%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU753^2 : 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 : n013.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 09:36:55 AM UTC 2026
% Result : Theorem 1.77s 1.47s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 29
% Syntax : Number of formulae : 160 ( 25 unt; 0 typ; 4 def)
% Number of atoms : 2692 ( 775 equ; 0 cnn)
% Maximal formula atoms : 16 ( 16 avg)
% Number of connectives : 4171 ( 402 ~; 374 |; 206 &;3056 @)
% ( 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 : 443 ( 0 ^; 342 !; 101 ?; 443 :)
% 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(f413,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f343,f369,f386,f396,f412]) ).
thf(f412,plain,
spl25_4,
inference(avatar_contradiction_clause,[status(thm)],[f411]) ).
thf(f411,plain,
( $false
| spl25_4 ),
inference(subsumption_resolution,[status(thm)],[f410,f119]) ).
thf(f119,plain,
( ( in @ sK24 @ ( powerset @ sK22 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( in @ sK23 @ ( powerset @ sK22 ) )
= $true )
& ( ( in @ sK24 @ ( powerset @ sK22 ) )
= $true )
& ( ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) )
!= ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( setextT = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( complementT_lem = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24])],[f73,f75,f74]) ).
thf(f74,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
!= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
=> ( ( ( in @ sK23 @ ( powerset @ sK22 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK22 ) )
= $true )
& ( ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ X2 ) )
!= ( setminus @ sK22 @ ( binintersect @ sK23 @ X2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f75,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK22 ) )
= $true )
& ( ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ X2 ) )
!= ( setminus @ sK22 @ ( binintersect @ sK23 @ X2 ) ) ) )
=> ( ( ( in @ sK24 @ ( powerset @ sK22 ) )
= $true )
& ( ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) )
!= ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f73,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
!= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( setextT = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( complementT_lem = $true ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) )
!= ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( setextT = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( complementT_lem = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) )
!= ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
~ ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) )
= ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) )
= ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',demorgan1) ).
thf(f410,plain,
( ( ( in @ sK24 @ ( powerset @ sK22 ) )
!= $true )
| spl25_4 ),
inference(trivial_inequality_removal,[status(thm)],[f409]) ).
thf(f409,plain,
( ( ( in @ sK24 @ ( powerset @ sK22 ) )
!= $true )
| ( $true != $true )
| spl25_4 ),
inference(superposition,[status(thm)],[f385,f157]) ).
thf(f157,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f141]) ).
thf(f141,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f99,f112]) ).
thf(f112,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f99,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( complementT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( complementT_lem = $true )
| ( ( ( in @ ( setminus @ sK14 @ sK13 ) @ ( powerset @ sK14 ) )
!= $true )
& ( $true
= ( in @ sK13 @ ( powerset @ sK14 ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) ) )
| ( complementT_lem != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f59,f60]) ).
thf(f60,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
!= $true )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
=> ( ( ( in @ ( setminus @ sK14 @ sK13 ) @ ( powerset @ sK14 ) )
!= $true )
& ( $true
= ( in @ sK13 @ ( powerset @ sK14 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f59,plain,
( ( ( complementT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
!= $true )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) ) )
| ( complementT_lem != $true ) ) ),
inference(rectify,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( complementT_lem = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( complementT_lem != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( complementT_lem = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( complementT_lem = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) )
= complementT_lem ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) )
= complementT_lem ),
file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',complementT_lem) ).
thf(f385,plain,
( ( ( in @ ( setminus @ sK22 @ sK24 ) @ ( powerset @ sK22 ) )
!= $true )
| spl25_4 ),
inference(avatar_component_clause,[status(thm)],[f383]) ).
thf(f383,definition,
( spl25_4
<=> ( ( in @ ( setminus @ sK22 @ sK24 ) @ ( powerset @ sK22 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl25_4])],[avatar_definition]) ).
