%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU512^1 : 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 : n024.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 1.15s 0.96s
% Output : Refutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 563 ( 163 equ; 0 cnn)
% Maximal formula atoms : 29 ( 20 avg)
% Number of connectives : 402 ( 12 ~; 17 |; 84 &; 159 @)
% ( 2 <=>; 113 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 67 usr; 33 con; 0-3 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 62 ( 18 ^; 38 !; 6 ?; 62 :)
% 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_59,type,
sK3: $i > $i ).
thf(func_def_60,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_61,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_62,type,
sK6: $i > $i ).
thf(func_def_63,type,
sK7: $i > $i > $i ).
thf(func_def_64,type,
sK8: $i > $i ).
thf(func_def_65,type,
sK9: $i > $i > $i ).
thf(func_def_66,type,
sK10: $i > $i > $i ).
thf(func_def_67,type,
sK11: $i > $i > $i ).
thf(func_def_68,type,
sK12: $i > $i ).
thf(func_def_69,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_70,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_71,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_72,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_73,type,
sK17: $i > $i > $i ).
thf(func_def_74,type,
sK18: $i > $i ).
thf(func_def_75,type,
sK19: $i > $i > $i ).
thf(func_def_76,type,
sK20: $i > $i > $i ).
thf(func_def_77,type,
sK21: $i > $i > $i ).
thf(func_def_78,type,
sK22: $i > $i > $i > $i ).
thf(func_def_79,type,
sK23: $i > $i ).
thf(func_def_80,type,
sK24: $i > $i > $i ).
thf(func_def_82,type,
sK25: ( $i > $i > $o ) > $i > $i ).
thf(func_def_83,type,
sK26: ( $i > $i > $o ) > $i > $i ).
thf(func_def_84,type,
sK27: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_85,type,
sK28: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_86,type,
sK29: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_87,type,
sK30: ( $i > $i > $o ) > $i > $i > $i ).
thf(f625,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f623]) ).
thf(f623,plain,
( ( sK1 != sK1 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f132,f342]) ).
thf(f342,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f341]) ).
thf(f341,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( ( X3 = X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f339]) ).
thf(f339,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( X3 = X1 )
| ( in @ X1 @ X2 ) )
= $false )
| ( $true
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f337]) ).
thf(f337,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( X3 = X1 )
| ( in @ X1 @ X2 ) )
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f336]) ).
thf(f336,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X3 @ X2 ) )
= ( ( X3 = X1 )
| ( in @ X1 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f335]) ).
thf(f335,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ X2 ) )
= ( ( Y0 = X1 )
| ( in @ X1 @ X2 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f334]) ).
thf(f334,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ X2 ) )
= ( ( Y0 = X1 )
| ( in @ X1 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f333]) ).
thf(f333,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y1 @ Y0 ) )
= ( ( Y1 = X1 )
| ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f332]) ).
thf(f332,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y1 @ Y0 ) )
= ( ( Y1 = X1 )
| ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f331]) ).
thf(f331,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
= ( ( Y2 = Y0 )
| ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
= ( ( Y2 = Y0 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f153,f119]) ).
thf(f119,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f99]) ).
thf(f99,plain,
( ( dsetconstrI = $true )
& ( notinemptyset = $true )
& ( exuE1 = $true )
& ( nonemptyE1 = $true )
& ( prop2setE = $true )
& ( setextAx = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( emptysetE = $true )
& ( exuE3e = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( nonemptyI = $true )
& ( emptysetimpfalse = $true )
& ( nonemptyI1 = $true )
& ( $true
!= ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) ) )
& ( powersetAx = $true )
& ( descrp = $true )
& ( replAx = $true )
& ( emptyI = $true )
& ( dsetconstrEL = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ( emptysetAx = $true )
& ( dsetconstrER = $true )
& ( wellorderingAx = $true )
& ( noeltsimpempty = $true )
& ( setext = $true )
& ( setadjoinAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f97,f98]) ).
thf(f98,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f97,plain,
( ( dsetconstrI = $true )
& ( notinemptyset = $true )
& ( exuE1 = $true )
& ( nonemptyE1 = $true )
& ( prop2setE = $true )
& ( setextAx = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( emptysetE = $true )
& ( exuE3e = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( nonemptyI = $true )
& ( emptysetimpfalse = $true )
& ( nonemptyI1 = $true )
& ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
& ( powersetAx = $true )
& ( descrp = $true )
& ( replAx = $true )
& ( emptyI = $true )
& ( dsetconstrEL = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ( emptysetAx = $true )
& ( dsetconstrER = $true )
& ( wellorderingAx = $true )
& ( noeltsimpempty = $true )
& ( setext = $true )
& ( setadjoinAx = $true ) ),
inference(flattening,[status(thm)],[f96]) ).
thf(f96,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
& ( 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)],[f56]) ).
thf(f56,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 )
=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f55]) ).
thf(f55,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
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,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
=> ! [X2: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f32,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
=> ! [X2: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9JX3iTHJoM/DTF2THF_10718.p',setadjoinIL) ).
thf(f153,plain,
( setadjoinAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
= ( ( Y2 = Y0 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( setadjoinAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
= ( ( Y2 = Y0 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
<=> ( ( in @ X2 @ X1 )
| ( X0 = X2 ) ) )
= setadjoinAx ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: $i,X3: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
<=> ( ( in @ X2 @ X3 )
| ( X1 = X2 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox2/tmp/tmp.9JX3iTHJoM/DTF2THF_10718.p',setadjoinAx) ).
thf(f132,plain,
( $true
!= ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU512^1 : 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
% 0.09/0.25 % Computer : n024.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8042.1875MB
% 0.09/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Feb 24 07:24:55 EST 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.31 ---- Original DTF file ---
% 0.09/0.31 thf(spec,logic,$$dhol).
% 0.09/0.31 %------------------------------------------------------------------------------
% 0.09/0.31 % File : SEU512^1 : TPTP v9.2.1. Released v3.7.0.
% 0.09/0.31 % Domain : Set Theory
% 0.09/0.31 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.09/0.31 % Version : Especial.
% 0.09/0.31 % English : (! x:i.! y:i.in x (setadjoin x y))
% 0.09/0.31
% 0.09/0.31 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.09/0.31 % Source : [Bro08]
% 0.09/0.31 % Names : ZFC014g [Bro08]
% 0.09/0.31
% 0.09/0.31 % Status : Theorem
% 0.09/0.31 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.09/0.31 % Syntax : Number of formulae : 71 ( 31 unt; 39 typ; 31 def)
% 0.09/0.31 % Number of atoms : 179 ( 40 equ; 0 cnn)
% 0.09/0.31 % Maximal formula atoms : 29 ( 5 avg)
% 0.09/0.31 % Number of connectives : 308 ( 7 ~; 3 |; 18 &; 201 @)
% 0.09/0.31 % ( 7 <=>; 72 =>; 0 <=; 0 <~>)
% 0.09/0.31 % Maximal formula depth : 34 ( 2 avg)
% 0.09/0.31 % Number of types : 2 ( 0 usr)
% 0.09/0.31 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.09/0.31 % Number of symbols : 41 ( 39 usr; 31 con; 0-2 aty)
% 0.09/0.31 % Number of variables : 103 ( 14 ^; 73 !; 16 ?; 103 :)
% 0.09/0.31 % SPC : TH0_THM_EQU_NAR
% 0.09/0.31
% 0.09/0.31 % Comments : http://mathgate.info/detsetitem.php?id=80
% 0.09/0.31 %------------------------------------------------------------------------------
% 0.09/0.31 thf(in_type,type,
% 0.09/0.31 in: $i > $i > $o ).
