1.42 setadjoin: $i > $i > $i ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinAx_type,type,
% 0.32/1.42 setadjoinAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinAx,definition,
% 0.32/1.42 ( setadjoinAx
% 0.32/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.42 <=> ( ( Xy = Xx )
% 0.32/1.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(powerset_type,type,
% 0.32/1.42 powerset: $i > $i ).
% 0.32/1.42
% 0.32/1.42 thf(powersetAx_type,type,
% 0.32/1.42 powersetAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(powersetAx,definition,
% 0.32/1.42 ( powersetAx
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ( in @ B @ ( powerset @ A ) )
% 0.32/1.42 <=> ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setunion_type,type,
% 0.32/1.42 setunion: $i > $i ).
% 0.32/1.42
% 0.32/1.42 thf(setunionAx_type,type,
% 0.32/1.42 setunionAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setunionAx,definition,
% 0.32/1.42 ( setunionAx
% 0.32/1.42 = ( ! [A: $i,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/1.42 <=> ? [B: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 & ( in @ B @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(omega_type,type,
% 0.32/1.42 omega: $i ).
% 0.32/1.42
% 0.32/1.42 thf(omega0Ax_type,type,
% 0.32/1.42 omega0Ax: $o ).
% 0.32/1.42
% 0.32/1.42 thf(omega0Ax,definition,
% 0.32/1.42 ( omega0Ax
% 0.32/1.42 = ( in @ emptyset @ omega ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(omegaSAx_type,type,
% 0.32/1.42 omegaSAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(omegaSAx,definition,
% 0.32/1.42 ( omegaSAx
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ omega )
% 0.32/1.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(omegaIndAx_type,type,
% 0.32/1.42 omegaIndAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(omegaIndAx,definition,
% 0.32/1.42 ( omegaIndAx
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ( ( in @ emptyset @ A )
% 0.32/1.42 & ! [Xx: $i] :
% 0.32/1.42 ( ( ( in @ Xx @ omega )
% 0.32/1.42 & ( in @ Xx @ A ) )
% 0.32/1.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.32/1.42 => ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ omega )
% 0.32/1.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(replAx_type,type,
% 0.32/1.42 replAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(replAx,definition,
% 0.32/1.42 ( replAx
% 0.32/1.42 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( exu
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.32/1.42 => ? [B: $i] :
% 0.32/1.42 ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 <=> ? [Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ A )
% 0.32/1.42 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(foundationAx_type,type,
% 0.32/1.42 foundationAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(foundationAx,definition,
% 0.32/1.42 ( foundationAx
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/1.42 => ? [B: $i] :
% 0.32/1.42 ( ( in @ B @ A )
% 0.32/1.42 & ~ ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(wellorderingAx_type,type,
% 0.32/1.42 wellorderingAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(wellorderingAx,definition,
% 0.32/1.42 ( wellorderingAx
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ? [B: $i] :
% 0.32/1.42 ( ! [C: $i] :
% 0.32/1.42 ( ( in @ C @ B )
% 0.32/1.42 => ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ C )
% 0.32/1.42 => ( in @ Xx @ A ) ) )
% 0.32/1.42 & ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( ( in @ Xx @ A )
% 0.32/1.42 & ( in @ Xy @ A ) )
% 0.32/1.42 => ( ! [C: $i] :
% 0.32/1.42 ( ( in @ C @ B )
% 0.32/1.42 => ( ( in @ Xx @ C )
% 0.32/1.42 <=> ( in @ Xy @ C ) ) )
% 0.32/1.42 => ( Xx = Xy ) ) )
% 0.32/1.42 & ! [C: $i,D: $i] :
% 0.32/1.42 ( ( ( in @ C @ B )
% 0.32/1.42 & ( in @ D @ B ) )
% 0.32/1.42 => ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ C )
% 0.32/1.42 => ( in @ Xx @ D ) )
% 0.32/1.42 | ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ D )
% 0.32/1.42 => ( in @ Xx @ C ) ) ) )
% 0.32/1.42 & ! [C: $i] :
% 0.32/1.42 ( ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ C )
% 0.32/1.42 => ( in @ Xx @ A ) )
% 0.32/1.42 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.32/1.42 => ? [D: $i,Xx: $i] :
% 0.32/1.42 ( ( in @ D @ B )
% 0.32/1.42 & ( in @ Xx @ C )
% 0.32/1.42 & ~ ? [Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ D )
% 0.32/1.42 & ( in @ Xy @ C ) )
% 0.32/1.42 & ! [E: $i] :
% 0.32/1.42 ( ( in @ E @ B )
% 0.32/1.42 => ( ! [Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ E )
% 0.32/1.42 => ( in @ Xy @ D ) )
% 0.32/1.42 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(descr_type,type,
% 0.32/1.42 descr: ( $i > $o ) > $i ).
% 0.32/1.42
% 0.32/1.42 thf(descrp_type,type,
% 0.32/1.42 descrp: $o ).
% 0.32/1.42
% 0.32/1.42 thf(descrp,definition,
% 0.32/1.42 ( descrp
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 => ( Xphi
% 0.32/1.42 @ ( descr
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstr_type,type,
% 0.32/1.42 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrI_type,type,
% 0.32/1.42 dsetconstrI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrI,definition,
% 0.32/1.42 ( dsetconstrI
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( ( Xphi @ Xx )
% 0.32/1.42 => ( in @ Xx
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrEL_type,type,
% 0.32/1.42 dsetconstrEL: $o ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrEL,definition,
% 0.32/1.42 ( dsetconstrEL
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrER_type,type,
% 0.32/1.42 dsetconstrER: $o ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrER,definition,
% 0.32/1.42 ( dsetconstrER
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuE1_type,type,
% 0.32/1.42 exuE1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuE1,definition,
% 0.32/1.42 ( exuE1
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 => ? [Xx: $i] :
% 0.32/1.42 ( ( Xphi @ Xx )
% 0.32/1.42 & ! [Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xy )
% 0.32/1.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(prop2set_type,type,
% 0.32/1.42 prop2set: $o > $i ).
