%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU576^2 : 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 : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:22 AM UTC 2026
% Result : Theorem 1.67s 1.45s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 532 ( 153 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 511 ( 67 ~; 55 |; 38 &; 318 @)
% ( 5 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 104 ( 0 ^; 79 !; 25 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_13,type,
sK5: $i > $i > $i ).
thf(f61,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f60,f29]) ).
thf(f29,plain,
( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( powersetI = $true )
& ( $true
= ( subset @ sK0 @ sK1 ) )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true )
& ( subsetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
=> ( ( $true
= ( subset @ sK0 @ sK1 ) )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( powersetI = $true )
& ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
& ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
& ( subsetE = $true )
& ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( powersetI = $true )
=> ( ( subsetE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( powersetI
=> ( subsetE
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetI
=> ( subsetE
=> ! [X1: $i,X0: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetI
=> ( subsetE
=> ! [X1: $i,X0: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kZDQveh3Vv/DTF2THF_6466.p',powersetI1) ).
thf(f60,plain,
( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true != $true )
| ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f50,f56]) ).
thf(f56,plain,
( ( in @ ( sK5 @ sK1 @ sK0 ) @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true != $true )
| ( ( in @ ( sK5 @ sK1 @ sK0 ) @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f52,f54]) ).
thf(f54,plain,
( ( in @ ( sK5 @ sK1 @ sK0 ) @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( in @ ( sK5 @ sK1 @ sK0 ) @ sK0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f29,f49]) ).
thf(f49,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( in @ ( sK5 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK5 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f31]) ).
thf(f31,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK5 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ ( sK5 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( in @ ( sK5 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ( ! [X5: $i] :
( ( $true
= ( in @ X5 @ sK7 ) )
| ( ( in @ X5 @ sK6 )
!= $true ) )
& ( ( in @ sK6 @ ( powerset @ sK7 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f24,f26,f25]) ).
thf(f25,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( ( in @ ( sK5 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( in @ ( sK5 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true ) )
& ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) ) )
=> ( ! [X5: $i] :
( ( $true
= ( in @ X5 @ sK7 ) )
| ( ( in @ X5 @ sK6 )
!= $true ) )
& ( ( in @ sK6 @ ( powerset @ sK7 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true ) )
& ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
<=> ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( powersetI = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( powersetI
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kZDQveh3Vv/DTF2THF_6466.p',powersetI) ).
thf(f52,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK0 )
!= $true )
| ( ( in @ X0 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK0 )
!= $true )
| ( ( in @ X0 @ sK1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f48,f30]) ).
thf(f30,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f48,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X3 @ X4 ) )
| ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( $true
!= ( subset @ X3 @ X4 ) )
| ( ( in @ X5 @ X4 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f28]) ).
thf(f28,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f32,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( $true
!= ( subset @ X3 @ X4 ) )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( subsetE = $true )
| ( ( $true
= ( in @ sK4 @ sK2 ) )
& ( ( in @ sK4 @ sK3 )
!= $true )
& ( $true
= ( subset @ sK2 @ sK3 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( $true
!= ( subset @ X3 @ X4 ) ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f20,f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true ) )
=> ( ( $true
= ( in @ sK4 @ sK2 ) )
& ( ( in @ sK4 @ sK3 )
!= $true )
& ( $true
= ( subset @ sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( $true
!= ( subset @ X3 @ X4 ) ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( subsetE = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( subset @ X2 @ X0 ) ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( subset @ X2 @ X0 ) ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( subset @ X2 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ X0 ) )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( in @ X1 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subsetE
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kZDQveh3Vv/DTF2THF_6466.p',subsetE) ).
thf(f50,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK5 @ X1 @ X0 ) @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK5 @ X1 @ X0 ) @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f39,f31]) ).
thf(f39,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK5 @ X1 @ X0 ) @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU576^2 : 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
% 0.13/0.32 % Computer : n028.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:27:27 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.47 ---- Original DTF file ---
% 0.18/0.47 thf(spec,logic,$$dhol).
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 % File : SEU576^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.47 % Domain : Set Theory
% 0.18/0.47 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.18/0.47 % Version : Especial > Reduced > Especial.
% 0.18/0.47 % English : (! A:i.! B:i.subset B A -> in B (powerset A))
% 0.18/0.47
% 0.18/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.47 % Source : [Bro08]
% 0.18/0.47 % Names : ZFC078l [Bro08]
% 0.18/0.47
% 0.18/0.47 % Status : Theorem
% 0.18/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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
% 0.18/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.18/0.47 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.18/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.18/0.47 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 18 @)
% 0.18/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.18/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.18/0.47 % Number of types : 2 ( 0 usr)
% 0.18/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.18/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.18/0.47 % SPC : TH0_THM_EQU_NAR
% 0.18/0.47
% 0.18/0.47 % Comments : http://mathgate.info/detsetitem.php?id=155
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 thf(in_type,type,
% 0.18/0.47 in: $i > $i > $o ).
