%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU523^1 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:04 AM UTC 2026
% Result : Theorem 1.54s 1.05s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 1118 ( 304 equ; 0 cnn)
% Maximal formula atoms : 44 ( 26 avg)
% Number of connectives : 822 ( 101 ~; 80 |; 155 &; 303 @)
% ( 6 <=>; 177 =>; 0 <=; 0 <~>)
% Maximal formula depth : 51 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 108 usr; 49 con; 0-3 aty)
% Number of variables : 84 ( 0 ^; 56 !; 28 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_63,type,
sP0: $i > $i > $o ).
thf(func_def_64,type,
sP1: $i > $o ).
thf(func_def_65,type,
sP2: $i > $i > $o ).
thf(func_def_66,type,
sP3: $i > $i > $o ).
thf(func_def_70,type,
sK7: $i > $i > $i ).
thf(func_def_74,type,
sK11: $i > $i > $i ).
thf(func_def_77,type,
sK14: $i > $o ).
thf(func_def_83,type,
sK20: $i > $o ).
thf(func_def_84,type,
sK21: $i > $i ).
thf(func_def_85,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_86,type,
sK23: $i > $i > $i ).
thf(func_def_87,type,
sK24: $i > $i > $i ).
thf(func_def_88,type,
sK25: $i > $i > $i ).
thf(func_def_89,type,
sK26: $i > $i > $i ).
thf(func_def_90,type,
sK27: $i > $i > $i > $i ).
thf(func_def_91,type,
sK28: $i > $i ).
thf(func_def_92,type,
sK29: $i > $i ).
thf(func_def_93,type,
sK30: $i > $i ).
thf(func_def_94,type,
sK31: $i > $i ).
thf(func_def_95,type,
sK32: $i > $i > $i ).
thf(func_def_96,type,
sK33: $i > $i > $i > $i ).
thf(func_def_97,type,
sK34: $i > $i > $i > $i ).
thf(func_def_98,type,
sK35: $i > $i > $i ).
thf(func_def_99,type,
sK36: $i > $i > $i ).
thf(func_def_101,type,
sK38: $i > $i ).
thf(func_def_102,type,
sK39: $i > $i ).
thf(func_def_103,type,
sK40: $i > $i ).
thf(func_def_104,type,
sK41: $i > $i > $i ).
thf(func_def_105,type,
sK42: $i > $o ).
thf(func_def_106,type,
sK43: ( $i > $o ) > $i ).
thf(func_def_114,type,
sK51: $i > $i > $i ).
thf(func_def_115,type,
sK52: $i > $i ).
thf(func_def_117,type,
sK54: $i > $o ).
thf(func_def_124,type,
sK61: $i > $i > $i ).
thf(func_def_139,type,
sK76: $i > $i > $i ).
thf(func_def_140,type,
sK77: $i > $i > $i ).
thf(func_def_146,type,
sK83: $i > $i ).
thf(func_def_148,type,
sK85: $i > $o ).
thf(func_def_153,type,
sK90: $i > $o ).
thf(func_def_155,type,
sK92: $i > $i ).
thf(func_def_157,type,
sK94: $i > $i ).
thf(func_def_159,type,
sK96: $i > $i ).
thf(func_def_161,type,
sK98: $i > $i ).
thf(func_def_169,type,
sK106: $i > $o ).
thf(func_def_173,type,
sK110: $i > $o ).
thf(func_def_176,type,
sK113: $i > $i > $o ).
thf(func_def_178,type,
sK115: $i > $i ).
thf(func_def_179,type,
sK116: $i > $i ).
thf(func_def_180,type,
sK117: $i > ( $i > $i > $o ) > $i ).
thf(func_def_181,type,
sK118: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_182,type,
sK119: $i > ( $i > $i > $o ) > $i ).
thf(func_def_184,type,
ph121:
!>[X0: $tType] : X0 ).
thf(f800,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f648,f649,f794]) ).
thf(f794,plain,
~ spl120_1,
inference(avatar_contradiction_clause,[status(thm)],[f793]) ).
thf(f793,plain,
( $false
| ~ spl120_1 ),
inference(trivial_inequality_removal,[status(thm)],[f785]) ).
thf(f785,plain,
( ( $true != $true )
| ~ spl120_1 ),
inference(superposition,[status(thm)],[f780,f502]) ).
thf(f502,plain,
( $true
= ( in @ sK73 @ ( setunion @ sK72 ) ) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
thf(f300,plain,
( ( setunionI = $true )
& ( setadjoinIL = $true )
& ( emptysetAx = $true )
& ( noeltsimpempty = $true )
& ( setbeta = $true )
& ( emptyinunitempty = $true )
& ( powersetE = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( descrp = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrEL = $true )
& ( setext = $true )
& ( emptysetimpfalse = $true )
& ( wellorderingAx = $true )
& ( emptyI = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( exuE3e = $true )
& ( powersetI = $true )
& ( omegaIndAx = $true )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK72 ) )
| ( $true = sK74 )
| ( $true
!= ( in @ sK73 @ X3 ) ) )
& ( $true != sK74 )
& ( $true
= ( in @ sK73 @ ( setunion @ sK72 ) ) )
& ( setadjoinIR = $true )
& ( setadjoinOr = $true )
& ( powersetAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73,sK74])],[f154,f299,f298]) ).
thf(f298,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $o] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true = X2 )
| ( ( in @ X1 @ X3 )
!= $true ) )
& ( $true != X2 ) )
& ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) ) )
=> ( ? [X2: $o] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK72 ) )
| ( $true = X2 )
| ( $true
!= ( in @ sK73 @ X3 ) ) )
& ( $true != X2 ) )
& ( $true
= ( in @ sK73 @ ( setunion @ sK72 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f299,plain,
( ? [X2: $o] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK72 ) )
| ( $true = X2 )
| ( $true
!= ( in @ sK73 @ X3 ) ) )
& ( $true != X2 ) )
=> ( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK72 ) )
| ( $true = sK74 )
| ( $true
!= ( in @ sK73 @ X3 ) ) )
& ( $true != sK74 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f154,plain,
( ( setunionI = $true )
& ( setadjoinIL = $true )
& ( emptysetAx = $true )
& ( noeltsimpempty = $true )
& ( setbeta = $true )
& ( emptyinunitempty = $true )
& ( powersetE = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( descrp = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrEL = $true )
& ( setext = $true )
& ( emptysetimpfalse = $true )
& ( wellorderingAx = $true )
& ( emptyI = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( exuE3e = $true )
& ( powersetI = $true )
& ( omegaIndAx = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $o] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true = X2 )
| ( ( in @ X1 @ X3 )
!= $true ) )
& ( $true != X2 ) )
& ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) ) )
& ( setadjoinIR = $true )
& ( setadjoinOr = $true )
& ( powersetAx = $true ) ),
inference(flattening,[status(thm)],[f153]) ).
thf(f153,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $o] :
( ( $true != X2 )
& ! [X3: $i] :
( ( $true = X2 )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X1 @ X3 )
!= $true ) ) )
& ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) ) )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f51]) ).
thf(f51,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( ( in @ X1 @ X3 )
= $true )
=> ( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true = X2 ) ) )
=> ( $true = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f50]) ).
thf(f50,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X0 )
=> X2 ) )
=> X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f44]) ).
thf(f44,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ! [X3: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X3 ) )
=> ! [X0: $o] :
( ! [X4: $i] :
( ( in @ X1 @ X4 )
=> ( ( in @ X4 @ X3 )
=> X0 ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
thf(f43,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ! [X3: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X3 ) )
=> ! [X0: $o] :
( ! [X4: $i] :
( ( in @ X1 @ X4 )
=> ( ( in @ X4 @ X3 )
=> X0 ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IwOMFljda7/DTF2THF_27242.p',setunionE) ).
thf(f780,plain,
( ( $true
!= ( in @ sK73 @ ( setunion @ sK72 ) ) )
| ~ spl120_1 ),
inference(trivial_inequality_removal,[status(thm)],[f779]) ).
thf(f779,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK73 @ ( setunion @ sK72 ) ) )
| ~ spl120_1 ),
inference(forward_demodulation,[status(thm)],[f777,f525]) ).
thf(f525,plain,
setunionAx = $true,
inference(cnf_transformation,[status(thm)],[f300]) ).
thf(f777,plain,
( ( $true
!= ( in @ sK73 @ ( setunion @ sK72 ) ) )
| ( setunionAx != $true )
| ~ spl120_1 ),
inference(trivial_inequality_removal,[status(thm)],[f776]) ).
thf(f776,plain,
( ( setunionAx != $true )
| ( $true
!= ( in @ sK73 @ ( setunion @ sK72 ) ) )
| ( $true != $true )
| ~ spl120_1 ),
inference(duplicate_literal_removal,[status(thm)],[f772]) ).
thf(f772,plain,
( ( $true != $true )
| ( setunionAx != $true )
| ( $true
!= ( in @ sK73 @ ( setunion @ sK72 ) ) )
| ( $true
!= ( in @ sK73 @ ( setunion @ sK72 ) ) )
| ~ spl120_1 ),
inference(superposition,[status(thm)],[f723,f484]) ).
thf(f484,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK61 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ ( setunion @ X0 ) ) )
| ( setunionAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
thf(f287,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( ( in @ ( sK61 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( in @ X1 @ ( sK61 @ X1 @ X0 ) )
= $true ) )
| ( $true
!= ( in @ X1 @ ( setunion @ X0 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X1 @ X3 )
!= $true ) ) ) )
| ( setunionAx != $true ) )
& ( ( setunionAx = $true )
| ( ( ( ( in @ sK63 @ ( setunion @ sK62 ) )
!= $true )
| ! [X6: $i] :
( ( $true
!= ( in @ X6 @ sK62 ) )
| ( $true
!= ( in @ sK63 @ X6 ) ) ) )
& ( ( ( in @ sK63 @ ( setunion @ sK62 ) )
= $true )
| ( ( $true
= ( in @ sK64 @ sK62 ) )
& ( ( in @ sK63 @ sK64 )
= $true ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62,sK63,sK64])],[f283,f286,f285,f284]) ).
thf(f284,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
=> ( ( ( in @ ( sK61 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( in @ X1 @ ( sK61 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f285,plain,
( ? [X4: $i,X5: $i] :
( ( ( ( in @ X5 @ ( setunion @ X4 ) )
!= $true )
| ! [X6: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( ( in @ X5 @ X6 )
!= $true ) ) )
& ( ( ( in @ X5 @ ( setunion @ X4 ) )
= $true )
| ? [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
& ( $true
= ( in @ X5 @ X7 ) ) ) ) )
=> ( ( ( ( in @ sK63 @ ( setunion @ sK62 ) )
!= $true )
| ! [X6: $i] :
( ( $true
!= ( in @ X6 @ sK62 ) )
| ( $true
!= ( in @ sK63 @ X6 ) ) ) )
& ( ( ( in @ sK63 @ ( setunion @ sK62 ) )
= $true )
| ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK62 ) )
& ( $true
= ( in @ sK63 @ X7 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f286,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK62 ) )
& ( $true
= ( in @ sK63 @ X7 ) ) )
=> ( ( $true
= ( in @ sK64 @ sK62 ) )
& ( ( in @ sK63 @ sK64 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f283,plain,
( ( ! [X0: $i,X1: $i] :
( ( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ ( setunion @ X0 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X1 @ X3 )
!= $true ) ) ) )
| ( setunionAx != $true ) )
& ( ( setunionAx = $true )
| ? [X4: $i,X5: $i] :
( ( ( ( in @ X5 @ ( setunion @ X4 ) )
!= $true )
| ! [X6: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( ( in @ X5 @ X6 )
!= $true ) ) )
& ( ( ( in @ X5 @ ( setunion @ X4 ) )
= $true )
| ? [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
& ( $true
= ( in @ X5 @ X7 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f282]) ).
