%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU712^2 : 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 : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:35 AM UTC 2026
% Result : Theorem 0.83s 0.89s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 616 ( 178 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 688 ( 75 ~; 74 |; 38 &; 468 @)
% ( 5 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 121 ( 0 ^; 96 !; 25 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_14,type,
sK7: $i > $i > $i ).
thf(f81,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f79,f33]) ).
thf(f33,plain,
( ( in @ ( powerset @ sK4 ) @ ( powerset @ ( powerset @ sK3 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( powersetI = $true )
& ( powersetE = $true )
& ( ( in @ ( powerset @ sK4 ) @ ( powerset @ ( powerset @ sK3 ) ) )
!= $true )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f16,f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( powerset @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ( ( in @ ( powerset @ sK4 ) @ ( powerset @ ( powerset @ sK3 ) ) )
!= $true )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( powersetI = $true )
& ( powersetE = $true )
& ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( powerset @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( powerset @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( powersetE = $true )
& ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( powersetI = $true )
=> ( ( powersetE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( $true
= ( in @ ( powerset @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( powersetI
=> ( powersetE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( powerset @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetI
=> ( powersetE
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( powerset @ X3 ) @ ( powerset @ ( powerset @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetI
=> ( powersetE
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( powerset @ X3 ) @ ( powerset @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ay8akARHlb/DTF2THF_970.p',powersetT_lem) ).
thf(f79,plain,
( ( in @ ( powerset @ sK4 ) @ ( powerset @ ( powerset @ sK3 ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( in @ ( powerset @ sK4 ) @ ( powerset @ ( powerset @ sK3 ) ) )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true != $true )
| ( ( in @ ( powerset @ sK4 ) @ ( powerset @ ( powerset @ sK3 ) ) )
= $true )
| ( ( in @ ( powerset @ sK4 ) @ ( powerset @ ( powerset @ sK3 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f49,f75]) ).
thf(f75,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK7 @ ( powerset @ sK4 ) @ X0 ) @ ( powerset @ sK3 ) ) )
| ( ( in @ ( powerset @ sK4 ) @ ( powerset @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( sK7 @ ( powerset @ sK4 ) @ X0 ) @ ( powerset @ sK3 ) ) )
| ( ( in @ ( powerset @ sK4 ) @ ( powerset @ X0 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ ( powerset @ sK4 ) @ ( powerset @ X0 ) )
= $true )
| ( $true
= ( in @ ( sK7 @ ( powerset @ sK4 ) @ X0 ) @ ( powerset @ sK3 ) ) )
| ( $true
= ( in @ ( sK7 @ ( powerset @ sK4 ) @ X0 ) @ ( powerset @ sK3 ) ) ) ),
inference(superposition,[status(thm)],[f60,f62]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK7 @ ( sK7 @ ( powerset @ X0 ) @ X1 ) @ X2 ) @ X0 )
= $true )
| ( $true
= ( in @ ( sK7 @ ( powerset @ X0 ) @ X1 ) @ ( powerset @ X2 ) ) )
| ( ( in @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK7 @ ( sK7 @ ( powerset @ X0 ) @ X1 ) @ X2 ) @ X0 )
= $true )
| ( ( in @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
= ( in @ ( sK7 @ ( powerset @ X0 ) @ X1 ) @ ( powerset @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f58,f48]) ).
thf(f48,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
| ( $true != $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f37,f35]) ).
thf(f35,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f37,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( powersetI = $true )
| ( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK6 ) )
| ( $true
= ( in @ X2 @ sK5 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
& ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true ) ) )
| ( powersetI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f24,f26,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) )
=> ( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK6 ) )
| ( $true
= ( in @ X2 @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( $true
!= ( in @ X5 @ X3 ) ) )
=> ( ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
& ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( $true
!= ( in @ X5 @ X3 ) ) ) )
| ( powersetI != $true ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( powersetI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( powersetI = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( powersetI = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( 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)],[f1]) ).
