%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU594^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.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 09:35:29 AM UTC 2026
% Result : Theorem 1.68s 1.34s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 611 ( 173 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 615 ( 90 ~; 76 |; 36 &; 378 @)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 145 ( 28 ^; 92 !; 25 ?; 145 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
binintersect: $i > $i > $i ).
thf(func_def_22,type,
sK9: $i > $i > $i ).
thf(func_def_26,type,
ph13:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
sK14: $i > $i ).
thf(f112,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f83,f104,f111]) ).
thf(f111,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
| ~ spl12_1 ),
inference(subsumption_resolution,[status(thm)],[f109,f42]) ).
thf(f42,plain,
( ( subset @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( in__Cong = $true )
& ( ( subset @ sK1 @ sK0 )
!= $true )
& ( sK1
= ( binintersect @ sK0 @ sK1 ) )
& ( subsetI1 = $true )
& ( binintersectEL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X1 ) )
=> ( ( ( subset @ sK1 @ sK0 )
!= $true )
& ( sK1
= ( binintersect @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( in__Cong = $true )
& ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X1 ) )
& ( subsetI1 = $true )
& ( binintersectEL = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X1 ) )
& ( binintersectEL = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( in__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( binintersectEL = $true )
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2THF_8549.p',binintersectSubset3) ).
thf(f109,plain,
( ( ( subset @ sK1 @ sK0 )
= $true )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $true != $true )
| ( ( subset @ sK1 @ sK0 )
= $true )
| ~ spl12_1 ),
inference(superposition,[status(thm)],[f70,f107]) ).
thf(f107,plain,
( ( $true
= ( in @ ( sK9 @ sK1 @ sK0 ) @ sK0 ) )
| ~ spl12_1 ),
inference(equality_resolution,[status(thm)],[f106]) ).
thf(f106,plain,
( ! [X0: $i] :
( ( sK0 != X0 )
| ( $true
= ( in @ ( sK9 @ sK1 @ sK0 ) @ X0 ) ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( sK9 @ sK1 @ sK0 ) @ X0 ) )
| ( $true != $true )
| ( sK0 != X0 ) )
| ~ spl12_1 ),
inference(superposition,[status(thm)],[f79,f75]) ).
thf(f75,plain,
( $true
= ( in @ ( sK9 @ sK1 @ sK0 ) @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( $true
= ( in @ ( sK9 @ sK1 @ sK0 ) @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f42,f69]) ).
thf(f69,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X1 ) )
| ( $true != $true )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f54,f40]) ).
thf(f40,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f54,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X1 ) )
| ( ( subset @ X1 @ X0 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X1 ) )
& ( $true
!= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ( ! [X5: $i] :
( ( ( in @ X5 @ sK11 )
!= $true )
| ( $true
= ( in @ X5 @ sK10 ) ) )
& ( ( subset @ sK11 @ sK10 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f34,f36,f35]) ).
thf(f35,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( $true
= ( in @ ( sK9 @ X1 @ X0 ) @ X1 ) )
& ( $true
!= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) )
& ( $true
!= ( subset @ X4 @ X3 ) ) )
=> ( ! [X5: $i] :
( ( ( in @ X5 @ sK11 )
!= $true )
| ( $true
= ( in @ X5 @ sK10 ) ) )
& ( ( subset @ sK11 @ sK10 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) )
& ( $true
!= ( subset @ X4 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
file('/export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2THF_8549.p',subsetI1) ).
thf(f79,plain,
( ! [X2: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( sK0 != X0 )
| ( ( in @ X2 @ X0 )
= $true ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl12_1
<=> ! [X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ sK1 ) )
| ( sK0 != X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition]) ).
thf(f70,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) )
| ( $true != $true )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f53,f40]) ).
thf(f53,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK9 @ X1 @ X0 ) @ X0 ) )
| ( ( subset @ X1 @ X0 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f104,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ( $false = $true )
| ~ spl12_2 ),
inference(backward_demodulation,[status(thm)],[f89,f97]) ).
thf(f97,plain,
( ( $false
= ( in @ ( sK14 @ sK1 ) @ sK1 ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $false = $true )
| ( $false
= ( in @ ( sK14 @ sK1 ) @ sK1 ) )
| ~ spl12_2 ),
inference(superposition,[status(thm)],[f89,f87]) ).