thf(f282,plain,
( ( ! [X0: $i,X1: $i] :
( ( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ ( setunion @ X0 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
| ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) ) ) )
| ( setunionAx != $true ) )
& ( ( setunionAx = $true )
| ? [X0: $i,X1: $i] :
( ( ( $true
!= ( in @ X1 @ ( setunion @ X0 ) ) )
| ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f98]) ).
thf(f98,plain,
( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
<=> ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) ) )
<=> ( setunionAx = $true ) ),
inference(fool_elimination,[status(thm)],[f97]) ).
thf(f97,plain,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
<=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( setunionAx
= ( ! [X3: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X3 ) )
<=> ? [X4: $i] :
( ( in @ X4 @ X3 )
& ( in @ X1 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IwOMFljda7/DTF2THF_27242.p',setunionAx) ).
thf(f723,plain,
( ! [X0: $i] :
( ( ( in @ ( sK61 @ sK73 @ X0 ) @ sK72 )
!= $true )
| ( ( in @ sK73 @ ( setunion @ X0 ) )
!= $true ) )
| ~ spl120_1 ),
inference(trivial_inequality_removal,[status(thm)],[f722]) ).
thf(f722,plain,
( ! [X0: $i] :
( ( ( in @ ( sK61 @ sK73 @ X0 ) @ sK72 )
!= $true )
| ( $true != $true )
| ( ( in @ sK73 @ ( setunion @ X0 ) )
!= $true ) )
| ~ spl120_1 ),
inference(forward_demodulation,[status(thm)],[f683,f525]) ).
thf(f683,plain,
( ! [X0: $i] :
( ( ( in @ sK73 @ ( setunion @ X0 ) )
!= $true )
| ( ( in @ ( sK61 @ sK73 @ X0 ) @ sK72 )
!= $true )
| ( setunionAx != $true ) )
| ~ spl120_1 ),
inference(trivial_inequality_removal,[status(thm)],[f662]) ).
thf(f662,plain,
( ! [X0: $i] :
( ( setunionAx != $true )
| ( $true != $true )
| ( ( in @ sK73 @ ( setunion @ X0 ) )
!= $true )
| ( ( in @ ( sK61 @ sK73 @ X0 ) @ sK72 )
!= $true ) )
| ~ spl120_1 ),
inference(superposition,[status(thm)],[f643,f483]) ).
thf(f483,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( sK61 @ X1 @ X0 ) )
= $true )
| ( $true
!= ( in @ X1 @ ( setunion @ X0 ) ) )
| ( setunionAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
thf(f643,plain,
( ! [X3: $i] :
( ( $true
!= ( in @ sK73 @ X3 ) )
| ( $true
!= ( in @ X3 @ sK72 ) ) )
| ~ spl120_1 ),
inference(avatar_component_clause,[status(thm)],[f642]) ).
thf(f642,definition,
( spl120_1
<=> ! [X3: $i] :
( ( $true
!= ( in @ sK73 @ X3 ) )
| ( $true
!= ( in @ X3 @ sK72 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl120_1])],[avatar_definition]) ).
thf(f649,plain,
~ spl120_2,
inference(avatar_split_clause,[status(thm)],[f503,f645]) ).
thf(f645,definition,
( spl120_2
<=> ( $true = sK74 ) ),
introduced(definition,[new_symbols(naming,[spl120_2])],[avatar_definition]) ).
thf(f503,plain,
$true != sK74,
inference(cnf_transformation,[status(thm)],[f300]) ).
thf(f648,plain,
( spl120_1
| spl120_2 ),
inference(avatar_split_clause,[status(thm)],[f504,f645,f642]) ).
thf(f504,plain,
! [X3: $i] :
( ( $true = sK74 )
| ( $true
!= ( in @ sK73 @ X3 ) )
| ( $true
!= ( in @ X3 @ sK72 ) ) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU523^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:25:30 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU523^1 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.32 % Domain : Set Theory
% 0.07/0.32 % Problem : Preliminary Notions - Power Sets and Unions
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English : (! A:i.! x:i.in x (setunion A) -> (! phi:o.(! B:i.in x B ->
% 0.07/0.32 % in B A -> phi) -> phi))
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.32 % Source : [Bro08]
% 0.07/0.32 % Names : ZFC025g [Bro08]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.40 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, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.07/0.32 % Syntax : Number of formulae : 93 ( 42 unt; 50 typ; 42 def)
% 0.07/0.32 % Number of atoms : 237 ( 54 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 42 ( 5 avg)
% 0.07/0.32 % Number of connectives : 395 ( 7 ~; 4 |; 18 &; 259 @)
% 0.07/0.32 % ( 7 <=>; 100 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 50 ( 2 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 53 ( 50 usr; 43 con; 0-2 aty)
% 0.07/0.32 % Number of variables : 130 ( 15 ^; 99 !; 16 ?; 130 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : http://mathgate.info/detsetitem.php?id=88
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(in_type,type,
% 0.07/0.32 in: $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(exu_type,type,
% 0.07/0.32 exu: ( $i > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(exu,definition,
% 0.07/0.32 ( exu
% 0.07/0.32 = ( ^ [Xphi: $i > $o] :
% 0.07/0.32 ? [Xx: $i] :
% 0.07/0.32 ( ( Xphi @ Xx )
% 0.07/0.32 & ! [Xy: $i] :
% 0.07/0.32 ( ( Xphi @ Xy )
% 0.07/0.32 => ( Xx = Xy ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setextAx_type,type,
% 0.07/0.32 setextAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setextAx,definition,
% 0.07/0.32 ( setextAx
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 <=> ( in @ Xx @ B ) )
% 0.07/0.32 => ( A = B ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyset_type,type,
% 0.07/0.32 emptyset: $i ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetAx_type,type,
% 0.07/0.32 emptysetAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetAx,definition,
% 0.07/0.32 ( emptysetAx
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoin_type,type,
% 0.07/0.32 setadjoin: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinAx_type,type,
% 0.07/0.32 setadjoinAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinAx,definition,
% 0.07/0.32 ( setadjoinAx
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.07/0.32 <=> ( ( Xy = Xx )
% 0.07/0.32 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(powerset_type,type,
% 0.07/0.32 powerset: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(powersetAx_type,type,
% 0.07/0.32 powersetAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(powersetAx,definition,
% 0.07/0.32 ( powersetAx
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.07/0.32 <=> ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setunion_type,type,
% 0.07/0.32 setunion: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(setunionAx_type,type,
% 0.07/0.32 setunionAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setunionAx,definition,
% 0.07/0.32 ( setunionAx
% 0.07/0.32 = ( ! [A: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.07/0.32 <=> ? [B: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 & ( in @ B @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(omega_type,type,
% 0.07/0.32 omega: $i ).
% 0.07/0.32
% 0.07/0.32 thf(omega0Ax_type,type,
% 0.07/0.32 omega0Ax: $o ).
% 0.07/0.32
% 0.07/0.32 thf(omega0Ax,definition,
% 0.07/0.32 ( omega0Ax
% 0.07/0.32 = ( in @ emptyset @ omega ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(omegaSAx_type,type,
% 0.07/0.32 omegaSAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(omegaSAx,definition,
% 0.07/0.32 ( omegaSAx
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ omega )
% 0.07/0.32 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(omegaIndAx_type,type,
% 0.07/0.32 omegaIndAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(omegaIndAx,definition,
% 0.07/0.32 ( omegaIndAx
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ( ( in @ emptyset @ A )
% 0.07/0.32 & ! [Xx: $i] :
% 0.07/0.32 ( ( ( in @ Xx @ omega )
% 0.07/0.32 & ( in @ Xx @ A ) )
% 0.07/0.32 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.07/0.32 => ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ omega )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(replAx_type,type,
% 0.07/0.32 replAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(replAx,definition,
% 0.07/0.32 ( replAx
% 0.07/0.32 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( exu
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.07/0.32 => ? [B: $i] :
% 0.07/0.32 ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 <=> ? [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ A )
% 0.07/0.32 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(foundationAx_type,type,
% 0.07/0.32 foundationAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(foundationAx,definition,
% 0.07/0.32 ( foundationAx
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.07/0.32 => ? [B: $i] :
% 0.07/0.32 ( ( in @ B @ A )
% 0.07/0.32 & ~ ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(wellorderingAx_type,type,
% 0.07/0.32 wellorderingAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(wellorderingAx,definition,
% 0.07/0.32 ( wellorderingAx
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ? [B: $i] :
% 0.07/0.32 ( ! [C: $i] :
% 0.07/0.32 ( ( in @ C @ B )
% 0.07/0.32 => ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ C )
% 0.07/0.32 => ( in @ Xx @ A ) ) )
% 0.07/0.32 & ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( ( in @ Xx @ A )
% 0.07/0.32 & ( in @ Xy @ A ) )
% 0.07/0.32 => ( ! [C: $i] :
% 0.07/0.32 ( ( in @ C @ B )
% 0.07/0.32 => ( ( in @ Xx @ C )
% 0.07/0.32 <=> ( in @ Xy @ C ) ) )
% 0.07/0.32 => ( Xx = Xy ) ) )
% 0.07/0.32 & ! [C: $i,D: $i] :
% 0.07/0.32 ( ( ( in @ C @ B )
% 0.07/0.32 & ( in @ D @ B ) )
% 0.07/0.32 => ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ C )
% 0.07/0.32 => ( in @ Xx @ D ) )
% 0.07/0.32 | ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ D )
% 0.07/0.32 => ( in @ Xx @ C ) ) ) )
% 0.07/0.32 & ! [C: $i] :
% 0.07/0.32 ( ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ C )
% 0.07/0.32 => ( in @ Xx @ A ) )
% 0.07/0.32 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.07/0.32 => ? [D: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ D @ B )
% 0.07/0.32 & ( in @ Xx @ C )
% 0.07/0.32 & ~ ? [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ D )
% 0.07/0.32 & ( in @ Xy @ C ) )
% 0.07/0.32 & ! [E: $i] :
% 0.07/0.32 ( ( in @ E @ B )
% 0.07/0.32 => ( ! [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ E )
% 0.07/0.32 => ( in @ Xy @ D ) )
% 0.07/0.32 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(descr_type,type,
% 0.07/0.32 descr: ( $i > $o ) > $i ).
% 0.07/0.32
% 0.07/0.32 thf(descrp_type,type,
% 0.07/0.32 descrp: $o ).
% 0.07/0.32
% 0.07/0.32 thf(descrp,definition,
% 0.07/0.32 ( descrp
% 0.07/0.32 = ( ! [Xphi: $i > $o] :
% 0.07/0.32 ( ( exu
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.07/0.32 => ( Xphi
% 0.07/0.32 @ ( descr
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstr_type,type,
% 0.07/0.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrI_type,type,
% 0.07/0.32 dsetconstrI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrI,definition,
% 0.07/0.32 ( dsetconstrI
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( ( Xphi @ Xx )
% 0.07/0.32 => ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrEL_type,type,
% 0.07/0.32 dsetconstrEL: $o ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrEL,definition,
% 0.07/0.32 ( dsetconstrEL
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrER_type,type,
% 0.07/0.32 dsetconstrER: $o ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrER,definition,
% 0.07/0.32 ( dsetconstrER
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.07/0.32 => ( Xphi @ Xx ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(exuE1_type,type,
% 0.07/0.32 exuE1: $o ).