% 0.09/0.31
% 0.09/0.31 thf(exu_type,type,
% 0.09/0.31 exu: ( $i > $o ) > $o ).
% 0.09/0.31
% 0.09/0.31 thf(exu,definition,
% 0.09/0.31 ( exu
% 0.09/0.31 = ( ^ [Xphi: $i > $o] :
% 0.09/0.31 ? [Xx: $i] :
% 0.09/0.31 ( ( Xphi @ Xx )
% 0.09/0.31 & ! [Xy: $i] :
% 0.09/0.31 ( ( Xphi @ Xy )
% 0.09/0.31 => ( Xx = Xy ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(setextAx_type,type,
% 0.09/0.31 setextAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(setextAx,definition,
% 0.09/0.31 ( setextAx
% 0.09/0.31 = ( ! [A: $i,B: $i] :
% 0.09/0.31 ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ A )
% 0.09/0.31 <=> ( in @ Xx @ B ) )
% 0.09/0.31 => ( A = B ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(emptyset_type,type,
% 0.09/0.31 emptyset: $i ).
% 0.09/0.31
% 0.09/0.31 thf(emptysetAx_type,type,
% 0.09/0.31 emptysetAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(emptysetAx,definition,
% 0.09/0.31 ( emptysetAx
% 0.09/0.31 = ( ! [Xx: $i] :
% 0.09/0.31 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(setadjoin_type,type,
% 0.09/0.31 setadjoin: $i > $i > $i ).
% 0.09/0.31
% 0.09/0.31 thf(setadjoinAx_type,type,
% 0.09/0.31 setadjoinAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(setadjoinAx,definition,
% 0.09/0.31 ( setadjoinAx
% 0.09/0.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.09/0.31 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.09/0.31 <=> ( ( Xy = Xx )
% 0.09/0.31 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(powerset_type,type,
% 0.09/0.31 powerset: $i > $i ).
% 0.09/0.31
% 0.09/0.31 thf(powersetAx_type,type,
% 0.09/0.31 powersetAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(powersetAx,definition,
% 0.09/0.31 ( powersetAx
% 0.09/0.31 = ( ! [A: $i,B: $i] :
% 0.09/0.31 ( ( in @ B @ ( powerset @ A ) )
% 0.09/0.31 <=> ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ B )
% 0.09/0.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(setunion_type,type,
% 0.09/0.31 setunion: $i > $i ).
% 0.09/0.31
% 0.09/0.31 thf(setunionAx_type,type,
% 0.09/0.31 setunionAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(setunionAx,definition,
% 0.09/0.31 ( setunionAx
% 0.09/0.31 = ( ! [A: $i,Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ ( setunion @ A ) )
% 0.09/0.31 <=> ? [B: $i] :
% 0.09/0.31 ( ( in @ Xx @ B )
% 0.09/0.31 & ( in @ B @ A ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(omega_type,type,
% 0.09/0.31 omega: $i ).
% 0.09/0.31
% 0.09/0.31 thf(omega0Ax_type,type,
% 0.09/0.31 omega0Ax: $o ).
% 0.09/0.31
% 0.09/0.31 thf(omega0Ax,definition,
% 0.09/0.31 ( omega0Ax
% 0.09/0.31 = ( in @ emptyset @ omega ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(omegaSAx_type,type,
% 0.09/0.31 omegaSAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(omegaSAx,definition,
% 0.09/0.31 ( omegaSAx
% 0.09/0.31 = ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ omega )
% 0.09/0.31 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(omegaIndAx_type,type,
% 0.09/0.31 omegaIndAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(omegaIndAx,definition,
% 0.09/0.31 ( omegaIndAx
% 0.09/0.31 = ( ! [A: $i] :
% 0.09/0.31 ( ( ( in @ emptyset @ A )
% 0.09/0.31 & ! [Xx: $i] :
% 0.09/0.31 ( ( ( in @ Xx @ omega )
% 0.09/0.31 & ( in @ Xx @ A ) )
% 0.09/0.31 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.09/0.31 => ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ omega )
% 0.09/0.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(replAx_type,type,
% 0.09/0.31 replAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(replAx,definition,
% 0.09/0.31 ( replAx
% 0.09/0.31 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.09/0.31 ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ A )
% 0.09/0.31 => ( exu
% 0.09/0.31 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.09/0.31 => ? [B: $i] :
% 0.09/0.31 ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ B )
% 0.09/0.31 <=> ? [Xy: $i] :
% 0.09/0.31 ( ( in @ Xy @ A )
% 0.09/0.31 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(foundationAx_type,type,
% 0.09/0.31 foundationAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(foundationAx,definition,
% 0.09/0.31 ( foundationAx
% 0.09/0.31 = ( ! [A: $i] :
% 0.09/0.31 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.09/0.31 => ? [B: $i] :
% 0.09/0.31 ( ( in @ B @ A )
% 0.09/0.31 & ~ ? [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ B )
% 0.09/0.31 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(wellorderingAx_type,type,
% 0.09/0.31 wellorderingAx: $o ).
% 0.09/0.31
% 0.09/0.31 thf(wellorderingAx,definition,
% 0.09/0.31 ( wellorderingAx
% 0.09/0.31 = ( ! [A: $i] :
% 0.09/0.31 ? [B: $i] :
% 0.09/0.31 ( ! [C: $i] :
% 0.09/0.31 ( ( in @ C @ B )
% 0.09/0.31 => ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ C )
% 0.09/0.31 => ( in @ Xx @ A ) ) )
% 0.09/0.31 & ! [Xx: $i,Xy: $i] :
% 0.09/0.31 ( ( ( in @ Xx @ A )
% 0.09/0.31 & ( in @ Xy @ A ) )
% 0.09/0.31 => ( ! [C: $i] :
% 0.09/0.31 ( ( in @ C @ B )
% 0.09/0.31 => ( ( in @ Xx @ C )
% 0.09/0.31 <=> ( in @ Xy @ C ) ) )
% 0.09/0.31 => ( Xx = Xy ) ) )
% 0.09/0.31 & ! [C: $i,D: $i] :
% 0.09/0.31 ( ( ( in @ C @ B )
% 0.09/0.31 & ( in @ D @ B ) )
% 0.09/0.31 => ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ C )
% 0.09/0.31 => ( in @ Xx @ D ) )
% 0.09/0.31 | ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ D )
% 0.09/0.31 => ( in @ Xx @ C ) ) ) )
% 0.09/0.31 & ! [C: $i] :
% 0.09/0.31 ( ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ C )
% 0.09/0.31 => ( in @ Xx @ A ) )
% 0.09/0.31 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.09/0.31 => ? [D: $i,Xx: $i] :
% 0.09/0.31 ( ( in @ D @ B )
% 0.09/0.31 & ( in @ Xx @ C )
% 0.09/0.31 & ~ ? [Xy: $i] :
% 0.09/0.31 ( ( in @ Xy @ D )
% 0.09/0.31 & ( in @ Xy @ C ) )
% 0.09/0.31 & ! [E: $i] :
% 0.09/0.31 ( ( in @ E @ B )
% 0.09/0.31 => ( ! [Xy: $i] :
% 0.09/0.31 ( ( in @ Xy @ E )
% 0.09/0.31 => ( in @ Xy @ D ) )
% 0.09/0.31 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(descr_type,type,
% 0.09/0.31 descr: ( $i > $o ) > $i ).
