%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU757^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:57 AM UTC 2026
% Result : Theorem 1.79s 1.54s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 29
% Syntax : Number of formulae : 159 ( 25 unt; 0 typ; 4 def)
% Number of atoms : 2667 ( 766 equ; 0 cnn)
% Maximal formula atoms : 16 ( 16 avg)
% Number of connectives : 4146 ( 401 ~; 374 |; 198 &;3040 @)
% ( 21 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 34 con; 0-3 aty)
% Number of variables : 440 ( 0 ^; 342 !; 98 ?; 440 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
binintersect: $i > $i > $i ).
thf(func_def_4,type,
setminus: $i > $i > $i ).
thf(func_def_14,type,
sP0: $i > $i > $i > $o ).
thf(func_def_15,type,
sK1: $i > $i > $i > $i ).
thf(func_def_16,type,
sK2: $i > $i > $i > $i ).
thf(f412,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f342,f368,f385,f395,f411]) ).
thf(f411,plain,
spl25_4,
inference(avatar_contradiction_clause,[status(thm)],[f410]) ).
thf(f410,plain,
( $false
| spl25_4 ),
inference(subsumption_resolution,[status(thm)],[f409,f90]) ).
thf(f90,plain,
( $true
= ( in @ sK8 @ ( powerset @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( binunionT_lem = $true )
& ( demorgan2b = $true )
& ( complementT_lem = $true )
& ( demorgan2a = $true )
& ( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true )
& ( ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) )
!= ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) )
& ( $true
= ( in @ sK8 @ ( powerset @ sK6 ) ) )
& ( setextT = $true )
& ( binintersectT_lem = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f25,f48,f47]) ).
thf(f47,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
!= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true )
& ? [X2: $i] :
( ( ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ X2 ) )
!= ( setminus @ sK6 @ ( binunion @ sK7 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK6 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,plain,
( ? [X2: $i] :
( ( ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ X2 ) )
!= ( setminus @ sK6 @ ( binunion @ sK7 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK6 ) ) ) )
=> ( ( ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) )
!= ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) )
& ( $true
= ( in @ sK8 @ ( powerset @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( binunionT_lem = $true )
& ( demorgan2b = $true )
& ( complementT_lem = $true )
& ( demorgan2a = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
!= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
& ( setextT = $true )
& ( binintersectT_lem = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
!= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
& ( demorgan2b = $true )
& ( demorgan2a = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan2a
=> ( demorgan2b
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan2a
=> ( demorgan2b
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan2a
=> ( demorgan2b
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',demorgan2) ).
thf(f409,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK6 ) ) )
| spl25_4 ),
inference(trivial_inequality_removal,[status(thm)],[f408]) ).
thf(f408,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK6 ) ) )
| spl25_4 ),
inference(superposition,[status(thm)],[f384,f153]) ).
thf(f153,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f119,f94]) ).
thf(f94,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f119,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( complementT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ( ( $true
!= ( in @ ( setminus @ sK24 @ sK23 ) @ ( powerset @ sK24 ) ) )
& ( ( in @ sK23 @ ( powerset @ sK24 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f73,f74]) ).
thf(f74,plain,
( ? [X2: $i,X3: $i] :
( ( ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) ) )
=> ( ( $true
!= ( in @ ( setminus @ sK24 @ sK23 ) @ ( powerset @ sK24 ) ) )
& ( ( in @ sK23 @ ( powerset @ sK24 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f73,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
!= $true )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true ) )
<=> ( complementT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( complementT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',complementT_lem) ).
thf(f384,plain,
( ( $true
!= ( in @ ( setminus @ sK6 @ sK8 ) @ ( powerset @ sK6 ) ) )
| spl25_4 ),
inference(avatar_component_clause,[status(thm)],[f382]) ).
thf(f382,definition,
( spl25_4
<=> ( $true
= ( in @ ( setminus @ sK6 @ sK8 ) @ ( powerset @ sK6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl25_4])],[avatar_definition]) ).
thf(f395,plain,
spl25_3,
inference(avatar_contradiction_clause,[status(thm)],[f394]) ).
thf(f394,plain,
( $false
| spl25_3 ),
inference(subsumption_resolution,[status(thm)],[f393,f92]) ).
thf(f92,plain,
( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f393,plain,
( ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| spl25_3 ),
inference(trivial_inequality_removal,[status(thm)],[f392]) ).
thf(f392,plain,
( ( $true != $true )
| ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| spl25_3 ),
inference(superposition,[status(thm)],[f380,f153]) ).
thf(f380,plain,
( ( $true
!= ( in @ ( setminus @ sK6 @ sK7 ) @ ( powerset @ sK6 ) ) )
| spl25_3 ),
inference(avatar_component_clause,[status(thm)],[f378]) ).
thf(f378,definition,
( spl25_3
<=> ( $true
= ( in @ ( setminus @ sK6 @ sK7 ) @ ( powerset @ sK6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl25_3])],[avatar_definition]) ).
thf(f385,plain,
( ~ spl25_3
| ~ spl25_4
| spl25_2 ),
inference(avatar_split_clause,[status(thm)],[f375,f339,f382,f378]) ).
thf(f339,definition,
( spl25_2
<=> ( ( in @ ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) @ ( powerset @ sK6 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl25_2])],[avatar_definition]) ).
thf(f375,plain,
( ( $true
!= ( in @ ( setminus @ sK6 @ sK7 ) @ ( powerset @ sK6 ) ) )
| ( $true
!= ( in @ ( setminus @ sK6 @ sK8 ) @ ( powerset @ sK6 ) ) )
| spl25_2 ),
inference(trivial_inequality_removal,[status(thm)],[f374]) ).
thf(f374,plain,
( ( $true
!= ( in @ ( setminus @ sK6 @ sK7 ) @ ( powerset @ sK6 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ ( setminus @ sK6 @ sK8 ) @ ( powerset @ sK6 ) ) )
| spl25_2 ),
inference(superposition,[status(thm)],[f341,f157]) ).
thf(f157,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( $true
= ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f109,f88]) ).
thf(f88,plain,
binintersectT_lem = $true,
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f109,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( $true
= ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) ) )
| ( binintersectT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( binintersectT_lem = $true )
| ( ( ( in @ sK18 @ ( powerset @ sK17 ) )
= $true )
& ( $true
= ( in @ sK19 @ ( powerset @ sK17 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK18 @ sK19 ) @ ( powerset @ sK17 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ! [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( $true
= ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) ) ) ) )
| ( binintersectT_lem != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f63,f65,f64]) ).
thf(f64,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true ) ) )
=> ( ( ( in @ sK18 @ ( powerset @ sK17 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK17 ) )
= $true )
& ( $true
!= ( in @ ( binintersect @ sK18 @ X2 ) @ ( powerset @ sK17 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f65,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK17 ) )
= $true )
& ( $true
!= ( in @ ( binintersect @ sK18 @ X2 ) @ ( powerset @ sK17 ) ) ) )
=> ( ( $true
= ( in @ sK19 @ ( powerset @ sK17 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK18 @ sK19 ) @ ( powerset @ sK17 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f63,plain,
( ( ( binintersectT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ! [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( $true
= ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) ) ) ) )
| ( binintersectT_lem != $true ) ) ),
inference(rectify,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( binintersectT_lem = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
!= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true ) ) )
| ( binintersectT_lem != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( binintersectT_lem = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( binintersectT_lem = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) )
= binintersectT_lem ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) )
= binintersectT_lem ),
file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',binintersectT_lem) ).
thf(f341,plain,
( ( ( in @ ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true )
| spl25_2 ),
inference(avatar_component_clause,[status(thm)],[f339]) ).
thf(f368,plain,
spl25_1,
inference(avatar_contradiction_clause,[status(thm)],[f367]) ).
thf(f367,plain,
( $false
| spl25_1 ),
inference(subsumption_resolution,[status(thm)],[f366,f92]) ).
thf(f366,plain,
( ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| spl25_1 ),
inference(subsumption_resolution,[status(thm)],[f365,f90]) ).
thf(f365,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK6 ) ) )
| ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| spl25_1 ),
inference(trivial_inequality_removal,[status(thm)],[f364]) ).
thf(f364,plain,
( ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK6 ) ) )
| ( $true != $true )
| spl25_1 ),
inference(superposition,[status(thm)],[f354,f154]) ).
thf(f154,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f116,f96]) ).
thf(f96,plain,
binunionT_lem = $true,
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f116,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( binunionT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ( ( ( in @ sK20 @ ( powerset @ sK21 ) )
= $true )
& ( ( in @ ( binunion @ sK20 @ sK22 ) @ ( powerset @ sK21 ) )
!= $true )
& ( $true
= ( in @ sK22 @ ( powerset @ sK21 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f68,f70,f69]) ).
thf(f69,plain,
( ? [X3: $i,X4: $i] :
( ( ( in @ X3 @ ( powerset @ X4 ) )
= $true )
& ? [X5: $i] :
( ( $true
!= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
& ( ( in @ X5 @ ( powerset @ X4 ) )
= $true ) ) )
=> ( ( ( in @ sK20 @ ( powerset @ sK21 ) )
= $true )
& ? [X5: $i] :
( ( ( in @ ( binunion @ sK20 @ X5 ) @ ( powerset @ sK21 ) )
!= $true )
& ( $true
= ( in @ X5 @ ( powerset @ sK21 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f70,plain,
( ? [X5: $i] :
( ( ( in @ ( binunion @ sK20 @ X5 ) @ ( powerset @ sK21 ) )
!= $true )
& ( $true
= ( in @ X5 @ ( powerset @ sK21 ) ) ) )
=> ( ( ( in @ ( binunion @ sK20 @ sK22 ) @ ( powerset @ sK21 ) )
!= $true )
& ( $true
= ( in @ sK22 @ ( powerset @ sK21 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f68,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ? [X3: $i,X4: $i] :
( ( ( in @ X3 @ ( powerset @ X4 ) )
= $true )
& ? [X5: $i] :
( ( $true
!= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
& ( ( in @ X5 @ ( powerset @ X4 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
<=> ( binunionT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( binunionT_lem = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binunionT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',binunionT_lem) ).
thf(f354,plain,
( ( ( in @ ( binunion @ sK7 @ sK8 ) @ ( powerset @ sK6 ) )
!= $true )
| spl25_1 ),
inference(trivial_inequality_removal,[status(thm)],[f353]) ).
thf(f353,plain,
( ( ( in @ ( binunion @ sK7 @ sK8 ) @ ( powerset @ sK6 ) )
!= $true )
| ( $true != $true )
| spl25_1 ),
inference(superposition,[status(thm)],[f337,f153]) ).
thf(f337,plain,
( ( ( in @ ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true )
| spl25_1 ),
inference(avatar_component_clause,[status(thm)],[f335]) ).
thf(f335,definition,
( spl25_1
<=> ( ( in @ ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) ) @ ( powerset @ sK6 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl25_1])],[avatar_definition]) ).
thf(f342,plain,
( ~ spl25_1
| ~ spl25_2 ),
inference(avatar_split_clause,[status(thm)],[f333,f339,f335]) ).
thf(f333,plain,
( ( ( in @ ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f332,f90]) ).
thf(f332,plain,
( ( $true
!= ( in @ sK8 @ ( powerset @ sK6 ) ) )
| ( ( in @ ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f318,f92]) ).
thf(f318,plain,
( ( ( in @ ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK6 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f286]) ).
thf(f286,plain,
( ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK6 ) ) )
| ( ( in @ ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) ) @ ( powerset @ sK6 ) )
!= $true )
| ( ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) )
!= ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) ) ) ),
inference(superposition,[status(thm)],[f91,f276]) ).
