%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU762^2 : 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 : n031.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 09:37:00 AM UTC 2026
% Result : Theorem 1.69s 1.36s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 110 ( 23 unt; 0 typ; 3 def)
% Number of atoms : 2055 ( 539 equ; 0 cnn)
% Maximal formula atoms : 14 ( 18 avg)
% Number of connectives : 2403 ( 272 ~; 226 |; 189 &;1602 @)
% ( 14 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 29 con; 0-2 aty)
% Number of variables : 286 ( 0 ^; 194 !; 92 ?; 286 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
binintersect: $i > $i > $i ).
thf(f197,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f148,f178,f188,f196]) ).
thf(f196,plain,
~ spl20_5,
inference(avatar_contradiction_clause,[status(thm)],[f195]) ).
thf(f195,plain,
( $false
| ~ spl20_5 ),
inference(subsumption_resolution,[status(thm)],[f194,f68]) ).
thf(f68,plain,
( $true
= ( in @ sK8 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) )
& ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) )
& ( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) )
& ( $true
= ( in @ sK8 @ ( powerset @ sK5 ) ) )
& ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ sK8 ) )
!= $true )
& ( $true
= ( subset @ sK6 @ sK8 ) )
& ( ( subset @ sK4 @ sK7 )
= $true )
& ( woz13rule2 = $true )
& ( woz13rule3 = $true )
& ( woz13rule1 = $true )
& ( binintersectT_lem = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f24,f36,f35,f34,f33]) ).
thf(f33,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
& ( $true
!= ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) )
& ( ( subset @ X2 @ X4 )
= $true )
& ( $true
= ( subset @ X0 @ X3 ) ) ) ) ) )
=> ( ( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK5 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK5 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK5 ) )
= $true )
& ( ( subset @ ( binintersect @ sK4 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( subset @ X2 @ X4 )
= $true )
& ( $true
= ( subset @ sK4 @ X3 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK5 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK5 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK5 ) )
= $true )
& ( ( subset @ ( binintersect @ sK4 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( subset @ X2 @ X4 )
= $true )
& ( $true
= ( subset @ sK4 @ X3 ) ) ) ) )
=> ( ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK5 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK5 ) )
= $true )
& ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( subset @ sK6 @ X4 )
= $true )
& ( $true
= ( subset @ sK4 @ X3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK5 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK5 ) )
= $true )
& ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( subset @ sK6 @ X4 )
= $true )
& ( $true
= ( subset @ sK4 @ X3 ) ) ) )
=> ( ( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK5 ) )
= $true )
& ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ X4 ) )
!= $true )
& ( ( subset @ sK6 @ X4 )
= $true )
& ( ( subset @ sK4 @ sK7 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK5 ) )
= $true )
& ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ X4 ) )
!= $true )
& ( ( subset @ sK6 @ X4 )
= $true )
& ( ( subset @ sK4 @ sK7 )
= $true ) )
=> ( ( $true
= ( in @ sK8 @ ( powerset @ sK5 ) ) )
& ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ sK8 ) )
!= $true )
& ( $true
= ( subset @ sK6 @ sK8 ) )
& ( ( subset @ sK4 @ sK7 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
& ( $true
!= ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) )
& ( ( subset @ X2 @ X4 )
= $true )
& ( $true
= ( subset @ X0 @ X3 ) ) ) ) ) )
& ( woz13rule2 = $true )
& ( woz13rule3 = $true )
& ( woz13rule1 = $true )
& ( binintersectT_lem = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) )
& ( ( subset @ X2 @ X4 )
= $true )
& ( $true
= ( subset @ X0 @ X3 ) )
& ( ( in @ X4 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( binintersectT_lem = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
=> ( ( $true
= ( subset @ X0 @ X3 ) )
=> ( ( ( subset @ X2 @ X4 )
= $true )
=> ( $true
= ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( binintersectT_lem
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ X3 )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( binintersectT_lem
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( binintersectT_lem
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',woz13rule4) ).
thf(f194,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ~ spl20_5 ),
inference(subsumption_resolution,[status(thm)],[f193,f70]) ).
thf(f70,plain,
( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f193,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ~ spl20_5 ),
inference(subsumption_resolution,[status(thm)],[f192,f69]) ).
thf(f69,plain,
( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f192,plain,
( ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ~ spl20_5 ),
inference(trivial_inequality_removal,[status(thm)],[f191]) ).
thf(f191,plain,
( ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ( $true != $true )
| ~ spl20_5 ),
inference(superposition,[status(thm)],[f190,f71]) ).
thf(f71,plain,
( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f190,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) )
| ~ spl20_5 ),
inference(trivial_inequality_removal,[status(thm)],[f189]) ).
thf(f189,plain,
( ! [X0: $i] :
( ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) ) )
| ~ spl20_5 ),
inference(superposition,[status(thm)],[f143,f112]) ).
thf(f112,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
= $true )
| ( $true != $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f85,f61]) ).
thf(f61,plain,
binintersectT_lem = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f85,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( binintersectT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( binintersectT_lem = $true )
| ( ( $true
= ( in @ sK18 @ ( powerset @ sK17 ) ) )
& ( ( in @ ( binintersect @ sK18 @ sK19 ) @ ( powerset @ sK17 ) )
!= $true )
& ( ( in @ sK19 @ ( powerset @ sK17 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true )
| ! [X5: $i] :
( ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true ) ) )
| ( binintersectT_lem != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f51,f53,f52]) ).
thf(f52,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK18 @ ( powerset @ sK17 ) ) )
& ? [X2: $i] :
( ( ( in @ ( binintersect @ sK18 @ X2 ) @ ( powerset @ sK17 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ sK17 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f53,plain,
( ? [X2: $i] :
( ( ( in @ ( binintersect @ sK18 @ X2 ) @ ( powerset @ sK17 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ sK17 ) )
= $true ) )
=> ( ( ( in @ ( binintersect @ sK18 @ sK19 ) @ ( powerset @ sK17 ) )
!= $true )
& ( ( in @ sK19 @ ( powerset @ sK17 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ( ( binintersectT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true )
| ! [X5: $i] :
( ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
= $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true ) ) )
| ( binintersectT_lem != $true ) ) ),
inference(rectify,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( binintersectT_lem = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( binintersectT_lem != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( binintersectT_lem = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true ) ) )
<=> ( binintersectT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( binintersectT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binintersectT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',binintersectT_lem) ).
thf(f143,plain,
( ! [X0: $i] :
( ( ( in @ ( binintersect @ sK4 @ sK6 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) )
| ~ spl20_5 ),
inference(avatar_component_clause,[status(thm)],[f142]) ).
thf(f142,definition,
( spl20_5
<=> ! [X0: $i] :
( ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binintersect @ sK4 @ sK6 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl20_5])],[avatar_definition]) ).
thf(f188,plain,
spl20_6,
inference(avatar_contradiction_clause,[status(thm)],[f187]) ).
thf(f187,plain,
( $false
| spl20_6 ),
inference(subsumption_resolution,[status(thm)],[f186,f68]) ).
thf(f186,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| spl20_6 ),
inference(subsumption_resolution,[status(thm)],[f185,f70]) ).
thf(f185,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| spl20_6 ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK5 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| spl20_6 ),
inference(superposition,[status(thm)],[f183,f71]) ).
thf(f183,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) )
| spl20_6 ),
inference(subsumption_resolution,[status(thm)],[f182,f66]) ).
thf(f66,plain,
( $true
= ( subset @ sK6 @ sK8 ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f182,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( $true
!= ( subset @ sK6 @ sK8 ) )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) )
| spl20_6 ),
inference(trivial_inequality_removal,[status(thm)],[f179]) ).
thf(f179,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( $true
!= ( subset @ sK6 @ sK8 ) )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) )
| spl20_6 ),
inference(superposition,[status(thm)],[f147,f114]) ).
thf(f114,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( subset @ X6 @ X7 )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( subset @ X6 @ X7 )
!= $true )
| ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f79,f64]) ).
