%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU511^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 09:35:00 AM UTC 2026
% Result : Theorem 1.99s 1.40s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 551 ( 150 equ; 0 cnn)
% Maximal formula atoms : 29 ( 17 avg)
% Number of connectives : 287 ( 24 ~; 0 |; 86 &; 60 @)
% ( 0 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 68 usr; 33 con; 0-3 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 30 ( 9 ^; 9 !; 12 ?; 30 :)
% 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_58,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_59,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_60,type,
sK5: $i > $i ).
thf(func_def_61,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_62,type,
sK7: $i > $i ).
thf(func_def_63,type,
sK8: $i > $i > $i ).
thf(func_def_64,type,
sK9: $i > $i ).
thf(func_def_65,type,
sK10: $i > $i > $i ).
thf(func_def_66,type,
sK11: $i > $i > $i ).
thf(func_def_67,type,
sK12: $i > $i > $i ).
thf(func_def_68,type,
sK13: $i > $i > $i ).
thf(func_def_69,type,
sK14: $i > $i > $i > $i ).
thf(func_def_70,type,
sK15: $i > $i ).
thf(func_def_71,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_72,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_73,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_74,type,
sK19: $i > $i ).
thf(func_def_75,type,
sK20: $i > $i > $i ).
thf(func_def_76,type,
sK21: $i > $i > $i ).
thf(func_def_77,type,
sK22: $i > $i ).
thf(func_def_78,type,
sK23: $i > $i > $i ).
thf(func_def_79,type,
sK24: $i > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK25: $i > ( $i > $i > $o ) > $i ).
thf(func_def_81,type,
sK26: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_82,type,
sK27: $i > ( $i > $i > $o ) > $i ).
thf(func_def_83,type,
sK28: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_84,type,
sK29: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_85,type,
sK30: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_86,type,
sK31: $i > $i > $i ).
thf(f591,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f590]) ).
thf(f590,plain,
$false = $true,
inference(superposition,[status(thm)],[f497,f588]) ).
thf(f588,plain,
( $true
= ( in @ sK1 @ emptyset ) ),
inference(superposition,[status(thm)],[f130,f226]) ).
thf(f226,plain,
emptyset = sK0,
inference(equality_proxy_clausification,[status(thm)],[f225]) ).
thf(f225,plain,
( $true
= ( emptyset = sK0 ) ),
inference(not_proxy_clausification,[status(thm)],[f224]) ).
thf(f224,plain,
( ( emptyset != sK0 )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f160]) ).
thf(f160,plain,
( ( ^ [Y0: $i] : ( emptyset != Y0 )
@ sK0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f131,f142]) ).
thf(f142,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f56]) ).
thf(f56,plain,
( nonempty
= ( ^ [X0: $i] : ( emptyset != X0 ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,axiom,
( nonempty
= ( ^ [X1: $i] : ( emptyset != X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jCFCl5ort6/DTF2THF_22688.p',nonempty) ).
thf(f131,plain,
( ( nonempty @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f97]) ).
thf(f97,plain,
( ( setunionAx = $true )
& ( replAx = $true )
& ( notinemptyset = $true )
& ( emptysetAx = $true )
& ( ( nonempty @ sK0 )
!= $true )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( noeltsimpempty = $true )
& ( exuE1 = $true )
& ( omegaSAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( exuE3e = $true )
& ( setextAx = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( dsetconstrER = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( emptysetimpfalse = $true )
& ( wellorderingAx = $true )
& ( emptysetE = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f94,f96,f95]) ).
thf(f95,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
& ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
=> ( ( ( nonempty @ sK0 )
!= $true )
& ? [X1: $i] :
( ( in @ X1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f96,plain,
( ? [X1: $i] :
( ( in @ X1 @ sK0 )
= $true )
=> ( ( in @ sK1 @ sK0 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f94,plain,
( ( setunionAx = $true )
& ( replAx = $true )
& ( notinemptyset = $true )
& ( emptysetAx = $true )
& ? [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
& ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
& ( noeltsimpempty = $true )
& ( exuE1 = $true )
& ( omegaSAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( exuE3e = $true )
& ( setextAx = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( dsetconstrER = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( emptysetimpfalse = $true )
& ( wellorderingAx = $true )
& ( emptysetE = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true ) ),
inference(flattening,[status(thm)],[f93]) ).
thf(f93,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
& ? [X1: $i] :
( ( in @ X1 @ X0 )
= $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)],[f59]) ).
thf(f59,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 )
=> ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
=> ( ( nonempty @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f58]) ).
thf(f58,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
=> ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,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
=> ! [X3: $i] :
( ? [X1: $i] : ( in @ X1 @ X3 )
=> ( nonempty @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
thf(f31,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
=> ! [X3: $i] :
( ? [X1: $i] : ( in @ X1 @ X3 )
=> ( nonempty @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jCFCl5ort6/DTF2THF_22688.p',nonemptyI1) ).
thf(f130,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f97]) ).
thf(f497,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
! [X1: $i] :
( ( ~ ( in @ X1 @ emptyset ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f495]) ).
thf(f495,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f178]) ).
thf(f178,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f147,f133]) ).
thf(f133,plain,
notinemptyset = $true,
inference(cnf_transformation,[status(thm)],[f97]) ).
thf(f147,plain,
( notinemptyset
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) ) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
thf(f77,plain,
( notinemptyset
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) ) ),
inference(fool_elimination,[status(thm)],[f76]) ).
