%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU516^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.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 09:35:02 AM UTC 2026
% Result : Theorem 1.96s 1.46s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 826 ( 246 equ; 0 cnn)
% Maximal formula atoms : 35 ( 30 avg)
% Number of connectives : 601 ( 55 ~; 56 |; 130 &; 222 @)
% ( 4 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 99 ( 96 usr; 40 con; 0-3 aty)
% Number of variables : 63 ( 0 ^; 42 !; 21 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_57,type,
sP1: $i > $i > $o ).
thf(func_def_58,type,
sP2: $i > $o ).
thf(func_def_59,type,
sP3: $i > $i > $o ).
thf(func_def_60,type,
sP4: $i > $i > $o ).
thf(func_def_62,type,
sK6: $i > $i > $o ).
thf(func_def_63,type,
sK7: $i > $i ).
thf(func_def_64,type,
sK8: $i > $i ).
thf(func_def_65,type,
sK9: ( $i > $i > $o ) > $i > $i ).
thf(func_def_66,type,
sK10: ( $i > $i > $o ) > $i > $i ).
thf(func_def_67,type,
sK11: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_68,type,
sK12: $i > $i ).
thf(func_def_70,type,
sK14: $i > $i ).
thf(func_def_74,type,
sK18: $i > $i > $i ).
thf(func_def_75,type,
sK19: $i > $i > $i ).
thf(func_def_76,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_77,type,
sK21: $i > $o ).
thf(func_def_78,type,
sK22: $i > $i ).
thf(func_def_84,type,
sK28: $i > $o ).
thf(func_def_88,type,
sK32: $i > $o ).
thf(func_def_93,type,
sK37: $i > $i ).
thf(func_def_101,type,
sK45: $i > $o ).
thf(func_def_102,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_103,type,
sK47: $i > $i ).
thf(func_def_106,type,
sK50: $i > $o ).
thf(func_def_109,type,
sK53: $i > $i > $i ).
thf(func_def_110,type,
sK54: $i > $i > $i ).
thf(func_def_111,type,
sK55: $i > $i > $i ).
thf(func_def_112,type,
sK56: $i > $i > $i ).
thf(func_def_113,type,
sK57: $i > $i > $i ).
thf(func_def_114,type,
sK58: $i > $i > $i > $i ).
thf(func_def_115,type,
sK59: $i > $i ).
thf(func_def_116,type,
sK60: $i > $i ).
thf(func_def_117,type,
sK61: $i > $i ).
thf(func_def_118,type,
sK62: $i > $i ).
thf(func_def_119,type,
sK63: $i > $i > $i ).
thf(func_def_120,type,
sK64: $i > $i > $i > $i ).
thf(func_def_121,type,
sK65: $i > $i > $i > $i ).
thf(func_def_122,type,
sK66: $i > $i > $i ).
thf(func_def_123,type,
sK67: $i > $i > $i ).
thf(func_def_125,type,
sK69: $i > $i ).
thf(func_def_126,type,
sK70: $i > $i ).
thf(func_def_127,type,
sK71: $i > $i ).
thf(func_def_128,type,
sK72: $i > $o ).
thf(func_def_132,type,
sK76: $i > $i ).
thf(func_def_141,type,
sK85: $i > $i > $i ).
thf(func_def_143,type,
sK87: $i > $o ).
thf(func_def_148,type,
sK92: $i > $i > $i ).
thf(func_def_151,type,
sK95: $i > $i ).
thf(func_def_157,type,
ph101:
!>[X0: $tType] : X0 ).
thf(f1022,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1021,f474]) ).
thf(f474,plain,
( $true
!= ( in @ sK98 @ sK97 ) ),
inference(cnf_transformation,[status(thm)],[f319]) ).
thf(f319,plain,
( ( noeltsimpempty = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ( omegaSAx = $true )
& ( wellorderingAx = $true )
& ( setunionAx = $true )
& ( setbeta = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( exuE3e = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( descrp = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( setext = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIL = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( prop2setE = $true )
& ( nonemptyI = $true )
& ( emptysetAx = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( $true
!= ( in @ sK98 @ sK97 ) )
& ( sK99 != sK98 )
& ( $true
= ( in @ sK98 @ ( setadjoin @ sK99 @ sK97 ) ) )
& ( emptyI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK97,sK98,sK99])],[f138,f318]) ).
thf(f318,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( X1 != X2 )
& ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) )
=> ( ( $true
!= ( in @ sK98 @ sK97 ) )
& ( sK99 != sK98 )
& ( $true
= ( in @ sK98 @ ( setadjoin @ sK99 @ sK97 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f138,plain,
( ( noeltsimpempty = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ( omegaSAx = $true )
& ( wellorderingAx = $true )
& ( setunionAx = $true )
& ( setbeta = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( exuE3e = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( descrp = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( setext = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIL = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( prop2setE = $true )
& ( nonemptyI = $true )
& ( emptysetAx = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( X1 != X2 )
& ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) )
& ( emptyI = $true ) ),
inference(flattening,[status(thm)],[f137]) ).
thf(f137,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X1 != X2 )
& ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) )
& ( 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)],[f95]) ).
thf(f95,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
=> ( ( X1 = X2 )
| ( $true
= ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f94]) ).
thf(f94,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
=> ( ( X1 = X2 )
| ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,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
=> ! [X3: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
=> ( ( X1 = X2 )
| ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f36,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
=> ! [X3: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
=> ( ( X1 = X2 )
| ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Kc4guPEzhN/DTF2THF_32630.p',setadjoinOr) ).
thf(f1021,plain,
( $true
= ( in @ sK98 @ sK97 ) ),
inference(subsumption_resolution,[status(thm)],[f995,f473]) ).
thf(f473,plain,
sK99 != sK98,
inference(cnf_transformation,[status(thm)],[f319]) ).
thf(f995,plain,
( ( sK99 = sK98 )
| ( $true
= ( in @ sK98 @ sK97 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f990]) ).
thf(f990,plain,
( ( sK99 = sK98 )
| ( $true
= ( in @ sK98 @ sK97 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f676,f472]) ).
thf(f472,plain,
( $true
= ( in @ sK98 @ ( setadjoin @ sK99 @ sK97 ) ) ),
inference(cnf_transformation,[status(thm)],[f319]) ).
thf(f676,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true )
| ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f530]) ).
thf(f530,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true )
| ( X0 = X1 )
| ( $true != $true )
| ( $true
= ( in @ X0 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f355,f485]) ).
thf(f485,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f319]) ).
thf(f355,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
thf(f190,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( ( $true
!= ( in @ sK25 @ sK27 ) )
& ( sK25 != sK26 ) )
| ( $true
!= ( in @ sK25 @ ( setadjoin @ sK26 @ sK27 ) ) ) )
& ( ( $true
= ( in @ sK25 @ sK27 ) )
| ( sK25 = sK26 )
| ( $true
= ( in @ sK25 @ ( setadjoin @ sK26 @ sK27 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f188,f189]) ).
thf(f189,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( ( in @ X3 @ X5 )
!= $true )
& ( X3 != X4 ) )
| ( $true
!= ( in @ X3 @ ( setadjoin @ X4 @ X5 ) ) ) )
& ( ( ( in @ X3 @ X5 )
= $true )
| ( X3 = X4 )
| ( $true
= ( in @ X3 @ ( setadjoin @ X4 @ X5 ) ) ) ) )
=> ( ( ( ( $true
!= ( in @ sK25 @ sK27 ) )
& ( sK25 != sK26 ) )
| ( $true
!= ( in @ sK25 @ ( setadjoin @ sK26 @ sK27 ) ) ) )
& ( ( $true
= ( in @ sK25 @ sK27 ) )
| ( sK25 = sK26 )
| ( $true
= ( in @ sK25 @ ( setadjoin @ sK26 @ sK27 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f188,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( ( in @ X3 @ X5 )
!= $true )
& ( X3 != X4 ) )
| ( $true
!= ( in @ X3 @ ( setadjoin @ X4 @ X5 ) ) ) )
& ( ( ( in @ X3 @ X5 )
= $true )
| ( X3 = X4 )
| ( $true
= ( in @ X3 @ ( setadjoin @ X4 @ X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f187]) ).