% 0.07/0.32
% 0.07/0.32 thf(exuE1,definition,
% 0.07/0.32 ( exuE1
% 0.07/0.32 = ( ! [Xphi: $i > $o] :
% 0.07/0.32 ( ( exu
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.07/0.32 => ? [Xx: $i] :
% 0.07/0.32 ( ( Xphi @ Xx )
% 0.07/0.32 & ! [Xy: $i] :
% 0.07/0.32 ( ( Xphi @ Xy )
% 0.07/0.32 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(prop2set_type,type,
% 0.07/0.32 prop2set: $o > $i ).
% 0.07/0.32
% 0.07/0.32 thf(prop2set,definition,
% 0.07/0.32 ( prop2set
% 0.07/0.32 = ( ^ [Xphi: $o] :
% 0.07/0.32 ( dsetconstr @ ( powerset @ emptyset )
% 0.07/0.32 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(prop2setE_type,type,
% 0.07/0.32 prop2setE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(prop2setE,definition,
% 0.07/0.32 ( prop2setE
% 0.07/0.32 = ( ! [Xphi: $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.07/0.32 => Xphi ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetE_type,type,
% 0.07/0.32 emptysetE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetE,definition,
% 0.07/0.32 ( emptysetE
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ emptyset )
% 0.07/0.32 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetimpfalse_type,type,
% 0.07/0.32 emptysetimpfalse: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetimpfalse,definition,
% 0.07/0.32 ( emptysetimpfalse
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ emptyset )
% 0.07/0.32 => $false ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(notinemptyset_type,type,
% 0.07/0.32 notinemptyset: $o ).
% 0.07/0.32
% 0.07/0.32 thf(notinemptyset,definition,
% 0.07/0.32 ( notinemptyset
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(exuE3e_type,type,
% 0.07/0.32 exuE3e: $o ).
% 0.07/0.32
% 0.07/0.32 thf(exuE3e,definition,
% 0.07/0.32 ( exuE3e
% 0.07/0.32 = ( ! [Xphi: $i > $o] :
% 0.07/0.32 ( ( exu
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.07/0.32 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setext_type,type,
% 0.07/0.32 setext: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setext,definition,
% 0.07/0.32 ( setext
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( in @ Xx @ B ) )
% 0.07/0.32 => ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) )
% 0.07/0.32 => ( A = B ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyI_type,type,
% 0.07/0.32 emptyI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyI,definition,
% 0.07/0.32 ( emptyI
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ~ ( in @ Xx @ A )
% 0.07/0.32 => ( A = emptyset ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(noeltsimpempty_type,type,
% 0.07/0.32 noeltsimpempty: $o ).
% 0.07/0.32
% 0.07/0.32 thf(noeltsimpempty,definition,
% 0.07/0.32 ( noeltsimpempty
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ~ ( in @ Xx @ A )
% 0.07/0.32 => ( A = emptyset ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setbeta_type,type,
% 0.07/0.32 setbeta: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setbeta,definition,
% 0.07/0.32 ( setbeta
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.07/0.32 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonempty_type,type,
% 0.07/0.32 nonempty: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonempty,definition,
% 0.07/0.32 ( nonempty
% 0.07/0.32 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyE1_type,type,
% 0.07/0.32 nonemptyE1: $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyE1,definition,
% 0.07/0.32 ( nonemptyE1
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ( nonempty @ A )
% 0.07/0.32 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyI_type,type,
% 0.07/0.32 nonemptyI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyI,definition,
% 0.07/0.32 ( nonemptyI
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( ( Xphi @ Xx )
% 0.07/0.32 => ( nonempty
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyI1_type,type,
% 0.07/0.32 nonemptyI1: $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyI1,definition,
% 0.07/0.32 ( nonemptyI1
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.07/0.32 => ( nonempty @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIL_type,type,
% 0.07/0.32 setadjoinIL: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIL,definition,
% 0.07/0.32 ( setadjoinIL
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyinunitempty_type,type,
% 0.07/0.32 emptyinunitempty: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyinunitempty,definition,
% 0.07/0.32 ( emptyinunitempty
% 0.07/0.32 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIR_type,type,
% 0.07/0.32 setadjoinIR: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIR,definition,
% 0.07/0.32 ( setadjoinIR
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ A )
% 0.07/0.32 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinE_type,type,
% 0.07/0.32 setadjoinE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinE,definition,
% 0.07/0.32 ( setadjoinE
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.07/0.32 => ! [Xphi: $o] :
% 0.07/0.32 ( ( ( Xy = Xx )
% 0.07/0.32 => Xphi )
% 0.07/0.32 => ( ( ( in @ Xy @ A )
% 0.07/0.32 => Xphi )
% 0.07/0.32 => Xphi ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinOr_type,type,
% 0.07/0.32 setadjoinOr: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinOr,definition,
% 0.07/0.32 ( setadjoinOr
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.07/0.32 => ( ( Xy = Xx )
% 0.07/0.32 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setoftrueEq_type,type,
% 0.07/0.32 setoftrueEq: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setoftrueEq,definition,
% 0.07/0.32 ( setoftrueEq
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xx: $i] : $true )
% 0.07/0.32 = A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(powersetI_type,type,
% 0.07/0.32 powersetI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(powersetI,definition,
% 0.07/0.32 ( powersetI
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) )
% 0.07/0.32 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyinPowerset_type,type,
% 0.07/0.32 emptyinPowerset: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyinPowerset,definition,
% 0.07/0.32 ( emptyinPowerset
% 0.07/0.32 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyInPowerset_type,type,
% 0.07/0.32 emptyInPowerset: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyInPowerset,definition,
% 0.07/0.32 ( emptyInPowerset
% 0.07/0.32 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(powersetE_type,type,
% 0.07/0.32 powersetE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(powersetE,definition,
% 0.07/0.32 ( powersetE
% 0.07/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.07/0.32 => ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setunionI_type,type,
% 0.07/0.32 setunionI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setunionI,definition,
% 0.07/0.32 ( setunionI
% 0.07/0.32 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( ( in @ B @ A )
% 0.07/0.32 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setunionE,conjecture,
% 0.07/0.32 ( setextAx
% 0.07/0.32 => ( emptysetAx
% 0.07/0.32 => ( setadjoinAx
% 0.07/0.32 => ( powersetAx
% 0.07/0.32 => ( setunionAx
% 0.07/0.32 => ( omega0Ax
% 0.07/0.32 => ( omegaSAx
% 0.07/0.32 => ( omegaIndAx
% 0.07/0.32 => ( replAx
% 0.07/0.32 => ( foundationAx
% 0.07/0.32 => ( wellorderingAx
% 0.07/0.32 => ( descrp
% 0.07/0.32 => ( dsetconstrI
% 0.07/0.32 => ( dsetconstrEL
% 0.07/0.32 => ( dsetconstrER
% 0.07/0.32 => ( exuE1
% 0.07/0.32 => ( prop2setE
% 0.07/0.32 => ( emptysetE
% 0.07/0.32 => ( emptysetimpfalse
% 0.07/0.32 => ( notinemptyset
% 0.07/0.32 => ( exuE3e
% 0.07/0.32 => ( setext
% 0.07/0.32 => ( emptyI
% 0.07/0.32 => ( noeltsimpempty
% 0.07/0.32 => ( setbeta
% 0.07/0.32 => ( nonemptyE1
% 0.07/0.32 => ( nonemptyI
% 0.07/0.32 => ( nonemptyI1
% 0.07/0.32 => ( setadjoinIL
% 0.07/0.32 => ( emptyinunitempty
% 0.07/0.32 => ( setadjoinIR
% 0.07/0.32 => ( setadjoinE
% 0.07/0.32 => ( setadjoinOr
% 0.07/0.32 => ( setoftrueEq
% 0.07/0.32 => ( powersetI
% 0.07/0.32 => ( emptyinPowerset
% 0.07/0.32 => ( emptyInPowerset
% 0.07/0.32 => ( powersetE
% 0.07/0.32 => ( setunionI
% 0.07/0.32 => ! [A: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.07/0.32 => ! [Xphi: $o] :
% 0.07/0.32 ( ! [B: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( ( in @ B @ A )
% 0.07/0.32 => Xphi ) )
% 0.07/0.32 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.13/0.95 ---- Embedded in THF ---
% 1.13/0.95 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.13/0.95 %%% Generated on Tue Feb 24 12:25:31 EST 2026
% 1.13/0.95 %%% using '$$dhol' embedding, version 1.3.0.
% 1.13/0.95 %%% Logic specification used:
% 1.13/0.95 %%% thf(spec, logic, $$dhol).
% 1.13/0.95
% 1.13/0.95 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IwOMFljda7/DTF2DTF27242.p
% See solution above
% 1.13/0.95 ------------------------
% 1.13/0.96 ---- Cleaned THF ---
% 1.13/0.96 thf(in_type,type,
% 1.13/0.96 in: $i > $i > $o ).
% 1.13/0.96
% 1.13/0.96 thf(exu_type,type,
% 1.13/0.96 exu: ( $i > $o ) > $o ).
% 1.13/0.96
% 1.13/0.96 thf(exu,definition,
% 1.13/0.96 ( exu
% 1.13/0.96 = ( ^ [Xphi: $i > $o] :
% 1.13/0.96 ? [Xx: $i] :
% 1.13/0.96 ( ( Xphi @ Xx )
% 1.13/0.96 & ! [Xy: $i] :
% 1.13/0.96 ( ( Xphi @ Xy )
% 1.13/0.96 => ( Xx = Xy ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setextAx_type,type,
% 1.13/0.96 setextAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setextAx,definition,
% 1.13/0.96 ( setextAx
% 1.13/0.96 = ( ! [A: $i,B: $i] :
% 1.13/0.96 ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ A )
% 1.13/0.96 <=> ( in @ Xx @ B ) )
% 1.13/0.96 => ( A = B ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(emptyset_type,type,
% 1.13/0.96 emptyset: $i ).
% 1.13/0.96
% 1.13/0.96 thf(emptysetAx_type,type,
% 1.13/0.96 emptysetAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(emptysetAx,definition,
% 1.13/0.96 ( emptysetAx
% 1.13/0.96 = ( ! [Xx: $i] :
% 1.13/0.96 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoin_type,type,
% 1.13/0.96 setadjoin: $i > $i > $i ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinAx_type,type,
% 1.13/0.96 setadjoinAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinAx,definition,
% 1.13/0.96 ( setadjoinAx
% 1.13/0.96 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.13/0.96 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.13/0.96 <=> ( ( Xy = Xx )
% 1.13/0.96 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(powerset_type,type,
% 1.13/0.96 powerset: $i > $i ).
% 1.13/0.96
% 1.13/0.96 thf(powersetAx_type,type,
% 1.13/0.96 powersetAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(powersetAx,definition,
% 1.13/0.96 ( powersetAx
% 1.13/0.96 = ( ! [A: $i,B: $i] :
% 1.13/0.96 ( ( in @ B @ ( powerset @ A ) )
% 1.13/0.96 <=> ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ B )
% 1.13/0.96 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setunion_type,type,
% 1.13/0.96 setunion: $i > $i ).