% 0.09/0.31
% 0.09/0.31 thf(descrp_type,type,
% 0.09/0.31 descrp: $o ).
% 0.09/0.31
% 0.09/0.31 thf(descrp,definition,
% 0.09/0.31 ( descrp
% 0.09/0.31 = ( ! [Xphi: $i > $o] :
% 0.09/0.31 ( ( exu
% 0.09/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.09/0.31 => ( Xphi
% 0.09/0.31 @ ( descr
% 0.09/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(dsetconstr_type,type,
% 0.09/0.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.09/0.31
% 0.09/0.31 thf(dsetconstrI_type,type,
% 0.09/0.31 dsetconstrI: $o ).
% 0.09/0.31
% 0.09/0.31 thf(dsetconstrI,definition,
% 0.09/0.31 ( dsetconstrI
% 0.09/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ A )
% 0.09/0.31 => ( ( Xphi @ Xx )
% 0.09/0.31 => ( in @ Xx
% 0.09/0.31 @ ( dsetconstr @ A
% 0.09/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(dsetconstrEL_type,type,
% 0.09/0.31 dsetconstrEL: $o ).
% 0.09/0.31
% 0.09/0.31 thf(dsetconstrEL,definition,
% 0.09/0.31 ( dsetconstrEL
% 0.09/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.09/0.31 ( ( in @ Xx
% 0.09/0.31 @ ( dsetconstr @ A
% 0.09/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.09/0.31 => ( in @ Xx @ A ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(dsetconstrER_type,type,
% 0.09/0.31 dsetconstrER: $o ).
% 0.09/0.31
% 0.09/0.31 thf(dsetconstrER,definition,
% 0.09/0.31 ( dsetconstrER
% 0.09/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.09/0.31 ( ( in @ Xx
% 0.09/0.31 @ ( dsetconstr @ A
% 0.09/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.09/0.31 => ( Xphi @ Xx ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(exuE1_type,type,
% 0.09/0.31 exuE1: $o ).
% 0.09/0.31
% 0.09/0.31 thf(exuE1,definition,
% 0.09/0.31 ( exuE1
% 0.09/0.31 = ( ! [Xphi: $i > $o] :
% 0.09/0.31 ( ( exu
% 0.09/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.09/0.31 => ? [Xx: $i] :
% 0.09/0.31 ( ( Xphi @ Xx )
% 0.09/0.31 & ! [Xy: $i] :
% 0.09/0.31 ( ( Xphi @ Xy )
% 0.09/0.31 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(prop2set_type,type,
% 0.09/0.31 prop2set: $o > $i ).
% 0.09/0.31
% 0.09/0.31 thf(prop2set,definition,
% 0.09/0.31 ( prop2set
% 0.09/0.31 = ( ^ [Xphi: $o] :
% 0.09/0.31 ( dsetconstr @ ( powerset @ emptyset )
% 0.09/0.31 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(prop2setE_type,type,
% 0.09/0.31 prop2setE: $o ).
% 0.09/0.31
% 0.09/0.31 thf(prop2setE,definition,
% 0.09/0.31 ( prop2setE
% 0.09/0.31 = ( ! [Xphi: $o,Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.09/0.31 => Xphi ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(emptysetE_type,type,
% 0.09/0.31 emptysetE: $o ).
% 0.09/0.31
% 0.09/0.31 thf(emptysetE,definition,
% 0.09/0.31 ( emptysetE
% 0.09/0.31 = ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ emptyset )
% 0.09/0.31 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(emptysetimpfalse_type,type,
% 0.09/0.31 emptysetimpfalse: $o ).
% 0.09/0.31
% 0.09/0.31 thf(emptysetimpfalse,definition,
% 0.09/0.31 ( emptysetimpfalse
% 0.09/0.31 = ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ emptyset )
% 0.09/0.31 => $false ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(notinemptyset_type,type,
% 0.09/0.31 notinemptyset: $o ).
% 0.09/0.31
% 0.09/0.31 thf(notinemptyset,definition,
% 0.09/0.31 ( notinemptyset
% 0.09/0.31 = ( ! [Xx: $i] :
% 0.09/0.31 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(exuE3e_type,type,
% 0.09/0.31 exuE3e: $o ).
% 0.09/0.31
% 0.09/0.31 thf(exuE3e,definition,
% 0.09/0.31 ( exuE3e
% 0.09/0.31 = ( ! [Xphi: $i > $o] :
% 0.09/0.31 ( ( exu
% 0.09/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.09/0.31 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(setext_type,type,
% 0.09/0.31 setext: $o ).
% 0.09/0.31
% 0.09/0.31 thf(setext,definition,
% 0.09/0.31 ( setext
% 0.09/0.31 = ( ! [A: $i,B: $i] :
% 0.09/0.31 ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ A )
% 0.09/0.31 => ( in @ Xx @ B ) )
% 0.09/0.31 => ( ! [Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ B )
% 0.09/0.31 => ( in @ Xx @ A ) )
% 0.09/0.31 => ( A = B ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(emptyI_type,type,
% 0.09/0.31 emptyI: $o ).
% 0.09/0.31
% 0.09/0.31 thf(emptyI,definition,
% 0.09/0.31 ( emptyI
% 0.09/0.31 = ( ! [A: $i] :
% 0.09/0.31 ( ! [Xx: $i] :
% 0.09/0.31 ~ ( in @ Xx @ A )
% 0.09/0.31 => ( A = emptyset ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(noeltsimpempty_type,type,
% 0.09/0.31 noeltsimpempty: $o ).
% 0.09/0.31
% 0.09/0.31 thf(noeltsimpempty,definition,
% 0.09/0.31 ( noeltsimpempty
% 0.09/0.31 = ( ! [A: $i] :
% 0.09/0.31 ( ! [Xx: $i] :
% 0.09/0.31 ~ ( in @ Xx @ A )
% 0.09/0.31 => ( A = emptyset ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(setbeta_type,type,
% 0.09/0.31 setbeta: $o ).
% 0.09/0.31
% 0.09/0.31 thf(setbeta,definition,
% 0.09/0.31 ( setbeta
% 0.09/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ A )
% 0.09/0.31 => ( ( in @ Xx
% 0.09/0.31 @ ( dsetconstr @ A
% 0.09/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.09/0.31 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(nonempty_type,type,
% 0.09/0.31 nonempty: $i > $o ).
% 0.09/0.31
% 0.09/0.31 thf(nonempty,definition,
% 0.09/0.31 ( nonempty
% 0.09/0.31 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(nonemptyE1_type,type,
% 0.09/0.31 nonemptyE1: $o ).
% 0.09/0.31
% 0.09/0.31 thf(nonemptyE1,definition,
% 0.09/0.31 ( nonemptyE1
% 0.09/0.31 = ( ! [A: $i] :
% 0.09/0.31 ( ( nonempty @ A )
% 0.09/0.31 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(nonemptyI_type,type,
% 0.09/0.31 nonemptyI: $o ).
% 0.09/0.31
% 0.09/0.31 thf(nonemptyI,definition,
% 0.09/0.31 ( nonemptyI
% 0.09/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.09/0.31 ( ( in @ Xx @ A )
% 0.09/0.31 => ( ( Xphi @ Xx )
% 0.09/0.31 => ( nonempty
% 0.09/0.31 @ ( dsetconstr @ A
% 0.09/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(nonemptyI1_type,type,
% 0.09/0.31 nonemptyI1: $o ).
