%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU732^2 : 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 : n007.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 09:36:45 AM UTC 2026
% Result : Theorem 0.31s 1.33s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 76 ( 32 unt; 0 typ; 4 def)
% Number of atoms : 718 ( 156 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 1027 ( 72 ~; 56 |; 36 &; 721 @)
% ( 4 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 13 con; 0-2 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 164 ( 49 ^; 97 !; 18 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binintersect: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(f104,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f70,f76,f91,f97,f103]) ).
thf(f103,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f22,f85]) ).
thf(f85,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl4_3
<=> ( ( in @ sK3 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f22,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( setminusER = $true )
& ( binintersectTELcontra = $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f17,f16,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ X3 @ ( binintersect @ sK1 @ X2 ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ X3 @ ( binintersect @ sK1 @ X2 ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ sK1 ) ) )
& ( ( in @ X3 @ ( binintersect @ sK1 @ sK2 ) )
= $true ) )
& ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ sK1 ) ) )
& ( ( in @ X3 @ ( binintersect @ sK1 @ sK2 ) )
= $true ) )
=> ( ( ( in @ sK3 @ sK0 )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( setminusER = $true )
& ( binintersectTELcontra = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectTELcontra = $true )
& ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( setminusER = $true )
=> ( ( binintersectTELcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setminusER = $true )
=> ( ( binintersectTELcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setminusER
=> ( binintersectTELcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setminusER
=> ( binintersectTELcontra
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ X3 ) )
=> ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setminusER
=> ( binintersectTELcontra
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ X3 ) )
=> ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CU7NAix9x9/DTF2THF_11609.p',complementTnotintersectT) ).
thf(f97,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true = $false )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f23,f89]) ).
thf(f89,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl4_4
<=> ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f23,plain,
( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f91,plain,
( spl4_3
| spl4_4
| ~ spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f80,f63,f87,f83]) ).
thf(f63,definition,
( spl4_1
<=> ! [X0: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK3 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f80,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f19,f64]) ).
thf(f64,plain,
( ! [X0: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK3 @ X0 )
= $false ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f19,plain,
( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f76,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f75]) ).
thf(f75,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f55,f68]) ).
thf(f68,plain,
( ( ( in @ sK3 @ sK1 )
= $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f66]) ).
thf(f66,definition,
( spl4_2
<=> ( ( in @ sK3 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f55,plain,
( ( in @ sK3 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f21,f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X3 @ X1 ) )
= $false )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( in @ X2 @ X1 ) )
= $true )
| ( ( in @ X2 @ ( setminus @ X3 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X3 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( setminus @ Y0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setminus @ Y0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setminus @ Y1 @ X1 ) )
=> ~ ( in @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setminus @ Y1 @ X1 ) )
=> ~ ( in @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f27,f25]) ).
thf(f25,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f27,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setminusER
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CU7NAix9x9/DTF2THF_11609.p',setminusER) ).
thf(f21,plain,
( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f70,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f60,f66,f63]) ).
thf(f60,plain,
! [X0: $i] :
( ( ( in @ sK3 @ X0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK3 @ sK1 )
= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK3 @ X0 )
= $false )
| ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK3 @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f20,f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X1 @ X3 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X4 @ X1 )
= $true )
| ( ( in @ X4 @ X2 )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
= $true )
| ( ( in @ X4 @ X2 )
= $false )
| ( ( in @ X4 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X2 ) )
= $false )
| ( ( ~ ( in @ X4 @ X1 ) )
= $false )
| ( ( ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
= $true )
| ( ( in @ X4 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( in @ X4 @ X1 )
=> ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X4 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ X1 )
=> ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) )
@ X4 )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) ) ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) )
@ X3 )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ X1 )
=> ~ ( in @ Y2 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ X1 )
=> ~ ( in @ Y2 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f26,f24]) ).
