%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU580^2 : 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 : n019.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 09:35:24 AM UTC 2026
% Result : Theorem 1.54s 1.32s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 436 ( 130 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 518 ( 58 ~; 47 |; 28 &; 360 @)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 139 ( 25 ^; 89 !; 25 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_11,type,
sK1: $i > $o ).
thf(func_def_13,type,
sK3: $i > $o ).
thf(func_def_17,type,
sK7: $i > $i > $i ).
thf(func_def_19,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f60,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
$true != $true,
inference(superposition,[status(thm)],[f44,f57]) ).
thf(f57,plain,
! [X0: $i,X1: $i > $o] :
( ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: $i,X1: $i > $o] :
( ( ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: $i,X1: $i > $o] :
( ( ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f45,f53]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ ( sK7 @ ( dsetconstr @ X0 @ X1 ) @ X2 ) @ X0 )
= $true )
| ( ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X2 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ ( sK7 @ ( dsetconstr @ X0 @ X1 ) @ X2 ) @ X0 )
= $true )
| ( ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X2 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f48,f46]) ).
thf(f46,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f34,f32]) ).
thf(f32,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( ( in
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK3 @ Y0 ) )
@ ( powerset @ sK4 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f14,f20]) ).
thf(f20,plain,
( ? [X0: $i > $o,X1: $i] :
( ( in
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( powerset @ X1 ) )
!= $true )
=> ( ( in
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK3 @ Y0 ) )
@ ( powerset @ sK4 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( powersetI = $true )
& ( dsetconstrEL = $true )
& ? [X0: $i > $o,X1: $i] :
( ( in
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( powerset @ X1 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X0: $i > $o,X1: $i] :
( ( in
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( powerset @ X1 ) )
!= $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( powersetI = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( in
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( dsetconstrEL
=> ( powersetI
=> ! [X0: $i > $o,X1: $i] :
( in
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
@ ( powerset @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrEL
=> ( powersetI
=> ! [X1: $i > $o,X0: $i] :
( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrEL
=> ( powersetI
=> ! [X1: $i > $o,X0: $i] :
( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8xE8RzS9cK/DTF2THF_5427.p',sepInPowerset) ).
thf(f34,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( powersetI = $true )
| ( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK6 ) )
| ( ( in @ X2 @ sK5 )
= $true ) )
& ( ( in @ sK6 @ ( powerset @ sK5 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true ) )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f23,f25,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
=> ( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK6 ) )
| ( ( in @ X2 @ sK5 )
= $true ) )
& ( ( in @ sK6 @ ( powerset @ sK5 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
!= $true ) )
=> ( ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
!= $true ) )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( powersetI = $true )
<=> ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( powersetI = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( powersetI
= ( ! [X0: $i,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X4 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8xE8RzS9cK/DTF2THF_5427.p',powersetI) ).
thf(f48,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5 @ ( dsetconstr @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true != $true )
| ( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f27,f31]) ).
thf(f31,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f27,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( dsetconstrEL = $true )
| ( ( $true
= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) )
& ( ( in @ sK2 @ sK0 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( $true
= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) )
& ( ( in @ sK2 @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox/tmp/tmp.8xE8RzS9cK/DTF2THF_5427.p',dsetconstrEL) ).
thf(f45,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f32]) ).
thf(f33,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f44,plain,
( ( in @ ( dsetconstr @ sK4 @ sK3 ) @ ( powerset @ sK4 ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( in
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK3 @ Y0 ) )
@ ( powerset @ sK4 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU580^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n019.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:27:39 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.38 thf(spec,logic,$$dhol).
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 % File : SEU580^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.38 % Domain : Set Theory
% 0.16/0.38 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.16/0.38 % Version : Especial > Reduced > Especial.