thf(f87,plain,
( ! [X1: $i] :
( ( $false
= ( in @ ( sK14 @ X1 ) @ sK1 ) )
| ( $false
= ( in @ ( sK14 @ X1 ) @ X1 ) ) )
| ~ spl12_2 ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ! [X1: $i] :
( ( in @ ( sK14 @ X1 ) @ X1 )
!= ( in @ ( sK14 @ X1 ) @ sK1 ) )
| ~ spl12_2 ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : ( in @ Y0 @ sK1 )
@ ( sK14 @ X1 ) )
!= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ ( sK14 @ X1 ) ) )
| ~ spl12_2 ),
inference(negative_extensionality,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : ( in @ Y0 @ sK1 ) )
!= ( ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl12_2
<=> ! [X1: $i] :
( ( ^ [Y0: $i] : ( in @ Y0 @ sK1 ) )
!= ( ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition]) ).
thf(f89,plain,
( ( $true
= ( in @ ( sK14 @ sK1 ) @ sK1 ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true
= ( in @ ( sK14 @ sK1 ) @ sK1 ) )
| ( $true != $true )
| ~ spl12_2 ),
inference(equality_factoring,[status(thm)],[f86]) ).
thf(f86,plain,
( ! [X1: $i] :
( ( $true
= ( in @ ( sK14 @ X1 ) @ sK1 ) )
| ( ( in @ ( sK14 @ X1 ) @ X1 )
= $true ) )
| ~ spl12_2 ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f83,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[status(thm)],[f76,f81,f78]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( ^ [Y0: $i] : ( in @ Y0 @ sK1 ) )
!= ( ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) )
| ( sK0 != X0 )
| ( $true
!= ( in @ X2 @ sK1 ) ) ),
inference(constrained_superposition,[status(thm)],[f73,f71]) ).
thf(f71,plain,
( ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ Y0 @ sK1 ) )
= sK1 ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( sK1
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f41,f38]) ).
thf(f38,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) )
= binintersect ),
file('/export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2THF_8549.p',binintersect) ).
thf(f41,plain,
( sK1
= ( binintersect @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f73,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ Y0 @ X3 ) ) ) )
| ( ( in @ X5 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ X4
@ X3 ) )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ X4
@ X3 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f44,f38,f39]) ).
thf(f39,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f44,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( ( in @ X5 @ X4 )
= $true )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( binintersectEL = $true )
| ( ( $true
= ( in @ sK4 @ ( binintersect @ sK3 @ sK2 ) ) )
& ( $true
!= ( in @ sK4 @ sK3 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( ( in @ X5 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f25,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
=> ( ( $true
= ( in @ sK4 @ ( binintersect @ sK3 @ sK2 ) ) )
& ( $true
!= ( in @ sK4 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( ( in @ X5 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( binintersectEL
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2THF_8549.p',binintersectEL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU594^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n028.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 12:27:57 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU594^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (! A:i.! B:i.binintersect A B = B -> subset B A)
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC096l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.67 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 12 ( 4 unt; 7 typ; 4 def)
% 0.18/0.45 % Number of atoms : 22 ( 7 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 5 ( 4 avg)
% 0.18/0.45 % Number of connectives : 34 ( 0 ~; 0 |; 0 &; 24 @)
% 0.18/0.45 % ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 9 ( 3 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 15 ( 3 ^; 12 !; 0 ?; 15 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=364
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstr_type,type,
% 0.18/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.45
% 0.18/0.45 thf(in__Cong_type,type,
% 0.18/0.45 in__Cong: $o ).
% 0.18/0.45
% 0.18/0.45 thf(in__Cong,definition,
% 0.18/0.45 ( in__Cong
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ( A = B )
% 0.18/0.45 => ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx = Xy )
% 0.18/0.45 => ( ( in @ Xx @ A )
% 0.18/0.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(subset_type,type,
% 0.18/0.45 subset: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(subsetI1_type,type,
% 0.18/0.45 subsetI1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(subsetI1,definition,
% 0.18/0.45 ( subsetI1
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xx @ B ) )
% 0.18/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(binintersect_type,type,
% 0.18/0.45 binintersect: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(binintersect,definition,
% 0.18/0.45 ( binintersect
% 0.18/0.45 = ( ^ [A: $i,B: $i] :
% 0.18/0.45 ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(binintersectEL_type,type,
% 0.18/0.45 binintersectEL: $o ).
