%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU592^2 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:28 AM UTC 2026
% Result : Theorem 1.51s 1.27s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 317 ( 68 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 506 ( 12 ~; 12 |; 6 &; 396 @)
% ( 0 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 7 con; 0-2 aty)
% ( 37 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 147 ( 78 ^; 63 !; 6 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_19,type,
sK3: $i > $i > $i ).
thf(func_def_21,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f67,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
$true != $true,
inference(superposition,[status(thm)],[f28,f61]) ).
thf(f61,plain,
! [X0: $i,X1: $i] :
( ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
@ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
@ X0 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: $i,X1: $i] :
( ( ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
@ X0 )
= $true )
| ( ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
@ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f36,f54]) ).
thf(f54,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in
@ ( sK3 @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) )
@ X1 )
= $true )
| ( ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) )
@ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in
@ ( sK3 @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) )
@ X1 )
= $true )
| ( $false = $true )
| ( ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) )
@ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f37,f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) )
= $false )
| ( ( in @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) )
=> ( in @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X1 ) ) )
=> ( in @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X1 ) ) )
=> ( in @ X2 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ X1 ) ) )
=> ( in @ Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ X1 ) ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y0 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f24]) ).
thf(f24,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y0 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f19]) ).
thf(f19,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) )
= binintersect ),
file('/export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2THF_21358.p',binintersect) ).
thf(f20,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( binintersect @ Y2 @ Y0 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( binintersect @ Y2 @ Y0 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X1 @ X0 ) )
= binintersectEL ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) )
= binintersectEL ),
file('/export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2THF_21358.p',binintersectEL) ).
thf(f21,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( subsetI2 = $true )
& ( ( subset @ ( binintersect @ sK1 @ sK0 ) @ sK1 )
!= $true )
& ( binintersectEL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
!= $true )
=> ( ( subset @ ( binintersect @ sK1 @ sK0 ) @ sK1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( subsetI2 = $true )
& ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
!= $true )
& ( binintersectEL = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
!= $true )
& ( binintersectEL = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( subsetI2 = $true )
=> ( ( binintersectEL = $true )
=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( subsetI2
=> ( binintersectEL
=> ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X1 @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( subsetI2
=> ( binintersectEL
=> ! [X1: $i,X0: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( subsetI2
=> ( binintersectEL
=> ! [X1: $i,X0: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2THF_21358.p',binintersectLsub) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK3 @ X1 @ X2 ) @ X2 )
= $true )
| ( ( subset @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) ) )
| ( ( subset @ X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f23,f18]) ).
thf(f18,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI2 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI2 ),
file('/export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2THF_21358.p',subsetI2) ).
thf(f23,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK3 @ X1 @ X2 ) @ X1 )
= $false )
| ( ( subset @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f28,plain,
( ( subset
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ Y0 @ sK0 ) )
@ sK1 )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( subset
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK1
@ sK0 )
@ sK1 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f22,f19]) ).
thf(f22,plain,
( ( subset @ ( binintersect @ sK1 @ sK0 ) @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU592^2 : 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
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:27:46 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SEU592^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.45 % Domain : Set Theory
% 0.30/0.45 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.30/0.45 % Version : Especial > Reduced > Especial.
% 0.30/0.45 % English : (! A:i.! B:i.subset (binintersect A B) A)
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.45 % Source : [Bro08]
% 0.30/0.45 % Names : ZFC094l [Bro08]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.30/0.45 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.30/0.45 % Number of atoms : 14 ( 3 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.30/0.45 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 20 @)
% 0.30/0.45 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 9 ( 3 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.30/0.45 % Number of variables : 11 ( 3 ^; 8 !; 0 ?; 11 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : http://mathgate.info/detsetitem.php?id=292
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(in_type,type,
% 0.30/0.45 in: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(dsetconstr_type,type,
% 0.30/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(subset_type,type,
% 0.30/0.45 subset: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(subsetI2_type,type,
% 0.30/0.45 subsetI2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(subsetI2,definition,
% 0.30/0.45 ( subsetI2
% 0.30/0.45 = ( ! [A: $i,B: $i] :
% 0.30/0.45 ( ! [Xx: $i] :
% 0.30/0.45 ( ( in @ Xx @ A )
% 0.30/0.45 => ( in @ Xx @ B ) )
% 0.30/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(binintersect_type,type,
% 0.30/0.45 binintersect: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(binintersect,definition,
% 0.30/0.45 ( binintersect
% 0.30/0.45 = ( ^ [A: $i,B: $i] :
% 0.30/0.45 ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL_type,type,
% 0.30/0.46 binintersectEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL,definition,
% 0.30/0.46 ( binintersectEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub,conjecture,
% 0.30/0.46 ( subsetI2
% 0.30/0.46 => ( binintersectEL
% 0.30/0.46 => ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.51/1.24 ---- Embedded in THF ---
% 1.51/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.24 %%% Generated on Tue Feb 24 12:27:46 EST 2026
% 1.51/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.24 %%% Logic specification used:
% 1.51/1.24 %%% thf(spec, logic, $$dhol).
