%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU758^2 : 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 : n002.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 09:36:58 AM UTC 2026
% Result : Theorem 1.73s 1.43s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 549 ( 151 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 559 ( 63 ~; 44 |; 48 &; 365 @)
% ( 5 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 117 ( 0 ^; 81 !; 36 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_4,type,
binintersect: $i > $i > $i ).
thf(f61,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f60,f52]) ).
thf(f52,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| ( $true
= ( in @ sK3 @ sK1 ) ) ),
inference(superposition,[status(thm)],[f50,f29]) ).
thf(f29,plain,
( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( binintersectEL = $true )
& ( powersetE = $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( ( in @ sK3 @ sK0 )
!= $true )
& ( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f19,f18,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( $true
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) )
=> ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ sK0 ) )
& ( ( in @ X3 @ ( binintersect @ sK1 @ X2 ) )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ sK0 ) )
& ( ( in @ X3 @ ( binintersect @ sK1 @ X2 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ sK0 ) )
& ( ( in @ X3 @ ( binintersect @ sK1 @ sK2 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ sK0 ) )
& ( ( in @ X3 @ ( binintersect @ sK1 @ sK2 ) )
= $true ) )
=> ( ( ( in @ sK3 @ sK0 )
!= $true )
& ( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( binintersectEL = $true )
& ( powersetE = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( $true
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( $true
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) )
& ( binintersectEL = $true )
& ( powersetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( powersetE = $true )
=> ( ( binintersectEL = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) )
=> ( ( in @ X3 @ X0 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( powersetE
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetE
=> ( binintersectEL
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X2 @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetE
=> ( binintersectEL
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X2 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3bgXq5UWwq/DTF2THF_12494.p',woz13rule0) ).
thf(f50,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f37,f34]) ).
thf(f34,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f37,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ( ( ( in @ sK6 @ sK5 )
!= $true )
& ( $true
= ( in @ sK6 @ ( binintersect @ sK5 @ sK4 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f22,f23]) ).
thf(f23,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
& ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) ) )
=> ( ( ( in @ sK6 @ sK5 )
!= $true )
& ( $true
= ( in @ sK6 @ ( binintersect @ sK5 @ sK4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
& ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
<=> ( binintersectEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3bgXq5UWwq/DTF2THF_12494.p',binintersectEL) ).
thf(f60,plain,
( $true
!= ( in @ sK3 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true
!= ( in @ sK3 @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f30,f56]) ).
thf(f56,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK1 )
!= $true )
| ( $true
= ( in @ X0 @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f49,f32]) ).
thf(f32,plain,
( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f49,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true != $true )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f41,f33]) ).
thf(f33,plain,
powersetE = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f41,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( powersetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ( ( $true
!= ( in @ sK8 @ sK7 ) )
& ( $true
= ( in @ sK8 @ sK9 ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f26,f27]) ).
thf(f27,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
& ( $true
= ( in @ X4 @ X5 ) )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) )
=> ( ( $true
!= ( in @ sK8 @ sK7 ) )
& ( $true
= ( in @ sK8 @ sK9 ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
& ( $true
= ( in @ X4 @ X5 ) )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ X2 ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
<=> ( powersetE = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
<=> ( powersetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( $true
= ( in @ X1 @ X0 ) ) ) )
<=> ( powersetE = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) )
= powersetE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= powersetE ),
file('/export/starexec/sandbox/tmp/tmp.3bgXq5UWwq/DTF2THF_12494.p',powersetE) ).
thf(f30,plain,
( ( in @ sK3 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU758^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:33:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU758^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Lemmas
% 0.19/0.46 % Version : Especial > Reduced > Especial.