thf(f276,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f273,f238]) ).
thf(f238,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f237]) ).
thf(f237,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f231]) ).
thf(f231,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X0 ) )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f196,f78]) ).
thf(f78,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X0 ) )
| ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( sP0 @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ( ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X0 ) )
& ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true
!= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 ) ) )
| ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f38,f39]) ).
thf(f39,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
& ( ( in @ X4 @ X1 )
= $true )
& ( ( in @ X4 @ X2 )
!= $true ) )
=> ( ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X0 ) )
& ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true
!= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( sP0 @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
& ( ( in @ X4 @ X1 )
= $true )
& ( ( in @ X4 @ X2 )
!= $true ) )
| ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( sP0 @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( sP0 @ X2 @ X1 @ X0 ) )
<=> ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f196,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK1 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f195]) ).
thf(f195,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( sK1 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f191]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK1 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 ) @ X0 ) )
| ( $true != $true )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f176,f77]) ).
thf(f77,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ ( sK1 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) )
| ( ( in @ ( sK1 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ ( sK1 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK1 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f76,f155]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f102,f93]) ).
thf(f93,plain,
demorgan2a = $true,
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( demorgan2a != $true ) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( demorgan2a != $true ) )
& ( ( demorgan2a = $true )
| ( ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true )
& ( ( in @ sK12 @ sK9 )
= $true )
& ( $true
!= ( in @ sK12 @ ( binintersect @ ( setminus @ sK9 @ sK10 ) @ ( setminus @ sK9 @ sK11 ) ) ) )
& ( ( in @ sK12 @ ( setminus @ sK9 @ ( binunion @ sK10 @ sK11 ) ) )
= $true )
& ( $true
= ( in @ sK11 @ ( powerset @ sK9 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f51,f54,f53,f52]) ).
thf(f52,plain,
( ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
& ( ( in @ X7 @ ( binintersect @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true )
& ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true ) )
& ( ( in @ X6 @ ( powerset @ X4 ) )
= $true ) ) )
=> ( ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ sK9 )
= $true )
& ( $true
!= ( in @ X7 @ ( binintersect @ ( setminus @ sK9 @ sK10 ) @ ( setminus @ sK9 @ X6 ) ) ) )
& ( $true
= ( in @ X7 @ ( setminus @ sK9 @ ( binunion @ sK10 @ X6 ) ) ) ) )
& ( ( in @ X6 @ ( powerset @ sK9 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f53,plain,
( ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ sK9 )
= $true )
& ( $true
!= ( in @ X7 @ ( binintersect @ ( setminus @ sK9 @ sK10 ) @ ( setminus @ sK9 @ X6 ) ) ) )
& ( $true
= ( in @ X7 @ ( setminus @ sK9 @ ( binunion @ sK10 @ X6 ) ) ) ) )
& ( ( in @ X6 @ ( powerset @ sK9 ) )
= $true ) )
=> ( ? [X7: $i] :
( ( ( in @ X7 @ sK9 )
= $true )
& ( $true
!= ( in @ X7 @ ( binintersect @ ( setminus @ sK9 @ sK10 ) @ ( setminus @ sK9 @ sK11 ) ) ) )
& ( $true
= ( in @ X7 @ ( setminus @ sK9 @ ( binunion @ sK10 @ sK11 ) ) ) ) )
& ( $true
= ( in @ sK11 @ ( powerset @ sK9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ? [X7: $i] :
( ( ( in @ X7 @ sK9 )
= $true )
& ( $true
!= ( in @ X7 @ ( binintersect @ ( setminus @ sK9 @ sK10 ) @ ( setminus @ sK9 @ sK11 ) ) ) )
& ( $true
= ( in @ X7 @ ( setminus @ sK9 @ ( binunion @ sK10 @ sK11 ) ) ) ) )
=> ( ( ( in @ sK12 @ sK9 )
= $true )
& ( $true
!= ( in @ sK12 @ ( binintersect @ ( setminus @ sK9 @ sK10 ) @ ( setminus @ sK9 @ sK11 ) ) ) )
& ( ( in @ sK12 @ ( setminus @ sK9 @ ( binunion @ sK10 @ sK11 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( demorgan2a != $true ) )
& ( ( demorgan2a = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
& ( ( in @ X7 @ ( binintersect @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true )
& ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true ) )
& ( ( in @ X6 @ ( powerset @ X4 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( demorgan2a != $true ) )
& ( ( demorgan2a = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
<=> ( demorgan2a = $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( demorgan2a = $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
=> ( $true
= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) )
<=> ( demorgan2a = $true ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) )
= demorgan2a ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) )
= demorgan2a ),
file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',demorgan2a) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f273,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X0 ) )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f272]) ).
thf(f272,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $true != $true )
| ( $true
= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X0 ) )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f268]) ).
thf(f268,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X0 ) )
| ( $true != $true )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $true
= ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X0 ) )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f207,f151]) ).
thf(f151,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( X0 = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( X0 = X2 )
| ( $true != $true )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f86,f89]) ).
thf(f89,plain,
setextT = $true,
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f86,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( setextT != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( X0 = X2 )
| ( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
!= $true )
& ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) ) )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( setextT != $true ) )
& ( ( setextT = $true )
| ( ( sK3 != sK5 )
& ! [X7: $i] :
( ( ( in @ X7 @ sK3 )
= $true )
| ( $true
!= ( in @ X7 @ sK4 ) )
| ( ( in @ X7 @ sK5 )
!= $true ) )
& ( ( sP0 @ sK5 @ sK3 @ sK4 )
!= $true )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ( $true
= ( in @ sK3 @ ( powerset @ sK4 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f42,f45,f44,f43]) ).
thf(f43,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
=> ( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
!= $true )
& ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( X4 != X6 )
& ! [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X7 @ X6 ) ) )
& ( $true
!= ( sP0 @ X6 @ X4 @ X5 ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) )
& ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) ) )
=> ( ? [X6: $i] :
( ( sK3 != X6 )
& ! [X7: $i] :
( ( ( in @ X7 @ sK3 )
= $true )
| ( $true
!= ( in @ X7 @ sK4 ) )
| ( $true
!= ( in @ X7 @ X6 ) ) )
& ( $true
!= ( sP0 @ X6 @ sK3 @ sK4 ) )
& ( ( in @ X6 @ ( powerset @ sK4 ) )
= $true ) )
& ( $true
= ( in @ sK3 @ ( powerset @ sK4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ? [X6: $i] :
( ( sK3 != X6 )
& ! [X7: $i] :
( ( ( in @ X7 @ sK3 )
= $true )
| ( $true
!= ( in @ X7 @ sK4 ) )
| ( $true
!= ( in @ X7 @ X6 ) ) )
& ( $true
!= ( sP0 @ X6 @ sK3 @ sK4 ) )
& ( ( in @ X6 @ ( powerset @ sK4 ) )
= $true ) )
=> ( ( sK3 != sK5 )
& ! [X7: $i] :
( ( ( in @ X7 @ sK3 )
= $true )
| ( $true
!= ( in @ X7 @ sK4 ) )
| ( ( in @ X7 @ sK5 )
!= $true ) )
& ( ( sP0 @ sK5 @ sK3 @ sK4 )
!= $true )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( X0 = X2 )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( setextT != $true ) )
& ( ( setextT = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( X4 != X6 )
& ! [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X7 @ X6 ) ) )
& ( $true
!= ( sP0 @ X6 @ X4 @ X5 ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) )
& ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( X1 = X2 )
| ? [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
& ( $true
= ( in @ X4 @ X0 ) )
& ( ( in @ X4 @ X2 )
= $true ) )
| ( $true
= ( sP0 @ X2 @ X1 @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( setextT != $true ) )
& ( ( setextT = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
| ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ X2 )
!= $true ) )
& ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( X1 = X2 )
| ? [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
& ( $true
= ( in @ X4 @ X0 ) )
& ( ( in @ X4 @ X2 )
= $true ) )
| ( $true
= ( sP0 @ X2 @ X1 @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( setextT = $true ) ),
inference(definition_folding,[status(thm)],[f33,f35]) ).
thf(f33,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( X1 = X2 )
| ? [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
& ( $true
= ( in @ X4 @ X0 ) )
& ( ( in @ X4 @ X2 )
= $true ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( setextT = $true ) ),
inference(flattening,[status(thm)],[f32]) ).
thf(f32,plain,
( ( setextT = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( X1 = X2 )
| ? [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
& ( ( in @ X4 @ X2 )
= $true )
& ( $true
= ( in @ X4 @ X0 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( setextT = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ( ( ( in @ X4 @ X2 )
= $true )
=> ( ( in @ X4 @ X1 )
= $true ) ) )
=> ( X1 = X2 ) ) ) ) ) ),
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 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ) )
= setextT ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ) )
= setextT ),
file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',setextT) ).
thf(f207,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 )
= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f206]) ).
thf(f206,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true != $true )
| ( ( in @ ( sK2 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) @ X0 )
!= $true )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X3 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f205]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X3 ) )
!= $true )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ ( sK2 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) @ X0 )
!= $true )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true != $true )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X3 ) )
!= $true )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 )
= $true )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) ) ),
inference(superposition,[status(thm)],[f158,f167]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK2 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK2 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ X0 )
!= $true )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X4 @ X3 )
= $true )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ( ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= X4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= X4 )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( in @ ( sK2 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
| ( ( in @ ( sK2 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ X0 )
!= $true )
| ( ( sP0 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X4 @ X3 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f152,f156]) ).
thf(f156,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( X0 = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( X0 = X2 )
| ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f85,f89]) ).
thf(f85,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( setextT != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f152,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( binintersect @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f103,f95]) ).
thf(f95,plain,
demorgan2b = $true,
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f103,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( demorgan2b != $true ) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( demorgan2b = $true )
| ( ( $true
= ( in @ sK15 @ ( powerset @ sK13 ) ) )
& ( ( in @ sK16 @ ( setminus @ sK13 @ ( binunion @ sK14 @ sK15 ) ) )
!= $true )
& ( $true
= ( in @ sK16 @ sK13 ) )
& ( ( in @ sK16 @ ( binintersect @ ( setminus @ sK13 @ sK14 ) @ ( setminus @ sK13 @ sK15 ) ) )
= $true )
& ( ( in @ sK14 @ ( powerset @ sK13 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( demorgan2b != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f57,f60,f59,f58]) ).
thf(f58,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK13 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK13 @ ( binunion @ sK14 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ sK13 )
= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ sK13 @ sK14 ) @ ( setminus @ sK13 @ X2 ) ) )
= $true ) ) )
& ( ( in @ sK14 @ ( powerset @ sK13 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f59,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK13 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK13 @ ( binunion @ sK14 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ sK13 )
= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ sK13 @ sK14 ) @ ( setminus @ sK13 @ X2 ) ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK15 @ ( powerset @ sK13 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ sK13 @ ( binunion @ sK14 @ sK15 ) ) ) )
& ( ( in @ X3 @ sK13 )
= $true )
& ( $true
= ( in @ X3 @ ( binintersect @ ( setminus @ sK13 @ sK14 ) @ ( setminus @ sK13 @ sK15 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f60,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ sK13 @ ( binunion @ sK14 @ sK15 ) ) ) )
& ( ( in @ X3 @ sK13 )
= $true )
& ( $true
= ( in @ X3 @ ( binintersect @ ( setminus @ sK13 @ sK14 ) @ ( setminus @ sK13 @ sK15 ) ) ) ) )
=> ( ( ( in @ sK16 @ ( setminus @ sK13 @ ( binunion @ sK14 @ sK15 ) ) )
!= $true )
& ( $true
= ( in @ sK16 @ sK13 ) )
& ( ( in @ sK16 @ ( binintersect @ ( setminus @ sK13 @ sK14 ) @ ( setminus @ sK13 @ sK15 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f57,plain,
( ( ( demorgan2b = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( demorgan2b != $true ) ) ),
inference(rectify,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( demorgan2b = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( demorgan2b != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( demorgan2b = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( demorgan2b = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) ) ) )
<=> ( demorgan2b = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
= demorgan2b ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
= demorgan2b ),
file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',demorgan2b) ).
thf(f158,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
!= $true )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( X0 = X2 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f87,f89]) ).
thf(f87,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
!= $true )
| ( ( sP0 @ X2 @ X0 @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( setextT != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f91,plain,
( ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) )
!= ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU757^2 : 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
% 0.18/0.34 % Computer : n007.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:32:23 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.48 ---- Original DTF file ---
% 0.21/0.48 thf(spec,logic,$$dhol).