% 1.51/1.24
% 1.51/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2DTF21358.p
% See solution above
% 1.51/1.24 ------------------------
% 1.51/1.25 ---- Cleaned THF ---
% 1.51/1.25 thf(in_type,type,
% 1.51/1.25 in: $i > $i > $o ).
% 1.51/1.25
% 1.51/1.25 thf(dsetconstr_type,type,
% 1.51/1.25 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.51/1.25
% 1.51/1.25 thf(subset_type,type,
% 1.51/1.25 subset: $i > $i > $o ).
% 1.51/1.25
% 1.51/1.25 thf(subsetI2_type,type,
% 1.51/1.25 subsetI2: $o ).
% 1.51/1.25
% 1.51/1.25 thf(subsetI2,definition,
% 1.51/1.25 ( subsetI2
% 1.51/1.25 = ( ! [A: $i,B: $i] :
% 1.51/1.25 ( ! [Xx: $i] :
% 1.51/1.25 ( ( in @ Xx @ A )
% 1.51/1.25 => ( in @ Xx @ B ) )
% 1.51/1.25 => ( subset @ A @ B ) ) ) ) ).
% 1.51/1.25
% 1.51/1.25 thf(binintersect_type,type,
% 1.51/1.25 binintersect: $i > $i > $i ).
% 1.51/1.25
% 1.51/1.25 thf(binintersect,definition,
% 1.51/1.25 ( binintersect
% 1.51/1.25 = ( ^ [A: $i,B: $i] :
% 1.51/1.25 ( dsetconstr @ A
% 1.51/1.25 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 1.51/1.25
% 1.51/1.25 thf(binintersectEL_type,type,
% 1.51/1.25 binintersectEL: $o ).
% 1.51/1.25
% 1.51/1.25 thf(binintersectEL,definition,
% 1.51/1.25 ( binintersectEL
% 1.51/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.51/1.25 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.51/1.25 => ( in @ Xx @ A ) ) ) ) ).
% 1.51/1.25
% 1.51/1.25 thf(binintersectLsub,conjecture,
% 1.51/1.25 ( subsetI2
% 1.51/1.25 => ( binintersectEL
% 1.51/1.25 => ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 1.51/1.25 ------------------------
% 1.51/1.27 % (21627)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_21358 for (2999ds/27Mi)
% 1.51/1.27 % (21626)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_21358 for (2999ds/4Mi)
% 1.51/1.27 % (21626)Instruction limit reached!
% 1.51/1.27 % (21626)------------------------------
% 1.51/1.27 % (21626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (21626)Termination reason: Unknown
% 1.51/1.27 % (21626)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (21626)Memory used [KB]: 5500
% 1.51/1.27 % (21626)Time elapsed: 0.003 s
% 1.51/1.27 % (21626)Instructions burned: 5 (million)
% 1.51/1.27 % (21626)------------------------------
% 1.51/1.27 % (21626)------------------------------
% 1.51/1.27 % (21627)First to succeed.
% 1.51/1.27 % (21627)Refutation found. Thanks to Tanya!
% 1.51/1.27 % SZS status Theorem for DTF2THF_21358
% 1.51/1.27 % SZS output start Proof for DTF2THF_21358
% 1.51/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.51/1.27 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.51/1.27 thf(func_def_2, type, subset: $i > $i > $o).
% 1.51/1.27 thf(func_def_5, type, binintersect: $i > $i > $i).
% 1.51/1.27 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.51/1.27 thf(func_def_19, type, sK3: $i > $i > $i).
% 1.51/1.27 thf(func_def_21, type, ph4: !>[X0: $tType]:(X0)).
% 1.51/1.27 thf(f67,plain,(
% 1.51/1.27 $false),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.51/1.27 thf(f66,plain,(
% 1.51/1.27 ($true != $true)),
% 1.51/1.27 inference(superposition,[status(thm)],[f28,f61])).
% 1.51/1.27 thf(f61,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (((subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ Y0 @ X1))) @ X0) = $true)) )),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.51/1.27 thf(f60,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ Y0 @ X1))) @ X0) = $true)) )),
% 1.51/1.27 inference(duplicate_literal_removal,[status(thm)],[f58])).