% 1.13/0.96
% 1.13/0.96 thf(setunionAx_type,type,
% 1.13/0.96 setunionAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setunionAx,definition,
% 1.13/0.96 ( setunionAx
% 1.13/0.96 = ( ! [A: $i,Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ ( setunion @ A ) )
% 1.13/0.96 <=> ? [B: $i] :
% 1.13/0.96 ( ( in @ Xx @ B )
% 1.13/0.96 & ( in @ B @ A ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(omega_type,type,
% 1.13/0.96 omega: $i ).
% 1.13/0.96
% 1.13/0.96 thf(omega0Ax_type,type,
% 1.13/0.96 omega0Ax: $o ).
% 1.13/0.96
% 1.13/0.96 thf(omega0Ax,definition,
% 1.13/0.96 ( omega0Ax
% 1.13/0.96 = ( in @ emptyset @ omega ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(omegaSAx_type,type,
% 1.13/0.96 omegaSAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(omegaSAx,definition,
% 1.13/0.96 ( omegaSAx
% 1.13/0.96 = ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ omega )
% 1.13/0.96 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(omegaIndAx_type,type,
% 1.13/0.96 omegaIndAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(omegaIndAx,definition,
% 1.13/0.96 ( omegaIndAx
% 1.13/0.96 = ( ! [A: $i] :
% 1.13/0.96 ( ( ( in @ emptyset @ A )
% 1.13/0.96 & ! [Xx: $i] :
% 1.13/0.96 ( ( ( in @ Xx @ omega )
% 1.13/0.96 & ( in @ Xx @ A ) )
% 1.13/0.96 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.13/0.96 => ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ omega )
% 1.13/0.96 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(replAx_type,type,
% 1.13/0.96 replAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(replAx,definition,
% 1.13/0.96 ( replAx
% 1.13/0.96 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.13/0.96 ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ A )
% 1.13/0.96 => ( exu
% 1.13/0.96 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.13/0.96 => ? [B: $i] :
% 1.13/0.96 ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ B )
% 1.13/0.96 <=> ? [Xy: $i] :
% 1.13/0.96 ( ( in @ Xy @ A )
% 1.13/0.96 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(foundationAx_type,type,
% 1.13/0.96 foundationAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(foundationAx,definition,
% 1.13/0.96 ( foundationAx
% 1.13/0.96 = ( ! [A: $i] :
% 1.13/0.96 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.13/0.96 => ? [B: $i] :
% 1.13/0.96 ( ( in @ B @ A )
% 1.13/0.96 & ~ ? [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ B )
% 1.13/0.96 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(wellorderingAx_type,type,
% 1.13/0.96 wellorderingAx: $o ).
% 1.13/0.96
% 1.13/0.96 thf(wellorderingAx,definition,
% 1.13/0.96 ( wellorderingAx
% 1.13/0.96 = ( ! [A: $i] :
% 1.13/0.96 ? [B: $i] :
% 1.13/0.96 ( ! [C: $i] :
% 1.13/0.96 ( ( in @ C @ B )
% 1.13/0.96 => ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ C )
% 1.13/0.96 => ( in @ Xx @ A ) ) )
% 1.13/0.96 & ! [Xx: $i,Xy: $i] :
% 1.13/0.96 ( ( ( in @ Xx @ A )
% 1.13/0.96 & ( in @ Xy @ A ) )
% 1.13/0.96 => ( ! [C: $i] :
% 1.13/0.96 ( ( in @ C @ B )
% 1.13/0.96 => ( ( in @ Xx @ C )
% 1.13/0.96 <=> ( in @ Xy @ C ) ) )
% 1.13/0.96 => ( Xx = Xy ) ) )
% 1.13/0.96 & ! [C: $i,D: $i] :
% 1.13/0.96 ( ( ( in @ C @ B )
% 1.13/0.96 & ( in @ D @ B ) )
% 1.13/0.96 => ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ C )
% 1.13/0.96 => ( in @ Xx @ D ) )
% 1.13/0.96 | ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ D )
% 1.13/0.96 => ( in @ Xx @ C ) ) ) )
% 1.13/0.96 & ! [C: $i] :
% 1.13/0.96 ( ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ C )
% 1.13/0.96 => ( in @ Xx @ A ) )
% 1.13/0.96 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.13/0.96 => ? [D: $i,Xx: $i] :
% 1.13/0.96 ( ( in @ D @ B )
% 1.13/0.96 & ( in @ Xx @ C )
% 1.13/0.96 & ~ ? [Xy: $i] :
% 1.13/0.96 ( ( in @ Xy @ D )
% 1.13/0.96 & ( in @ Xy @ C ) )
% 1.13/0.96 & ! [E: $i] :
% 1.13/0.96 ( ( in @ E @ B )
% 1.13/0.96 => ( ! [Xy: $i] :
% 1.13/0.96 ( ( in @ Xy @ E )
% 1.13/0.96 => ( in @ Xy @ D ) )
% 1.13/0.96 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(descr_type,type,
% 1.13/0.96 descr: ( $i > $o ) > $i ).
% 1.13/0.96
% 1.13/0.96 thf(descrp_type,type,
% 1.13/0.96 descrp: $o ).
% 1.13/0.96
% 1.13/0.96 thf(descrp,definition,
% 1.13/0.96 ( descrp
% 1.13/0.96 = ( ! [Xphi: $i > $o] :
% 1.13/0.96 ( ( exu
% 1.13/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.13/0.96 => ( Xphi
% 1.13/0.96 @ ( descr
% 1.13/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(dsetconstr_type,type,
% 1.13/0.96 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.13/0.96
% 1.13/0.96 thf(dsetconstrI_type,type,
% 1.13/0.96 dsetconstrI: $o ).
% 1.13/0.96
% 1.13/0.96 thf(dsetconstrI,definition,
% 1.13/0.96 ( dsetconstrI
% 1.13/0.96 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ A )
% 1.13/0.96 => ( ( Xphi @ Xx )
% 1.13/0.96 => ( in @ Xx
% 1.13/0.96 @ ( dsetconstr @ A
% 1.13/0.96 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(dsetconstrEL_type,type,
% 1.13/0.96 dsetconstrEL: $o ).
% 1.13/0.96
% 1.13/0.96 thf(dsetconstrEL,definition,
% 1.13/0.96 ( dsetconstrEL
% 1.13/0.96 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.13/0.96 ( ( in @ Xx
% 1.13/0.96 @ ( dsetconstr @ A
% 1.13/0.96 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.13/0.96 => ( in @ Xx @ A ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(dsetconstrER_type,type,
% 1.13/0.96 dsetconstrER: $o ).
% 1.13/0.96
% 1.13/0.96 thf(dsetconstrER,definition,
% 1.13/0.96 ( dsetconstrER
% 1.13/0.96 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.13/0.96 ( ( in @ Xx
% 1.13/0.96 @ ( dsetconstr @ A
% 1.13/0.96 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.13/0.96 => ( Xphi @ Xx ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(exuE1_type,type,
% 1.13/0.96 exuE1: $o ).
% 1.13/0.96
% 1.13/0.96 thf(exuE1,definition,
% 1.13/0.96 ( exuE1
% 1.13/0.96 = ( ! [Xphi: $i > $o] :
% 1.13/0.96 ( ( exu
% 1.13/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.13/0.96 => ? [Xx: $i] :
% 1.13/0.96 ( ( Xphi @ Xx )
% 1.13/0.96 & ! [Xy: $i] :
% 1.13/0.96 ( ( Xphi @ Xy )
% 1.13/0.96 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(prop2set_type,type,
% 1.13/0.96 prop2set: $o > $i ).
% 1.13/0.96
% 1.13/0.96 thf(prop2set,definition,
% 1.13/0.96 ( prop2set
% 1.13/0.96 = ( ^ [Xphi: $o] :
% 1.13/0.96 ( dsetconstr @ ( powerset @ emptyset )
% 1.13/0.96 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(prop2setE_type,type,
% 1.13/0.96 prop2setE: $o ).
% 1.13/0.96
% 1.13/0.96 thf(prop2setE,definition,
% 1.13/0.96 ( prop2setE
% 1.13/0.96 = ( ! [Xphi: $o,Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.13/0.96 => Xphi ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(emptysetE_type,type,
% 1.13/0.96 emptysetE: $o ).
% 1.13/0.96
% 1.13/0.96 thf(emptysetE,definition,
% 1.13/0.96 ( emptysetE
% 1.13/0.96 = ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ emptyset )
% 1.13/0.96 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(emptysetimpfalse_type,type,
% 1.13/0.96 emptysetimpfalse: $o ).
% 1.13/0.96
% 1.13/0.96 thf(emptysetimpfalse,definition,
% 1.13/0.96 ( emptysetimpfalse
% 1.13/0.96 = ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ emptyset )
% 1.13/0.96 => $false ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(notinemptyset_type,type,
% 1.13/0.96 notinemptyset: $o ).
% 1.13/0.96
% 1.13/0.96 thf(notinemptyset,definition,
% 1.13/0.96 ( notinemptyset
% 1.13/0.96 = ( ! [Xx: $i] :
% 1.13/0.96 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(exuE3e_type,type,
% 1.13/0.96 exuE3e: $o ).
% 1.13/0.96
% 1.13/0.96 thf(exuE3e,definition,
% 1.13/0.96 ( exuE3e
% 1.13/0.96 = ( ! [Xphi: $i > $o] :
% 1.13/0.96 ( ( exu
% 1.13/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.13/0.96 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setext_type,type,
% 1.13/0.96 setext: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setext,definition,
% 1.13/0.96 ( setext
% 1.13/0.96 = ( ! [A: $i,B: $i] :
% 1.13/0.96 ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ A )
% 1.13/0.96 => ( in @ Xx @ B ) )
% 1.13/0.96 => ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ B )
% 1.13/0.96 => ( in @ Xx @ A ) )
% 1.13/0.96 => ( A = B ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(emptyI_type,type,
% 1.13/0.96 emptyI: $o ).
% 1.13/0.96
% 1.13/0.96 thf(emptyI,definition,
% 1.13/0.96 ( emptyI
% 1.13/0.96 = ( ! [A: $i] :
% 1.13/0.96 ( ! [Xx: $i] :
% 1.13/0.96 ~ ( in @ Xx @ A )
% 1.13/0.96 => ( A = emptyset ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(noeltsimpempty_type,type,
% 1.13/0.96 noeltsimpempty: $o ).
% 1.13/0.96
% 1.13/0.96 thf(noeltsimpempty,definition,
% 1.13/0.96 ( noeltsimpempty
% 1.13/0.96 = ( ! [A: $i] :
% 1.13/0.96 ( ! [Xx: $i] :
% 1.13/0.96 ~ ( in @ Xx @ A )
% 1.13/0.96 => ( A = emptyset ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setbeta_type,type,
% 1.13/0.96 setbeta: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setbeta,definition,
% 1.13/0.96 ( setbeta
% 1.13/0.96 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ A )
% 1.13/0.96 => ( ( in @ Xx
% 1.13/0.96 @ ( dsetconstr @ A
% 1.13/0.96 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.13/0.96 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(nonempty_type,type,
% 1.13/0.96 nonempty: $i > $o ).