% 0.18/0.45
% 0.18/0.45 thf(binintersectEL,definition,
% 0.18/0.45 ( binintersectEL
% 0.18/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(binintersectSubset3,conjecture,
% 0.18/0.45 ( in__Cong
% 0.18/0.45 => ( subsetI1
% 0.18/0.45 => ( binintersectEL
% 0.18/0.45 => ! [A: $i,B: $i] :
% 0.18/0.45 ( ( ( binintersect @ A @ B )
% 0.18/0.45 = B )
% 0.18/0.45 => ( subset @ B @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.68/1.31 ---- Embedded in THF ---
% 1.68/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.31 %%% Generated on Tue Feb 24 12:27:58 EST 2026
% 1.68/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.31 %%% Logic specification used:
% 1.68/1.31 %%% thf(spec, logic, $$dhol).
% 1.68/1.31
% 1.68/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2DTF8549.p
% See solution above
% 1.68/1.31 ------------------------
% 1.68/1.32 ---- Cleaned THF ---
% 1.68/1.32 thf(in_type,type,
% 1.68/1.32 in: $i > $i > $o ).
% 1.68/1.32
% 1.68/1.32 thf(dsetconstr_type,type,
% 1.68/1.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.68/1.32
% 1.68/1.32 thf(in__Cong_type,type,
% 1.68/1.32 in__Cong: $o ).
% 1.68/1.32
% 1.68/1.32 thf(in__Cong,definition,
% 1.68/1.32 ( in__Cong
% 1.68/1.32 = ( ! [A: $i,B: $i] :
% 1.68/1.32 ( ( A = B )
% 1.68/1.32 => ! [Xx: $i,Xy: $i] :
% 1.68/1.32 ( ( Xx = Xy )
% 1.68/1.32 => ( ( in @ Xx @ A )
% 1.68/1.32 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 1.68/1.32
% 1.68/1.32 thf(subset_type,type,
% 1.68/1.32 subset: $i > $i > $o ).
% 1.68/1.32
% 1.68/1.32 thf(subsetI1_type,type,
% 1.68/1.32 subsetI1: $o ).
% 1.68/1.32
% 1.68/1.32 thf(subsetI1,definition,
% 1.68/1.32 ( subsetI1
% 1.68/1.32 = ( ! [A: $i,B: $i] :
% 1.68/1.32 ( ! [Xx: $i] :
% 1.68/1.32 ( ( in @ Xx @ A )
% 1.68/1.32 => ( in @ Xx @ B ) )
% 1.68/1.32 => ( subset @ A @ B ) ) ) ) ).
% 1.68/1.32
% 1.68/1.32 thf(binintersect_type,type,
% 1.68/1.32 binintersect: $i > $i > $i ).
% 1.68/1.32
% 1.68/1.32 thf(binintersect,definition,
% 1.68/1.32 ( binintersect
% 1.68/1.32 = ( ^ [A: $i,B: $i] :
% 1.68/1.32 ( dsetconstr @ A
% 1.68/1.32 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 1.68/1.32
% 1.68/1.32 thf(binintersectEL_type,type,
% 1.68/1.32 binintersectEL: $o ).
% 1.68/1.32
% 1.68/1.32 thf(binintersectEL,definition,
% 1.68/1.32 ( binintersectEL
% 1.68/1.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.68/1.32 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.68/1.32 => ( in @ Xx @ A ) ) ) ) ).
% 1.68/1.32
% 1.68/1.32 thf(binintersectSubset3,conjecture,
% 1.68/1.32 ( in__Cong
% 1.68/1.32 => ( subsetI1
% 1.68/1.32 => ( binintersectEL
% 1.68/1.32 => ! [A: $i,B: $i] :
% 1.68/1.32 ( ( ( binintersect @ A @ B )
% 1.68/1.32 = B )
% 1.68/1.32 => ( subset @ B @ A ) ) ) ) ) ).
% 1.68/1.32 ------------------------
% 1.68/1.34 % (8738)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8549 for (3000ds/18Mi)
% 1.68/1.34 % (8732)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8549 for (3000ds/183Mi)
% 1.68/1.34 % (8733)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_8549 for (3000ds/4Mi)
% 1.68/1.34 % (8738)First to succeed.
% 1.68/1.34 % (8733)Instruction limit reached!