thf(f1,axiom,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ay8akARHlb/DTF2THF_970.p',powersetI) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( sK7 @ ( powerset @ X0 ) @ X1 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( powerset @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X2 @ ( sK7 @ ( powerset @ X0 ) @ X1 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f50,f48]) ).
thf(f50,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f31,f34]) ).
thf(f34,plain,
powersetE = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true )
| ( powersetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ( ( $true
= ( in @ sK0 @ sK1 ) )
& ( ( in @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ sK1 @ ( powerset @ sK2 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19]) ).
thf(f19,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
& ( $true
!= ( in @ X3 @ X5 ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) )
=> ( ( $true
= ( in @ sK0 @ sK1 ) )
& ( ( in @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ sK1 @ ( powerset @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
& ( $true
!= ( in @ X3 @ X5 ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( $true
!= ( in @ X1 @ X0 ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( powersetE = $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ( powersetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( powersetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( $true
= ( in @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) )
= powersetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= powersetE ),
file('/export/starexec/sandbox/tmp/tmp.ay8akARHlb/DTF2THF_970.p',powersetE) ).
thf(f60,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK7 @ X0 @ sK3 ) @ sK4 ) )
| ( ( in @ X0 @ ( powerset @ sK3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK7 @ X0 @ sK3 ) @ sK4 ) )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ sK3 ) )
= $true ) ),
inference(superposition,[status(thm)],[f49,f57]) ).
thf(f57,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK3 ) )
| ( ( in @ X0 @ sK4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ sK4 )
!= $true )
| ( $true
= ( in @ X0 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f50,f32]) ).
thf(f32,plain,
( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f49,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( $true != $true )
| ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f36,f35]) ).
thf(f36,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU712^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n024.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 07:31:40 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.32 thf(spec,logic,$$dhol).
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 % File : SEU712^2 : TPTP v9.2.1. Released v3.7.0.
% 0.08/0.32 % Domain : Set Theory
% 0.08/0.32 % Problem : Typed Set Theory - Types of Set Operators
% 0.08/0.32 % Version : Especial > Reduced > Especial.
% 0.08/0.32 % English : (! A:i.! X:i.in X (powerset A) ->
% 0.08/0.32 % in (powerset X) (powerset (powerset A)))
% 0.08/0.32
% 0.08/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.08/0.32 % Source : [Bro08]
% 0.08/0.32 % Names : ZFC214l [Bro08]
% 0.08/0.32
% 0.08/0.32 % Status : Theorem
% 0.08/0.32 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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 v4.0.1, 0.33 v3.7.0
% 0.08/0.32 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.08/0.32 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.08/0.32 % Maximal formula atoms : 4 ( 4 avg)
% 0.08/0.32 % Number of connectives : 29 ( 0 ~; 0 |; 0 &; 22 @)
% 0.08/0.32 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.08/0.32 % Maximal formula depth : 9 ( 4 avg)
% 0.08/0.32 % Number of types : 2 ( 0 usr)
% 0.08/0.32 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.08/0.32 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.08/0.32 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.08/0.32 % SPC : TH0_THM_EQU_NAR
% 0.08/0.32
% 0.08/0.32 % Comments : http://mathgate.info/detsetitem.php?id=269
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 thf(in_type,type,
% 0.08/0.32 in: $i > $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(powerset_type,type,
% 0.08/0.32 powerset: $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(powersetI_type,type,
% 0.08/0.32 powersetI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powersetI,definition,
% 0.08/0.32 ( powersetI
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ A ) )
% 0.08/0.32 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powersetE_type,type,
% 0.08/0.32 powersetE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powersetE,definition,
% 0.08/0.32 ( powersetE
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.08/0.32 => ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powersetT_lem,conjecture,
% 0.08/0.32 ( powersetI
% 0.08/0.32 => ( powersetE
% 0.08/0.32 => ! [A: $i,X: $i] :
% 0.08/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.32 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 ------------------------
% 0.83/0.87 ---- Embedded in THF ---
% 0.83/0.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.83/0.87 %%% Generated on Tue Feb 24 07:31:41 EST 2026
% 0.83/0.87 %%% using '$$dhol' embedding, version 1.3.0.