% 0.32/1.42
% 0.32/1.42 thf(prop2set,definition,
% 0.32/1.42 ( prop2set
% 0.32/1.42 = ( ^ [Xphi: $o] :
% 0.32/1.42 ( dsetconstr @ ( powerset @ emptyset )
% 0.32/1.42 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(prop2setE_type,type,
% 0.32/1.42 prop2setE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(prop2setE,definition,
% 0.32/1.42 ( prop2setE
% 0.32/1.42 = ( ! [Xphi: $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.32/1.42 => Xphi ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetE_type,type,
% 0.32/1.42 emptysetE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetE,definition,
% 0.32/1.42 ( emptysetE
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ emptyset )
% 0.32/1.42 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetimpfalse_type,type,
% 0.32/1.42 emptysetimpfalse: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetimpfalse,definition,
% 0.32/1.42 ( emptysetimpfalse
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ emptyset )
% 0.32/1.42 => $false ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(notinemptyset_type,type,
% 0.32/1.42 notinemptyset: $o ).
% 0.32/1.42
% 0.32/1.42 thf(notinemptyset,definition,
% 0.32/1.42 ( notinemptyset
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuE3e_type,type,
% 0.32/1.42 exuE3e: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuE3e,definition,
% 0.32/1.42 ( exuE3e
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setext_type,type,
% 0.32/1.42 setext: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setext,definition,
% 0.32/1.42 ( setext
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( in @ Xx @ B ) )
% 0.32/1.42 => ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 => ( in @ Xx @ A ) )
% 0.32/1.42 => ( A = B ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyI_type,type,
% 0.32/1.42 emptyI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptyI,definition,
% 0.32/1.42 ( emptyI
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ~ ( in @ Xx @ A )
% 0.32/1.42 => ( A = emptyset ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(noeltsimpempty_type,type,
% 0.32/1.42 noeltsimpempty: $o ).
% 0.32/1.42
% 0.32/1.42 thf(noeltsimpempty,definition,
% 0.32/1.42 ( noeltsimpempty
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ~ ( in @ Xx @ A )
% 0.32/1.42 => ( A = emptyset ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setbeta_type,type,
% 0.32/1.42 setbeta: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setbeta,definition,
% 0.32/1.42 ( setbeta
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( ( in @ Xx
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.42 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonempty_type,type,
% 0.32/1.42 nonempty: $i > $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonempty,definition,
% 0.32/1.42 ( nonempty
% 0.32/1.42 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyE1_type,type,
% 0.32/1.42 nonemptyE1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyE1,definition,
% 0.32/1.42 ( nonemptyE1
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ( nonempty @ A )
% 0.32/1.42 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyI_type,type,
% 0.32/1.42 nonemptyI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyI,definition,
% 0.32/1.42 ( nonemptyI
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( ( Xphi @ Xx )
% 0.32/1.42 => ( nonempty
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyI1_type,type,
% 0.32/1.42 nonemptyI1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyI1,definition,
% 0.32/1.42 ( nonemptyI1
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/1.42 => ( nonempty @ A ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinIL_type,type,
% 0.32/1.42 setadjoinIL: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinIL,definition,
% 0.32/1.42 ( setadjoinIL
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyinunitempty_type,type,
% 0.32/1.42 emptyinunitempty: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptyinunitempty,definition,
% 0.32/1.42 ( emptyinunitempty
% 0.32/1.42 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinIR_type,type,
% 0.32/1.42 setadjoinIR: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinIR,definition,
% 0.32/1.42 ( setadjoinIR
% 0.32/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ A )
% 0.32/1.42 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinE,conjecture,
% 0.32/1.42 ( setextAx
% 0.32/1.42 => ( emptysetAx
% 0.32/1.42 => ( setadjoinAx
% 0.32/1.42 => ( powersetAx
% 0.32/1.42 => ( setunionAx
% 0.32/1.42 => ( omega0Ax
% 0.32/1.42 => ( omegaSAx
% 0.32/1.42 => ( omegaIndAx
% 0.32/1.42 => ( replAx
% 0.32/1.42 => ( foundationAx
% 0.32/1.42 => ( wellorderingAx
% 0.32/1.42 => ( descrp
% 0.32/1.42 => ( dsetconstrI
% 0.32/1.42 => ( dsetconstrEL
% 0.32/1.42 => ( dsetconstrER
% 0.32/1.42 => ( exuE1
% 0.32/1.42 => ( prop2setE
% 0.32/1.42 => ( emptysetE
% 0.32/1.42 => ( emptysetimpfalse
% 0.32/1.42 => ( notinemptyset
% 0.32/1.42 => ( exuE3e
% 0.32/1.42 => ( setext
% 0.32/1.42 => ( emptyI
% 0.32/1.42 => ( noeltsimpempty
% 0.32/1.42 => ( setbeta
% 0.32/1.42 => ( nonemptyE1
% 0.32/1.42 => ( nonemptyI
% 0.32/1.42 => ( nonemptyI1
% 0.32/1.42 => ( setadjoinIL
% 0.32/1.42 => ( emptyinunitempty
% 0.32/1.42 => ( setadjoinIR
% 0.32/1.42 => ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.42 => ! [Xphi: $o] :
% 0.32/1.42 ( ( ( Xy = Xx )
% 0.32/1.42 => Xphi )
% 0.32/1.42 => ( ( ( in @ Xy @ A )
% 0.32/1.42 => Xphi )
% 0.32/1.42 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.42 ------------------------
% 0.32/1.43 % (29841)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_29721 for (2999ds/2Mi)
% 0.32/1.43 % (29840)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/2Mi)
% 0.32/1.43 % (29843)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/18Mi)
% 0.32/1.43 % (29840)Instruction limit reached!