% 0.09/0.31
% 0.09/0.31 thf(nonemptyI1,definition,
% 0.09/0.31 ( nonemptyI1
% 0.09/0.31 = ( ! [A: $i] :
% 0.09/0.31 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.09/0.31 => ( nonempty @ A ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 thf(setadjoinIL,conjecture,
% 0.09/0.31 ( setextAx
% 0.09/0.31 => ( emptysetAx
% 0.09/0.31 => ( setadjoinAx
% 0.09/0.31 => ( powersetAx
% 0.09/0.31 => ( setunionAx
% 0.09/0.31 => ( omega0Ax
% 0.09/0.31 => ( omegaSAx
% 0.09/0.31 => ( omegaIndAx
% 0.09/0.31 => ( replAx
% 0.09/0.31 => ( foundationAx
% 0.09/0.31 => ( wellorderingAx
% 0.09/0.31 => ( descrp
% 0.09/0.31 => ( dsetconstrI
% 0.09/0.31 => ( dsetconstrEL
% 0.09/0.31 => ( dsetconstrER
% 0.09/0.31 => ( exuE1
% 0.09/0.31 => ( prop2setE
% 0.09/0.31 => ( emptysetE
% 0.09/0.31 => ( emptysetimpfalse
% 0.09/0.31 => ( notinemptyset
% 0.09/0.31 => ( exuE3e
% 0.09/0.31 => ( setext
% 0.09/0.31 => ( emptyI
% 0.09/0.31 => ( noeltsimpempty
% 0.09/0.31 => ( setbeta
% 0.09/0.31 => ( nonemptyE1
% 0.09/0.31 => ( nonemptyI
% 0.09/0.31 => ( nonemptyI1
% 0.09/0.31 => ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.09/0.31
% 0.09/0.31 %------------------------------------------------------------------------------
% 0.09/0.31 ------------------------
% 1.15/0.92 ---- Embedded in THF ---
% 1.15/0.92 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.15/0.92 %%% Generated on Tue Feb 24 07:24:56 EST 2026
% 1.15/0.92 %%% using '$$dhol' embedding, version 1.3.0.
% 1.15/0.92 %%% Logic specification used:
% 1.15/0.92 %%% thf(spec, logic, $$dhol).
% 1.15/0.92
% 1.15/0.92 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.9JX3iTHJoM/DTF2DTF10718.p
% See solution above
% 1.15/0.92 ------------------------
% 1.15/0.93 ---- Cleaned THF ---
% 1.15/0.93 thf(in_type,type,
% 1.15/0.93 in: $i > $i > $o ).
% 1.15/0.93
% 1.15/0.93 thf(exu_type,type,
% 1.15/0.93 exu: ( $i > $o ) > $o ).
% 1.15/0.93
% 1.15/0.93 thf(exu,definition,
% 1.15/0.93 ( exu
% 1.15/0.93 = ( ^ [Xphi: $i > $o] :
% 1.15/0.93 ? [Xx: $i] :
% 1.15/0.93 ( ( Xphi @ Xx )
% 1.15/0.93 & ! [Xy: $i] :
% 1.15/0.93 ( ( Xphi @ Xy )
% 1.15/0.93 => ( Xx = Xy ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(setextAx_type,type,
% 1.15/0.93 setextAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(setextAx,definition,
% 1.15/0.93 ( setextAx
% 1.15/0.93 = ( ! [A: $i,B: $i] :
% 1.15/0.93 ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ A )
% 1.15/0.93 <=> ( in @ Xx @ B ) )
% 1.15/0.93 => ( A = B ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(emptyset_type,type,
% 1.15/0.93 emptyset: $i ).
% 1.15/0.93
% 1.15/0.93 thf(emptysetAx_type,type,
% 1.15/0.93 emptysetAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(emptysetAx,definition,
% 1.15/0.93 ( emptysetAx
% 1.15/0.93 = ( ! [Xx: $i] :
% 1.15/0.93 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(setadjoin_type,type,
% 1.15/0.93 setadjoin: $i > $i > $i ).
% 1.15/0.93
% 1.15/0.93 thf(setadjoinAx_type,type,
% 1.15/0.93 setadjoinAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(setadjoinAx,definition,
% 1.15/0.93 ( setadjoinAx
% 1.15/0.93 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.15/0.93 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.15/0.93 <=> ( ( Xy = Xx )
% 1.15/0.93 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(powerset_type,type,
% 1.15/0.93 powerset: $i > $i ).
% 1.15/0.93
% 1.15/0.93 thf(powersetAx_type,type,
% 1.15/0.93 powersetAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(powersetAx,definition,
% 1.15/0.93 ( powersetAx
% 1.15/0.93 = ( ! [A: $i,B: $i] :
% 1.15/0.93 ( ( in @ B @ ( powerset @ A ) )
% 1.15/0.93 <=> ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ B )
% 1.15/0.93 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(setunion_type,type,
% 1.15/0.93 setunion: $i > $i ).
% 1.15/0.93
% 1.15/0.93 thf(setunionAx_type,type,
% 1.15/0.93 setunionAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(setunionAx,definition,
% 1.15/0.93 ( setunionAx
% 1.15/0.93 = ( ! [A: $i,Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ ( setunion @ A ) )
% 1.15/0.93 <=> ? [B: $i] :
% 1.15/0.93 ( ( in @ Xx @ B )
% 1.15/0.93 & ( in @ B @ A ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(omega_type,type,
% 1.15/0.93 omega: $i ).
% 1.15/0.93
% 1.15/0.93 thf(omega0Ax_type,type,
% 1.15/0.93 omega0Ax: $o ).
% 1.15/0.93
% 1.15/0.93 thf(omega0Ax,definition,
% 1.15/0.93 ( omega0Ax
% 1.15/0.93 = ( in @ emptyset @ omega ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(omegaSAx_type,type,
% 1.15/0.93 omegaSAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(omegaSAx,definition,
% 1.15/0.93 ( omegaSAx
% 1.15/0.93 = ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ omega )
% 1.15/0.93 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(omegaIndAx_type,type,
% 1.15/0.93 omegaIndAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(omegaIndAx,definition,
% 1.15/0.93 ( omegaIndAx
% 1.15/0.93 = ( ! [A: $i] :
% 1.15/0.93 ( ( ( in @ emptyset @ A )
% 1.15/0.93 & ! [Xx: $i] :
% 1.15/0.93 ( ( ( in @ Xx @ omega )
% 1.15/0.93 & ( in @ Xx @ A ) )
% 1.15/0.93 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.15/0.93 => ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ omega )
% 1.15/0.93 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(replAx_type,type,
% 1.15/0.93 replAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(replAx,definition,
% 1.15/0.93 ( replAx
% 1.15/0.93 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.15/0.93 ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ A )
% 1.15/0.93 => ( exu
% 1.15/0.93 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.15/0.93 => ? [B: $i] :
% 1.15/0.93 ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ B )
% 1.15/0.93 <=> ? [Xy: $i] :
% 1.15/0.93 ( ( in @ Xy @ A )
% 1.15/0.93 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(foundationAx_type,type,
% 1.15/0.93 foundationAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(foundationAx,definition,
% 1.15/0.93 ( foundationAx
% 1.15/0.93 = ( ! [A: $i] :
% 1.15/0.93 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.15/0.93 => ? [B: $i] :
% 1.15/0.93 ( ( in @ B @ A )
% 1.15/0.93 & ~ ? [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ B )
% 1.15/0.93 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(wellorderingAx_type,type,
% 1.15/0.93 wellorderingAx: $o ).