thf(f187,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f186]) ).
thf(f186,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
<=> ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 ) ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
<=> ( ( X0 = X1 )
| ( in @ X0 @ X2 ) ) )
= setadjoinAx ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
<=> ( ( X1 = X2 )
| ( in @ X2 @ X3 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox2/tmp/tmp.Kc4guPEzhN/DTF2THF_32630.p',setadjoinAx) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU516^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.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 12:25:27 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU516^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : (! x:i.! A:i.! y:i.in y (setadjoin x A) -> y = x | in y A)
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC018g [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 79 ( 35 unt; 43 typ; 35 def)
% 0.31/0.47 % Number of atoms : 200 ( 46 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 35 ( 5 avg)
% 0.31/0.47 % Number of connectives : 342 ( 7 ~; 4 |; 18 &; 223 @)
% 0.31/0.47 % ( 7 <=>; 83 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 40 ( 2 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 45 ( 43 usr; 35 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 113 ( 14 ^; 83 !; 16 ?; 113 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=457
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu_type,type,
% 0.31/0.47 exu: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu,definition,
% 0.31/0.47 ( exu
% 0.31/0.47 = ( ^ [Xphi: $i > $o] :
% 0.31/0.47 ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx_type,type,
% 0.31/0.47 setextAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx,definition,
% 0.31/0.47 ( setextAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xx @ B ) )
% 0.31/0.47 => ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset_type,type,
% 0.31/0.47 emptyset: $i ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx_type,type,
% 0.31/0.47 emptysetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx,definition,
% 0.31/0.47 ( emptysetAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin_type,type,
% 0.31/0.47 setadjoin: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx_type,type,
% 0.31/0.47 setadjoinAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx,definition,
% 0.31/0.47 ( setadjoinAx
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 <=> ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset_type,type,
% 0.31/0.47 powerset: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx_type,type,
% 0.31/0.47 powersetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx,definition,
% 0.31/0.47 ( powersetAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 <=> ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion_type,type,
% 0.31/0.47 setunion: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx_type,type,
% 0.31/0.47 setunionAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx,definition,
% 0.31/0.47 ( setunionAx
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 <=> ? [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega_type,type,
% 0.31/0.47 omega: $i ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax_type,type,
% 0.31/0.47 omega0Ax: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax,definition,
% 0.31/0.47 ( omega0Ax
% 0.31/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx_type,type,
% 0.31/0.47 omegaSAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx,definition,
% 0.31/0.47 ( omegaSAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx_type,type,
% 0.31/0.47 omegaIndAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx,definition,
% 0.31/0.47 ( omegaIndAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( ( in @ emptyset @ A )
% 0.31/0.47 & ! [Xx: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ omega )
% 0.31/0.47 & ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(replAx_type,type,
% 0.31/0.47 replAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(replAx,definition,
% 0.31/0.47 ( replAx
% 0.31/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 <=> ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx_type,type,
% 0.31/0.47 foundationAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx,definition,
% 0.31/0.47 ( foundationAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ( ( in @ B @ A )
% 0.31/0.47 & ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx_type,type,
% 0.31/0.47 wellorderingAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx,definition,
% 0.31/0.47 ( wellorderingAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ? [B: $i] :
% 0.31/0.47 ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) ) )
% 0.31/0.47 & ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ A )
% 0.31/0.47 & ( in @ Xy @ A ) )
% 0.31/0.47 => ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ( ( in @ Xx @ C )
% 0.31/0.47 <=> ( in @ Xy @ C ) ) )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 & ! [C: $i,D: $i] :
% 0.31/0.47 ( ( ( in @ C @ B )
% 0.31/0.47 & ( in @ D @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ D ) )
% 0.31/0.47 | ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ D )
% 0.31/0.47 => ( in @ Xx @ C ) ) ) )
% 0.31/0.47 & ! [C: $i] :
% 0.31/0.47 ( ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/0.47 => ? [D: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ D @ B )
% 0.31/0.47 & ( in @ Xx @ C )
% 0.31/0.47 & ~ ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ D )
% 0.31/0.47 & ( in @ Xy @ C ) )
% 0.31/0.47 & ! [E: $i] :
% 0.31/0.47 ( ( in @ E @ B )
% 0.31/0.47 => ( ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ E )
% 0.31/0.47 => ( in @ Xy @ D ) )
% 0.31/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr_type,type,
% 0.31/0.47 descr: ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(descrp_type,type,
% 0.31/0.47 descrp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descrp,definition,
% 0.31/0.47 ( descrp
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 @ ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr_type,type,
% 0.31/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI_type,type,
% 0.31/0.47 dsetconstrI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI,definition,
% 0.31/0.47 ( dsetconstrI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL_type,type,
% 0.31/0.47 dsetconstrEL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL,definition,
% 0.31/0.47 ( dsetconstrEL
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER_type,type,
% 0.31/0.47 dsetconstrER: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER,definition,
% 0.31/0.47 ( dsetconstrER
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1_type,type,
% 0.31/0.47 exuE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1,definition,
% 0.31/0.47 ( exuE1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set_type,type,
% 0.31/0.47 prop2set: $o > $i ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set,definition,
% 0.31/0.47 ( prop2set
% 0.31/0.47 = ( ^ [Xphi: $o] :
% 0.31/0.47 ( dsetconstr @ ( powerset @ emptyset )
% 0.31/0.47 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE_type,type,
% 0.31/0.47 prop2setE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE,definition,
% 0.31/0.47 ( prop2setE
% 0.31/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE_type,type,
% 0.31/0.47 emptysetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE,definition,
% 0.31/0.47 ( emptysetE
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse_type,type,
% 0.31/0.47 emptysetimpfalse: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse,definition,
% 0.31/0.47 ( emptysetimpfalse
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => $false ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset_type,type,
% 0.31/0.47 notinemptyset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset,definition,
% 0.31/0.47 ( notinemptyset
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e_type,type,
% 0.31/0.47 exuE3e: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e,definition,
% 0.31/0.47 ( exuE3e
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setext_type,type,
% 0.31/0.47 setext: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setext,definition,
% 0.31/0.47 ( setext
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( A = B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI_type,type,
% 0.31/0.47 emptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI,definition,
% 0.31/0.47 ( emptyI
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty_type,type,
% 0.31/0.47 noeltsimpempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty,definition,
% 0.31/0.47 ( noeltsimpempty
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta_type,type,
% 0.31/0.47 setbeta: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta,definition,
% 0.31/0.47 ( setbeta
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty_type,type,
% 0.31/0.47 nonempty: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty,definition,
% 0.31/0.47 ( nonempty
% 0.31/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1_type,type,
% 0.31/0.47 nonemptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1,definition,
% 0.31/0.47 ( nonemptyE1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI_type,type,
% 0.31/0.47 nonemptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI,definition,
% 0.31/0.47 ( nonemptyI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( nonempty
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1_type,type,
% 0.31/0.47 nonemptyI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1,definition,
% 0.31/0.47 ( nonemptyI1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL_type,type,
% 0.31/0.47 setadjoinIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL,definition,
% 0.31/0.47 ( setadjoinIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty_type,type,
% 0.31/0.47 emptyinunitempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty,definition,
% 0.31/0.47 ( emptyinunitempty
% 0.31/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR_type,type,
% 0.31/0.47 setadjoinIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR,definition,
% 0.31/0.47 ( setadjoinIR
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE_type,type,
% 0.31/0.47 setadjoinE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE,definition,
% 0.31/0.47 ( setadjoinE
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ( ( Xy = Xx )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xy @ A )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr,conjecture,
% 0.31/0.47 ( setextAx
% 0.31/0.47 => ( emptysetAx
% 0.31/0.47 => ( setadjoinAx
% 0.31/0.47 => ( powersetAx
% 0.31/0.47 => ( setunionAx
% 0.31/0.47 => ( omega0Ax
% 0.31/0.47 => ( omegaSAx
% 0.31/0.47 => ( omegaIndAx
% 0.31/0.47 => ( replAx
% 0.31/0.47 => ( foundationAx
% 0.31/0.47 => ( wellorderingAx
% 0.31/0.47 => ( descrp
% 0.31/0.47 => ( dsetconstrI
% 0.31/0.47 => ( dsetconstrEL
% 0.31/0.47 => ( dsetconstrER
% 0.31/0.47 => ( exuE1
% 0.31/0.47 => ( prop2setE
% 0.31/0.47 => ( emptysetE
% 0.31/0.47 => ( emptysetimpfalse
% 0.31/0.47 => ( notinemptyset
% 0.31/0.47 => ( exuE3e
% 0.31/0.47 => ( setext
% 0.31/0.47 => ( emptyI
% 0.31/0.47 => ( noeltsimpempty
% 0.31/0.47 => ( setbeta
% 0.31/0.47 => ( nonemptyE1
% 0.31/0.47 => ( nonemptyI
% 0.31/0.47 => ( nonemptyI1
% 0.31/0.47 => ( setadjoinIL
% 0.31/0.47 => ( emptyinunitempty
% 0.31/0.47 => ( setadjoinIR
% 0.31/0.47 => ( setadjoinE
% 0.31/0.47 => ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.84/1.35 ---- Embedded in THF ---
% 1.84/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.84/1.35 %%% Generated on Tue Feb 24 12:25:28 EST 2026
% 1.84/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.84/1.35 %%% Logic specification used:
% 1.84/1.35 %%% thf(spec, logic, $$dhol).