% 0.32/1.43 % (29840)------------------------------
% 0.32/1.43 % (29840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (29840)Termination reason: Unknown
% 0.32/1.44 % (29840)Termination phase: shuffling
% 0.32/1.44
% 0.32/1.44 % (29841)Instruction limit reached!
% 0.32/1.44 % (29841)------------------------------
% 0.32/1.44 % (29841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.44 % (29841)Termination reason: Unknown
% 0.32/1.44 % (29841)Termination phase: shuffling
% 0.32/1.44
% 0.32/1.44 % (29841)Memory used [KB]: 1151
% 0.32/1.44 % (29841)Time elapsed: 0.003 s
% 0.32/1.44 % (29841)Instructions burned: 5 (million)
% 0.32/1.44 % (29841)------------------------------
% 0.32/1.44 % (29841)------------------------------
% 0.32/1.44 % (29840)Memory used [KB]: 1023
% 0.32/1.44 % (29840)Time elapsed: 0.002 s
% 0.32/1.44 % (29840)Instructions burned: 2 (million)
% 0.32/1.44 % (29840)------------------------------
% 0.32/1.44 % (29840)------------------------------
% 0.32/1.44 % (29843)Instruction limit reached!
% 0.32/1.44 % (29843)------------------------------
% 0.32/1.44 % (29843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.44 % (29843)Termination reason: Unknown
% 0.32/1.44 % (29843)Termination phase: Function definition elimination
% 0.32/1.44
% 0.32/1.44 % (29843)Memory used [KB]: 1407
% 0.32/1.44 % (29843)Time elapsed: 0.007 s
% 0.32/1.44 % (29843)Instructions burned: 19 (million)
% 0.32/1.44 % (29843)------------------------------
% 0.32/1.44 % (29843)------------------------------
% 0.32/1.44 % (29837)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/183Mi)
% 0.32/1.44 % (29842)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_29721 for (2999ds/275Mi)
% 0.32/1.44 % (29839)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_29721 for (2999ds/27Mi)
% 0.32/1.44 % (29838)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_29721 for (2999ds/4Mi)
% 0.32/1.44 % (29838)Instruction limit reached!
% 0.32/1.44 % (29838)------------------------------
% 0.32/1.44 % (29838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.44 % (29838)Termination reason: Unknown
% 0.32/1.44 % (29838)Termination phase: shuffling
% 0.32/1.44
% 0.32/1.44 % (29838)Memory used [KB]: 1151
% 0.32/1.44 % (29838)Time elapsed: 0.003 s
% 0.32/1.44 % (29838)Instructions burned: 6 (million)
% 0.32/1.44 % (29838)------------------------------
% 0.32/1.44 % (29838)------------------------------
% 0.32/1.45 % (29844)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/3Mi)
% 0.32/1.45 % (29844)Instruction limit reached!
% 0.32/1.45 % (29844)------------------------------
% 0.32/1.45 % (29844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.45 % (29844)Termination reason: Unknown
% 0.32/1.45 % (29844)Termination phase: shuffling
% 0.32/1.45
% 0.32/1.45 % (29844)Memory used [KB]: 1023
% 0.32/1.45 % (29844)Time elapsed: 0.002 s
% 0.32/1.45 % (29844)Instructions burned: 3 (million)
% 0.32/1.45 % (29844)------------------------------
% 0.32/1.45 % (29844)------------------------------
% 0.32/1.45 % (29846)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_29721 for (2999ds/15Mi)
% 0.32/1.45 % (29847)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_29721 for (2999ds/3Mi)
% 0.32/1.46 % (29847)Instruction limit reached!
% 0.32/1.46 % (29847)------------------------------
% 0.32/1.46 % (29847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (29847)Termination reason: Unknown
% 0.32/1.46 % (29847)Termination phase: shuffling
% 0.32/1.46
% 0.32/1.46 % (29847)Memory used [KB]: 1151
% 0.32/1.46 % (29847)Time elapsed: 0.003 s
% 0.32/1.46 % (29847)Instructions burned: 4 (million)
% 0.32/1.46 % (29847)------------------------------
% 0.32/1.46 % (29847)------------------------------
% 0.32/1.46 % (29845)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_29721 for (2999ds/37Mi)
% 0.32/1.46 % (29839)Instruction limit reached!
% 0.32/1.46 % (29839)------------------------------
% 0.32/1.46 % (29839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (29839)Termination reason: Unknown
% 0.32/1.46 % (29839)Termination phase: Saturation
% 0.32/1.46
% 0.32/1.46 % (29839)Memory used [KB]: 5756
% 0.32/1.46 % (29839)Time elapsed: 0.017 s
% 0.32/1.46 % (29839)Instructions burned: 28 (million)
% 0.32/1.46 % (29839)------------------------------
% 0.32/1.46 % (29839)------------------------------
% 0.32/1.46 % (29848)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_29721 for (2999ds/1041Mi)
% 0.32/1.46 % (29846)Instruction limit reached!
% 0.32/1.46 % (29846)------------------------------
% 0.32/1.46 % (29846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (29846)Termination reason: Unknown
% 0.32/1.46 % (29846)Termination phase: Property scanning
% 0.32/1.46
% 0.32/1.46 % (29846)Memory used [KB]: 1535
% 0.32/1.46 % (29846)Time elapsed: 0.007 s
% 0.32/1.46 % (29846)Instructions burned: 16 (million)
% 0.32/1.46 % (29846)------------------------------
% 0.32/1.46 % (29846)------------------------------
% 0.32/1.47 % (29849)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/7Mi)
% 0.32/1.47 % (29849)Instruction limit reached!
% 0.32/1.47 % (29849)------------------------------
% 0.32/1.47 % (29849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.47 % (29849)Termination reason: Unknown
% 0.32/1.47 % (29849)Termination phase: SInE selection
% 0.32/1.47
% 0.32/1.47 % (29849)Memory used [KB]: 1151
% 0.32/1.47 % (29849)Time elapsed: 0.005 s
% 0.32/1.47 % (29849)Instructions burned: 10 (million)
% 0.32/1.47 % (29849)------------------------------
% 0.32/1.47 % (29849)------------------------------
% 0.32/1.47 % (29851)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_29721 for (2999ds/3Mi)
% 0.32/1.47 % (29851)Instruction limit reached!