% 1.15/0.93
% 1.15/0.93 thf(wellorderingAx,definition,
% 1.15/0.93 ( wellorderingAx
% 1.15/0.93 = ( ! [A: $i] :
% 1.15/0.93 ? [B: $i] :
% 1.15/0.93 ( ! [C: $i] :
% 1.15/0.93 ( ( in @ C @ B )
% 1.15/0.93 => ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ C )
% 1.15/0.93 => ( in @ Xx @ A ) ) )
% 1.15/0.93 & ! [Xx: $i,Xy: $i] :
% 1.15/0.93 ( ( ( in @ Xx @ A )
% 1.15/0.93 & ( in @ Xy @ A ) )
% 1.15/0.93 => ( ! [C: $i] :
% 1.15/0.93 ( ( in @ C @ B )
% 1.15/0.93 => ( ( in @ Xx @ C )
% 1.15/0.93 <=> ( in @ Xy @ C ) ) )
% 1.15/0.93 => ( Xx = Xy ) ) )
% 1.15/0.93 & ! [C: $i,D: $i] :
% 1.15/0.93 ( ( ( in @ C @ B )
% 1.15/0.93 & ( in @ D @ B ) )
% 1.15/0.93 => ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ C )
% 1.15/0.93 => ( in @ Xx @ D ) )
% 1.15/0.93 | ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ D )
% 1.15/0.93 => ( in @ Xx @ C ) ) ) )
% 1.15/0.93 & ! [C: $i] :
% 1.15/0.93 ( ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ C )
% 1.15/0.93 => ( in @ Xx @ A ) )
% 1.15/0.93 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.15/0.93 => ? [D: $i,Xx: $i] :
% 1.15/0.93 ( ( in @ D @ B )
% 1.15/0.93 & ( in @ Xx @ C )
% 1.15/0.93 & ~ ? [Xy: $i] :
% 1.15/0.93 ( ( in @ Xy @ D )
% 1.15/0.93 & ( in @ Xy @ C ) )
% 1.15/0.93 & ! [E: $i] :
% 1.15/0.93 ( ( in @ E @ B )
% 1.15/0.93 => ( ! [Xy: $i] :
% 1.15/0.93 ( ( in @ Xy @ E )
% 1.15/0.93 => ( in @ Xy @ D ) )
% 1.15/0.93 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(descr_type,type,
% 1.15/0.93 descr: ( $i > $o ) > $i ).
% 1.15/0.93
% 1.15/0.93 thf(descrp_type,type,
% 1.15/0.93 descrp: $o ).
% 1.15/0.93
% 1.15/0.93 thf(descrp,definition,
% 1.15/0.93 ( descrp
% 1.15/0.93 = ( ! [Xphi: $i > $o] :
% 1.15/0.93 ( ( exu
% 1.15/0.93 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.15/0.93 => ( Xphi
% 1.15/0.93 @ ( descr
% 1.15/0.93 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(dsetconstr_type,type,
% 1.15/0.93 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.15/0.93
% 1.15/0.93 thf(dsetconstrI_type,type,
% 1.15/0.93 dsetconstrI: $o ).
% 1.15/0.93
% 1.15/0.93 thf(dsetconstrI,definition,
% 1.15/0.93 ( dsetconstrI
% 1.15/0.93 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ A )
% 1.15/0.93 => ( ( Xphi @ Xx )
% 1.15/0.93 => ( in @ Xx
% 1.15/0.93 @ ( dsetconstr @ A
% 1.15/0.93 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(dsetconstrEL_type,type,
% 1.15/0.93 dsetconstrEL: $o ).
% 1.15/0.93
% 1.15/0.93 thf(dsetconstrEL,definition,
% 1.15/0.93 ( dsetconstrEL
% 1.15/0.93 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.15/0.93 ( ( in @ Xx
% 1.15/0.93 @ ( dsetconstr @ A
% 1.15/0.93 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.15/0.93 => ( in @ Xx @ A ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(dsetconstrER_type,type,
% 1.15/0.93 dsetconstrER: $o ).
% 1.15/0.93
% 1.15/0.93 thf(dsetconstrER,definition,
% 1.15/0.93 ( dsetconstrER
% 1.15/0.93 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.15/0.93 ( ( in @ Xx
% 1.15/0.93 @ ( dsetconstr @ A
% 1.15/0.93 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.15/0.93 => ( Xphi @ Xx ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(exuE1_type,type,
% 1.15/0.93 exuE1: $o ).
% 1.15/0.93
% 1.15/0.93 thf(exuE1,definition,
% 1.15/0.93 ( exuE1
% 1.15/0.93 = ( ! [Xphi: $i > $o] :
% 1.15/0.93 ( ( exu
% 1.15/0.93 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.15/0.93 => ? [Xx: $i] :
% 1.15/0.93 ( ( Xphi @ Xx )
% 1.15/0.93 & ! [Xy: $i] :
% 1.15/0.93 ( ( Xphi @ Xy )
% 1.15/0.93 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(prop2set_type,type,
% 1.15/0.93 prop2set: $o > $i ).
% 1.15/0.93
% 1.15/0.93 thf(prop2set,definition,
% 1.15/0.93 ( prop2set
% 1.15/0.93 = ( ^ [Xphi: $o] :
% 1.15/0.93 ( dsetconstr @ ( powerset @ emptyset )
% 1.15/0.93 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(prop2setE_type,type,
% 1.15/0.93 prop2setE: $o ).
% 1.15/0.93
% 1.15/0.93 thf(prop2setE,definition,
% 1.15/0.93 ( prop2setE
% 1.15/0.93 = ( ! [Xphi: $o,Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.15/0.93 => Xphi ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(emptysetE_type,type,
% 1.15/0.93 emptysetE: $o ).
% 1.15/0.93
% 1.15/0.93 thf(emptysetE,definition,
% 1.15/0.93 ( emptysetE
% 1.15/0.93 = ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ emptyset )
% 1.15/0.93 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(emptysetimpfalse_type,type,
% 1.15/0.93 emptysetimpfalse: $o ).
% 1.15/0.93
% 1.15/0.93 thf(emptysetimpfalse,definition,
% 1.15/0.93 ( emptysetimpfalse
% 1.15/0.93 = ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ emptyset )
% 1.15/0.93 => $false ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(notinemptyset_type,type,
% 1.15/0.93 notinemptyset: $o ).
% 1.15/0.93
% 1.15/0.93 thf(notinemptyset,definition,
% 1.15/0.93 ( notinemptyset
% 1.15/0.93 = ( ! [Xx: $i] :
% 1.15/0.93 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(exuE3e_type,type,
% 1.15/0.93 exuE3e: $o ).
% 1.15/0.93
% 1.15/0.93 thf(exuE3e,definition,
% 1.15/0.93 ( exuE3e
% 1.15/0.93 = ( ! [Xphi: $i > $o] :
% 1.15/0.93 ( ( exu
% 1.15/0.93 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.15/0.93 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(setext_type,type,
% 1.15/0.93 setext: $o ).
% 1.15/0.93
% 1.15/0.93 thf(setext,definition,
% 1.15/0.93 ( setext
% 1.15/0.93 = ( ! [A: $i,B: $i] :
% 1.15/0.93 ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ A )
% 1.15/0.93 => ( in @ Xx @ B ) )
% 1.15/0.93 => ( ! [Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ B )
% 1.15/0.93 => ( in @ Xx @ A ) )
% 1.15/0.93 => ( A = B ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(emptyI_type,type,
% 1.15/0.93 emptyI: $o ).
