%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU735^2 : 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 : n020.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 09:36:46 AM UTC 2026
% Result : Theorem 1.55s 1.28s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 27 unt; 0 typ; 2 def)
% Number of atoms : 381 ( 78 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 628 ( 20 ~; 17 |; 18 &; 499 @)
% ( 2 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 10 con; 0-2 aty)
% ( 24 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 29 ^; 47 !; 11 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
setminus: $i > $i > $i ).
thf(f75,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f54,f62,f74]) ).
thf(f74,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $false = $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f17,f48]) ).
thf(f48,plain,
( ( $false
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl3_1
<=> ( $false
= ( in @ sK0 @ ( powerset @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f17,plain,
( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( powersetI1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ ( setminus @ sK1 @ ( binintersect @ sK0 @ sK2 ) ) ) )
!= $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
!= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ ( setminus @ sK1 @ ( binintersect @ sK0 @ X2 ) ) ) )
!= $true ) )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ ( setminus @ sK1 @ ( binintersect @ sK0 @ X2 ) ) ) )
!= $true ) )
=> ( ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ ( setminus @ sK1 @ ( binintersect @ sK0 @ sK2 ) ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( powersetI1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
!= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
!= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( complementSubsetComplementIntersect = $true )
& ( powersetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( powersetI1 = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( powersetI1
=> ( complementSubsetComplementIntersect
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetI1
=> ( complementSubsetComplementIntersect
=> ! [X2: $i,X0: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetI1
=> ( complementSubsetComplementIntersect
=> ! [X2: $i,X0: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.A4wZJUpYeH/DTF2THF_10558.p',complementInPowersetComplementIntersect) ).
thf(f62,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f61]) ).
thf(f61,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $false = $true )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f19,f52]) ).
thf(f52,plain,
( ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl3_2
<=> ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f19,plain,
( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f54,plain,
( spl3_2
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f43,f46,f50]) ).
thf(f43,plain,
( ( $false
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f40,f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( subset @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( subset @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( subset @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( subset @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( subset @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ ( setminus @ Y0 @ X1 ) @ ( setminus @ Y0 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f22,f20]) ).
thf(f20,plain,
complementSubsetComplementIntersect = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f22,plain,
( complementSubsetComplementIntersect
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( complementSubsetComplementIntersect
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ Y0 ) @ ( setminus @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) )
= complementSubsetComplementIntersect ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ ( binintersect @ X2 @ X3 ) ) ) ) )
= complementSubsetComplementIntersect ),
file('/export/starexec/sandbox/tmp/tmp.A4wZJUpYeH/DTF2THF_10558.p',complementSubsetComplementIntersect) ).
thf(f40,plain,
( $false
= ( subset @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ ( binintersect @ sK0 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $false
= ( subset @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ ( binintersect @ sK0 @ sK2 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
| ( $false
= ( subset @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
=> ( in @ X2 @ ( powerset @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( in @ Y0 @ ( powerset @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f23,f21]) ).
thf(f21,plain,
powersetI1 = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f23,plain,
( powersetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( powersetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( powersetI1
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( powersetI1
= ( ! [X1: $i,X0: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.A4wZJUpYeH/DTF2THF_10558.p',powersetI1) ).
thf(f18,plain,
( ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ ( setminus @ sK1 @ ( binintersect @ sK0 @ sK2 ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU735^2 : 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
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:32:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEU735^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.19/0.45 % Version : Especial > Reduced > Especial.
% 0.19/0.45 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.19/0.45 % in (setminus A X) (powerset (setminus A (binintersect X Y)))))
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.45 % Source : [Bro08]
% 0.19/0.45 % Names : ZFC237l [Bro08]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 10 ( 2 unt; 7 typ; 2 def)
% 0.19/0.45 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 5 ( 4 avg)
% 0.19/0.45 % Number of connectives : 41 ( 0 ~; 0 |; 0 &; 34 @)
% 0.19/0.45 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 13 ( 5 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 8 ( 7 usr; 2 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : http://mathgate.info/detsetitem.php?id=297
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(in_type,type,
% 0.19/0.45 in: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(powerset_type,type,
% 0.19/0.45 powerset: $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(subset_type,type,
% 0.19/0.45 subset: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(powersetI1_type,type,
% 0.19/0.45 powersetI1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(powersetI1,definition,
% 0.19/0.45 ( powersetI1
% 0.19/0.45 = ( ! [A: $i,B: $i] :
% 0.19/0.45 ( ( subset @ B @ A )
% 0.19/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(binintersect_type,type,
% 0.19/0.45 binintersect: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(setminus_type,type,
% 0.19/0.45 setminus: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(complementSubsetComplementIntersect_type,type,
% 0.19/0.45 complementSubsetComplementIntersect: $o ).