% 0.32/1.47 % (29851)------------------------------
% 0.32/1.47 % (29851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.47 % (29851)Termination reason: Unknown
% 0.32/1.47 % (29851)Termination phase: shuffling
% 0.32/1.47
% 0.32/1.47 % (29851)Memory used [KB]: 1023
% 0.32/1.47 % (29851)Time elapsed: 0.002 s
% 0.32/1.47 % (29851)Instructions burned: 3 (million)
% 0.32/1.47 % (29851)------------------------------
% 0.32/1.47 % (29851)------------------------------
% 0.32/1.47 % (29850)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/16Mi)
% 0.32/1.47 % (29845)Instruction limit reached!
% 0.32/1.47 % (29845)------------------------------
% 0.32/1.47 % (29845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.47 % (29845)Termination reason: Unknown
% 0.32/1.47 % (29845)Termination phase: Saturation
% 0.32/1.47
% 0.32/1.47 % (29845)Memory used [KB]: 5884
% 0.32/1.47 % (29845)Time elapsed: 0.021 s
% 0.32/1.47 % (29845)Instructions burned: 38 (million)
% 0.32/1.47 % (29845)------------------------------
% 0.32/1.47 % (29845)------------------------------
% 0.32/1.48 % (29852)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_29721 for (2999ds/3Mi)
% 0.32/1.48 % (29852)Instruction limit reached!
% 0.32/1.48 % (29852)------------------------------
% 0.32/1.48 % (29852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (29852)Termination reason: Unknown
% 0.32/1.48 % (29852)Termination phase: shuffling
% 0.32/1.48
% 0.32/1.48 % (29852)Memory used [KB]: 1023
% 0.32/1.48 % (29852)Time elapsed: 0.002 s
% 0.32/1.48 % (29852)Instructions burned: 4 (million)
% 0.32/1.48 % (29852)------------------------------
% 0.32/1.48 % (29852)------------------------------
% 0.32/1.48 % (29850)Instruction limit reached!
% 0.32/1.48 % (29850)------------------------------
% 0.32/1.48 % (29850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (29850)Termination reason: Unknown
% 0.32/1.48 % (29850)Termination phase: Twee Goal Transformation
% 0.32/1.48
% 0.32/1.48 % (29850)Memory used [KB]: 1279
% 0.32/1.48 % (29850)Time elapsed: 0.010 s
% 0.32/1.48 % (29850)Instructions burned: 18 (million)
% 0.32/1.48 % (29850)------------------------------
% 0.32/1.48 % (29850)------------------------------
% 0.32/1.48 % (29853)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/7Mi)
% 0.32/1.48 % (29853)Instruction limit reached!
% 0.32/1.48 % (29853)------------------------------
% 0.32/1.48 % (29853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (29853)Termination reason: Unknown
% 0.32/1.48 % (29853)Termination phase: Property scanning
% 0.32/1.48
% 0.32/1.48 % (29853)Memory used [KB]: 1151
% 0.32/1.48 % (29853)Time elapsed: 0.004 s
% 0.32/1.48 % (29853)Instructions burned: 7 (million)
% 0.32/1.48 % (29853)------------------------------
% 0.32/1.48 % (29853)------------------------------
% 0.32/1.49 % (29855)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/4Mi)
% 0.32/1.49 % (29856)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/18Mi)
% 0.32/1.49 % (29855)Instruction limit reached!
% 0.32/1.49 % (29855)------------------------------
% 0.32/1.49 % (29855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.49 % (29855)Termination reason: Unknown
% 0.32/1.49 % (29855)Termination phase: shuffling
% 0.32/1.49
% 0.32/1.49 % (29855)Memory used [KB]: 1151
% 0.32/1.49 % (29855)Time elapsed: 0.003 s
% 0.32/1.49 % (29855)Instructions burned: 4 (million)
% 0.32/1.49 % (29855)------------------------------
% 0.32/1.49 % (29855)------------------------------
% 0.32/1.49 % (29854)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/3Mi)
% 0.32/1.49 % (29857)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/710Mi)
% 0.32/1.49 % (29854)Instruction limit reached!
% 0.32/1.49 % (29854)------------------------------
% 0.32/1.49 % (29854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.49 % (29854)Termination reason: Unknown
% 0.32/1.49 % (29854)Termination phase: shuffling
% 0.32/1.49
% 0.32/1.49 % (29854)Memory used [KB]: 1023
% 0.32/1.49 % (29854)Time elapsed: 0.004 s
% 0.32/1.49 % (29854)Instructions burned: 4 (million)
% 0.32/1.49 % (29854)------------------------------
% 0.32/1.49 % (29854)------------------------------
% 2.04/1.50 % (29856)Instruction limit reached!
% 2.04/1.50 % (29856)------------------------------
% 2.04/1.50 % (29856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.50 % (29856)Termination reason: Unknown
% 2.04/1.50 % (29856)Termination phase: Saturation
% 2.04/1.50
% 2.04/1.50 % (29856)Memory used [KB]: 5756
% 2.04/1.50 % (29856)Time elapsed: 0.008 s
% 2.04/1.50 % (29856)Instructions burned: 20 (million)
% 2.04/1.50 % (29856)------------------------------
% 2.04/1.50 % (29856)------------------------------
% 2.04/1.50 % (29858)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/6Mi)
% 2.04/1.50 % (29858)Instruction limit reached!