thf(f76,plain,
( notinemptyset
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,axiom,
( notinemptyset
= ( ! [X1: $i] :
~ ( in @ X1 @ emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jCFCl5ort6/DTF2THF_22688.p',notinemptyset) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU511^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:24:56 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEU511^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English : (! A:i.(? x:i.in x A) -> nonempty A)
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.45 % Source : [Bro08]
% 0.29/0.45 % Names : ZFC013g [Bro08]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.29/0.45 % Syntax : Number of formulae : 69 ( 30 unt; 38 typ; 30 def)
% 0.29/0.45 % Number of atoms : 175 ( 39 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 29 ( 5 avg)
% 0.29/0.45 % Number of connectives : 303 ( 7 ~; 3 |; 18 &; 197 @)
% 0.29/0.45 % ( 7 <=>; 71 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 33 ( 2 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 40 ( 38 usr; 30 con; 0-2 aty)
% 0.29/0.45 % Number of variables : 101 ( 14 ^; 71 !; 16 ?; 101 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : http://mathgate.info/detsetitem.php?id=431
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(in_type,type,
% 0.29/0.45 in: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu_type,type,
% 0.29/0.45 exu: ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu,definition,
% 0.29/0.45 ( exu
% 0.29/0.45 = ( ^ [Xphi: $i > $o] :
% 0.29/0.45 ? [Xx: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 & ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setextAx_type,type,
% 0.29/0.45 setextAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setextAx,definition,
% 0.29/0.45 ( setextAx
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 <=> ( in @ Xx @ B ) )
% 0.29/0.45 => ( A = B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyset_type,type,
% 0.29/0.45 emptyset: $i ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetAx_type,type,
% 0.29/0.45 emptysetAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetAx,definition,
% 0.29/0.45 ( emptysetAx
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoin_type,type,
% 0.29/0.45 setadjoin: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinAx_type,type,
% 0.29/0.45 setadjoinAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinAx,definition,
% 0.29/0.45 ( setadjoinAx
% 0.29/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.45 <=> ( ( Xy = Xx )
% 0.29/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powerset_type,type,
% 0.29/0.45 powerset: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(powersetAx_type,type,
% 0.29/0.45 powersetAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powersetAx,definition,
% 0.29/0.45 ( powersetAx
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.45 <=> ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setunion_type,type,
% 0.29/0.45 setunion: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(setunionAx_type,type,
% 0.29/0.45 setunionAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setunionAx,definition,
% 0.29/0.45 ( setunionAx
% 0.29/0.45 = ( ! [A: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.45 <=> ? [B: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omega_type,type,
% 0.29/0.45 omega: $i ).
% 0.29/0.45
% 0.29/0.45 thf(omega0Ax_type,type,
% 0.29/0.45 omega0Ax: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omega0Ax,definition,
% 0.29/0.45 ( omega0Ax
% 0.29/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omegaSAx_type,type,
% 0.29/0.45 omegaSAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omegaSAx,definition,
% 0.29/0.45 ( omegaSAx
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ omega )
% 0.29/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omegaIndAx_type,type,
% 0.29/0.45 omegaIndAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omegaIndAx,definition,
% 0.29/0.45 ( omegaIndAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( ( in @ emptyset @ A )
% 0.29/0.45 & ! [Xx: $i] :
% 0.29/0.45 ( ( ( in @ Xx @ omega )
% 0.29/0.45 & ( in @ Xx @ A ) )
% 0.29/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ omega )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(replAx_type,type,
% 0.29/0.45 replAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(replAx,definition,
% 0.29/0.45 ( replAx
% 0.29/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.45 => ? [B: $i] :
% 0.29/0.45 ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 <=> ? [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ A )
% 0.29/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(foundationAx_type,type,
% 0.29/0.45 foundationAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(foundationAx,definition,
% 0.29/0.45 ( foundationAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.45 => ? [B: $i] :
% 0.29/0.45 ( ( in @ B @ A )
% 0.29/0.45 & ~ ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(wellorderingAx_type,type,
% 0.29/0.45 wellorderingAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(wellorderingAx,definition,
% 0.29/0.45 ( wellorderingAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ? [B: $i] :
% 0.29/0.45 ( ! [C: $i] :
% 0.29/0.45 ( ( in @ C @ B )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ C )
% 0.29/0.45 => ( in @ Xx @ A ) ) )
% 0.29/0.45 & ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( ( in @ Xx @ A )
% 0.29/0.45 & ( in @ Xy @ A ) )
% 0.29/0.45 => ( ! [C: $i] :
% 0.29/0.45 ( ( in @ C @ B )
% 0.29/0.45 => ( ( in @ Xx @ C )
% 0.29/0.45 <=> ( in @ Xy @ C ) ) )
% 0.29/0.45 => ( Xx = Xy ) ) )
% 0.29/0.45 & ! [C: $i,D: $i] :
% 0.29/0.45 ( ( ( in @ C @ B )
% 0.29/0.45 & ( in @ D @ B ) )
% 0.29/0.45 => ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ C )
% 0.29/0.45 => ( in @ Xx @ D ) )
% 0.29/0.45 | ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ D )
% 0.29/0.45 => ( in @ Xx @ C ) ) ) )
% 0.29/0.45 & ! [C: $i] :
% 0.29/0.45 ( ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ C )
% 0.29/0.45 => ( in @ Xx @ A ) )
% 0.29/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.45 => ? [D: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ D @ B )
% 0.29/0.45 & ( in @ Xx @ C )
% 0.29/0.45 & ~ ? [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ D )
% 0.29/0.45 & ( in @ Xy @ C ) )
% 0.29/0.45 & ! [E: $i] :
% 0.29/0.45 ( ( in @ E @ B )
% 0.29/0.45 => ( ! [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ E )
% 0.29/0.45 => ( in @ Xy @ D ) )
% 0.29/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(descr_type,type,
% 0.29/0.45 descr: ( $i > $o ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(descrp_type,type,
% 0.29/0.45 descrp: $o ).
% 0.29/0.45
% 0.29/0.45 thf(descrp,definition,
% 0.29/0.45 ( descrp
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ( Xphi
% 0.29/0.45 @ ( descr
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstr_type,type,
% 0.29/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrI_type,type,
% 0.29/0.45 dsetconstrI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrI,definition,
% 0.29/0.45 ( dsetconstrI
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 => ( in @ Xx
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrEL_type,type,
% 0.29/0.45 dsetconstrEL: $o ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrEL,definition,
% 0.29/0.45 ( dsetconstrEL
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrER_type,type,
% 0.29/0.45 dsetconstrER: $o ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrER,definition,
% 0.29/0.45 ( dsetconstrER
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuE1_type,type,
% 0.29/0.45 exuE1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuE1,definition,
% 0.29/0.45 ( exuE1
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ? [Xx: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 & ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(prop2set_type,type,
% 0.29/0.45 prop2set: $o > $i ).
% 0.29/0.45
% 0.29/0.45 thf(prop2set,definition,
% 0.29/0.45 ( prop2set
% 0.29/0.45 = ( ^ [Xphi: $o] :
% 0.29/0.45 ( dsetconstr @ ( powerset @ emptyset )
% 0.29/0.45 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(prop2setE_type,type,
% 0.29/0.45 prop2setE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(prop2setE,definition,
% 0.29/0.45 ( prop2setE
% 0.29/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.45 => Xphi ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetE_type,type,
% 0.29/0.45 emptysetE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetE,definition,
% 0.29/0.45 ( emptysetE
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ emptyset )
% 0.29/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetimpfalse_type,type,
% 0.29/0.45 emptysetimpfalse: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetimpfalse,definition,
% 0.29/0.45 ( emptysetimpfalse
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ emptyset )
% 0.29/0.45 => $false ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notinemptyset_type,type,
% 0.29/0.45 notinemptyset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notinemptyset,definition,
% 0.29/0.45 ( notinemptyset
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuE3e_type,type,
% 0.29/0.45 exuE3e: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuE3e,definition,
% 0.29/0.45 ( exuE3e
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setext_type,type,
% 0.29/0.45 setext: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setext,definition,
% 0.29/0.45 ( setext
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) )
% 0.29/0.45 => ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 => ( in @ Xx @ A ) )
% 0.29/0.45 => ( A = B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyI_type,type,
% 0.29/0.45 emptyI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptyI,definition,
% 0.29/0.45 ( emptyI
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ A )
% 0.29/0.45 => ( A = emptyset ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(noeltsimpempty_type,type,
% 0.29/0.45 noeltsimpempty: $o ).