% 0.19/0.45
% 0.19/0.45 thf(complementSubsetComplementIntersect,definition,
% 0.19/0.45 ( complementSubsetComplementIntersect
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(complementInPowersetComplementIntersect,conjecture,
% 0.19/0.45 ( powersetI1
% 0.19/0.45 => ( complementSubsetComplementIntersect
% 0.19/0.45 => ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.55/1.25 ---- Embedded in THF ---
% 1.55/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.25 %%% Generated on Tue Feb 24 12:32:43 EST 2026
% 1.55/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.25 %%% Logic specification used:
% 1.55/1.25 %%% thf(spec, logic, $$dhol).
% 1.55/1.25
% 1.55/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.A4wZJUpYeH/DTF2DTF10558.p
% See solution above
% 1.55/1.25 ------------------------
% 1.55/1.26 ---- Cleaned THF ---
% 1.55/1.26 thf(in_type,type,
% 1.55/1.26 in: $i > $i > $o ).
% 1.55/1.26
% 1.55/1.26 thf(powerset_type,type,
% 1.55/1.26 powerset: $i > $i ).
% 1.55/1.26
% 1.55/1.26 thf(subset_type,type,
% 1.55/1.26 subset: $i > $i > $o ).
% 1.55/1.26
% 1.55/1.26 thf(powersetI1_type,type,
% 1.55/1.26 powersetI1: $o ).
% 1.55/1.26
% 1.55/1.26 thf(powersetI1,definition,
% 1.55/1.26 ( powersetI1
% 1.55/1.26 = ( ! [A: $i,B: $i] :
% 1.55/1.26 ( ( subset @ B @ A )
% 1.55/1.26 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(binintersect_type,type,
% 1.55/1.26 binintersect: $i > $i > $i ).
% 1.55/1.26
% 1.55/1.26 thf(setminus_type,type,
% 1.55/1.26 setminus: $i > $i > $i ).
% 1.55/1.26
% 1.55/1.26 thf(complementSubsetComplementIntersect_type,type,
% 1.55/1.26 complementSubsetComplementIntersect: $o ).
% 1.55/1.26
% 1.55/1.26 thf(complementSubsetComplementIntersect,definition,
% 1.55/1.26 ( complementSubsetComplementIntersect
% 1.55/1.26 = ( ! [A: $i,X: $i] :
% 1.55/1.26 ( ( in @ X @ ( powerset @ A ) )
% 1.55/1.26 => ! [Y: $i] :
% 1.55/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 1.55/1.26 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 1.55/1.26
% 1.55/1.26 thf(complementInPowersetComplementIntersect,conjecture,
% 1.55/1.26 ( powersetI1
% 1.55/1.26 => ( complementSubsetComplementIntersect
% 1.55/1.26 => ! [A: $i,X: $i] :
% 1.55/1.26 ( ( in @ X @ ( powerset @ A ) )
% 1.55/1.26 => ! [Y: $i] :
% 1.55/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 1.55/1.26 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 1.55/1.26 ------------------------
% 1.55/1.28 % (10748)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10558 for (2999ds/183Mi)
% 1.55/1.28 % (10748)First to succeed.
% 1.55/1.28 % (10748)Refutation found. Thanks to Tanya!
% 1.55/1.28 % SZS status Theorem for DTF2THF_10558
% 1.55/1.28 % SZS output start Proof for DTF2THF_10558
% 1.55/1.28 thf(func_def_0, type, in: $i > $i > $o).
% 1.55/1.28 thf(func_def_1, type, powerset: $i > $i).
% 1.55/1.28 thf(func_def_2, type, subset: $i > $i > $o).