% 0.19/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.19/0.46 % (! x:i.in x (binintersect X Y) -> in x A)))
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.46 % Source : [Bro08]
% 0.19/0.46 % Names : ZFC260l [Bro08]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.19/0.46 % Number of atoms : 15 ( 2 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 6 ( 5 avg)
% 0.19/0.46 % Number of connectives : 33 ( 0 ~; 0 |; 0 &; 25 @)
% 0.19/0.46 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 13 ( 5 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : http://mathgate.info/detsetitem.php?id=319
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(in_type,type,
% 0.19/0.46 in: $i > $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(powerset_type,type,
% 0.19/0.46 powerset: $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(powersetE_type,type,
% 0.19/0.46 powersetE: $o ).
% 0.19/0.46
% 0.19/0.46 thf(powersetE,definition,
% 0.19/0.46 ( powersetE
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.46 => ( ( in @ Xx @ B )
% 0.19/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersect_type,type,
% 0.19/0.46 binintersect: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectEL_type,type,
% 0.19/0.46 binintersectEL: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectEL,definition,
% 0.19/0.46 ( binintersectEL
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(woz13rule0,conjecture,
% 0.19/0.46 ( powersetE
% 0.19/0.46 => ( binintersectEL
% 0.19/0.46 => ! [A: $i,X: $i] :
% 0.19/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.46 => ! [Y: $i] :
% 0.19/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.46 => ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.19/0.46 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.53/1.40 ---- Embedded in THF ---
% 1.73/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.73/1.40 %%% Generated on Tue Feb 24 12:33:19 EST 2026
% 1.73/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 1.73/1.40 %%% Logic specification used:
% 1.73/1.40 %%% thf(spec, logic, $$dhol).
% 1.73/1.40
% 1.73/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3bgXq5UWwq/DTF2DTF12494.p
% See solution above
% 1.73/1.40 ------------------------
% 1.73/1.41 ---- Cleaned THF ---
% 1.73/1.41 thf(in_type,type,
% 1.73/1.41 in: $i > $i > $o ).
% 1.73/1.41
% 1.73/1.41 thf(powerset_type,type,
% 1.73/1.41 powerset: $i > $i ).
% 1.73/1.41
% 1.73/1.41 thf(powersetE_type,type,
% 1.73/1.41 powersetE: $o ).
% 1.73/1.41
% 1.73/1.41 thf(powersetE,definition,
% 1.73/1.41 ( powersetE
% 1.73/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.73/1.41 ( ( in @ B @ ( powerset @ A ) )
% 1.73/1.41 => ( ( in @ Xx @ B )
% 1.73/1.41 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.73/1.41
% 1.73/1.41 thf(binintersect_type,type,
% 1.73/1.41 binintersect: $i > $i > $i ).
% 1.73/1.41
% 1.73/1.41 thf(binintersectEL_type,type,
% 1.73/1.41 binintersectEL: $o ).
% 1.73/1.41
% 1.73/1.41 thf(binintersectEL,definition,
% 1.73/1.41 ( binintersectEL
% 1.73/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.73/1.41 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.73/1.41 => ( in @ Xx @ A ) ) ) ) ).
% 1.73/1.41
% 1.73/1.41 thf(woz13rule0,conjecture,
% 1.73/1.41 ( powersetE
% 1.73/1.41 => ( binintersectEL
% 1.73/1.41 => ! [A: $i,X: $i] :
% 1.73/1.41 ( ( in @ X @ ( powerset @ A ) )
% 1.73/1.41 => ! [Y: $i] :
% 1.73/1.41 ( ( in @ Y @ ( powerset @ A ) )
% 1.73/1.41 => ! [Xx: $i] :
% 1.73/1.41 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 1.73/1.41 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.73/1.41 ------------------------
% 1.73/1.43 % (12592)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_12494 for (2999ds/4Mi)
% 1.73/1.43 % (12595)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_12494 for (2999ds/2Mi)
% 1.73/1.43 % (12593)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_12494 for (2999ds/27Mi)
% 1.73/1.43 % (12596)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_12494 for (2999ds/275Mi)
% 1.73/1.43 % (12594)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12494 for (2999ds/2Mi)
% 1.73/1.43 % (12591)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12494 for (2999ds/183Mi)
% 1.73/1.43 % (12597)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12494 for (2999ds/18Mi)
% 1.73/1.43 % (12594)Instruction limit reached!