% 0.16/0.38 % English : (! A:i.! phi:i>o.in (dsetconstr A (^ x:i.phi x)) (powerset A))
% 0.16/0.38
% 0.16/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.38 % Source : [Bro08]
% 0.16/0.38 % Names : ZFC082l [Bro08]
% 0.16/0.38
% 0.16/0.38 % Status : Theorem
% 0.16/0.38 % Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.16/0.38 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.16/0.38 % Number of atoms : 12 ( 2 equ; 0 cnn)
% 0.16/0.38 % Maximal formula atoms : 3 ( 4 avg)
% 0.16/0.38 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 20 @)
% 0.16/0.38 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.16/0.38 % Maximal formula depth : 10 ( 4 avg)
% 0.16/0.38 % Number of types : 2 ( 0 usr)
% 0.16/0.38 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.16/0.38 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.16/0.38 % Number of variables : 10 ( 2 ^; 8 !; 0 ?; 10 :)
% 0.16/0.38 % SPC : TH0_THM_EQU_NAR
% 0.16/0.38
% 0.16/0.38 % Comments : http://mathgate.info/detsetitem.php?id=258
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 thf(in_type,type,
% 0.16/0.38 in: $i > $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(powerset_type,type,
% 0.16/0.38 powerset: $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstr_type,type,
% 0.16/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrEL_type,type,
% 0.16/0.38 dsetconstrEL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrEL,definition,
% 0.16/0.38 ( dsetconstrEL
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powersetI_type,type,
% 0.16/0.38 powersetI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetI,definition,
% 0.16/0.38 ( powersetI
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) )
% 0.16/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sepInPowerset,conjecture,
% 0.16/0.38 ( dsetconstrEL
% 0.16/0.38 => ( powersetI
% 0.16/0.38 => ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( in
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 @ ( powerset @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 ------------------------
% 1.36/1.28 ---- Embedded in THF ---
% 1.36/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.28 %%% Generated on Tue Feb 24 12:27:40 EST 2026
% 1.36/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.28 %%% Logic specification used:
% 1.36/1.28 %%% thf(spec, logic, $$dhol).
% 1.36/1.28
% 1.36/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8xE8RzS9cK/DTF2DTF5427.p
% See solution above
% 1.36/1.28 ------------------------
% 1.36/1.29 ---- Cleaned THF ---
% 1.36/1.29 thf(in_type,type,
% 1.36/1.29 in: $i > $i > $o ).
% 1.36/1.29
% 1.36/1.29 thf(powerset_type,type,
% 1.36/1.29 powerset: $i > $i ).
% 1.36/1.29
% 1.36/1.29 thf(dsetconstr_type,type,
% 1.36/1.29 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.36/1.29
% 1.36/1.29 thf(dsetconstrEL_type,type,
% 1.36/1.29 dsetconstrEL: $o ).
% 1.36/1.29
% 1.36/1.29 thf(dsetconstrEL,definition,
% 1.36/1.29 ( dsetconstrEL
% 1.36/1.29 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.36/1.29 ( ( in @ Xx
% 1.36/1.29 @ ( dsetconstr @ A
% 1.36/1.29 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.36/1.29 => ( in @ Xx @ A ) ) ) ) ).
% 1.36/1.29
% 1.36/1.29 thf(powersetI_type,type,
% 1.36/1.29 powersetI: $o ).
% 1.36/1.29
% 1.36/1.29 thf(powersetI,definition,
% 1.36/1.29 ( powersetI
% 1.36/1.29 = ( ! [A: $i,B: $i] :
% 1.36/1.29 ( ! [Xx: $i] :
% 1.36/1.29 ( ( in @ Xx @ B )
% 1.36/1.29 => ( in @ Xx @ A ) )
% 1.36/1.29 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.36/1.29
% 1.36/1.29 thf(sepInPowerset,conjecture,
% 1.36/1.29 ( dsetconstrEL
% 1.36/1.29 => ( powersetI
% 1.36/1.29 => ! [A: $i,Xphi: $i > $o] :
% 1.36/1.29 ( in
% 1.36/1.29 @ ( dsetconstr @ A
% 1.36/1.29 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.36/1.29 @ ( powerset @ A ) ) ) ) ).
