%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU506^2 : 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 : n001.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 09:34:59 AM UTC 2026
% Result : Theorem 1.49s 1.29s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 525 ( 171 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 466 ( 90 ~; 63 |; 46 &; 224 @)
% ( 7 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 111 ( 0 ^; 84 !; 27 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_9,type,
sK2: $i > $i > $i ).
thf(func_def_10,type,
sK3: $i > $i > $i ).
thf(f91,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f66,f81,f86]) ).
thf(f86,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[status(thm)],[f85]) ).
thf(f85,plain,
( $false
| ~ spl7_1 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true != $true )
| ~ spl7_1 ),
inference(superposition,[status(thm)],[f43,f62]) ).
thf(f62,plain,
( ! [X1: $o] : ( $true = X1 )
| ~ spl7_1 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl7_1
<=> ! [X1: $o] : ( $true = X1 ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f43,plain,
! [X1: $i] :
( ( in @ X1 @ sK6 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( emptyset != sK6 )
& ! [X1: $i] :
( ( in @ X1 @ sK6 )
!= $true )
& ( emptysetE = $true )
& ( setext = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f17,f29]) ).
thf(f29,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) )
=> ( ( emptyset != sK6 )
& ! [X1: $i] :
( ( in @ X1 @ sK6 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) )
& ( emptysetE = $true )
& ( setext = $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) )
& ( setext = $true )
& ( emptysetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( emptysetE = $true )
=> ( ( setext = $true )
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
=> ( emptyset = X0 ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( emptysetE = $true )
=> ( ( setext = $true )
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
=> ( emptyset = X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( emptysetE
=> ( setext
=> ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( emptyset = X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( emptysetE
=> ( setext
=> ! [X2: $i] :
( ! [X0: $i] :
~ ( in @ X0 @ X2 )
=> ( emptyset = X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( emptysetE
=> ( setext
=> ! [X2: $i] :
( ! [X0: $i] :
~ ( in @ X0 @ X2 )
=> ( emptyset = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IsKlZLpBcN/DTF2THF_6185.p',emptyI) ).
thf(f81,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[status(thm)],[f80]) ).
thf(f80,plain,
( $false
| ~ spl7_2 ),
inference(subsumption_resolution,[status(thm)],[f79,f44]) ).
thf(f44,plain,
emptyset != sK6,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f79,plain,
( ( emptyset = sK6 )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( emptyset = sK6 )
| ( $true != $true )
| ~ spl7_2 ),
inference(superposition,[status(thm)],[f43,f73]) ).
thf(f73,plain,
( ! [X0: $i] :
( ( ( in @ ( sK2 @ emptyset @ X0 ) @ X0 )
= $true )
| ( emptyset = X0 ) )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ! [X0: $i] :
( ( emptyset = X0 )
| ( $true != $true )
| ( ( in @ ( sK2 @ emptyset @ X0 ) @ X0 )
= $true ) )
| ~ spl7_2 ),
inference(superposition,[status(thm)],[f65,f56]) ).
thf(f56,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true )
| ( X0 = X1 )
| ( ( in @ ( sK2 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true != $true )
| ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(definition_unfolding,[status(thm)],[f37,f41]) ).
thf(f41,plain,
setext = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f37,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X0 ) @ X0 )
= $true )
| ( X0 = X1 )
| ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true )
| ( setext != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ ( sK2 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( in @ ( sK2 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( X0 = X1 )
| ( ( ( in @ ( sK3 @ X1 @ X0 ) @ X0 )
!= $true )
& ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true ) ) )
| ( setext != $true ) )
& ( ( setext = $true )
| ( ! [X6: $i] :
( ( ( in @ X6 @ sK5 )
= $true )
| ( ( in @ X6 @ sK4 )
!= $true ) )
& ( sK5 != sK4 )
& ! [X7: $i] :
( ( ( in @ X7 @ sK4 )
= $true )
| ( $true
!= ( in @ X7 @ sK5 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f24,f27,f26,f25]) ).