% 1.68/1.34 % (8733)------------------------------
% 1.68/1.34 % (8733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (8733)Termination reason: Unknown
% 1.68/1.34 % (8733)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (8733)Memory used [KB]: 5500
% 1.68/1.34 % (8733)Time elapsed: 0.004 s
% 1.68/1.34 % (8733)Instructions burned: 5 (million)
% 1.68/1.34 % (8733)------------------------------
% 1.68/1.34 % (8733)------------------------------
% 1.68/1.34 % (8734)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_8549 for (3000ds/27Mi)
% 1.68/1.34 % (8735)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8549 for (3000ds/2Mi)
% 1.68/1.34 % (8736)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_8549 for (3000ds/2Mi)
% 1.68/1.34 % (8737)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_8549 for (3000ds/275Mi)
% 1.68/1.34 % (8738)Refutation found. Thanks to Tanya!
% 1.68/1.34 % SZS status Theorem for DTF2THF_8549
% 1.68/1.34 % SZS output start Proof for DTF2THF_8549
% 1.68/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.68/1.34 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.68/1.34 thf(func_def_4, type, subset: $i > $i > $o).
% 1.68/1.34 thf(func_def_6, type, binintersect: $i > $i > $i).
% 1.68/1.34 thf(func_def_22, type, sK9: $i > $i > $i).
% 1.68/1.34 thf(func_def_26, type, ph13: !>[X0: $tType]:(X0)).
% 1.68/1.34 thf(func_def_27, type, sK14: $i > $i).
% 1.68/1.34 thf(f112,plain,(
% 1.68/1.34 $false),
% 1.68/1.34 inference(avatar_sat_refutation,[status(thm)],[f83,f104,f111])).
% 1.68/1.34 thf(f111,plain,(
% 1.68/1.34 ~spl12_1),
% 1.68/1.34 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.68/1.34 thf(f110,plain,(
% 1.68/1.34 $false | ~spl12_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f109,f42])).
% 1.68/1.34 thf(f42,plain,(
% 1.68/1.34 ((subset @ sK1 @ sK0) != $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.68/1.34 thf(f23,plain,(
% 1.68/1.34 (in__Cong = $true) & (((subset @ sK1 @ sK0) != $true) & (sK1 = (binintersect @ sK0 @ sK1))) & (subsetI1 = $true) & (binintersectEL = $true)),
% 1.68/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f22])).
% 1.68/1.34 thf(f22,plain,(
% 1.68/1.34 ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ((binintersect @ X0 @ X1) = X1)) => (((subset @ sK1 @ sK0) != $true) & (sK1 = (binintersect @ sK0 @ sK1)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f19,plain,(
% 1.68/1.34 (in__Cong = $true) & ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ((binintersect @ X0 @ X1) = X1)) & (subsetI1 = $true) & (binintersectEL = $true)),
% 1.68/1.34 inference(flattening,[status(thm)],[f18])).
% 1.68/1.34 thf(f18,plain,(
% 1.68/1.34 ((? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ((binintersect @ X0 @ X1) = X1)) & (binintersectEL = $true)) & (subsetI1 = $true)) & (in__Cong = $true)),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f12])).
% 1.68/1.34 thf(f12,plain,(
% 1.68/1.34 ~((in__Cong = $true) => ((subsetI1 = $true) => ((binintersectEL = $true) => ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) => ((subset @ X1 @ X0) = $true)))))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f11])).
% 1.68/1.34 thf(f11,plain,(
% 1.68/1.34 ~(in__Cong => (subsetI1 => (binintersectEL => ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) => (subset @ X1 @ X0)))))),
% 1.68/1.34 inference(rectify,[status(thm)],[f6])).
% 1.68/1.34 thf(f6,negated_conjecture,(
% 1.68/1.34 ~(in__Cong => (subsetI1 => (binintersectEL => ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) => (subset @ X1 @ X0)))))),
% 1.68/1.34 inference(negated_conjecture,[status(cth)],[f5])).
% 1.68/1.34 thf(f5,conjecture,(
% 1.68/1.34 in__Cong => (subsetI1 => (binintersectEL => ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) => (subset @ X1 @ X0))))),
% 1.68/1.34 file('/export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2THF_8549.p',binintersectSubset3)).
% 1.68/1.34 thf(f109,plain,(
% 1.68/1.34 ((subset @ sK1 @ sK0) = $true) | ~spl12_1),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.68/1.34 thf(f108,plain,(
% 1.68/1.34 ($true != $true) | ((subset @ sK1 @ sK0) = $true) | ~spl12_1),
% 1.68/1.34 inference(superposition,[status(thm)],[f70,f107])).