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 % File : SEU757^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.48 % Domain : Set Theory
% 0.21/0.48 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.21/0.48 % Version : Especial > Reduced > Especial.
% 0.21/0.48 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.21/0.48 % setminus A (binunion X Y) = binintersect (setminus A X)
% 0.21/0.48 % (setminus A Y)))
% 0.21/0.48
% 0.21/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.48 % Source : [Bro08]
% 0.21/0.48 % Names : ZFC259l [Bro08]
% 0.21/0.48
% 0.21/0.48 % Status : Theorem
% 0.21/0.48 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.57 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% 0.21/0.48 % Syntax : Number of formulae : 18 ( 6 unt; 11 typ; 6 def)
% 0.21/0.48 % Number of atoms : 48 ( 8 equ; 0 cnn)
% 0.21/0.48 % Maximal formula atoms : 9 ( 6 avg)
% 0.21/0.48 % Number of connectives : 137 ( 0 ~; 0 |; 0 &; 108 @)
% 0.21/0.48 % ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% 0.21/0.48 % Maximal formula depth : 14 ( 3 avg)
% 0.21/0.48 % Number of types : 2 ( 0 usr)
% 0.21/0.48 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.21/0.48 % Number of symbols : 12 ( 11 usr; 6 con; 0-2 aty)
% 0.21/0.48 % Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% 0.21/0.48 % SPC : TH0_THM_EQU_NAR
% 0.21/0.48
% 0.21/0.48 % Comments : http://mathgate.info/detsetitem.php?id=318
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 thf(in_type,type,
% 0.21/0.48 in: $i > $i > $o ).
% 0.21/0.48
% 0.21/0.48 thf(powerset_type,type,
% 0.21/0.48 powerset: $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(binunion_type,type,
% 0.21/0.48 binunion: $i > $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(binintersect_type,type,
% 0.21/0.48 binintersect: $i > $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(setminus_type,type,
% 0.21/0.48 setminus: $i > $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(binintersectT_lem_type,type,
% 0.21/0.48 binintersectT_lem: $o ).
% 0.21/0.48
% 0.21/0.48 thf(binintersectT_lem,definition,
% 0.21/0.48 ( binintersectT_lem
% 0.21/0.48 = ( ! [A: $i,X: $i] :
% 0.21/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.48 => ! [Y: $i] :
% 0.21/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(binunionT_lem_type,type,
% 0.21/0.48 binunionT_lem: $o ).
% 0.21/0.48
% 0.21/0.48 thf(binunionT_lem,definition,
% 0.21/0.48 ( binunionT_lem
% 0.21/0.48 = ( ! [A: $i,X: $i] :
% 0.21/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.48 => ! [Y: $i] :
% 0.21/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.48 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(complementT_lem_type,type,
% 0.21/0.48 complementT_lem: $o ).
% 0.21/0.48
% 0.21/0.48 thf(complementT_lem,definition,
% 0.21/0.48 ( complementT_lem
% 0.21/0.48 = ( ! [A: $i,X: $i] :
% 0.21/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setextT_type,type,
% 0.21/0.48 setextT: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setextT,definition,
% 0.21/0.48 ( setextT
% 0.21/0.48 = ( ! [A: $i,X: $i] :
% 0.21/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.48 => ! [Y: $i] :
% 0.21/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.48 => ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( ( in @ Xx @ X )
% 0.21/0.48 => ( in @ Xx @ Y ) ) )
% 0.21/0.48 => ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( ( in @ Xx @ Y )
% 0.21/0.48 => ( in @ Xx @ X ) ) )
% 0.21/0.48 => ( X = Y ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(demorgan2a_type,type,
% 0.21/0.48 demorgan2a: $o ).
% 0.21/0.48
% 0.21/0.48 thf(demorgan2a,definition,
% 0.21/0.48 ( demorgan2a
% 0.21/0.48 = ( ! [A: $i,X: $i] :
% 0.21/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.48 => ! [Y: $i] :
% 0.21/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.21/0.48 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(demorgan2b_type,type,
% 0.21/0.48 demorgan2b: $o ).
% 0.21/0.48
% 0.21/0.48 thf(demorgan2b,definition,
% 0.21/0.48 ( demorgan2b
% 0.21/0.48 = ( ! [A: $i,X: $i] :
% 0.21/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.48 => ! [Y: $i] :
% 0.33/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.48 => ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.33/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(demorgan2,conjecture,
% 0.33/0.48 ( binintersectT_lem
% 0.33/0.48 => ( binunionT_lem
% 0.33/0.48 => ( complementT_lem
% 0.33/0.48 => ( setextT
% 0.33/0.48 => ( demorgan2a
% 0.33/0.48 => ( demorgan2b
% 0.33/0.48 => ! [A: $i,X: $i] :
% 0.33/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.48 => ! [Y: $i] :
% 0.33/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.48 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.33/0.48 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 ------------------------
% 1.74/1.41 ---- Embedded in THF ---
% 1.74/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.74/1.42 %%% Generated on Tue Feb 24 12:32:24 EST 2026
% 1.74/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.74/1.42 %%% Logic specification used:
% 1.74/1.42 %%% thf(spec, logic, $$dhol).
% 1.74/1.42
% 1.74/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2DTF15114.p
% See solution above
% 1.74/1.42 ------------------------
% 1.74/1.43 ---- Cleaned THF ---
% 1.74/1.43 thf(in_type,type,
% 1.74/1.43 in: $i > $i > $o ).
% 1.74/1.43
% 1.74/1.43 thf(powerset_type,type,
% 1.74/1.43 powerset: $i > $i ).
% 1.74/1.43
% 1.74/1.43 thf(binunion_type,type,
% 1.74/1.43 binunion: $i > $i > $i ).
% 1.74/1.43
% 1.74/1.43 thf(binintersect_type,type,
% 1.74/1.43 binintersect: $i > $i > $i ).
% 1.74/1.43
% 1.74/1.43 thf(setminus_type,type,
% 1.74/1.43 setminus: $i > $i > $i ).
% 1.74/1.43
% 1.74/1.43 thf(binintersectT_lem_type,type,
% 1.74/1.43 binintersectT_lem: $o ).
% 1.74/1.43
% 1.74/1.43 thf(binintersectT_lem,definition,
% 1.74/1.43 ( binintersectT_lem
% 1.74/1.43 = ( ! [A: $i,X: $i] :
% 1.74/1.43 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.43 => ! [Y: $i] :
% 1.74/1.43 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.43 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.74/1.43
% 1.74/1.43 thf(binunionT_lem_type,type,
% 1.74/1.43 binunionT_lem: $o ).
% 1.74/1.43
% 1.74/1.43 thf(binunionT_lem,definition,
% 1.74/1.43 ( binunionT_lem
% 1.74/1.43 = ( ! [A: $i,X: $i] :
% 1.74/1.43 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.43 => ! [Y: $i] :
% 1.74/1.43 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.43 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.74/1.43
% 1.74/1.43 thf(complementT_lem_type,type,
% 1.74/1.43 complementT_lem: $o ).
% 1.74/1.43
% 1.74/1.43 thf(complementT_lem,definition,
% 1.74/1.43 ( complementT_lem
% 1.74/1.43 = ( ! [A: $i,X: $i] :
% 1.74/1.43 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.43 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.74/1.43
% 1.74/1.43 thf(setextT_type,type,
% 1.74/1.43 setextT: $o ).
% 1.74/1.43
% 1.74/1.43 thf(setextT,definition,
% 1.74/1.43 ( setextT
% 1.74/1.43 = ( ! [A: $i,X: $i] :
% 1.74/1.43 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.43 => ! [Y: $i] :
% 1.74/1.43 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.43 => ( ! [Xx: $i] :
% 1.74/1.43 ( ( in @ Xx @ A )
% 1.74/1.43 => ( ( in @ Xx @ X )
% 1.74/1.43 => ( in @ Xx @ Y ) ) )
% 1.74/1.43 => ( ! [Xx: $i] :
% 1.74/1.43 ( ( in @ Xx @ A )
% 1.74/1.43 => ( ( in @ Xx @ Y )
% 1.74/1.43 => ( in @ Xx @ X ) ) )
% 1.74/1.43 => ( X = Y ) ) ) ) ) ) ) ).
% 1.74/1.43
% 1.74/1.43 thf(demorgan2a_type,type,
% 1.74/1.43 demorgan2a: $o ).
% 1.74/1.43
% 1.74/1.43 thf(demorgan2a,definition,
% 1.74/1.43 ( demorgan2a
% 1.74/1.43 = ( ! [A: $i,X: $i] :
% 1.74/1.43 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.43 => ! [Y: $i] :
% 1.74/1.43 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.43 => ! [Xx: $i] :
% 1.74/1.43 ( ( in @ Xx @ A )
% 1.74/1.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 1.74/1.43 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 1.74/1.43
% 1.74/1.43 thf(demorgan2b_type,type,
% 1.74/1.43 demorgan2b: $o ).
% 1.74/1.43
% 1.74/1.43 thf(demorgan2b,definition,
% 1.74/1.43 ( demorgan2b
% 1.74/1.43 = ( ! [A: $i,X: $i] :
% 1.74/1.43 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.43 => ! [Y: $i] :
% 1.74/1.43 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.43 => ! [Xx: $i] :
% 1.74/1.43 ( ( in @ Xx @ A )
% 1.74/1.43 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 1.74/1.43 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 1.74/1.43
% 1.74/1.43 thf(demorgan2,conjecture,
% 1.74/1.43 ( binintersectT_lem
% 1.74/1.43 => ( binunionT_lem
% 1.74/1.43 => ( complementT_lem
% 1.74/1.43 => ( setextT
% 1.74/1.43 => ( demorgan2a
% 1.74/1.43 => ( demorgan2b
% 1.74/1.43 => ! [A: $i,X: $i] :
% 1.74/1.43 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.43 => ! [Y: $i] :
% 1.74/1.43 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.43 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 1.74/1.43 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 1.74/1.43 ------------------------
% 1.74/1.45 % (15214)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/2Mi)
% 1.74/1.45 % (15211)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/183Mi)
% 1.74/1.45 % (15216)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_15114 for (2999ds/275Mi)
% 1.74/1.45 % (15213)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_15114 for (2999ds/27Mi)
% 1.74/1.45 % (15212)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_15114 for (2999ds/4Mi)
% 1.74/1.45 % (15215)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_15114 for (2999ds/2Mi)
% 1.74/1.45 % (15217)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/18Mi)
% 1.74/1.45 % (15214)Instruction limit reached!
% 1.74/1.45 % (15214)------------------------------
% 1.74/1.45 % (15214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (15214)Termination reason: Unknown
% 1.74/1.45 % (15214)Termination phase: Property scanning
% 1.74/1.45 % (15215)Instruction limit reached!