thf(f64,plain,
woz13rule2 = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f79,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( subset @ X6 @ X7 )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( woz13rule2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( woz13rule2 = $true )
| ( ( ( in @ sK14 @ ( powerset @ sK13 ) )
= $true )
& ( ( subset @ ( binintersect @ sK14 @ sK15 ) @ sK16 )
!= $true )
& ( $true
= ( subset @ sK15 @ sK16 ) )
& ( ( in @ sK16 @ ( powerset @ sK13 ) )
= $true )
& ( ( in @ sK15 @ ( powerset @ sK13 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( subset @ X6 @ X7 )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) ) )
| ( woz13rule2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f45,f48,f47,f46]) ).
thf(f46,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( ( in @ sK14 @ ( powerset @ sK13 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK14 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ sK13 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK13 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK14 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ sK13 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK13 ) ) ) )
=> ( ? [X3: $i] :
( ( $true
!= ( subset @ ( binintersect @ sK14 @ sK15 ) @ X3 ) )
& ( ( subset @ sK15 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ sK13 ) )
= $true ) )
& ( ( in @ sK15 @ ( powerset @ sK13 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,plain,
( ? [X3: $i] :
( ( $true
!= ( subset @ ( binintersect @ sK14 @ sK15 ) @ X3 ) )
& ( ( subset @ sK15 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ sK13 ) )
= $true ) )
=> ( ( ( subset @ ( binintersect @ sK14 @ sK15 ) @ sK16 )
!= $true )
& ( $true
= ( subset @ sK15 @ sK16 ) )
& ( ( in @ sK16 @ ( powerset @ sK13 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ( ( woz13rule2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( subset @ X6 @ X7 )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) ) )
| ( woz13rule2 != $true ) ) ),
inference(rectify,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( woz13rule2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( woz13rule2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( woz13rule2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ( woz13rule2 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( woz13rule2 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ X2 @ X3 )
= $true )
=> ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
= woz13rule2 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
= woz13rule2 ),
file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',woz13rule2) ).
thf(f147,plain,
( ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK8 )
!= $true )
| spl20_6 ),
inference(avatar_component_clause,[status(thm)],[f145]) ).
thf(f145,definition,
( spl20_6
<=> ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl20_6])],[avatar_definition]) ).
thf(f178,plain,
spl20_4,
inference(avatar_contradiction_clause,[status(thm)],[f177]) ).
thf(f177,plain,
( $false
| spl20_4 ),
inference(subsumption_resolution,[status(thm)],[f176,f70]) ).
thf(f176,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| spl20_4 ),
inference(subsumption_resolution,[status(thm)],[f175,f69]) ).
thf(f175,plain,
( ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| spl20_4 ),
inference(trivial_inequality_removal,[status(thm)],[f174]) ).
thf(f174,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| spl20_4 ),
inference(superposition,[status(thm)],[f173,f71]) ).
thf(f173,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true ) )
| spl20_4 ),
inference(subsumption_resolution,[status(thm)],[f171,f65]) ).
thf(f65,plain,
( ( subset @ sK4 @ sK7 )
= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f171,plain,
( ! [X0: $i] :
( ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ sK4 @ sK7 )
!= $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) ) )
| spl20_4 ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( subset @ sK4 @ sK7 )
!= $true )
| ( $true != $true )
| ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true ) )
| spl20_4 ),
inference(superposition,[status(thm)],[f140,f113]) ).
thf(f113,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X7 )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X7 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f55,f62]) ).
thf(f62,plain,
woz13rule1 = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f55,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X7 )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( woz13rule1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( woz13rule1 = $true )
| ( ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( ( subset @ ( binintersect @ sK1 @ sK2 ) @ sK3 )
!= $true )
& ( ( in @ sK3 @ ( powerset @ sK0 ) )
= $true )
& ( ( subset @ sK1 @ sK3 )
= $true )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X7 )
!= $true ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( woz13rule1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f28,f31,f30,f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X3 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK1 @ X2 ) @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK0 ) ) )
& ( ( subset @ sK1 @ X3 )
= $true ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK1 @ X2 ) @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK0 ) ) )
& ( ( subset @ sK1 @ X3 )
= $true ) ) )
=> ( ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK1 @ sK2 ) @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK0 ) ) )
& ( ( subset @ sK1 @ X3 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK1 @ sK2 ) @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK0 ) ) )
& ( ( subset @ sK1 @ X3 )
= $true ) )
=> ( ( ( subset @ ( binintersect @ sK1 @ sK2 ) @ sK3 )
!= $true )
& ( ( in @ sK3 @ ( powerset @ sK0 ) )
= $true )
& ( ( subset @ sK1 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ( woz13rule1 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X3 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( ( subset @ ( binintersect @ X5 @ X6 ) @ X7 )
= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X7 )
!= $true ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( woz13rule1 != $true ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( woz13rule1 = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( subset @ ( binintersect @ X0 @ X2 ) @ X3 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ( $true
= ( subset @ X0 @ X3 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( subset @ ( binintersect @ X0 @ X2 ) @ X3 )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( subset @ X0 @ X3 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( woz13rule1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( woz13rule1 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( subset @ ( binintersect @ X0 @ X2 ) @ X3 )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( subset @ X0 @ X3 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ ( binintersect @ X0 @ X2 ) @ X3 )
= $true )
| ( $true
!= ( subset @ X0 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( woz13rule1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ( ( $true
= ( subset @ X0 @ X3 ) )
=> ( ( subset @ ( binintersect @ X0 @ X2 ) @ X3 )
= $true ) ) ) ) )
<=> ( woz13rule1 = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ X3 )
=> ( subset @ ( binintersect @ X0 @ X2 ) @ X3 ) ) ) ) )
= woz13rule1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
= woz13rule1 ),
file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',woz13rule1) ).
thf(f140,plain,
( ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK7 )
!= $true )
| spl20_4 ),
inference(avatar_component_clause,[status(thm)],[f138]) ).
thf(f138,definition,
( spl20_4
<=> ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl20_4])],[avatar_definition]) ).
thf(f148,plain,
( ~ spl20_4
| spl20_5
| ~ spl20_6 ),
inference(avatar_split_clause,[status(thm)],[f136,f145,f142,f138]) ).
thf(f136,plain,
! [X0: $i] :
( ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK7 )
!= $true )
| ( ( in @ ( binintersect @ sK4 @ sK6 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK8 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ ( binintersect @ sK4 @ sK6 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK7 )
!= $true )
| ( ( subset @ ( binintersect @ sK4 @ sK6 ) @ sK8 )
!= $true ) ),
inference(superposition,[status(thm)],[f67,f115]) ).
thf(f115,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ ( binintersect @ X6 @ X7 ) )
= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X6 )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X7 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X7 )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X6 )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X6 @ X7 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f72,f63]) ).
thf(f63,plain,
woz13rule3 = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f72,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ X6 )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X6 @ X7 ) )
= $true )
| ( ( subset @ X5 @ X7 )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( woz13rule3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( woz13rule3 = $true )
| ( ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true )
& ( ( subset @ sK10 @ sK11 )
= $true )
& ( $true
= ( in @ sK12 @ ( powerset @ sK9 ) ) )
& ( $true
!= ( subset @ sK10 @ ( binintersect @ sK11 @ sK12 ) ) )
& ( ( subset @ sK10 @ sK12 )
= $true )
& ( ( in @ sK11 @ ( powerset @ sK9 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( ( subset @ X5 @ X6 )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X6 @ X7 ) )
= $true )
| ( ( subset @ X5 @ X7 )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) ) )
| ( woz13rule3 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f39,f42,f41,f40]) ).