% 1.13/0.96
% 1.13/0.96 thf(nonempty,definition,
% 1.13/0.96 ( nonempty
% 1.13/0.96 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(nonemptyE1_type,type,
% 1.13/0.96 nonemptyE1: $o ).
% 1.13/0.96
% 1.13/0.96 thf(nonemptyE1,definition,
% 1.13/0.96 ( nonemptyE1
% 1.13/0.96 = ( ! [A: $i] :
% 1.13/0.96 ( ( nonempty @ A )
% 1.13/0.96 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(nonemptyI_type,type,
% 1.13/0.96 nonemptyI: $o ).
% 1.13/0.96
% 1.13/0.96 thf(nonemptyI,definition,
% 1.13/0.96 ( nonemptyI
% 1.13/0.96 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ A )
% 1.13/0.96 => ( ( Xphi @ Xx )
% 1.13/0.96 => ( nonempty
% 1.13/0.96 @ ( dsetconstr @ A
% 1.13/0.96 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(nonemptyI1_type,type,
% 1.13/0.96 nonemptyI1: $o ).
% 1.13/0.96
% 1.13/0.96 thf(nonemptyI1,definition,
% 1.13/0.96 ( nonemptyI1
% 1.13/0.96 = ( ! [A: $i] :
% 1.13/0.96 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.13/0.96 => ( nonempty @ A ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinIL_type,type,
% 1.13/0.96 setadjoinIL: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinIL,definition,
% 1.13/0.96 ( setadjoinIL
% 1.13/0.96 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(emptyinunitempty_type,type,
% 1.13/0.96 emptyinunitempty: $o ).
% 1.13/0.96
% 1.13/0.96 thf(emptyinunitempty,definition,
% 1.13/0.96 ( emptyinunitempty
% 1.13/0.96 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinIR_type,type,
% 1.13/0.96 setadjoinIR: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinIR,definition,
% 1.13/0.96 ( setadjoinIR
% 1.13/0.96 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.13/0.96 ( ( in @ Xy @ A )
% 1.13/0.96 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinE_type,type,
% 1.13/0.96 setadjoinE: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinE,definition,
% 1.13/0.96 ( setadjoinE
% 1.13/0.96 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.13/0.96 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.13/0.96 => ! [Xphi: $o] :
% 1.13/0.96 ( ( ( Xy = Xx )
% 1.13/0.96 => Xphi )
% 1.13/0.96 => ( ( ( in @ Xy @ A )
% 1.13/0.96 => Xphi )
% 1.13/0.96 => Xphi ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinOr_type,type,
% 1.13/0.96 setadjoinOr: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setadjoinOr,definition,
% 1.13/0.96 ( setadjoinOr
% 1.13/0.96 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.13/0.96 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.13/0.96 => ( ( Xy = Xx )
% 1.13/0.96 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setoftrueEq_type,type,
% 1.13/0.96 setoftrueEq: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setoftrueEq,definition,
% 1.13/0.96 ( setoftrueEq
% 1.13/0.96 = ( ! [A: $i] :
% 1.13/0.96 ( ( dsetconstr @ A
% 1.13/0.96 @ ^ [Xx: $i] : $true )
% 1.13/0.96 = A ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(powersetI_type,type,
% 1.13/0.96 powersetI: $o ).
% 1.13/0.96
% 1.13/0.96 thf(powersetI,definition,
% 1.13/0.96 ( powersetI
% 1.13/0.96 = ( ! [A: $i,B: $i] :
% 1.13/0.96 ( ! [Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ B )
% 1.13/0.96 => ( in @ Xx @ A ) )
% 1.13/0.96 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(emptyinPowerset_type,type,
% 1.13/0.96 emptyinPowerset: $o ).
% 1.13/0.96
% 1.13/0.96 thf(emptyinPowerset,definition,
% 1.13/0.96 ( emptyinPowerset
% 1.13/0.96 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(emptyInPowerset_type,type,
% 1.13/0.96 emptyInPowerset: $o ).
% 1.13/0.96
% 1.13/0.96 thf(emptyInPowerset,definition,
% 1.13/0.96 ( emptyInPowerset
% 1.13/0.96 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(powersetE_type,type,
% 1.13/0.96 powersetE: $o ).
% 1.13/0.96
% 1.13/0.96 thf(powersetE,definition,
% 1.13/0.96 ( powersetE
% 1.13/0.96 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.13/0.96 ( ( in @ B @ ( powerset @ A ) )
% 1.13/0.96 => ( ( in @ Xx @ B )
% 1.13/0.96 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setunionI_type,type,
% 1.13/0.96 setunionI: $o ).
% 1.13/0.96
% 1.13/0.96 thf(setunionI,definition,
% 1.13/0.96 ( setunionI
% 1.13/0.96 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.13/0.96 ( ( in @ Xx @ B )
% 1.13/0.96 => ( ( in @ B @ A )
% 1.13/0.96 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.13/0.96
% 1.13/0.96 thf(setunionE,conjecture,
% 1.13/0.96 ( setextAx
% 1.13/0.96 => ( emptysetAx
% 1.13/0.96 => ( setadjoinAx
% 1.13/0.96 => ( powersetAx
% 1.13/0.96 => ( setunionAx
% 1.13/0.96 => ( omega0Ax
% 1.13/0.96 => ( omegaSAx
% 1.13/0.96 => ( omegaIndAx
% 1.13/0.96 => ( replAx
% 1.13/0.96 => ( foundationAx
% 1.13/0.96 => ( wellorderingAx
% 1.13/0.96 => ( descrp
% 1.13/0.96 => ( dsetconstrI
% 1.13/0.96 => ( dsetconstrEL
% 1.13/0.96 => ( dsetconstrER
% 1.13/0.96 => ( exuE1
% 1.13/0.96 => ( prop2setE
% 1.13/0.96 => ( emptysetE
% 1.13/0.96 => ( emptysetimpfalse
% 1.13/0.96 => ( notinemptyset
% 1.13/0.96 => ( exuE3e
% 1.13/0.96 => ( setext
% 1.13/0.96 => ( emptyI
% 1.13/0.96 => ( noeltsimpempty
% 1.13/0.96 => ( setbeta
% 1.13/0.96 => ( nonemptyE1
% 1.13/0.96 => ( nonemptyI
% 1.13/0.96 => ( nonemptyI1
% 1.13/0.96 => ( setadjoinIL
% 1.13/0.96 => ( emptyinunitempty
% 1.13/0.96 => ( setadjoinIR
% 1.13/0.96 => ( setadjoinE
% 1.13/0.96 => ( setadjoinOr
% 1.13/0.96 => ( setoftrueEq
% 1.13/0.96 => ( powersetI
% 1.13/0.96 => ( emptyinPowerset
% 1.13/0.96 => ( emptyInPowerset
% 1.13/0.96 => ( powersetE
% 1.13/0.96 => ( setunionI
% 1.13/0.96 => ! [A: $i,Xx: $i] :
% 1.13/0.96 ( ( in @ Xx @ ( setunion @ A ) )
% 1.13/0.96 => ! [Xphi: $o] :
% 1.13/0.96 ( ! [B: $i] :
% 1.13/0.96 ( ( in @ Xx @ B )
% 1.13/0.96 => ( ( in @ B @ A )
% 1.13/0.96 => Xphi ) )
% 1.13/0.96 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.13/0.96 ------------------------
% 1.13/0.98 % (27362)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/2Mi)
% 1.13/0.98 % (27364)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_27242 for (2999ds/275Mi)
% 1.13/0.98 % (27363)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_27242 for (2999ds/2Mi)
% 1.13/0.98 % (27359)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/183Mi)
% 1.13/0.98 % (27360)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_27242 for (2999ds/4Mi)
% 1.13/0.98 % (27365)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/18Mi)
% 1.13/0.98 % (27361)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_27242 for (2999ds/27Mi)
% 1.13/0.98 % (27362)Instruction limit reached!
% 1.13/0.98 % (27362)------------------------------
% 1.13/0.98 % (27362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/0.98 % (27362)Termination reason: Unknown
% 1.13/0.98 % (27362)Termination phase: shuffling
% 1.13/0.98
% 1.13/0.98 % (27362)Memory used [KB]: 1023
% 1.13/0.98 % (27363)Instruction limit reached!
% 1.13/0.98 % (27363)------------------------------
% 1.13/0.98 % (27363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/0.98 % (27362)Time elapsed: 0.002 s
% 1.13/0.98 % (27362)Instructions burned: 2 (million)
% 1.13/0.98 % (27362)------------------------------
% 1.13/0.98 % (27362)------------------------------
% 1.13/0.98 % (27363)Termination reason: Unknown
% 1.13/0.98 % (27363)Termination phase: shuffling
% 1.13/0.98
% 1.13/0.98 % (27363)Memory used [KB]: 1023
% 1.13/0.98 % (27363)Time elapsed: 0.002 s
% 1.13/0.98 % (27363)Instructions burned: 3 (million)
% 1.13/0.98 % (27363)------------------------------
% 1.13/0.98 % (27363)------------------------------
% 1.13/0.98 % (27360)Instruction limit reached!
% 1.13/0.98 % (27360)------------------------------
% 1.13/0.98 % (27360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/0.98 % (27360)Termination reason: Unknown
% 1.13/0.98 % (27360)Termination phase: shuffling
% 1.13/0.98
% 1.13/0.98 % (27360)Memory used [KB]: 1151
% 1.13/0.98 % (27360)Time elapsed: 0.003 s
% 1.13/0.98 % (27360)Instructions burned: 6 (million)
% 1.13/0.98 % (27360)------------------------------
% 1.13/0.98 % (27360)------------------------------
% 1.13/0.98 % (27365)Instruction limit reached!
% 1.13/0.98 % (27365)------------------------------
% 1.13/0.98 % (27365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/0.98 % (27365)Termination reason: Unknown
% 1.13/0.98 % (27365)Termination phase: Property scanning
% 1.13/0.98
% 1.13/0.98 % (27365)Memory used [KB]: 1535
% 1.13/0.98 % (27365)Time elapsed: 0.007 s
% 1.13/0.98 % (27365)Instructions burned: 20 (million)
% 1.13/0.98 % (27365)------------------------------
% 1.13/0.98 % (27365)------------------------------
% 1.13/0.98 % (27361)Instruction limit reached!
% 1.13/0.98 % (27361)------------------------------
% 1.13/0.98 % (27361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/0.98 % (27361)Termination reason: Unknown
% 1.13/0.98 % (27361)Termination phase: Saturation
% 1.13/0.98
% 1.13/0.98 % (27361)Memory used [KB]: 5756
% 1.13/0.98 % (27361)Time elapsed: 0.009 s
% 1.13/0.98 % (27361)Instructions burned: 28 (million)
% 1.13/0.98 % (27361)------------------------------
% 1.13/0.98 % (27361)------------------------------
% 1.13/0.99 % (27366)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/3Mi)
% 1.13/0.99 % (27368)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_27242 for (2999ds/15Mi)
% 1.13/0.99 % (27366)Instruction limit reached!