% 1.73/1.43 % (12594)------------------------------
% 1.73/1.43 % (12594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.43 % (12594)Termination reason: Unknown
% 1.73/1.43 % (12595)Instruction limit reached!
% 1.73/1.43 % (12595)------------------------------
% 1.73/1.43 % (12595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.43 % (12594)Termination phase: Saturation
% 1.73/1.43
% 1.73/1.43 % (12594)Memory used [KB]: 1023
% 1.73/1.43 % (12594)Time elapsed: 0.003 s
% 1.73/1.43 % (12594)Instructions burned: 3 (million)
% 1.73/1.43 % (12594)------------------------------
% 1.73/1.43 % (12594)------------------------------
% 1.73/1.43 % (12595)Termination reason: Unknown
% 1.73/1.43 % (12595)Termination phase: Property scanning
% 1.73/1.43
% 1.73/1.43 % (12595)Memory used [KB]: 895
% 1.73/1.43 % (12595)Time elapsed: 0.003 s
% 1.73/1.43 % (12595)Instructions burned: 3 (million)
% 1.73/1.43 % (12595)------------------------------
% 1.73/1.43 % (12595)------------------------------
% 1.73/1.43 % (12592)Instruction limit reached!
% 1.73/1.43 % (12592)------------------------------
% 1.73/1.43 % (12592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.43 % (12592)Termination reason: Unknown
% 1.73/1.43 % (12592)Termination phase: Saturation
% 1.73/1.43
% 1.73/1.43 % (12592)Memory used [KB]: 5500
% 1.73/1.43 % (12592)Time elapsed: 0.004 s
% 1.73/1.43 % (12592)Instructions burned: 4 (million)
% 1.73/1.43 % (12592)------------------------------
% 1.73/1.43 % (12592)------------------------------
% 1.73/1.43 % (12596)First to succeed.
% 1.73/1.43 % (12591)Also succeeded, but the first one will report.
% 1.73/1.43 % (12596)Refutation found. Thanks to Tanya!
% 1.73/1.43 % SZS status Theorem for DTF2THF_12494
% 1.73/1.43 % SZS output start Proof for DTF2THF_12494
% 1.73/1.43 thf(func_def_0, type, in: $i > $i > $o).
% 1.73/1.43 thf(func_def_1, type, powerset: $i > $i).
% 1.73/1.43 thf(func_def_4, type, binintersect: $i > $i > $i).
% 1.73/1.43 thf(f61,plain,(
% 1.73/1.43 $false),
% 1.73/1.43 inference(subsumption_resolution,[status(thm)],[f60,f52])).
% 1.73/1.43 thf(f52,plain,(
% 1.73/1.43 ($true = (in @ sK3 @ sK1))),
% 1.73/1.43 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.73/1.43 thf(f51,plain,(
% 1.73/1.43 ($true != $true) | ($true = (in @ sK3 @ sK1))),
% 1.73/1.43 inference(superposition,[status(thm)],[f50,f29])).
% 1.73/1.43 thf(f29,plain,(
% 1.73/1.43 ($true = (in @ sK3 @ (binintersect @ sK1 @ sK2)))),
% 1.73/1.43 inference(cnf_transformation,[status(thm)],[f20])).
% 1.73/1.43 thf(f20,plain,(
% 1.73/1.43 (binintersectEL = $true) & (powersetE = $true) & (((in @ sK1 @ (powerset @ sK0)) = $true) & (($true = (in @ sK2 @ (powerset @ sK0))) & (((in @ sK3 @ sK0) != $true) & ($true = (in @ sK3 @ (binintersect @ sK1 @ sK2))))))),
% 1.73/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f19,f18,f17])).