% 0.83/0.87 %%% Logic specification used:
% 0.83/0.87 %%% thf(spec, logic, $$dhol).
% 0.83/0.87
% 0.83/0.87 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ay8akARHlb/DTF2DTF970.p
% See solution above
% 0.83/0.87 ------------------------
% 0.83/0.87 ---- Cleaned THF ---
% 0.83/0.87 thf(in_type,type,
% 0.83/0.87 in: $i > $i > $o ).
% 0.83/0.87
% 0.83/0.87 thf(powerset_type,type,
% 0.83/0.87 powerset: $i > $i ).
% 0.83/0.87
% 0.83/0.87 thf(powersetI_type,type,
% 0.83/0.87 powersetI: $o ).
% 0.83/0.87
% 0.83/0.87 thf(powersetI,definition,
% 0.83/0.87 ( powersetI
% 0.83/0.87 = ( ! [A: $i,B: $i] :
% 0.83/0.87 ( ! [Xx: $i] :
% 0.83/0.87 ( ( in @ Xx @ B )
% 0.83/0.87 => ( in @ Xx @ A ) )
% 0.83/0.87 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.83/0.87
% 0.83/0.87 thf(powersetE_type,type,
% 0.83/0.87 powersetE: $o ).
% 0.83/0.87
% 0.83/0.87 thf(powersetE,definition,
% 0.83/0.87 ( powersetE
% 0.83/0.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.83/0.87 ( ( in @ B @ ( powerset @ A ) )
% 0.83/0.87 => ( ( in @ Xx @ B )
% 0.83/0.87 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.83/0.87
% 0.83/0.87 thf(powersetT_lem,conjecture,
% 0.83/0.87 ( powersetI
% 0.83/0.87 => ( powersetE
% 0.83/0.87 => ! [A: $i,X: $i] :
% 0.83/0.87 ( ( in @ X @ ( powerset @ A ) )
% 0.83/0.87 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.83/0.87 ------------------------
% 0.83/0.89 % (1280)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_970 for (3000ds/27Mi)
% 0.83/0.89 % (1281)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_970 for (3000ds/2Mi)
% 0.83/0.89 % (1284)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_970 for (3000ds/18Mi)
% 0.83/0.89 % (1279)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_970 for (3000ds/4Mi)
% 0.83/0.89 % (1278)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_970 for (3000ds/183Mi)
% 0.83/0.89 % (1283)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_970 for (3000ds/275Mi)
% 0.83/0.89 % (1282)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_970 for (3000ds/2Mi)
% 0.83/0.89 % (1281)Instruction limit reached!
% 0.83/0.89 % (1281)------------------------------
% 0.83/0.89 % (1281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (1281)Termination reason: Unknown
% 0.83/0.89 % (1281)Termination phase: Saturation
% 0.83/0.89
% 0.83/0.89 % (1281)Memory used [KB]: 5500
% 0.83/0.89 % (1281)Time elapsed: 0.002 s
% 0.83/0.89 % (1281)Instructions burned: 2 (million)
% 0.83/0.89 % (1281)------------------------------
% 0.83/0.89 % (1281)------------------------------
% 0.83/0.89 % (1282)Instruction limit reached!
% 0.83/0.89 % (1282)------------------------------
% 0.83/0.89 % (1282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (1282)Termination reason: Unknown
% 0.83/0.89 % (1282)Termination phase: Saturation
% 0.83/0.89
% 0.83/0.89 % (1282)Memory used [KB]: 5500
% 0.83/0.89 % (1282)Time elapsed: 0.002 s
% 0.83/0.89 % (1282)Instructions burned: 3 (million)
% 0.83/0.89 % (1282)------------------------------
% 0.83/0.89 % (1282)------------------------------
% 0.83/0.89 % (1279)Instruction limit reached!