% 1.15/0.93
% 1.15/0.93 thf(emptyI,definition,
% 1.15/0.93 ( emptyI
% 1.15/0.93 = ( ! [A: $i] :
% 1.15/0.93 ( ! [Xx: $i] :
% 1.15/0.93 ~ ( in @ Xx @ A )
% 1.15/0.93 => ( A = emptyset ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(noeltsimpempty_type,type,
% 1.15/0.93 noeltsimpempty: $o ).
% 1.15/0.93
% 1.15/0.93 thf(noeltsimpempty,definition,
% 1.15/0.93 ( noeltsimpempty
% 1.15/0.93 = ( ! [A: $i] :
% 1.15/0.93 ( ! [Xx: $i] :
% 1.15/0.93 ~ ( in @ Xx @ A )
% 1.15/0.93 => ( A = emptyset ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(setbeta_type,type,
% 1.15/0.93 setbeta: $o ).
% 1.15/0.93
% 1.15/0.93 thf(setbeta,definition,
% 1.15/0.93 ( setbeta
% 1.15/0.93 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ A )
% 1.15/0.93 => ( ( in @ Xx
% 1.15/0.93 @ ( dsetconstr @ A
% 1.15/0.93 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.15/0.93 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(nonempty_type,type,
% 1.15/0.93 nonempty: $i > $o ).
% 1.15/0.93
% 1.15/0.93 thf(nonempty,definition,
% 1.15/0.93 ( nonempty
% 1.15/0.93 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(nonemptyE1_type,type,
% 1.15/0.93 nonemptyE1: $o ).
% 1.15/0.93
% 1.15/0.93 thf(nonemptyE1,definition,
% 1.15/0.93 ( nonemptyE1
% 1.15/0.93 = ( ! [A: $i] :
% 1.15/0.93 ( ( nonempty @ A )
% 1.15/0.93 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(nonemptyI_type,type,
% 1.15/0.93 nonemptyI: $o ).
% 1.15/0.93
% 1.15/0.93 thf(nonemptyI,definition,
% 1.15/0.93 ( nonemptyI
% 1.15/0.93 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.15/0.93 ( ( in @ Xx @ A )
% 1.15/0.93 => ( ( Xphi @ Xx )
% 1.15/0.93 => ( nonempty
% 1.15/0.93 @ ( dsetconstr @ A
% 1.15/0.93 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(nonemptyI1_type,type,
% 1.15/0.93 nonemptyI1: $o ).
% 1.15/0.93
% 1.15/0.93 thf(nonemptyI1,definition,
% 1.15/0.93 ( nonemptyI1
% 1.15/0.93 = ( ! [A: $i] :
% 1.15/0.93 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.15/0.93 => ( nonempty @ A ) ) ) ) ).
% 1.15/0.93
% 1.15/0.93 thf(setadjoinIL,conjecture,
% 1.15/0.93 ( setextAx
% 1.15/0.93 => ( emptysetAx
% 1.15/0.93 => ( setadjoinAx
% 1.15/0.93 => ( powersetAx
% 1.15/0.93 => ( setunionAx
% 1.15/0.93 => ( omega0Ax
% 1.15/0.93 => ( omegaSAx
% 1.15/0.93 => ( omegaIndAx
% 1.15/0.93 => ( replAx
% 1.15/0.93 => ( foundationAx
% 1.15/0.93 => ( wellorderingAx
% 1.15/0.93 => ( descrp
% 1.15/0.93 => ( dsetconstrI
% 1.15/0.93 => ( dsetconstrEL
% 1.15/0.93 => ( dsetconstrER
% 1.15/0.93 => ( exuE1
% 1.15/0.93 => ( prop2setE
% 1.15/0.93 => ( emptysetE
% 1.15/0.93 => ( emptysetimpfalse
% 1.15/0.93 => ( notinemptyset
% 1.15/0.93 => ( exuE3e
% 1.15/0.93 => ( setext
% 1.15/0.93 => ( emptyI
% 1.15/0.93 => ( noeltsimpempty
% 1.15/0.93 => ( setbeta
% 1.15/0.93 => ( nonemptyE1
% 1.15/0.93 => ( nonemptyI
% 1.15/0.93 => ( nonemptyI1
% 1.15/0.93 => ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.15/0.93 ------------------------
% 1.15/0.95 % (10820)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_10718 for (2999ds/2Mi)
% 1.15/0.95 % (10819)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10718 for (2999ds/2Mi)
% 1.15/0.95 % (10821)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_10718 for (2999ds/275Mi)
% 1.15/0.95 % (10816)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10718 for (2999ds/183Mi)
% 1.15/0.95 % (10818)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_10718 for (2999ds/27Mi)
% 1.15/0.95 % (10817)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_10718 for (2999ds/4Mi)
% 1.15/0.95 % (10822)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10718 for (2999ds/18Mi)
% 1.15/0.95 % (10819)Instruction limit reached!
% 1.15/0.95 % (10819)------------------------------
% 1.15/0.95 % (10819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.95 % (10819)Termination reason: Unknown
% 1.15/0.95 % (10820)Instruction limit reached!
% 1.15/0.95 % (10820)------------------------------
% 1.15/0.95 % (10820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.95 % (10820)Termination reason: Unknown
% 1.15/0.95 % (10820)Termination phase: shuffling
% 1.15/0.95
% 1.15/0.95 % (10820)Memory used [KB]: 1023
% 1.15/0.95 % (10820)Time elapsed: 0.002 s
% 1.15/0.95 % (10820)Instructions burned: 2 (million)
% 1.15/0.95 % (10820)------------------------------
% 1.15/0.95 % (10820)------------------------------
% 1.15/0.95 % (10819)Termination phase: shuffling
% 1.15/0.95
% 1.15/0.95 % (10819)Memory used [KB]: 1023
% 1.15/0.95 % (10819)Time elapsed: 0.002 s
% 1.15/0.95 % (10819)Instructions burned: 2 (million)
% 1.15/0.95 % (10819)------------------------------
% 1.15/0.95 % (10819)------------------------------
% 1.15/0.95 % (10817)Instruction limit reached!
% 1.15/0.95 % (10817)------------------------------
% 1.15/0.95 % (10817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.95 % (10817)Termination reason: Unknown
% 1.15/0.95 % (10817)Termination phase: shuffling
% 1.15/0.95
% 1.15/0.95 % (10817)Memory used [KB]: 1151
% 1.15/0.95 % (10817)Time elapsed: 0.003 s
% 1.15/0.95 % (10817)Instructions burned: 6 (million)
% 1.15/0.95 % (10817)------------------------------
% 1.15/0.95 % (10817)------------------------------
% 1.15/0.95 % (10822)Instruction limit reached!
% 1.15/0.95 % (10822)------------------------------
% 1.15/0.95 % (10822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.95 % (10822)Termination reason: Unknown
% 1.15/0.95 % (10822)Termination phase: Property scanning
% 1.15/0.95
% 1.15/0.95 % (10822)Memory used [KB]: 1407
% 1.15/0.95 % (10822)Time elapsed: 0.006 s
% 1.15/0.95 % (10822)Instructions burned: 18 (million)
% 1.15/0.95 % (10822)------------------------------
% 1.15/0.95 % (10822)------------------------------
% 1.15/0.95 % (10818)Instruction limit reached!