% 1.84/1.35
% 1.84/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Kc4guPEzhN/DTF2DTF32630.p
% See solution above
% 1.84/1.35 ------------------------
% 1.84/1.37 ---- Cleaned THF ---
% 1.84/1.37 thf(in_type,type,
% 1.84/1.37 in: $i > $i > $o ).
% 1.84/1.37
% 1.84/1.37 thf(exu_type,type,
% 1.84/1.37 exu: ( $i > $o ) > $o ).
% 1.84/1.37
% 1.84/1.37 thf(exu,definition,
% 1.84/1.37 ( exu
% 1.84/1.37 = ( ^ [Xphi: $i > $o] :
% 1.84/1.37 ? [Xx: $i] :
% 1.84/1.37 ( ( Xphi @ Xx )
% 1.84/1.37 & ! [Xy: $i] :
% 1.84/1.37 ( ( Xphi @ Xy )
% 1.84/1.37 => ( Xx = Xy ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setextAx_type,type,
% 1.84/1.37 setextAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(setextAx,definition,
% 1.84/1.37 ( setextAx
% 1.84/1.37 = ( ! [A: $i,B: $i] :
% 1.84/1.37 ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ A )
% 1.84/1.37 <=> ( in @ Xx @ B ) )
% 1.84/1.37 => ( A = B ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(emptyset_type,type,
% 1.84/1.37 emptyset: $i ).
% 1.84/1.37
% 1.84/1.37 thf(emptysetAx_type,type,
% 1.84/1.37 emptysetAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(emptysetAx,definition,
% 1.84/1.37 ( emptysetAx
% 1.84/1.37 = ( ! [Xx: $i] :
% 1.84/1.37 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoin_type,type,
% 1.84/1.37 setadjoin: $i > $i > $i ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinAx_type,type,
% 1.84/1.37 setadjoinAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinAx,definition,
% 1.84/1.37 ( setadjoinAx
% 1.84/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.84/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.84/1.37 <=> ( ( Xy = Xx )
% 1.84/1.37 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(powerset_type,type,
% 1.84/1.37 powerset: $i > $i ).
% 1.84/1.37
% 1.84/1.37 thf(powersetAx_type,type,
% 1.84/1.37 powersetAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(powersetAx,definition,
% 1.84/1.37 ( powersetAx
% 1.84/1.37 = ( ! [A: $i,B: $i] :
% 1.84/1.37 ( ( in @ B @ ( powerset @ A ) )
% 1.84/1.37 <=> ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ B )
% 1.84/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setunion_type,type,
% 1.84/1.37 setunion: $i > $i ).
% 1.84/1.37
% 1.84/1.37 thf(setunionAx_type,type,
% 1.84/1.37 setunionAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(setunionAx,definition,
% 1.84/1.37 ( setunionAx
% 1.84/1.37 = ( ! [A: $i,Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ ( setunion @ A ) )
% 1.84/1.37 <=> ? [B: $i] :
% 1.84/1.37 ( ( in @ Xx @ B )
% 1.84/1.37 & ( in @ B @ A ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(omega_type,type,
% 1.84/1.37 omega: $i ).
% 1.84/1.37
% 1.84/1.37 thf(omega0Ax_type,type,
% 1.84/1.37 omega0Ax: $o ).
% 1.84/1.37
% 1.84/1.37 thf(omega0Ax,definition,
% 1.84/1.37 ( omega0Ax
% 1.84/1.37 = ( in @ emptyset @ omega ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(omegaSAx_type,type,
% 1.84/1.37 omegaSAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(omegaSAx,definition,
% 1.84/1.37 ( omegaSAx
% 1.84/1.37 = ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ omega )
% 1.84/1.37 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(omegaIndAx_type,type,
% 1.84/1.37 omegaIndAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(omegaIndAx,definition,
% 1.84/1.37 ( omegaIndAx
% 1.84/1.37 = ( ! [A: $i] :
% 1.84/1.37 ( ( ( in @ emptyset @ A )
% 1.84/1.37 & ! [Xx: $i] :
% 1.84/1.37 ( ( ( in @ Xx @ omega )
% 1.84/1.37 & ( in @ Xx @ A ) )
% 1.84/1.37 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.84/1.37 => ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ omega )
% 1.84/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(replAx_type,type,
% 1.84/1.37 replAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(replAx,definition,
% 1.84/1.37 ( replAx
% 1.84/1.37 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.84/1.37 ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ A )
% 1.84/1.37 => ( exu
% 1.84/1.37 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.84/1.37 => ? [B: $i] :
% 1.84/1.37 ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ B )
% 1.84/1.37 <=> ? [Xy: $i] :
% 1.84/1.37 ( ( in @ Xy @ A )
% 1.84/1.37 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(foundationAx_type,type,
% 1.84/1.37 foundationAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(foundationAx,definition,
% 1.84/1.37 ( foundationAx
% 1.84/1.37 = ( ! [A: $i] :
% 1.84/1.37 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.84/1.37 => ? [B: $i] :
% 1.84/1.37 ( ( in @ B @ A )
% 1.84/1.37 & ~ ? [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ B )
% 1.84/1.37 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(wellorderingAx_type,type,
% 1.84/1.37 wellorderingAx: $o ).
% 1.84/1.37
% 1.84/1.37 thf(wellorderingAx,definition,
% 1.84/1.37 ( wellorderingAx
% 1.84/1.37 = ( ! [A: $i] :
% 1.84/1.37 ? [B: $i] :
% 1.84/1.37 ( ! [C: $i] :
% 1.84/1.37 ( ( in @ C @ B )
% 1.84/1.37 => ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ C )
% 1.84/1.37 => ( in @ Xx @ A ) ) )
% 1.84/1.37 & ! [Xx: $i,Xy: $i] :
% 1.84/1.37 ( ( ( in @ Xx @ A )
% 1.84/1.37 & ( in @ Xy @ A ) )
% 1.84/1.37 => ( ! [C: $i] :
% 1.84/1.37 ( ( in @ C @ B )
% 1.84/1.37 => ( ( in @ Xx @ C )
% 1.84/1.37 <=> ( in @ Xy @ C ) ) )
% 1.84/1.37 => ( Xx = Xy ) ) )
% 1.84/1.37 & ! [C: $i,D: $i] :
% 1.84/1.37 ( ( ( in @ C @ B )
% 1.84/1.37 & ( in @ D @ B ) )
% 1.84/1.37 => ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ C )
% 1.84/1.37 => ( in @ Xx @ D ) )
% 1.84/1.37 | ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ D )
% 1.84/1.37 => ( in @ Xx @ C ) ) ) )
% 1.84/1.37 & ! [C: $i] :
% 1.84/1.37 ( ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ C )
% 1.84/1.37 => ( in @ Xx @ A ) )
% 1.84/1.37 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.84/1.37 => ? [D: $i,Xx: $i] :
% 1.84/1.37 ( ( in @ D @ B )
% 1.84/1.37 & ( in @ Xx @ C )
% 1.84/1.37 & ~ ? [Xy: $i] :
% 1.84/1.37 ( ( in @ Xy @ D )
% 1.84/1.37 & ( in @ Xy @ C ) )
% 1.84/1.37 & ! [E: $i] :
% 1.84/1.37 ( ( in @ E @ B )
% 1.84/1.37 => ( ! [Xy: $i] :
% 1.84/1.37 ( ( in @ Xy @ E )
% 1.84/1.37 => ( in @ Xy @ D ) )
% 1.84/1.37 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(descr_type,type,
% 1.84/1.37 descr: ( $i > $o ) > $i ).