% 1.13/0.99 % (27366)------------------------------
% 1.13/0.99 % (27366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/0.99 % (27366)Termination reason: Unknown
% 1.13/0.99 % (27366)Termination phase: shuffling
% 1.13/0.99
% 1.13/0.99 % (27366)Memory used [KB]: 1023
% 1.13/0.99 % (27366)Time elapsed: 0.002 s
% 1.13/0.99 % (27366)Instructions burned: 4 (million)
% 1.13/0.99 % (27366)------------------------------
% 1.13/0.99 % (27366)------------------------------
% 1.13/0.99 % (27367)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_27242 for (2999ds/37Mi)
% 1.13/0.99 % (27369)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_27242 for (2999ds/3Mi)
% 1.13/0.99 % (27368)Instruction limit reached!
% 1.13/0.99 % (27368)------------------------------
% 1.13/0.99 % (27368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/0.99 % (27368)Termination reason: Unknown
% 1.13/0.99 % (27368)Termination phase: Preprocessing 3
% 1.13/0.99
% 1.13/0.99 % (27368)Memory used [KB]: 1535
% 1.13/0.99 % (27368)Time elapsed: 0.006 s
% 1.13/0.99 % (27368)Instructions burned: 17 (million)
% 1.13/0.99 % (27368)------------------------------
% 1.13/0.99 % (27368)------------------------------
% 1.13/0.99 % (27369)Instruction limit reached!
% 1.13/0.99 % (27369)------------------------------
% 1.13/0.99 % (27369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/0.99 % (27369)Termination reason: Unknown
% 1.13/0.99 % (27369)Termination phase: shuffling
% 1.13/0.99
% 1.13/0.99 % (27369)Memory used [KB]: 1023
% 1.13/0.99 % (27369)Time elapsed: 0.002 s
% 1.13/0.99 % (27369)Instructions burned: 4 (million)
% 1.13/0.99 % (27369)------------------------------
% 1.13/0.99 % (27369)------------------------------
% 1.13/0.99 % (27370)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_27242 for (2999ds/1041Mi)
% 1.13/1.00 % (27371)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/7Mi)
% 1.13/1.00 % (27371)Instruction limit reached!
% 1.13/1.00 % (27371)------------------------------
% 1.13/1.00 % (27371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/1.00 % (27371)Termination reason: Unknown
% 1.13/1.00 % (27371)Termination phase: Property scanning
% 1.13/1.00
% 1.13/1.00 % (27371)Memory used [KB]: 1151
% 1.13/1.00 % (27371)Time elapsed: 0.003 s
% 1.13/1.00 % (27371)Instructions burned: 7 (million)
% 1.13/1.00 % (27371)------------------------------
% 1.13/1.00 % (27371)------------------------------
% 1.13/1.00 % (27367)Instruction limit reached!
% 1.13/1.00 % (27367)------------------------------
% 1.13/1.00 % (27367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/1.00 % (27367)Termination reason: Unknown
% 1.13/1.00 % (27367)Termination phase: Saturation
% 1.13/1.00
% 1.13/1.00 % (27367)Memory used [KB]: 6012
% 1.13/1.00 % (27367)Time elapsed: 0.011 s
% 1.13/1.00 % (27367)Instructions burned: 39 (million)
% 1.13/1.00 % (27367)------------------------------
% 1.13/1.00 % (27367)------------------------------
% 1.13/1.00 % (27372)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/16Mi)
% 1.13/1.00 % (27373)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_27242 for (2999ds/3Mi)
% 1.13/1.00 % (27373)Instruction limit reached!
% 1.13/1.00 % (27373)------------------------------
% 1.13/1.00 % (27373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/1.00 % (27373)Termination reason: Unknown
% 1.13/1.00 % (27373)Termination phase: shuffling
% 1.13/1.00
% 1.13/1.00 % (27373)Memory used [KB]: 1023
% 1.13/1.00 % (27373)Time elapsed: 0.002 s
% 1.13/1.00 % (27373)Instructions burned: 3 (million)
% 1.13/1.00 % (27373)------------------------------
% 1.13/1.00 % (27373)------------------------------
% 1.13/1.01 % (27372)Instruction limit reached!
% 1.13/1.01 % (27372)------------------------------
% 1.13/1.01 % (27372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/1.01 % (27372)Termination reason: Unknown
% 1.13/1.01 % (27372)Termination phase: Twee Goal Transformation
% 1.13/1.01
% 1.13/1.01 % (27372)Memory used [KB]: 1279
% 1.13/1.01 % (27372)Time elapsed: 0.006 s
% 1.13/1.01 % (27372)Instructions burned: 18 (million)
% 1.13/1.01 % (27372)------------------------------
% 1.13/1.01 % (27372)------------------------------
% 1.13/1.01 % (27374)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_27242 for (2999ds/3Mi)
% 1.13/1.01 % (27374)Instruction limit reached!
% 1.13/1.01 % (27374)------------------------------
% 1.13/1.01 % (27374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/1.01 % (27374)Termination reason: Unknown
% 1.13/1.01 % (27374)Termination phase: shuffling
% 1.13/1.01
% 1.13/1.01 % (27374)Memory used [KB]: 1023
% 1.13/1.01 % (27374)Time elapsed: 0.002 s
% 1.13/1.01 % (27374)Instructions burned: 3 (million)
% 1.13/1.01 % (27374)------------------------------
% 1.13/1.01 % (27374)------------------------------
% 1.13/1.01 % (27375)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/7Mi)
% 1.13/1.01 % (27375)Instruction limit reached!
% 1.13/1.01 % (27375)------------------------------
% 1.13/1.01 % (27375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/1.01 % (27375)Termination reason: Unknown
% 1.13/1.01 % (27375)Termination phase: shuffling
% 1.13/1.01
% 1.13/1.01 % (27375)Memory used [KB]: 1151
% 1.13/1.01 % (27375)Time elapsed: 0.003 s
% 1.13/1.01 % (27375)Instructions burned: 7 (million)
% 1.13/1.01 % (27375)------------------------------
% 1.13/1.01 % (27375)------------------------------
% 1.13/1.01 % (27376)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/3Mi)
% 1.13/1.01 % (27376)Instruction limit reached!
% 1.13/1.01 % (27376)------------------------------
% 1.13/1.01 % (27376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.13/1.01 % (27376)Termination reason: Unknown
% 1.13/1.01 % (27376)Termination phase: shuffling
% 1.13/1.01
% 1.13/1.01 % (27376)Memory used [KB]: 1023
% 1.13/1.01 % (27376)Time elapsed: 0.002 s
% 1.13/1.01 % (27376)Instructions burned: 4 (million)
% 1.13/1.01 % (27376)------------------------------
% 1.13/1.01 % (27376)------------------------------
% 1.54/1.02 % (27377)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/4Mi)
% 1.54/1.02 % (27377)Instruction limit reached!
% 1.54/1.02 % (27377)------------------------------
% 1.54/1.02 % (27377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.02 % (27377)Termination reason: Unknown
% 1.54/1.02 % (27377)Termination phase: shuffling
% 1.54/1.02
% 1.54/1.02 % (27377)Memory used [KB]: 1151
% 1.54/1.02 % (27377)Time elapsed: 0.003 s
% 1.54/1.02 % (27377)Instructions burned: 7 (million)
% 1.54/1.02 % (27377)------------------------------
% 1.54/1.02 % (27377)------------------------------
% 1.54/1.02 % (27378)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/18Mi)
% 1.54/1.02 % (27379)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/710Mi)
% 1.54/1.02 % (27380)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/6Mi)
% 1.54/1.02 % (27378)Instruction limit reached!
% 1.54/1.02 % (27378)------------------------------
% 1.54/1.02 % (27378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.02 % (27378)Termination reason: Unknown
% 1.54/1.02 % (27378)Termination phase: Saturation
% 1.54/1.02
% 1.54/1.02 % (27378)Memory used [KB]: 5756
% 1.54/1.02 % (27378)Time elapsed: 0.006 s
% 1.54/1.02 % (27378)Instructions burned: 18 (million)
% 1.54/1.02 % (27378)------------------------------
% 1.54/1.02 % (27378)------------------------------
% 1.54/1.03 % (27380)Instruction limit reached!
% 1.54/1.03 % (27380)------------------------------
% 1.54/1.03 % (27380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.03 % (27380)Termination reason: Unknown
% 1.54/1.03 % (27380)Termination phase: shuffling
% 1.54/1.03
% 1.54/1.03 % (27380)Memory used [KB]: 1151
% 1.54/1.03 % (27380)Time elapsed: 0.003 s
% 1.54/1.03 % (27380)Instructions burned: 6 (million)
% 1.54/1.03 % (27380)------------------------------
% 1.54/1.03 % (27380)------------------------------
% 1.54/1.03 % (27381)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_27242 for (2999ds/902Mi)
% 1.54/1.03 % (27359)Instruction limit reached!
% 1.54/1.03 % (27359)------------------------------
% 1.54/1.03 % (27359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.03 % (27359)Termination reason: Unknown
% 1.54/1.03 % (27359)Termination phase: Saturation
% 1.54/1.03
% 1.54/1.03 % (27359)Memory used [KB]: 6908
% 1.54/1.03 % (27359)Time elapsed: 0.057 s
% 1.54/1.03 % (27359)Instructions burned: 183 (million)
% 1.54/1.03 % (27359)------------------------------
% 1.54/1.03 % (27359)------------------------------
% 1.54/1.03 % (27382)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_27242 for (2999ds/21Mi)
% 1.54/1.04 % (27383)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/5Mi)
% 1.54/1.04 % (27383)Instruction limit reached!
% 1.54/1.04 % (27383)------------------------------
% 1.54/1.04 % (27383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.04 % (27383)Termination reason: Unknown
% 1.54/1.04 % (27383)Termination phase: Property scanning
% 1.54/1.04
% 1.54/1.04 % (27383)Memory used [KB]: 1151
% 1.54/1.04 % (27383)Time elapsed: 0.003 s
% 1.54/1.04 % (27383)Instructions burned: 7 (million)
% 1.54/1.04 % (27383)------------------------------
% 1.54/1.04 % (27383)------------------------------
% 1.54/1.04 % (27382)Instruction limit reached!
% 1.54/1.04 % (27382)------------------------------
% 1.54/1.04 % (27382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.04 % (27382)Termination reason: Unknown
% 1.54/1.04 % (27382)Termination phase: Property scanning
% 1.54/1.04
% 1.54/1.04 % (27382)Memory used [KB]: 1279
% 1.54/1.04 % (27382)Time elapsed: 0.007 s
% 1.54/1.04 % (27382)Instructions burned: 23 (million)
% 1.54/1.04 % (27382)------------------------------
% 1.54/1.04 % (27382)------------------------------
% 1.54/1.04 % (27384)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_27242 for (2999ds/6Mi)
% 1.54/1.04 % (27384)Instruction limit reached!
% 1.54/1.04 % (27384)------------------------------
% 1.54/1.04 % (27384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.04 % (27384)Termination reason: Unknown
% 1.54/1.04 % (27384)Termination phase: Property scanning
% 1.54/1.04
% 1.54/1.04 % (27384)Memory used [KB]: 1151
% 1.54/1.04 % (27384)Time elapsed: 0.003 s
% 1.54/1.04 % (27384)Instructions burned: 7 (million)
% 1.54/1.04 % (27384)------------------------------
% 1.54/1.04 % (27384)------------------------------
% 1.54/1.05 % (27381)First to succeed.
% 1.54/1.05 % (27385)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27242 for (2999ds/377Mi)
% 1.54/1.05 % (27381)Refutation found. Thanks to Tanya!
