%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU573^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 09:35:21 AM UTC 2026
% Result : Theorem 1.50s 1.27s
% Output : Refutation 1.50s
% 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 ( 6 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_10,type,
sK2: $i > $i > $i ).
thf(f61,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f59,f29]) ).
thf(f29,plain,
( $true
!= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( subsetE = $true )
& ( powersetI = $true )
& ( $true
!= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( $true
= ( subset @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) )
=> ( ( $true
!= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( $true
= ( subset @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( subsetE = $true )
& ( powersetI = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) )
& ( subsetE = $true )
& ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( powersetI = $true )
=> ( ( subsetE = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( powersetI
=> ( subsetE
=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetI
=> ( subsetE
=> ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetI
=> ( subsetE
=> ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LDnT06Nu3f/DTF2THF_7577.p',subset2powerset) ).
thf(f59,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f49,f56]) ).
thf(f56,plain,
( ( in @ ( sK2 @ sK1 @ sK0 ) @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( in @ ( sK2 @ sK1 @ sK0 ) @ sK0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f52,f54]) ).
thf(f54,plain,
( $true
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ( $true
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK1 ) ) ),
inference(superposition,[status(thm)],[f29,f48]) ).
thf(f48,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X1 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f35,f30]) ).
thf(f30,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f35,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X1 ) )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X1 ) )
& ( $true
!= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) ) ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ( ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK4 ) )
| ( $true
= ( in @ X5 @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f20,f22,f21]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( $true
= ( in @ ( sK2 @ X1 @ X0 ) @ X1 ) )
& ( $true
!= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
& ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) ) )
=> ( ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK4 ) )
| ( $true
= ( in @ X5 @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ? [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
& ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetI = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI ),
file('/export/starexec/sandbox2/tmp/tmp.LDnT06Nu3f/DTF2THF_7577.p',powersetI) ).
thf(f52,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f50,f28]) ).
thf(f28,plain,
( $true
= ( subset @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f50,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X5 @ X3 ) )
| ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( $true
!= ( subset @ X5 @ X3 ) )
| ( $true
= ( in @ X4 @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f36,f31]) ).
thf(f31,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f36,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( subset @ X5 @ X3 ) )
| ( ( in @ X4 @ X5 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( subsetE = $true )
| ( ( $true
!= ( in @ sK6 @ sK5 ) )
& ( ( subset @ sK7 @ sK5 )
= $true )
& ( $true
= ( in @ sK6 @ sK7 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( subset @ X5 @ X3 ) )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f25,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( ( subset @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
=> ( ( $true
!= ( in @ sK6 @ sK5 ) )
& ( ( subset @ sK7 @ sK5 )
= $true )
& ( $true
= ( in @ sK6 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( ( subset @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( subset @ X5 @ X3 ) )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( subsetE = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( $true
= ( in @ X0 @ X1 ) ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ X2 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox2/tmp/tmp.LDnT06Nu3f/DTF2THF_7577.p',subsetE) ).
thf(f49,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( $true
!= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f34,f30]) ).
thf(f34,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( $true
!= ( in @ ( sK2 @ X1 @ X0 ) @ X0 ) )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU573^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n031.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 12:28:18 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEU573^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.47 % Domain : Set Theory
% 0.20/0.47 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.20/0.47 % Version : Especial > Reduced > Especial.
% 0.20/0.47 % English : (! A:i.! B:i.subset A B -> in A (powerset B))
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.47 % Source : [Bro08]
% 0.20/0.47 % Names : ZFC075l [Bro08]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % 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
% 0.20/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.20/0.47 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.20/0.47 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 18 @)
% 0.20/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : http://mathgate.info/detsetitem.php?id=153
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(in_type,type,
% 0.20/0.47 in: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(powerset_type,type,
% 0.20/0.47 powerset: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI_type,type,
% 0.20/0.47 powersetI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI,definition,
% 0.20/0.47 ( powersetI
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subset_type,type,
% 0.20/0.47 subset: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE_type,type,
% 0.20/0.47 subsetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE,definition,
% 0.20/0.47 ( subsetE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subset2powerset,conjecture,
% 0.20/0.47 ( powersetI
% 0.20/0.47 => ( subsetE
% 0.20/0.47 => ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.50/1.24 ---- Embedded in THF ---
% 1.50/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.24 %%% Generated on Tue Feb 24 12:28:19 EST 2026
% 1.50/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.24 %%% Logic specification used:
% 1.50/1.24 %%% thf(spec, logic, $$dhol).