% 1.74/1.45 % (15215)------------------------------
% 1.74/1.45 % (15215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (15215)Termination reason: Unknown
% 1.74/1.45 % (15215)Termination phase: Property scanning
% 1.74/1.45
% 1.74/1.45 % (15215)Memory used [KB]: 1023
% 1.74/1.45
% 1.74/1.45 % (15214)Memory used [KB]: 1023
% 1.74/1.45 % (15215)Time elapsed: 0.003 s
% 1.74/1.45 % (15215)Instructions burned: 3 (million)
% 1.74/1.45 % (15214)Time elapsed: 0.003 s
% 1.74/1.45 % (15214)Instructions burned: 3 (million)
% 1.74/1.45 % (15215)------------------------------
% 1.74/1.45 % (15215)------------------------------
% 1.74/1.45 % (15214)------------------------------
% 1.74/1.45 % (15214)------------------------------
% 1.74/1.45 % (15212)Instruction limit reached!
% 1.74/1.45 % (15212)------------------------------
% 1.74/1.45 % (15212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (15212)Termination reason: Unknown
% 1.74/1.45 % (15212)Termination phase: Property scanning
% 1.74/1.45
% 1.74/1.45 % (15212)Memory used [KB]: 1023
% 1.74/1.45 % (15212)Time elapsed: 0.004 s
% 1.74/1.45 % (15212)Instructions burned: 5 (million)
% 1.74/1.45 % (15212)------------------------------
% 1.74/1.45 % (15212)------------------------------
% 1.74/1.46 % (15217)Instruction limit reached!
% 1.74/1.46 % (15217)------------------------------
% 1.74/1.46 % (15217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (15217)Termination reason: Unknown
% 1.74/1.46 % (15217)Termination phase: Saturation
% 1.74/1.46
% 1.74/1.46 % (15217)Memory used [KB]: 5628
% 1.74/1.46 % (15217)Time elapsed: 0.011 s
% 1.74/1.46 % (15217)Instructions burned: 18 (million)
% 1.74/1.46 % (15217)------------------------------
% 1.74/1.46 % (15217)------------------------------
% 1.74/1.46 % (15213)Instruction limit reached!
% 1.74/1.46 % (15213)------------------------------
% 1.74/1.46 % (15213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (15213)Termination reason: Unknown
% 1.74/1.46 % (15213)Termination phase: Saturation
% 1.74/1.46
% 1.74/1.46 % (15213)Memory used [KB]: 5628
% 1.74/1.46 % (15213)Time elapsed: 0.015 s
% 1.74/1.46 % (15213)Instructions burned: 27 (million)
% 1.74/1.46 % (15213)------------------------------
% 1.74/1.46 % (15213)------------------------------
% 1.74/1.46 % (15218)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/3Mi)
% 1.74/1.46 % (15219)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_15114 for (2999ds/37Mi)
% 1.74/1.46 % (15221)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_15114 for (2999ds/15Mi)
% 1.74/1.47 % (15218)Instruction limit reached!
% 1.74/1.47 % (15218)------------------------------
% 1.74/1.47 % (15218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (15218)Termination reason: Unknown
% 1.74/1.47 % (15218)Termination phase: Preprocessing 3
% 1.74/1.47
% 1.74/1.47 % (15218)Memory used [KB]: 1023
% 1.74/1.47 % (15218)Time elapsed: 0.003 s
% 1.74/1.47 % (15218)Instructions burned: 4 (million)
% 1.74/1.47 % (15218)------------------------------
% 1.74/1.47 % (15218)------------------------------
% 1.74/1.47 % (15221)Instruction limit reached!
% 1.74/1.47 % (15221)------------------------------
% 1.74/1.47 % (15221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (15221)Termination reason: Unknown
% 1.74/1.47 % (15222)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_15114 for (2999ds/3Mi)
% 1.74/1.47 % (15221)Termination phase: Saturation
% 1.74/1.47
% 1.74/1.47 % (15221)Memory used [KB]: 5628
% 1.74/1.47 % (15221)Time elapsed: 0.009 s
% 1.74/1.47 % (15221)Instructions burned: 15 (million)
% 1.74/1.47 % (15221)------------------------------
% 1.74/1.47 % (15221)------------------------------
% 1.74/1.47 % (15222)Instruction limit reached!
% 1.74/1.47 % (15222)------------------------------
% 1.74/1.47 % (15222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (15222)Termination reason: Unknown
% 1.74/1.47 % (15222)Termination phase: Preprocessing 1
% 1.74/1.47
% 1.74/1.47 % (15222)Memory used [KB]: 1023
% 1.74/1.47 % (15222)Time elapsed: 0.003 s
% 1.74/1.47 % (15222)Instructions burned: 4 (million)
% 1.74/1.47 % (15222)------------------------------
% 1.74/1.47 % (15222)------------------------------
% 1.74/1.48 % (15223)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/1041Mi)
% 1.74/1.48 % (15224)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/7Mi)
% 1.74/1.48 % (15219)Instruction limit reached!
% 1.74/1.48 % (15219)------------------------------
% 1.74/1.48 % (15219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (15219)Termination reason: Unknown
% 1.74/1.48 % (15219)Termination phase: Saturation
% 1.74/1.48
% 1.74/1.48 % (15219)Memory used [KB]: 5628
% 1.74/1.48 % (15219)Time elapsed: 0.019 s
% 1.74/1.48 % (15219)Instructions burned: 38 (million)
% 1.74/1.48 % (15219)------------------------------
% 1.74/1.48 % (15219)------------------------------
% 1.74/1.48 % (15224)Instruction limit reached!
% 1.74/1.48 % (15224)------------------------------
% 1.74/1.48 % (15224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (15224)Termination reason: Unknown
% 1.74/1.48 % (15224)Termination phase: Saturation
% 1.74/1.48
% 1.74/1.48 % (15224)Memory used [KB]: 1023
% 1.74/1.48 % (15224)Time elapsed: 0.005 s
% 1.74/1.48 % (15224)Instructions burned: 8 (million)
% 1.74/1.48 % (15224)------------------------------
% 1.74/1.48 % (15224)------------------------------
% 1.74/1.49 % (15225)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/16Mi)
% 1.74/1.49 % (15226)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/3Mi)
% 1.74/1.49 % (15226)Instruction limit reached!
% 1.74/1.49 % (15226)------------------------------
% 1.74/1.49 % (15226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.49 % (15226)Termination reason: Unknown
% 1.74/1.49 % (15226)Termination phase: SInE selection
% 1.74/1.49
% 1.74/1.49 % (15226)Memory used [KB]: 1023
% 1.74/1.49 % (15226)Time elapsed: 0.003 s
% 1.74/1.49 % (15226)Instructions burned: 4 (million)
% 1.74/1.49 % (15226)------------------------------
% 1.74/1.49 % (15226)------------------------------
% 1.74/1.50 % (15225)Instruction limit reached!
% 1.74/1.50 % (15225)------------------------------
% 1.74/1.50 % (15225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.50 % (15225)Termination reason: Unknown
% 1.74/1.50 % (15225)Termination phase: Saturation
% 1.74/1.50
% 1.74/1.50 % (15225)Memory used [KB]: 5884
% 1.74/1.50 % (15225)Time elapsed: 0.010 s
% 1.74/1.50 % (15225)Instructions burned: 16 (million)
% 1.74/1.50 % (15225)------------------------------
% 1.74/1.50 % (15225)------------------------------
% 1.79/1.50 % (15227)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/3Mi)
% 1.79/1.50 % (15227)Instruction limit reached!
% 1.79/1.50 % (15227)------------------------------
% 1.79/1.50 % (15227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.50 % (15227)Termination reason: Unknown
% 1.79/1.50 % (15227)Termination phase: shuffling
% 1.79/1.50
% 1.79/1.50 % (15227)Memory used [KB]: 1023
% 1.79/1.50 % (15227)Time elapsed: 0.003 s
% 1.79/1.50 % (15227)Instructions burned: 4 (million)
% 1.79/1.50 % (15227)------------------------------
% 1.79/1.50 % (15227)------------------------------
% 1.79/1.50 % (15228)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/7Mi)
% 1.79/1.50 % (15228)Instruction limit reached!
% 1.79/1.50 % (15228)------------------------------
% 1.79/1.50 % (15228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.50 % (15228)Termination reason: Unknown
% 1.79/1.50 % (15228)Termination phase: Saturation
% 1.79/1.50
% 1.79/1.50 % (15228)Memory used [KB]: 5500
% 1.79/1.50 % (15228)Time elapsed: 0.005 s
% 1.79/1.50 % (15228)Instructions burned: 8 (million)
% 1.79/1.50 % (15228)------------------------------
% 1.79/1.50 % (15228)------------------------------
% 1.79/1.51 % (15229)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/3Mi)
% 1.79/1.51 % (15229)Instruction limit reached!
% 1.79/1.51 % (15229)------------------------------
% 1.79/1.51 % (15229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.51 % (15229)Termination reason: Unknown
% 1.79/1.51 % (15229)Termination phase: Unused predicate definition removal
% 1.79/1.51
% 1.79/1.51 % (15229)Memory used [KB]: 1023
% 1.79/1.51 % (15229)Time elapsed: 0.003 s
% 1.79/1.51 % (15229)Instructions burned: 4 (million)
% 1.79/1.51 % (15229)------------------------------
% 1.79/1.51 % (15229)------------------------------
% 1.79/1.51 % (15230)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/4Mi)
% 1.79/1.51 % (15230)Instruction limit reached!
% 1.79/1.51 % (15230)------------------------------
% 1.79/1.51 % (15230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.51 % (15230)Termination reason: Unknown
% 1.79/1.51 % (15230)Termination phase: Function definition elimination
% 1.79/1.51
% 1.79/1.51 % (15230)Memory used [KB]: 1023
% 1.79/1.51 % (15230)Time elapsed: 0.004 s
% 1.79/1.51 % (15230)Instructions burned: 5 (million)
% 1.79/1.51 % (15230)------------------------------
% 1.79/1.51 % (15230)------------------------------
% 1.79/1.51 % (15231)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/18Mi)
% 1.79/1.52 % (15232)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/710Mi)
% 1.79/1.52 % (15231)Instruction limit reached!
% 1.79/1.52 % (15231)------------------------------
% 1.79/1.52 % (15231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.52 % (15231)Termination reason: Unknown
% 1.79/1.52 % (15231)Termination phase: Saturation
% 1.79/1.52
% 1.79/1.52 % (15231)Memory used [KB]: 5628
% 1.79/1.52 % (15231)Time elapsed: 0.010 s
% 1.79/1.52 % (15231)Instructions burned: 19 (million)
% 1.79/1.52 % (15231)------------------------------
% 1.79/1.52 % (15231)------------------------------
% 1.79/1.52 % (15233)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/6Mi)
% 1.79/1.53 % (15233)Instruction limit reached!
% 1.79/1.53 % (15233)------------------------------
% 1.79/1.53 % (15233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.53 % (15233)Termination reason: Unknown
% 1.79/1.53 % (15233)Termination phase: Property scanning
% 1.79/1.53
% 1.79/1.53 % (15233)Memory used [KB]: 1023
% 1.79/1.53 % (15233)Time elapsed: 0.004 s
% 1.79/1.53 % (15233)Instructions burned: 6 (million)
% 1.79/1.53 % (15233)------------------------------
% 1.79/1.53 % (15233)------------------------------
% 1.79/1.53 % (15234)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/902Mi)
% 1.79/1.53 % (15211)Instruction limit reached!