% 1.68/1.34 thf(f107,plain,(
% 1.68/1.34 ($true = (in @ (sK9 @ sK1 @ sK0) @ sK0)) | ~spl12_1),
% 1.68/1.34 inference(equality_resolution,[status(thm)],[f106])).
% 1.68/1.34 thf(f106,plain,(
% 1.68/1.34 ( ! [X0 : $i] : ((sK0 != X0) | ($true = (in @ (sK9 @ sK1 @ sK0) @ X0))) ) | ~spl12_1),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.68/1.34 thf(f105,plain,(
% 1.68/1.34 ( ! [X0 : $i] : (($true = (in @ (sK9 @ sK1 @ sK0) @ X0)) | ($true != $true) | (sK0 != X0)) ) | ~spl12_1),
% 1.68/1.34 inference(superposition,[status(thm)],[f79,f75])).
% 1.68/1.34 thf(f75,plain,(
% 1.68/1.34 ($true = (in @ (sK9 @ sK1 @ sK0) @ sK1))),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.68/1.34 thf(f74,plain,(
% 1.68/1.34 ($true = (in @ (sK9 @ sK1 @ sK0) @ sK1)) | ($true != $true)),
% 1.68/1.34 inference(superposition,[status(thm)],[f42,f69])).
% 1.68/1.34 thf(f69,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ($true = (in @ (sK9 @ X1 @ X0) @ X1))) )),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.68/1.34 thf(f63,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK9 @ X1 @ X0) @ X1)) | ($true != $true) | ((subset @ X1 @ X0) = $true)) )),
% 1.68/1.34 inference(definition_unfolding,[status(thm)],[f54,f40])).
% 1.68/1.34 thf(f40,plain,(
% 1.68/1.34 (subsetI1 = $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.68/1.34 thf(f54,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK9 @ X1 @ X0) @ X1)) | ((subset @ X1 @ X0) = $true) | (subsetI1 != $true)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f37])).
% 1.68/1.34 thf(f37,plain,(
% 1.68/1.34 (! [X0 : $i,X1 : $i] : ((($true = (in @ (sK9 @ X1 @ X0) @ X1)) & ($true != (in @ (sK9 @ X1 @ X0) @ X0))) | ((subset @ X1 @ X0) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | (! [X5 : $i] : (((in @ X5 @ sK11) != $true) | ($true = (in @ X5 @ sK10))) & ((subset @ sK11 @ sK10) != $true)))),
% 1.68/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f34,f36,f35])).
% 1.68/1.34 thf(f35,plain,(
% 1.68/1.34 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) => (($true = (in @ (sK9 @ X1 @ X0) @ X1)) & ($true != (in @ (sK9 @ X1 @ X0) @ X0))))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f36,plain,(
% 1.68/1.34 ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ((in @ X5 @ X3) = $true)) & ($true != (subset @ X4 @ X3))) => (! [X5 : $i] : (((in @ X5 @ sK11) != $true) | ($true = (in @ X5 @ sK10))) & ((subset @ sK11 @ sK10) != $true))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f34,plain,(
% 1.68/1.34 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ((in @ X5 @ X3) = $true)) & ($true != (subset @ X4 @ X3))))),
% 1.68/1.34 inference(rectify,[status(thm)],[f33])).
% 1.68/1.34 thf(f33,plain,(
% 1.68/1.34 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ((subset @ X1 @ X0) != $true)))),
% 1.68/1.34 inference(nnf_transformation,[status(thm)],[f21])).
% 1.68/1.34 thf(f21,plain,(
% 1.68/1.34 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((subset @ X1 @ X0) = $true)) <=> (subsetI1 = $true)),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f10])).
% 1.68/1.34 thf(f10,plain,(
% 1.68/1.34 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((subset @ X1 @ X0) = $true))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f9])).
% 1.68/1.34 thf(f9,plain,(
% 1.68/1.34 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 1.68/1.34 inference(rectify,[status(thm)],[f2])).
% 1.68/1.34 thf(f2,axiom,(
% 1.68/1.34 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.68/1.34 file('/export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2THF_8549.p',subsetI1)).
% 1.68/1.34 thf(f79,plain,(
% 1.68/1.34 ( ! [X2 : $i,X0 : $i] : (($true != (in @ X2 @ sK1)) | (sK0 != X0) | ((in @ X2 @ X0) = $true)) ) | ~spl12_1),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.68/1.34 thf(f78,definition,(
% 1.68/1.34 spl12_1 <=> ! [X2 : $i,X0 : $i] : (((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ sK1)) | (sK0 != X0))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition])).