% 1.36/1.29 ------------------------
% 1.54/1.31 % (5527)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5427 for (2999ds/2Mi)
% 1.54/1.31 % (5528)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_5427 for (2999ds/2Mi)
% 1.54/1.31 % (5524)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5427 for (2999ds/183Mi)
% 1.54/1.31 % (5526)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_5427 for (2999ds/27Mi)
% 1.54/1.31 % (5525)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_5427 for (2999ds/4Mi)
% 1.54/1.31 % (5529)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_5427 for (2999ds/275Mi)
% 1.54/1.31 % (5530)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5427 for (2999ds/18Mi)
% 1.54/1.31 % (5527)Instruction limit reached!
% 1.54/1.31 % (5527)------------------------------
% 1.54/1.31 % (5527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.31 % (5527)Termination reason: Unknown
% 1.54/1.31 % (5527)Termination phase: Saturation
% 1.54/1.31 % (5528)Instruction limit reached!
% 1.54/1.31 % (5528)------------------------------
% 1.54/1.31 % (5528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.31 % (5528)Termination reason: Unknown
% 1.54/1.31 % (5528)Termination phase: Saturation
% 1.54/1.31
% 1.54/1.31 % (5528)Memory used [KB]: 895
% 1.54/1.31 % (5528)Time elapsed: 0.003 s
% 1.54/1.31 % (5528)Instructions burned: 2 (million)
% 1.54/1.31 % (5528)------------------------------
% 1.54/1.31 % (5528)------------------------------
% 1.54/1.31
% 1.54/1.31 % (5527)Memory used [KB]: 5500
% 1.54/1.31 % (5527)Time elapsed: 0.003 s
% 1.54/1.31 % (5527)Instructions burned: 2 (million)
% 1.54/1.31 % (5527)------------------------------
% 1.54/1.31 % (5527)------------------------------
% 1.54/1.31 % (5525)Instruction limit reached!
% 1.54/1.31 % (5525)------------------------------
% 1.54/1.31 % (5525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.31 % (5525)Termination reason: Unknown
% 1.54/1.31 % (5525)Termination phase: Saturation
% 1.54/1.31
% 1.54/1.31 % (5525)Memory used [KB]: 5500
% 1.54/1.31 % (5525)Time elapsed: 0.004 s
% 1.54/1.31 % (5525)Instructions burned: 4 (million)
% 1.54/1.31 % (5525)------------------------------
% 1.54/1.31 % (5525)------------------------------
% 1.54/1.31 % (5529)First to succeed.
% 1.54/1.32 % (5530)Also succeeded, but the first one will report.
% 1.54/1.32 % (5524)Also succeeded, but the first one will report.
% 1.54/1.32 % (5529)Refutation found. Thanks to Tanya!
% 1.54/1.32 % SZS status Theorem for DTF2THF_5427
% 1.54/1.32 % SZS output start Proof for DTF2THF_5427
% 1.54/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.54/1.32 thf(func_def_1, type, powerset: $i > $i).
% 1.54/1.32 thf(func_def_2, type, dsetconstr: $i > ($i > $o) > $i).
% 1.54/1.32 thf(func_def_11, type, sK1: $i > $o).
% 1.54/1.32 thf(func_def_13, type, sK3: $i > $o).
% 1.54/1.32 thf(func_def_17, type, sK7: $i > $i > $i).
% 1.54/1.32 thf(func_def_19, type, ph9: !>[X0: $tType]:(X0)).
% 1.54/1.32 thf(f60,plain,(
% 1.54/1.32 $false),
% 1.54/1.32 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.54/1.32 thf(f59,plain,(
% 1.54/1.32 ($true != $true)),
% 1.54/1.32 inference(superposition,[status(thm)],[f44,f57])).