thf(f25,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ X0 ) ) )
=> ( ( ( in @ ( sK2 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( in @ ( sK2 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
! [X0: $i,X1: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
=> ( ( ( in @ ( sK3 @ X1 @ X0 ) @ X0 )
!= $true )
& ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
| ( $true
!= ( in @ X6 @ X4 ) ) )
& ( X4 != X5 )
& ! [X7: $i] :
( ( $true
= ( in @ X7 @ X4 ) )
| ( ( in @ X7 @ X5 )
!= $true ) ) )
=> ( ! [X6: $i] :
( ( ( in @ X6 @ sK5 )
= $true )
| ( ( in @ X6 @ sK4 )
!= $true ) )
& ( sK5 != sK4 )
& ! [X7: $i] :
( ( ( in @ X7 @ sK4 )
= $true )
| ( $true
!= ( in @ X7 @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ X0 ) ) )
| ( X0 = X1 )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) )
| ( setext != $true ) )
& ( ( setext = $true )
| ? [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
| ( $true
!= ( in @ X6 @ X4 ) ) )
& ( X4 != X5 )
& ! [X7: $i] :
( ( $true
= ( in @ X7 @ X4 ) )
| ( ( in @ X7 @ X5 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X1: $i,X0: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( X0 = X1 )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ X0 ) ) ) )
| ( setext != $true ) )
& ( ( setext = $true )
| ? [X1: $i,X0: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( X0 != X1 )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( X0 = X1 )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ X0 ) ) ) )
<=> ( setext = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ( X0 = X1 )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ X0 ) ) ) )
<=> ( setext = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ X3 @ X0 )
= $true ) )
=> ( X0 = X1 ) ) )
<=> ( setext = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X0 ) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setext
= ( ! [X2: $i,X3: $i] :
( ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ( in @ X0 @ X3 ) )
=> ( ! [X0: $i] :
( ( in @ X0 @ X3 )
=> ( in @ X0 @ X2 ) )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IsKlZLpBcN/DTF2THF_6185.p',setext) ).
thf(f65,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ~ spl7_2 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl7_2
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f66,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f57,f64,f61]) ).
thf(f57,plain,
! [X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: $i,X1: $o] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( $true = X1 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f42]) ).
thf(f42,plain,
emptysetE = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f33,plain,
! [X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ! [X0: $i] :
( ! [X1: $o] : ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ( ( sK1 != $true )
& ( ( in @ sK0 @ emptyset )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f21,f20]) ).
thf(f20,plain,
( ? [X2: $i] :
( ? [X3: $o] : ( $true != X3 )
& ( ( in @ X2 @ emptyset )
= $true ) )
=> ( ? [X3: $o] : ( $true != X3 )
& ( ( in @ sK0 @ emptyset )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X3: $o] : ( $true != X3 )
=> ( sK1 != $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( ! [X0: $i] :
( ! [X1: $o] : ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X2: $i] :
( ? [X3: $o] : ( $true != X3 )
& ( ( in @ X2 @ emptyset )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ! [X0: $i] :
( ! [X1: $o] : ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X0: $i] :
( ? [X1: $o] : ( $true != X1 )
& ( ( in @ X0 @ emptyset )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i] :
( ! [X1: $o] : ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) )
<=> ( emptysetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ! [X1: $o] : ( $true = X1 ) )
<=> ( emptysetE = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 )
= emptysetE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 )
= emptysetE ),
file('/export/starexec/sandbox/tmp/tmp.IsKlZLpBcN/DTF2THF_6185.p',emptysetE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU506^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n001.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:25:20 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SEU506^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.47 % Domain : Set Theory
% 0.21/0.47 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.21/0.47 % Version : Especial > Reduced > Especial.
% 0.21/0.47 % English : (! A:i.(! x:i.~(in x A)) -> A = emptyset)
% 0.21/0.47
% 0.21/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.47 % Source : [Bro08]
% 0.21/0.47 % Names : ZFC008l [Bro08]
% 0.21/0.47 % : ZFC009l [Bro08]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.21/0.47 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.21/0.47 % Number of atoms : 14 ( 4 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.21/0.47 % Number of connectives : 21 ( 1 ~; 0 |; 0 &; 12 @)
% 0.21/0.47 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 9 ( 4 avg)
% 0.21/0.47 % Number of types : 2 ( 0 usr)
% 0.21/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.21/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : http://mathgate.info/detsetitem.php?id=386
% 0.21/0.47 % : http://mathgate.info/detsetitem.php?id=480
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(in_type,type,
% 0.21/0.47 in: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(emptyset_type,type,
% 0.21/0.47 emptyset: $i ).