% 0.29/0.45
% 0.29/0.45 thf(noeltsimpempty,definition,
% 0.29/0.45 ( noeltsimpempty
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ A )
% 0.29/0.45 => ( A = emptyset ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setbeta_type,type,
% 0.29/0.45 setbeta: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setbeta,definition,
% 0.29/0.45 ( setbeta
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ( in @ Xx
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonempty_type,type,
% 0.29/0.45 nonempty: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(nonempty,definition,
% 0.29/0.45 ( nonempty
% 0.29/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyE1_type,type,
% 0.29/0.45 nonemptyE1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyE1,definition,
% 0.29/0.45 ( nonemptyE1
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( nonempty @ A )
% 0.29/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyI_type,type,
% 0.29/0.45 nonemptyI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyI,definition,
% 0.29/0.45 ( nonemptyI
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 => ( nonempty
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyI1,conjecture,
% 0.29/0.45 ( setextAx
% 0.29/0.45 => ( emptysetAx
% 0.29/0.45 => ( setadjoinAx
% 0.29/0.45 => ( powersetAx
% 0.29/0.45 => ( setunionAx
% 0.29/0.45 => ( omega0Ax
% 0.29/0.45 => ( omegaSAx
% 0.29/0.45 => ( omegaIndAx
% 0.29/0.45 => ( replAx
% 0.29/0.45 => ( foundationAx
% 0.29/0.45 => ( wellorderingAx
% 0.29/0.45 => ( descrp
% 0.29/0.45 => ( dsetconstrI
% 0.29/0.45 => ( dsetconstrEL
% 0.29/0.45 => ( dsetconstrER
% 0.29/0.45 => ( exuE1
% 0.29/0.45 => ( prop2setE
% 0.29/0.45 => ( emptysetE
% 0.29/0.45 => ( emptysetimpfalse
% 0.29/0.45 => ( notinemptyset
% 0.29/0.45 => ( exuE3e
% 0.29/0.45 => ( setext
% 0.29/0.45 => ( emptyI
% 0.29/0.45 => ( noeltsimpempty
% 0.29/0.45 => ( setbeta
% 0.29/0.45 => ( nonemptyE1
% 0.29/0.45 => ( nonemptyI
% 0.29/0.45 => ! [A: $i] :
% 0.29/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.45 => ( nonempty @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.89/1.33 ---- Embedded in THF ---
% 1.89/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.89/1.33 %%% Generated on Tue Feb 24 12:24:57 EST 2026
% 1.89/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.89/1.33 %%% Logic specification used:
% 1.89/1.33 %%% thf(spec, logic, $$dhol).
% 1.89/1.33
% 1.89/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jCFCl5ort6/DTF2DTF22688.p
% See solution above
% 1.89/1.33 ------------------------
% 1.89/1.34 ---- Cleaned THF ---
% 1.89/1.34 thf(in_type,type,
% 1.89/1.34 in: $i > $i > $o ).
% 1.89/1.34
% 1.89/1.34 thf(exu_type,type,
% 1.89/1.34 exu: ( $i > $o ) > $o ).
% 1.89/1.34
% 1.89/1.34 thf(exu,definition,
% 1.89/1.34 ( exu
% 1.89/1.34 = ( ^ [Xphi: $i > $o] :
% 1.89/1.34 ? [Xx: $i] :
% 1.89/1.34 ( ( Xphi @ Xx )
% 1.89/1.34 & ! [Xy: $i] :
% 1.89/1.34 ( ( Xphi @ Xy )
% 1.89/1.34 => ( Xx = Xy ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(setextAx_type,type,
% 1.89/1.34 setextAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(setextAx,definition,
% 1.89/1.34 ( setextAx
% 1.89/1.34 = ( ! [A: $i,B: $i] :
% 1.89/1.34 ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ A )
% 1.89/1.34 <=> ( in @ Xx @ B ) )
% 1.89/1.34 => ( A = B ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(emptyset_type,type,
% 1.89/1.34 emptyset: $i ).
% 1.89/1.34
% 1.89/1.34 thf(emptysetAx_type,type,
% 1.89/1.34 emptysetAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(emptysetAx,definition,
% 1.89/1.34 ( emptysetAx
% 1.89/1.34 = ( ! [Xx: $i] :
% 1.89/1.34 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(setadjoin_type,type,
% 1.89/1.34 setadjoin: $i > $i > $i ).
% 1.89/1.34
% 1.89/1.34 thf(setadjoinAx_type,type,
% 1.89/1.34 setadjoinAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(setadjoinAx,definition,
% 1.89/1.34 ( setadjoinAx
% 1.89/1.34 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.89/1.34 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.89/1.34 <=> ( ( Xy = Xx )
% 1.89/1.34 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(powerset_type,type,
% 1.89/1.34 powerset: $i > $i ).
% 1.89/1.34
% 1.89/1.34 thf(powersetAx_type,type,
% 1.89/1.34 powersetAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(powersetAx,definition,
% 1.89/1.34 ( powersetAx
% 1.89/1.34 = ( ! [A: $i,B: $i] :
% 1.89/1.34 ( ( in @ B @ ( powerset @ A ) )
% 1.89/1.34 <=> ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ B )
% 1.89/1.34 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(setunion_type,type,
% 1.89/1.34 setunion: $i > $i ).
% 1.89/1.34
% 1.89/1.34 thf(setunionAx_type,type,
% 1.89/1.34 setunionAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(setunionAx,definition,
% 1.89/1.34 ( setunionAx
% 1.89/1.34 = ( ! [A: $i,Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ ( setunion @ A ) )
% 1.89/1.34 <=> ? [B: $i] :
% 1.89/1.34 ( ( in @ Xx @ B )
% 1.89/1.34 & ( in @ B @ A ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(omega_type,type,
% 1.89/1.34 omega: $i ).
% 1.89/1.34
% 1.89/1.34 thf(omega0Ax_type,type,
% 1.89/1.34 omega0Ax: $o ).