% 1.73/1.43 thf(f17,plain,(
% 1.73/1.43 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (((in @ X3 @ X0) != $true) & ($true = (in @ X3 @ (binintersect @ X1 @ X2)))))) => (((in @ sK1 @ (powerset @ sK0)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true != (in @ X3 @ sK0)) & ((in @ X3 @ (binintersect @ sK1 @ X2)) = $true))))),
% 1.73/1.43 introduced(definition,[],[choice_axiom])).
% 1.73/1.43 thf(f18,plain,(
% 1.73/1.43 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true != (in @ X3 @ sK0)) & ((in @ X3 @ (binintersect @ sK1 @ X2)) = $true))) => (($true = (in @ sK2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true != (in @ X3 @ sK0)) & ((in @ X3 @ (binintersect @ sK1 @ sK2)) = $true)))),
% 1.73/1.43 introduced(definition,[],[choice_axiom])).
% 1.73/1.43 thf(f19,plain,(
% 1.73/1.43 ? [X3 : $i] : (($true != (in @ X3 @ sK0)) & ((in @ X3 @ (binintersect @ sK1 @ sK2)) = $true)) => (((in @ sK3 @ sK0) != $true) & ($true = (in @ sK3 @ (binintersect @ sK1 @ sK2))))),
% 1.73/1.43 introduced(definition,[],[choice_axiom])).
% 1.73/1.43 thf(f15,plain,(
% 1.73/1.43 (binintersectEL = $true) & (powersetE = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (((in @ X3 @ X0) != $true) & ($true = (in @ X3 @ (binintersect @ X1 @ X2))))))),
% 1.73/1.43 inference(flattening,[status(thm)],[f14])).
% 1.73/1.43 thf(f14,plain,(
% 1.73/1.43 (? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (((in @ X3 @ X0) != $true) & ($true = (in @ X3 @ (binintersect @ X1 @ X2)))))) & (binintersectEL = $true)) & (powersetE = $true)),
% 1.73/1.43 inference(ennf_transformation,[status(thm)],[f9])).
% 1.73/1.43 thf(f9,plain,(
% 1.73/1.43 ~((powersetE = $true) => ((binintersectEL = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ (binintersect @ X1 @ X2))) => ((in @ X3 @ X0) = $true))))))),
% 1.73/1.43 inference(fool_elimination,[status(thm)],[f8])).
% 1.73/1.43 thf(f8,plain,(
% 1.73/1.43 ~(powersetE => (binintersectEL => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (binintersect @ X1 @ X2)) => (in @ X3 @ X0))))))),
% 1.73/1.43 inference(rectify,[status(thm)],[f4])).
% 1.73/1.43 thf(f4,negated_conjecture,(
% 1.73/1.43 ~(powersetE => (binintersectEL => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ X0))))))),
% 1.73/1.43 inference(negated_conjecture,[status(cth)],[f3])).
% 1.73/1.43 thf(f3,conjecture,(
% 1.73/1.43 powersetE => (binintersectEL => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ X0)))))),
% 1.73/1.43 file('/export/starexec/sandbox/tmp/tmp.3bgXq5UWwq/DTF2THF_12494.p',woz13rule0)).
% 1.73/1.43 thf(f50,plain,(
% 1.73/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (binintersect @ X1 @ X0))) | ((in @ X2 @ X1) = $true)) )),
% 1.73/1.43 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.73/1.43 thf(f42,plain,(
% 1.73/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (binintersect @ X1 @ X0))) | ((in @ X2 @ X1) = $true) | ($true != $true)) )),
% 1.73/1.43 inference(definition_unfolding,[status(thm)],[f37,f34])).
% 1.73/1.43 thf(f34,plain,(
% 1.73/1.43 (binintersectEL = $true)),
% 1.73/1.43 inference(cnf_transformation,[status(thm)],[f20])).
% 1.73/1.43 thf(f37,plain,(
% 1.73/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) | ($true != (in @ X2 @ (binintersect @ X1 @ X0))) | (binintersectEL != $true)) )),
% 1.73/1.43 inference(cnf_transformation,[status(thm)],[f24])).