% 1.50/1.24
% 1.50/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LDnT06Nu3f/DTF2DTF7577.p
% See solution above
% 1.50/1.24 ------------------------
% 1.50/1.25 ---- Cleaned THF ---
% 1.50/1.25 thf(in_type,type,
% 1.50/1.25 in: $i > $i > $o ).
% 1.50/1.25
% 1.50/1.25 thf(powerset_type,type,
% 1.50/1.25 powerset: $i > $i ).
% 1.50/1.25
% 1.50/1.25 thf(powersetI_type,type,
% 1.50/1.25 powersetI: $o ).
% 1.50/1.25
% 1.50/1.25 thf(powersetI,definition,
% 1.50/1.25 ( powersetI
% 1.50/1.25 = ( ! [A: $i,B: $i] :
% 1.50/1.25 ( ! [Xx: $i] :
% 1.50/1.25 ( ( in @ Xx @ B )
% 1.50/1.25 => ( in @ Xx @ A ) )
% 1.50/1.25 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.50/1.25
% 1.50/1.25 thf(subset_type,type,
% 1.50/1.25 subset: $i > $i > $o ).
% 1.50/1.25
% 1.50/1.25 thf(subsetE_type,type,
% 1.50/1.25 subsetE: $o ).
% 1.50/1.25
% 1.50/1.25 thf(subsetE,definition,
% 1.50/1.25 ( subsetE
% 1.50/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.50/1.25 ( ( subset @ A @ B )
% 1.50/1.25 => ( ( in @ Xx @ A )
% 1.50/1.25 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.50/1.25
% 1.50/1.25 thf(subset2powerset,conjecture,
% 1.50/1.25 ( powersetI
% 1.50/1.25 => ( subsetE
% 1.50/1.25 => ! [A: $i,B: $i] :
% 1.50/1.25 ( ( subset @ A @ B )
% 1.50/1.25 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 1.50/1.25 ------------------------
% 1.50/1.26 % (7727)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_7577 for (2999ds/4Mi)
% 1.50/1.26 % (7732)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7577 for (2999ds/18Mi)
% 1.50/1.26 % (7729)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7577 for (2999ds/2Mi)
% 1.50/1.26 % (7727)Instruction limit reached!
% 1.50/1.26 % (7727)------------------------------
% 1.50/1.26 % (7727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (7727)Termination reason: Unknown
% 1.50/1.26 % (7727)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (7727)Memory used [KB]: 5500
% 1.50/1.26 % (7727)Time elapsed: 0.003 s
% 1.50/1.26 % (7727)Instructions burned: 4 (million)
% 1.50/1.26 % (7727)------------------------------
% 1.50/1.26 % (7727)------------------------------
% 1.50/1.26 % (7729)Instruction limit reached!
% 1.50/1.26 % (7729)------------------------------
% 1.50/1.26 % (7729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (7729)Termination reason: Unknown
% 1.50/1.26 % (7729)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (7729)Memory used [KB]: 5500
% 1.50/1.26 % (7729)Time elapsed: 0.002 s
% 1.50/1.26 % (7729)Instructions burned: 3 (million)
% 1.50/1.26 % (7729)------------------------------
% 1.50/1.26 % (7729)------------------------------
% 1.50/1.26 % (7732)First to succeed.
% 1.50/1.27 % (7732)Refutation found. Thanks to Tanya!