% 1.79/1.53 % (15211)------------------------------
% 1.79/1.53 % (15211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.53 % (15211)Termination reason: Unknown
% 1.79/1.53 % (15211)Termination phase: Saturation
% 1.79/1.53
% 1.79/1.53 % (15211)Memory used [KB]: 6268
% 1.79/1.53 % (15211)Time elapsed: 0.087 s
% 1.79/1.53 % (15211)Instructions burned: 183 (million)
% 1.79/1.53 % (15211)------------------------------
% 1.79/1.53 % (15211)------------------------------
% 1.79/1.53 % (15216)First to succeed.
% 1.79/1.53 % (15234)Refutation not found, incomplete strategy
% 1.79/1.53 % (15234)------------------------------
% 1.79/1.53 % (15234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.53 % (15234)Termination reason: Refutation not found, incomplete strategy
% 1.79/1.53
% 1.79/1.53
% 1.79/1.53 % (15234)Memory used [KB]: 5628
% 1.79/1.53 % (15234)Time elapsed: 0.006 s
% 1.79/1.53 % (15234)Instructions burned: 9 (million)
% 1.79/1.53 % (15234)------------------------------
% 1.79/1.53 % (15234)------------------------------
% 1.79/1.54 % (15235)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_15114 for (2999ds/21Mi)
% 1.79/1.54 % (15216)Refutation found. Thanks to Tanya!
% 1.79/1.54 % SZS status Theorem for DTF2THF_15114
% 1.79/1.54 % SZS output start Proof for DTF2THF_15114
% 1.79/1.54 thf(func_def_0, type, in: $i > $i > $o).
% 1.79/1.54 thf(func_def_1, type, powerset: $i > $i).
% 1.79/1.54 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.79/1.54 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.79/1.54 thf(func_def_4, type, setminus: $i > $i > $i).
% 1.79/1.54 thf(func_def_14, type, sP0: $i > $i > $i > $o).
% 1.79/1.54 thf(func_def_15, type, sK1: $i > $i > $i > $i).
% 1.79/1.54 thf(func_def_16, type, sK2: $i > $i > $i > $i).
% 1.79/1.54 thf(f412,plain,(
% 1.79/1.54 $false),
% 1.79/1.54 inference(avatar_sat_refutation,[status(thm)],[f342,f368,f385,f395,f411])).
% 1.79/1.54 thf(f411,plain,(
% 1.79/1.54 spl25_4),
% 1.79/1.54 inference(avatar_contradiction_clause,[status(thm)],[f410])).
% 1.79/1.54 thf(f410,plain,(
% 1.79/1.54 $false | spl25_4),
% 1.79/1.54 inference(subsumption_resolution,[status(thm)],[f409,f90])).
% 1.79/1.54 thf(f90,plain,(
% 1.79/1.54 ($true = (in @ sK8 @ (powerset @ sK6)))),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 thf(f49,plain,(
% 1.79/1.54 (binunionT_lem = $true) & (demorgan2b = $true) & (complementT_lem = $true) & (demorgan2a = $true) & (((in @ sK7 @ (powerset @ sK6)) = $true) & (((setminus @ sK6 @ (binunion @ sK7 @ sK8)) != (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8))) & ($true = (in @ sK8 @ (powerset @ sK6))))) & (setextT = $true) & (binintersectT_lem = $true)),
% 1.79/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f25,f48,f47])).
% 1.79/1.54 thf(f47,plain,(
% 1.79/1.54 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) != (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) & ((in @ X2 @ (powerset @ X0)) = $true))) => (((in @ sK7 @ (powerset @ sK6)) = $true) & ? [X2 : $i] : (((binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ X2)) != (setminus @ sK6 @ (binunion @ sK7 @ X2))) & ($true = (in @ X2 @ (powerset @ sK6)))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f48,plain,(
% 1.79/1.54 ? [X2 : $i] : (((binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ X2)) != (setminus @ sK6 @ (binunion @ sK7 @ X2))) & ($true = (in @ X2 @ (powerset @ sK6)))) => (((setminus @ sK6 @ (binunion @ sK7 @ sK8)) != (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8))) & ($true = (in @ sK8 @ (powerset @ sK6))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f25,plain,(
% 1.79/1.54 (binunionT_lem = $true) & (demorgan2b = $true) & (complementT_lem = $true) & (demorgan2a = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) != (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) & ((in @ X2 @ (powerset @ X0)) = $true))) & (setextT = $true) & (binintersectT_lem = $true)),
% 1.79/1.54 inference(flattening,[status(thm)],[f24])).
% 1.79/1.54 thf(f24,plain,(
% 1.79/1.54 (((((? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) != (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) & ((in @ X2 @ (powerset @ X0)) = $true))) & (demorgan2b = $true)) & (demorgan2a = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)),
% 1.79/1.54 inference(ennf_transformation,[status(thm)],[f19])).
% 1.79/1.54 thf(f19,plain,(
% 1.79/1.54 ~((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((demorgan2a = $true) => ((demorgan2b = $true) => ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))))))),
% 1.79/1.54 inference(fool_elimination,[status(thm)],[f18])).
% 1.79/1.54 thf(f18,plain,(
% 1.79/1.54 ~(binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan2a => (demorgan2b => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))))))),
% 1.79/1.54 inference(rectify,[status(thm)],[f8])).
% 1.79/1.54 thf(f8,negated_conjecture,(
% 1.79/1.54 ~(binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan2a => (demorgan2b => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))))))),
% 1.79/1.54 inference(negated_conjecture,[status(cth)],[f7])).
% 1.79/1.54 thf(f7,conjecture,(
% 1.79/1.54 binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan2a => (demorgan2b => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))))))),
% 1.79/1.54 file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',demorgan2)).
% 1.79/1.54 thf(f409,plain,(
% 1.79/1.54 ($true != (in @ sK8 @ (powerset @ sK6))) | spl25_4),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f408])).
% 1.79/1.54 thf(f408,plain,(
% 1.79/1.54 ($true != $true) | ($true != (in @ sK8 @ (powerset @ sK6))) | spl25_4),
% 1.79/1.54 inference(superposition,[status(thm)],[f384,f153])).
% 1.79/1.54 thf(f153,plain,(
% 1.79/1.54 ( ! [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.79/1.54 thf(f148,plain,(
% 1.79/1.54 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true)) )),
% 1.79/1.54 inference(definition_unfolding,[status(thm)],[f119,f94])).
% 1.79/1.54 thf(f94,plain,(
% 1.79/1.54 (complementT_lem = $true)),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 thf(f119,plain,(
% 1.79/1.54 ( ! [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true) | ($true != (in @ X0 @ (powerset @ X1))) | (complementT_lem != $true)) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f75])).
% 1.79/1.54 thf(f75,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | (($true != (in @ (setminus @ sK24 @ sK23) @ (powerset @ sK24))) & ((in @ sK23 @ (powerset @ sK24)) = $true)))),
% 1.79/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f73,f74])).
% 1.79/1.54 thf(f74,plain,(
% 1.79/1.54 ? [X2 : $i,X3 : $i] : (((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) != $true) & ($true = (in @ X2 @ (powerset @ X3)))) => (($true != (in @ (setminus @ sK24 @ sK23) @ (powerset @ sK24))) & ((in @ sK23 @ (powerset @ sK24)) = $true))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f73,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : (((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) != $true) & ($true = (in @ X2 @ (powerset @ X3)))))),
% 1.79/1.54 inference(rectify,[status(thm)],[f72])).
% 1.79/1.54 thf(f72,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) != $true) & ($true = (in @ X0 @ (powerset @ X1)))))),
% 1.79/1.54 inference(nnf_transformation,[status(thm)],[f28])).
% 1.79/1.54 thf(f28,plain,(
% 1.79/1.54 ! [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (complementT_lem = $true)),
% 1.79/1.54 inference(ennf_transformation,[status(thm)],[f11])).
% 1.79/1.54 thf(f11,plain,(
% 1.79/1.54 ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true)) <=> (complementT_lem = $true)),
% 1.79/1.54 inference(fool_elimination,[status(thm)],[f10])).
% 1.79/1.54 thf(f10,plain,(
% 1.79/1.54 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
% 1.79/1.54 inference(rectify,[status(thm)],[f3])).
% 1.79/1.54 thf(f3,axiom,(
% 1.79/1.54 (complementT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.79/1.54 file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',complementT_lem)).
% 1.79/1.54 thf(f384,plain,(
% 1.79/1.54 ($true != (in @ (setminus @ sK6 @ sK8) @ (powerset @ sK6))) | spl25_4),
% 1.79/1.54 inference(avatar_component_clause,[status(thm)],[f382])).
% 1.79/1.54 thf(f382,definition,(
% 1.79/1.54 spl25_4 <=> ($true = (in @ (setminus @ sK6 @ sK8) @ (powerset @ sK6)))),
% 1.79/1.54 introduced(definition,[new_symbols(naming,[spl25_4])],[avatar_definition])).
% 1.79/1.54 thf(f395,plain,(
% 1.79/1.54 spl25_3),
% 1.79/1.54 inference(avatar_contradiction_clause,[status(thm)],[f394])).
% 1.79/1.54 thf(f394,plain,(
% 1.79/1.54 $false | spl25_3),
% 1.79/1.54 inference(subsumption_resolution,[status(thm)],[f393,f92])).
% 1.79/1.54 thf(f92,plain,(
% 1.79/1.54 ((in @ sK7 @ (powerset @ sK6)) = $true)),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 thf(f393,plain,(
% 1.79/1.54 ((in @ sK7 @ (powerset @ sK6)) != $true) | spl25_3),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f392])).
% 1.79/1.54 thf(f392,plain,(
% 1.79/1.54 ($true != $true) | ((in @ sK7 @ (powerset @ sK6)) != $true) | spl25_3),
% 1.79/1.54 inference(superposition,[status(thm)],[f380,f153])).
% 1.79/1.54 thf(f380,plain,(
% 1.79/1.54 ($true != (in @ (setminus @ sK6 @ sK7) @ (powerset @ sK6))) | spl25_3),
% 1.79/1.54 inference(avatar_component_clause,[status(thm)],[f378])).
% 1.79/1.54 thf(f378,definition,(
% 1.79/1.54 spl25_3 <=> ($true = (in @ (setminus @ sK6 @ sK7) @ (powerset @ sK6)))),
% 1.79/1.54 introduced(definition,[new_symbols(naming,[spl25_3])],[avatar_definition])).
% 1.79/1.54 thf(f385,plain,(
% 1.79/1.54 ~spl25_3 | ~spl25_4 | spl25_2),
% 1.79/1.54 inference(avatar_split_clause,[status(thm)],[f375,f339,f382,f378])).
% 1.79/1.54 thf(f339,definition,(
% 1.79/1.54 spl25_2 <=> ((in @ (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8)) @ (powerset @ sK6)) = $true)),
% 1.79/1.54 introduced(definition,[new_symbols(naming,[spl25_2])],[avatar_definition])).
% 1.79/1.54 thf(f375,plain,(
% 1.79/1.54 ($true != (in @ (setminus @ sK6 @ sK7) @ (powerset @ sK6))) | ($true != (in @ (setminus @ sK6 @ sK8) @ (powerset @ sK6))) | spl25_2),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f374])).
% 1.79/1.54 thf(f374,plain,(
% 1.79/1.54 ($true != (in @ (setminus @ sK6 @ sK7) @ (powerset @ sK6))) | ($true != $true) | ($true != (in @ (setminus @ sK6 @ sK8) @ (powerset @ sK6))) | spl25_2),
% 1.79/1.54 inference(superposition,[status(thm)],[f341,f157])).