% 1.55/1.28 thf(func_def_5, type, binintersect: $i > $i > $i).
% 1.55/1.28 thf(func_def_6, type, setminus: $i > $i > $i).
% 1.55/1.28 thf(f75,plain,(
% 1.55/1.28 $false),
% 1.55/1.28 inference(avatar_sat_refutation,[status(thm)],[f54,f62,f74])).
% 1.55/1.28 thf(f74,plain,(
% 1.55/1.28 ~spl3_1),
% 1.55/1.28 inference(avatar_contradiction_clause,[status(thm)],[f73])).
% 1.55/1.28 thf(f73,plain,(
% 1.55/1.28 $false | ~spl3_1),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.55/1.28 thf(f67,plain,(
% 1.55/1.28 ($false = $true) | ~spl3_1),
% 1.55/1.28 inference(superposition,[status(thm)],[f17,f48])).
% 1.55/1.28 thf(f48,plain,(
% 1.55/1.28 ($false = (in @ sK0 @ (powerset @ sK1))) | ~spl3_1),
% 1.55/1.28 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.55/1.28 thf(f46,definition,(
% 1.55/1.28 spl3_1 <=> ($false = (in @ sK0 @ (powerset @ sK1)))),
% 1.55/1.28 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.55/1.28 thf(f17,plain,(
% 1.55/1.28 ((in @ sK0 @ (powerset @ sK1)) = $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f16])).
% 1.55/1.28 thf(f16,plain,(
% 1.55/1.28 (powersetI1 = $true) & (complementSubsetComplementIntersect = $true) & ((((in @ sK2 @ (powerset @ sK1)) = $true) & ((in @ (setminus @ sK1 @ sK0) @ (powerset @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)))) != $true)) & ((in @ sK0 @ (powerset @ sK1)) = $true))),
% 1.55/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15,f14])).
% 1.55/1.28 thf(f14,plain,(
% 1.55/1.28 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((in @ (setminus @ X1 @ X0) @ (powerset @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) != $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2 : $i] : (((in @ X2 @ (powerset @ sK1)) = $true) & ((in @ (setminus @ sK1 @ sK0) @ (powerset @ (setminus @ sK1 @ (binintersect @ sK0 @ X2)))) != $true)) & ((in @ sK0 @ (powerset @ sK1)) = $true))),
% 1.55/1.28 introduced(definition,[],[choice_axiom])).
% 1.55/1.28 thf(f15,plain,(
% 1.55/1.28 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK1)) = $true) & ((in @ (setminus @ sK1 @ sK0) @ (powerset @ (setminus @ sK1 @ (binintersect @ sK0 @ X2)))) != $true)) => (((in @ sK2 @ (powerset @ sK1)) = $true) & ((in @ (setminus @ sK1 @ sK0) @ (powerset @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)))) != $true))),
% 1.55/1.28 introduced(definition,[],[choice_axiom])).
% 1.55/1.28 thf(f13,plain,(
% 1.55/1.28 (powersetI1 = $true) & (complementSubsetComplementIntersect = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((in @ (setminus @ X1 @ X0) @ (powerset @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) != $true)) & ((in @ X0 @ (powerset @ X1)) = $true))),
% 1.55/1.28 inference(flattening,[status(thm)],[f12])).
% 1.55/1.28 thf(f12,plain,(
% 1.55/1.28 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((in @ (setminus @ X1 @ X0) @ (powerset @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) != $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (complementSubsetComplementIntersect = $true)) & (powersetI1 = $true)),
% 1.55/1.28 inference(ennf_transformation,[status(thm)],[f9])).
% 1.55/1.28 thf(f9,plain,(
% 1.55/1.28 ~((powersetI1 = $true) => ((complementSubsetComplementIntersect = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ((in @ (setminus @ X1 @ X0) @ (powerset @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) = $true)))))),
% 1.55/1.28 inference(fool_elimination,[status(thm)],[f8])).
% 1.55/1.28 thf(f8,plain,(
% 1.55/1.28 ~(powersetI1 => (complementSubsetComplementIntersect => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ (setminus @ X1 @ (binintersect @ X0 @ X2))))))))),
% 1.55/1.28 inference(rectify,[status(thm)],[f4])).