% 1.50/1.27 % SZS status Theorem for DTF2THF_7577
% 1.50/1.27 % SZS output start Proof for DTF2THF_7577
% 1.50/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.50/1.27 thf(func_def_1, type, powerset: $i > $i).
% 1.50/1.27 thf(func_def_4, type, subset: $i > $i > $o).
% 1.50/1.27 thf(func_def_10, type, sK2: $i > $i > $i).
% 1.50/1.27 thf(f61,plain,(
% 1.50/1.27 $false),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f59,f29])).
% 1.50/1.27 thf(f29,plain,(
% 1.50/1.27 ($true != (in @ sK1 @ (powerset @ sK0)))),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.27 thf(f18,plain,(
% 1.50/1.27 (subsetE = $true) & (powersetI = $true) & (($true != (in @ sK1 @ (powerset @ sK0))) & ($true = (subset @ sK1 @ sK0)))),
% 1.50/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17])).
% 1.50/1.27 thf(f17,plain,(
% 1.50/1.27 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ($true = (subset @ X1 @ X0))) => (($true != (in @ sK1 @ (powerset @ sK0))) & ($true = (subset @ sK1 @ sK0)))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f16,plain,(
% 1.50/1.27 (subsetE = $true) & (powersetI = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ($true = (subset @ X1 @ X0)))),
% 1.50/1.27 inference(flattening,[status(thm)],[f15])).
% 1.50/1.27 thf(f15,plain,(
% 1.50/1.27 (? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ($true = (subset @ X1 @ X0))) & (subsetE = $true)) & (powersetI = $true)),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f7])).
% 1.50/1.27 thf(f7,plain,(
% 1.50/1.27 ~((powersetI = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) => ((in @ X1 @ (powerset @ X0)) = $true))))),
% 1.50/1.27 inference(fool_elimination,[status(thm)],[f6])).
% 1.50/1.27 thf(f6,plain,(
% 1.50/1.27 ~(powersetI => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0)))))),
% 1.50/1.27 inference(rectify,[status(thm)],[f4])).
% 1.50/1.27 thf(f4,negated_conjecture,(
% 1.50/1.27 ~(powersetI => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1)))))),
% 1.50/1.27 inference(negated_conjecture,[status(cth)],[f3])).
% 1.50/1.27 thf(f3,conjecture,(
% 1.50/1.27 powersetI => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 1.50/1.27 file('/export/starexec/sandbox2/tmp/tmp.LDnT06Nu3f/DTF2THF_7577.p',subset2powerset)).
% 1.50/1.27 thf(f59,plain,(
% 1.50/1.27 ($true = (in @ sK1 @ (powerset @ sK0)))),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.50/1.27 thf(f57,plain,(
% 1.50/1.27 ($true = (in @ sK1 @ (powerset @ sK0))) | ($true != $true)),
% 1.50/1.27 inference(superposition,[status(thm)],[f49,f56])).
% 1.50/1.27 thf(f56,plain,(
% 1.50/1.27 ((in @ (sK2 @ sK1 @ sK0) @ sK0) = $true)),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.50/1.27 thf(f55,plain,(
% 1.50/1.27 ((in @ (sK2 @ sK1 @ sK0) @ sK0) = $true) | ($true != $true)),
% 1.50/1.27 inference(superposition,[status(thm)],[f52,f54])).
% 1.50/1.27 thf(f54,plain,(
% 1.50/1.27 ($true = (in @ (sK2 @ sK1 @ sK0) @ sK1))),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.50/1.27 thf(f53,plain,(
% 1.50/1.27 ($true != $true) | ($true = (in @ (sK2 @ sK1 @ sK0) @ sK1))),
% 1.50/1.27 inference(superposition,[status(thm)],[f29,f48])).
% 1.50/1.27 thf(f48,plain,(
% 1.50/1.27 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true = (in @ (sK2 @ X1 @ X0) @ X1))) )),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.50/1.27 thf(f40,plain,(
% 1.50/1.27 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (in @ (sK2 @ X1 @ X0) @ X1)) | ((in @ X1 @ (powerset @ X0)) = $true)) )),
% 1.50/1.27 inference(definition_unfolding,[status(thm)],[f35,f30])).