% 1.68/1.34 thf(f70,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK9 @ X1 @ X0) @ X0)) | ((subset @ X1 @ X0) = $true)) )),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.68/1.34 thf(f64,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK9 @ X1 @ X0) @ X0)) | ($true != $true) | ((subset @ X1 @ X0) = $true)) )),
% 1.68/1.34 inference(definition_unfolding,[status(thm)],[f53,f40])).
% 1.68/1.34 thf(f53,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK9 @ X1 @ X0) @ X0)) | ((subset @ X1 @ X0) = $true) | (subsetI1 != $true)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f37])).
% 1.68/1.34 thf(f104,plain,(
% 1.68/1.34 ~spl12_2),
% 1.68/1.34 inference(avatar_contradiction_clause,[status(thm)],[f103])).
% 1.68/1.34 thf(f103,plain,(
% 1.68/1.34 $false | ~spl12_2),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.68/1.34 thf(f102,plain,(
% 1.68/1.34 ($false = $true) | ~spl12_2),
% 1.68/1.34 inference(backward_demodulation,[status(thm)],[f89,f97])).
% 1.68/1.34 thf(f97,plain,(
% 1.68/1.34 ($false = (in @ (sK14 @ sK1) @ sK1)) | ~spl12_2),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.68/1.34 thf(f93,plain,(
% 1.68/1.34 ($false = $true) | ($false = (in @ (sK14 @ sK1) @ sK1)) | ~spl12_2),
% 1.68/1.34 inference(superposition,[status(thm)],[f89,f87])).
% 1.68/1.34 thf(f87,plain,(
% 1.68/1.34 ( ! [X1 : $i] : (($false = (in @ (sK14 @ X1) @ sK1)) | ($false = (in @ (sK14 @ X1) @ X1))) ) | ~spl12_2),
% 1.68/1.34 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.68/1.34 thf(f85,plain,(
% 1.68/1.34 ( ! [X1 : $i] : (((in @ (sK14 @ X1) @ X1) != (in @ (sK14 @ X1) @ sK1))) ) | ~spl12_2),
% 1.68/1.34 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.68/1.34 thf(f84,plain,(
% 1.68/1.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: (in @ Y0 @ sK1)) @ (sK14 @ X1)) != ((^[Y0 : $i]: (in @ Y0 @ X1)) @ (sK14 @ X1)))) ) | ~spl12_2),
% 1.68/1.34 inference(negative_extensionality,[status(thm)],[f82])).
% 1.68/1.34 thf(f82,plain,(
% 1.68/1.34 ( ! [X1 : $i] : (((^[Y0 : $i]: (in @ Y0 @ sK1)) != (^[Y0 : $i]: (in @ Y0 @ X1)))) ) | ~spl12_2),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.68/1.34 thf(f81,definition,(
% 1.68/1.34 spl12_2 <=> ! [X1 : $i] : ((^[Y0 : $i]: (in @ Y0 @ sK1)) != (^[Y0 : $i]: (in @ Y0 @ X1)))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition])).
% 1.68/1.34 thf(f89,plain,(
% 1.68/1.34 ($true = (in @ (sK14 @ sK1) @ sK1)) | ~spl12_2),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.68/1.34 thf(f88,plain,(
% 1.68/1.34 ($true = (in @ (sK14 @ sK1) @ sK1)) | ($true != $true) | ~spl12_2),
% 1.68/1.34 inference(equality_factoring,[status(thm)],[f86])).
% 1.68/1.34 thf(f86,plain,(
% 1.68/1.34 ( ! [X1 : $i] : (($true = (in @ (sK14 @ X1) @ sK1)) | ((in @ (sK14 @ X1) @ X1) = $true)) ) | ~spl12_2),
% 1.68/1.34 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.68/1.34 thf(f83,plain,(
% 1.68/1.34 spl12_1 | spl12_2),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f76,f81,f78])).
% 1.68/1.34 thf(f76,plain,(
% 1.68/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ((^[Y0 : $i]: (in @ Y0 @ sK1)) != (^[Y0 : $i]: (in @ Y0 @ X1))) | (sK0 != X0) | ($true != (in @ X2 @ sK1))) )),
% 1.68/1.34 inference(constrained_superposition,[status(thm)],[f73,f71])).