thf(f40,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( ( subset @ X1 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ sK10 @ X2 )
= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK9 ) ) )
& ( ( subset @ sK10 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( $true
= ( subset @ sK10 @ X3 ) ) )
& ( ( in @ X2 @ ( powerset @ sK9 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ sK10 @ X2 )
= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK9 ) ) )
& ( ( subset @ sK10 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( $true
= ( subset @ sK10 @ X3 ) ) )
& ( ( in @ X2 @ ( powerset @ sK9 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( ( subset @ sK10 @ sK11 )
= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK9 ) ) )
& ( ( subset @ sK10 @ ( binintersect @ sK11 @ X3 ) )
!= $true )
& ( $true
= ( subset @ sK10 @ X3 ) ) )
& ( ( in @ sK11 @ ( powerset @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ? [X3: $i] :
( ( ( subset @ sK10 @ sK11 )
= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK9 ) ) )
& ( ( subset @ sK10 @ ( binintersect @ sK11 @ X3 ) )
!= $true )
& ( $true
= ( subset @ sK10 @ X3 ) ) )
=> ( ( ( subset @ sK10 @ sK11 )
= $true )
& ( $true
= ( in @ sK12 @ ( powerset @ sK9 ) ) )
& ( $true
!= ( subset @ sK10 @ ( binintersect @ sK11 @ sK12 ) ) )
& ( ( subset @ sK10 @ sK12 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ( ( woz13rule3 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( ( subset @ X1 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( ( subset @ X5 @ X6 )
!= $true )
| ( ( in @ X7 @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X6 @ X7 ) )
= $true )
| ( ( subset @ X5 @ X7 )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) ) )
| ( woz13rule3 != $true ) ) ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( woz13rule3 = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( $true
= ( subset @ X0 @ X3 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( subset @ X0 @ X3 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( woz13rule3 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( woz13rule3 = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( subset @ X0 @ X3 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true
!= ( subset @ X0 @ X3 ) )
| ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( woz13rule3 = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ( ( ( subset @ X0 @ X2 )
= $true )
=> ( ( $true
= ( subset @ X0 @ X3 ) )
=> ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
= $true ) ) ) ) ) )
<=> ( woz13rule3 = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ X2 )
=> ( ( subset @ X0 @ X3 )
=> ( subset @ X0 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) )
= woz13rule3 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X2 )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) )
= woz13rule3 ),
file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',woz13rule3) ).
thf(f67,plain,
( ( subset @ ( binintersect @ sK4 @ sK6 ) @ ( binintersect @ sK7 @ sK8 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU762^2 : 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 : n031.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 12:34:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SEU762^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.47 % Domain : Set Theory
% 0.21/0.47 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Lemmas
% 0.21/0.47 % Version : Especial > Reduced > Especial.
% 0.21/0.47 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.21/0.47 % (! Z:i.in Z (powerset A) -> (! W:i.in W (powerset A) ->
% 0.21/0.47 % subset X Z -> subset Y W -> subset (binintersect X Y)
% 0.21/0.47 % (binintersect Z W)))))
% 0.21/0.47
% 0.21/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.47 % Source : [Bro08]
% 0.21/0.47 % Names : ZFC264l [Bro08]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.21/0.47 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.21/0.47 % Number of atoms : 38 ( 4 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 11 ( 7 avg)
% 0.21/0.47 % Number of connectives : 105 ( 0 ~; 0 |; 0 &; 80 @)
% 0.21/0.47 % ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 20 ( 5 avg)
% 0.21/0.47 % Number of types : 2 ( 0 usr)
% 0.21/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.21/0.47 % Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : http://mathgate.info/detsetitem.php?id=323
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(in_type,type,
% 0.21/0.47 in: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(powerset_type,type,
% 0.21/0.47 powerset: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(subset_type,type,
% 0.21/0.47 subset: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersect_type,type,
% 0.21/0.47 binintersect: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectT_lem_type,type,
% 0.21/0.47 binintersectT_lem: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectT_lem,definition,
% 0.21/0.47 ( binintersectT_lem
% 0.21/0.47 = ( ! [A: $i,X: $i] :
% 0.21/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.47 => ! [Y: $i] :
% 0.21/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(woz13rule1_type,type,
% 0.21/0.47 woz13rule1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(woz13rule1,definition,
% 0.21/0.47 ( woz13rule1
% 0.21/0.47 = ( ! [A: $i,X: $i] :
% 0.21/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.47 => ! [Y: $i] :
% 0.21/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.47 => ! [Z: $i] :
% 0.21/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.21/0.47 => ( ( subset @ X @ Z )
% 0.21/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(woz13rule2_type,type,
% 0.21/0.47 woz13rule2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(woz13rule2,definition,
% 0.21/0.47 ( woz13rule2
% 0.21/0.47 = ( ! [A: $i,X: $i] :
% 0.21/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.47 => ! [Y: $i] :
% 0.21/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.47 => ! [Z: $i] :
% 0.21/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.21/0.47 => ( ( subset @ Y @ Z )
% 0.21/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(woz13rule3_type,type,
% 0.21/0.47 woz13rule3: $o ).
% 0.21/0.47
% 0.21/0.47 thf(woz13rule3,definition,
% 0.21/0.47 ( woz13rule3
% 0.21/0.47 = ( ! [A: $i,X: $i] :
% 0.21/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.47 => ! [Y: $i] :
% 0.21/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.47 => ! [Z: $i] :
% 0.21/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.21/0.47 => ( ( subset @ X @ Y )
% 0.21/0.47 => ( ( subset @ X @ Z )
% 0.21/0.47 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(woz13rule4,conjecture,
% 0.21/0.47 ( binintersectT_lem
% 0.21/0.47 => ( woz13rule1
% 0.21/0.47 => ( woz13rule2
% 0.21/0.47 => ( woz13rule3
% 0.21/0.47 => ! [A: $i,X: $i] :
% 0.21/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.47 => ! [Y: $i] :
% 0.21/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.47 => ! [Z: $i] :
% 0.21/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.21/0.47 => ! [W: $i] :
% 0.21/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.21/0.47 => ( ( subset @ X @ Z )
% 0.21/0.47 => ( ( subset @ Y @ W )
% 0.21/0.47 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.69/1.31 ---- Embedded in THF ---
% 1.69/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.69/1.32 %%% Generated on Tue Feb 24 12:34:19 EST 2026
% 1.69/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.69/1.32 %%% Logic specification used:
% 1.69/1.32 %%% thf(spec, logic, $$dhol).
% 1.69/1.32
% 1.69/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2DTF1245.p
% See solution above
% 1.69/1.32 ------------------------
% 1.69/1.32 ---- Cleaned THF ---
% 1.69/1.32 thf(in_type,type,
% 1.69/1.32 in: $i > $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(powerset_type,type,
% 1.69/1.32 powerset: $i > $i ).
% 1.69/1.32
% 1.69/1.32 thf(subset_type,type,
% 1.69/1.32 subset: $i > $i > $o ).
% 1.69/1.32
% 1.69/1.32 thf(binintersect_type,type,
% 1.69/1.32 binintersect: $i > $i > $i ).
% 1.69/1.32
% 1.69/1.32 thf(binintersectT_lem_type,type,
% 1.69/1.32 binintersectT_lem: $o ).
% 1.69/1.32
% 1.69/1.32 thf(binintersectT_lem,definition,
% 1.69/1.32 ( binintersectT_lem
% 1.69/1.32 = ( ! [A: $i,X: $i] :
% 1.69/1.32 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.32 => ! [Y: $i] :
% 1.69/1.32 ( ( in @ Y @ ( powerset @ A ) )
% 1.69/1.32 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(woz13rule1_type,type,
% 1.69/1.32 woz13rule1: $o ).
% 1.69/1.32
% 1.69/1.32 thf(woz13rule1,definition,
% 1.69/1.32 ( woz13rule1
% 1.69/1.32 = ( ! [A: $i,X: $i] :
% 1.69/1.32 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.32 => ! [Y: $i] :
% 1.69/1.32 ( ( in @ Y @ ( powerset @ A ) )
% 1.69/1.32 => ! [Z: $i] :
% 1.69/1.32 ( ( in @ Z @ ( powerset @ A ) )
% 1.69/1.32 => ( ( subset @ X @ Z )
% 1.69/1.32 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(woz13rule2_type,type,
% 1.69/1.32 woz13rule2: $o ).