% 1.51/1.27 thf(f58,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (((subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ Y0 @ X1))) @ X0) = $true) | ((subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ Y0 @ X1))) @ X0) = $true) | ($false = $true)) )),
% 1.51/1.27 inference(superposition,[status(thm)],[f36,f54])).
% 1.51/1.27 thf(f54,plain,(
% 1.51/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ Y0 @ X2)))) @ X1) = $true) | ((subset @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ Y0 @ X2))) @ X0) = $true)) )),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.51/1.27 thf(f53,plain,(
% 1.51/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ Y0 @ X2)))) @ X1) = $true) | ($false = $true) | ((subset @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ Y0 @ X2))) @ X0) = $true)) )),
% 1.51/1.27 inference(superposition,[status(thm)],[f37,f45])).
% 1.51/1.27 thf(f45,plain,(
% 1.51/1.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (in @ Y0 @ X1)))) = $false) | ((in @ X2 @ X3) = $true)) )),
% 1.51/1.27 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.51/1.27 thf(f44,plain,(
% 1.51/1.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (in @ Y0 @ X1)))) => (in @ X2 @ X3)))) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.51/1.27 thf(f43,plain,(
% 1.51/1.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ (dsetconstr @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ X1)))) => (in @ X2 @ Y0))) @ X3) = $true)) )),
% 1.51/1.27 inference(pi_clausification,[status(thm)],[f42])).
% 1.51/1.27 thf(f42,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (dsetconstr @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ X1)))) => (in @ X2 @ Y0)))) = $true)) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.51/1.27 thf(f41,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ X1)))) => (in @ Y0 @ Y1))))) @ X2) = $true)) )),
% 1.51/1.27 inference(pi_clausification,[status(thm)],[f40])).
% 1.51/1.27 thf(f40,plain,(
% 1.51/1.27 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ X1)))) => (in @ Y0 @ Y1)))))))) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.51/1.27 thf(f39,plain,(
% 1.51/1.27 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))) => (in @ Y1 @ Y2))))))) @ X1) = $true)) )),
% 1.51/1.27 inference(pi_clausification,[status(thm)],[f38])).
% 1.51/1.27 thf(f38,plain,(
% 1.51/1.27 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))) => (in @ Y1 @ Y2)))))))) = $true)),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.51/1.27 thf(f27,plain,(
% 1.51/1.27 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ ((^[Y3 : $i]: ((^[Y4 : $i]: (dsetconstr @ Y3 @ (^[Y5 : $i]: (in @ Y5 @ Y4)))))) @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) = $true)),
% 1.51/1.27 inference(definition_unfolding,[status(thm)],[f21,f24])).
% 1.51/1.27 thf(f24,plain,(
% 1.51/1.27 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ ((^[Y3 : $i]: ((^[Y4 : $i]: (dsetconstr @ Y3 @ (^[Y5 : $i]: (in @ Y5 @ Y4)))))) @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))),
% 1.51/1.27 inference(definition_unfolding,[status(thm)],[f20,f19])).
% 1.51/1.27 thf(f19,plain,(
% 1.51/1.27 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.27 thf(f13,plain,(
% 1.51/1.27 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f2])).
% 1.51/1.27 thf(f2,axiom,(
% 1.51/1.27 ((^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))) = binintersect)),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2THF_21358.p',binintersect)).
% 1.51/1.27 thf(f20,plain,(
% 1.51/1.27 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.51/1.27 thf(f10,plain,(
% 1.51/1.27 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f9])).
% 1.51/1.27 thf(f9,plain,(
% 1.51/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X0)) = binintersectEL)),
% 1.51/1.27 inference(rectify,[status(thm)],[f3])).
% 1.51/1.27 thf(f3,axiom,(
% 1.51/1.27 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)) = binintersectEL)),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2THF_21358.p',binintersectEL)).
% 1.51/1.27 thf(f21,plain,(
% 1.51/1.27 (binintersectEL = $true)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f17])).
% 1.51/1.27 thf(f17,plain,(
% 1.51/1.27 (subsetI2 = $true) & ((subset @ (binintersect @ sK1 @ sK0) @ sK1) != $true) & (binintersectEL = $true)),
% 1.51/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16])).
% 1.51/1.27 thf(f16,plain,(
% 1.51/1.27 ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true) => ((subset @ (binintersect @ sK1 @ sK0) @ sK1) != $true)),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f15,plain,(
% 1.51/1.27 (subsetI2 = $true) & ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true) & (binintersectEL = $true)),
% 1.51/1.27 inference(flattening,[status(thm)],[f14])).