% 1.50/1.27 thf(f30,plain,(
% 1.50/1.27 (powersetI = $true)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.27 thf(f35,plain,(
% 1.50/1.27 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true = (in @ (sK2 @ X1 @ X0) @ X1)) | (powersetI != $true)) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f23])).
% 1.50/1.27 thf(f23,plain,(
% 1.50/1.27 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | (($true = (in @ (sK2 @ X1 @ X0) @ X1)) & ($true != (in @ (sK2 @ X1 @ X0) @ X0)))) | (powersetI != $true)) & ((powersetI = $true) | (($true != (in @ sK4 @ (powerset @ sK3))) & ! [X5 : $i] : (($true != (in @ X5 @ sK4)) | ($true = (in @ X5 @ sK3)))))),
% 1.50/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f20,f22,f21])).
% 1.50/1.27 thf(f21,plain,(
% 1.50/1.27 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) => (($true = (in @ (sK2 @ X1 @ X0) @ X1)) & ($true != (in @ (sK2 @ X1 @ X0) @ X0))))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f22,plain,(
% 1.50/1.27 ? [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (powerset @ X3))) & ! [X5 : $i] : (((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ X3)))) => (($true != (in @ sK4 @ (powerset @ sK3))) & ! [X5 : $i] : (($true != (in @ X5 @ sK4)) | ($true = (in @ X5 @ sK3))))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f20,plain,(
% 1.50/1.27 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (powersetI != $true)) & ((powersetI = $true) | ? [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (powerset @ X3))) & ! [X5 : $i] : (((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ X3)))))),
% 1.50/1.27 inference(rectify,[status(thm)],[f19])).
% 1.50/1.27 thf(f19,plain,(
% 1.50/1.27 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (powersetI != $true)) & ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))))),
% 1.50/1.27 inference(nnf_transformation,[status(thm)],[f12])).
% 1.50/1.27 thf(f12,plain,(
% 1.50/1.27 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) <=> (powersetI = $true)),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f9])).
% 1.50/1.27 thf(f9,plain,(
% 1.50/1.27 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((in @ X1 @ (powerset @ X0)) = $true)) <=> (powersetI = $true)),
% 1.50/1.27 inference(fool_elimination,[status(thm)],[f8])).
% 1.50/1.27 thf(f8,plain,(
% 1.50/1.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 1.50/1.27 inference(rectify,[status(thm)],[f1])).
% 1.50/1.27 thf(f1,axiom,(
% 1.50/1.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 1.50/1.27 file('/export/starexec/sandbox2/tmp/tmp.LDnT06Nu3f/DTF2THF_7577.p',powersetI)).
% 1.50/1.27 thf(f52,plain,(
% 1.50/1.27 ( ! [X0 : $i] : (($true != (in @ X0 @ sK1)) | ($true = (in @ X0 @ sK0))) )),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.50/1.27 thf(f51,plain,(
% 1.50/1.27 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ X0 @ sK1)) | ($true = (in @ X0 @ sK0))) )),
% 1.50/1.27 inference(superposition,[status(thm)],[f50,f28])).
% 1.50/1.27 thf(f28,plain,(
% 1.50/1.27 ($true = (subset @ sK1 @ sK0))),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.27 thf(f50,plain,(
% 1.50/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X5 @ X3)) | ($true = (in @ X4 @ X3)) | ((in @ X4 @ X5) != $true)) )),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.50/1.27 thf(f47,plain,(
% 1.50/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X4 @ X5) != $true) | ($true != (subset @ X5 @ X3)) | ($true = (in @ X4 @ X3))) )),
% 1.50/1.27 inference(definition_unfolding,[status(thm)],[f36,f31])).
% 1.50/1.27 thf(f31,plain,(
% 1.50/1.27 (subsetE = $true)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.27 thf(f36,plain,(
% 1.50/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ X3)) | ($true != (subset @ X5 @ X3)) | ((in @ X4 @ X5) != $true) | (subsetE != $true)) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f27])).