% 1.69/1.32
% 1.69/1.32 thf(woz13rule2,definition,
% 1.69/1.32 ( woz13rule2
% 1.69/1.32 = ( ! [A: $i,X: $i] :
% 1.69/1.32 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.32 => ! [Y: $i] :
% 1.69/1.32 ( ( in @ Y @ ( powerset @ A ) )
% 1.69/1.32 => ! [Z: $i] :
% 1.69/1.32 ( ( in @ Z @ ( powerset @ A ) )
% 1.69/1.32 => ( ( subset @ Y @ Z )
% 1.69/1.32 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(woz13rule3_type,type,
% 1.69/1.32 woz13rule3: $o ).
% 1.69/1.32
% 1.69/1.32 thf(woz13rule3,definition,
% 1.69/1.32 ( woz13rule3
% 1.69/1.32 = ( ! [A: $i,X: $i] :
% 1.69/1.32 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.32 => ! [Y: $i] :
% 1.69/1.32 ( ( in @ Y @ ( powerset @ A ) )
% 1.69/1.32 => ! [Z: $i] :
% 1.69/1.32 ( ( in @ Z @ ( powerset @ A ) )
% 1.69/1.32 => ( ( subset @ X @ Y )
% 1.69/1.32 => ( ( subset @ X @ Z )
% 1.69/1.32 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 1.69/1.32
% 1.69/1.32 thf(woz13rule4,conjecture,
% 1.69/1.32 ( binintersectT_lem
% 1.69/1.32 => ( woz13rule1
% 1.69/1.32 => ( woz13rule2
% 1.69/1.32 => ( woz13rule3
% 1.69/1.32 => ! [A: $i,X: $i] :
% 1.69/1.32 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.32 => ! [Y: $i] :
% 1.69/1.32 ( ( in @ Y @ ( powerset @ A ) )
% 1.69/1.32 => ! [Z: $i] :
% 1.69/1.32 ( ( in @ Z @ ( powerset @ A ) )
% 1.69/1.32 => ! [W: $i] :
% 1.69/1.32 ( ( in @ W @ ( powerset @ A ) )
% 1.69/1.32 => ( ( subset @ X @ Z )
% 1.69/1.32 => ( ( subset @ Y @ W )
% 1.69/1.32 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.69/1.32 ------------------------
% 1.69/1.34 % (1570)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_1245 for (2999ds/4Mi)
% 1.69/1.34 % (1570)Instruction limit reached!
% 1.69/1.34 % (1570)------------------------------
% 1.69/1.34 % (1570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1570)Termination reason: Unknown
% 1.69/1.34 % (1570)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (1570)Memory used [KB]: 5500
% 1.69/1.34 % (1570)Time elapsed: 0.003 s
% 1.69/1.34 % (1570)Instructions burned: 6 (million)
% 1.69/1.34 % (1570)------------------------------
% 1.69/1.34 % (1570)------------------------------
% 1.69/1.34 % (1569)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1245 for (2999ds/183Mi)
% 1.69/1.34 % (1571)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_1245 for (2999ds/27Mi)
% 1.69/1.34 % (1572)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1245 for (2999ds/2Mi)
% 1.69/1.34 % (1573)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_1245 for (2999ds/2Mi)
% 1.69/1.34 % (1575)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1245 for (2999ds/18Mi)
% 1.69/1.34 % (1574)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_1245 for (2999ds/275Mi)
% 1.69/1.35 % (1572)Instruction limit reached!
% 1.69/1.35 % (1572)------------------------------
% 1.69/1.35 % (1572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (1572)Termination reason: Unknown
% 1.69/1.35 % (1572)Termination phase: shuffling
% 1.69/1.35
% 1.69/1.35 % (1572)Memory used [KB]: 1023
% 1.69/1.35 % (1572)Time elapsed: 0.003 s
% 1.69/1.35 % (1572)Instructions burned: 2 (million)
% 1.69/1.35 % (1572)------------------------------
% 1.69/1.35 % (1572)------------------------------
% 1.69/1.35 % (1573)Instruction limit reached!
% 1.69/1.35 % (1573)------------------------------
% 1.69/1.35 % (1573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (1573)Termination reason: Unknown
% 1.69/1.35 % (1573)Termination phase: shuffling
% 1.69/1.35
% 1.69/1.35 % (1573)Memory used [KB]: 1023
% 1.69/1.35 % (1573)Time elapsed: 0.003 s
% 1.69/1.35 % (1573)Instructions burned: 2 (million)
% 1.69/1.35 % (1573)------------------------------
% 1.69/1.35 % (1573)------------------------------
% 1.69/1.35 % (1576)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1245 for (2999ds/3Mi)
% 1.69/1.35 % (1576)Instruction limit reached!
% 1.69/1.35 % (1576)------------------------------
% 1.69/1.35 % (1576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (1576)Termination reason: Unknown
% 1.69/1.35 % (1576)Termination phase: Property scanning
% 1.69/1.35
% 1.69/1.35 % (1576)Memory used [KB]: 1023
% 1.69/1.35 % (1576)Time elapsed: 0.002 s
% 1.69/1.35 % (1576)Instructions burned: 4 (million)
% 1.69/1.35 % (1576)------------------------------
% 1.69/1.35 % (1576)------------------------------
% 1.69/1.36 % (1575)Instruction limit reached!
% 1.69/1.36 % (1575)------------------------------
% 1.69/1.36 % (1575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (1575)Termination reason: Unknown
% 1.69/1.36 % (1575)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (1575)Memory used [KB]: 5628
% 1.69/1.36 % (1575)Time elapsed: 0.013 s
% 1.69/1.36 % (1575)Instructions burned: 18 (million)
% 1.69/1.36 % (1575)------------------------------
% 1.69/1.36 % (1575)------------------------------
% 1.69/1.36 % (1574)First to succeed.
% 1.69/1.36 % (1579)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1245 for (2999ds/3Mi)
% 1.69/1.36 % (1579)Instruction limit reached!
% 1.69/1.36 % (1579)------------------------------
% 1.69/1.36 % (1579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (1579)Termination reason: Unknown
% 1.69/1.36 % (1579)Termination phase: Preprocessing 3
% 1.69/1.36
% 1.69/1.36 % (1579)Memory used [KB]: 1023
% 1.69/1.36 % (1579)Time elapsed: 0.002 s
% 1.69/1.36 % (1579)Instructions burned: 3 (million)
% 1.69/1.36 % (1579)------------------------------
% 1.69/1.36 % (1579)------------------------------
% 1.69/1.36 % (1571)Instruction limit reached!
% 1.69/1.36 % (1571)------------------------------
% 1.69/1.36 % (1571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (1571)Termination reason: Unknown
% 1.69/1.36 % (1571)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (1571)Memory used [KB]: 5628
% 1.69/1.36 % (1571)Time elapsed: 0.019 s
% 1.69/1.36 % (1571)Instructions burned: 27 (million)
% 1.69/1.36 % (1571)------------------------------
% 1.69/1.36 % (1571)------------------------------
% 1.69/1.36 % (1577)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_1245 for (2999ds/37Mi)
% 1.69/1.36 % (1578)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_1245 for (2999ds/15Mi)
% 1.69/1.36 % (1569)Also succeeded, but the first one will report.
% 1.69/1.36 % (1574)Refutation found. Thanks to Tanya!
% 1.69/1.36 % SZS status Theorem for DTF2THF_1245
% 1.69/1.36 % SZS output start Proof for DTF2THF_1245
% 1.69/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.36 thf(func_def_1, type, powerset: $i > $i).
% 1.69/1.36 thf(func_def_2, type, subset: $i > $i > $o).
% 1.69/1.36 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.69/1.36 thf(f197,plain,(
% 1.69/1.36 $false),
% 1.69/1.36 inference(avatar_sat_refutation,[status(thm)],[f148,f178,f188,f196])).
% 1.69/1.36 thf(f196,plain,(
% 1.69/1.36 ~spl20_5),
% 1.69/1.36 inference(avatar_contradiction_clause,[status(thm)],[f195])).
% 1.69/1.36 thf(f195,plain,(
% 1.69/1.36 $false | ~spl20_5),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f194,f68])).