thf(f24,plain,
binintersectTELcontra = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f26,plain,
( binintersectTELcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( binintersectTELcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X1 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) )
= binintersectTELcontra ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X3 )
=> ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) )
= binintersectTELcontra ),
file('/export/starexec/sandbox/tmp/tmp.CU7NAix9x9/DTF2THF_11609.p',binintersectTELcontra) ).
thf(f20,plain,
( ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU732^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n007.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:31:38 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU732^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.30/0.46 % (! x:i.in x A -> in x (setminus A X) ->
% 0.30/0.46 % ~(in x (binintersect X Y)))))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC234l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.30/0.46 % Number of atoms : 18 ( 2 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 6 avg)
% 0.30/0.46 % Number of connectives : 51 ( 4 ~; 0 |; 0 &; 36 @)
% 0.30/0.46 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 15 ( 6 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=294
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect_type,type,
% 0.30/0.46 binintersect: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setminus_type,type,
% 0.30/0.46 setminus: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER_type,type,
% 0.30/0.46 setminusER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER,definition,
% 0.30/0.46 ( setminusER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectTELcontra_type,type,
% 0.30/0.46 binintersectTELcontra: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectTELcontra,definition,
% 0.30/0.46 ( binintersectTELcontra
% 0.30/0.46 = ( ! [A: $i,X: $i] :
% 0.30/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.46 => ! [Y: $i] :
% 0.30/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ X )
% 0.30/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(complementTnotintersectT,conjecture,
% 0.30/0.46 ( setminusER
% 0.30/0.46 => ( binintersectTELcontra
% 0.30/0.46 => ! [A: $i,X: $i] :
% 0.30/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.46 => ! [Y: $i] :
% 0.30/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.30/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 12:31:39 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CU7NAix9x9/DTF2DTF11609.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(in_type,type,
% 0.31/1.31 in: $i > $i > $o ).
% 0.31/1.31
% 0.31/1.31 thf(powerset_type,type,
% 0.31/1.31 powerset: $i > $i ).
% 0.31/1.31
% 0.31/1.31 thf(binintersect_type,type,
% 0.31/1.31 binintersect: $i > $i > $i ).
% 0.31/1.31
% 0.31/1.31 thf(setminus_type,type,
% 0.31/1.31 setminus: $i > $i > $i ).
% 0.31/1.31
% 0.31/1.31 thf(setminusER_type,type,
% 0.31/1.31 setminusER: $o ).
% 0.31/1.31
% 0.31/1.31 thf(setminusER,definition,
% 0.31/1.31 ( setminusER
% 0.31/1.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/1.31 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(binintersectTELcontra_type,type,
% 0.31/1.31 binintersectTELcontra: $o ).
% 0.31/1.31
% 0.31/1.31 thf(binintersectTELcontra,definition,
% 0.31/1.31 ( binintersectTELcontra
% 0.31/1.31 = ( ! [A: $i,X: $i] :
% 0.31/1.31 ( ( in @ X @ ( powerset @ A ) )
% 0.31/1.31 => ! [Y: $i] :
% 0.31/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/1.31 => ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ A )
% 0.31/1.31 => ( ~ ( in @ Xx @ X )
% 0.31/1.31 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(complementTnotintersectT,conjecture,
% 0.31/1.31 ( setminusER
% 0.31/1.31 => ( binintersectTELcontra
% 0.31/1.31 => ! [A: $i,X: $i] :
% 0.31/1.31 ( ( in @ X @ ( powerset @ A ) )
% 0.31/1.31 => ! [Y: $i] :
% 0.31/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/1.31 => ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ A )
% 0.31/1.31 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/1.31 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/1.31 ------------------------
% 0.31/1.33 % (11798)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11609 for (2999ds/183Mi)
% 0.31/1.33 % (11799)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_11609 for (2999ds/4Mi)
% 0.31/1.33 % (11800)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_11609 for (2999ds/27Mi)
% 0.31/1.33 % (11799)Instruction limit reached!