% 1.73/1.43 thf(f24,plain,(
% 1.73/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) | ($true != (in @ X2 @ (binintersect @ X1 @ X0)))) | (binintersectEL != $true)) & ((binintersectEL = $true) | (((in @ sK6 @ sK5) != $true) & ($true = (in @ sK6 @ (binintersect @ sK5 @ sK4)))))),
% 1.73/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f22,f23])).
% 1.73/1.43 thf(f23,plain,(
% 1.73/1.43 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) & ($true = (in @ X5 @ (binintersect @ X4 @ X3)))) => (((in @ sK6 @ sK5) != $true) & ($true = (in @ sK6 @ (binintersect @ sK5 @ sK4))))),
% 1.73/1.43 introduced(definition,[],[choice_axiom])).
% 1.73/1.43 thf(f22,plain,(
% 1.73/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) | ($true != (in @ X2 @ (binintersect @ X1 @ X0)))) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) & ($true = (in @ X5 @ (binintersect @ X4 @ X3)))))),
% 1.73/1.43 inference(rectify,[status(thm)],[f21])).
% 1.73/1.43 thf(f21,plain,(
% 1.73/1.43 (! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ (binintersect @ X0 @ X1)) = $true)))),
% 1.73/1.43 inference(nnf_transformation,[status(thm)],[f16])).
% 1.73/1.43 thf(f16,plain,(
% 1.73/1.43 ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) <=> (binintersectEL = $true)),
% 1.73/1.43 inference(ennf_transformation,[status(thm)],[f11])).
% 1.73/1.43 thf(f11,plain,(
% 1.73/1.43 ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) => ((in @ X2 @ X0) = $true)) <=> (binintersectEL = $true)),
% 1.73/1.43 inference(fool_elimination,[status(thm)],[f10])).
% 1.73/1.43 thf(f10,plain,(
% 1.73/1.43 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.73/1.43 inference(rectify,[status(thm)],[f2])).
% 1.73/1.43 thf(f2,axiom,(
% 1.73/1.43 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.73/1.43 file('/export/starexec/sandbox/tmp/tmp.3bgXq5UWwq/DTF2THF_12494.p',binintersectEL)).
% 1.73/1.43 thf(f60,plain,(
% 1.73/1.43 ($true != (in @ sK3 @ sK1))),
% 1.73/1.43 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.73/1.43 thf(f59,plain,(
% 1.73/1.43 ($true != (in @ sK3 @ sK1)) | ($true != $true)),
% 1.73/1.43 inference(superposition,[status(thm)],[f30,f56])).
% 1.73/1.43 thf(f56,plain,(
% 1.73/1.43 ( ! [X0 : $i] : (($true = (in @ X0 @ sK0)) | ((in @ X0 @ sK1) != $true)) )),
% 1.73/1.43 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.73/1.43 thf(f54,plain,(
% 1.73/1.43 ( ! [X0 : $i] : (((in @ X0 @ sK1) != $true) | ($true = (in @ X0 @ sK0)) | ($true != $true)) )),
% 1.73/1.43 inference(superposition,[status(thm)],[f49,f32])).
% 1.73/1.43 thf(f32,plain,(
% 1.73/1.43 ((in @ sK1 @ (powerset @ sK0)) = $true)),
% 1.73/1.43 inference(cnf_transformation,[status(thm)],[f20])).
% 1.73/1.43 thf(f49,plain,(
% 1.73/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X0))) | ($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2))) )),
% 1.73/1.43 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.73/1.43 thf(f45,plain,(
% 1.73/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ X2)) | ($true != (in @ X2 @ (powerset @ X0))) | ($true != $true) | ($true = (in @ X1 @ X0))) )),
% 1.73/1.43 inference(definition_unfolding,[status(thm)],[f41,f33])).
% 1.73/1.43 thf(f33,plain,(
% 1.73/1.43 (powersetE = $true)),
% 1.73/1.43 inference(cnf_transformation,[status(thm)],[f20])).