% 1.54/1.32 thf(f57,plain,(
% 1.54/1.32 ( ! [X0 : $i,X1 : $i > $o] : (((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0)) = $true)) )),
% 1.54/1.32 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.54/1.32 thf(f56,plain,(
% 1.54/1.32 ( ! [X0 : $i,X1 : $i > $o] : (((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0)) = $true) | ($true != $true)) )),
% 1.54/1.32 inference(duplicate_literal_removal,[status(thm)],[f54])).
% 1.54/1.32 thf(f54,plain,(
% 1.54/1.32 ( ! [X0 : $i,X1 : $i > $o] : (((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0)) = $true) | ((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0)) = $true) | ($true != $true)) )),
% 1.54/1.32 inference(superposition,[status(thm)],[f45,f53])).
% 1.54/1.32 thf(f53,plain,(
% 1.54/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ (sK7 @ (dsetconstr @ X0 @ X1) @ X2) @ X0) = $true) | ((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X2)) = $true)) )),
% 1.54/1.32 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.54/1.32 thf(f52,plain,(
% 1.54/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ (sK7 @ (dsetconstr @ X0 @ X1) @ X2) @ X0) = $true) | ((in @ (dsetconstr @ X0 @ X1) @ (powerset @ X2)) = $true) | ($true != $true)) )),
% 1.54/1.32 inference(superposition,[status(thm)],[f48,f46])).
% 1.54/1.32 thf(f46,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X4) = $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.54/1.32 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.54/1.32 thf(f42,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ X4 @ (powerset @ X3)) = $true) | ((in @ (sK7 @ X4 @ X3) @ X4) = $true)) )),
% 1.54/1.32 inference(definition_unfolding,[status(thm)],[f34,f32])).
% 1.54/1.32 thf(f32,plain,(
% 1.54/1.32 (powersetI = $true)),
% 1.54/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.54/1.32 thf(f21,plain,(
% 1.54/1.32 (powersetI = $true) & (dsetconstrEL = $true) & ((in @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK3 @ Y0))) @ (powerset @ sK4)) != $true)),
% 1.54/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f14,f20])).
% 1.54/1.32 thf(f20,plain,(
% 1.54/1.32 ? [X0 : $i > $o,X1 : $i] : ((in @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (powerset @ X1)) != $true) => ((in @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK3 @ Y0))) @ (powerset @ sK4)) != $true)),
% 1.54/1.32 introduced(definition,[],[choice_axiom])).
% 1.54/1.32 thf(f14,plain,(
% 1.54/1.32 (powersetI = $true) & (dsetconstrEL = $true) & ? [X0 : $i > $o,X1 : $i] : ((in @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (powerset @ X1)) != $true)),
% 1.54/1.32 inference(flattening,[status(thm)],[f13])).
% 1.54/1.32 thf(f13,plain,(
% 1.54/1.32 (? [X0 : $i > $o,X1 : $i] : ((in @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (powerset @ X1)) != $true) & (powersetI = $true)) & (dsetconstrEL = $true)),
% 1.54/1.32 inference(ennf_transformation,[status(thm)],[f7])).
% 1.54/1.32 thf(f7,plain,(
% 1.54/1.32 ~((dsetconstrEL = $true) => ((powersetI = $true) => ! [X0 : $i > $o,X1 : $i] : ((in @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (powerset @ X1)) = $true)))),
% 1.54/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.54/1.32 thf(f6,plain,(
% 1.54/1.32 ~(dsetconstrEL => (powersetI => ! [X0 : $i > $o,X1 : $i] : (in @ (dsetconstr @ X1 @ (^[X2 : $i] : (X0 @ X2))) @ (powerset @ X1))))),
% 1.54/1.32 inference(rectify,[status(thm)],[f4])).
% 1.54/1.32 thf(f4,negated_conjecture,(
% 1.54/1.32 ~(dsetconstrEL => (powersetI => ! [X1 : $i > $o,X0 : $i] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ (powerset @ X0))))),
% 1.54/1.32 inference(negated_conjecture,[status(cth)],[f3])).