% 1.69/1.36 thf(f68,plain,(
% 1.69/1.36 ($true = (in @ sK8 @ (powerset @ sK5)))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f37,plain,(
% 1.69/1.36 (($true = (in @ sK4 @ (powerset @ sK5))) & (($true = (in @ sK6 @ (powerset @ sK5))) & (($true = (in @ sK7 @ (powerset @ sK5))) & (($true = (in @ sK8 @ (powerset @ sK5))) & ((subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ sK8)) != $true) & ($true = (subset @ sK6 @ sK8)) & ((subset @ sK4 @ sK7) = $true))))) & (woz13rule2 = $true) & (woz13rule3 = $true) & (woz13rule1 = $true) & (binintersectT_lem = $true)),
% 1.69/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f24,f36,f35,f34,f33])).
% 1.69/1.36 thf(f33,plain,(
% 1.69/1.36 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ X1)) = $true) & ($true != (subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4))) & ((subset @ X2 @ X4) = $true) & ($true = (subset @ X0 @ X3)))))) => (($true = (in @ sK4 @ (powerset @ sK5))) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK5))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ sK5)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK5)) = $true) & ((subset @ (binintersect @ sK4 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ((subset @ X2 @ X4) = $true) & ($true = (subset @ sK4 @ X3))))))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f34,plain,(
% 1.69/1.36 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK5))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ sK5)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK5)) = $true) & ((subset @ (binintersect @ sK4 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ((subset @ X2 @ X4) = $true) & ($true = (subset @ sK4 @ X3))))) => (($true = (in @ sK6 @ (powerset @ sK5))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ sK5)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK5)) = $true) & ((subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ X3 @ X4)) != $true) & ((subset @ sK6 @ X4) = $true) & ($true = (subset @ sK4 @ X3)))))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f35,plain,(
% 1.69/1.36 ? [X3 : $i] : (((in @ X3 @ (powerset @ sK5)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK5)) = $true) & ((subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ X3 @ X4)) != $true) & ((subset @ sK6 @ X4) = $true) & ($true = (subset @ sK4 @ X3)))) => (($true = (in @ sK7 @ (powerset @ sK5))) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK5)) = $true) & ((subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ X4)) != $true) & ((subset @ sK6 @ X4) = $true) & ((subset @ sK4 @ sK7) = $true)))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f36,plain,(
% 1.69/1.36 ? [X4 : $i] : (((in @ X4 @ (powerset @ sK5)) = $true) & ((subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ X4)) != $true) & ((subset @ sK6 @ X4) = $true) & ((subset @ sK4 @ sK7) = $true)) => (($true = (in @ sK8 @ (powerset @ sK5))) & ((subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ sK8)) != $true) & ($true = (subset @ sK6 @ sK8)) & ((subset @ sK4 @ sK7) = $true))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f24,plain,(
% 1.69/1.36 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ X1)) = $true) & ($true != (subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4))) & ((subset @ X2 @ X4) = $true) & ($true = (subset @ X0 @ X3)))))) & (woz13rule2 = $true) & (woz13rule3 = $true) & (woz13rule1 = $true) & (binintersectT_lem = $true)),
% 1.69/1.36 inference(flattening,[status(thm)],[f23])).
% 1.69/1.36 thf(f23,plain,(
% 1.69/1.36 (((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((($true != (subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4))) & ((subset @ X2 @ X4) = $true)) & ($true = (subset @ X0 @ X3))) & ((in @ X4 @ (powerset @ X1)) = $true)) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (binintersectT_lem = $true)),
% 1.69/1.36 inference(ennf_transformation,[status(thm)],[f13])).
% 1.69/1.36 thf(f13,plain,(
% 1.69/1.36 ~((binintersectT_lem = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => ! [X4 : $i] : (((in @ X4 @ (powerset @ X1)) = $true) => (($true = (subset @ X0 @ X3)) => (((subset @ X2 @ X4) = $true) => ($true = (subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)))))))))))))),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f12])).
% 1.69/1.36 thf(f12,plain,(
% 1.69/1.36 ~(binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X1)) => ((subset @ X0 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4))))))))))))),
% 1.69/1.36 inference(rectify,[status(thm)],[f6])).
% 1.69/1.36 thf(f6,negated_conjecture,(
% 1.69/1.36 ~(binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X1 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4))))))))))))),
% 1.69/1.36 inference(negated_conjecture,[status(cth)],[f5])).
% 1.69/1.36 thf(f5,conjecture,(
% 1.69/1.36 binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X1 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4)))))))))))),
% 1.69/1.36 file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',woz13rule4)).
% 1.69/1.36 thf(f194,plain,(
% 1.69/1.36 ($true != (in @ sK8 @ (powerset @ sK5))) | ~spl20_5),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f193,f70])).
% 1.69/1.36 thf(f70,plain,(
% 1.69/1.36 ($true = (in @ sK6 @ (powerset @ sK5)))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f193,plain,(
% 1.69/1.36 ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK8 @ (powerset @ sK5))) | ~spl20_5),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f192,f69])).
% 1.69/1.36 thf(f69,plain,(
% 1.69/1.36 ($true = (in @ sK7 @ (powerset @ sK5)))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f192,plain,(
% 1.69/1.36 ($true != (in @ sK7 @ (powerset @ sK5))) | ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK8 @ (powerset @ sK5))) | ~spl20_5),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f191])).
% 1.69/1.36 thf(f191,plain,(
% 1.69/1.36 ($true != (in @ sK7 @ (powerset @ sK5))) | ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK8 @ (powerset @ sK5))) | ($true != $true) | ~spl20_5),
% 1.69/1.36 inference(superposition,[status(thm)],[f190,f71])).
% 1.69/1.36 thf(f71,plain,(
% 1.69/1.36 ($true = (in @ sK4 @ (powerset @ sK5)))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f190,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($true != (in @ sK4 @ (powerset @ X0))) | ((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true)) ) | ~spl20_5),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f189])).
% 1.69/1.36 thf(f189,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ($true != $true) | ($true != (in @ sK4 @ (powerset @ X0)))) ) | ~spl20_5),
% 1.69/1.36 inference(superposition,[status(thm)],[f143,f112])).
% 1.69/1.36 thf(f112,plain,(
% 1.69/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ((in @ X5 @ (powerset @ X3)) != $true) | ((in @ X4 @ (powerset @ X3)) != $true)) )),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.69/1.36 thf(f111,plain,(
% 1.69/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X3)) != $true) | ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ($true != $true) | ((in @ X4 @ (powerset @ X3)) != $true)) )),
% 1.69/1.36 inference(definition_unfolding,[status(thm)],[f85,f61])).
% 1.69/1.36 thf(f61,plain,(
% 1.69/1.36 (binintersectT_lem = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f85,plain,(
% 1.69/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X3)) != $true) | ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ((in @ X5 @ (powerset @ X3)) != $true) | (binintersectT_lem != $true)) )),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f54])).
% 1.69/1.36 thf(f54,plain,(
% 1.69/1.36 ((binintersectT_lem = $true) | (($true = (in @ sK18 @ (powerset @ sK17))) & (((in @ (binintersect @ sK18 @ sK19) @ (powerset @ sK17)) != $true) & ((in @ sK19 @ (powerset @ sK17)) = $true)))) & (! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) != $true) | ! [X5 : $i] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ((in @ X5 @ (powerset @ X3)) != $true))) | (binintersectT_lem != $true))),
% 1.69/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f51,f53,f52])).
% 1.69/1.36 thf(f52,plain,(
% 1.69/1.36 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true))) => (($true = (in @ sK18 @ (powerset @ sK17))) & ? [X2 : $i] : (((in @ (binintersect @ sK18 @ X2) @ (powerset @ sK17)) != $true) & ((in @ X2 @ (powerset @ sK17)) = $true)))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f53,plain,(
% 1.69/1.36 ? [X2 : $i] : (((in @ (binintersect @ sK18 @ X2) @ (powerset @ sK17)) != $true) & ((in @ X2 @ (powerset @ sK17)) = $true)) => (((in @ (binintersect @ sK18 @ sK19) @ (powerset @ sK17)) != $true) & ((in @ sK19 @ (powerset @ sK17)) = $true))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f51,plain,(
% 1.69/1.36 ((binintersectT_lem = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)))) & (! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) != $true) | ! [X5 : $i] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ((in @ X5 @ (powerset @ X3)) != $true))) | (binintersectT_lem != $true))),
% 1.69/1.36 inference(rectify,[status(thm)],[f50])).