% 0.83/0.89 % (1279)------------------------------
% 0.83/0.89 % (1279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (1279)Termination reason: Unknown
% 0.83/0.89 % (1279)Termination phase: Saturation
% 0.83/0.89
% 0.83/0.89 % (1279)Memory used [KB]: 5500
% 0.83/0.89 % (1279)Time elapsed: 0.003 s
% 0.83/0.89 % (1279)Instructions burned: 5 (million)
% 0.83/0.89 % (1279)------------------------------
% 0.83/0.89 % (1279)------------------------------
% 0.83/0.89 % (1283)First to succeed.
% 0.83/0.89 % (1283)Refutation found. Thanks to Tanya!
% 0.83/0.89 % SZS status Theorem for DTF2THF_970
% 0.83/0.89 % SZS output start Proof for DTF2THF_970
% 0.83/0.89 thf(func_def_0, type, in: $i > $i > $o).
% 0.83/0.89 thf(func_def_1, type, powerset: $i > $i).
% 0.83/0.89 thf(func_def_14, type, sK7: $i > $i > $i).
% 0.83/0.89 thf(f81,plain,(
% 0.83/0.89 $false),
% 0.83/0.89 inference(subsumption_resolution,[status(thm)],[f79,f33])).
% 0.83/0.89 thf(f33,plain,(
% 0.83/0.89 ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))) != $true)),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f22])).
% 0.83/0.89 thf(f22,plain,(
% 0.83/0.89 (powersetI = $true) & (powersetE = $true) & (((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))) != $true) & ((in @ sK4 @ (powerset @ sK3)) = $true))),
% 0.83/0.89 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f16,f21])).
% 0.83/0.89 thf(f21,plain,(
% 0.83/0.89 ? [X0 : $i,X1 : $i] : (($true != (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))) != $true) & ((in @ sK4 @ (powerset @ sK3)) = $true))),
% 0.83/0.89 introduced(definition,[],[choice_axiom])).
% 0.83/0.89 thf(f16,plain,(
% 0.83/0.89 (powersetI = $true) & (powersetE = $true) & ? [X0 : $i,X1 : $i] : (($true != (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true))),
% 0.83/0.89 inference(flattening,[status(thm)],[f15])).
% 0.83/0.89 thf(f15,plain,(
% 0.83/0.89 (? [X0 : $i,X1 : $i] : (($true != (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (powersetE = $true)) & (powersetI = $true)),
% 0.83/0.89 inference(ennf_transformation,[status(thm)],[f7])).
% 0.83/0.89 thf(f7,plain,(
% 0.83/0.89 ~((powersetI = $true) => ((powersetE = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ($true = (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))))))),
% 0.83/0.89 inference(fool_elimination,[status(thm)],[f6])).
% 0.83/0.89 thf(f6,plain,(
% 0.83/0.89 ~(powersetI => (powersetE => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0))))))),
% 0.83/0.89 inference(rectify,[status(thm)],[f4])).
% 0.83/0.89 thf(f4,negated_conjecture,(
% 0.83/0.89 ~(powersetI => (powersetE => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (powerset @ X3) @ (powerset @ (powerset @ X0))))))),
% 0.83/0.89 inference(negated_conjecture,[status(cth)],[f3])).
% 0.83/0.89 thf(f3,conjecture,(
% 0.83/0.89 powersetI => (powersetE => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (powerset @ X3) @ (powerset @ (powerset @ X0)))))),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.ay8akARHlb/DTF2THF_970.p',powersetT_lem)).
% 0.83/0.89 thf(f79,plain,(
% 0.83/0.89 ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))) = $true)),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 0.83/0.89 thf(f78,plain,(
% 0.83/0.89 ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))) = $true) | ($true != $true)),
% 0.83/0.89 inference(duplicate_literal_removal,[status(thm)],[f77])).
% 0.83/0.89 thf(f77,plain,(
% 0.83/0.89 ($true != $true) | ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))) = $true) | ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))) = $true)),
% 0.83/0.89 inference(superposition,[status(thm)],[f49,f75])).