thf(f396,plain,
spl25_3,
inference(avatar_contradiction_clause,[status(thm)],[f395]) ).
thf(f395,plain,
( $false
| spl25_3 ),
inference(subsumption_resolution,[status(thm)],[f394,f120]) ).
thf(f120,plain,
( ( in @ sK23 @ ( powerset @ sK22 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f394,plain,
( ( ( in @ sK23 @ ( powerset @ sK22 ) )
!= $true )
| spl25_3 ),
inference(trivial_inequality_removal,[status(thm)],[f393]) ).
thf(f393,plain,
( ( $true != $true )
| ( ( in @ sK23 @ ( powerset @ sK22 ) )
!= $true )
| spl25_3 ),
inference(superposition,[status(thm)],[f381,f157]) ).
thf(f381,plain,
( ( $true
!= ( in @ ( setminus @ sK22 @ sK23 ) @ ( powerset @ sK22 ) ) )
| spl25_3 ),
inference(avatar_component_clause,[status(thm)],[f379]) ).
thf(f379,definition,
( spl25_3
<=> ( $true
= ( in @ ( setminus @ sK22 @ sK23 ) @ ( powerset @ sK22 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl25_3])],[avatar_definition]) ).
thf(f386,plain,
( ~ spl25_3
| ~ spl25_4
| spl25_2 ),
inference(avatar_split_clause,[status(thm)],[f377,f340,f383,f379]) ).
thf(f340,definition,
( spl25_2
<=> ( ( in @ ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) @ ( powerset @ sK22 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl25_2])],[avatar_definition]) ).
thf(f377,plain,
( ( ( in @ ( setminus @ sK22 @ sK24 ) @ ( powerset @ sK22 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ sK22 @ sK23 ) @ ( powerset @ sK22 ) ) )
| spl25_2 ),
inference(trivial_inequality_removal,[status(thm)],[f375]) ).
thf(f375,plain,
( ( $true != $true )
| ( ( in @ ( setminus @ sK22 @ sK24 ) @ ( powerset @ sK22 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ sK22 @ sK23 ) @ ( powerset @ sK22 ) ) )
| spl25_2 ),
inference(superposition,[status(thm)],[f342,f159]) ).
thf(f159,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) )
= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f89,f114]) ).
thf(f114,plain,
binunionT_lem = $true,
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f89,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) )
= $true )
| ( binunionT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( binunionT_lem = $true )
| ( ( $true
= ( in @ sK6 @ ( powerset @ sK7 ) ) )
& ( ( in @ sK8 @ ( powerset @ sK7 ) )
= $true )
& ( $true
!= ( in @ ( binunion @ sK6 @ sK8 ) @ ( powerset @ sK7 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) )
= $true ) ) )
| ( binunionT_lem != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f48,f50,f49]) ).
thf(f49,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
!= $true ) ) )
=> ( ( $true
= ( in @ sK6 @ ( powerset @ sK7 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK7 ) )
= $true )
& ( ( in @ ( binunion @ sK6 @ X2 ) @ ( powerset @ sK7 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f50,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK7 ) )
= $true )
& ( ( in @ ( binunion @ sK6 @ X2 ) @ ( powerset @ sK7 ) )
!= $true ) )
=> ( ( ( in @ sK8 @ ( powerset @ sK7 ) )
= $true )
& ( $true
!= ( in @ ( binunion @ sK6 @ sK8 ) @ ( powerset @ sK7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,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 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) )
= $true ) ) )
| ( binunionT_lem != $true ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( binunionT_lem = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
| ( binunionT_lem != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( binunionT_lem = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
<=> ( binunionT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',binunionT_lem) ).
thf(f342,plain,
( ( ( in @ ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) @ ( powerset @ sK22 ) )
!= $true )
| spl25_2 ),
inference(avatar_component_clause,[status(thm)],[f340]) ).
thf(f369,plain,
spl25_1,
inference(avatar_contradiction_clause,[status(thm)],[f368]) ).