% 1.89/1.34
% 1.89/1.34 thf(omega0Ax,definition,
% 1.89/1.34 ( omega0Ax
% 1.89/1.34 = ( in @ emptyset @ omega ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(omegaSAx_type,type,
% 1.89/1.34 omegaSAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(omegaSAx,definition,
% 1.89/1.34 ( omegaSAx
% 1.89/1.34 = ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ omega )
% 1.89/1.34 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(omegaIndAx_type,type,
% 1.89/1.34 omegaIndAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(omegaIndAx,definition,
% 1.89/1.34 ( omegaIndAx
% 1.89/1.34 = ( ! [A: $i] :
% 1.89/1.34 ( ( ( in @ emptyset @ A )
% 1.89/1.34 & ! [Xx: $i] :
% 1.89/1.34 ( ( ( in @ Xx @ omega )
% 1.89/1.34 & ( in @ Xx @ A ) )
% 1.89/1.34 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.89/1.34 => ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ omega )
% 1.89/1.34 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(replAx_type,type,
% 1.89/1.34 replAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(replAx,definition,
% 1.89/1.34 ( replAx
% 1.89/1.34 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.89/1.34 ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ A )
% 1.89/1.34 => ( exu
% 1.89/1.34 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.89/1.34 => ? [B: $i] :
% 1.89/1.34 ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ B )
% 1.89/1.34 <=> ? [Xy: $i] :
% 1.89/1.34 ( ( in @ Xy @ A )
% 1.89/1.34 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(foundationAx_type,type,
% 1.89/1.34 foundationAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(foundationAx,definition,
% 1.89/1.34 ( foundationAx
% 1.89/1.34 = ( ! [A: $i] :
% 1.89/1.34 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.89/1.34 => ? [B: $i] :
% 1.89/1.34 ( ( in @ B @ A )
% 1.89/1.34 & ~ ? [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ B )
% 1.89/1.34 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(wellorderingAx_type,type,
% 1.89/1.34 wellorderingAx: $o ).
% 1.89/1.34
% 1.89/1.34 thf(wellorderingAx,definition,
% 1.89/1.34 ( wellorderingAx
% 1.89/1.34 = ( ! [A: $i] :
% 1.89/1.34 ? [B: $i] :
% 1.89/1.34 ( ! [C: $i] :
% 1.89/1.34 ( ( in @ C @ B )
% 1.89/1.34 => ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ C )
% 1.89/1.34 => ( in @ Xx @ A ) ) )
% 1.89/1.34 & ! [Xx: $i,Xy: $i] :
% 1.89/1.34 ( ( ( in @ Xx @ A )
% 1.89/1.34 & ( in @ Xy @ A ) )
% 1.89/1.34 => ( ! [C: $i] :
% 1.89/1.34 ( ( in @ C @ B )
% 1.89/1.34 => ( ( in @ Xx @ C )
% 1.89/1.34 <=> ( in @ Xy @ C ) ) )
% 1.89/1.34 => ( Xx = Xy ) ) )
% 1.89/1.34 & ! [C: $i,D: $i] :
% 1.89/1.34 ( ( ( in @ C @ B )
% 1.89/1.34 & ( in @ D @ B ) )
% 1.89/1.34 => ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ C )
% 1.89/1.34 => ( in @ Xx @ D ) )
% 1.89/1.34 | ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ D )
% 1.89/1.34 => ( in @ Xx @ C ) ) ) )
% 1.89/1.34 & ! [C: $i] :
% 1.89/1.34 ( ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ C )
% 1.89/1.34 => ( in @ Xx @ A ) )
% 1.89/1.34 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.89/1.34 => ? [D: $i,Xx: $i] :
% 1.89/1.34 ( ( in @ D @ B )
% 1.89/1.34 & ( in @ Xx @ C )
% 1.89/1.34 & ~ ? [Xy: $i] :
% 1.89/1.34 ( ( in @ Xy @ D )
% 1.89/1.34 & ( in @ Xy @ C ) )
% 1.89/1.34 & ! [E: $i] :
% 1.89/1.34 ( ( in @ E @ B )
% 1.89/1.34 => ( ! [Xy: $i] :
% 1.89/1.34 ( ( in @ Xy @ E )
% 1.89/1.34 => ( in @ Xy @ D ) )
% 1.89/1.34 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(descr_type,type,
% 1.89/1.34 descr: ( $i > $o ) > $i ).
% 1.89/1.34
% 1.89/1.34 thf(descrp_type,type,
% 1.89/1.34 descrp: $o ).
% 1.89/1.34
% 1.89/1.34 thf(descrp,definition,
% 1.89/1.34 ( descrp
% 1.89/1.34 = ( ! [Xphi: $i > $o] :
% 1.89/1.34 ( ( exu
% 1.89/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.89/1.34 => ( Xphi
% 1.89/1.34 @ ( descr
% 1.89/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(dsetconstr_type,type,
% 1.89/1.34 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.89/1.34
% 1.89/1.34 thf(dsetconstrI_type,type,
% 1.89/1.34 dsetconstrI: $o ).
% 1.89/1.34
% 1.89/1.34 thf(dsetconstrI,definition,
% 1.89/1.34 ( dsetconstrI
% 1.89/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ A )
% 1.89/1.34 => ( ( Xphi @ Xx )
% 1.89/1.34 => ( in @ Xx
% 1.89/1.34 @ ( dsetconstr @ A
% 1.89/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(dsetconstrEL_type,type,
% 1.89/1.34 dsetconstrEL: $o ).
% 1.89/1.34
% 1.89/1.34 thf(dsetconstrEL,definition,
% 1.89/1.34 ( dsetconstrEL
% 1.89/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.34 ( ( in @ Xx
% 1.89/1.34 @ ( dsetconstr @ A
% 1.89/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.89/1.34 => ( in @ Xx @ A ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(dsetconstrER_type,type,
% 1.89/1.34 dsetconstrER: $o ).
% 1.89/1.34
% 1.89/1.34 thf(dsetconstrER,definition,
% 1.89/1.34 ( dsetconstrER
% 1.89/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.34 ( ( in @ Xx
% 1.89/1.34 @ ( dsetconstr @ A
% 1.89/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.89/1.34 => ( Xphi @ Xx ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(exuE1_type,type,
% 1.89/1.34 exuE1: $o ).
% 1.89/1.34
% 1.89/1.34 thf(exuE1,definition,
% 1.89/1.34 ( exuE1
% 1.89/1.34 = ( ! [Xphi: $i > $o] :
% 1.89/1.34 ( ( exu
% 1.89/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.89/1.34 => ? [Xx: $i] :
% 1.89/1.34 ( ( Xphi @ Xx )
% 1.89/1.34 & ! [Xy: $i] :
% 1.89/1.34 ( ( Xphi @ Xy )
% 1.89/1.34 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(prop2set_type,type,
% 1.89/1.34 prop2set: $o > $i ).