% 1.84/1.37
% 1.84/1.37 thf(descrp_type,type,
% 1.84/1.37 descrp: $o ).
% 1.84/1.37
% 1.84/1.37 thf(descrp,definition,
% 1.84/1.37 ( descrp
% 1.84/1.37 = ( ! [Xphi: $i > $o] :
% 1.84/1.37 ( ( exu
% 1.84/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.84/1.37 => ( Xphi
% 1.84/1.37 @ ( descr
% 1.84/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(dsetconstr_type,type,
% 1.84/1.37 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.84/1.37
% 1.84/1.37 thf(dsetconstrI_type,type,
% 1.84/1.37 dsetconstrI: $o ).
% 1.84/1.37
% 1.84/1.37 thf(dsetconstrI,definition,
% 1.84/1.37 ( dsetconstrI
% 1.84/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ A )
% 1.84/1.37 => ( ( Xphi @ Xx )
% 1.84/1.37 => ( in @ Xx
% 1.84/1.37 @ ( dsetconstr @ A
% 1.84/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(dsetconstrEL_type,type,
% 1.84/1.37 dsetconstrEL: $o ).
% 1.84/1.37
% 1.84/1.37 thf(dsetconstrEL,definition,
% 1.84/1.37 ( dsetconstrEL
% 1.84/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.84/1.37 ( ( in @ Xx
% 1.84/1.37 @ ( dsetconstr @ A
% 1.84/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.84/1.37 => ( in @ Xx @ A ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(dsetconstrER_type,type,
% 1.84/1.37 dsetconstrER: $o ).
% 1.84/1.37
% 1.84/1.37 thf(dsetconstrER,definition,
% 1.84/1.37 ( dsetconstrER
% 1.84/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.84/1.37 ( ( in @ Xx
% 1.84/1.37 @ ( dsetconstr @ A
% 1.84/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.84/1.37 => ( Xphi @ Xx ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(exuE1_type,type,
% 1.84/1.37 exuE1: $o ).
% 1.84/1.37
% 1.84/1.37 thf(exuE1,definition,
% 1.84/1.37 ( exuE1
% 1.84/1.37 = ( ! [Xphi: $i > $o] :
% 1.84/1.37 ( ( exu
% 1.84/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.84/1.37 => ? [Xx: $i] :
% 1.84/1.37 ( ( Xphi @ Xx )
% 1.84/1.37 & ! [Xy: $i] :
% 1.84/1.37 ( ( Xphi @ Xy )
% 1.84/1.37 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(prop2set_type,type,
% 1.84/1.37 prop2set: $o > $i ).
% 1.84/1.37
% 1.84/1.37 thf(prop2set,definition,
% 1.84/1.37 ( prop2set
% 1.84/1.37 = ( ^ [Xphi: $o] :
% 1.84/1.37 ( dsetconstr @ ( powerset @ emptyset )
% 1.84/1.37 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(prop2setE_type,type,
% 1.84/1.37 prop2setE: $o ).
% 1.84/1.37
% 1.84/1.37 thf(prop2setE,definition,
% 1.84/1.37 ( prop2setE
% 1.84/1.37 = ( ! [Xphi: $o,Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.84/1.37 => Xphi ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(emptysetE_type,type,
% 1.84/1.37 emptysetE: $o ).
% 1.84/1.37
% 1.84/1.37 thf(emptysetE,definition,
% 1.84/1.37 ( emptysetE
% 1.84/1.37 = ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ emptyset )
% 1.84/1.37 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(emptysetimpfalse_type,type,
% 1.84/1.37 emptysetimpfalse: $o ).
% 1.84/1.37
% 1.84/1.37 thf(emptysetimpfalse,definition,
% 1.84/1.37 ( emptysetimpfalse
% 1.84/1.37 = ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ emptyset )
% 1.84/1.37 => $false ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(notinemptyset_type,type,
% 1.84/1.37 notinemptyset: $o ).
% 1.84/1.37
% 1.84/1.37 thf(notinemptyset,definition,
% 1.84/1.37 ( notinemptyset
% 1.84/1.37 = ( ! [Xx: $i] :
% 1.84/1.37 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(exuE3e_type,type,
% 1.84/1.37 exuE3e: $o ).
% 1.84/1.37
% 1.84/1.37 thf(exuE3e,definition,
% 1.84/1.37 ( exuE3e
% 1.84/1.37 = ( ! [Xphi: $i > $o] :
% 1.84/1.37 ( ( exu
% 1.84/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.84/1.37 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setext_type,type,
% 1.84/1.37 setext: $o ).
% 1.84/1.37
% 1.84/1.37 thf(setext,definition,
% 1.84/1.37 ( setext
% 1.84/1.37 = ( ! [A: $i,B: $i] :
% 1.84/1.37 ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ A )
% 1.84/1.37 => ( in @ Xx @ B ) )
% 1.84/1.37 => ( ! [Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ B )
% 1.84/1.37 => ( in @ Xx @ A ) )
% 1.84/1.37 => ( A = B ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(emptyI_type,type,
% 1.84/1.37 emptyI: $o ).
% 1.84/1.37
% 1.84/1.37 thf(emptyI,definition,
% 1.84/1.37 ( emptyI
% 1.84/1.37 = ( ! [A: $i] :
% 1.84/1.37 ( ! [Xx: $i] :
% 1.84/1.37 ~ ( in @ Xx @ A )
% 1.84/1.37 => ( A = emptyset ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(noeltsimpempty_type,type,
% 1.84/1.37 noeltsimpempty: $o ).
% 1.84/1.37
% 1.84/1.37 thf(noeltsimpempty,definition,
% 1.84/1.37 ( noeltsimpempty
% 1.84/1.37 = ( ! [A: $i] :
% 1.84/1.37 ( ! [Xx: $i] :
% 1.84/1.37 ~ ( in @ Xx @ A )
% 1.84/1.37 => ( A = emptyset ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setbeta_type,type,
% 1.84/1.37 setbeta: $o ).
% 1.84/1.37
% 1.84/1.37 thf(setbeta,definition,
% 1.84/1.37 ( setbeta
% 1.84/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ A )
% 1.84/1.37 => ( ( in @ Xx
% 1.84/1.37 @ ( dsetconstr @ A
% 1.84/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.84/1.37 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(nonempty_type,type,
% 1.84/1.37 nonempty: $i > $o ).
% 1.84/1.37
% 1.84/1.37 thf(nonempty,definition,
% 1.84/1.37 ( nonempty
% 1.84/1.37 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(nonemptyE1_type,type,
% 1.84/1.37 nonemptyE1: $o ).
% 1.84/1.37
% 1.84/1.37 thf(nonemptyE1,definition,
% 1.84/1.37 ( nonemptyE1
% 1.84/1.37 = ( ! [A: $i] :
% 1.84/1.37 ( ( nonempty @ A )
% 1.84/1.37 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(nonemptyI_type,type,
% 1.84/1.37 nonemptyI: $o ).
% 1.84/1.37
% 1.84/1.37 thf(nonemptyI,definition,
% 1.84/1.37 ( nonemptyI
% 1.84/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.84/1.37 ( ( in @ Xx @ A )
% 1.84/1.37 => ( ( Xphi @ Xx )
% 1.84/1.37 => ( nonempty
% 1.84/1.37 @ ( dsetconstr @ A
% 1.84/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(nonemptyI1_type,type,
% 1.84/1.37 nonemptyI1: $o ).