% 1.54/1.32 thf(f3,conjecture,(
% 1.54/1.32 dsetconstrEL => (powersetI => ! [X1 : $i > $o,X0 : $i] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ (powerset @ X0)))),
% 1.54/1.32 file('/export/starexec/sandbox/tmp/tmp.8xE8RzS9cK/DTF2THF_5427.p',sepInPowerset)).
% 1.54/1.32 thf(f34,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X4) = $true) | ((in @ X4 @ (powerset @ X3)) = $true) | (powersetI != $true)) )),
% 1.54/1.32 inference(cnf_transformation,[status(thm)],[f26])).
% 1.54/1.32 thf(f26,plain,(
% 1.54/1.32 ((powersetI = $true) | (! [X2 : $i] : (($true != (in @ X2 @ sK6)) | ((in @ X2 @ sK5) = $true)) & ((in @ sK6 @ (powerset @ sK5)) != $true))) & (! [X3 : $i,X4 : $i] : ((((in @ (sK7 @ X4 @ X3) @ X4) = $true) & ((in @ (sK7 @ X4 @ X3) @ X3) != $true)) | ((in @ X4 @ (powerset @ X3)) = $true)) | (powersetI != $true))),
% 1.54/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f23,f25,f24])).
% 1.54/1.32 thf(f24,plain,(
% 1.54/1.32 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) = $true)) & ((in @ X1 @ (powerset @ X0)) != $true)) => (! [X2 : $i] : (($true != (in @ X2 @ sK6)) | ((in @ X2 @ sK5) = $true)) & ((in @ sK6 @ (powerset @ sK5)) != $true))),
% 1.54/1.32 introduced(definition,[],[choice_axiom])).
% 1.54/1.32 thf(f25,plain,(
% 1.54/1.32 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) != $true)) => (((in @ (sK7 @ X4 @ X3) @ X4) = $true) & ((in @ (sK7 @ X4 @ X3) @ X3) != $true)))),
% 1.54/1.32 introduced(definition,[],[choice_axiom])).
% 1.54/1.32 thf(f23,plain,(
% 1.54/1.32 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) = $true)) & ((in @ X1 @ (powerset @ X0)) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) != $true)) | ((in @ X4 @ (powerset @ X3)) = $true)) | (powersetI != $true))),
% 1.54/1.32 inference(rectify,[status(thm)],[f22])).
% 1.54/1.32 thf(f22,plain,(
% 1.54/1.32 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) = $true)) & ((in @ X1 @ (powerset @ X0)) != $true))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) != $true)) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI != $true))),
% 1.54/1.32 inference(nnf_transformation,[status(thm)],[f15])).
% 1.54/1.32 thf(f15,plain,(
% 1.54/1.32 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) != $true)) | ((in @ X1 @ (powerset @ X0)) = $true))),
% 1.54/1.32 inference(ennf_transformation,[status(thm)],[f11])).
% 1.54/1.32 thf(f11,plain,(
% 1.54/1.32 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X1)) => ((in @ X2 @ X0) = $true)) => ((in @ X1 @ (powerset @ X0)) = $true))),
% 1.54/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.54/1.32 thf(f10,plain,(
% 1.54/1.32 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 1.54/1.32 inference(rectify,[status(thm)],[f2])).
% 1.54/1.32 thf(f2,axiom,(
% 1.54/1.32 (powersetI = ! [X0 : $i,X4 : $i] : (! [X2 : $i] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (in @ X4 @ (powerset @ X0))))),
% 1.54/1.32 file('/export/starexec/sandbox/tmp/tmp.8xE8RzS9cK/DTF2THF_5427.p',powersetI)).
% 1.54/1.32 thf(f48,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ (dsetconstr @ X3 @ X4)) != $true) | ((in @ X5 @ X3) = $true)) )),
% 1.54/1.32 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.54/1.32 thf(f47,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true) | ((in @ X5 @ X3) = $true)) )),
% 1.54/1.32 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.54/1.32 thf(f39,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (($true != $true) | ((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true) | ((in @ X5 @ X3) = $true)) )),
% 1.54/1.32 inference(definition_unfolding,[status(thm)],[f27,f31])).