% 1.89/1.34
% 1.89/1.34 thf(prop2set,definition,
% 1.89/1.34 ( prop2set
% 1.89/1.34 = ( ^ [Xphi: $o] :
% 1.89/1.34 ( dsetconstr @ ( powerset @ emptyset )
% 1.89/1.34 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(prop2setE_type,type,
% 1.89/1.34 prop2setE: $o ).
% 1.89/1.34
% 1.89/1.34 thf(prop2setE,definition,
% 1.89/1.34 ( prop2setE
% 1.89/1.34 = ( ! [Xphi: $o,Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.89/1.34 => Xphi ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(emptysetE_type,type,
% 1.89/1.34 emptysetE: $o ).
% 1.89/1.34
% 1.89/1.34 thf(emptysetE,definition,
% 1.89/1.34 ( emptysetE
% 1.89/1.34 = ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ emptyset )
% 1.89/1.34 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(emptysetimpfalse_type,type,
% 1.89/1.34 emptysetimpfalse: $o ).
% 1.89/1.34
% 1.89/1.34 thf(emptysetimpfalse,definition,
% 1.89/1.34 ( emptysetimpfalse
% 1.89/1.34 = ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ emptyset )
% 1.89/1.34 => $false ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(notinemptyset_type,type,
% 1.89/1.34 notinemptyset: $o ).
% 1.89/1.34
% 1.89/1.34 thf(notinemptyset,definition,
% 1.89/1.34 ( notinemptyset
% 1.89/1.34 = ( ! [Xx: $i] :
% 1.89/1.34 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(exuE3e_type,type,
% 1.89/1.34 exuE3e: $o ).
% 1.89/1.34
% 1.89/1.34 thf(exuE3e,definition,
% 1.89/1.34 ( exuE3e
% 1.89/1.34 = ( ! [Xphi: $i > $o] :
% 1.89/1.34 ( ( exu
% 1.89/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.89/1.34 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(setext_type,type,
% 1.89/1.34 setext: $o ).
% 1.89/1.34
% 1.89/1.34 thf(setext,definition,
% 1.89/1.34 ( setext
% 1.89/1.34 = ( ! [A: $i,B: $i] :
% 1.89/1.34 ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ A )
% 1.89/1.34 => ( in @ Xx @ B ) )
% 1.89/1.34 => ( ! [Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ B )
% 1.89/1.34 => ( in @ Xx @ A ) )
% 1.89/1.34 => ( A = B ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(emptyI_type,type,
% 1.89/1.34 emptyI: $o ).
% 1.89/1.34
% 1.89/1.34 thf(emptyI,definition,
% 1.89/1.34 ( emptyI
% 1.89/1.34 = ( ! [A: $i] :
% 1.89/1.34 ( ! [Xx: $i] :
% 1.89/1.34 ~ ( in @ Xx @ A )
% 1.89/1.34 => ( A = emptyset ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(noeltsimpempty_type,type,
% 1.89/1.34 noeltsimpempty: $o ).
% 1.89/1.34
% 1.89/1.34 thf(noeltsimpempty,definition,
% 1.89/1.34 ( noeltsimpempty
% 1.89/1.34 = ( ! [A: $i] :
% 1.89/1.34 ( ! [Xx: $i] :
% 1.89/1.34 ~ ( in @ Xx @ A )
% 1.89/1.34 => ( A = emptyset ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(setbeta_type,type,
% 1.89/1.34 setbeta: $o ).
% 1.89/1.34
% 1.89/1.34 thf(setbeta,definition,
% 1.89/1.34 ( setbeta
% 1.89/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ A )
% 1.89/1.34 => ( ( in @ Xx
% 1.89/1.34 @ ( dsetconstr @ A
% 1.89/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.89/1.34 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(nonempty_type,type,
% 1.89/1.34 nonempty: $i > $o ).
% 1.89/1.34
% 1.89/1.34 thf(nonempty,definition,
% 1.89/1.34 ( nonempty
% 1.89/1.34 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(nonemptyE1_type,type,
% 1.89/1.34 nonemptyE1: $o ).
% 1.89/1.34
% 1.89/1.34 thf(nonemptyE1,definition,
% 1.89/1.34 ( nonemptyE1
% 1.89/1.34 = ( ! [A: $i] :
% 1.89/1.34 ( ( nonempty @ A )
% 1.89/1.34 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(nonemptyI_type,type,
% 1.89/1.34 nonemptyI: $o ).
% 1.89/1.34
% 1.89/1.34 thf(nonemptyI,definition,
% 1.89/1.34 ( nonemptyI
% 1.89/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.34 ( ( in @ Xx @ A )
% 1.89/1.34 => ( ( Xphi @ Xx )
% 1.89/1.34 => ( nonempty
% 1.89/1.34 @ ( dsetconstr @ A
% 1.89/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.89/1.34
% 1.89/1.34 thf(nonemptyI1,conjecture,
% 1.89/1.34 ( setextAx
% 1.89/1.34 => ( emptysetAx
% 1.89/1.34 => ( setadjoinAx
% 1.89/1.34 => ( powersetAx
% 1.89/1.34 => ( setunionAx
% 1.89/1.34 => ( omega0Ax
% 1.89/1.34 => ( omegaSAx
% 1.89/1.34 => ( omegaIndAx
% 1.89/1.34 => ( replAx
% 1.89/1.34 => ( foundationAx
% 1.89/1.34 => ( wellorderingAx
% 1.89/1.34 => ( descrp
% 1.89/1.34 => ( dsetconstrI
% 1.89/1.34 => ( dsetconstrEL
% 1.89/1.34 => ( dsetconstrER
% 1.89/1.34 => ( exuE1
% 1.89/1.34 => ( prop2setE
% 1.89/1.34 => ( emptysetE
% 1.89/1.34 => ( emptysetimpfalse
% 1.89/1.34 => ( notinemptyset
% 1.89/1.34 => ( exuE3e
% 1.89/1.34 => ( setext
% 1.89/1.34 => ( emptyI
% 1.89/1.34 => ( noeltsimpempty
% 1.89/1.34 => ( setbeta
% 1.89/1.34 => ( nonemptyE1
% 1.89/1.34 => ( nonemptyI
% 1.89/1.34 => ! [A: $i] :
% 1.89/1.34 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.89/1.34 => ( nonempty @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.89/1.34 ------------------------
% 1.89/1.36 % (22968)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22688 for (2999ds/2Mi)
% 1.89/1.36 % (22967)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_22688 for (2999ds/27Mi)
% 1.89/1.36 % (22968)Instruction limit reached!