% 0.18/0.47
% 0.18/0.47 thf(powerset_type,type,
% 0.18/0.47 powerset: $i > $i ).
% 0.18/0.47
% 0.18/0.47 thf(powersetI_type,type,
% 0.18/0.47 powersetI: $o ).
% 0.18/0.47
% 0.18/0.47 thf(powersetI,definition,
% 0.18/0.47 ( powersetI
% 0.18/0.47 = ( ! [A: $i,B: $i] :
% 0.18/0.47 ( ! [Xx: $i] :
% 0.18/0.47 ( ( in @ Xx @ B )
% 0.18/0.47 => ( in @ Xx @ A ) )
% 0.18/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(subset_type,type,
% 0.18/0.47 subset: $i > $i > $o ).
% 0.18/0.47
% 0.18/0.47 thf(subsetE_type,type,
% 0.18/0.47 subsetE: $o ).
% 0.18/0.47
% 0.18/0.47 thf(subsetE,definition,
% 0.18/0.47 ( subsetE
% 0.18/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.47 ( ( subset @ A @ B )
% 0.18/0.47 => ( ( in @ Xx @ A )
% 0.18/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(powersetI1,conjecture,
% 0.18/0.47 ( powersetI
% 0.18/0.47 => ( subsetE
% 0.18/0.47 => ! [A: $i,B: $i] :
% 0.18/0.47 ( ( subset @ B @ A )
% 0.18/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 ------------------------
% 1.67/1.41 ---- Embedded in THF ---
% 1.67/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.41 %%% Generated on Tue Feb 24 12:27:28 EST 2026
% 1.67/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.41 %%% Logic specification used:
% 1.67/1.41 %%% thf(spec, logic, $$dhol).
% 1.67/1.41
% 1.67/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kZDQveh3Vv/DTF2DTF6466.p
% See solution above
% 1.67/1.41 ------------------------
% 1.67/1.42 ---- Cleaned THF ---
% 1.67/1.42 thf(in_type,type,
% 1.67/1.42 in: $i > $i > $o ).
% 1.67/1.42
% 1.67/1.42 thf(powerset_type,type,
% 1.67/1.42 powerset: $i > $i ).
% 1.67/1.42
% 1.67/1.42 thf(powersetI_type,type,
% 1.67/1.42 powersetI: $o ).
% 1.67/1.42
% 1.67/1.42 thf(powersetI,definition,
% 1.67/1.42 ( powersetI
% 1.67/1.42 = ( ! [A: $i,B: $i] :
% 1.67/1.42 ( ! [Xx: $i] :
% 1.67/1.42 ( ( in @ Xx @ B )
% 1.67/1.42 => ( in @ Xx @ A ) )
% 1.67/1.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.67/1.42
% 1.67/1.42 thf(subset_type,type,
% 1.67/1.42 subset: $i > $i > $o ).
% 1.67/1.42
% 1.67/1.42 thf(subsetE_type,type,
% 1.67/1.42 subsetE: $o ).
% 1.67/1.42
% 1.67/1.42 thf(subsetE,definition,
% 1.67/1.42 ( subsetE
% 1.67/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.67/1.42 ( ( subset @ A @ B )
% 1.67/1.42 => ( ( in @ Xx @ A )
% 1.67/1.42 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.67/1.42
% 1.67/1.42 thf(powersetI1,conjecture,
% 1.67/1.42 ( powersetI
% 1.67/1.42 => ( subsetE
% 1.67/1.42 => ! [A: $i,B: $i] :
% 1.67/1.42 ( ( subset @ B @ A )
% 1.67/1.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.67/1.42 ------------------------
% 1.67/1.44 % (6594)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6466 for (3000ds/2Mi)
% 1.67/1.44 % (6593)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_6466 for (3000ds/27Mi)
% 1.67/1.44 % (6596)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_6466 for (3000ds/275Mi)
% 1.67/1.44 % (6595)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_6466 for (3000ds/2Mi)
% 1.67/1.44 % (6592)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_6466 for (3000ds/4Mi)
% 1.67/1.44 % (6591)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6466 for (3000ds/183Mi)
% 1.67/1.44 % (6597)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6466 for (3000ds/18Mi)
% 1.67/1.44 % (6594)Instruction limit reached!