% 1.54/1.32 thf(f31,plain,(
% 1.54/1.32 (dsetconstrEL = $true)),
% 1.54/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.54/1.32 thf(f27,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true) | ((in @ X5 @ X3) = $true) | (dsetconstrEL != $true)) )),
% 1.54/1.32 inference(cnf_transformation,[status(thm)],[f19])).
% 1.54/1.32 thf(f19,plain,(
% 1.54/1.32 ((dsetconstrEL = $true) | (($true = (in @ sK2 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))))) & ((in @ sK2 @ sK0) != $true))) & (! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true) | ((in @ X5 @ X3) = $true)) | (dsetconstrEL != $true))),
% 1.54/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18])).
% 1.54/1.32 thf(f18,plain,(
% 1.54/1.32 ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) & ((in @ X2 @ X0) != $true)) => (($true = (in @ sK2 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))))) & ((in @ sK2 @ sK0) != $true))),
% 1.54/1.32 introduced(definition,[],[choice_axiom])).
% 1.54/1.32 thf(f17,plain,(
% 1.54/1.32 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) & ((in @ X2 @ X0) != $true))) & (! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true) | ((in @ X5 @ X3) = $true)) | (dsetconstrEL != $true))),
% 1.54/1.32 inference(rectify,[status(thm)],[f16])).
% 1.54/1.32 thf(f16,plain,(
% 1.54/1.32 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) & ((in @ X2 @ X0) != $true))) & (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X2 @ X0) = $true)) | (dsetconstrEL != $true))),
% 1.54/1.32 inference(nnf_transformation,[status(thm)],[f12])).
% 1.54/1.32 thf(f12,plain,(
% 1.54/1.32 (dsetconstrEL = $true) <=> ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X2 @ X0) = $true))),
% 1.54/1.32 inference(ennf_transformation,[status(thm)],[f9])).
% 1.54/1.32 thf(f9,plain,(
% 1.54/1.32 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) => ((in @ X2 @ X0) = $true)) <=> (dsetconstrEL = $true)),
% 1.54/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.54/1.32 thf(f8,plain,(
% 1.54/1.32 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 1.54/1.32 inference(rectify,[status(thm)],[f1])).
% 1.54/1.32 thf(f1,axiom,(
% 1.54/1.32 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 1.54/1.32 file('/export/starexec/sandbox/tmp/tmp.8xE8RzS9cK/DTF2THF_5427.p',dsetconstrEL)).
% 1.54/1.32 thf(f45,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.54/1.32 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.54/1.32 thf(f43,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ (sK7 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.54/1.32 inference(definition_unfolding,[status(thm)],[f33,f32])).
% 1.54/1.32 thf(f33,plain,(
% 1.54/1.32 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true) | (powersetI != $true)) )),
% 1.54/1.32 inference(cnf_transformation,[status(thm)],[f26])).
% 1.54/1.32 thf(f44,plain,(
% 1.54/1.32 ((in @ (dsetconstr @ sK4 @ sK3) @ (powerset @ sK4)) != $true)),
% 1.54/1.32 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.54/1.32 thf(f30,plain,(
% 1.54/1.32 ((in @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK3 @ Y0))) @ (powerset @ sK4)) != $true)),
% 1.54/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.54/1.32 % SZS output end Proof for DTF2THF_5427
% 1.54/1.32 % (5529)------------------------------
% 1.54/1.32 % (5529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.32 % (5529)Termination reason: Refutation
% 1.54/1.32
% 1.54/1.32 % (5529)Memory used [KB]: 5500
% 1.54/1.32 % (5529)Time elapsed: 0.006 s
% 1.54/1.32 % (5529)Instructions burned: 6 (million)
% 1.54/1.32 % (5529)------------------------------
% 1.54/1.32 % (5529)------------------------------
% 1.54/1.32 % (5523)Success in time 0.01 s
%------------------------------------------------------------------------------