% 0.83/0.89 thf(f75,plain,(
% 0.83/0.89 ( ! [X0 : $i] : (($true = (in @ (sK7 @ (powerset @ sK4) @ X0) @ (powerset @ sK3))) | ((in @ (powerset @ sK4) @ (powerset @ X0)) = $true)) )),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 0.83/0.89 thf(f74,plain,(
% 0.83/0.89 ( ! [X0 : $i] : (($true != $true) | ($true = (in @ (sK7 @ (powerset @ sK4) @ X0) @ (powerset @ sK3))) | ((in @ (powerset @ sK4) @ (powerset @ X0)) = $true)) )),
% 0.83/0.89 inference(duplicate_literal_removal,[status(thm)],[f69])).
% 0.83/0.89 thf(f69,plain,(
% 0.83/0.89 ( ! [X0 : $i] : (($true != $true) | ((in @ (powerset @ sK4) @ (powerset @ X0)) = $true) | ($true = (in @ (sK7 @ (powerset @ sK4) @ X0) @ (powerset @ sK3))) | ($true = (in @ (sK7 @ (powerset @ sK4) @ X0) @ (powerset @ sK3)))) )),
% 0.83/0.89 inference(superposition,[status(thm)],[f60,f62])).
% 0.83/0.89 thf(f62,plain,(
% 0.83/0.89 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK7 @ (sK7 @ (powerset @ X0) @ X1) @ X2) @ X0) = $true) | ($true = (in @ (sK7 @ (powerset @ X0) @ X1) @ (powerset @ X2))) | ((in @ (powerset @ X0) @ (powerset @ X1)) = $true)) )),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 0.83/0.89 thf(f61,plain,(
% 0.83/0.89 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK7 @ (sK7 @ (powerset @ X0) @ X1) @ X2) @ X0) = $true) | ((in @ (powerset @ X0) @ (powerset @ X1)) = $true) | ($true = (in @ (sK7 @ (powerset @ X0) @ X1) @ (powerset @ X2)))) )),
% 0.83/0.89 inference(superposition,[status(thm)],[f58,f48])).
% 0.83/0.89 thf(f48,plain,(
% 0.83/0.89 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK7 @ X4 @ X3) @ X4)) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 0.83/0.89 thf(f46,plain,(
% 0.83/0.89 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK7 @ X4 @ X3) @ X4)) | ($true != $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 0.83/0.89 inference(definition_unfolding,[status(thm)],[f37,f35])).
% 0.83/0.89 thf(f35,plain,(
% 0.83/0.89 (powersetI = $true)),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f22])).
% 0.83/0.89 thf(f37,plain,(
% 0.83/0.89 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ($true = (in @ (sK7 @ X4 @ X3) @ X4)) | (powersetI != $true)) )),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f27])).
% 0.83/0.89 thf(f27,plain,(
% 0.83/0.89 ((powersetI = $true) | (($true != (in @ sK6 @ (powerset @ sK5))) & ! [X2 : $i] : (($true != (in @ X2 @ sK6)) | ($true = (in @ X2 @ sK5))))) & (! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | (($true = (in @ (sK7 @ X4 @ X3) @ X4)) & ((in @ (sK7 @ X4 @ X3) @ X3) != $true))) | (powersetI != $true))),
% 0.83/0.89 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f24,f26,f25])).
% 0.83/0.89 thf(f25,plain,(
% 0.83/0.89 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))) => (($true != (in @ sK6 @ (powerset @ sK5))) & ! [X2 : $i] : (($true != (in @ X2 @ sK6)) | ($true = (in @ X2 @ sK5))))),
% 0.83/0.89 introduced(definition,[],[choice_axiom])).
% 0.83/0.89 thf(f26,plain,(
% 0.83/0.89 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = (in @ X5 @ X4)) & ($true != (in @ X5 @ X3))) => (($true = (in @ (sK7 @ X4 @ X3) @ X4)) & ((in @ (sK7 @ X4 @ X3) @ X3) != $true)))),
% 0.83/0.89 introduced(definition,[],[choice_axiom])).