% 1.84/1.37
% 1.84/1.37 thf(nonemptyI1,definition,
% 1.84/1.37 ( nonemptyI1
% 1.84/1.37 = ( ! [A: $i] :
% 1.84/1.37 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.84/1.37 => ( nonempty @ A ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinIL_type,type,
% 1.84/1.37 setadjoinIL: $o ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinIL,definition,
% 1.84/1.37 ( setadjoinIL
% 1.84/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(emptyinunitempty_type,type,
% 1.84/1.37 emptyinunitempty: $o ).
% 1.84/1.37
% 1.84/1.37 thf(emptyinunitempty,definition,
% 1.84/1.37 ( emptyinunitempty
% 1.84/1.37 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinIR_type,type,
% 1.84/1.37 setadjoinIR: $o ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinIR,definition,
% 1.84/1.37 ( setadjoinIR
% 1.84/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.84/1.37 ( ( in @ Xy @ A )
% 1.84/1.37 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinE_type,type,
% 1.84/1.37 setadjoinE: $o ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinE,definition,
% 1.84/1.37 ( setadjoinE
% 1.84/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.84/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.84/1.37 => ! [Xphi: $o] :
% 1.84/1.37 ( ( ( Xy = Xx )
% 1.84/1.37 => Xphi )
% 1.84/1.37 => ( ( ( in @ Xy @ A )
% 1.84/1.37 => Xphi )
% 1.84/1.37 => Xphi ) ) ) ) ) ).
% 1.84/1.37
% 1.84/1.37 thf(setadjoinOr,conjecture,
% 1.84/1.37 ( setextAx
% 1.84/1.37 => ( emptysetAx
% 1.84/1.37 => ( setadjoinAx
% 1.84/1.37 => ( powersetAx
% 1.84/1.37 => ( setunionAx
% 1.84/1.37 => ( omega0Ax
% 1.84/1.37 => ( omegaSAx
% 1.84/1.37 => ( omegaIndAx
% 1.84/1.37 => ( replAx
% 1.84/1.37 => ( foundationAx
% 1.84/1.37 => ( wellorderingAx
% 1.84/1.37 => ( descrp
% 1.84/1.37 => ( dsetconstrI
% 1.84/1.37 => ( dsetconstrEL
% 1.84/1.37 => ( dsetconstrER
% 1.84/1.37 => ( exuE1
% 1.84/1.37 => ( prop2setE
% 1.84/1.37 => ( emptysetE
% 1.84/1.37 => ( emptysetimpfalse
% 1.84/1.37 => ( notinemptyset
% 1.84/1.37 => ( exuE3e
% 1.84/1.37 => ( setext
% 1.84/1.37 => ( emptyI
% 1.84/1.37 => ( noeltsimpempty
% 1.84/1.37 => ( setbeta
% 1.84/1.37 => ( nonemptyE1
% 1.84/1.37 => ( nonemptyI
% 1.84/1.37 => ( nonemptyI1
% 1.84/1.37 => ( setadjoinIL
% 1.84/1.37 => ( emptyinunitempty
% 1.84/1.37 => ( setadjoinIR
% 1.84/1.37 => ( setadjoinE
% 1.84/1.37 => ! [Xx: $i,A: $i,Xy: $i] :
% 1.84/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.84/1.37 => ( ( Xy = Xx )
% 1.84/1.37 | ( in @ Xy @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.84/1.37 ------------------------
% 1.84/1.39 % (32749)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/2Mi)
% 1.84/1.39 % (32750)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_32630 for (2999ds/2Mi)
% 1.84/1.39 % (32749)Instruction limit reached!
% 1.84/1.39 % (32749)------------------------------
% 1.84/1.39 % (32749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.39 % (32749)Termination reason: Unknown
% 1.84/1.39 % (32749)Termination phase: shuffling
% 1.84/1.39
% 1.84/1.39 % (32749)Memory used [KB]: 1023
% 1.84/1.39 % (32749)Time elapsed: 0.003 s
% 1.84/1.39 % (32749)Instructions burned: 4 (million)
% 1.84/1.39 % (32749)------------------------------
% 1.84/1.39 % (32749)------------------------------
% 1.84/1.39 % (32750)Instruction limit reached!
% 1.84/1.39 % (32750)------------------------------
% 1.84/1.39 % (32750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.39 % (32750)Termination reason: Unknown
% 1.84/1.39 % (32750)Termination phase: shuffling
% 1.84/1.39
% 1.84/1.39 % (32750)Memory used [KB]: 1023
% 1.84/1.39 % (32750)Time elapsed: 0.002 s
% 1.84/1.39 % (32750)Instructions burned: 3 (million)
% 1.84/1.39 % (32750)------------------------------
% 1.84/1.39 % (32750)------------------------------
% 1.84/1.40 % (32746)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/183Mi)
% 1.84/1.40 % (32748)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_32630 for (2999ds/27Mi)
% 1.84/1.40 % (32747)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_32630 for (2999ds/4Mi)
% 1.84/1.40 % (32751)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_32630 for (2999ds/275Mi)
% 1.84/1.40 % (32752)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/18Mi)
% 1.96/1.40 % (32747)Instruction limit reached!
% 1.96/1.40 % (32747)------------------------------
% 1.96/1.40 % (32747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.40 % (32747)Termination reason: Unknown
% 1.96/1.40 % (32747)Termination phase: shuffling
% 1.96/1.40
% 1.96/1.40 % (32747)Memory used [KB]: 1151
% 1.96/1.40 % (32747)Time elapsed: 0.005 s
% 1.96/1.40 % (32747)Instructions burned: 5 (million)
% 1.96/1.40 % (32747)------------------------------
% 1.96/1.40 % (32747)------------------------------
% 1.96/1.40 % (32754)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_32630 for (2999ds/37Mi)
% 1.96/1.40 % (32753)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/3Mi)
% 1.96/1.40 % (32753)Instruction limit reached!
% 1.96/1.40 % (32753)------------------------------
% 1.96/1.40 % (32753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.40 % (32753)Termination reason: Unknown
% 1.96/1.40 % (32753)Termination phase: shuffling
% 1.96/1.40
% 1.96/1.40 % (32753)Memory used [KB]: 1023
% 1.96/1.40 % (32753)Time elapsed: 0.003 s
% 1.96/1.40 % (32753)Instructions burned: 4 (million)
% 1.96/1.40 % (32753)------------------------------
% 1.96/1.40 % (32753)------------------------------
% 1.96/1.41 % (32752)Instruction limit reached!
% 1.96/1.41 % (32752)------------------------------
% 1.96/1.41 % (32752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.41 % (32752)Termination reason: Unknown
% 1.96/1.41 % (32752)Termination phase: Property scanning
% 1.96/1.41
% 1.96/1.41 % (32752)Memory used [KB]: 1407
% 1.96/1.41 % (32752)Time elapsed: 0.012 s
% 1.96/1.41 % (32752)Instructions burned: 18 (million)
% 1.96/1.41 % (32752)------------------------------
% 1.96/1.41 % (32752)------------------------------
% 1.96/1.41 % (32754)Instruction limit reached!
% 1.96/1.41 % (32754)------------------------------
% 1.96/1.41 % (32754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.41 % (32754)Termination reason: Unknown
% 1.96/1.41 % (32754)Termination phase: Saturation
% 1.96/1.41
% 1.96/1.41 % (32754)Memory used [KB]: 5884
% 1.96/1.41 % (32754)Time elapsed: 0.011 s
% 1.96/1.41 % (32754)Instructions burned: 38 (million)
% 1.96/1.41 % (32754)------------------------------
% 1.96/1.41 % (32754)------------------------------
% 1.96/1.41 % (32748)Instruction limit reached!