% 1.79/1.54 thf(f157,plain,(
% 1.79/1.54 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ (binintersect @ X4 @ X5) @ (powerset @ X3))) | ($true != (in @ X4 @ (powerset @ X3))) | ((in @ X5 @ (powerset @ X3)) != $true)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.79/1.54 thf(f143,plain,(
% 1.79/1.54 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X5 @ (powerset @ X3)) != $true) | ($true = (in @ (binintersect @ X4 @ X5) @ (powerset @ X3))) | ($true != (in @ X4 @ (powerset @ X3)))) )),
% 1.79/1.54 inference(definition_unfolding,[status(thm)],[f109,f88])).
% 1.79/1.54 thf(f88,plain,(
% 1.79/1.54 (binintersectT_lem = $true)),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 thf(f109,plain,(
% 1.79/1.54 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (powerset @ X3))) | ((in @ X5 @ (powerset @ X3)) != $true) | ($true = (in @ (binintersect @ X4 @ X5) @ (powerset @ X3))) | (binintersectT_lem != $true)) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f66])).
% 1.79/1.54 thf(f66,plain,(
% 1.79/1.54 ((binintersectT_lem = $true) | (((in @ sK18 @ (powerset @ sK17)) = $true) & (($true = (in @ sK19 @ (powerset @ sK17))) & ($true != (in @ (binintersect @ sK18 @ sK19) @ (powerset @ sK17)))))) & (! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (powerset @ X3))) | ! [X5 : $i] : (((in @ X5 @ (powerset @ X3)) != $true) | ($true = (in @ (binintersect @ X4 @ X5) @ (powerset @ X3))))) | (binintersectT_lem != $true))),
% 1.79/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f63,f65,f64])).
% 1.79/1.54 thf(f64,plain,(
% 1.79/1.54 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true))) => (((in @ sK18 @ (powerset @ sK17)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ sK17)) = $true) & ($true != (in @ (binintersect @ sK18 @ X2) @ (powerset @ sK17)))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f65,plain,(
% 1.79/1.54 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK17)) = $true) & ($true != (in @ (binintersect @ sK18 @ X2) @ (powerset @ sK17)))) => (($true = (in @ sK19 @ (powerset @ sK17))) & ($true != (in @ (binintersect @ sK18 @ sK19) @ (powerset @ sK17))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f63,plain,(
% 1.79/1.54 ((binintersectT_lem = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true)))) & (! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (powerset @ X3))) | ! [X5 : $i] : (((in @ X5 @ (powerset @ X3)) != $true) | ($true = (in @ (binintersect @ X4 @ X5) @ (powerset @ X3))))) | (binintersectT_lem != $true))),
% 1.79/1.54 inference(rectify,[status(thm)],[f62])).
% 1.79/1.54 thf(f62,plain,(
% 1.79/1.54 ((binintersectT_lem = $true) | ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) != $true)))) & (! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true))) | (binintersectT_lem != $true))),
% 1.79/1.54 inference(nnf_transformation,[status(thm)],[f29])).
% 1.79/1.54 thf(f29,plain,(
% 1.79/1.54 (binintersectT_lem = $true) <=> ! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true)))),
% 1.79/1.54 inference(ennf_transformation,[status(thm)],[f23])).
% 1.79/1.54 thf(f23,plain,(
% 1.79/1.54 (binintersectT_lem = $true) <=> ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true)))),
% 1.79/1.54 inference(fool_elimination,[status(thm)],[f22])).
% 1.79/1.54 thf(f22,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))) = binintersectT_lem)),
% 1.79/1.54 inference(rectify,[status(thm)],[f1])).
% 1.79/1.54 thf(f1,axiom,(
% 1.79/1.54 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))) = binintersectT_lem)),
% 1.79/1.54 file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',binintersectT_lem)).
% 1.79/1.54 thf(f341,plain,(
% 1.79/1.54 ((in @ (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8)) @ (powerset @ sK6)) != $true) | spl25_2),
% 1.79/1.54 inference(avatar_component_clause,[status(thm)],[f339])).
% 1.79/1.54 thf(f368,plain,(
% 1.79/1.54 spl25_1),
% 1.79/1.54 inference(avatar_contradiction_clause,[status(thm)],[f367])).
% 1.79/1.54 thf(f367,plain,(
% 1.79/1.54 $false | spl25_1),
% 1.79/1.54 inference(subsumption_resolution,[status(thm)],[f366,f92])).
% 1.79/1.54 thf(f366,plain,(
% 1.79/1.54 ((in @ sK7 @ (powerset @ sK6)) != $true) | spl25_1),
% 1.79/1.54 inference(subsumption_resolution,[status(thm)],[f365,f90])).
% 1.79/1.54 thf(f365,plain,(
% 1.79/1.54 ($true != (in @ sK8 @ (powerset @ sK6))) | ((in @ sK7 @ (powerset @ sK6)) != $true) | spl25_1),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f364])).
% 1.79/1.54 thf(f364,plain,(
% 1.79/1.54 ((in @ sK7 @ (powerset @ sK6)) != $true) | ($true != (in @ sK8 @ (powerset @ sK6))) | ($true != $true) | spl25_1),
% 1.79/1.54 inference(superposition,[status(thm)],[f354,f154])).
% 1.79/1.54 thf(f154,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.79/1.54 thf(f144,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true) | ($true != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.79/1.54 inference(definition_unfolding,[status(thm)],[f116,f96])).
% 1.79/1.54 thf(f96,plain,(
% 1.79/1.54 (binunionT_lem = $true)),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 thf(f116,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | (binunionT_lem != $true)) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f71])).
% 1.79/1.54 thf(f71,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | (((in @ sK20 @ (powerset @ sK21)) = $true) & (((in @ (binunion @ sK20 @ sK22) @ (powerset @ sK21)) != $true) & ($true = (in @ sK22 @ (powerset @ sK21))))))),
% 1.79/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f68,f70,f69])).
% 1.79/1.54 thf(f69,plain,(
% 1.79/1.54 ? [X3 : $i,X4 : $i] : (((in @ X3 @ (powerset @ X4)) = $true) & ? [X5 : $i] : (($true != (in @ (binunion @ X3 @ X5) @ (powerset @ X4))) & ((in @ X5 @ (powerset @ X4)) = $true))) => (((in @ sK20 @ (powerset @ sK21)) = $true) & ? [X5 : $i] : (((in @ (binunion @ sK20 @ X5) @ (powerset @ sK21)) != $true) & ($true = (in @ X5 @ (powerset @ sK21)))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f70,plain,(
% 1.79/1.54 ? [X5 : $i] : (((in @ (binunion @ sK20 @ X5) @ (powerset @ sK21)) != $true) & ($true = (in @ X5 @ (powerset @ sK21)))) => (((in @ (binunion @ sK20 @ sK22) @ (powerset @ sK21)) != $true) & ($true = (in @ sK22 @ (powerset @ sK21))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f68,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X3 : $i,X4 : $i] : (((in @ X3 @ (powerset @ X4)) = $true) & ? [X5 : $i] : (($true != (in @ (binunion @ X3 @ X5) @ (powerset @ X4))) & ((in @ X5 @ (powerset @ X4)) = $true))))),
% 1.79/1.54 inference(rectify,[status(thm)],[f67])).
% 1.79/1.54 thf(f67,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) != $true) & ((in @ X2 @ (powerset @ X1)) = $true))))),
% 1.79/1.54 inference(nnf_transformation,[status(thm)],[f34])).
% 1.79/1.54 thf(f34,plain,(
% 1.79/1.54 ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true))) <=> (binunionT_lem = $true)),
% 1.79/1.54 inference(ennf_transformation,[status(thm)],[f17])).
% 1.79/1.54 thf(f17,plain,(
% 1.79/1.54 (binunionT_lem = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true)))),
% 1.79/1.54 inference(fool_elimination,[status(thm)],[f16])).
% 1.79/1.54 thf(f16,plain,(
% 1.79/1.54 (binunionT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))))),
% 1.79/1.54 inference(rectify,[status(thm)],[f2])).
% 1.79/1.54 thf(f2,axiom,(
% 1.79/1.54 (binunionT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))))),
% 1.79/1.54 file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',binunionT_lem)).
% 1.79/1.54 thf(f354,plain,(
% 1.79/1.54 ((in @ (binunion @ sK7 @ sK8) @ (powerset @ sK6)) != $true) | spl25_1),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f353])).
% 1.79/1.54 thf(f353,plain,(
% 1.79/1.54 ((in @ (binunion @ sK7 @ sK8) @ (powerset @ sK6)) != $true) | ($true != $true) | spl25_1),
% 1.79/1.54 inference(superposition,[status(thm)],[f337,f153])).
% 1.79/1.54 thf(f337,plain,(
% 1.79/1.54 ((in @ (setminus @ sK6 @ (binunion @ sK7 @ sK8)) @ (powerset @ sK6)) != $true) | spl25_1),
% 1.79/1.54 inference(avatar_component_clause,[status(thm)],[f335])).
% 1.79/1.54 thf(f335,definition,(
% 1.79/1.54 spl25_1 <=> ((in @ (setminus @ sK6 @ (binunion @ sK7 @ sK8)) @ (powerset @ sK6)) = $true)),
% 1.79/1.54 introduced(definition,[new_symbols(naming,[spl25_1])],[avatar_definition])).
% 1.79/1.54 thf(f342,plain,(
% 1.79/1.54 ~spl25_1 | ~spl25_2),
% 1.79/1.54 inference(avatar_split_clause,[status(thm)],[f333,f339,f335])).
% 1.79/1.54 thf(f333,plain,(
% 1.79/1.54 ((in @ (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8)) @ (powerset @ sK6)) != $true) | ((in @ (setminus @ sK6 @ (binunion @ sK7 @ sK8)) @ (powerset @ sK6)) != $true)),
% 1.79/1.54 inference(subsumption_resolution,[status(thm)],[f332,f90])).
% 1.79/1.54 thf(f332,plain,(
% 1.79/1.54 ($true != (in @ sK8 @ (powerset @ sK6))) | ((in @ (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8)) @ (powerset @ sK6)) != $true) | ((in @ (setminus @ sK6 @ (binunion @ sK7 @ sK8)) @ (powerset @ sK6)) != $true)),
% 1.79/1.54 inference(subsumption_resolution,[status(thm)],[f318,f92])).
% 1.79/1.54 thf(f318,plain,(
% 1.79/1.54 ((in @ (setminus @ sK6 @ (binunion @ sK7 @ sK8)) @ (powerset @ sK6)) != $true) | ((in @ (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8)) @ (powerset @ sK6)) != $true) | ((in @ sK7 @ (powerset @ sK6)) != $true) | ($true != (in @ sK8 @ (powerset @ sK6)))),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f286])).
% 1.79/1.54 thf(f286,plain,(
% 1.79/1.54 ((in @ sK7 @ (powerset @ sK6)) != $true) | ((in @ (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8)) @ (powerset @ sK6)) != $true) | ($true != (in @ sK8 @ (powerset @ sK6))) | ((in @ (setminus @ sK6 @ (binunion @ sK7 @ sK8)) @ (powerset @ sK6)) != $true) | ((setminus @ sK6 @ (binunion @ sK7 @ sK8)) != (setminus @ sK6 @ (binunion @ sK7 @ sK8)))),
% 1.79/1.54 inference(superposition,[status(thm)],[f91,f276])).
% 1.79/1.54 thf(f276,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.79/1.54 inference(subsumption_resolution,[status(thm)],[f273,f238])).
% 1.79/1.54 thf(f238,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X0)) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f237])).
% 1.79/1.54 thf(f237,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ($true != $true) | ($true != (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X0)) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.79/1.54 inference(duplicate_literal_removal,[status(thm)],[f231])).