% 0.83/0.89 thf(f24,plain,(
% 0.83/0.89 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)))) & (! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ? [X5 : $i] : (($true = (in @ X5 @ X4)) & ($true != (in @ X5 @ X3)))) | (powersetI != $true))),
% 0.83/0.89 inference(rectify,[status(thm)],[f23])).
% 0.83/0.89 thf(f23,plain,(
% 0.83/0.89 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)))) & (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (powersetI != $true))),
% 0.83/0.89 inference(nnf_transformation,[status(thm)],[f12])).
% 0.83/0.89 thf(f12,plain,(
% 0.83/0.89 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)))),
% 0.83/0.89 inference(ennf_transformation,[status(thm)],[f11])).
% 0.83/0.89 thf(f11,plain,(
% 0.83/0.89 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((in @ X1 @ (powerset @ X0)) = $true))),
% 0.83/0.89 inference(fool_elimination,[status(thm)],[f10])).
% 0.83/0.89 thf(f10,plain,(
% 0.83/0.89 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.83/0.89 inference(rectify,[status(thm)],[f1])).
% 0.83/0.89 thf(f1,axiom,(
% 0.83/0.89 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.ay8akARHlb/DTF2THF_970.p',powersetI)).
% 0.83/0.89 thf(f58,plain,(
% 0.83/0.89 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (sK7 @ (powerset @ X0) @ X1))) | ((in @ X2 @ X0) = $true) | ((in @ (powerset @ X0) @ (powerset @ X1)) = $true)) )),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 0.83/0.89 thf(f55,plain,(
% 0.83/0.89 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (powerset @ X0) @ (powerset @ X1)) = $true) | ($true != (in @ X2 @ (sK7 @ (powerset @ X0) @ X1))) | ((in @ X2 @ X0) = $true) | ($true != $true)) )),
% 0.83/0.89 inference(superposition,[status(thm)],[f50,f48])).
% 0.83/0.89 thf(f50,plain,(
% 0.83/0.89 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X2)) != $true) | ($true != (in @ X0 @ X1)) | ((in @ X0 @ X2) = $true)) )),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 0.83/0.89 thf(f40,plain,(
% 0.83/0.89 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X0 @ X1)) | ((in @ X0 @ X2) = $true) | ((in @ X1 @ (powerset @ X2)) != $true)) )),
% 0.83/0.89 inference(definition_unfolding,[status(thm)],[f31,f34])).
% 0.83/0.89 thf(f34,plain,(
% 0.83/0.89 (powersetE = $true)),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f22])).
% 0.83/0.89 thf(f31,plain,(
% 0.83/0.89 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ((in @ X0 @ X2) = $true) | ((in @ X1 @ (powerset @ X2)) != $true) | (powersetE != $true)) )),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f20])).
% 0.83/0.89 thf(f20,plain,(
% 0.83/0.89 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) | ((in @ X0 @ X2) = $true) | ((in @ X1 @ (powerset @ X2)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | (($true = (in @ sK0 @ sK1)) & ((in @ sK0 @ sK2) != $true) & ($true = (in @ sK1 @ (powerset @ sK2)))))),
% 0.83/0.89 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19])).
% 0.83/0.89 thf(f19,plain,(
% 0.83/0.89 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) & ($true != (in @ X3 @ X5)) & ((in @ X4 @ (powerset @ X5)) = $true)) => (($true = (in @ sK0 @ sK1)) & ((in @ sK0 @ sK2) != $true) & ($true = (in @ sK1 @ (powerset @ sK2))))),
% 0.83/0.89 introduced(definition,[],[choice_axiom])).
% 0.83/0.89 thf(f18,plain,(
% 0.83/0.89 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) | ((in @ X0 @ X2) = $true) | ((in @ X1 @ (powerset @ X2)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) & ($true != (in @ X3 @ X5)) & ((in @ X4 @ (powerset @ X5)) = $true)))),
% 0.83/0.89 inference(rectify,[status(thm)],[f17])).