% 2.04/1.50 % (29858)------------------------------
% 2.04/1.50 % (29858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.50 % (29858)Termination reason: Unknown
% 2.04/1.50 % (29858)Termination phase: Property scanning
% 2.04/1.50
% 2.04/1.50 % (29858)Memory used [KB]: 1151
% 2.04/1.50 % (29858)Time elapsed: 0.004 s
% 2.04/1.50 % (29858)Instructions burned: 8 (million)
% 2.04/1.50 % (29858)------------------------------
% 2.04/1.50 % (29858)------------------------------
% 2.04/1.51 % (29860)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_29721 for (2999ds/21Mi)
% 2.04/1.51 % (29859)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_29721 for (2999ds/902Mi)
% 2.04/1.51 % (29860)Instruction limit reached!
% 2.04/1.51 % (29860)------------------------------
% 2.04/1.51 % (29860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.51 % (29860)Termination reason: Unknown
% 2.04/1.51 % (29860)Termination phase: Saturation
% 2.04/1.51
% 2.04/1.51 % (29860)Memory used [KB]: 5628
% 2.04/1.51 % (29860)Time elapsed: 0.008 s
% 2.04/1.51 % (29860)Instructions burned: 21 (million)
% 2.04/1.51 % (29860)------------------------------
% 2.04/1.51 % (29860)------------------------------
% 2.04/1.51 % (29861)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/5Mi)
% 2.04/1.52 % (29861)Instruction limit reached!
% 2.04/1.52 % (29861)------------------------------
% 2.04/1.52 % (29861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.52 % (29861)Termination reason: Unknown
% 2.04/1.52 % (29861)Termination phase: Property scanning
% 2.04/1.52
% 2.04/1.52 % (29861)Memory used [KB]: 1151
% 2.04/1.52 % (29861)Time elapsed: 0.004 s
% 2.04/1.52 % (29861)Instructions burned: 8 (million)
% 2.04/1.52 % (29861)------------------------------
% 2.04/1.52 % (29861)------------------------------
% 2.04/1.52 % (29862)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_29721 for (2999ds/6Mi)
% 2.04/1.53 % (29862)Instruction limit reached!
% 2.04/1.53 % (29862)------------------------------
% 2.04/1.53 % (29862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.53 % (29862)Termination reason: Unknown
% 2.04/1.53 % (29862)Termination phase: Property scanning
% 2.04/1.53
% 2.04/1.53 % (29862)Memory used [KB]: 1151
% 2.04/1.53 % (29862)Time elapsed: 0.004 s
% 2.04/1.53 % (29862)Instructions burned: 7 (million)
% 2.04/1.53 % (29862)------------------------------
% 2.04/1.53 % (29862)------------------------------
% 2.04/1.53 % (29863)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29721 for (2999ds/377Mi)
% 2.04/1.53 % (29842)First to succeed.
% 2.04/1.53 % (29842)Refutation found. Thanks to Tanya!
% 2.04/1.53 % SZS status Theorem for DTF2THF_29721
% 2.04/1.53 % SZS output start Proof for DTF2THF_29721
% 2.04/1.53 thf(func_def_0, type, in: $i > $i > $o).
% 2.04/1.53 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.04/1.53 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.04/1.53 thf(func_def_8, type, powerset: $i > $i).
% 2.04/1.53 thf(func_def_10, type, setunion: $i > $i).
% 2.04/1.53 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.04/1.53 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.04/1.53 thf(func_def_26, type, prop2set: $o > $i).
% 2.04/1.53 thf(func_def_36, type, nonempty: $i > $o).
% 2.04/1.53 thf(func_def_56, type, sP1: $i > $i > $o).
% 2.04/1.53 thf(func_def_57, type, sP2: $i > $o).
% 2.04/1.53 thf(func_def_58, type, sP3: $i > $i > $o).
% 2.04/1.53 thf(func_def_59, type, sP4: $i > $i > $o).
% 2.04/1.53 thf(func_def_60, type, sK5: $i > $o).
% 2.04/1.53 thf(func_def_65, type, sK10: $i > $i > $i).
% 2.04/1.53 thf(func_def_66, type, sK11: $i > $i > $i).
% 2.04/1.53 thf(func_def_75, type, sK20: $i > $i > $o).
% 2.04/1.53 thf(func_def_77, type, sK22: $i > $i).
% 2.04/1.53 thf(func_def_78, type, sK23: $i > $i).
% 2.04/1.53 thf(func_def_79, type, sK24: $i > ($i > $i > $o) > $i).
% 2.04/1.53 thf(func_def_80, type, sK25: $i > $i > ($i > $i > $o) > $i).
% 2.04/1.53 thf(func_def_81, type, sK26: $i > ($i > $i > $o) > $i).
% 2.04/1.53 thf(func_def_87, type, sK32: $i > $o).
% 2.04/1.53 thf(func_def_89, type, sK34: $i > $i > $i).
% 2.04/1.53 thf(func_def_90, type, sK35: $i > $i > $i).
% 2.04/1.53 thf(func_def_91, type, sK36: $i > $i > $i).
% 2.04/1.53 thf(func_def_92, type, sK37: $i > $i > $i).
% 2.04/1.53 thf(func_def_93, type, sK38: $i > $i > $i > $i).
% 2.04/1.53 thf(func_def_94, type, sK39: $i > $i).
% 2.04/1.53 thf(func_def_95, type, sK40: $i > $i).
% 2.04/1.53 thf(func_def_96, type, sK41: $i > $i).
% 2.04/1.53 thf(func_def_97, type, sK42: $i > $i).
% 2.04/1.53 thf(func_def_98, type, sK43: $i > $i > $i).
% 2.04/1.53 thf(func_def_99, type, sK44: $i > $i > $i > $i).
% 2.04/1.53 thf(func_def_100, type, sK45: $i > $i > $i > $i).
% 2.04/1.53 thf(func_def_101, type, sK46: $i > $i > $i).
% 2.04/1.53 thf(func_def_102, type, sK47: $i > $i > $i).
% 2.04/1.53 thf(func_def_104, type, sK49: $i > $i).
% 2.04/1.53 thf(func_def_105, type, sK50: $i > $i).