% 0.21/0.47
% 0.21/0.47 thf(emptysetE_type,type,
% 0.21/0.47 emptysetE: $o ).
% 0.21/0.47
% 0.21/0.47 thf(emptysetE,definition,
% 0.21/0.47 ( emptysetE
% 0.21/0.47 = ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ emptyset )
% 0.21/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setext_type,type,
% 0.21/0.47 setext: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setext,definition,
% 0.21/0.47 ( setext
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ Xx @ B ) )
% 0.21/0.47 => ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ B )
% 0.21/0.47 => ( in @ Xx @ A ) )
% 0.21/0.47 => ( A = B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(emptyI,conjecture,
% 0.21/0.47 ( emptysetE
% 0.21/0.47 => ( setext
% 0.21/0.47 => ! [A: $i] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ~ ( in @ Xx @ A )
% 0.21/0.47 => ( A = emptyset ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 12:25:21 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.IsKlZLpBcN/DTF2DTF6185.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(in_type,type,
% 1.49/1.26 in: $i > $i > $o ).
% 1.49/1.26
% 1.49/1.26 thf(emptyset_type,type,
% 1.49/1.26 emptyset: $i ).
% 1.49/1.26
% 1.49/1.26 thf(emptysetE_type,type,
% 1.49/1.26 emptysetE: $o ).
% 1.49/1.26
% 1.49/1.26 thf(emptysetE,definition,
% 1.49/1.26 ( emptysetE
% 1.49/1.26 = ( ! [Xx: $i] :
% 1.49/1.26 ( ( in @ Xx @ emptyset )
% 1.49/1.26 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.49/1.26
% 1.49/1.26 thf(setext_type,type,
% 1.49/1.26 setext: $o ).
% 1.49/1.26
% 1.49/1.26 thf(setext,definition,
% 1.49/1.26 ( setext
% 1.49/1.26 = ( ! [A: $i,B: $i] :
% 1.49/1.26 ( ! [Xx: $i] :
% 1.49/1.26 ( ( in @ Xx @ A )
% 1.49/1.26 => ( in @ Xx @ B ) )
% 1.49/1.26 => ( ! [Xx: $i] :
% 1.49/1.26 ( ( in @ Xx @ B )
% 1.49/1.26 => ( in @ Xx @ A ) )
% 1.49/1.26 => ( A = B ) ) ) ) ) ).
% 1.49/1.26
% 1.49/1.26 thf(emptyI,conjecture,
% 1.49/1.26 ( emptysetE
% 1.49/1.26 => ( setext
% 1.49/1.26 => ! [A: $i] :
% 1.49/1.26 ( ! [Xx: $i] :
% 1.49/1.26 ~ ( in @ Xx @ A )
% 1.49/1.26 => ( A = emptyset ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.28 % (6514)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_6185 for (2999ds/4Mi)
% 1.49/1.28 % (6514)Instruction limit reached!
% 1.49/1.28 % (6514)------------------------------
% 1.49/1.28 % (6514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (6514)Termination reason: Unknown
% 1.49/1.28 % (6514)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (6514)Memory used [KB]: 5500
% 1.49/1.28 % (6514)Time elapsed: 0.003 s
% 1.49/1.28 % (6514)Instructions burned: 4 (million)
% 1.49/1.28 % (6514)------------------------------
% 1.49/1.28 % (6514)------------------------------
% 1.49/1.29 % (6513)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6185 for (2999ds/183Mi)
% 1.49/1.29 % (6515)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_6185 for (2999ds/27Mi)
% 1.49/1.29 % (6516)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6185 for (2999ds/2Mi)
% 1.49/1.29 % (6517)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_6185 for (2999ds/2Mi)
% 1.49/1.29 % (6518)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_6185 for (2999ds/275Mi)
% 1.49/1.29 % (6519)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6185 for (2999ds/18Mi)
% 1.49/1.29 % (6516)Instruction limit reached!