% 1.69/1.36 thf(f50,plain,(
% 1.69/1.36 ((binintersectT_lem = $true) | ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) != $true) & ($true = (in @ X2 @ (powerset @ X1)))))) & (! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true) | ($true != (in @ X2 @ (powerset @ X1))))) | (binintersectT_lem != $true))),
% 1.69/1.36 inference(nnf_transformation,[status(thm)],[f18])).
% 1.69/1.36 thf(f18,plain,(
% 1.69/1.36 (binintersectT_lem = $true) <=> ! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true) | ($true != (in @ X2 @ (powerset @ X1)))))),
% 1.69/1.36 inference(ennf_transformation,[status(thm)],[f11])).
% 1.69/1.36 thf(f11,plain,(
% 1.69/1.36 ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true))) <=> (binintersectT_lem = $true)),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f10])).
% 1.69/1.36 thf(f10,plain,(
% 1.69/1.36 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))),
% 1.69/1.36 inference(rectify,[status(thm)],[f1])).
% 1.69/1.36 thf(f1,axiom,(
% 1.69/1.36 (binintersectT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 1.69/1.36 file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',binintersectT_lem)).
% 1.69/1.36 thf(f143,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ (binintersect @ sK4 @ sK6) @ (powerset @ X0)) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true)) ) | ~spl20_5),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f142])).
% 1.69/1.36 thf(f142,definition,(
% 1.69/1.36 spl20_5 <=> ! [X0 : $i] : (((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ (binintersect @ sK4 @ sK6) @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true))),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl20_5])],[avatar_definition])).
% 1.69/1.36 thf(f188,plain,(
% 1.69/1.36 spl20_6),
% 1.69/1.36 inference(avatar_contradiction_clause,[status(thm)],[f187])).
% 1.69/1.36 thf(f187,plain,(
% 1.69/1.36 $false | spl20_6),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f186,f68])).
% 1.69/1.36 thf(f186,plain,(
% 1.69/1.36 ($true != (in @ sK8 @ (powerset @ sK5))) | spl20_6),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f185,f70])).
% 1.69/1.36 thf(f185,plain,(
% 1.69/1.36 ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK8 @ (powerset @ sK5))) | spl20_6),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.69/1.36 thf(f184,plain,(
% 1.69/1.36 ($true != (in @ sK8 @ (powerset @ sK5))) | ($true != $true) | ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_6),
% 1.69/1.36 inference(superposition,[status(thm)],[f183,f71])).
% 1.69/1.36 thf(f183,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($true != (in @ sK4 @ (powerset @ X0))) | ((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true)) ) | spl20_6),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f182,f66])).
% 1.69/1.36 thf(f66,plain,(
% 1.69/1.36 ($true = (subset @ sK6 @ sK8))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f182,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($true != (in @ sK4 @ (powerset @ X0))) | ($true != (subset @ sK6 @ sK8)) | ((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true)) ) | spl20_6),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f179])).
% 1.69/1.36 thf(f179,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($true != (in @ sK4 @ (powerset @ X0))) | ($true != (subset @ sK6 @ sK8)) | ((in @ sK6 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ sK8 @ (powerset @ X0)) != $true)) ) | spl20_6),
% 1.69/1.36 inference(superposition,[status(thm)],[f147,f114])).
% 1.69/1.36 thf(f114,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((subset @ X6 @ X7) != $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true)) )),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.69/1.36 thf(f107,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((subset @ X6 @ X7) != $true) | ((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true)) )),
% 1.69/1.36 inference(definition_unfolding,[status(thm)],[f79,f64])).
% 1.69/1.36 thf(f64,plain,(
% 1.69/1.36 (woz13rule2 = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f79,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((subset @ X6 @ X7) != $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | (woz13rule2 != $true)) )),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f49])).
% 1.69/1.36 thf(f49,plain,(
% 1.69/1.36 ((woz13rule2 = $true) | (((in @ sK14 @ (powerset @ sK13)) = $true) & ((((subset @ (binintersect @ sK14 @ sK15) @ sK16) != $true) & ($true = (subset @ sK15 @ sK16)) & ((in @ sK16 @ (powerset @ sK13)) = $true)) & ((in @ sK15 @ (powerset @ sK13)) = $true)))) & (! [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ! [X6 : $i] : (! [X7 : $i] : (((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((subset @ X6 @ X7) != $true) | ((in @ X7 @ (powerset @ X4)) != $true)) | ((in @ X6 @ (powerset @ X4)) != $true))) | (woz13rule2 != $true))),
% 1.69/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f45,f48,f47,f46])).
% 1.69/1.36 thf(f46,plain,(
% 1.69/1.36 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((subset @ X2 @ X3) = $true) & ((in @ X3 @ (powerset @ X0)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))) => (((in @ sK14 @ (powerset @ sK13)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ sK14 @ X2) @ X3) != $true) & ((subset @ X2 @ X3) = $true) & ((in @ X3 @ (powerset @ sK13)) = $true)) & ($true = (in @ X2 @ (powerset @ sK13)))))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f47,plain,(
% 1.69/1.36 ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ sK14 @ X2) @ X3) != $true) & ((subset @ X2 @ X3) = $true) & ((in @ X3 @ (powerset @ sK13)) = $true)) & ($true = (in @ X2 @ (powerset @ sK13)))) => (? [X3 : $i] : (($true != (subset @ (binintersect @ sK14 @ sK15) @ X3)) & ((subset @ sK15 @ X3) = $true) & ((in @ X3 @ (powerset @ sK13)) = $true)) & ((in @ sK15 @ (powerset @ sK13)) = $true))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f48,plain,(
% 1.69/1.36 ? [X3 : $i] : (($true != (subset @ (binintersect @ sK14 @ sK15) @ X3)) & ((subset @ sK15 @ X3) = $true) & ((in @ X3 @ (powerset @ sK13)) = $true)) => (((subset @ (binintersect @ sK14 @ sK15) @ sK16) != $true) & ($true = (subset @ sK15 @ sK16)) & ((in @ sK16 @ (powerset @ sK13)) = $true))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f45,plain,(
% 1.69/1.36 ((woz13rule2 = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((subset @ X2 @ X3) = $true) & ((in @ X3 @ (powerset @ X0)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)))) & (! [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ! [X6 : $i] : (! [X7 : $i] : (((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((subset @ X6 @ X7) != $true) | ((in @ X7 @ (powerset @ X4)) != $true)) | ((in @ X6 @ (powerset @ X4)) != $true))) | (woz13rule2 != $true))),
% 1.69/1.36 inference(rectify,[status(thm)],[f44])).
% 1.69/1.36 thf(f44,plain,(
% 1.69/1.36 ((woz13rule2 = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((subset @ X2 @ X3) = $true) & ((in @ X3 @ (powerset @ X0)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)))) & (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X2 @ X3) != $true) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (woz13rule2 != $true))),
% 1.69/1.36 inference(nnf_transformation,[status(thm)],[f20])).
% 1.69/1.36 thf(f20,plain,(
% 1.69/1.36 (woz13rule2 = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X2 @ X3) != $true) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)))),
% 1.69/1.36 inference(flattening,[status(thm)],[f19])).
% 1.69/1.36 thf(f19,plain,(
% 1.69/1.36 (woz13rule2 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X2 @ X3) != $true)) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 1.69/1.36 inference(ennf_transformation,[status(thm)],[f15])).
% 1.69/1.36 thf(f15,plain,(
% 1.69/1.36 (woz13rule2 = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) => (((subset @ X2 @ X3) = $true) => ((subset @ (binintersect @ X1 @ X2) @ X3) = $true)))))),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.36 thf(f14,plain,(
% 1.69/1.36 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))) = woz13rule2)),
% 1.69/1.36 inference(rectify,[status(thm)],[f3])).
% 1.69/1.36 thf(f3,axiom,(
% 1.69/1.36 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))) = woz13rule2)),
% 1.69/1.36 file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',woz13rule2)).