% 1.79/1.54 thf(f231,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X0)) | ($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X0))) )),
% 1.79/1.54 inference(superposition,[status(thm)],[f196,f78])).
% 1.79/1.54 thf(f78,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X0)) | ($true != (sP0 @ X2 @ X1 @ X0))) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f40])).
% 1.79/1.54 thf(f40,plain,(
% 1.79/1.54 ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (sP0 @ X2 @ X1 @ X0)) | ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true))) & ((($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X0)) & ($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X1)) & ($true != (in @ (sK1 @ X2 @ X1 @ X0) @ X2))) | ($true != (sP0 @ X2 @ X1 @ X0))))),
% 1.79/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f38,f39])).
% 1.79/1.54 thf(f39,plain,(
% 1.79/1.54 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X0)) & ((in @ X4 @ X1) = $true) & ((in @ X4 @ X2) != $true)) => (($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X0)) & ($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X1)) & ($true != (in @ (sK1 @ X2 @ X1 @ X0) @ X2))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f38,plain,(
% 1.79/1.54 ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (sP0 @ X2 @ X1 @ X0)) | ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true))) & (? [X4 : $i] : (($true = (in @ X4 @ X0)) & ((in @ X4 @ X1) = $true) & ((in @ X4 @ X2) != $true)) | ($true != (sP0 @ X2 @ X1 @ X0))))),
% 1.79/1.54 inference(rectify,[status(thm)],[f37])).
% 1.79/1.54 thf(f37,plain,(
% 1.79/1.54 ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (sP0 @ X2 @ X1 @ X0)) | ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true))) & (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true)) | ($true != (sP0 @ X2 @ X1 @ X0))))),
% 1.79/1.54 inference(nnf_transformation,[status(thm)],[f35])).
% 1.79/1.54 thf(f35,plain,(
% 1.79/1.54 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (sP0 @ X2 @ X1 @ X0)) <=> ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true)))),
% 1.79/1.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.79/1.54 thf(f196,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK1 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0)) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) != $true)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f195])).
% 1.79/1.54 thf(f195,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ (sK1 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0)) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true)) )),
% 1.79/1.54 inference(duplicate_literal_removal,[status(thm)],[f191])).
% 1.79/1.54 thf(f191,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK1 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0)) | ($true != $true) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.79/1.54 inference(superposition,[status(thm)],[f176,f77])).
% 1.79/1.54 thf(f77,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X1)) | ($true != (sP0 @ X2 @ X1 @ X0))) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f40])).
% 1.79/1.54 thf(f176,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (sK1 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binunion @ X1 @ X2)))) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4)) | ((in @ (sK1 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.79/1.54 thf(f172,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (sK1 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binunion @ X1 @ X2)))) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4)) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ (sK1 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0) != $true)) )),
% 1.79/1.54 inference(superposition,[status(thm)],[f76,f155])).
% 1.79/1.54 thf(f155,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.79/1.54 thf(f128,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true)) )),
% 1.79/1.54 inference(definition_unfolding,[status(thm)],[f102,f93])).
% 1.79/1.54 thf(f93,plain,(
% 1.79/1.54 (demorgan2a = $true)),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 thf(f102,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (demorgan2a != $true)) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f55])).
% 1.79/1.54 thf(f55,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (demorgan2a != $true)) & ((demorgan2a = $true) | (((in @ sK10 @ (powerset @ sK9)) = $true) & ((((in @ sK12 @ sK9) = $true) & ($true != (in @ sK12 @ (binintersect @ (setminus @ sK9 @ sK10) @ (setminus @ sK9 @ sK11)))) & ((in @ sK12 @ (setminus @ sK9 @ (binunion @ sK10 @ sK11))) = $true)) & ($true = (in @ sK11 @ (powerset @ sK9))))))),
% 1.79/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f51,f54,f53,f52])).
% 1.79/1.54 thf(f52,plain,(
% 1.79/1.54 ? [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ X4) = $true) & ((in @ X7 @ (binintersect @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true) & ((in @ X7 @ (setminus @ X4 @ (binunion @ X5 @ X6))) = $true)) & ((in @ X6 @ (powerset @ X4)) = $true))) => (((in @ sK10 @ (powerset @ sK9)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ sK9) = $true) & ($true != (in @ X7 @ (binintersect @ (setminus @ sK9 @ sK10) @ (setminus @ sK9 @ X6)))) & ($true = (in @ X7 @ (setminus @ sK9 @ (binunion @ sK10 @ X6))))) & ((in @ X6 @ (powerset @ sK9)) = $true)))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f53,plain,(
% 1.79/1.54 ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ sK9) = $true) & ($true != (in @ X7 @ (binintersect @ (setminus @ sK9 @ sK10) @ (setminus @ sK9 @ X6)))) & ($true = (in @ X7 @ (setminus @ sK9 @ (binunion @ sK10 @ X6))))) & ((in @ X6 @ (powerset @ sK9)) = $true)) => (? [X7 : $i] : (((in @ X7 @ sK9) = $true) & ($true != (in @ X7 @ (binintersect @ (setminus @ sK9 @ sK10) @ (setminus @ sK9 @ sK11)))) & ($true = (in @ X7 @ (setminus @ sK9 @ (binunion @ sK10 @ sK11))))) & ($true = (in @ sK11 @ (powerset @ sK9))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f54,plain,(
% 1.79/1.54 ? [X7 : $i] : (((in @ X7 @ sK9) = $true) & ($true != (in @ X7 @ (binintersect @ (setminus @ sK9 @ sK10) @ (setminus @ sK9 @ sK11)))) & ($true = (in @ X7 @ (setminus @ sK9 @ (binunion @ sK10 @ sK11))))) => (((in @ sK12 @ sK9) = $true) & ($true != (in @ sK12 @ (binintersect @ (setminus @ sK9 @ sK10) @ (setminus @ sK9 @ sK11)))) & ((in @ sK12 @ (setminus @ sK9 @ (binunion @ sK10 @ sK11))) = $true))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f51,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (demorgan2a != $true)) & ((demorgan2a = $true) | ? [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ X4) = $true) & ((in @ X7 @ (binintersect @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true) & ((in @ X7 @ (setminus @ X4 @ (binunion @ X5 @ X6))) = $true)) & ((in @ X6 @ (powerset @ X4)) = $true))))),
% 1.79/1.54 inference(rectify,[status(thm)],[f50])).
% 1.79/1.54 thf(f50,plain,(
% 1.79/1.54 (! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) | ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true))) | (demorgan2a != $true)) & ((demorgan2a = $true) | ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) & ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true))))),
% 1.79/1.54 inference(nnf_transformation,[status(thm)],[f27])).
% 1.79/1.54 thf(f27,plain,(
% 1.79/1.54 ! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) | ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true))) <=> (demorgan2a = $true)),
% 1.79/1.54 inference(flattening,[status(thm)],[f26])).
% 1.79/1.54 thf(f26,plain,(
% 1.79/1.54 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((($true = (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) | ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) != $true)) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (demorgan2a = $true)),
% 1.79/1.54 inference(ennf_transformation,[status(thm)],[f21])).
% 1.79/1.54 thf(f21,plain,(
% 1.79/1.54 ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) = $true) => ($true = (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))))))) <=> (demorgan2a = $true)),
% 1.79/1.54 inference(fool_elimination,[status(thm)],[f20])).
% 1.79/1.54 thf(f20,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) => (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))))))) = demorgan2a)),
% 1.79/1.54 inference(rectify,[status(thm)],[f5])).
% 1.79/1.54 thf(f5,axiom,(
% 1.79/1.54 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))) = demorgan2a)),
% 1.79/1.54 file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',demorgan2a)).
% 1.79/1.54 thf(f76,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK1 @ X2 @ X1 @ X0) @ X2)) | ($true != (sP0 @ X2 @ X1 @ X0))) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f40])).
% 1.79/1.54 thf(f273,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X0)) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))) | ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f272])).
% 1.79/1.54 thf(f272,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))) | ($true != $true) | ($true = (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X0)) | ($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ((in @ X2 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.79/1.54 inference(duplicate_literal_removal,[status(thm)],[f268])).
% 1.79/1.54 thf(f268,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X0)) | ($true != $true) | ($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))) | ($true = (sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X0)) | ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.79/1.54 inference(superposition,[status(thm)],[f207,f151])).
% 1.79/1.54 thf(f151,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) | ((sP0 @ X2 @ X0 @ X1) = $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true) | (X0 = X2)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.79/1.54 thf(f121,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) | (X0 = X2) | ($true != $true) | ((sP0 @ X2 @ X0 @ X1) = $true)) )),
% 1.79/1.54 inference(definition_unfolding,[status(thm)],[f86,f89])).
% 1.79/1.54 thf(f89,plain,(
% 1.79/1.54 (setextT = $true)),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 thf(f86,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) | ((sP0 @ X2 @ X0 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | (setextT != $true)) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f46])).
% 1.79/1.54 thf(f46,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((X0 = X2) | (((in @ (sK2 @ X2 @ X1 @ X0) @ X0) != $true) & ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) & ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X2))) | ((sP0 @ X2 @ X0 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) | (setextT != $true)) & ((setextT = $true) | (((sK3 != sK5) & ! [X7 : $i] : (((in @ X7 @ sK3) = $true) | ($true != (in @ X7 @ sK4)) | ((in @ X7 @ sK5) != $true)) & ((sP0 @ sK5 @ sK3 @ sK4) != $true) & ((in @ sK5 @ (powerset @ sK4)) = $true)) & ($true = (in @ sK3 @ (powerset @ sK4)))))),
% 1.79/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f42,f45,f44,f43])).
% 1.79/1.54 thf(f43,plain,(
% 1.79/1.54 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) = $true)) => (((in @ (sK2 @ X2 @ X1 @ X0) @ X0) != $true) & ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) & ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X2))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f44,plain,(
% 1.79/1.54 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : ((X4 != X6) & ! [X7 : $i] : (((in @ X7 @ X4) = $true) | ($true != (in @ X7 @ X5)) | ($true != (in @ X7 @ X6))) & ($true != (sP0 @ X6 @ X4 @ X5)) & ($true = (in @ X6 @ (powerset @ X5)))) & ($true = (in @ X4 @ (powerset @ X5)))) => (? [X6 : $i] : ((sK3 != X6) & ! [X7 : $i] : (((in @ X7 @ sK3) = $true) | ($true != (in @ X7 @ sK4)) | ($true != (in @ X7 @ X6))) & ($true != (sP0 @ X6 @ sK3 @ sK4)) & ((in @ X6 @ (powerset @ sK4)) = $true)) & ($true = (in @ sK3 @ (powerset @ sK4))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f45,plain,(
% 1.79/1.54 ? [X6 : $i] : ((sK3 != X6) & ! [X7 : $i] : (((in @ X7 @ sK3) = $true) | ($true != (in @ X7 @ sK4)) | ($true != (in @ X7 @ X6))) & ($true != (sP0 @ X6 @ sK3 @ sK4)) & ((in @ X6 @ (powerset @ sK4)) = $true)) => ((sK3 != sK5) & ! [X7 : $i] : (((in @ X7 @ sK3) = $true) | ($true != (in @ X7 @ sK4)) | ((in @ X7 @ sK5) != $true)) & ((sP0 @ sK5 @ sK3 @ sK4) != $true) & ((in @ sK5 @ (powerset @ sK4)) = $true))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f42,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((X0 = X2) | ? [X3 : $i] : (((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) = $true)) | ((sP0 @ X2 @ X0 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) | (setextT != $true)) & ((setextT = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : ((X4 != X6) & ! [X7 : $i] : (((in @ X7 @ X4) = $true) | ($true != (in @ X7 @ X5)) | ($true != (in @ X7 @ X6))) & ($true != (sP0 @ X6 @ X4 @ X5)) & ($true = (in @ X6 @ (powerset @ X5)))) & ($true = (in @ X4 @ (powerset @ X5)))))),
% 1.79/1.54 inference(rectify,[status(thm)],[f41])).