% 1.54/1.05 % SZS status Theorem for DTF2THF_27242
% 1.54/1.05 % SZS output start Proof for DTF2THF_27242
% 1.54/1.05 thf(func_def_0, type, in: $i > $i > $o).
% 1.54/1.05 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.54/1.05 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.54/1.05 thf(func_def_8, type, powerset: $i > $i).
% 1.54/1.05 thf(func_def_10, type, setunion: $i > $i).
% 1.54/1.05 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.54/1.05 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.54/1.05 thf(func_def_26, type, prop2set: $o > $i).
% 1.54/1.05 thf(func_def_36, type, nonempty: $i > $o).
% 1.54/1.05 thf(func_def_63, type, sP0: $i > $i > $o).
% 1.54/1.05 thf(func_def_64, type, sP1: $i > $o).
% 1.54/1.05 thf(func_def_65, type, sP2: $i > $i > $o).
% 1.54/1.05 thf(func_def_66, type, sP3: $i > $i > $o).
% 1.54/1.05 thf(func_def_70, type, sK7: $i > $i > $i).
% 1.54/1.05 thf(func_def_74, type, sK11: $i > $i > $i).
% 1.54/1.05 thf(func_def_77, type, sK14: $i > $o).
% 1.54/1.05 thf(func_def_83, type, sK20: $i > $o).
% 1.54/1.05 thf(func_def_84, type, sK21: $i > $i).
% 1.54/1.05 thf(func_def_85, type, sK22: ($i > $o) > $i).
% 1.54/1.05 thf(func_def_86, type, sK23: $i > $i > $i).
% 1.54/1.05 thf(func_def_87, type, sK24: $i > $i > $i).
% 1.54/1.05 thf(func_def_88, type, sK25: $i > $i > $i).
% 1.54/1.05 thf(func_def_89, type, sK26: $i > $i > $i).
% 1.54/1.05 thf(func_def_90, type, sK27: $i > $i > $i > $i).
% 1.54/1.05 thf(func_def_91, type, sK28: $i > $i).
% 1.54/1.05 thf(func_def_92, type, sK29: $i > $i).
% 1.54/1.05 thf(func_def_93, type, sK30: $i > $i).
% 1.54/1.05 thf(func_def_94, type, sK31: $i > $i).
% 1.54/1.05 thf(func_def_95, type, sK32: $i > $i > $i).
% 1.54/1.05 thf(func_def_96, type, sK33: $i > $i > $i > $i).
% 1.54/1.05 thf(func_def_97, type, sK34: $i > $i > $i > $i).
% 1.54/1.05 thf(func_def_98, type, sK35: $i > $i > $i).
% 1.54/1.05 thf(func_def_99, type, sK36: $i > $i > $i).
% 1.54/1.05 thf(func_def_101, type, sK38: $i > $i).
% 1.54/1.05 thf(func_def_102, type, sK39: $i > $i).
% 1.54/1.05 thf(func_def_103, type, sK40: $i > $i).
% 1.54/1.05 thf(func_def_104, type, sK41: $i > $i > $i).
% 1.54/1.05 thf(func_def_105, type, sK42: $i > $o).
% 1.54/1.05 thf(func_def_106, type, sK43: ($i > $o) > $i).
% 1.54/1.05 thf(func_def_114, type, sK51: $i > $i > $i).
% 1.54/1.05 thf(func_def_115, type, sK52: $i > $i).
% 1.54/1.05 thf(func_def_117, type, sK54: $i > $o).
% 1.54/1.05 thf(func_def_124, type, sK61: $i > $i > $i).
% 1.54/1.05 thf(func_def_139, type, sK76: $i > $i > $i).
% 1.54/1.05 thf(func_def_140, type, sK77: $i > $i > $i).
% 1.54/1.05 thf(func_def_146, type, sK83: $i > $i).
% 1.54/1.05 thf(func_def_148, type, sK85: $i > $o).
% 1.54/1.05 thf(func_def_153, type, sK90: $i > $o).
% 1.54/1.05 thf(func_def_155, type, sK92: $i > $i).
% 1.54/1.05 thf(func_def_157, type, sK94: $i > $i).
% 1.54/1.05 thf(func_def_159, type, sK96: $i > $i).
% 1.54/1.05 thf(func_def_161, type, sK98: $i > $i).
% 1.54/1.05 thf(func_def_169, type, sK106: $i > $o).
% 1.54/1.05 thf(func_def_173, type, sK110: $i > $o).
% 1.54/1.05 thf(func_def_176, type, sK113: $i > $i > $o).
% 1.54/1.05 thf(func_def_178, type, sK115: $i > $i).
% 1.54/1.05 thf(func_def_179, type, sK116: $i > $i).
% 1.54/1.05 thf(func_def_180, type, sK117: $i > ($i > $i > $o) > $i).
% 1.54/1.05 thf(func_def_181, type, sK118: $i > $i > ($i > $i > $o) > $i).
% 1.54/1.05 thf(func_def_182, type, sK119: $i > ($i > $i > $o) > $i).
% 1.54/1.05 thf(func_def_184, type, ph121: !>[X0: $tType]:(X0)).
% 1.54/1.05 thf(f800,plain,(
% 1.54/1.05 $false),
% 1.54/1.05 inference(avatar_sat_refutation,[status(thm)],[f648,f649,f794])).
% 1.54/1.05 thf(f794,plain,(
% 1.54/1.05 ~spl120_1),
% 1.54/1.05 inference(avatar_contradiction_clause,[status(thm)],[f793])).
% 1.54/1.05 thf(f793,plain,(
% 1.54/1.05 $false | ~spl120_1),
% 1.54/1.05 inference(trivial_inequality_removal,[status(thm)],[f785])).
% 1.54/1.05 thf(f785,plain,(
% 1.54/1.05 ($true != $true) | ~spl120_1),
% 1.54/1.05 inference(superposition,[status(thm)],[f780,f502])).
% 1.54/1.05 thf(f502,plain,(
% 1.54/1.05 ($true = (in @ sK73 @ (setunion @ sK72)))),
% 1.54/1.05 inference(cnf_transformation,[status(thm)],[f300])).
% 1.54/1.05 thf(f300,plain,(
% 1.54/1.05 (setunionI = $true) & (setadjoinIL = $true) & (emptysetAx = $true) & (noeltsimpempty = $true) & (setbeta = $true) & (emptyinunitempty = $true) & (powersetE = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (descrp = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (omegaSAx = $true) & (setunionAx = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (replAx = $true) & (setextAx = $true) & (foundationAx = $true) & (prop2setE = $true) & (emptysetE = $true) & (notinemptyset = $true) & (emptyInPowerset = $true) & (dsetconstrEL = $true) & (setext = $true) & (emptysetimpfalse = $true) & (wellorderingAx = $true) & (emptyI = $true) & (nonemptyE1 = $true) & (omega0Ax = $true) & (exuE3e = $true) & (powersetI = $true) & (omegaIndAx = $true) & ((! [X3 : $i] : (($true != (in @ X3 @ sK72)) | ($true = sK74) | ($true != (in @ sK73 @ X3))) & ($true != sK74)) & ($true = (in @ sK73 @ (setunion @ sK72)))) & (setadjoinIR = $true) & (setadjoinOr = $true) & (powersetAx = $true)),
% 1.54/1.05 inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73,sK74])],[f154,f299,f298])).
% 1.54/1.05 thf(f298,plain,(
% 1.54/1.05 ? [X0 : $i,X1 : $i] : (? [X2 : $o] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = X2) | ((in @ X1 @ X3) != $true)) & ($true != X2)) & ($true = (in @ X1 @ (setunion @ X0)))) => (? [X2 : $o] : (! [X3 : $i] : (($true != (in @ X3 @ sK72)) | ($true = X2) | ($true != (in @ sK73 @ X3))) & ($true != X2)) & ($true = (in @ sK73 @ (setunion @ sK72))))),
% 1.54/1.05 introduced(definition,[],[choice_axiom])).
% 1.54/1.05 thf(f299,plain,(
% 1.54/1.05 ? [X2 : $o] : (! [X3 : $i] : (($true != (in @ X3 @ sK72)) | ($true = X2) | ($true != (in @ sK73 @ X3))) & ($true != X2)) => (! [X3 : $i] : (($true != (in @ X3 @ sK72)) | ($true = sK74) | ($true != (in @ sK73 @ X3))) & ($true != sK74))),
% 1.54/1.05 introduced(definition,[],[choice_axiom])).
% 1.54/1.05 thf(f154,plain,(
% 1.54/1.05 (setunionI = $true) & (setadjoinIL = $true) & (emptysetAx = $true) & (noeltsimpempty = $true) & (setbeta = $true) & (emptyinunitempty = $true) & (powersetE = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (descrp = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (omegaSAx = $true) & (setunionAx = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (replAx = $true) & (setextAx = $true) & (foundationAx = $true) & (prop2setE = $true) & (emptysetE = $true) & (notinemptyset = $true) & (emptyInPowerset = $true) & (dsetconstrEL = $true) & (setext = $true) & (emptysetimpfalse = $true) & (wellorderingAx = $true) & (emptyI = $true) & (nonemptyE1 = $true) & (omega0Ax = $true) & (exuE3e = $true) & (powersetI = $true) & (omegaIndAx = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $o] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = X2) | ((in @ X1 @ X3) != $true)) & ($true != X2)) & ($true = (in @ X1 @ (setunion @ X0)))) & (setadjoinIR = $true) & (setadjoinOr = $true) & (powersetAx = $true)),
% 1.54/1.05 inference(flattening,[status(thm)],[f153])).
% 1.54/1.05 thf(f153,plain,(
% 1.54/1.05 ((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $o] : (($true != X2) & ! [X3 : $i] : ((($true = X2) | ($true != (in @ X3 @ X0))) | ((in @ X1 @ X3) != $true))) & ($true = (in @ X1 @ (setunion @ X0)))) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 1.54/1.05 inference(ennf_transformation,[status(thm)],[f51])).
% 1.54/1.05 thf(f51,plain,(
% 1.54/1.05 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setunion @ X0))) => ! [X2 : $o] : (! [X3 : $i] : (((in @ X1 @ X3) = $true) => (($true = (in @ X3 @ X0)) => ($true = X2))) => ($true = X2))))))))))))))))))))))))))))))))))))))))))),
% 1.54/1.05 inference(fool_elimination,[status(thm)],[f50])).
% 1.54/1.05 thf(f50,plain,(
% 1.54/1.05 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))))))))))))))))))))))))))))))))))))))))),
% 1.54/1.05 inference(rectify,[status(thm)],[f44])).
% 1.54/1.05 thf(f44,negated_conjecture,(
% 1.54/1.05 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => ! [X3 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X3)) => ! [X0 : $o] : (! [X4 : $i] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => X0)) => X0)))))))))))))))))))))))))))))))))))))))))),
% 1.54/1.05 inference(negated_conjecture,[status(cth)],[f43])).
% 1.54/1.05 thf(f43,conjecture,(
% 1.54/1.05 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => ! [X3 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X3)) => ! [X0 : $o] : (! [X4 : $i] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => X0)) => X0))))))))))))))))))))))))))))))))))))))))),
% 1.54/1.05 file('/export/starexec/sandbox2/tmp/tmp.IwOMFljda7/DTF2THF_27242.p',setunionE)).