% 1.69/1.36 thf(f147,plain,(
% 1.69/1.36 ((subset @ (binintersect @ sK4 @ sK6) @ sK8) != $true) | spl20_6),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f145])).
% 1.69/1.36 thf(f145,definition,(
% 1.69/1.36 spl20_6 <=> ((subset @ (binintersect @ sK4 @ sK6) @ sK8) = $true)),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl20_6])],[avatar_definition])).
% 1.69/1.36 thf(f178,plain,(
% 1.69/1.36 spl20_4),
% 1.69/1.36 inference(avatar_contradiction_clause,[status(thm)],[f177])).
% 1.69/1.36 thf(f177,plain,(
% 1.69/1.36 $false | spl20_4),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f176,f70])).
% 1.69/1.36 thf(f176,plain,(
% 1.69/1.36 ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_4),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f175,f69])).
% 1.69/1.36 thf(f175,plain,(
% 1.69/1.36 ($true != (in @ sK7 @ (powerset @ sK5))) | ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_4),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f174])).
% 1.69/1.36 thf(f174,plain,(
% 1.69/1.36 ($true != $true) | ($true != (in @ sK7 @ (powerset @ sK5))) | ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_4),
% 1.69/1.36 inference(superposition,[status(thm)],[f173,f71])).
% 1.69/1.36 thf(f173,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($true != (in @ sK4 @ (powerset @ X0))) | ((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true)) ) | spl20_4),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f171,f65])).
% 1.69/1.36 thf(f65,plain,(
% 1.69/1.36 ((subset @ sK4 @ sK7) = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f171,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((subset @ sK4 @ sK7) != $true) | ($true != (in @ sK4 @ (powerset @ X0)))) ) | spl20_4),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.69/1.36 thf(f170,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($true != (in @ sK4 @ (powerset @ X0))) | ((subset @ sK4 @ sK7) != $true) | ($true != $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ sK6 @ (powerset @ X0)) != $true)) ) | spl20_4),
% 1.69/1.36 inference(superposition,[status(thm)],[f140,f113])).
% 1.69/1.36 thf(f113,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X7) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X7 @ (powerset @ X4)) != $true)) )),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.69/1.36 thf(f94,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X7) != $true) | ($true != $true)) )),
% 1.69/1.36 inference(definition_unfolding,[status(thm)],[f55,f62])).
% 1.69/1.36 thf(f62,plain,(
% 1.69/1.36 (woz13rule1 = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f55,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X7) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (woz13rule1 != $true)) )),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f32])).
% 1.69/1.36 thf(f32,plain,(
% 1.69/1.36 ((woz13rule1 = $true) | ((($true = (in @ sK2 @ (powerset @ sK0))) & (((subset @ (binintersect @ sK1 @ sK2) @ sK3) != $true) & ((in @ sK3 @ (powerset @ sK0)) = $true) & ((subset @ sK1 @ sK3) = $true))) & ($true = (in @ sK1 @ (powerset @ sK0))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ! [X7 : $i] : (((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X7) != $true))) | ((in @ X5 @ (powerset @ X4)) != $true)) | (woz13rule1 != $true))),
% 1.69/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f28,f31,f30,f29])).
% 1.69/1.36 thf(f29,plain,(
% 1.69/1.36 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ X1 @ X3) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK0))) & ? [X3 : $i] : (((subset @ (binintersect @ sK1 @ X2) @ X3) != $true) & ($true = (in @ X3 @ (powerset @ sK0))) & ((subset @ sK1 @ X3) = $true))) & ($true = (in @ sK1 @ (powerset @ sK0))))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f30,plain,(
% 1.69/1.36 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK0))) & ? [X3 : $i] : (((subset @ (binintersect @ sK1 @ X2) @ X3) != $true) & ($true = (in @ X3 @ (powerset @ sK0))) & ((subset @ sK1 @ X3) = $true))) => (($true = (in @ sK2 @ (powerset @ sK0))) & ? [X3 : $i] : (((subset @ (binintersect @ sK1 @ sK2) @ X3) != $true) & ($true = (in @ X3 @ (powerset @ sK0))) & ((subset @ sK1 @ X3) = $true)))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f31,plain,(
% 1.69/1.36 ? [X3 : $i] : (((subset @ (binintersect @ sK1 @ sK2) @ X3) != $true) & ($true = (in @ X3 @ (powerset @ sK0))) & ((subset @ sK1 @ X3) = $true)) => (((subset @ (binintersect @ sK1 @ sK2) @ sK3) != $true) & ((in @ sK3 @ (powerset @ sK0)) = $true) & ((subset @ sK1 @ sK3) = $true))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f28,plain,(
% 1.69/1.36 ((woz13rule1 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ X1 @ X3) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ! [X7 : $i] : (((subset @ (binintersect @ X5 @ X6) @ X7) = $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X7) != $true))) | ((in @ X5 @ (powerset @ X4)) != $true)) | (woz13rule1 != $true))),
% 1.69/1.36 inference(rectify,[status(thm)],[f27])).
% 1.69/1.36 thf(f27,plain,(
% 1.69/1.36 ((woz13rule1 = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (((subset @ (binintersect @ X0 @ X2) @ X3) != $true) & ((in @ X3 @ (powerset @ X1)) = $true) & ($true = (subset @ X0 @ X3)))) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3 : $i] : (((subset @ (binintersect @ X0 @ X2) @ X3) = $true) | ((in @ X3 @ (powerset @ X1)) != $true) | ($true != (subset @ X0 @ X3)))) | ($true != (in @ X0 @ (powerset @ X1)))) | (woz13rule1 != $true))),
% 1.69/1.36 inference(nnf_transformation,[status(thm)],[f22])).
% 1.69/1.36 thf(f22,plain,(
% 1.69/1.36 (woz13rule1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3 : $i] : (((subset @ (binintersect @ X0 @ X2) @ X3) = $true) | ((in @ X3 @ (powerset @ X1)) != $true) | ($true != (subset @ X0 @ X3)))) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.69/1.36 inference(flattening,[status(thm)],[f21])).
% 1.69/1.36 thf(f21,plain,(
% 1.69/1.36 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((subset @ (binintersect @ X0 @ X2) @ X3) = $true) | ($true != (subset @ X0 @ X3))) | ((in @ X3 @ (powerset @ X1)) != $true)) | ($true != (in @ X2 @ (powerset @ X1)))) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (woz13rule1 = $true)),
% 1.69/1.36 inference(ennf_transformation,[status(thm)],[f9])).
% 1.69/1.36 thf(f9,plain,(
% 1.69/1.36 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => (($true = (subset @ X0 @ X3)) => ((subset @ (binintersect @ X0 @ X2) @ X3) = $true))))) <=> (woz13rule1 = $true)),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f8])).
% 1.69/1.36 thf(f8,plain,(
% 1.69/1.36 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X0 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))) = woz13rule1)),
% 1.69/1.36 inference(rectify,[status(thm)],[f2])).
% 1.69/1.36 thf(f2,axiom,(
% 1.69/1.36 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))) = woz13rule1)),
% 1.69/1.36 file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',woz13rule1)).
% 1.69/1.36 thf(f140,plain,(
% 1.69/1.36 ((subset @ (binintersect @ sK4 @ sK6) @ sK7) != $true) | spl20_4),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f138])).
% 1.69/1.36 thf(f138,definition,(
% 1.69/1.36 spl20_4 <=> ((subset @ (binintersect @ sK4 @ sK6) @ sK7) = $true)),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl20_4])],[avatar_definition])).
% 1.69/1.36 thf(f148,plain,(
% 1.69/1.36 ~spl20_4 | spl20_5 | ~spl20_6),
% 1.69/1.36 inference(avatar_split_clause,[status(thm)],[f136,f145,f142,f138])).