% 1.67/1.44 % (6594)------------------------------
% 1.67/1.44 % (6594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (6594)Termination reason: Unknown
% 1.67/1.44 % (6594)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (6594)Memory used [KB]: 5500
% 1.67/1.44 % (6594)Time elapsed: 0.003 s
% 1.67/1.44 % (6594)Instructions burned: 2 (million)
% 1.67/1.44 % (6594)------------------------------
% 1.67/1.44 % (6594)------------------------------
% 1.67/1.44 % (6595)Instruction limit reached!
% 1.67/1.44 % (6595)------------------------------
% 1.67/1.44 % (6595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (6595)Termination reason: Unknown
% 1.67/1.44 % (6595)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (6595)Memory used [KB]: 5500
% 1.67/1.44 % (6595)Time elapsed: 0.003 s
% 1.67/1.44 % (6595)Instructions burned: 3 (million)
% 1.67/1.44 % (6595)------------------------------
% 1.67/1.44 % (6595)------------------------------
% 1.67/1.44 % (6592)Instruction limit reached!
% 1.67/1.44 % (6592)------------------------------
% 1.67/1.44 % (6592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (6592)Termination reason: Unknown
% 1.67/1.44 % (6592)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (6592)Memory used [KB]: 5500
% 1.67/1.44 % (6592)Time elapsed: 0.004 s
% 1.67/1.44 % (6592)Instructions burned: 4 (million)
% 1.67/1.44 % (6592)------------------------------
% 1.67/1.44 % (6592)------------------------------
% 1.67/1.44 % (6597)First to succeed.
% 1.67/1.44 % (6596)Also succeeded, but the first one will report.
% 1.67/1.45 % (6597)Refutation found. Thanks to Tanya!
% 1.67/1.45 % SZS status Theorem for DTF2THF_6466
% 1.67/1.45 % SZS output start Proof for DTF2THF_6466
% 1.67/1.45 thf(func_def_0, type, in: $i > $i > $o).
% 1.67/1.45 thf(func_def_1, type, powerset: $i > $i).
% 1.67/1.45 thf(func_def_4, type, subset: $i > $i > $o).
% 1.67/1.45 thf(func_def_13, type, sK5: $i > $i > $i).
% 1.67/1.45 thf(f61,plain,(
% 1.67/1.45 $false),
% 1.67/1.45 inference(subsumption_resolution,[status(thm)],[f60,f29])).
% 1.67/1.45 thf(f29,plain,(
% 1.67/1.45 ((in @ sK0 @ (powerset @ sK1)) != $true)),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.45 thf(f18,plain,(
% 1.67/1.45 (powersetI = $true) & (($true = (subset @ sK0 @ sK1)) & ((in @ sK0 @ (powerset @ sK1)) != $true)) & (subsetE = $true)),
% 1.67/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17])).
% 1.67/1.45 thf(f17,plain,(
% 1.67/1.45 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((in @ X0 @ (powerset @ X1)) != $true)) => (($true = (subset @ sK0 @ sK1)) & ((in @ sK0 @ (powerset @ sK1)) != $true))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f16,plain,(
% 1.67/1.45 (powersetI = $true) & ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((in @ X0 @ (powerset @ X1)) != $true)) & (subsetE = $true)),
% 1.67/1.45 inference(flattening,[status(thm)],[f15])).
% 1.67/1.45 thf(f15,plain,(
% 1.67/1.45 (? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((in @ X0 @ (powerset @ X1)) != $true)) & (subsetE = $true)) & (powersetI = $true)),
% 1.67/1.45 inference(ennf_transformation,[status(thm)],[f7])).
% 1.67/1.45 thf(f7,plain,(
% 1.67/1.45 ~((powersetI = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => ((in @ X0 @ (powerset @ X1)) = $true))))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f6])).
% 1.67/1.45 thf(f6,plain,(
% 1.67/1.45 ~(powersetI => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1)))))),
% 1.67/1.45 inference(rectify,[status(thm)],[f4])).
% 1.67/1.45 thf(f4,negated_conjecture,(
% 1.67/1.45 ~(powersetI => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0)))))),
% 1.67/1.45 inference(negated_conjecture,[status(cth)],[f3])).
% 1.67/1.45 thf(f3,conjecture,(
% 1.67/1.45 powersetI => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 1.67/1.45 file('/export/starexec/sandbox/tmp/tmp.kZDQveh3Vv/DTF2THF_6466.p',powersetI1)).