% 0.31/1.33 % (11799)------------------------------
% 0.31/1.33 % (11799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (11799)Termination reason: Unknown
% 0.31/1.33 % (11799)Termination phase: Saturation
% 0.31/1.33
% 0.31/1.33 % (11799)Memory used [KB]: 5500
% 0.31/1.33 % (11799)Time elapsed: 0.003 s
% 0.31/1.33 % (11799)Instructions burned: 6 (million)
% 0.31/1.33 % (11799)------------------------------
% 0.31/1.33 % (11799)------------------------------
% 0.31/1.33 % (11798)First to succeed.
% 0.31/1.33 % (11798)Refutation found. Thanks to Tanya!
% 0.31/1.33 % SZS status Theorem for DTF2THF_11609
% 0.31/1.33 % SZS output start Proof for DTF2THF_11609
% 0.31/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 0.31/1.33 thf(func_def_1, type, powerset: $i > $i).
% 0.31/1.33 thf(func_def_2, type, binintersect: $i > $i > $i).
% 0.31/1.33 thf(func_def_3, type, setminus: $i > $i > $i).
% 0.31/1.33 thf(f104,plain,(
% 0.31/1.33 $false),
% 0.31/1.33 inference(avatar_sat_refutation,[status(thm)],[f70,f76,f91,f97,f103])).
% 0.31/1.33 thf(f103,plain,(
% 0.31/1.33 ~spl4_3),
% 0.31/1.33 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 0.31/1.33 thf(f102,plain,(
% 0.31/1.33 $false | ~spl4_3),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 0.31/1.33 thf(f99,plain,(
% 0.31/1.33 ($true = $false) | ~spl4_3),
% 0.31/1.33 inference(superposition,[status(thm)],[f22,f85])).
% 0.31/1.33 thf(f85,plain,(
% 0.31/1.33 ((in @ sK3 @ sK0) = $false) | ~spl4_3),
% 0.31/1.33 inference(avatar_component_clause,[status(thm)],[f83])).
% 0.31/1.33 thf(f83,definition,(
% 0.31/1.33 spl4_3 <=> ((in @ sK3 @ sK0) = $false)),
% 0.31/1.33 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 0.31/1.33 thf(f22,plain,(
% 0.31/1.33 ((in @ sK3 @ sK0) = $true)),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.33 thf(f18,plain,(
% 0.31/1.33 (setminusER = $true) & (binintersectTELcontra = $true) & (((in @ sK1 @ (powerset @ sK0)) = $true) & ((((in @ sK3 @ sK0) = $true) & ((in @ sK3 @ (setminus @ sK0 @ sK1)) = $true) & ((in @ sK3 @ (binintersect @ sK1 @ sK2)) = $true)) & ((in @ sK2 @ (powerset @ sK0)) = $true)))),
% 0.31/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f17,f16,f15])).
% 0.31/1.33 thf(f15,plain,(
% 0.31/1.33 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ (setminus @ X0 @ X1)) = $true) & ((in @ X3 @ (binintersect @ X1 @ X2)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))) => (((in @ sK1 @ (powerset @ sK0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ($true = (in @ X3 @ (setminus @ sK0 @ sK1))) & ($true = (in @ X3 @ (binintersect @ sK1 @ X2)))) & ($true = (in @ X2 @ (powerset @ sK0)))))),
% 0.31/1.33 introduced(definition,[],[choice_axiom])).
% 0.31/1.33 thf(f16,plain,(
% 0.31/1.33 ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ($true = (in @ X3 @ (setminus @ sK0 @ sK1))) & ($true = (in @ X3 @ (binintersect @ sK1 @ X2)))) & ($true = (in @ X2 @ (powerset @ sK0)))) => (? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ($true = (in @ X3 @ (setminus @ sK0 @ sK1))) & ((in @ X3 @ (binintersect @ sK1 @ sK2)) = $true)) & ((in @ sK2 @ (powerset @ sK0)) = $true))),
% 0.31/1.33 introduced(definition,[],[choice_axiom])).