% 1.49/1.29 % (6516)------------------------------
% 1.49/1.29 % (6516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (6516)Termination reason: Unknown
% 1.49/1.29 % (6516)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (6516)Memory used [KB]: 5500
% 1.49/1.29 % (6516)Time elapsed: 0.004 s
% 1.49/1.29 % (6516)Instructions burned: 3 (million)
% 1.49/1.29 % (6516)------------------------------
% 1.49/1.29 % (6516)------------------------------
% 1.49/1.29 % (6517)Instruction limit reached!
% 1.49/1.29 % (6517)------------------------------
% 1.49/1.29 % (6517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (6517)Termination reason: Unknown
% 1.49/1.29 % (6517)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (6517)Memory used [KB]: 5500
% 1.49/1.29 % (6517)Time elapsed: 0.004 s
% 1.49/1.29 % (6517)Instructions burned: 3 (million)
% 1.49/1.29 % (6517)------------------------------
% 1.49/1.29 % (6517)------------------------------
% 1.49/1.29 % (6520)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6185 for (2999ds/3Mi)
% 1.49/1.29 % (6520)Instruction limit reached!
% 1.49/1.29 % (6520)------------------------------
% 1.49/1.29 % (6520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (6520)Termination reason: Unknown
% 1.49/1.29 % (6520)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (6520)Memory used [KB]: 5500
% 1.49/1.29 % (6520)Time elapsed: 0.002 s
% 1.49/1.29 % (6520)Instructions burned: 3 (million)
% 1.49/1.29 % (6520)------------------------------
% 1.49/1.29 % (6520)------------------------------
% 1.49/1.29 % (6518)First to succeed.
% 1.49/1.29 % (6513)Also succeeded, but the first one will report.
% 1.49/1.29 % (6518)Refutation found. Thanks to Tanya!
% 1.49/1.29 % SZS status Theorem for DTF2THF_6185
% 1.49/1.29 % SZS output start Proof for DTF2THF_6185
% 1.49/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.49/1.29 thf(func_def_9, type, sK2: $i > $i > $i).
% 1.49/1.29 thf(func_def_10, type, sK3: $i > $i > $i).
% 1.49/1.29 thf(f91,plain,(
% 1.49/1.29 $false),
% 1.49/1.29 inference(avatar_sat_refutation,[status(thm)],[f66,f81,f86])).
% 1.49/1.29 thf(f86,plain,(
% 1.49/1.29 ~spl7_1),
% 1.49/1.29 inference(avatar_contradiction_clause,[status(thm)],[f85])).
% 1.49/1.29 thf(f85,plain,(
% 1.49/1.29 $false | ~spl7_1),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.49/1.29 thf(f83,plain,(
% 1.49/1.29 ($true != $true) | ~spl7_1),
% 1.49/1.29 inference(superposition,[status(thm)],[f43,f62])).
% 1.49/1.29 thf(f62,plain,(
% 1.49/1.29 ( ! [X1 : $o] : (($true = X1)) ) | ~spl7_1),
% 1.49/1.29 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.49/1.29 thf(f61,definition,(
% 1.49/1.29 spl7_1 <=> ! [X1 : $o] : ($true = X1)),
% 1.49/1.29 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 1.49/1.29 thf(f43,plain,(
% 1.49/1.29 ( ! [X1 : $i] : (((in @ X1 @ sK6) != $true)) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.29 thf(f30,plain,(
% 1.49/1.29 ((emptyset != sK6) & ! [X1 : $i] : ((in @ X1 @ sK6) != $true)) & (emptysetE = $true) & (setext = $true)),
% 1.49/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f17,f29])).
% 1.49/1.29 thf(f29,plain,(
% 1.49/1.29 ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : ((in @ X1 @ X0) != $true)) => ((emptyset != sK6) & ! [X1 : $i] : ((in @ X1 @ sK6) != $true))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f17,plain,(
% 1.49/1.29 ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : ((in @ X1 @ X0) != $true)) & (emptysetE = $true) & (setext = $true)),
% 1.49/1.29 inference(flattening,[status(thm)],[f16])).