% 1.68/1.34 thf(f71,plain,(
% 1.68/1.34 ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))) = sK1)),
% 1.68/1.34 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.68/1.34 thf(f55,plain,(
% 1.68/1.34 (sK1 = ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK0 @ sK1))),
% 1.68/1.34 inference(definition_unfolding,[status(thm)],[f41,f38])).
% 1.68/1.34 thf(f38,plain,(
% 1.68/1.34 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.68/1.34 thf(f8,plain,(
% 1.68/1.34 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f3])).
% 1.68/1.34 thf(f3,axiom,(
% 1.68/1.34 ((^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))) = binintersect)),
% 1.68/1.34 file('/export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2THF_8549.p',binintersect)).
% 1.68/1.34 thf(f41,plain,(
% 1.68/1.34 (sK1 = (binintersect @ sK0 @ sK1))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.68/1.34 thf(f73,plain,(
% 1.68/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (in @ Y0 @ X3))))) | ((in @ X5 @ X4) = $true)) )),
% 1.68/1.34 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.68/1.34 thf(f72,plain,(
% 1.68/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ X4 @ X3)) != $true) | ((in @ X5 @ X4) = $true)) )),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.68/1.34 thf(f58,plain,(
% 1.68/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X5 @ X4) = $true) | ((in @ X5 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ X4 @ X3)) != $true)) )),
% 1.68/1.34 inference(definition_unfolding,[status(thm)],[f44,f38,f39])).
% 1.68/1.34 thf(f39,plain,(
% 1.68/1.34 (binintersectEL = $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.68/1.34 thf(f44,plain,(
% 1.68/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (binintersect @ X4 @ X3))) | ((in @ X5 @ X4) = $true) | (binintersectEL != $true)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f27])).
% 1.68/1.34 thf(f27,plain,(
% 1.68/1.34 ((binintersectEL = $true) | (($true = (in @ sK4 @ (binintersect @ sK3 @ sK2))) & ($true != (in @ sK4 @ sK3)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (binintersect @ X4 @ X3))) | ((in @ X5 @ X4) = $true)) | (binintersectEL != $true))),
% 1.68/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f25,f26])).
% 1.68/1.34 thf(f26,plain,(
% 1.68/1.34 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true)) => (($true = (in @ sK4 @ (binintersect @ sK3 @ sK2))) & ($true != (in @ sK4 @ sK3)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f25,plain,(
% 1.68/1.34 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (binintersect @ X4 @ X3))) | ((in @ X5 @ X4) = $true)) | (binintersectEL != $true))),
% 1.68/1.34 inference(rectify,[status(thm)],[f24])).
% 1.68/1.34 thf(f24,plain,(
% 1.68/1.34 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) != $true) | ((in @ X2 @ X1) = $true)) | (binintersectEL != $true))),
% 1.68/1.34 inference(nnf_transformation,[status(thm)],[f20])).
% 1.68/1.34 thf(f20,plain,(
% 1.68/1.34 (binintersectEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) != $true) | ((in @ X2 @ X1) = $true))),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f14])).
% 1.68/1.34 thf(f14,plain,(
% 1.68/1.34 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) => ((in @ X2 @ X1) = $true)) <=> (binintersectEL = $true)),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f13])).
% 1.68/1.34 thf(f13,plain,(
% 1.68/1.34 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X1 @ X0)) => (in @ X2 @ X1)))),
% 1.68/1.34 inference(rectify,[status(thm)],[f4])).
% 1.68/1.34 thf(f4,axiom,(
% 1.68/1.34 (binintersectEL = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.68/1.34 file('/export/starexec/sandbox2/tmp/tmp.Dahhe658KW/DTF2THF_8549.p',binintersectEL)).
% 1.68/1.34 % SZS output end Proof for DTF2THF_8549
% 1.68/1.34 % (8738)------------------------------
% 1.68/1.34 % (8738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (8738)Termination reason: Refutation
% 1.68/1.34
% 1.68/1.34 % (8738)Memory used [KB]: 5628
% 1.68/1.34 % (8738)Time elapsed: 0.007 s
% 1.68/1.34 % (8738)Instructions burned: 9 (million)
% 1.68/1.34 % (8738)------------------------------
% 1.68/1.34 % (8738)------------------------------
% 1.68/1.34 % (8731)Success in time 0.017 s
%------------------------------------------------------------------------------