% 1.54/1.05 thf(f780,plain,(
% 1.54/1.05 ($true != (in @ sK73 @ (setunion @ sK72))) | ~spl120_1),
% 1.54/1.05 inference(trivial_inequality_removal,[status(thm)],[f779])).
% 1.54/1.05 thf(f779,plain,(
% 1.54/1.05 ($true != $true) | ($true != (in @ sK73 @ (setunion @ sK72))) | ~spl120_1),
% 1.54/1.05 inference(forward_demodulation,[status(thm)],[f777,f525])).
% 1.54/1.05 thf(f525,plain,(
% 1.54/1.05 (setunionAx = $true)),
% 1.54/1.05 inference(cnf_transformation,[status(thm)],[f300])).
% 1.54/1.05 thf(f777,plain,(
% 1.54/1.05 ($true != (in @ sK73 @ (setunion @ sK72))) | (setunionAx != $true) | ~spl120_1),
% 1.54/1.05 inference(trivial_inequality_removal,[status(thm)],[f776])).
% 1.54/1.05 thf(f776,plain,(
% 1.54/1.05 (setunionAx != $true) | ($true != (in @ sK73 @ (setunion @ sK72))) | ($true != $true) | ~spl120_1),
% 1.54/1.05 inference(duplicate_literal_removal,[status(thm)],[f772])).
% 1.54/1.05 thf(f772,plain,(
% 1.54/1.05 ($true != $true) | (setunionAx != $true) | ($true != (in @ sK73 @ (setunion @ sK72))) | ($true != (in @ sK73 @ (setunion @ sK72))) | ~spl120_1),
% 1.54/1.05 inference(superposition,[status(thm)],[f723,f484])).
% 1.54/1.05 thf(f484,plain,(
% 1.54/1.05 ( ! [X0 : $i,X1 : $i] : (((in @ (sK61 @ X1 @ X0) @ X0) = $true) | ($true != (in @ X1 @ (setunion @ X0))) | (setunionAx != $true)) )),
% 1.54/1.05 inference(cnf_transformation,[status(thm)],[f287])).
% 1.54/1.05 thf(f287,plain,(
% 1.54/1.05 (! [X0 : $i,X1 : $i] : (((((in @ (sK61 @ X1 @ X0) @ X0) = $true) & ((in @ X1 @ (sK61 @ X1 @ X0)) = $true)) | ($true != (in @ X1 @ (setunion @ X0)))) & (($true = (in @ X1 @ (setunion @ X0))) | ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ((in @ X1 @ X3) != $true)))) | (setunionAx != $true)) & ((setunionAx = $true) | ((((in @ sK63 @ (setunion @ sK62)) != $true) | ! [X6 : $i] : (($true != (in @ X6 @ sK62)) | ($true != (in @ sK63 @ X6)))) & (((in @ sK63 @ (setunion @ sK62)) = $true) | (($true = (in @ sK64 @ sK62)) & ((in @ sK63 @ sK64) = $true)))))),
% 1.54/1.05 inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62,sK63,sK64])],[f283,f286,f285,f284])).
% 1.54/1.05 thf(f284,plain,(
% 1.54/1.05 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X1 @ X2))) => (((in @ (sK61 @ X1 @ X0) @ X0) = $true) & ((in @ X1 @ (sK61 @ X1 @ X0)) = $true)))),
% 1.54/1.05 introduced(definition,[],[choice_axiom])).
% 1.54/1.05 thf(f285,plain,(
% 1.54/1.05 ? [X4 : $i,X5 : $i] : ((((in @ X5 @ (setunion @ X4)) != $true) | ! [X6 : $i] : (((in @ X6 @ X4) != $true) | ((in @ X5 @ X6) != $true))) & (((in @ X5 @ (setunion @ X4)) = $true) | ? [X7 : $i] : (((in @ X7 @ X4) = $true) & ($true = (in @ X5 @ X7))))) => ((((in @ sK63 @ (setunion @ sK62)) != $true) | ! [X6 : $i] : (($true != (in @ X6 @ sK62)) | ($true != (in @ sK63 @ X6)))) & (((in @ sK63 @ (setunion @ sK62)) = $true) | ? [X7 : $i] : (($true = (in @ X7 @ sK62)) & ($true = (in @ sK63 @ X7)))))),
% 1.54/1.05 introduced(definition,[],[choice_axiom])).
% 1.54/1.05 thf(f286,plain,(
% 1.54/1.05 ? [X7 : $i] : (($true = (in @ X7 @ sK62)) & ($true = (in @ sK63 @ X7))) => (($true = (in @ sK64 @ sK62)) & ((in @ sK63 @ sK64) = $true))),
% 1.54/1.05 introduced(definition,[],[choice_axiom])).
% 1.54/1.05 thf(f283,plain,(
% 1.54/1.05 (! [X0 : $i,X1 : $i] : ((? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X1 @ X2))) | ($true != (in @ X1 @ (setunion @ X0)))) & (($true = (in @ X1 @ (setunion @ X0))) | ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ((in @ X1 @ X3) != $true)))) | (setunionAx != $true)) & ((setunionAx = $true) | ? [X4 : $i,X5 : $i] : ((((in @ X5 @ (setunion @ X4)) != $true) | ! [X6 : $i] : (((in @ X6 @ X4) != $true) | ((in @ X5 @ X6) != $true))) & (((in @ X5 @ (setunion @ X4)) = $true) | ? [X7 : $i] : (((in @ X7 @ X4) = $true) & ($true = (in @ X5 @ X7))))))),
% 1.54/1.05 inference(rectify,[status(thm)],[f282])).
% 1.54/1.05 thf(f282,plain,(
% 1.54/1.05 (! [X0 : $i,X1 : $i] : ((? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X1 @ X2))) | ($true != (in @ X1 @ (setunion @ X0)))) & (($true = (in @ X1 @ (setunion @ X0))) | ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ($true != (in @ X1 @ X2))))) | (setunionAx != $true)) & ((setunionAx = $true) | ? [X0 : $i,X1 : $i] : ((($true != (in @ X1 @ (setunion @ X0))) | ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ($true != (in @ X1 @ X2)))) & (($true = (in @ X1 @ (setunion @ X0))) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X1 @ X2))))))),
% 1.54/1.05 inference(nnf_transformation,[status(thm)],[f98])).
% 1.54/1.05 thf(f98,plain,(
% 1.54/1.05 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X1 @ X2))) <=> ($true = (in @ X1 @ (setunion @ X0)))) <=> (setunionAx = $true)),
% 1.54/1.05 inference(fool_elimination,[status(thm)],[f97])).
% 1.54/1.05 thf(f97,plain,(
% 1.54/1.05 (setunionAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2))))),
% 1.54/1.05 inference(rectify,[status(thm)],[f6])).
% 1.54/1.05 thf(f6,axiom,(
% 1.54/1.05 (setunionAx = ! [X3 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X3)) <=> ? [X4 : $i] : ((in @ X4 @ X3) & (in @ X1 @ X4))))),
% 1.54/1.05 file('/export/starexec/sandbox2/tmp/tmp.IwOMFljda7/DTF2THF_27242.p',setunionAx)).
% 1.54/1.05 thf(f723,plain,(
% 1.54/1.05 ( ! [X0 : $i] : (((in @ (sK61 @ sK73 @ X0) @ sK72) != $true) | ((in @ sK73 @ (setunion @ X0)) != $true)) ) | ~spl120_1),
% 1.54/1.05 inference(trivial_inequality_removal,[status(thm)],[f722])).
% 1.54/1.05 thf(f722,plain,(
% 1.54/1.05 ( ! [X0 : $i] : (((in @ (sK61 @ sK73 @ X0) @ sK72) != $true) | ($true != $true) | ((in @ sK73 @ (setunion @ X0)) != $true)) ) | ~spl120_1),
% 1.54/1.05 inference(forward_demodulation,[status(thm)],[f683,f525])).
% 1.54/1.05 thf(f683,plain,(
% 1.54/1.05 ( ! [X0 : $i] : (((in @ sK73 @ (setunion @ X0)) != $true) | ((in @ (sK61 @ sK73 @ X0) @ sK72) != $true) | (setunionAx != $true)) ) | ~spl120_1),
% 1.54/1.05 inference(trivial_inequality_removal,[status(thm)],[f662])).
% 1.54/1.05 thf(f662,plain,(
% 1.54/1.05 ( ! [X0 : $i] : ((setunionAx != $true) | ($true != $true) | ((in @ sK73 @ (setunion @ X0)) != $true) | ((in @ (sK61 @ sK73 @ X0) @ sK72) != $true)) ) | ~spl120_1),
% 1.54/1.05 inference(superposition,[status(thm)],[f643,f483])).
% 1.54/1.05 thf(f483,plain,(
% 1.54/1.05 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (sK61 @ X1 @ X0)) = $true) | ($true != (in @ X1 @ (setunion @ X0))) | (setunionAx != $true)) )),
% 1.54/1.05 inference(cnf_transformation,[status(thm)],[f287])).
% 1.54/1.05 thf(f643,plain,(
% 1.54/1.05 ( ! [X3 : $i] : (($true != (in @ sK73 @ X3)) | ($true != (in @ X3 @ sK72))) ) | ~spl120_1),
% 1.54/1.05 inference(avatar_component_clause,[status(thm)],[f642])).
% 1.54/1.05 thf(f642,definition,(
% 1.54/1.05 spl120_1 <=> ! [X3 : $i] : (($true != (in @ sK73 @ X3)) | ($true != (in @ X3 @ sK72)))),
% 1.54/1.05 introduced(definition,[new_symbols(naming,[spl120_1])],[avatar_definition])).
% 1.54/1.05 thf(f649,plain,(
% 1.54/1.05 ~spl120_2),
% 1.54/1.05 inference(avatar_split_clause,[status(thm)],[f503,f645])).
% 1.54/1.05 thf(f645,definition,(
% 1.54/1.05 spl120_2 <=> ($true = sK74)),
% 1.54/1.05 introduced(definition,[new_symbols(naming,[spl120_2])],[avatar_definition])).
% 1.54/1.05 thf(f503,plain,(
% 1.54/1.05 ($true != sK74)),
% 1.54/1.05 inference(cnf_transformation,[status(thm)],[f300])).
% 1.54/1.05 thf(f648,plain,(
% 1.54/1.05 spl120_1 | spl120_2),
% 1.54/1.05 inference(avatar_split_clause,[status(thm)],[f504,f645,f642])).
% 1.54/1.05 thf(f504,plain,(
% 1.54/1.05 ( ! [X3 : $i] : (($true = sK74) | ($true != (in @ sK73 @ X3)) | ($true != (in @ X3 @ sK72))) )),
% 1.54/1.05 inference(cnf_transformation,[status(thm)],[f300])).
% 1.54/1.05 % SZS output end Proof for DTF2THF_27242
% 1.54/1.05 % (27381)------------------------------
% 1.54/1.05 % (27381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.05 % (27381)Termination reason: Refutation
% 1.54/1.05
% 1.54/1.05 % (27381)Memory used [KB]: 6268
% 1.54/1.05 % (27381)Time elapsed: 0.019 s
% 1.54/1.05 % (27381)Instructions burned: 56 (million)
% 1.54/1.05 % (27381)------------------------------
% 1.54/1.05 % (27381)------------------------------
% 1.54/1.05 % (27358)Success in time 0.085 s
%------------------------------------------------------------------------------