% 1.69/1.36 thf(f136,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ((subset @ (binintersect @ sK4 @ sK6) @ sK7) != $true) | ((in @ (binintersect @ sK4 @ sK6) @ (powerset @ X0)) != $true) | ((subset @ (binintersect @ sK4 @ sK6) @ sK8) != $true)) )),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.69/1.36 thf(f133,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($true != $true) | ((in @ (binintersect @ sK4 @ sK6) @ (powerset @ X0)) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ((subset @ (binintersect @ sK4 @ sK6) @ sK7) != $true) | ((subset @ (binintersect @ sK4 @ sK6) @ sK8) != $true)) )),
% 1.69/1.36 inference(superposition,[status(thm)],[f67,f115])).
% 1.69/1.36 thf(f115,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ (binintersect @ X6 @ X7)) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) != $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X7) != $true)) )),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.69/1.36 thf(f101,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X7) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ X5 @ (binintersect @ X6 @ X7)) = $true) | ($true != $true)) )),
% 1.69/1.36 inference(definition_unfolding,[status(thm)],[f72,f63])).
% 1.69/1.36 thf(f63,plain,(
% 1.69/1.36 (woz13rule3 = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 thf(f72,plain,(
% 1.69/1.36 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) != $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((subset @ X5 @ (binintersect @ X6 @ X7)) = $true) | ((subset @ X5 @ X7) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | (woz13rule3 != $true)) )),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f43])).
% 1.69/1.36 thf(f43,plain,(
% 1.69/1.36 ((woz13rule3 = $true) | (((in @ sK10 @ (powerset @ sK9)) = $true) & ((((subset @ sK10 @ sK11) = $true) & ($true = (in @ sK12 @ (powerset @ sK9))) & ($true != (subset @ sK10 @ (binintersect @ sK11 @ sK12))) & ((subset @ sK10 @ sK12) = $true)) & ((in @ sK11 @ (powerset @ sK9)) = $true)))) & (! [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ! [X6 : $i] : (! [X7 : $i] : (((subset @ X5 @ X6) != $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((subset @ X5 @ (binintersect @ X6 @ X7)) = $true) | ((subset @ X5 @ X7) != $true)) | ((in @ X6 @ (powerset @ X4)) != $true))) | (woz13rule3 != $true))),
% 1.69/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f39,f42,f41,f40])).
% 1.69/1.36 thf(f40,plain,(
% 1.69/1.36 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ X1 @ X2) = $true) & ((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ X1 @ (binintersect @ X2 @ X3)) != $true) & ((subset @ X1 @ X3) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))) => (((in @ sK10 @ (powerset @ sK9)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ sK10 @ X2) = $true) & ($true = (in @ X3 @ (powerset @ sK9))) & ((subset @ sK10 @ (binintersect @ X2 @ X3)) != $true) & ($true = (subset @ sK10 @ X3))) & ((in @ X2 @ (powerset @ sK9)) = $true)))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f41,plain,(
% 1.69/1.36 ? [X2 : $i] : (? [X3 : $i] : (((subset @ sK10 @ X2) = $true) & ($true = (in @ X3 @ (powerset @ sK9))) & ((subset @ sK10 @ (binintersect @ X2 @ X3)) != $true) & ($true = (subset @ sK10 @ X3))) & ((in @ X2 @ (powerset @ sK9)) = $true)) => (? [X3 : $i] : (((subset @ sK10 @ sK11) = $true) & ($true = (in @ X3 @ (powerset @ sK9))) & ((subset @ sK10 @ (binintersect @ sK11 @ X3)) != $true) & ($true = (subset @ sK10 @ X3))) & ((in @ sK11 @ (powerset @ sK9)) = $true))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f42,plain,(
% 1.69/1.36 ? [X3 : $i] : (((subset @ sK10 @ sK11) = $true) & ($true = (in @ X3 @ (powerset @ sK9))) & ((subset @ sK10 @ (binintersect @ sK11 @ X3)) != $true) & ($true = (subset @ sK10 @ X3))) => (((subset @ sK10 @ sK11) = $true) & ($true = (in @ sK12 @ (powerset @ sK9))) & ($true != (subset @ sK10 @ (binintersect @ sK11 @ sK12))) & ((subset @ sK10 @ sK12) = $true))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f39,plain,(
% 1.69/1.36 ((woz13rule3 = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ X1 @ X2) = $true) & ((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ X1 @ (binintersect @ X2 @ X3)) != $true) & ((subset @ X1 @ X3) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)))) & (! [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ! [X6 : $i] : (! [X7 : $i] : (((subset @ X5 @ X6) != $true) | ((in @ X7 @ (powerset @ X4)) != $true) | ((subset @ X5 @ (binintersect @ X6 @ X7)) = $true) | ((subset @ X5 @ X7) != $true)) | ((in @ X6 @ (powerset @ X4)) != $true))) | (woz13rule3 != $true))),
% 1.69/1.36 inference(rectify,[status(thm)],[f38])).
% 1.69/1.36 thf(f38,plain,(
% 1.69/1.36 ((woz13rule3 = $true) | ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ X0 @ X2) = $true) & ((in @ X3 @ (powerset @ X1)) = $true) & ((subset @ X0 @ (binintersect @ X2 @ X3)) != $true) & ($true = (subset @ X0 @ X3))) & ($true = (in @ X2 @ (powerset @ X1)))))) & (! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (((subset @ X0 @ X2) != $true) | ((in @ X3 @ (powerset @ X1)) != $true) | ((subset @ X0 @ (binintersect @ X2 @ X3)) = $true) | ($true != (subset @ X0 @ X3))) | ($true != (in @ X2 @ (powerset @ X1))))) | (woz13rule3 != $true))),
% 1.69/1.36 inference(nnf_transformation,[status(thm)],[f26])).
% 1.69/1.36 thf(f26,plain,(
% 1.69/1.36 (woz13rule3 = $true) <=> ! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (((subset @ X0 @ X2) != $true) | ((in @ X3 @ (powerset @ X1)) != $true) | ((subset @ X0 @ (binintersect @ X2 @ X3)) = $true) | ($true != (subset @ X0 @ X3))) | ($true != (in @ X2 @ (powerset @ X1)))))),
% 1.69/1.36 inference(flattening,[status(thm)],[f25])).
% 1.69/1.36 thf(f25,plain,(
% 1.69/1.36 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((((subset @ X0 @ (binintersect @ X2 @ X3)) = $true) | ($true != (subset @ X0 @ X3))) | ((subset @ X0 @ X2) != $true)) | ((in @ X3 @ (powerset @ X1)) != $true)) | ($true != (in @ X2 @ (powerset @ X1)))) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (woz13rule3 = $true)),
% 1.69/1.36 inference(ennf_transformation,[status(thm)],[f17])).
% 1.69/1.36 thf(f17,plain,(
% 1.69/1.36 ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => (((subset @ X0 @ X2) = $true) => (($true = (subset @ X0 @ X3)) => ((subset @ X0 @ (binintersect @ X2 @ X3)) = $true)))))) <=> (woz13rule3 = $true)),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.36 thf(f16,plain,(
% 1.69/1.36 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X0 @ X2) => ((subset @ X0 @ X3) => (subset @ X0 @ (binintersect @ X2 @ X3))))))) = woz13rule3)),
% 1.69/1.36 inference(rectify,[status(thm)],[f4])).
% 1.69/1.36 thf(f4,axiom,(
% 1.69/1.36 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3))))))) = woz13rule3)),
% 1.69/1.36 file('/export/starexec/sandbox/tmp/tmp.7zhMgDORmQ/DTF2THF_1245.p',woz13rule3)).
% 1.69/1.36 thf(f67,plain,(
% 1.69/1.36 ((subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ sK8)) != $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f37])).
% 1.69/1.36 % SZS output end Proof for DTF2THF_1245
% 1.69/1.36 % (1574)------------------------------
% 1.69/1.36 % (1574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (1574)Termination reason: Refutation
% 1.69/1.36
% 1.69/1.36 % (1574)Memory used [KB]: 5756
% 1.69/1.36 % (1574)Time elapsed: 0.020 s
% 1.69/1.36 % (1574)Instructions burned: 18 (million)
% 1.69/1.36 % (1574)------------------------------
% 1.69/1.36 % (1574)------------------------------
% 1.69/1.36 % (1568)Success in time 0.034 s
%------------------------------------------------------------------------------