% 1.89/1.36 % (22968)------------------------------
% 1.89/1.36 % (22968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.36 % (22968)Termination reason: Unknown
% 1.89/1.36 % (22968)Termination phase: shuffling
% 1.89/1.36
% 1.89/1.36 % (22968)Memory used [KB]: 1023
% 1.89/1.36 % (22968)Time elapsed: 0.002 s
% 1.89/1.36 % (22968)Instructions burned: 4 (million)
% 1.89/1.36 % (22968)------------------------------
% 1.89/1.36 % (22968)------------------------------
% 1.89/1.37 % (22965)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22688 for (2999ds/183Mi)
% 1.89/1.37 % (22966)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_22688 for (2999ds/4Mi)
% 1.89/1.37 % (22969)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_22688 for (2999ds/2Mi)
% 1.89/1.37 % (22970)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_22688 for (2999ds/275Mi)
% 1.89/1.37 % (22971)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22688 for (2999ds/18Mi)
% 1.89/1.37 % (22969)Instruction limit reached!
% 1.89/1.37 % (22969)------------------------------
% 1.89/1.37 % (22969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.37 % (22969)Termination reason: Unknown
% 1.89/1.37 % (22969)Termination phase: shuffling
% 1.89/1.37
% 1.89/1.37 % (22969)Memory used [KB]: 1023
% 1.89/1.37 % (22969)Time elapsed: 0.003 s
% 1.89/1.37 % (22969)Instructions burned: 2 (million)
% 1.89/1.37 % (22969)------------------------------
% 1.89/1.37 % (22969)------------------------------
% 1.89/1.37 % (22966)Instruction limit reached!
% 1.89/1.37 % (22966)------------------------------
% 1.89/1.37 % (22966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.37 % (22966)Termination reason: Unknown
% 1.89/1.37 % (22966)Termination phase: shuffling
% 1.89/1.37
% 1.89/1.37 % (22966)Memory used [KB]: 1023
% 1.89/1.37 % (22966)Time elapsed: 0.004 s
% 1.89/1.37 % (22966)Instructions burned: 4 (million)
% 1.89/1.37 % (22966)------------------------------
% 1.89/1.37 % (22966)------------------------------
% 1.89/1.37 % (22967)Instruction limit reached!
% 1.89/1.37 % (22967)------------------------------
% 1.89/1.37 % (22967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.37 % (22967)Termination reason: Unknown
% 1.89/1.37 % (22967)Termination phase: Saturation
% 1.89/1.37
% 1.89/1.37 % (22967)Memory used [KB]: 5756
% 1.89/1.37 % (22967)Time elapsed: 0.010 s
% 1.89/1.37 % (22967)Instructions burned: 29 (million)
% 1.89/1.37 % (22967)------------------------------
% 1.89/1.37 % (22967)------------------------------
% 1.89/1.37 % (22972)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22688 for (2999ds/3Mi)
% 1.89/1.37 % (22972)Instruction limit reached!
% 1.89/1.37 % (22972)------------------------------
% 1.89/1.37 % (22972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.37 % (22972)Termination reason: Unknown
% 1.89/1.37 % (22972)Termination phase: shuffling
% 1.89/1.37
% 1.89/1.37 % (22972)Memory used [KB]: 1023
% 1.89/1.37 % (22972)Time elapsed: 0.002 s
% 1.89/1.37 % (22972)Instructions burned: 4 (million)
% 1.89/1.37 % (22972)------------------------------
% 1.89/1.37 % (22972)------------------------------
% 1.89/1.38 % (22971)Instruction limit reached!
% 1.89/1.38 % (22971)------------------------------
% 1.89/1.38 % (22971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.38 % (22971)Termination reason: Unknown
% 1.89/1.38 % (22971)Termination phase: Property scanning
% 1.89/1.38
% 1.89/1.38 % (22971)Memory used [KB]: 1407
% 1.89/1.38 % (22971)Time elapsed: 0.012 s
% 1.89/1.38 % (22971)Instructions burned: 18 (million)
% 1.89/1.38 % (22971)------------------------------
% 1.89/1.38 % (22971)------------------------------
% 1.89/1.38 % (22975)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_22688 for (2999ds/3Mi)
% 1.89/1.38 % (22975)Instruction limit reached!
% 1.89/1.38 % (22975)------------------------------
% 1.89/1.38 % (22975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.38 % (22975)Termination reason: Unknown
% 1.89/1.38 % (22975)Termination phase: shuffling
% 1.89/1.38
% 1.89/1.38 % (22975)Memory used [KB]: 1023
% 1.89/1.38 % (22975)Time elapsed: 0.003 s
% 1.89/1.38 % (22975)Instructions burned: 4 (million)
% 1.89/1.38 % (22975)------------------------------
% 1.89/1.38 % (22975)------------------------------
% 1.89/1.38 % (22976)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_22688 for (2999ds/1041Mi)
% 1.89/1.39 % (22973)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_22688 for (2999ds/37Mi)
% 1.89/1.39 % (22974)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_22688 for (2999ds/15Mi)
% 1.89/1.39 % (22978)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22688 for (2999ds/16Mi)
% 1.89/1.39 % (22974)Instruction limit reached!
% 1.89/1.39 % (22974)------------------------------
% 1.89/1.39 % (22974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.39 % (22974)Termination reason: Unknown
% 1.89/1.39 % (22974)Termination phase: Property scanning
% 1.89/1.39
% 1.89/1.39 % (22974)Memory used [KB]: 1407
% 1.89/1.39 % (22974)Time elapsed: 0.010 s
% 1.89/1.39 % (22974)Instructions burned: 15 (million)
% 1.89/1.39 % (22974)------------------------------
% 1.89/1.39 % (22974)------------------------------
% 1.89/1.39 % (22977)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22688 for (2999ds/7Mi)
% 1.99/1.40 % (22978)Instruction limit reached!
% 1.99/1.40 % (22978)------------------------------
% 1.99/1.40 % (22978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.99/1.40 % (22978)Termination reason: Unknown
% 1.99/1.40 % (22978)Termination phase: Property scanning
% 1.99/1.40
% 1.99/1.40 % (22978)Memory used [KB]: 1279
% 1.99/1.40 % (22978)Time elapsed: 0.007 s
% 1.99/1.40 % (22978)Instructions burned: 18 (million)
% 1.99/1.40 % (22978)------------------------------
% 1.99/1.40 % (22978)------------------------------
% 1.99/1.40 % (22965)First to succeed.
% 1.99/1.40 % (22977)Instruction limit reached!