% 1.79/1.54 thf(f41,plain,(
% 1.79/1.54 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((X1 = X2) | ? [X4 : $i] : (((in @ X4 @ X1) != $true) & ($true = (in @ X4 @ X0)) & ((in @ X4 @ X2) = $true)) | ($true = (sP0 @ X2 @ X1 @ X0)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (setextT != $true)) & ((setextT = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((X1 != X2) & ! [X4 : $i] : (((in @ X4 @ X1) = $true) | ($true != (in @ X4 @ X0)) | ((in @ X4 @ X2) != $true)) & ($true != (sP0 @ X2 @ X1 @ X0)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.79/1.54 inference(nnf_transformation,[status(thm)],[f36])).
% 1.79/1.54 thf(f36,plain,(
% 1.79/1.54 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((X1 = X2) | ? [X4 : $i] : (((in @ X4 @ X1) != $true) & ($true = (in @ X4 @ X0)) & ((in @ X4 @ X2) = $true)) | ($true = (sP0 @ X2 @ X1 @ X0)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (setextT = $true)),
% 1.79/1.54 inference(definition_folding,[status(thm)],[f33,f35])).
% 1.79/1.54 thf(f33,plain,(
% 1.79/1.54 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((X1 = X2) | ? [X4 : $i] : (((in @ X4 @ X1) != $true) & ($true = (in @ X4 @ X0)) & ((in @ X4 @ X2) = $true)) | ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (setextT = $true)),
% 1.79/1.54 inference(flattening,[status(thm)],[f32])).
% 1.79/1.54 thf(f32,plain,(
% 1.79/1.54 (setextT = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((X1 = X2) | ? [X4 : $i] : ((((in @ X4 @ X1) != $true) & ((in @ X4 @ X2) = $true)) & ($true = (in @ X4 @ X0)))) | ? [X3 : $i] : ((((in @ X3 @ X2) != $true) & ((in @ X3 @ X1) = $true)) & ((in @ X3 @ X0) = $true))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 1.79/1.54 inference(ennf_transformation,[status(thm)],[f15])).
% 1.79/1.54 thf(f15,plain,(
% 1.79/1.54 (setextT = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => (! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ X1) = $true) => ((in @ X3 @ X2) = $true))) => (! [X4 : $i] : (($true = (in @ X4 @ X0)) => (((in @ X4 @ X2) = $true) => ((in @ X4 @ X1) = $true))) => (X1 = X2)))))),
% 1.79/1.54 inference(fool_elimination,[status(thm)],[f14])).
% 1.79/1.54 thf(f14,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ X2) => (in @ X4 @ X1))) => (X1 = X2))))) = setextT)),
% 1.79/1.54 inference(rectify,[status(thm)],[f4])).
% 1.79/1.54 thf(f4,axiom,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ X1))) => (X1 = X2))))) = setextT)),
% 1.79/1.54 file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',setextT)).
% 1.79/1.54 thf(f207,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) = $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f206])).
% 1.79/1.54 thf(f206,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ($true != $true) | ((in @ (sK2 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) @ X0) != $true) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)) != $true)) )),
% 1.79/1.54 inference(duplicate_literal_removal,[status(thm)],[f205])).
% 1.79/1.54 thf(f205,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)) != $true) | ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ (sK2 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) @ X0) != $true) | ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ($true != $true) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)) != $true) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) = $true) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) )),
% 1.79/1.54 inference(superposition,[status(thm)],[f158,f167])).
% 1.79/1.54 thf(f167,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true = (in @ (sK2 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binunion @ X1 @ X2)))) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (sK2 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0) != $true) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X4 @ X3) = $true) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ($true != (in @ X4 @ (powerset @ X3))) | ((binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = X4)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.79/1.54 thf(f166,plain,(
% 1.79/1.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = X4) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (in @ (sK2 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binunion @ X1 @ X2)))) | ((in @ (sK2 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0) != $true) | ((sP0 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X4 @ X3) = $true) | ($true != $true) | ($true != (in @ X4 @ (powerset @ X3))) | ($true != (in @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.79/1.54 inference(superposition,[status(thm)],[f152,f156])).
% 1.79/1.54 thf(f156,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X2)) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((sP0 @ X2 @ X0 @ X1) = $true) | (X0 = X2)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.79/1.54 thf(f122,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((sP0 @ X2 @ X0 @ X1) = $true) | (X0 = X2) | ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X2))) )),
% 1.79/1.54 inference(definition_unfolding,[status(thm)],[f85,f89])).
% 1.79/1.54 thf(f85,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X2)) | ((sP0 @ X2 @ X0 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | (setextT != $true)) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f46])).
% 1.79/1.54 thf(f152,plain,(
% 1.79/1.54 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (binintersect @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (setminus @ X4 @ (binunion @ X5 @ X6))) = $true)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.79/1.54 thf(f139,plain,(
% 1.79/1.54 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ X4) != $true) | ((in @ X7 @ (binintersect @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true) | ((in @ X7 @ (setminus @ X4 @ (binunion @ X5 @ X6))) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ($true != $true) | ((in @ X5 @ (powerset @ X4)) != $true)) )),
% 1.79/1.54 inference(definition_unfolding,[status(thm)],[f103,f95])).
% 1.79/1.54 thf(f95,plain,(
% 1.79/1.54 (demorgan2b = $true)),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 thf(f103,plain,(
% 1.79/1.54 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X7 @ (setminus @ X4 @ (binunion @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (binintersect @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (demorgan2b != $true)) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f61])).
% 1.79/1.54 thf(f61,plain,(
% 1.79/1.54 ((demorgan2b = $true) | ((($true = (in @ sK15 @ (powerset @ sK13))) & (((in @ sK16 @ (setminus @ sK13 @ (binunion @ sK14 @ sK15))) != $true) & ($true = (in @ sK16 @ sK13)) & ((in @ sK16 @ (binintersect @ (setminus @ sK13 @ sK14) @ (setminus @ sK13 @ sK15))) = $true))) & ((in @ sK14 @ (powerset @ sK13)) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ! [X7 : $i] : (((in @ X7 @ (setminus @ X4 @ (binunion @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (binintersect @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true))) | ((in @ X5 @ (powerset @ X4)) != $true)) | (demorgan2b != $true))),
% 1.79/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f57,f60,f59,f58])).
% 1.79/1.54 thf(f58,plain,(
% 1.79/1.54 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK13))) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK13 @ (binunion @ sK14 @ X2))) != $true) & ((in @ X3 @ sK13) = $true) & ((in @ X3 @ (binintersect @ (setminus @ sK13 @ sK14) @ (setminus @ sK13 @ X2))) = $true))) & ((in @ sK14 @ (powerset @ sK13)) = $true))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f59,plain,(
% 1.79/1.54 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK13))) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK13 @ (binunion @ sK14 @ X2))) != $true) & ((in @ X3 @ sK13) = $true) & ((in @ X3 @ (binintersect @ (setminus @ sK13 @ sK14) @ (setminus @ sK13 @ X2))) = $true))) => (($true = (in @ sK15 @ (powerset @ sK13))) & ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ sK13 @ (binunion @ sK14 @ sK15)))) & ((in @ X3 @ sK13) = $true) & ($true = (in @ X3 @ (binintersect @ (setminus @ sK13 @ sK14) @ (setminus @ sK13 @ sK15))))))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f60,plain,(
% 1.79/1.54 ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ sK13 @ (binunion @ sK14 @ sK15)))) & ((in @ X3 @ sK13) = $true) & ($true = (in @ X3 @ (binintersect @ (setminus @ sK13 @ sK14) @ (setminus @ sK13 @ sK15))))) => (((in @ sK16 @ (setminus @ sK13 @ (binunion @ sK14 @ sK15))) != $true) & ($true = (in @ sK16 @ sK13)) & ((in @ sK16 @ (binintersect @ (setminus @ sK13 @ sK14) @ (setminus @ sK13 @ sK15))) = $true))),
% 1.79/1.54 introduced(definition,[],[choice_axiom])).
% 1.79/1.54 thf(f57,plain,(
% 1.79/1.54 ((demorgan2b = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ! [X7 : $i] : (((in @ X7 @ (setminus @ X4 @ (binunion @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (binintersect @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true))) | ((in @ X5 @ (powerset @ X4)) != $true)) | (demorgan2b != $true))),
% 1.79/1.54 inference(rectify,[status(thm)],[f56])).
% 1.79/1.54 thf(f56,plain,(
% 1.79/1.54 ((demorgan2b = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) != $true))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (demorgan2b != $true))),
% 1.79/1.54 inference(nnf_transformation,[status(thm)],[f31])).
% 1.79/1.54 thf(f31,plain,(
% 1.79/1.54 (demorgan2b = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) != $true))) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 1.79/1.54 inference(flattening,[status(thm)],[f30])).
% 1.79/1.54 thf(f30,plain,(
% 1.79/1.54 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) = $true) | ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) != $true)) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (demorgan2b = $true)),
% 1.79/1.54 inference(ennf_transformation,[status(thm)],[f13])).
% 1.79/1.54 thf(f13,plain,(
% 1.79/1.54 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) = $true))))) <=> (demorgan2b = $true)),
% 1.79/1.54 inference(fool_elimination,[status(thm)],[f12])).
% 1.79/1.54 thf(f12,plain,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) => (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))))))) = demorgan2b)),
% 1.79/1.54 inference(rectify,[status(thm)],[f6])).
% 1.79/1.54 thf(f6,axiom,(
% 1.79/1.54 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) => (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))))))) = demorgan2b)),
% 1.79/1.54 file('/export/starexec/sandbox/tmp/tmp.DwLC7FElnb/DTF2THF_15114.p',demorgan2b)).
% 1.79/1.54 thf(f158,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X2 @ X1 @ X0) @ X0) != $true) | (X0 = X2) | ($true != (in @ X0 @ (powerset @ X1))) | ((sP0 @ X2 @ X0 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 1.79/1.54 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.79/1.54 thf(f120,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((sP0 @ X2 @ X0 @ X1) = $true) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X0) != $true) | ($true != $true) | ($true != (in @ X0 @ (powerset @ X1))) | (X0 = X2) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 1.79/1.54 inference(definition_unfolding,[status(thm)],[f87,f89])).
% 1.79/1.54 thf(f87,plain,(
% 1.79/1.54 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X0) != $true) | ((sP0 @ X2 @ X0 @ X1) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | (setextT != $true)) )),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f46])).
% 1.79/1.54 thf(f91,plain,(
% 1.79/1.54 ((setminus @ sK6 @ (binunion @ sK7 @ sK8)) != (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8)))),
% 1.79/1.54 inference(cnf_transformation,[status(thm)],[f49])).
% 1.79/1.54 % SZS output end Proof for DTF2THF_15114
% 1.79/1.54 % (15216)------------------------------
% 1.79/1.54 % (15216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.54 % (15216)Termination reason: Refutation
% 1.79/1.54
% 1.79/1.54 % (15216)Memory used [KB]: 6140
% 1.79/1.54 % (15216)Time elapsed: 0.095 s
% 1.79/1.54 % (15216)Instructions burned: 182 (million)
% 1.79/1.54 % (15216)------------------------------
% 1.79/1.54 % (15216)------------------------------
% 1.79/1.54 % (15210)Success in time 0.099 s
%------------------------------------------------------------------------------