% 0.31/1.33 thf(f17,plain,(
% 0.31/1.33 ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ($true = (in @ X3 @ (setminus @ sK0 @ sK1))) & ((in @ X3 @ (binintersect @ sK1 @ sK2)) = $true)) => (((in @ sK3 @ sK0) = $true) & ((in @ sK3 @ (setminus @ sK0 @ sK1)) = $true) & ((in @ sK3 @ (binintersect @ sK1 @ sK2)) = $true))),
% 0.31/1.33 introduced(definition,[],[choice_axiom])).
% 0.31/1.33 thf(f14,plain,(
% 0.31/1.33 (setminusER = $true) & (binintersectTELcontra = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ (setminus @ X0 @ X1)) = $true) & ((in @ X3 @ (binintersect @ X1 @ X2)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)))),
% 0.31/1.33 inference(flattening,[status(thm)],[f13])).
% 0.31/1.33 thf(f13,plain,(
% 0.31/1.33 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ (binintersect @ X1 @ X2)) = $true) & ((in @ X3 @ (setminus @ X0 @ X1)) = $true)) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binintersectTELcontra = $true)) & (setminusER = $true)),
% 0.31/1.33 inference(ennf_transformation,[status(thm)],[f12])).
% 0.31/1.33 thf(f12,plain,(
% 0.31/1.33 ~((setminusER = $true) => ((binintersectTELcontra = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ (setminus @ X0 @ X1)) = $true) => ((in @ X3 @ (binintersect @ X1 @ X2)) != $true)))))))),
% 0.31/1.33 inference(flattening,[status(thm)],[f11])).
% 0.31/1.33 thf(f11,plain,(
% 0.31/1.33 ~((setminusER = $true) => ((binintersectTELcontra = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ (setminus @ X0 @ X1)) = $true) => ~((in @ X3 @ (binintersect @ X1 @ X2)) = $true)))))))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 0.31/1.33 thf(f10,plain,(
% 0.31/1.33 ~(setminusER => (binintersectTELcontra => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => ~(in @ X3 @ (binintersect @ X1 @ X2))))))))),
% 0.31/1.33 inference(rectify,[status(thm)],[f4])).
% 0.31/1.33 thf(f4,negated_conjecture,(
% 0.31/1.33 ~(setminusER => (binintersectTELcontra => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => ~(in @ X2 @ (binintersect @ X3 @ X4))))))))),
% 0.31/1.33 inference(negated_conjecture,[status(cth)],[f3])).
% 0.31/1.33 thf(f3,conjecture,(
% 0.31/1.33 setminusER => (binintersectTELcontra => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => ~(in @ X2 @ (binintersect @ X3 @ X4)))))))),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.CU7NAix9x9/DTF2THF_11609.p',complementTnotintersectT)).
% 0.31/1.33 thf(f97,plain,(
% 0.31/1.33 ~spl4_4),
% 0.31/1.33 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 0.31/1.33 thf(f96,plain,(
% 0.31/1.33 $false | ~spl4_4),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 0.31/1.33 thf(f93,plain,(
% 0.31/1.33 ($true = $false) | ~spl4_4),
% 0.31/1.33 inference(superposition,[status(thm)],[f23,f89])).
% 0.31/1.33 thf(f89,plain,(
% 0.31/1.33 ((in @ sK1 @ (powerset @ sK0)) = $false) | ~spl4_4),
% 0.31/1.33 inference(avatar_component_clause,[status(thm)],[f87])).
% 0.31/1.33 thf(f87,definition,(
% 0.31/1.33 spl4_4 <=> ((in @ sK1 @ (powerset @ sK0)) = $false)),
% 0.31/1.33 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 0.31/1.33 thf(f23,plain,(
% 0.31/1.33 ((in @ sK1 @ (powerset @ sK0)) = $true)),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.33 thf(f91,plain,(
% 0.31/1.33 spl4_3 | spl4_4 | ~spl4_1),
% 0.31/1.33 inference(avatar_split_clause,[status(thm)],[f80,f63,f87,f83])).