% 1.96/1.41 % (32748)------------------------------
% 1.96/1.41 % (32748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.41 % (32748)Termination reason: Unknown
% 1.96/1.41 % (32748)Termination phase: Saturation
% 1.96/1.41
% 1.96/1.41 % (32748)Memory used [KB]: 5756
% 1.96/1.41 % (32748)Time elapsed: 0.017 s
% 1.96/1.41 % (32748)Instructions burned: 28 (million)
% 1.96/1.41 % (32748)------------------------------
% 1.96/1.41 % (32748)------------------------------
% 1.96/1.41 % (32756)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_32630 for (2999ds/3Mi)
% 1.96/1.41 % (32756)Instruction limit reached!
% 1.96/1.41 % (32756)------------------------------
% 1.96/1.41 % (32756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.41 % (32756)Termination reason: Unknown
% 1.96/1.41 % (32756)Termination phase: shuffling
% 1.96/1.41
% 1.96/1.41 % (32756)Memory used [KB]: 1023
% 1.96/1.41 % (32756)Time elapsed: 0.003 s
% 1.96/1.41 % (32756)Instructions burned: 4 (million)
% 1.96/1.41 % (32756)------------------------------
% 1.96/1.41 % (32756)------------------------------
% 1.96/1.41 % (32755)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_32630 for (2999ds/15Mi)
% 1.96/1.42 % (32758)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/7Mi)
% 1.96/1.42 % (32758)Instruction limit reached!
% 1.96/1.42 % (32758)------------------------------
% 1.96/1.42 % (32758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.42 % (32758)Termination reason: Unknown
% 1.96/1.42 % (32758)Termination phase: Property scanning
% 1.96/1.42
% 1.96/1.42 % (32758)Memory used [KB]: 1151
% 1.96/1.42 % (32758)Time elapsed: 0.003 s
% 1.96/1.42 % (32758)Instructions burned: 8 (million)
% 1.96/1.42 % (32758)------------------------------
% 1.96/1.42 % (32758)------------------------------
% 1.96/1.42 % (32755)Instruction limit reached!
% 1.96/1.42 % (32755)------------------------------
% 1.96/1.42 % (32755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.42 % (32755)Termination reason: Unknown
% 1.96/1.42 % (32755)Termination phase: Property scanning
% 1.96/1.42
% 1.96/1.42 % (32755)Memory used [KB]: 1535
% 1.96/1.42 % (32755)Time elapsed: 0.008 s
% 1.96/1.42 % (32755)Instructions burned: 16 (million)
% 1.96/1.42 % (32755)------------------------------
% 1.96/1.42 % (32755)------------------------------
% 1.96/1.42 % (32760)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_32630 for (2999ds/3Mi)
% 1.96/1.42 % (32757)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_32630 for (2999ds/1041Mi)
% 1.96/1.42 % (32760)Instruction limit reached!
% 1.96/1.42 % (32760)------------------------------
% 1.96/1.42 % (32760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.42 % (32760)Termination reason: Unknown
% 1.96/1.42 % (32760)Termination phase: shuffling
% 1.96/1.42
% 1.96/1.42 % (32760)Memory used [KB]: 1023
% 1.96/1.42 % (32760)Time elapsed: 0.003 s
% 1.96/1.42 % (32760)Instructions burned: 4 (million)
% 1.96/1.42 % (32760)------------------------------
% 1.96/1.42 % (32760)------------------------------
% 1.96/1.43 % (32759)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/16Mi)
% 1.96/1.43 % (32761)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_32630 for (2999ds/3Mi)
% 1.96/1.43 % (32761)Instruction limit reached!
% 1.96/1.43 % (32761)------------------------------
% 1.96/1.43 % (32761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.43 % (32761)Termination reason: Unknown
% 1.96/1.43 % (32761)Termination phase: shuffling
% 1.96/1.43
% 1.96/1.43 % (32761)Memory used [KB]: 1023
% 1.96/1.43 % (32761)Time elapsed: 0.002 s
% 1.96/1.43 % (32761)Instructions burned: 4 (million)
% 1.96/1.43 % (32761)------------------------------
% 1.96/1.43 % (32761)------------------------------
% 1.96/1.43 % (32762)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/7Mi)
% 1.96/1.43 % (32762)Instruction limit reached!
% 1.96/1.43 % (32762)------------------------------
% 1.96/1.43 % (32762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.43 % (32762)Termination reason: Unknown
% 1.96/1.43 % (32762)Termination phase: Property scanning
% 1.96/1.43
% 1.96/1.43 % (32762)Memory used [KB]: 1151
% 1.96/1.43 % (32762)Time elapsed: 0.004 s
% 1.96/1.43 % (32762)Instructions burned: 8 (million)
% 1.96/1.43 % (32762)------------------------------
% 1.96/1.43 % (32762)------------------------------
% 1.96/1.43 % (32763)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/3Mi)
% 1.96/1.44 % (32763)Instruction limit reached!
% 1.96/1.44 % (32763)------------------------------
% 1.96/1.44 % (32763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.44 % (32763)Termination reason: Unknown
% 1.96/1.44 % (32763)Termination phase: shuffling
% 1.96/1.44
% 1.96/1.44 % (32763)Memory used [KB]: 1151
% 1.96/1.44 % (32763)Time elapsed: 0.002 s
% 1.96/1.44 % (32763)Instructions burned: 4 (million)
% 1.96/1.44 % (32763)------------------------------
% 1.96/1.44 % (32763)------------------------------
% 1.96/1.44 % (32759)Instruction limit reached!
% 1.96/1.44 % (32759)------------------------------
% 1.96/1.44 % (32759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.44 % (32759)Termination reason: Unknown
% 1.96/1.44 % (32759)Termination phase: Twee Goal Transformation
% 1.96/1.44
% 1.96/1.44 % (32759)Memory used [KB]: 1279
% 1.96/1.44 % (32759)Time elapsed: 0.010 s
% 1.96/1.44 % (32759)Instructions burned: 16 (million)
% 1.96/1.44 % (32759)------------------------------
% 1.96/1.44 % (32759)------------------------------
% 1.96/1.44 % (32764)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/4Mi)
% 1.96/1.44 % (32764)Instruction limit reached!
% 1.96/1.44 % (32764)------------------------------
% 1.96/1.44 % (32764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.44 % (32764)Termination reason: Unknown
% 1.96/1.44 % (32764)Termination phase: shuffling
% 1.96/1.44
% 1.96/1.44 % (32764)Memory used [KB]: 1151
% 1.96/1.44 % (32764)Time elapsed: 0.002 s
% 1.96/1.44 % (32764)Instructions burned: 4 (million)
% 1.96/1.44 % (32764)------------------------------
% 1.96/1.44 % (32764)------------------------------
% 1.96/1.44 % (32765)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/18Mi)
% 1.96/1.45 % (32766)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/710Mi)
% 1.96/1.45 % (32765)Instruction limit reached!
% 1.96/1.45 % (32765)------------------------------
% 1.96/1.45 % (32765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.45 % (32765)Termination reason: Unknown
% 1.96/1.45 % (32765)Termination phase: Saturation
% 1.96/1.45
% 1.96/1.45 % (32765)Memory used [KB]: 5628
% 1.96/1.45 % (32765)Time elapsed: 0.007 s
% 1.96/1.45 % (32765)Instructions burned: 18 (million)
% 1.96/1.45 % (32765)------------------------------
% 1.96/1.45 % (32765)------------------------------
% 1.96/1.45 % (300)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_32630 for (2999ds/902Mi)
% 1.96/1.45 % (32767)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32630 for (2999ds/6Mi)
% 1.96/1.46 % (32751)First to succeed.
% 1.96/1.46 % (32767)Instruction limit reached!
% 1.96/1.46 % (32767)------------------------------
% 1.96/1.46 % (32767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.46 % (32767)Termination reason: Unknown
% 1.96/1.46 % (32767)Termination phase: shuffling
% 1.96/1.46
% 1.96/1.46 % (32767)Memory used [KB]: 1151
% 1.96/1.46 % (32767)Time elapsed: 0.005 s
% 1.96/1.46 % (32767)Instructions burned: 6 (million)
% 1.96/1.46 % (32767)------------------------------
% 1.96/1.46 % (32767)------------------------------
% 1.96/1.46 % (32751)Refutation found. Thanks to Tanya!