% 2.04/1.53 thf(func_def_106, type, sK51: $i > $i).
% 2.04/1.53 thf(func_def_107, type, sK52: $i > $i > $i).
% 2.04/1.53 thf(func_def_108, type, sK53: $i > $o).
% 2.04/1.53 thf(func_def_109, type, sK54: ($i > $o) > $i).
% 2.04/1.53 thf(func_def_113, type, sK58: $i > $o).
% 2.04/1.53 thf(func_def_119, type, sK64: $i > $i).
% 2.04/1.53 thf(func_def_120, type, sK65: $i > $i).
% 2.04/1.53 thf(func_def_122, type, sK67: $i > $i).
% 2.04/1.53 thf(func_def_125, type, sK70: $i > $o).
% 2.04/1.53 thf(func_def_127, type, sK72: $i > $i).
% 2.04/1.53 thf(func_def_130, type, sK75: $i > $i).
% 2.04/1.53 thf(func_def_133, type, sK78: $i > $i > $i).
% 2.04/1.53 thf(func_def_138, type, sK83: $i > $i > $i).
% 2.04/1.53 thf(func_def_144, type, sK89: $i > $o).
% 2.04/1.53 thf(func_def_145, type, sK90: $i > $i).
% 2.04/1.53 thf(func_def_149, type, sK94: $i > $o).
% 2.04/1.53 thf(func_def_150, type, sK95: $i > $i).
% 2.04/1.53 thf(func_def_151, type, sK96: ($i > $o) > $i).
% 2.04/1.53 thf(func_def_153, type, ph98: !>[X0: $tType]:(X0)).
% 2.04/1.53 thf(f1016,plain,(
% 2.04/1.53 $false),
% 2.04/1.53 inference(avatar_sat_refutation,[status(thm)],[f660,f665,f666,f1009])).
% 2.04/1.53 thf(f1009,plain,(
% 2.04/1.53 spl97_1 | spl97_3),
% 2.04/1.53 inference(avatar_contradiction_clause,[status(thm)],[f1008])).
% 2.04/1.53 thf(f1008,plain,(
% 2.04/1.53 $false | (spl97_1 | spl97_3)),
% 2.04/1.53 inference(subsumption_resolution,[status(thm)],[f1007,f664])).
% 2.04/1.53 thf(f664,plain,(
% 2.04/1.53 ((in @ sK29 @ sK28) != $true) | spl97_3),
% 2.04/1.53 inference(avatar_component_clause,[status(thm)],[f662])).
% 2.04/1.53 thf(f662,definition,(
% 2.04/1.53 spl97_3 <=> ((in @ sK29 @ sK28) = $true)),
% 2.04/1.53 introduced(definition,[new_symbols(naming,[spl97_3])],[avatar_definition])).
% 2.04/1.53 thf(f1007,plain,(
% 2.04/1.53 ((in @ sK29 @ sK28) = $true) | spl97_1),
% 2.04/1.53 inference(subsumption_resolution,[status(thm)],[f1002,f655])).
% 2.04/1.53 thf(f655,plain,(
% 2.04/1.53 (sK29 != sK27) | spl97_1),
% 2.04/1.53 inference(avatar_component_clause,[status(thm)],[f653])).
% 2.04/1.53 thf(f653,definition,(
% 2.04/1.53 spl97_1 <=> (sK29 = sK27)),
% 2.04/1.53 introduced(definition,[new_symbols(naming,[spl97_1])],[avatar_definition])).
% 2.04/1.53 thf(f1002,plain,(
% 2.04/1.53 (sK29 = sK27) | ((in @ sK29 @ sK28) = $true)),
% 2.04/1.53 inference(trivial_inequality_removal,[status(thm)],[f981])).
% 2.04/1.53 thf(f981,plain,(
% 2.04/1.53 (sK29 = sK27) | ($true != $true) | ((in @ sK29 @ sK28) = $true)),
% 2.04/1.53 inference(superposition,[status(thm)],[f600,f380])).
% 2.04/1.53 thf(f380,plain,(
% 2.04/1.53 ($true = (in @ sK29 @ (setadjoin @ sK27 @ sK28)))),
% 2.04/1.53 inference(cnf_transformation,[status(thm)],[f189])).
% 2.04/1.53 thf(f189,plain,(
% 2.04/1.53 (setext = $true) & (setextAx = $true) & (dsetconstrEL = $true) & (nonemptyI1 = $true) & (($true = (in @ sK29 @ (setadjoin @ sK27 @ sK28))) & ((sK30 != $true) & ((sK30 = $true) | ((in @ sK29 @ sK28) != $true)) & ((sK29 != sK27) | (sK30 = $true)))) & (setadjoinAx = $true) & (emptysetE = $true) & (emptysetAx = $true) & (omegaIndAx = $true) & (replAx = $true) & (foundationAx = $true) & (dsetconstrER = $true) & (emptyinunitempty = $true) & (emptyI = $true) & (exuE3e = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (emptysetimpfalse = $true) & (omegaSAx = $true) & (nonemptyI = $true) & (omega0Ax = $true) & (powersetAx = $true) & (notinemptyset = $true) & (setadjoinIR = $true) & (wellorderingAx = $true) & (setadjoinIL = $true) & (setunionAx = $true) & (prop2setE = $true) & (setbeta = $true) & (dsetconstrI = $true) & (exuE1 = $true) & (descrp = $true)),
% 2.04/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30])],[f136,f188,f187])).
% 2.04/1.53 thf(f187,plain,(
% 2.04/1.53 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setadjoin @ X0 @ X1)) = $true) & ? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != (in @ X2 @ X1))) & ((X0 != X2) | ($true = X3)))) => (($true = (in @ sK29 @ (setadjoin @ sK27 @ sK28))) & ? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ sK29 @ sK28) != $true)) & ((sK29 != sK27) | ($true = X3))))),
% 2.04/1.53 introduced(definition,[],[choice_axiom])).