% 0.31/1.33 thf(f63,definition,(
% 0.31/1.33 spl4_1 <=> ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) = $false) | ((in @ sK1 @ (powerset @ X0)) = $false) | ((in @ sK3 @ X0) = $false))),
% 0.31/1.33 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 0.31/1.33 thf(f80,plain,(
% 0.31/1.33 ((in @ sK3 @ sK0) = $false) | ((in @ sK1 @ (powerset @ sK0)) = $false) | ~spl4_1),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 0.31/1.33 thf(f79,plain,(
% 0.31/1.33 ((in @ sK3 @ sK0) = $false) | ($true = $false) | ((in @ sK1 @ (powerset @ sK0)) = $false) | ~spl4_1),
% 0.31/1.33 inference(superposition,[status(thm)],[f19,f64])).
% 0.31/1.33 thf(f64,plain,(
% 0.31/1.33 ( ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) = $false) | ((in @ sK1 @ (powerset @ X0)) = $false) | ((in @ sK3 @ X0) = $false)) ) | ~spl4_1),
% 0.31/1.33 inference(avatar_component_clause,[status(thm)],[f63])).
% 0.31/1.33 thf(f19,plain,(
% 0.31/1.33 ((in @ sK2 @ (powerset @ sK0)) = $true)),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.33 thf(f76,plain,(
% 0.31/1.33 ~spl4_2),
% 0.31/1.33 inference(avatar_contradiction_clause,[status(thm)],[f75])).
% 0.31/1.33 thf(f75,plain,(
% 0.31/1.33 $false | ~spl4_2),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 0.31/1.33 thf(f72,plain,(
% 0.31/1.33 ($true = $false) | ~spl4_2),
% 0.31/1.33 inference(superposition,[status(thm)],[f55,f68])).
% 0.31/1.33 thf(f68,plain,(
% 0.31/1.33 ((in @ sK3 @ sK1) = $true) | ~spl4_2),
% 0.31/1.33 inference(avatar_component_clause,[status(thm)],[f66])).
% 0.31/1.33 thf(f66,definition,(
% 0.31/1.33 spl4_2 <=> ((in @ sK3 @ sK1) = $true)),
% 0.31/1.33 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 0.31/1.33 thf(f55,plain,(
% 0.31/1.33 ((in @ sK3 @ sK1) = $false)),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 0.31/1.33 thf(f53,plain,(
% 0.31/1.33 ((in @ sK3 @ sK1) = $false) | ($true = $false)),
% 0.31/1.33 inference(superposition,[status(thm)],[f21,f37])).
% 0.31/1.33 thf(f37,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (setminus @ X3 @ X1)) = $false) | ((in @ X2 @ X1) = $false)) )),
% 0.31/1.33 inference(not_proxy_clausification,[status(thm)],[f36])).
% 0.31/1.33 thf(f36,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (in @ X2 @ X1)) = $true) | ((in @ X2 @ (setminus @ X3 @ X1)) = $false)) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 0.31/1.33 thf(f35,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ (setminus @ X3 @ X1)) => (~ (in @ X2 @ X1))) = $true)) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f34])).
% 0.31/1.33 thf(f34,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ (setminus @ Y0 @ X1)) => (~ (in @ X2 @ X1)))) @ X3) = $true)) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f33])).
% 0.31/1.33 thf(f33,plain,(
% 0.31/1.33 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (setminus @ Y0 @ X1)) => (~ (in @ X2 @ X1))))) = $true)) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f32])).
% 0.31/1.33 thf(f32,plain,(
% 0.31/1.33 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setminus @ Y1 @ X1)) => (~ (in @ Y0 @ X1)))))) @ X2) = $true)) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f31])).
% 0.31/1.33 thf(f31,plain,(
% 0.31/1.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setminus @ Y1 @ X1)) => (~ (in @ Y0 @ X1))))))) = $true)) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f30])).