% 1.15/0.95 % (10818)------------------------------
% 1.15/0.95 % (10818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.95 % (10818)Termination reason: Unknown
% 1.15/0.95 % (10818)Termination phase: Saturation
% 1.15/0.95
% 1.15/0.95 % (10818)Memory used [KB]: 5756
% 1.15/0.95 % (10818)Time elapsed: 0.009 s
% 1.15/0.95 % (10818)Instructions burned: 28 (million)
% 1.15/0.95 % (10818)------------------------------
% 1.15/0.95 % (10818)------------------------------
% 1.15/0.96 % (10823)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10718 for (2999ds/3Mi)
% 1.15/0.96 % (10825)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_10718 for (2999ds/15Mi)
% 1.15/0.96 % (10823)Instruction limit reached!
% 1.15/0.96 % (10823)------------------------------
% 1.15/0.96 % (10823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.96 % (10823)Termination reason: Unknown
% 1.15/0.96 % (10823)Termination phase: shuffling
% 1.15/0.96
% 1.15/0.96 % (10823)Memory used [KB]: 1023
% 1.15/0.96 % (10823)Time elapsed: 0.002 s
% 1.15/0.96 % (10823)Instructions burned: 4 (million)
% 1.15/0.96 % (10823)------------------------------
% 1.15/0.96 % (10823)------------------------------
% 1.15/0.96 % (10824)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_10718 for (2999ds/37Mi)
% 1.15/0.96 % (10826)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_10718 for (2999ds/3Mi)
% 1.15/0.96 % (10816)First to succeed.
% 1.15/0.96 % (10825)Instruction limit reached!
% 1.15/0.96 % (10825)------------------------------
% 1.15/0.96 % (10825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.96 % (10825)Termination reason: Unknown
% 1.15/0.96 % (10825)Termination phase: Property scanning
% 1.15/0.96 % (10826)Instruction limit reached!
% 1.15/0.96 % (10826)------------------------------
% 1.15/0.96 % (10826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.96
% 1.15/0.96 % (10825)Memory used [KB]: 1407
% 1.15/0.96 % (10825)Time elapsed: 0.006 s
% 1.15/0.96 % (10825)Instructions burned: 18 (million)
% 1.15/0.96 % (10825)------------------------------
% 1.15/0.96 % (10825)------------------------------
% 1.15/0.96 % (10826)Termination reason: Unknown
% 1.15/0.96 % (10826)Termination phase: shuffling
% 1.15/0.96
% 1.15/0.96 % (10826)Memory used [KB]: 1023
% 1.15/0.96 % (10826)Time elapsed: 0.002 s
% 1.15/0.96 % (10826)Instructions burned: 4 (million)
% 1.15/0.96 % (10826)------------------------------
% 1.15/0.96 % (10826)------------------------------
% 1.15/0.96 % (10827)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_10718 for (2999ds/1041Mi)
% 1.15/0.96 % (10816)Refutation found. Thanks to Tanya!
% 1.15/0.96 % SZS status Theorem for DTF2THF_10718
% 1.15/0.96 % SZS output start Proof for DTF2THF_10718
% 1.15/0.96 thf(func_def_0, type, in: $i > $i > $o).
% 1.15/0.96 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.15/0.96 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.15/0.96 thf(func_def_8, type, powerset: $i > $i).
% 1.15/0.96 thf(func_def_10, type, setunion: $i > $i).
% 1.15/0.96 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.15/0.96 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.15/0.96 thf(func_def_26, type, prop2set: $o > $i).
% 1.15/0.96 thf(func_def_36, type, nonempty: $i > $o).
% 1.15/0.96 thf(func_def_59, type, sK3: $i > $i).
% 1.15/0.96 thf(func_def_60, type, sK4: ($i > $o) > $i).
% 1.15/0.96 thf(func_def_61, type, sK5: ($i > $o) > $i > $i).
% 1.15/0.96 thf(func_def_62, type, sK6: $i > $i).
% 1.15/0.96 thf(func_def_63, type, sK7: $i > $i > $i).
% 1.15/0.96 thf(func_def_64, type, sK8: $i > $i).
% 1.15/0.96 thf(func_def_65, type, sK9: $i > $i > $i).
% 1.15/0.96 thf(func_def_66, type, sK10: $i > $i > $i).
% 1.15/0.96 thf(func_def_67, type, sK11: $i > $i > $i).
% 1.15/0.96 thf(func_def_68, type, sK12: $i > $i).
% 1.15/0.96 thf(func_def_69, type, sK13: ($i > $o) > $i > $i).
% 1.15/0.96 thf(func_def_70, type, sK14: ($i > $o) > $i).
% 1.15/0.96 thf(func_def_71, type, sK15: ($i > $o) > $i).
% 1.15/0.96 thf(func_def_72, type, sK16: ($i > $o) > $i > $i).
% 1.15/0.96 thf(func_def_73, type, sK17: $i > $i > $i).
% 1.15/0.96 thf(func_def_74, type, sK18: $i > $i).
% 1.15/0.96 thf(func_def_75, type, sK19: $i > $i > $i).
% 1.15/0.96 thf(func_def_76, type, sK20: $i > $i > $i).
% 1.15/0.96 thf(func_def_77, type, sK21: $i > $i > $i).
% 1.15/0.96 thf(func_def_78, type, sK22: $i > $i > $i > $i).
% 1.15/0.96 thf(func_def_79, type, sK23: $i > $i).
% 1.15/0.96 thf(func_def_80, type, sK24: $i > $i > $i).
% 1.15/0.96 thf(func_def_82, type, sK25: ($i > $i > $o) > $i > $i).
% 1.15/0.96 thf(func_def_83, type, sK26: ($i > $i > $o) > $i > $i).
% 1.15/0.96 thf(func_def_84, type, sK27: $i > ($i > $i > $o) > $i > $i).
% 1.15/0.96 thf(func_def_85, type, sK28: $i > ($i > $i > $o) > $i > $i).
% 1.15/0.96 thf(func_def_86, type, sK29: $i > ($i > $i > $o) > $i > $i).
% 1.15/0.96 thf(func_def_87, type, sK30: ($i > $i > $o) > $i > $i > $i).
% 1.15/0.96 thf(f625,plain,(
% 1.15/0.96 $false),
% 1.15/0.96 inference(trivial_inequality_removal,[status(thm)],[f623])).
% 1.15/0.96 thf(f623,plain,(
% 1.15/0.96 (sK1 != sK1) | ($true != $true)),
% 1.15/0.96 inference(superposition,[status(thm)],[f132,f342])).
% 1.15/0.96 thf(f342,plain,(
% 1.15/0.96 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X3 @ X2))) | (X1 != X3)) )),
% 1.15/0.96 inference(equality_proxy_clausification,[status(thm)],[f341])).
% 1.15/0.96 thf(f341,plain,(
% 1.15/0.96 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X3 @ X2))) | ((X3 = X1) = $false)) )),
% 1.15/0.96 inference(binary_proxy_clausification,[status(thm)],[f339])).
% 1.15/0.96 thf(f339,plain,(
% 1.15/0.96 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((X3 = X1) | (in @ X1 @ X2)) = $false) | ($true = (in @ X1 @ (setadjoin @ X3 @ X2)))) )),
% 1.15/0.96 inference(binary_proxy_clausification,[status(thm)],[f337])).
% 1.15/0.96 thf(f337,plain,(
% 1.15/0.96 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((X3 = X1) | (in @ X1 @ X2)) = (in @ X1 @ (setadjoin @ X3 @ X2)))) )),
% 1.15/0.96 inference(binary_proxy_clausification,[status(thm)],[f336])).