% 1.67/1.45 thf(f60,plain,(
% 1.67/1.45 ((in @ sK0 @ (powerset @ sK1)) = $true)),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.67/1.45 thf(f57,plain,(
% 1.67/1.45 ($true != $true) | ((in @ sK0 @ (powerset @ sK1)) = $true)),
% 1.67/1.45 inference(superposition,[status(thm)],[f50,f56])).
% 1.67/1.45 thf(f56,plain,(
% 1.67/1.45 ((in @ (sK5 @ sK1 @ sK0) @ sK1) = $true)),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.67/1.45 thf(f55,plain,(
% 1.67/1.45 ($true != $true) | ((in @ (sK5 @ sK1 @ sK0) @ sK1) = $true)),
% 1.67/1.45 inference(superposition,[status(thm)],[f52,f54])).
% 1.67/1.45 thf(f54,plain,(
% 1.67/1.45 ((in @ (sK5 @ sK1 @ sK0) @ sK0) = $true)),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.67/1.45 thf(f53,plain,(
% 1.67/1.45 ((in @ (sK5 @ sK1 @ sK0) @ sK0) = $true) | ($true != $true)),
% 1.67/1.45 inference(superposition,[status(thm)],[f29,f49])).
% 1.67/1.45 thf(f49,plain,(
% 1.67/1.45 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) | ((in @ (sK5 @ X1 @ X0) @ X0) = $true)) )),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.67/1.45 thf(f45,plain,(
% 1.67/1.45 ( ! [X0 : $i,X1 : $i] : (((in @ (sK5 @ X1 @ X0) @ X0) = $true) | ($true != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) )),
% 1.67/1.45 inference(definition_unfolding,[status(thm)],[f38,f31])).
% 1.67/1.45 thf(f31,plain,(
% 1.67/1.45 (powersetI = $true)),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.45 thf(f38,plain,(
% 1.67/1.45 ( ! [X0 : $i,X1 : $i] : (((in @ (sK5 @ X1 @ X0) @ X0) = $true) | ((in @ X0 @ (powerset @ X1)) = $true) | (powersetI != $true)) )),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f27])).
% 1.67/1.45 thf(f27,plain,(
% 1.67/1.45 (! [X0 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X0) @ X1) != $true) & ((in @ (sK5 @ X1 @ X0) @ X0) = $true)) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | (! [X5 : $i] : (($true = (in @ X5 @ sK7)) | ((in @ X5 @ sK6) != $true)) & ((in @ sK6 @ (powerset @ sK7)) != $true)))),
% 1.67/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f24,f26,f25])).
% 1.67/1.45 thf(f25,plain,(
% 1.67/1.45 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) => (((in @ (sK5 @ X1 @ X0) @ X1) != $true) & ((in @ (sK5 @ X1 @ X0) @ X0) = $true)))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f26,plain,(
% 1.67/1.45 ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true)) & ($true != (in @ X3 @ (powerset @ X4)))) => (! [X5 : $i] : (($true = (in @ X5 @ sK7)) | ((in @ X5 @ sK6) != $true)) & ((in @ sK6 @ (powerset @ sK7)) != $true))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f24,plain,(
% 1.67/1.45 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true)) & ($true != (in @ X3 @ (powerset @ X4)))))),
% 1.67/1.45 inference(rectify,[status(thm)],[f23])).
% 1.67/1.45 thf(f23,plain,(
% 1.67/1.45 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) & ((in @ X0 @ (powerset @ X1)) != $true)))),
% 1.67/1.45 inference(nnf_transformation,[status(thm)],[f12])).
% 1.67/1.45 thf(f12,plain,(
% 1.67/1.45 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((in @ X0 @ (powerset @ X1)) = $true)) <=> (powersetI = $true)),
% 1.67/1.45 inference(ennf_transformation,[status(thm)],[f9])).
% 1.67/1.45 thf(f9,plain,(
% 1.67/1.45 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((in @ X0 @ (powerset @ X1)) = $true))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f8])).
% 1.67/1.45 thf(f8,plain,(
% 1.67/1.45 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 1.67/1.45 inference(rectify,[status(thm)],[f1])).
% 1.67/1.45 thf(f1,axiom,(
% 1.67/1.45 (powersetI = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 1.67/1.45 file('/export/starexec/sandbox/tmp/tmp.kZDQveh3Vv/DTF2THF_6466.p',powersetI)).
% 1.67/1.45 thf(f52,plain,(
% 1.67/1.45 ( ! [X0 : $i] : (((in @ X0 @ sK0) != $true) | ((in @ X0 @ sK1) = $true)) )),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.67/1.45 thf(f51,plain,(
% 1.67/1.45 ( ! [X0 : $i] : (((in @ X0 @ sK0) != $true) | ((in @ X0 @ sK1) = $true) | ($true != $true)) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f48,f30])).