% 1.49/1.29 thf(f16,plain,(
% 1.49/1.29 (? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : ((in @ X1 @ X0) != $true)) & (setext = $true)) & (emptysetE = $true)),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f12])).
% 1.49/1.29 thf(f12,plain,(
% 1.49/1.29 ~((emptysetE = $true) => ((setext = $true) => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) != $true) => (emptyset = X0))))),
% 1.49/1.29 inference(flattening,[status(thm)],[f11])).
% 1.49/1.29 thf(f11,plain,(
% 1.49/1.29 ~((emptysetE = $true) => ((setext = $true) => ! [X0 : $i] : (! [X1 : $i] : ~((in @ X1 @ X0) = $true) => (emptyset = X0))))),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.49/1.29 thf(f10,plain,(
% 1.49/1.29 ~(emptysetE => (setext => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (emptyset = X0))))),
% 1.49/1.29 inference(rectify,[status(thm)],[f4])).
% 1.49/1.29 thf(f4,negated_conjecture,(
% 1.49/1.29 ~(emptysetE => (setext => ! [X2 : $i] : (! [X0 : $i] : ~(in @ X0 @ X2) => (emptyset = X2))))),
% 1.49/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.49/1.29 thf(f3,conjecture,(
% 1.49/1.29 emptysetE => (setext => ! [X2 : $i] : (! [X0 : $i] : ~(in @ X0 @ X2) => (emptyset = X2)))),
% 1.49/1.29 file('/export/starexec/sandbox/tmp/tmp.IsKlZLpBcN/DTF2THF_6185.p',emptyI)).
% 1.49/1.29 thf(f81,plain,(
% 1.49/1.29 ~spl7_2),
% 1.49/1.29 inference(avatar_contradiction_clause,[status(thm)],[f80])).
% 1.49/1.29 thf(f80,plain,(
% 1.49/1.29 $false | ~spl7_2),
% 1.49/1.29 inference(subsumption_resolution,[status(thm)],[f79,f44])).
% 1.49/1.29 thf(f44,plain,(
% 1.49/1.29 (emptyset != sK6)),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.29 thf(f79,plain,(
% 1.49/1.29 (emptyset = sK6) | ~spl7_2),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.49/1.29 thf(f77,plain,(
% 1.49/1.29 (emptyset = sK6) | ($true != $true) | ~spl7_2),
% 1.49/1.29 inference(superposition,[status(thm)],[f43,f73])).
% 1.49/1.29 thf(f73,plain,(
% 1.49/1.29 ( ! [X0 : $i] : (((in @ (sK2 @ emptyset @ X0) @ X0) = $true) | (emptyset = X0)) ) | ~spl7_2),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.49/1.29 thf(f72,plain,(
% 1.49/1.29 ( ! [X0 : $i] : ((emptyset = X0) | ($true != $true) | ((in @ (sK2 @ emptyset @ X0) @ X0) = $true)) ) | ~spl7_2),
% 1.49/1.29 inference(superposition,[status(thm)],[f65,f56])).
% 1.49/1.29 thf(f56,plain,(
% 1.49/1.29 ( ! [X0 : $i,X1 : $i] : (((in @ (sK3 @ X1 @ X0) @ X1) = $true) | (X0 = X1) | ((in @ (sK2 @ X1 @ X0) @ X0) = $true)) )),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.49/1.29 thf(f51,plain,(
% 1.49/1.29 ( ! [X0 : $i,X1 : $i] : (((in @ (sK2 @ X1 @ X0) @ X0) = $true) | ($true != $true) | ((in @ (sK3 @ X1 @ X0) @ X1) = $true) | (X0 = X1)) )),
% 1.49/1.29 inference(definition_unfolding,[status(thm)],[f37,f41])).
% 1.49/1.29 thf(f41,plain,(
% 1.49/1.29 (setext = $true)),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.29 thf(f37,plain,(
% 1.49/1.29 ( ! [X0 : $i,X1 : $i] : (((in @ (sK2 @ X1 @ X0) @ X0) = $true) | (X0 = X1) | ((in @ (sK3 @ X1 @ X0) @ X1) = $true) | (setext != $true)) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f28])).