% 0.31/1.33 thf(f30,plain,(
% 0.31/1.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (~ (in @ Y1 @ Y0)))))))) @ X1))) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f29])).
% 0.31/1.33 thf(f29,plain,(
% 0.31/1.33 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (~ (in @ Y1 @ Y0))))))))) = $true)),
% 0.31/1.33 inference(definition_unfolding,[status(thm)],[f27,f25])).
% 0.31/1.33 thf(f25,plain,(
% 0.31/1.33 (setminusER = $true)),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.33 thf(f27,plain,(
% 0.31/1.33 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (~ (in @ Y1 @ Y0))))))))))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f7])).
% 0.31/1.33 thf(f7,plain,(
% 0.31/1.33 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (~ (in @ Y1 @ Y0))))))))))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f6])).
% 0.31/1.33 thf(f6,plain,(
% 0.31/1.33 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X0 @ X2)) => ~(in @ X1 @ X2)))),
% 0.31/1.33 inference(rectify,[status(thm)],[f1])).
% 0.31/1.33 thf(f1,axiom,(
% 0.31/1.33 (setminusER = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.CU7NAix9x9/DTF2THF_11609.p',setminusER)).
% 0.31/1.33 thf(f21,plain,(
% 0.31/1.33 ((in @ sK3 @ (setminus @ sK0 @ sK1)) = $true)),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.33 thf(f70,plain,(
% 0.31/1.33 spl4_1 | spl4_2),
% 0.31/1.33 inference(avatar_split_clause,[status(thm)],[f60,f66,f63])).
% 0.31/1.33 thf(f60,plain,(
% 0.31/1.33 ( ! [X0 : $i] : (((in @ sK3 @ X0) = $false) | ((in @ sK1 @ (powerset @ X0)) = $false) | ((in @ sK3 @ sK1) = $true) | ((in @ sK2 @ (powerset @ X0)) = $false)) )),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 0.31/1.33 thf(f57,plain,(
% 0.31/1.33 ( ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) = $false) | ((in @ sK3 @ X0) = $false) | ($true = $false) | ((in @ sK1 @ (powerset @ X0)) = $false) | ((in @ sK3 @ sK1) = $true)) )),
% 0.31/1.33 inference(superposition,[status(thm)],[f20,f51])).
% 0.31/1.33 thf(f51,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ (binintersect @ X1 @ X3)) = $false) | ((in @ X3 @ (powerset @ X2)) = $false) | ((in @ X4 @ X1) = $true) | ((in @ X4 @ X2) = $false) | ((in @ X1 @ (powerset @ X2)) = $false)) )),
% 0.31/1.33 inference(not_proxy_clausification,[status(thm)],[f50])).
% 0.31/1.33 thf(f50,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X3 @ (powerset @ X2)) = $false) | ((in @ X1 @ (powerset @ X2)) = $false) | ((~ (in @ X4 @ (binintersect @ X1 @ X3))) = $true) | ((in @ X4 @ X2) = $false) | ((in @ X4 @ X1) = $true)) )),
% 0.31/1.33 inference(not_proxy_clausification,[status(thm)],[f49])).
% 0.31/1.33 thf(f49,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | ((in @ X3 @ (powerset @ X2)) = $false) | ((~ (in @ X4 @ X1)) = $false) | ((~ (in @ X4 @ (binintersect @ X1 @ X3))) = $true) | ((in @ X4 @ X2) = $false)) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 0.31/1.33 thf(f48,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((~ (in @ X4 @ X1)) => (~ (in @ X4 @ (binintersect @ X1 @ X3)))) = $true) | ((in @ X1 @ (powerset @ X2)) = $false) | ((in @ X3 @ (powerset @ X2)) = $false) | ((in @ X4 @ X2) = $false)) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 0.31/1.33 thf(f47,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ X2) => ((~ (in @ X4 @ X1)) => (~ (in @ X4 @ (binintersect @ X1 @ X3))))) = $true) | ((in @ X3 @ (powerset @ X2)) = $false) | ((in @ X1 @ (powerset @ X2)) = $false)) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f46])).