% 1.67/1.45 thf(f30,plain,(
% 1.67/1.45 ($true = (subset @ sK0 @ sK1))),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.45 thf(f48,plain,(
% 1.67/1.45 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X3 @ X4)) | ((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true)) )),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.67/1.45 thf(f43,plain,(
% 1.67/1.45 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ($true != (subset @ X3 @ X4)) | ((in @ X5 @ X4) = $true) | ($true != $true)) )),
% 1.67/1.45 inference(definition_unfolding,[status(thm)],[f32,f28])).
% 1.67/1.45 thf(f28,plain,(
% 1.67/1.45 (subsetE = $true)),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.45 thf(f32,plain,(
% 1.67/1.45 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true) | ($true != (subset @ X3 @ X4)) | (subsetE != $true)) )),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.45 thf(f22,plain,(
% 1.67/1.45 ((subsetE = $true) | (($true = (in @ sK4 @ sK2)) & ((in @ sK4 @ sK3) != $true) & ($true = (subset @ sK2 @ sK3)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true) | ($true != (subset @ X3 @ X4))) | (subsetE != $true))),
% 1.67/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f20,f21])).
% 1.67/1.45 thf(f21,plain,(
% 1.67/1.45 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true) & ((subset @ X0 @ X1) = $true)) => (($true = (in @ sK4 @ sK2)) & ((in @ sK4 @ sK3) != $true) & ($true = (subset @ sK2 @ sK3)))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f20,plain,(
% 1.67/1.45 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true) & ((subset @ X0 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true) | ($true != (subset @ X3 @ X4))) | (subsetE != $true))),
% 1.67/1.45 inference(rectify,[status(thm)],[f19])).
% 1.67/1.45 thf(f19,plain,(
% 1.67/1.45 ((subsetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ X2)) & ((in @ X1 @ X0) != $true) & ($true = (subset @ X2 @ X0)))) & (! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ X2)) | ((in @ X1 @ X0) = $true) | ($true != (subset @ X2 @ X0))) | (subsetE != $true))),
% 1.67/1.45 inference(nnf_transformation,[status(thm)],[f14])).
% 1.67/1.45 thf(f14,plain,(
% 1.67/1.45 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ X2)) | ((in @ X1 @ X0) = $true) | ($true != (subset @ X2 @ X0)))),
% 1.67/1.45 inference(flattening,[status(thm)],[f13])).
% 1.67/1.45 thf(f13,plain,(
% 1.67/1.45 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0) = $true) | ($true != (in @ X1 @ X2))) | ($true != (subset @ X2 @ X0)))),
% 1.67/1.45 inference(ennf_transformation,[status(thm)],[f11])).
% 1.67/1.45 thf(f11,plain,(
% 1.67/1.45 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ X0)) => (($true = (in @ X1 @ X2)) => ((in @ X1 @ X0) = $true)))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.45 thf(f10,plain,(
% 1.67/1.45 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0))))),
% 1.67/1.45 inference(rectify,[status(thm)],[f2])).
% 1.67/1.45 thf(f2,axiom,(
% 1.67/1.45 (subsetE = ! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.67/1.45 file('/export/starexec/sandbox/tmp/tmp.kZDQveh3Vv/DTF2THF_6466.p',subsetE)).
% 1.67/1.45 thf(f50,plain,(
% 1.67/1.45 ( ! [X0 : $i,X1 : $i] : (((in @ (sK5 @ X1 @ X0) @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) )),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.67/1.45 thf(f44,plain,(
% 1.67/1.45 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK5 @ X1 @ X0) @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) )),
% 1.67/1.45 inference(definition_unfolding,[status(thm)],[f39,f31])).
% 1.67/1.45 thf(f39,plain,(
% 1.67/1.45 ( ! [X0 : $i,X1 : $i] : (((in @ (sK5 @ X1 @ X0) @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true) | (powersetI != $true)) )),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f27])).
% 1.67/1.45 % SZS output end Proof for DTF2THF_6466
% 1.67/1.45 % (6597)------------------------------
% 1.67/1.45 % (6597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (6597)Termination reason: Refutation
% 1.67/1.45
% 1.67/1.45 % (6597)Memory used [KB]: 5500
% 1.67/1.45 % (6597)Time elapsed: 0.006 s
% 1.67/1.45 % (6597)Instructions burned: 4 (million)
% 1.67/1.45 % (6597)------------------------------
% 1.67/1.45 % (6597)------------------------------
% 1.67/1.45 % (6590)Success in time 0.02 s
%------------------------------------------------------------------------------