% 1.49/1.29 thf(f28,plain,(
% 1.49/1.29 (! [X0 : $i,X1 : $i] : ((((in @ (sK2 @ X1 @ X0) @ X1) != $true) & ((in @ (sK2 @ X1 @ X0) @ X0) = $true)) | (X0 = X1) | (((in @ (sK3 @ X1 @ X0) @ X0) != $true) & ((in @ (sK3 @ X1 @ X0) @ X1) = $true))) | (setext != $true)) & ((setext = $true) | (! [X6 : $i] : (((in @ X6 @ sK5) = $true) | ((in @ X6 @ sK4) != $true)) & (sK5 != sK4) & ! [X7 : $i] : (((in @ X7 @ sK4) = $true) | ($true != (in @ X7 @ sK5)))))),
% 1.49/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f24,f27,f26,f25])).
% 1.49/1.29 thf(f25,plain,(
% 1.49/1.29 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ($true = (in @ X2 @ X0))) => (((in @ (sK2 @ X1 @ X0) @ X1) != $true) & ((in @ (sK2 @ X1 @ X0) @ X0) = $true)))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f26,plain,(
% 1.49/1.29 ! [X0 : $i,X1 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true)) => (((in @ (sK3 @ X1 @ X0) @ X0) != $true) & ((in @ (sK3 @ X1 @ X0) @ X1) = $true)))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f27,plain,(
% 1.49/1.29 ? [X4 : $i,X5 : $i] : (! [X6 : $i] : (((in @ X6 @ X5) = $true) | ($true != (in @ X6 @ X4))) & (X4 != X5) & ! [X7 : $i] : (($true = (in @ X7 @ X4)) | ((in @ X7 @ X5) != $true))) => (! [X6 : $i] : (((in @ X6 @ sK5) = $true) | ((in @ X6 @ sK4) != $true)) & (sK5 != sK4) & ! [X7 : $i] : (((in @ X7 @ sK4) = $true) | ($true != (in @ X7 @ sK5))))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f24,plain,(
% 1.49/1.29 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ($true = (in @ X2 @ X0))) | (X0 = X1) | ? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true))) | (setext != $true)) & ((setext = $true) | ? [X4 : $i,X5 : $i] : (! [X6 : $i] : (((in @ X6 @ X5) = $true) | ($true != (in @ X6 @ X4))) & (X4 != X5) & ! [X7 : $i] : (($true = (in @ X7 @ X4)) | ((in @ X7 @ X5) != $true))))),
% 1.49/1.29 inference(rectify,[status(thm)],[f23])).
% 1.49/1.29 thf(f23,plain,(
% 1.49/1.29 (! [X1 : $i,X0 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true)) | (X0 = X1) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ($true = (in @ X2 @ X0)))) | (setext != $true)) & ((setext = $true) | ? [X1 : $i,X0 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) = $true) | ((in @ X3 @ X1) != $true)) & (X0 != X1) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ($true != (in @ X2 @ X0)))))),
% 1.49/1.29 inference(nnf_transformation,[status(thm)],[f15])).
% 1.49/1.29 thf(f15,plain,(
% 1.49/1.29 ! [X1 : $i,X0 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true)) | (X0 = X1) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ($true = (in @ X2 @ X0)))) <=> (setext = $true)),
% 1.49/1.29 inference(flattening,[status(thm)],[f14])).
% 1.49/1.29 thf(f14,plain,(
% 1.49/1.29 ! [X1 : $i,X0 : $i] : (((X0 = X1) | ? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true))) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ($true = (in @ X2 @ X0)))) <=> (setext = $true)),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f7])).
% 1.49/1.29 thf(f7,plain,(
% 1.49/1.29 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X0)) => ((in @ X2 @ X1) = $true)) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => ((in @ X3 @ X0) = $true)) => (X0 = X1))) <=> (setext = $true)),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.49/1.29 thf(f6,plain,(
% 1.49/1.29 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 1.49/1.29 inference(rectify,[status(thm)],[f2])).