% 1.55/1.28 thf(f4,negated_conjecture,(
% 1.55/1.28 ~(powersetI1 => (complementSubsetComplementIntersect => ! [X2 : $i,X0 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X2) @ (powerset @ (setminus @ X0 @ (binintersect @ X2 @ X3))))))))),
% 1.55/1.28 inference(negated_conjecture,[status(cth)],[f3])).
% 1.55/1.28 thf(f3,conjecture,(
% 1.55/1.28 powersetI1 => (complementSubsetComplementIntersect => ! [X2 : $i,X0 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X2) @ (powerset @ (setminus @ X0 @ (binintersect @ X2 @ X3)))))))),
% 1.55/1.28 file('/export/starexec/sandbox/tmp/tmp.A4wZJUpYeH/DTF2THF_10558.p',complementInPowersetComplementIntersect)).
% 1.55/1.28 thf(f62,plain,(
% 1.55/1.28 ~spl3_2),
% 1.55/1.28 inference(avatar_contradiction_clause,[status(thm)],[f61])).
% 1.55/1.28 thf(f61,plain,(
% 1.55/1.28 $false | ~spl3_2),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.55/1.28 thf(f57,plain,(
% 1.55/1.28 ($false = $true) | ~spl3_2),
% 1.55/1.28 inference(superposition,[status(thm)],[f19,f52])).
% 1.55/1.28 thf(f52,plain,(
% 1.55/1.28 ($false = (in @ sK2 @ (powerset @ sK1))) | ~spl3_2),
% 1.55/1.28 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.55/1.28 thf(f50,definition,(
% 1.55/1.28 spl3_2 <=> ($false = (in @ sK2 @ (powerset @ sK1)))),
% 1.55/1.28 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.55/1.28 thf(f19,plain,(
% 1.55/1.28 ((in @ sK2 @ (powerset @ sK1)) = $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f16])).
% 1.55/1.28 thf(f54,plain,(
% 1.55/1.28 spl3_2 | spl3_1),
% 1.55/1.28 inference(avatar_split_clause,[status(thm)],[f43,f46,f50])).
% 1.55/1.28 thf(f43,plain,(
% 1.55/1.28 ($false = (in @ sK0 @ (powerset @ sK1))) | ($false = (in @ sK2 @ (powerset @ sK1)))),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.55/1.28 thf(f42,plain,(
% 1.55/1.28 ($false = (in @ sK0 @ (powerset @ sK1))) | ($false = (in @ sK2 @ (powerset @ sK1))) | ($false = $true)),
% 1.55/1.28 inference(superposition,[status(thm)],[f40,f33])).
% 1.55/1.28 thf(f33,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (subset @ (setminus @ X2 @ X1) @ (setminus @ X2 @ (binintersect @ X1 @ X3)))) | ($false = (in @ X1 @ (powerset @ X2))) | ($false = (in @ X3 @ (powerset @ X2)))) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.55/1.28 thf(f32,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (powerset @ X2))) | (((in @ X3 @ (powerset @ X2)) => (subset @ (setminus @ X2 @ X1) @ (setminus @ X2 @ (binintersect @ X1 @ X3)))) = $true)) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.55/1.28 thf(f31,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (powerset @ X2))) | (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (subset @ (setminus @ X2 @ X1) @ (setminus @ X2 @ (binintersect @ X1 @ Y0))))) @ X3) = $true)) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f30])).
% 1.55/1.28 thf(f30,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (subset @ (setminus @ X2 @ X1) @ (setminus @ X2 @ (binintersect @ X1 @ Y0)))))) = $true) | ($false = (in @ X1 @ (powerset @ X2)))) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.55/1.28 thf(f29,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (subset @ (setminus @ X2 @ X1) @ (setminus @ X2 @ (binintersect @ X1 @ Y0))))))) = $true)) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.55/1.28 thf(f28,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ X1) @ (setminus @ Y0 @ (binintersect @ X1 @ Y1)))))))) @ X2) = $true)) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f27])).
% 1.55/1.28 thf(f27,plain,(
% 1.55/1.28 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ X1) @ (setminus @ Y0 @ (binintersect @ X1 @ Y1))))))))) = $true)) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.55/1.28 thf(f26,plain,(
% 1.55/1.28 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (subset @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) @ X1) = $true)) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f24])).