% 1.99/1.40 % (22977)------------------------------
% 1.99/1.40 % (22977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.99/1.40 % (22977)Termination reason: Unknown
% 1.99/1.40 % (22977)Termination phase: Property scanning
% 1.99/1.40
% 1.99/1.40 % (22977)Memory used [KB]: 1151
% 1.99/1.40 % (22977)Time elapsed: 0.005 s
% 1.99/1.40 % (22977)Instructions burned: 7 (million)
% 1.99/1.40 % (22977)------------------------------
% 1.99/1.40 % (22977)------------------------------
% 1.99/1.40 % (22965)Refutation found. Thanks to Tanya!
% 1.99/1.40 % SZS status Theorem for DTF2THF_22688
% 1.99/1.40 % SZS output start Proof for DTF2THF_22688
% 1.99/1.40 thf(func_def_0, type, in: $i > $i > $o).
% 1.99/1.40 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.99/1.40 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.99/1.40 thf(func_def_8, type, powerset: $i > $i).
% 1.99/1.40 thf(func_def_10, type, setunion: $i > $i).
% 1.99/1.40 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.99/1.40 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.99/1.40 thf(func_def_26, type, prop2set: $o > $i).
% 1.99/1.40 thf(func_def_36, type, nonempty: $i > $o).
% 1.99/1.40 thf(func_def_58, type, sK3: ($i > $o) > $i).
% 1.99/1.40 thf(func_def_59, type, sK4: ($i > $o) > $i > $i).
% 1.99/1.40 thf(func_def_60, type, sK5: $i > $i).
% 1.99/1.40 thf(func_def_61, type, sK6: ($i > $o) > $i > $i).
% 1.99/1.40 thf(func_def_62, type, sK7: $i > $i).
% 1.99/1.40 thf(func_def_63, type, sK8: $i > $i > $i).
% 1.99/1.40 thf(func_def_64, type, sK9: $i > $i).
% 1.99/1.40 thf(func_def_65, type, sK10: $i > $i > $i).
% 1.99/1.40 thf(func_def_66, type, sK11: $i > $i > $i).
% 1.99/1.40 thf(func_def_67, type, sK12: $i > $i > $i).
% 1.99/1.40 thf(func_def_68, type, sK13: $i > $i > $i).
% 1.99/1.40 thf(func_def_69, type, sK14: $i > $i > $i > $i).
% 1.99/1.40 thf(func_def_70, type, sK15: $i > $i).
% 1.99/1.40 thf(func_def_71, type, sK16: ($i > $o) > $i).
% 1.99/1.40 thf(func_def_72, type, sK17: ($i > $o) > $i > $i).
% 1.99/1.40 thf(func_def_73, type, sK18: ($i > $o) > $i > $i).
% 1.99/1.40 thf(func_def_74, type, sK19: $i > $i).
% 1.99/1.40 thf(func_def_75, type, sK20: $i > $i > $i).
% 1.99/1.40 thf(func_def_76, type, sK21: $i > $i > $i).
% 1.99/1.40 thf(func_def_77, type, sK22: $i > $i).
% 1.99/1.40 thf(func_def_78, type, sK23: $i > $i > $i).
% 1.99/1.40 thf(func_def_79, type, sK24: $i > ($i > $i > $o) > $i).
% 1.99/1.40 thf(func_def_80, type, sK25: $i > ($i > $i > $o) > $i).
% 1.99/1.40 thf(func_def_81, type, sK26: $i > $i > ($i > $i > $o) > $i).
% 1.99/1.40 thf(func_def_82, type, sK27: $i > ($i > $i > $o) > $i).
% 1.99/1.40 thf(func_def_83, type, sK28: $i > $i > ($i > $i > $o) > $i).
% 1.99/1.40 thf(func_def_84, type, sK29: $i > $i > ($i > $i > $o) > $i).
% 1.99/1.40 thf(func_def_85, type, sK30: $i > $i > ($i > $i > $o) > $i).
% 1.99/1.40 thf(func_def_86, type, sK31: $i > $i > $i).
% 1.99/1.40 thf(f591,plain,(
% 1.99/1.40 $false),
% 1.99/1.40 inference(trivial_inequality_removal,[status(thm)],[f590])).
% 1.99/1.40 thf(f590,plain,(
% 1.99/1.40 ($false = $true)),
% 1.99/1.40 inference(superposition,[status(thm)],[f497,f588])).
% 1.99/1.40 thf(f588,plain,(
% 1.99/1.40 ($true = (in @ sK1 @ emptyset))),
% 1.99/1.40 inference(superposition,[status(thm)],[f130,f226])).
% 1.99/1.40 thf(f226,plain,(
% 1.99/1.40 (emptyset = sK0)),
% 1.99/1.40 inference(equality_proxy_clausification,[status(thm)],[f225])).
% 1.99/1.40 thf(f225,plain,(
% 1.99/1.40 ($true = (emptyset = sK0))),
% 1.99/1.40 inference(not_proxy_clausification,[status(thm)],[f224])).
% 1.99/1.40 thf(f224,plain,(
% 1.99/1.40 ((~ (emptyset = sK0)) != $true)),
% 1.99/1.40 inference(beta_eta_normalization,[status(thm)],[f160])).
% 1.99/1.40 thf(f160,plain,(
% 1.99/1.40 (((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK0) != $true)),
% 1.99/1.40 inference(definition_unfolding,[status(thm)],[f131,f142])).
% 1.99/1.40 thf(f142,plain,(
% 1.99/1.40 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 1.99/1.40 inference(cnf_transformation,[status(thm)],[f57])).
% 1.99/1.40 thf(f57,plain,(
% 1.99/1.40 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 1.99/1.40 inference(fool_elimination,[status(thm)],[f56])).
% 1.99/1.40 thf(f56,plain,(
% 1.99/1.40 (nonempty = (^[X0 : $i] : ((emptyset != X0))))),
% 1.99/1.40 inference(rectify,[status(thm)],[f28])).
% 1.99/1.40 thf(f28,axiom,(
% 1.99/1.40 (nonempty = (^[X1 : $i] : ((emptyset != X1))))),
% 1.99/1.40 file('/export/starexec/sandbox/tmp/tmp.jCFCl5ort6/DTF2THF_22688.p',nonempty)).
% 1.99/1.40 thf(f131,plain,(
% 1.99/1.40 ((nonempty @ sK0) != $true)),
% 1.99/1.40 inference(cnf_transformation,[status(thm)],[f97])).