% 0.83/0.89 thf(f17,plain,(
% 0.83/0.89 (! [X1 : $i,X2 : $i,X0 : $i] : (($true != (in @ X1 @ X2)) | ($true = (in @ X1 @ X0)) | ((in @ X2 @ (powerset @ X0)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X1 @ X2)) & ($true != (in @ X1 @ X0)) & ((in @ X2 @ (powerset @ X0)) = $true)))),
% 0.83/0.89 inference(nnf_transformation,[status(thm)],[f14])).
% 0.83/0.89 thf(f14,plain,(
% 0.83/0.89 ! [X1 : $i,X2 : $i,X0 : $i] : (($true != (in @ X1 @ X2)) | ($true = (in @ X1 @ X0)) | ((in @ X2 @ (powerset @ X0)) != $true)) <=> (powersetE = $true)),
% 0.83/0.89 inference(flattening,[status(thm)],[f13])).
% 0.83/0.89 thf(f13,plain,(
% 0.83/0.89 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true))),
% 0.83/0.89 inference(ennf_transformation,[status(thm)],[f9])).
% 0.83/0.89 thf(f9,plain,(
% 0.83/0.89 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => (($true = (in @ X1 @ X2)) => ($true = (in @ X1 @ X0))))),
% 0.83/0.89 inference(fool_elimination,[status(thm)],[f8])).
% 0.83/0.89 thf(f8,plain,(
% 0.83/0.89 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((in @ X1 @ X2) => (in @ X1 @ X0))) = powersetE)),
% 0.83/0.89 inference(rectify,[status(thm)],[f2])).
% 0.83/0.89 thf(f2,axiom,(
% 0.83/0.89 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.ay8akARHlb/DTF2THF_970.p',powersetE)).
% 0.83/0.89 thf(f60,plain,(
% 0.83/0.89 ( ! [X0 : $i] : (($true != (in @ (sK7 @ X0 @ sK3) @ sK4)) | ((in @ X0 @ (powerset @ sK3)) = $true)) )),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 0.83/0.89 thf(f59,plain,(
% 0.83/0.89 ( ! [X0 : $i] : (($true != (in @ (sK7 @ X0 @ sK3) @ sK4)) | ($true != $true) | ((in @ X0 @ (powerset @ sK3)) = $true)) )),
% 0.83/0.89 inference(superposition,[status(thm)],[f49,f57])).
% 0.83/0.89 thf(f57,plain,(
% 0.83/0.89 ( ! [X0 : $i] : (($true = (in @ X0 @ sK3)) | ((in @ X0 @ sK4) != $true)) )),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 0.83/0.89 thf(f54,plain,(
% 0.83/0.89 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK4) != $true) | ($true = (in @ X0 @ sK3))) )),
% 0.83/0.89 inference(superposition,[status(thm)],[f50,f32])).
% 0.83/0.89 thf(f32,plain,(
% 0.83/0.89 ((in @ sK4 @ (powerset @ sK3)) = $true)),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f22])).
% 0.83/0.89 thf(f49,plain,(
% 0.83/0.89 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 0.83/0.89 thf(f47,plain,(
% 0.83/0.89 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ($true != $true) | ((in @ (sK7 @ X4 @ X3) @ X3) != $true)) )),
% 0.83/0.89 inference(definition_unfolding,[status(thm)],[f36,f35])).
% 0.83/0.89 thf(f36,plain,(
% 0.83/0.89 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ((in @ (sK7 @ X4 @ X3) @ X3) != $true) | (powersetI != $true)) )),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f27])).
% 0.83/0.89 % SZS output end Proof for DTF2THF_970
% 0.83/0.89 % (1283)------------------------------
% 0.83/0.89 % (1283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (1283)Termination reason: Refutation
% 0.83/0.89
% 0.83/0.89 % (1283)Memory used [KB]: 5500
% 0.83/0.89 % (1283)Time elapsed: 0.005 s
% 0.83/0.89 % (1283)Instructions burned: 8 (million)
% 0.83/0.89 % (1283)------------------------------
% 0.83/0.89 % (1283)------------------------------
% 0.83/0.89 % (1277)Success in time 0.013 s
%------------------------------------------------------------------------------