% 1.55/1.28 thf(f24,plain,(
% 1.55/1.28 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (subset @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))) = $true)),
% 1.55/1.28 inference(definition_unfolding,[status(thm)],[f22,f20])).
% 1.55/1.28 thf(f20,plain,(
% 1.55/1.28 (complementSubsetComplementIntersect = $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f16])).
% 1.55/1.28 thf(f22,plain,(
% 1.55/1.28 (complementSubsetComplementIntersect = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (subset @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.55/1.28 thf(f11,plain,(
% 1.55/1.28 (complementSubsetComplementIntersect = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (subset @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))),
% 1.55/1.28 inference(fool_elimination,[status(thm)],[f10])).
% 1.55/1.28 thf(f10,plain,(
% 1.55/1.28 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) = complementSubsetComplementIntersect)),
% 1.55/1.28 inference(rectify,[status(thm)],[f2])).
% 1.55/1.28 thf(f2,axiom,(
% 1.55/1.28 (! [X0 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ (binintersect @ X2 @ X3))))) = complementSubsetComplementIntersect)),
% 1.55/1.28 file('/export/starexec/sandbox/tmp/tmp.A4wZJUpYeH/DTF2THF_10558.p',complementSubsetComplementIntersect)).
% 1.55/1.28 thf(f40,plain,(
% 1.55/1.28 ($false = (subset @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2))))),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.55/1.28 thf(f39,plain,(
% 1.55/1.28 ($false = (subset @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)))) | ($true != $true)),
% 1.55/1.28 inference(superposition,[status(thm)],[f18,f38])).
% 1.55/1.28 thf(f38,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) | ($false = (subset @ X2 @ X1))) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.55/1.28 thf(f37,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : ((((subset @ X2 @ X1) => (in @ X2 @ (powerset @ X1))) = $true)) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.55/1.28 thf(f36,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ X1) => (in @ Y0 @ (powerset @ X1)))) @ X2))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f35])).
% 1.55/1.28 thf(f35,plain,(
% 1.55/1.28 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X1) => (in @ Y0 @ (powerset @ X1))))) = $true)) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.55/1.28 thf(f34,plain,(
% 1.55/1.28 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0)))))) @ X1) = $true)) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f25])).
% 1.55/1.28 thf(f25,plain,(
% 1.55/1.28 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) = $true)),
% 1.55/1.28 inference(definition_unfolding,[status(thm)],[f23,f21])).
% 1.55/1.28 thf(f21,plain,(
% 1.55/1.28 (powersetI1 = $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f16])).
% 1.55/1.28 thf(f23,plain,(
% 1.55/1.28 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.55/1.28 thf(f7,plain,(
% 1.55/1.28 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 1.55/1.28 inference(fool_elimination,[status(thm)],[f6])).
% 1.55/1.28 thf(f6,plain,(
% 1.55/1.28 (powersetI1 = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 1.55/1.28 inference(rectify,[status(thm)],[f1])).
% 1.55/1.28 thf(f1,axiom,(
% 1.55/1.28 (powersetI1 = ! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 1.55/1.28 file('/export/starexec/sandbox/tmp/tmp.A4wZJUpYeH/DTF2THF_10558.p',powersetI1)).
% 1.55/1.28 thf(f18,plain,(
% 1.55/1.28 ((in @ (setminus @ sK1 @ sK0) @ (powerset @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)))) != $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f16])).
% 1.55/1.28 % SZS output end Proof for DTF2THF_10558
% 1.55/1.28 % (10748)------------------------------
% 1.55/1.28 % (10748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (10748)Termination reason: Refutation
% 1.55/1.28
% 1.55/1.28 % (10748)Memory used [KB]: 5500
% 1.55/1.28 % (10748)Time elapsed: 0.005 s
% 1.55/1.28 % (10748)Instructions burned: 6 (million)
% 1.55/1.28 % (10748)------------------------------
% 1.55/1.28 % (10748)------------------------------
% 1.55/1.28 % (10747)Success in time 0.016 s
%------------------------------------------------------------------------------