% 1.73/1.43 thf(f41,plain,(
% 1.73/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true != (in @ X2 @ (powerset @ X0))) | (powersetE != $true)) )),
% 1.73/1.43 inference(cnf_transformation,[status(thm)],[f28])).
% 1.73/1.43 thf(f28,plain,(
% 1.73/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true != (in @ X2 @ (powerset @ X0)))) | (powersetE != $true)) & ((powersetE = $true) | (($true != (in @ sK8 @ sK7)) & ($true = (in @ sK8 @ sK9)) & ($true = (in @ sK9 @ (powerset @ sK7)))))),
% 1.73/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f26,f27])).
% 1.73/1.43 thf(f27,plain,(
% 1.73/1.43 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) & ($true = (in @ X4 @ X5)) & ($true = (in @ X5 @ (powerset @ X3)))) => (($true != (in @ sK8 @ sK7)) & ($true = (in @ sK8 @ sK9)) & ($true = (in @ sK9 @ (powerset @ sK7))))),
% 1.73/1.43 introduced(definition,[],[choice_axiom])).
% 1.73/1.43 thf(f26,plain,(
% 1.73/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true != (in @ X2 @ (powerset @ X0)))) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) & ($true = (in @ X4 @ X5)) & ($true = (in @ X5 @ (powerset @ X3)))))),
% 1.73/1.43 inference(rectify,[status(thm)],[f25])).
% 1.73/1.43 thf(f25,plain,(
% 1.73/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true != (in @ X2 @ (powerset @ X0)))) | (powersetE != $true)) & ((powersetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) & ($true = (in @ X1 @ X2)) & ($true = (in @ X2 @ (powerset @ X0)))))),
% 1.73/1.43 inference(nnf_transformation,[status(thm)],[f13])).
% 1.73/1.43 thf(f13,plain,(
% 1.73/1.43 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true != (in @ X2 @ (powerset @ X0)))) <=> (powersetE = $true)),
% 1.73/1.43 inference(flattening,[status(thm)],[f12])).
% 1.73/1.43 thf(f12,plain,(
% 1.73/1.43 ! [X2 : $i,X1 : $i,X0 : $i] : ((($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2))) | ($true != (in @ X2 @ (powerset @ X0)))) <=> (powersetE = $true)),
% 1.73/1.43 inference(ennf_transformation,[status(thm)],[f7])).
% 1.73/1.43 thf(f7,plain,(
% 1.73/1.43 ! [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => (($true = (in @ X1 @ X2)) => ($true = (in @ X1 @ X0)))) <=> (powersetE = $true)),
% 1.73/1.43 inference(fool_elimination,[status(thm)],[f6])).
% 1.73/1.43 thf(f6,plain,(
% 1.73/1.43 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((in @ X1 @ X2) => (in @ X1 @ X0))) = powersetE)),
% 1.73/1.43 inference(rectify,[status(thm)],[f1])).
% 1.73/1.43 thf(f1,axiom,(
% 1.73/1.43 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 1.73/1.43 file('/export/starexec/sandbox/tmp/tmp.3bgXq5UWwq/DTF2THF_12494.p',powersetE)).
% 1.73/1.43 thf(f30,plain,(
% 1.73/1.43 ((in @ sK3 @ sK0) != $true)),
% 1.73/1.43 inference(cnf_transformation,[status(thm)],[f20])).
% 1.73/1.43 % SZS output end Proof for DTF2THF_12494
% 1.73/1.43 % (12596)------------------------------
% 1.73/1.43 % (12596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.43 % (12596)Termination reason: Refutation
% 1.73/1.43
% 1.73/1.43 % (12596)Memory used [KB]: 5500
% 1.73/1.43 % (12596)Time elapsed: 0.006 s
% 1.73/1.43 % (12596)Instructions burned: 4 (million)
% 1.73/1.43 % (12596)------------------------------
% 1.73/1.43 % (12596)------------------------------
% 1.73/1.43 % (12590)Success in time 0.021 s
%------------------------------------------------------------------------------