% 1.49/1.29 thf(f2,axiom,(
% 1.49/1.29 (setext = ! [X2 : $i,X3 : $i] : (! [X0 : $i] : ((in @ X0 @ X2) => (in @ X0 @ X3)) => (! [X0 : $i] : ((in @ X0 @ X3) => (in @ X0 @ X2)) => (X2 = X3))))),
% 1.49/1.29 file('/export/starexec/sandbox/tmp/tmp.IsKlZLpBcN/DTF2THF_6185.p',setext)).
% 1.49/1.29 thf(f65,plain,(
% 1.49/1.29 ( ! [X0 : $i] : (((in @ X0 @ emptyset) != $true)) ) | ~spl7_2),
% 1.49/1.29 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.49/1.29 thf(f64,definition,(
% 1.49/1.29 spl7_2 <=> ! [X0 : $i] : ((in @ X0 @ emptyset) != $true)),
% 1.49/1.29 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 1.49/1.29 thf(f66,plain,(
% 1.49/1.29 spl7_1 | spl7_2),
% 1.49/1.29 inference(avatar_split_clause,[status(thm)],[f57,f64,f61])).
% 1.49/1.29 thf(f57,plain,(
% 1.49/1.29 ( ! [X0 : $i,X1 : $o] : (($true = X1) | ((in @ X0 @ emptyset) != $true)) )),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.49/1.29 thf(f45,plain,(
% 1.49/1.29 ( ! [X0 : $i,X1 : $o] : (((in @ X0 @ emptyset) != $true) | ($true = X1) | ($true != $true)) )),
% 1.49/1.29 inference(definition_unfolding,[status(thm)],[f33,f42])).
% 1.49/1.29 thf(f42,plain,(
% 1.49/1.29 (emptysetE = $true)),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.29 thf(f33,plain,(
% 1.49/1.29 ( ! [X0 : $i,X1 : $o] : (($true = X1) | ((in @ X0 @ emptyset) != $true) | (emptysetE != $true)) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f22])).
% 1.49/1.29 thf(f22,plain,(
% 1.49/1.29 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | ((sK1 != $true) & ((in @ sK0 @ emptyset) = $true)))),
% 1.49/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f21,f20])).
% 1.49/1.29 thf(f20,plain,(
% 1.49/1.29 ? [X2 : $i] : (? [X3 : $o] : ($true != X3) & ((in @ X2 @ emptyset) = $true)) => (? [X3 : $o] : ($true != X3) & ((in @ sK0 @ emptyset) = $true))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f21,plain,(
% 1.49/1.29 ? [X3 : $o] : ($true != X3) => (sK1 != $true)),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f19,plain,(
% 1.49/1.29 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X2 : $i] : (? [X3 : $o] : ($true != X3) & ((in @ X2 @ emptyset) = $true)))),
% 1.49/1.29 inference(rectify,[status(thm)],[f18])).
% 1.49/1.29 thf(f18,plain,(
% 1.49/1.29 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true)))),
% 1.49/1.29 inference(nnf_transformation,[status(thm)],[f13])).
% 1.49/1.29 thf(f13,plain,(
% 1.49/1.29 ! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) <=> (emptysetE = $true)),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f9])).
% 1.49/1.29 thf(f9,plain,(
% 1.49/1.29 ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.49/1.29 thf(f8,plain,(
% 1.49/1.29 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 1.49/1.29 inference(rectify,[status(thm)],[f1])).
% 1.49/1.29 thf(f1,axiom,(
% 1.49/1.29 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 1.49/1.29 file('/export/starexec/sandbox/tmp/tmp.IsKlZLpBcN/DTF2THF_6185.p',emptysetE)).
% 1.49/1.29 % SZS output end Proof for DTF2THF_6185
% 1.49/1.29 % (6518)------------------------------
% 1.49/1.29 % (6518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (6518)Termination reason: Refutation
% 1.49/1.29
% 1.49/1.29 % (6518)Memory used [KB]: 5500
% 1.49/1.29 % (6518)Time elapsed: 0.008 s
% 1.49/1.29 % (6518)Instructions burned: 5 (million)
% 1.49/1.29 % (6518)------------------------------
% 1.49/1.29 % (6518)------------------------------
% 1.49/1.29 % (6512)Success in time 0.023 s
%------------------------------------------------------------------------------