% 1.99/1.40 thf(f97,plain,(
% 1.99/1.40 (setunionAx = $true) & (replAx = $true) & (notinemptyset = $true) & (emptysetAx = $true) & (((nonempty @ sK0) != $true) & ((in @ sK1 @ sK0) = $true)) & (noeltsimpempty = $true) & (exuE1 = $true) & (omegaSAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (exuE3e = $true) & (setextAx = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (dsetconstrER = $true) & (emptyI = $true) & (foundationAx = $true) & (emptysetimpfalse = $true) & (wellorderingAx = $true) & (emptysetE = $true) & (descrp = $true) & (dsetconstrI = $true) & (setbeta = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (setext = $true) & (nonemptyI = $true) & (nonemptyE1 = $true)),
% 1.99/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f94,f96,f95])).
% 1.99/1.40 thf(f95,plain,(
% 1.99/1.40 ? [X0 : $i] : (((nonempty @ X0) != $true) & ? [X1 : $i] : ((in @ X1 @ X0) = $true)) => (((nonempty @ sK0) != $true) & ? [X1 : $i] : ((in @ X1 @ sK0) = $true))),
% 1.99/1.40 introduced(definition,[],[choice_axiom])).
% 1.99/1.40 thf(f96,plain,(
% 1.99/1.40 ? [X1 : $i] : ((in @ X1 @ sK0) = $true) => ((in @ sK1 @ sK0) = $true)),
% 1.99/1.40 introduced(definition,[],[choice_axiom])).
% 1.99/1.40 thf(f94,plain,(
% 1.99/1.40 (setunionAx = $true) & (replAx = $true) & (notinemptyset = $true) & (emptysetAx = $true) & ? [X0 : $i] : (((nonempty @ X0) != $true) & ? [X1 : $i] : ((in @ X1 @ X0) = $true)) & (noeltsimpempty = $true) & (exuE1 = $true) & (omegaSAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (exuE3e = $true) & (setextAx = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (dsetconstrER = $true) & (emptyI = $true) & (foundationAx = $true) & (emptysetimpfalse = $true) & (wellorderingAx = $true) & (emptysetE = $true) & (descrp = $true) & (dsetconstrI = $true) & (setbeta = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (setext = $true) & (nonemptyI = $true) & (nonemptyE1 = $true)),
% 1.99/1.40 inference(flattening,[status(thm)],[f93])).
% 1.99/1.40 thf(f93,plain,(
% 1.99/1.40 ((((((((((((((((((((((((((? [X0 : $i] : (((nonempty @ X0) != $true) & ? [X1 : $i] : ((in @ X1 @ X0) = $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)),
% 1.99/1.40 inference(ennf_transformation,[status(thm)],[f59])).
% 1.99/1.40 thf(f59,plain,(
% 1.99/1.40 ~((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) => ! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) => ((nonempty @ X0) = $true)))))))))))))))))))))))))))))),
% 1.99/1.40 inference(fool_elimination,[status(thm)],[f58])).
% 1.99/1.40 thf(f58,plain,(
% 1.99/1.40 ~(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 => ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))))))))))))))))))))))))))))),
% 1.99/1.40 inference(rectify,[status(thm)],[f32])).
% 1.99/1.40 thf(f32,negated_conjecture,(
% 1.99/1.40 ~(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 => ! [X3 : $i] : (? [X1 : $i] : (in @ X1 @ X3) => (nonempty @ X3)))))))))))))))))))))))))))))),
% 1.99/1.40 inference(negated_conjecture,[status(cth)],[f31])).
% 1.99/1.40 thf(f31,conjecture,(
% 1.99/1.40 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 => ! [X3 : $i] : (? [X1 : $i] : (in @ X1 @ X3) => (nonempty @ X3))))))))))))))))))))))))))))),
% 1.99/1.40 file('/export/starexec/sandbox/tmp/tmp.jCFCl5ort6/DTF2THF_22688.p',nonemptyI1)).
% 1.99/1.40 thf(f130,plain,(
% 1.99/1.40 ((in @ sK1 @ sK0) = $true)),
% 1.99/1.40 inference(cnf_transformation,[status(thm)],[f97])).
% 1.99/1.40 thf(f497,plain,(
% 1.99/1.40 ( ! [X1 : $i] : (((in @ X1 @ emptyset) = $false)) )),
% 1.99/1.40 inference(not_proxy_clausification,[status(thm)],[f496])).
% 1.99/1.40 thf(f496,plain,(
% 1.99/1.40 ( ! [X1 : $i] : (((~ (in @ X1 @ emptyset)) = $true)) )),
% 1.99/1.40 inference(beta_eta_normalization,[status(thm)],[f495])).
% 1.99/1.40 thf(f495,plain,(
% 1.99/1.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (~ (in @ Y0 @ emptyset))) @ X1) = $true)) )),
% 1.99/1.40 inference(pi_clausification,[status(thm)],[f178])).
% 1.99/1.40 thf(f178,plain,(
% 1.99/1.40 ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) = $true)),
% 1.99/1.40 inference(definition_unfolding,[status(thm)],[f147,f133])).
% 1.99/1.40 thf(f133,plain,(
% 1.99/1.40 (notinemptyset = $true)),
% 1.99/1.40 inference(cnf_transformation,[status(thm)],[f97])).
% 1.99/1.40 thf(f147,plain,(
% 1.99/1.40 (notinemptyset = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))),
% 1.99/1.40 inference(cnf_transformation,[status(thm)],[f77])).
% 1.99/1.40 thf(f77,plain,(
% 1.99/1.40 (notinemptyset = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))),
% 1.99/1.40 inference(fool_elimination,[status(thm)],[f76])).
% 1.99/1.40 thf(f76,plain,(
% 1.99/1.40 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 1.99/1.40 inference(rectify,[status(thm)],[f22])).
% 1.99/1.40 thf(f22,axiom,(
% 1.99/1.40 (notinemptyset = ! [X1 : $i] : ~(in @ X1 @ emptyset))),
% 1.99/1.40 file('/export/starexec/sandbox/tmp/tmp.jCFCl5ort6/DTF2THF_22688.p',notinemptyset)).
% 1.99/1.40 % SZS output end Proof for DTF2THF_22688
% 1.99/1.40 % (22965)------------------------------
% 1.99/1.40 % (22965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.99/1.40 % (22965)Termination reason: Refutation
% 1.99/1.40
% 1.99/1.40 % (22965)Memory used [KB]: 6012
% 1.99/1.40 % (22965)Time elapsed: 0.033 s
% 1.99/1.40 % (22965)Instructions burned: 54 (million)
% 1.99/1.40 % (22965)------------------------------
% 1.99/1.40 % (22965)------------------------------
% 1.99/1.40 % (22964)Success in time 0.046 s
%------------------------------------------------------------------------------