% 0.31/1.33 thf(f46,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ X1)) => (~ (in @ Y0 @ (binintersect @ X1 @ X3)))))) @ X4) = $true) | ((in @ X3 @ (powerset @ X2)) = $false)) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f45])).
% 0.31/1.33 thf(f45,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (powerset @ X2)) = $false) | ((in @ X1 @ (powerset @ X2)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ X1)) => (~ (in @ Y0 @ (binintersect @ X1 @ X3))))))) = $true)) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 0.31/1.33 thf(f44,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ X1)) => (~ (in @ Y0 @ (binintersect @ X1 @ X3)))))))) = $true) | ((in @ X1 @ (powerset @ X2)) = $false)) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f43])).
% 0.31/1.33 thf(f43,plain,(
% 0.31/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ X1)) => (~ (in @ Y1 @ (binintersect @ X1 @ Y0))))))))) @ X3) = $true) | ((in @ X1 @ (powerset @ X2)) = $false)) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f42])).
% 0.31/1.33 thf(f42,plain,(
% 0.31/1.33 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ X1)) => (~ (in @ Y1 @ (binintersect @ X1 @ Y0)))))))))) = $true)) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 0.31/1.33 thf(f41,plain,(
% 0.31/1.33 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ X1)) => (~ (in @ Y1 @ (binintersect @ X1 @ Y0))))))))))) = $true)) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f40])).
% 0.31/1.33 thf(f40,plain,(
% 0.31/1.33 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ X1)) => (~ (in @ Y2 @ (binintersect @ X1 @ Y1)))))))))))) @ X2) = $true)) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f39])).
% 0.31/1.33 thf(f39,plain,(
% 0.31/1.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ X1)) => (~ (in @ Y2 @ (binintersect @ X1 @ Y1))))))))))))) = $true)) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f38])).
% 0.31/1.33 thf(f38,plain,(
% 0.31/1.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2)))))))))))))) @ X1) = $true)) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f28])).
% 0.31/1.33 thf(f28,plain,(
% 0.31/1.33 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2))))))))))))))) = $true)),
% 0.31/1.33 inference(definition_unfolding,[status(thm)],[f26,f24])).
% 0.31/1.33 thf(f24,plain,(
% 0.31/1.33 (binintersectTELcontra = $true)),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.33 thf(f26,plain,(
% 0.31/1.33 (binintersectTELcontra = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2))))))))))))))))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 0.31/1.33 thf(f9,plain,(
% 0.31/1.33 (binintersectTELcontra = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2))))))))))))))))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 0.31/1.33 thf(f8,plain,(
% 0.31/1.33 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ X1) => ~(in @ X3 @ (binintersect @ X1 @ X2)))))) = binintersectTELcontra)),
% 0.31/1.33 inference(rectify,[status(thm)],[f2])).
% 0.31/1.33 thf(f2,axiom,(
% 0.31/1.33 (! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X3) => ~(in @ X2 @ (binintersect @ X3 @ X4)))))) = binintersectTELcontra)),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.CU7NAix9x9/DTF2THF_11609.p',binintersectTELcontra)).
% 0.31/1.33 thf(f20,plain,(
% 0.31/1.33 ((in @ sK3 @ (binintersect @ sK1 @ sK2)) = $true)),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.33 % SZS output end Proof for DTF2THF_11609
% 0.31/1.33 % (11798)------------------------------
% 0.31/1.33 % (11798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (11798)Termination reason: Refutation
% 0.31/1.33
% 0.31/1.33 % (11798)Memory used [KB]: 5628
% 0.31/1.33 % (11798)Time elapsed: 0.006 s
% 0.31/1.33 % (11798)Instructions burned: 8 (million)
% 0.31/1.33 % (11798)------------------------------
% 0.31/1.33 % (11798)------------------------------
% 0.31/1.33 % (11797)Success in time 0.009 s
%------------------------------------------------------------------------------