% 2.04/1.53 thf(f188,plain,(
% 2.04/1.53 ? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ sK29 @ sK28) != $true)) & ((sK29 != sK27) | ($true = X3))) => ((sK30 != $true) & ((sK30 = $true) | ((in @ sK29 @ sK28) != $true)) & ((sK29 != sK27) | (sK30 = $true)))),
% 2.04/1.53 introduced(definition,[],[choice_axiom])).
% 2.04/1.53 thf(f136,plain,(
% 2.04/1.53 (setext = $true) & (setextAx = $true) & (dsetconstrEL = $true) & (nonemptyI1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setadjoin @ X0 @ X1)) = $true) & ? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != (in @ X2 @ X1))) & ((X0 != X2) | ($true = X3)))) & (setadjoinAx = $true) & (emptysetE = $true) & (emptysetAx = $true) & (omegaIndAx = $true) & (replAx = $true) & (foundationAx = $true) & (dsetconstrER = $true) & (emptyinunitempty = $true) & (emptyI = $true) & (exuE3e = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (emptysetimpfalse = $true) & (omegaSAx = $true) & (nonemptyI = $true) & (omega0Ax = $true) & (powersetAx = $true) & (notinemptyset = $true) & (setadjoinIR = $true) & (wellorderingAx = $true) & (setadjoinIL = $true) & (setunionAx = $true) & (prop2setE = $true) & (setbeta = $true) & (dsetconstrI = $true) & (exuE1 = $true) & (descrp = $true)),
% 2.04/1.53 inference(flattening,[status(thm)],[f135])).
% 2.04/1.53 thf(f135,plain,(
% 2.04/1.53 ((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : ((($true != X3) & (($true = X3) | ($true != (in @ X2 @ X1)))) & ((X0 != X2) | ($true = X3))) & ((in @ X2 @ (setadjoin @ X0 @ X1)) = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.04/1.53 inference(ennf_transformation,[status(thm)],[f96])).
% 2.04/1.53 thf(f96,plain,(
% 2.04/1.53 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setadjoin @ X0 @ X1)) = $true) => ! [X3 : $o] : (((X0 = X2) => ($true = X3)) => ((($true = (in @ X2 @ X1)) => ($true = X3)) => ($true = X3)))))))))))))))))))))))))))))))))))),
% 2.04/1.53 inference(fool_elimination,[status(thm)],[f95])).
% 2.04/1.53 thf(f95,plain,(
% 2.04/1.53 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ! [X3 : $o] : (((X0 = X2) => X3) => (((in @ X2 @ X1) => X3) => X3))))))))))))))))))))))))))))))))))),
% 2.04/1.53 inference(rectify,[status(thm)],[f36])).
% 2.04/1.53 thf(f36,negated_conjecture,(
% 2.04/1.53 ~(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 => ! [X1 : $i,X3 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ! [X0 : $o] : (((X1 = X2) => X0) => (((in @ X2 @ X3) => X0) => X0))))))))))))))))))))))))))))))))))),
% 2.04/1.53 inference(negated_conjecture,[status(cth)],[f35])).
% 2.04/1.53 thf(f35,conjecture,(
% 2.04/1.53 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 => ! [X1 : $i,X3 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ! [X0 : $o] : (((X1 = X2) => X0) => (((in @ X2 @ X3) => X0) => X0)))))))))))))))))))))))))))))))))),
% 2.04/1.53 file('/export/starexec/sandbox/tmp/tmp.WdysWW27tQ/DTF2THF_29721.p',setadjoinE)).
% 2.04/1.53 thf(f600,plain,(
% 2.04/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setadjoin @ X5 @ X3)) != $true) | (X4 = X5) | ((in @ X4 @ X3) = $true)) )),
% 2.04/1.53 inference(trivial_inequality_removal,[status(thm)],[f505])).
% 2.04/1.53 thf(f505,plain,(
% 2.04/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) = $true) | (X4 = X5) | ($true != $true) | ((in @ X4 @ (setadjoin @ X5 @ X3)) != $true)) )),
% 2.04/1.53 inference(definition_unfolding,[status(thm)],[f323,f376])).
% 2.04/1.53 thf(f376,plain,(
% 2.04/1.53 (setadjoinAx = $true)),
% 2.04/1.53 inference(cnf_transformation,[status(thm)],[f189])).
% 2.04/1.53 thf(f323,plain,(
% 2.04/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((X4 = X5) | ((in @ X4 @ X3) = $true) | ((in @ X4 @ (setadjoin @ X5 @ X3)) != $true) | (setadjoinAx != $true)) )),
% 2.04/1.53 inference(cnf_transformation,[status(thm)],[f162])).
% 2.04/1.53 thf(f162,plain,(
% 2.04/1.53 ((setadjoinAx = $true) | ((((sK14 != sK13) & ((in @ sK13 @ sK12) != $true)) | ($true != (in @ sK13 @ (setadjoin @ sK14 @ sK12)))) & ((sK14 = sK13) | ((in @ sK13 @ sK12) = $true) | ($true = (in @ sK13 @ (setadjoin @ sK14 @ sK12)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ (setadjoin @ X5 @ X3)) = $true) | ((X4 != X5) & ((in @ X4 @ X3) != $true))) & ((X4 = X5) | ((in @ X4 @ X3) = $true) | ((in @ X4 @ (setadjoin @ X5 @ X3)) != $true))) | (setadjoinAx != $true))),
% 2.04/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f160,f161])).
% 2.04/1.53 thf(f161,plain,(
% 2.04/1.53 ? [X0 : $i,X1 : $i,X2 : $i] : ((((X1 != X2) & ($true != (in @ X1 @ X0))) | ($true != (in @ X1 @ (setadjoin @ X2 @ X0)))) & ((X1 = X2) | ($true = (in @ X1 @ X0)) | ($true = (in @ X1 @ (setadjoin @ X2 @ X0))))) => ((((sK14 != sK13) & ((in @ sK13 @ sK12) != $true)) | ($true != (in @ sK13 @ (setadjoin @ sK14 @ sK12)))) & ((sK14 = sK13) | ((in @ sK13 @ sK12) = $true) | ($true = (in @ sK13 @ (setadjoin @ sK14 @ sK12)))))),
% 2.04/1.53 introduced(definition,[],[choice_axiom])).