% 1.15/0.96 thf(f336,plain,(
% 1.15/0.96 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X3 @ X2)) = ((X3 = X1) | (in @ X1 @ X2))) = $true)) )),
% 1.15/0.96 inference(beta_eta_normalization,[status(thm)],[f335])).
% 1.15/0.96 thf(f335,plain,(
% 1.15/0.96 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ X2)) = ((Y0 = X1) | (in @ X1 @ X2)))) @ X3) = $true)) )),
% 1.15/0.96 inference(pi_clausification,[status(thm)],[f334])).
% 1.15/0.96 thf(f334,plain,(
% 1.15/0.96 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ X2)) = ((Y0 = X1) | (in @ X1 @ X2))))))) )),
% 1.15/0.96 inference(beta_eta_normalization,[status(thm)],[f333])).
% 1.15/0.96 thf(f333,plain,(
% 1.15/0.96 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y1 @ Y0)) = ((Y1 = X1) | (in @ X1 @ Y0)))))) @ X2))) )),
% 1.15/0.96 inference(pi_clausification,[status(thm)],[f332])).
% 1.15/0.96 thf(f332,plain,(
% 1.15/0.96 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y1 @ Y0)) = ((Y1 = X1) | (in @ X1 @ Y0))))))))) )),
% 1.15/0.96 inference(beta_eta_normalization,[status(thm)],[f331])).
% 1.15/0.96 thf(f331,plain,(
% 1.15/0.96 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) = ((Y2 = Y0) | (in @ Y0 @ Y1)))))))) @ X1) = $true)) )),
% 1.15/0.96 inference(pi_clausification,[status(thm)],[f186])).
% 1.15/0.96 thf(f186,plain,(
% 1.15/0.96 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) = ((Y2 = Y0) | (in @ Y0 @ Y1))))))))))),
% 1.15/0.96 inference(definition_unfolding,[status(thm)],[f153,f119])).
% 1.15/0.96 thf(f119,plain,(
% 1.15/0.96 (setadjoinAx = $true)),
% 1.15/0.96 inference(cnf_transformation,[status(thm)],[f99])).
% 1.15/0.96 thf(f99,plain,(
% 1.15/0.96 (dsetconstrI = $true) & (notinemptyset = $true) & (exuE1 = $true) & (nonemptyE1 = $true) & (prop2setE = $true) & (setextAx = $true) & (omegaSAx = $true) & (setunionAx = $true) & (emptysetE = $true) & (exuE3e = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (nonemptyI = $true) & (emptysetimpfalse = $true) & (nonemptyI1 = $true) & ($true != (in @ sK1 @ (setadjoin @ sK1 @ sK0))) & (powersetAx = $true) & (descrp = $true) & (replAx = $true) & (emptyI = $true) & (dsetconstrEL = $true) & (setbeta = $true) & (foundationAx = $true) & (emptysetAx = $true) & (dsetconstrER = $true) & (wellorderingAx = $true) & (noeltsimpempty = $true) & (setext = $true) & (setadjoinAx = $true)),
% 1.15/0.96 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f97,f98])).
% 1.15/0.96 thf(f98,plain,(
% 1.15/0.96 ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))) => ($true != (in @ sK1 @ (setadjoin @ sK1 @ sK0)))),
% 1.15/0.96 introduced(definition,[],[choice_axiom])).
% 1.15/0.96 thf(f97,plain,(
% 1.15/0.96 (dsetconstrI = $true) & (notinemptyset = $true) & (exuE1 = $true) & (nonemptyE1 = $true) & (prop2setE = $true) & (setextAx = $true) & (omegaSAx = $true) & (setunionAx = $true) & (emptysetE = $true) & (exuE3e = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (nonemptyI = $true) & (emptysetimpfalse = $true) & (nonemptyI1 = $true) & ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))) & (powersetAx = $true) & (descrp = $true) & (replAx = $true) & (emptyI = $true) & (dsetconstrEL = $true) & (setbeta = $true) & (foundationAx = $true) & (emptysetAx = $true) & (dsetconstrER = $true) & (wellorderingAx = $true) & (noeltsimpempty = $true) & (setext = $true) & (setadjoinAx = $true)),
% 1.15/0.96 inference(flattening,[status(thm)],[f96])).
% 1.15/0.96 thf(f96,plain,(
% 1.15/0.96 (((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))) & (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)),
% 1.15/0.96 inference(ennf_transformation,[status(thm)],[f56])).
% 1.15/0.96 thf(f56,plain,(
% 1.15/0.96 ~((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) => ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0)))))))))))))))))))))))))))))))),
% 1.15/0.96 inference(fool_elimination,[status(thm)],[f55])).
% 1.15/0.96 thf(f55,plain,(
% 1.15/0.96 ~(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 => ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0))))))))))))))))))))))))))))))),
% 1.15/0.96 inference(rectify,[status(thm)],[f33])).
% 1.15/0.96 thf(f33,negated_conjecture,(
% 1.15/0.96 ~(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 => ! [X2 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X2))))))))))))))))))))))))))))))),
% 1.15/0.96 inference(negated_conjecture,[status(cth)],[f32])).
% 1.15/0.96 thf(f32,conjecture,(
% 1.15/0.96 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 => ! [X2 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X2)))))))))))))))))))))))))))))),
% 1.15/0.97 file('/export/starexec/sandbox2/tmp/tmp.9JX3iTHJoM/DTF2THF_10718.p',setadjoinIL)).
% 1.15/0.97 thf(f153,plain,(
% 1.15/0.97 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) = ((Y2 = Y0) | (in @ Y0 @ Y1))))))))))),
% 1.15/0.97 inference(cnf_transformation,[status(thm)],[f73])).
% 1.15/0.97 thf(f73,plain,(
% 1.15/0.97 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) = ((Y2 = Y0) | (in @ Y0 @ Y1))))))))))),
% 1.15/0.97 inference(fool_elimination,[status(thm)],[f72])).
% 1.15/0.97 thf(f72,plain,(
% 1.15/0.97 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) <=> ((in @ X2 @ X1) | (X0 = X2))) = setadjoinAx)),
% 1.15/0.97 inference(rectify,[status(thm)],[f4])).
% 1.15/0.97 thf(f4,axiom,(
% 1.15/0.97 (! [X1 : $i,X3 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) <=> ((in @ X2 @ X3) | (X1 = X2))) = setadjoinAx)),
% 1.15/0.97 file('/export/starexec/sandbox2/tmp/tmp.9JX3iTHJoM/DTF2THF_10718.p',setadjoinAx)).
% 1.15/0.97 thf(f132,plain,(
% 1.15/0.97 ($true != (in @ sK1 @ (setadjoin @ sK1 @ sK0)))),
% 1.15/0.97 inference(cnf_transformation,[status(thm)],[f99])).
% 1.15/0.97 % SZS output end Proof for DTF2THF_10718
% 1.15/0.97 % (10816)------------------------------
% 1.15/0.97 % (10816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/0.97 % (10816)Termination reason: Refutation
% 1.15/0.97
% 1.15/0.97 % (10816)Memory used [KB]: 6012
% 1.15/0.97 % (10816)Time elapsed: 0.018 s
% 1.15/0.97 % (10816)Instructions burned: 53 (million)
% 1.15/0.97 % (10816)------------------------------
% 1.15/0.97 % (10816)------------------------------
% 1.15/0.97 % (10815)Success in time 0.018 s
%------------------------------------------------------------------------------