% 1.96/1.46 % SZS status Theorem for DTF2THF_32630
% 1.96/1.46 % SZS output start Proof for DTF2THF_32630
% 1.96/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.96/1.46 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.96/1.46 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.96/1.46 thf(func_def_8, type, powerset: $i > $i).
% 1.96/1.46 thf(func_def_10, type, setunion: $i > $i).
% 1.96/1.46 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.96/1.46 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.96/1.46 thf(func_def_26, type, prop2set: $o > $i).
% 1.96/1.46 thf(func_def_36, type, nonempty: $i > $o).
% 1.96/1.46 thf(func_def_57, type, sP1: $i > $i > $o).
% 1.96/1.46 thf(func_def_58, type, sP2: $i > $o).
% 1.96/1.46 thf(func_def_59, type, sP3: $i > $i > $o).
% 1.96/1.46 thf(func_def_60, type, sP4: $i > $i > $o).
% 1.96/1.46 thf(func_def_62, type, sK6: $i > $i > $o).
% 1.96/1.46 thf(func_def_63, type, sK7: $i > $i).
% 1.96/1.46 thf(func_def_64, type, sK8: $i > $i).
% 1.96/1.46 thf(func_def_65, type, sK9: ($i > $i > $o) > $i > $i).
% 1.96/1.46 thf(func_def_66, type, sK10: ($i > $i > $o) > $i > $i).
% 1.96/1.46 thf(func_def_67, type, sK11: $i > ($i > $i > $o) > $i > $i).
% 1.96/1.46 thf(func_def_68, type, sK12: $i > $i).
% 1.96/1.46 thf(func_def_70, type, sK14: $i > $i).
% 1.96/1.46 thf(func_def_74, type, sK18: $i > $i > $i).
% 1.96/1.46 thf(func_def_75, type, sK19: $i > $i > $i).
% 1.96/1.46 thf(func_def_76, type, sK20: ($i > $o) > $i).
% 1.96/1.46 thf(func_def_77, type, sK21: $i > $o).
% 1.96/1.46 thf(func_def_78, type, sK22: $i > $i).
% 1.96/1.46 thf(func_def_84, type, sK28: $i > $o).
% 1.96/1.46 thf(func_def_88, type, sK32: $i > $o).
% 1.96/1.46 thf(func_def_93, type, sK37: $i > $i).
% 1.96/1.46 thf(func_def_101, type, sK45: $i > $o).
% 1.96/1.46 thf(func_def_102, type, sK46: ($i > $o) > $i).
% 1.96/1.46 thf(func_def_103, type, sK47: $i > $i).
% 1.96/1.46 thf(func_def_106, type, sK50: $i > $o).
% 1.96/1.46 thf(func_def_109, type, sK53: $i > $i > $i).
% 1.96/1.46 thf(func_def_110, type, sK54: $i > $i > $i).
% 1.96/1.46 thf(func_def_111, type, sK55: $i > $i > $i).
% 1.96/1.46 thf(func_def_112, type, sK56: $i > $i > $i).
% 1.96/1.46 thf(func_def_113, type, sK57: $i > $i > $i).
% 1.96/1.46 thf(func_def_114, type, sK58: $i > $i > $i > $i).
% 1.96/1.46 thf(func_def_115, type, sK59: $i > $i).
% 1.96/1.46 thf(func_def_116, type, sK60: $i > $i).
% 1.96/1.46 thf(func_def_117, type, sK61: $i > $i).
% 1.96/1.46 thf(func_def_118, type, sK62: $i > $i).
% 1.96/1.46 thf(func_def_119, type, sK63: $i > $i > $i).
% 1.96/1.46 thf(func_def_120, type, sK64: $i > $i > $i > $i).
% 1.96/1.46 thf(func_def_121, type, sK65: $i > $i > $i > $i).
% 1.96/1.46 thf(func_def_122, type, sK66: $i > $i > $i).
% 1.96/1.46 thf(func_def_123, type, sK67: $i > $i > $i).
% 1.96/1.46 thf(func_def_125, type, sK69: $i > $i).
% 1.96/1.46 thf(func_def_126, type, sK70: $i > $i).
% 1.96/1.46 thf(func_def_127, type, sK71: $i > $i).
% 1.96/1.46 thf(func_def_128, type, sK72: $i > $o).
% 1.96/1.46 thf(func_def_132, type, sK76: $i > $i).
% 1.96/1.46 thf(func_def_141, type, sK85: $i > $i > $i).
% 1.96/1.46 thf(func_def_143, type, sK87: $i > $o).
% 1.96/1.46 thf(func_def_148, type, sK92: $i > $i > $i).
% 1.96/1.46 thf(func_def_151, type, sK95: $i > $i).
% 1.96/1.46 thf(func_def_157, type, ph101: !>[X0: $tType]:(X0)).
% 1.96/1.46 thf(f1022,plain,(
% 1.96/1.46 $false),
% 1.96/1.46 inference(subsumption_resolution,[status(thm)],[f1021,f474])).
% 1.96/1.46 thf(f474,plain,(
% 1.96/1.46 ($true != (in @ sK98 @ sK97))),
% 1.96/1.46 inference(cnf_transformation,[status(thm)],[f319])).
% 1.96/1.46 thf(f319,plain,(
% 1.96/1.46 (noeltsimpempty = $true) & (dsetconstrI = $true) & (foundationAx = $true) & (omegaSAx = $true) & (wellorderingAx = $true) & (setunionAx = $true) & (setbeta = $true) & (replAx = $true) & (omegaIndAx = $true) & (nonemptyE1 = $true) & (exuE3e = $true) & (emptyinunitempty = $true) & (omega0Ax = $true) & (exuE1 = $true) & (descrp = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (setext = $true) & (setadjoinAx = $true) & (powersetAx = $true) & (nonemptyI1 = $true) & (setadjoinIL = $true) & (setextAx = $true) & (notinemptyset = $true) & (prop2setE = $true) & (nonemptyI = $true) & (emptysetAx = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (($true != (in @ sK98 @ sK97)) & (sK99 != sK98) & ($true = (in @ sK98 @ (setadjoin @ sK99 @ sK97)))) & (emptyI = $true)),
% 1.96/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK97,sK98,sK99])],[f138,f318])).
% 1.96/1.46 thf(f318,plain,(
% 1.96/1.46 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) & (X1 != X2) & ($true = (in @ X1 @ (setadjoin @ X2 @ X0)))) => (($true != (in @ sK98 @ sK97)) & (sK99 != sK98) & ($true = (in @ sK98 @ (setadjoin @ sK99 @ sK97))))),
% 1.96/1.46 introduced(definition,[],[choice_axiom])).
% 1.96/1.46 thf(f138,plain,(
% 1.96/1.46 (noeltsimpempty = $true) & (dsetconstrI = $true) & (foundationAx = $true) & (omegaSAx = $true) & (wellorderingAx = $true) & (setunionAx = $true) & (setbeta = $true) & (replAx = $true) & (omegaIndAx = $true) & (nonemptyE1 = $true) & (exuE3e = $true) & (emptyinunitempty = $true) & (omega0Ax = $true) & (exuE1 = $true) & (descrp = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (setext = $true) & (setadjoinAx = $true) & (powersetAx = $true) & (nonemptyI1 = $true) & (setadjoinIL = $true) & (setextAx = $true) & (notinemptyset = $true) & (prop2setE = $true) & (nonemptyI = $true) & (emptysetAx = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) & (X1 != X2) & ($true = (in @ X1 @ (setadjoin @ X2 @ X0)))) & (emptyI = $true)),
% 1.96/1.46 inference(flattening,[status(thm)],[f137])).
% 1.96/1.46 thf(f137,plain,(
% 1.96/1.46 (((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((X1 != X2) & ($true != (in @ X1 @ X0))) & ($true = (in @ X1 @ (setadjoin @ X2 @ X0)))) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 1.96/1.46 inference(ennf_transformation,[status(thm)],[f95])).
% 1.96/1.46 thf(f95,plain,(
% 1.96/1.46 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setadjoin @ X2 @ X0))) => ((X1 = X2) | ($true = (in @ X1 @ X0))))))))))))))))))))))))))))))))))))),
% 1.96/1.46 inference(fool_elimination,[status(thm)],[f94])).