% 2.04/1.53 thf(f160,plain,(
% 2.04/1.53 ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((X1 != X2) & ($true != (in @ X1 @ X0))) | ($true != (in @ X1 @ (setadjoin @ X2 @ X0)))) & ((X1 = X2) | ($true = (in @ X1 @ X0)) | ($true = (in @ X1 @ (setadjoin @ X2 @ X0)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ (setadjoin @ X5 @ X3)) = $true) | ((X4 != X5) & ((in @ X4 @ X3) != $true))) & ((X4 = X5) | ((in @ X4 @ X3) = $true) | ((in @ X4 @ (setadjoin @ X5 @ X3)) != $true))) | (setadjoinAx != $true))),
% 2.04/1.53 inference(rectify,[status(thm)],[f159])).
% 2.04/1.53 thf(f159,plain,(
% 2.04/1.53 ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((X1 != X2) & ($true != (in @ X1 @ X0))) | ($true != (in @ X1 @ (setadjoin @ X2 @ X0)))) & ((X1 = X2) | ($true = (in @ X1 @ X0)) | ($true = (in @ X1 @ (setadjoin @ X2 @ X0)))))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X1 @ (setadjoin @ X2 @ X0))) | ((X1 != X2) & ($true != (in @ X1 @ X0)))) & ((X1 = X2) | ($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ (setadjoin @ X2 @ X0))))) | (setadjoinAx != $true))),
% 2.04/1.53 inference(flattening,[status(thm)],[f158])).
% 2.04/1.53 thf(f158,plain,(
% 2.04/1.53 ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((X1 != X2) & ($true != (in @ X1 @ X0))) | ($true != (in @ X1 @ (setadjoin @ X2 @ X0)))) & (((X1 = X2) | ($true = (in @ X1 @ X0))) | ($true = (in @ X1 @ (setadjoin @ X2 @ X0)))))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X1 @ (setadjoin @ X2 @ X0))) | ((X1 != X2) & ($true != (in @ X1 @ X0)))) & (((X1 = X2) | ($true = (in @ X1 @ X0))) | ($true != (in @ X1 @ (setadjoin @ X2 @ X0))))) | (setadjoinAx != $true))),
% 2.04/1.53 inference(nnf_transformation,[status(thm)],[f102])).
% 2.04/1.53 thf(f102,plain,(
% 2.04/1.53 (setadjoinAx = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setadjoin @ X2 @ X0))) <=> ((X1 = X2) | ($true = (in @ X1 @ X0))))),
% 2.04/1.53 inference(fool_elimination,[status(thm)],[f101])).
% 2.04/1.53 thf(f101,plain,(
% 2.04/1.53 (setadjoinAx = ! [X0 : $i,X1 : $i,X2 : $i] : (((X1 = X2) | (in @ X1 @ X0)) <=> (in @ X1 @ (setadjoin @ X2 @ X0))))),
% 2.04/1.53 inference(rectify,[status(thm)],[f4])).
% 2.04/1.53 thf(f4,axiom,(
% 2.04/1.53 (setadjoinAx = ! [X3 : $i,X2 : $i,X1 : $i] : (((X1 = X2) | (in @ X2 @ X3)) <=> (in @ X2 @ (setadjoin @ X1 @ X3))))),
% 2.04/1.53 file('/export/starexec/sandbox/tmp/tmp.WdysWW27tQ/DTF2THF_29721.p',setadjoinAx)).
% 2.04/1.53 thf(f666,plain,(
% 2.04/1.53 ~spl97_2),
% 2.04/1.53 inference(avatar_split_clause,[status(thm)],[f379,f657])).
% 2.04/1.53 thf(f657,definition,(
% 2.04/1.53 spl97_2 <=> (sK30 = $true)),
% 2.04/1.53 introduced(definition,[new_symbols(naming,[spl97_2])],[avatar_definition])).
% 2.04/1.53 thf(f379,plain,(
% 2.04/1.53 (sK30 != $true)),
% 2.04/1.53 inference(cnf_transformation,[status(thm)],[f189])).
% 2.04/1.53 thf(f665,plain,(
% 2.04/1.53 spl97_2 | ~spl97_3),
% 2.04/1.53 inference(avatar_split_clause,[status(thm)],[f378,f662,f657])).
% 2.04/1.53 thf(f378,plain,(
% 2.04/1.53 ((in @ sK29 @ sK28) != $true) | (sK30 = $true)),
% 2.04/1.53 inference(cnf_transformation,[status(thm)],[f189])).
% 2.04/1.53 thf(f660,plain,(
% 2.04/1.53 ~spl97_1 | spl97_2),
% 2.04/1.53 inference(avatar_split_clause,[status(thm)],[f377,f657,f653])).
% 2.04/1.53 thf(f377,plain,(
% 2.04/1.53 (sK30 = $true) | (sK29 != sK27)),
% 2.04/1.53 inference(cnf_transformation,[status(thm)],[f189])).
% 2.04/1.53 % SZS output end Proof for DTF2THF_29721
% 2.04/1.53 % (29842)------------------------------
% 2.04/1.53 % (29842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.53 % (29842)Termination reason: Refutation
% 2.04/1.53
% 2.04/1.53 % (29842)Memory used [KB]: 6524
% 2.04/1.53 % (29842)Time elapsed: 0.094 s
% 2.04/1.53 % (29842)Instructions burned: 171 (million)
% 2.04/1.53 % (29842)------------------------------
% 2.04/1.53 % (29842)------------------------------
% 2.04/1.53 % (29836)Success in time 0.108 s
%------------------------------------------------------------------------------