% 1.50/1.27 thf(f27,plain,(
% 1.50/1.27 ((subsetE = $true) | (($true != (in @ sK6 @ sK5)) & ((subset @ sK7 @ sK5) = $true) & ($true = (in @ sK6 @ sK7)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ X3)) | ($true != (subset @ X5 @ X3)) | ((in @ X4 @ X5) != $true)) | (subsetE != $true))),
% 1.50/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f25,f26])).
% 1.50/1.27 thf(f26,plain,(
% 1.50/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) & ((subset @ X2 @ X0) = $true) & ($true = (in @ X1 @ X2))) => (($true != (in @ sK6 @ sK5)) & ((subset @ sK7 @ sK5) = $true) & ($true = (in @ sK6 @ sK7)))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f25,plain,(
% 1.50/1.27 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) & ((subset @ X2 @ X0) = $true) & ($true = (in @ X1 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ X3)) | ($true != (subset @ X5 @ X3)) | ((in @ X4 @ X5) != $true)) | (subsetE != $true))),
% 1.50/1.27 inference(rectify,[status(thm)],[f24])).
% 1.50/1.27 thf(f24,plain,(
% 1.50/1.27 ((subsetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) & ($true = (subset @ X1 @ X2)) & ($true = (in @ X0 @ X1)))) & (! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) = $true) | ($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1))) | (subsetE != $true))),
% 1.50/1.27 inference(nnf_transformation,[status(thm)],[f14])).
% 1.50/1.27 thf(f14,plain,(
% 1.50/1.27 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) = $true) | ($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1)))),
% 1.50/1.27 inference(flattening,[status(thm)],[f13])).
% 1.50/1.27 thf(f13,plain,(
% 1.50/1.27 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2) = $true) | ($true != (in @ X0 @ X1))) | ($true != (subset @ X1 @ X2))) <=> (subsetE = $true)),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f11])).
% 1.50/1.27 thf(f11,plain,(
% 1.50/1.27 ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) => (($true = (in @ X0 @ X1)) => ((in @ X0 @ X2) = $true))) <=> (subsetE = $true)),
% 1.50/1.27 inference(fool_elimination,[status(thm)],[f10])).
% 1.50/1.27 thf(f10,plain,(
% 1.50/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = subsetE)),
% 1.50/1.27 inference(rectify,[status(thm)],[f2])).
% 1.50/1.27 thf(f2,axiom,(
% 1.50/1.27 (! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.50/1.27 file('/export/starexec/sandbox2/tmp/tmp.LDnT06Nu3f/DTF2THF_7577.p',subsetE)).
% 1.50/1.27 thf(f49,plain,(
% 1.50/1.27 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK2 @ X1 @ X0) @ X0)) | ((in @ X1 @ (powerset @ X0)) = $true)) )),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.50/1.27 thf(f41,plain,(
% 1.50/1.27 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true != (in @ (sK2 @ X1 @ X0) @ X0)) | ($true != $true)) )),
% 1.50/1.27 inference(definition_unfolding,[status(thm)],[f34,f30])).
% 1.50/1.27 thf(f34,plain,(
% 1.50/1.27 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true != (in @ (sK2 @ X1 @ X0) @ X0)) | (powersetI != $true)) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f23])).
% 1.50/1.27 % SZS output end Proof for DTF2THF_7577
% 1.50/1.27 % (7732)------------------------------
% 1.50/1.27 % (7732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (7732)Termination reason: Refutation
% 1.50/1.27
% 1.50/1.27 % (7732)Memory used [KB]: 5500
% 1.50/1.27 % (7732)Time elapsed: 0.005 s
% 1.50/1.27 % (7732)Instructions burned: 5 (million)
% 1.50/1.27 % (7732)------------------------------
% 1.50/1.27 % (7732)------------------------------
% 1.50/1.27 % (7725)Success in time 0.014 s
%------------------------------------------------------------------------------