% 1.96/1.46 thf(f94,plain,(
% 1.96/1.46 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ X0)) => ((X1 = X2) | (in @ X1 @ X0)))))))))))))))))))))))))))))))))))),
% 1.96/1.46 inference(rectify,[status(thm)],[f37])).
% 1.96/1.46 thf(f37,negated_conjecture,(
% 1.96/1.46 ~(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 => ! [X3 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ((X1 = X2) | (in @ X2 @ X3)))))))))))))))))))))))))))))))))))),
% 1.96/1.46 inference(negated_conjecture,[status(cth)],[f36])).
% 1.96/1.46 thf(f36,conjecture,(
% 1.96/1.46 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 => ! [X3 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ((X1 = X2) | (in @ X2 @ X3))))))))))))))))))))))))))))))))))),
% 1.96/1.46 file('/export/starexec/sandbox2/tmp/tmp.Kc4guPEzhN/DTF2THF_32630.p',setadjoinOr)).
% 1.96/1.46 thf(f1021,plain,(
% 1.96/1.46 ($true = (in @ sK98 @ sK97))),
% 1.96/1.46 inference(subsumption_resolution,[status(thm)],[f995,f473])).
% 1.96/1.46 thf(f473,plain,(
% 1.96/1.46 (sK99 != sK98)),
% 1.96/1.46 inference(cnf_transformation,[status(thm)],[f319])).
% 1.96/1.46 thf(f995,plain,(
% 1.96/1.46 (sK99 = sK98) | ($true = (in @ sK98 @ sK97))),
% 1.96/1.46 inference(trivial_inequality_removal,[status(thm)],[f990])).
% 1.96/1.46 thf(f990,plain,(
% 1.96/1.46 (sK99 = sK98) | ($true = (in @ sK98 @ sK97)) | ($true != $true)),
% 1.96/1.46 inference(superposition,[status(thm)],[f676,f472])).
% 1.96/1.46 thf(f472,plain,(
% 1.96/1.46 ($true = (in @ sK98 @ (setadjoin @ sK99 @ sK97)))),
% 1.96/1.46 inference(cnf_transformation,[status(thm)],[f319])).
% 1.96/1.46 thf(f676,plain,(
% 1.96/1.46 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ X2)) != $true) | ($true = (in @ X0 @ X2)) | (X0 = X1)) )),
% 1.96/1.46 inference(trivial_inequality_removal,[status(thm)],[f530])).
% 1.96/1.46 thf(f530,plain,(
% 1.96/1.46 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ X2)) != $true) | (X0 = X1) | ($true != $true) | ($true = (in @ X0 @ X2))) )),
% 1.96/1.46 inference(definition_unfolding,[status(thm)],[f355,f485])).
% 1.96/1.46 thf(f485,plain,(
% 1.96/1.46 (setadjoinAx = $true)),
% 1.96/1.46 inference(cnf_transformation,[status(thm)],[f319])).
% 1.96/1.46 thf(f355,plain,(
% 1.96/1.46 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X2)) | (X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ X2)) != $true) | (setadjoinAx != $true)) )),
% 1.96/1.46 inference(cnf_transformation,[status(thm)],[f190])).
% 1.96/1.46 thf(f190,plain,(
% 1.96/1.46 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ X2)) = $true) | (($true != (in @ X0 @ X2)) & (X0 != X1))) & (($true = (in @ X0 @ X2)) | (X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ X2)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | (((($true != (in @ sK25 @ sK27)) & (sK25 != sK26)) | ($true != (in @ sK25 @ (setadjoin @ sK26 @ sK27)))) & (($true = (in @ sK25 @ sK27)) | (sK25 = sK26) | ($true = (in @ sK25 @ (setadjoin @ sK26 @ sK27))))))),
% 1.96/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f188,f189])).
% 1.96/1.46 thf(f189,plain,(
% 1.96/1.46 ? [X3 : $i,X4 : $i,X5 : $i] : (((((in @ X3 @ X5) != $true) & (X3 != X4)) | ($true != (in @ X3 @ (setadjoin @ X4 @ X5)))) & (((in @ X3 @ X5) = $true) | (X3 = X4) | ($true = (in @ X3 @ (setadjoin @ X4 @ X5))))) => (((($true != (in @ sK25 @ sK27)) & (sK25 != sK26)) | ($true != (in @ sK25 @ (setadjoin @ sK26 @ sK27)))) & (($true = (in @ sK25 @ sK27)) | (sK25 = sK26) | ($true = (in @ sK25 @ (setadjoin @ sK26 @ sK27)))))),
% 1.96/1.46 introduced(definition,[],[choice_axiom])).
% 1.96/1.46 thf(f188,plain,(
% 1.96/1.46 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ X2)) = $true) | (($true != (in @ X0 @ X2)) & (X0 != X1))) & (($true = (in @ X0 @ X2)) | (X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ X2)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((((in @ X3 @ X5) != $true) & (X3 != X4)) | ($true != (in @ X3 @ (setadjoin @ X4 @ X5)))) & (((in @ X3 @ X5) = $true) | (X3 = X4) | ($true = (in @ X3 @ (setadjoin @ X4 @ X5))))))),
% 1.96/1.46 inference(rectify,[status(thm)],[f187])).
% 1.96/1.46 thf(f187,plain,(
% 1.96/1.46 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ X2)) = $true) | (($true != (in @ X0 @ X2)) & (X0 != X1))) & (($true = (in @ X0 @ X2)) | (X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ X2)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((($true != (in @ X0 @ X2)) & (X0 != X1)) | ((in @ X0 @ (setadjoin @ X1 @ X2)) != $true)) & (($true = (in @ X0 @ X2)) | (X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ X2)) = $true))))),
% 1.96/1.46 inference(flattening,[status(thm)],[f186])).
% 1.96/1.46 thf(f186,plain,(
% 1.96/1.46 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ X2)) = $true) | (($true != (in @ X0 @ X2)) & (X0 != X1))) & ((($true = (in @ X0 @ X2)) | (X0 = X1)) | ((in @ X0 @ (setadjoin @ X1 @ X2)) != $true))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((($true != (in @ X0 @ X2)) & (X0 != X1)) | ((in @ X0 @ (setadjoin @ X1 @ X2)) != $true)) & ((($true = (in @ X0 @ X2)) | (X0 = X1)) | ((in @ X0 @ (setadjoin @ X1 @ X2)) = $true))))),
% 1.96/1.46 inference(nnf_transformation,[status(thm)],[f73])).
% 1.96/1.46 thf(f73,plain,(
% 1.96/1.46 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setadjoin @ X1 @ X2)) = $true) <=> (($true = (in @ X0 @ X2)) | (X0 = X1))) <=> (setadjoinAx = $true)),
% 1.96/1.46 inference(fool_elimination,[status(thm)],[f72])).
% 1.96/1.46 thf(f72,plain,(
% 1.96/1.46 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X1 @ X2)) <=> ((X0 = X1) | (in @ X0 @ X2))) = setadjoinAx)),
% 1.96/1.46 inference(rectify,[status(thm)],[f4])).
% 1.96/1.46 thf(f4,axiom,(
% 1.96/1.46 (! [X2 : $i,X1 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) <=> ((X1 = X2) | (in @ X2 @ X3))) = setadjoinAx)),
% 1.96/1.46 file('/export/starexec/sandbox2/tmp/tmp.Kc4guPEzhN/DTF2THF_32630.p',setadjoinAx)).
% 1.96/1.46 % SZS output end Proof for DTF2THF_32630
% 1.96/1.46 % (32751)------------------------------
% 1.96/1.46 % (32751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.96/1.46 % (32751)Termination reason: Refutation
% 1.96/1.46
% 1.96/1.46 % (32751)Memory used [KB]: 6524
% 1.96/1.46 % (32751)Time elapsed: 0.063 s
% 1.96/1.46 % (32751)Instructions burned: 155 (million)
% 1.96/1.46 % (32751)------------------------------
% 1.96/1.46 % (32751)------------------------------
% 1.96/1.46 % (32745)Success in time 0.072 s
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