% 1.51/1.27 thf(f14,plain,(
% 1.51/1.27 (? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true) & (binintersectEL = $true)) & (subsetI2 = $true)),
% 1.51/1.27 inference(ennf_transformation,[status(thm)],[f12])).
% 1.51/1.27 thf(f12,plain,(
% 1.51/1.27 ~((subsetI2 = $true) => ((binintersectEL = $true) => ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true)))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f11])).
% 1.51/1.27 thf(f11,plain,(
% 1.51/1.27 ~(subsetI2 => (binintersectEL => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X1)))),
% 1.51/1.27 inference(rectify,[status(thm)],[f5])).
% 1.51/1.27 thf(f5,negated_conjecture,(
% 1.51/1.27 ~(subsetI2 => (binintersectEL => ! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0)))),
% 1.51/1.27 inference(negated_conjecture,[status(cth)],[f4])).
% 1.51/1.27 thf(f4,conjecture,(
% 1.51/1.27 subsetI2 => (binintersectEL => ! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2THF_21358.p',binintersectLsub)).
% 1.51/1.27 thf(f37,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : (((in @ (sK3 @ X1 @ X2) @ X2) = $true) | ((subset @ X2 @ X1) = $true)) )),
% 1.51/1.27 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.51/1.27 thf(f35,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK3 @ X1 @ X2) @ X2) => (in @ (sK3 @ X1 @ X2) @ X1))) | ((subset @ X2 @ X1) = $true)) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.51/1.27 thf(f34,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : (((subset @ X2 @ X1) = $true) | (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK3 @ X1 @ X2)) = $false)) )),
% 1.51/1.27 inference(sigma_clausification,[status(thm)],[f33])).
% 1.51/1.27 thf(f33,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : (((subset @ X2 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = $false)) )),
% 1.51/1.27 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.51/1.27 thf(f32,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (subset @ X2 @ X1)) = $true)) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.51/1.27 thf(f31,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))) @ X2) = $true)) )),
% 1.51/1.27 inference(pi_clausification,[status(thm)],[f30])).
% 1.51/1.27 thf(f30,plain,(
% 1.51/1.27 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1)))) = $true)) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.51/1.27 thf(f29,plain,(
% 1.51/1.27 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))) @ X1) = $true)) )),
% 1.51/1.27 inference(pi_clausification,[status(thm)],[f25])).
% 1.51/1.27 thf(f25,plain,(
% 1.51/1.27 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) = $true)),
% 1.51/1.27 inference(definition_unfolding,[status(thm)],[f23,f18])).
% 1.51/1.27 thf(f18,plain,(
% 1.51/1.27 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f8])).
% 1.51/1.27 thf(f8,plain,(
% 1.51/1.27 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.51/1.27 thf(f7,plain,(
% 1.51/1.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 1.51/1.27 inference(rectify,[status(thm)],[f1])).
% 1.51/1.27 thf(f1,axiom,(
% 1.51/1.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.OZ4rChwKDO/DTF2THF_21358.p',subsetI2)).
% 1.51/1.27 thf(f23,plain,(
% 1.51/1.27 (subsetI2 = $true)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f17])).
% 1.51/1.27 thf(f36,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : (((in @ (sK3 @ X1 @ X2) @ X1) = $false) | ((subset @ X2 @ X1) = $true)) )),
% 1.51/1.27 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.51/1.27 thf(f28,plain,(
% 1.51/1.27 ((subset @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ Y0 @ sK0))) @ sK1) != $true)),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.51/1.27 thf(f26,plain,(
% 1.51/1.27 ((subset @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK1 @ sK0) @ sK1) != $true)),
% 1.51/1.27 inference(definition_unfolding,[status(thm)],[f22,f19])).
% 1.51/1.27 thf(f22,plain,(
% 1.51/1.27 ((subset @ (binintersect @ sK1 @ sK0) @ sK1) != $true)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f17])).
% 1.51/1.27 % SZS output end Proof for DTF2THF_21358
% 1.51/1.27 % (21627)------------------------------
% 1.51/1.27 % (21627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (21627)Termination reason: Refutation
% 1.51/1.27
% 1.51/1.27 % (21627)Memory used [KB]: 5500
% 1.51/1.27 % (21627)Time elapsed: 0.005 s
% 1.51/1.27 % (21627)Instructions burned: 7 (million)
% 1.51/1.27 % (21627)------------------------------
% 1.51/1.27 % (21627)------------------------------
% 1.51/1.27 % (21624)Success in time 0.015 s
%------------------------------------------------------------------------------