thf(f368,plain,
( $false
| spl25_1 ),
inference(subsumption_resolution,[status(thm)],[f367,f119]) ).
thf(f367,plain,
( ( ( in @ sK24 @ ( powerset @ sK22 ) )
!= $true )
| spl25_1 ),
inference(subsumption_resolution,[status(thm)],[f366,f120]) ).
thf(f366,plain,
( ( ( in @ sK23 @ ( powerset @ sK22 ) )
!= $true )
| ( ( in @ sK24 @ ( powerset @ sK22 ) )
!= $true )
| spl25_1 ),
inference(trivial_inequality_removal,[status(thm)],[f365]) ).
thf(f365,plain,
( ( ( in @ sK24 @ ( powerset @ sK22 ) )
!= $true )
| ( $true != $true )
| ( ( in @ sK23 @ ( powerset @ sK22 ) )
!= $true )
| spl25_1 ),
inference(superposition,[status(thm)],[f355,f156]) ).
thf(f156,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f111,f113]) ).
thf(f113,plain,
binintersectT_lem = $true,
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f111,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( binintersectT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ( ( ( in @ sK20 @ ( powerset @ sK19 ) )
= $true )
& ( ( in @ ( binintersect @ sK20 @ sK21 ) @ ( powerset @ sK19 ) )
!= $true )
& ( ( in @ sK21 @ ( powerset @ sK19 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21])],[f69,f71,f70]) ).
thf(f70,plain,
( ? [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
& ? [X5: $i] :
( ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
!= $true )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) ) )
=> ( ( ( in @ sK20 @ ( powerset @ sK19 ) )
= $true )
& ? [X5: $i] :
( ( $true
!= ( in @ ( binintersect @ sK20 @ X5 ) @ ( powerset @ sK19 ) ) )
& ( ( in @ X5 @ ( powerset @ sK19 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f71,plain,
( ? [X5: $i] :
( ( $true
!= ( in @ ( binintersect @ sK20 @ X5 ) @ ( powerset @ sK19 ) ) )
& ( ( in @ X5 @ ( powerset @ sK19 ) )
= $true ) )
=> ( ( ( in @ ( binintersect @ sK20 @ sK21 ) @ ( powerset @ sK19 ) )
!= $true )
& ( ( in @ sK21 @ ( powerset @ sK19 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f69,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ? [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
& ? [X5: $i] :
( ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
!= $true )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
<=> ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
<=> ( binintersectT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) )
= binintersectT_lem ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $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.HsoFkBrQ2u/DTF2THF_8599.p',binintersectT_lem) ).
thf(f355,plain,
( ( ( in @ ( binintersect @ sK23 @ sK24 ) @ ( powerset @ sK22 ) )
!= $true )
| spl25_1 ),
inference(trivial_inequality_removal,[status(thm)],[f354]) ).
thf(f354,plain,
( ( $true != $true )
| ( ( in @ ( binintersect @ sK23 @ sK24 ) @ ( powerset @ sK22 ) )
!= $true )
| spl25_1 ),
inference(superposition,[status(thm)],[f338,f157]) ).
thf(f338,plain,
( ( $true
!= ( in @ ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) ) @ ( powerset @ sK22 ) ) )
| spl25_1 ),
inference(avatar_component_clause,[status(thm)],[f336]) ).
thf(f336,definition,
( spl25_1
<=> ( $true
= ( in @ ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) ) @ ( powerset @ sK22 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl25_1])],[avatar_definition]) ).
thf(f343,plain,
( ~ spl25_1
| ~ spl25_2 ),
inference(avatar_split_clause,[status(thm)],[f334,f340,f336]) ).
thf(f334,plain,
( ( $true
!= ( in @ ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) ) @ ( powerset @ sK22 ) ) )
| ( ( in @ ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) @ ( powerset @ sK22 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f333,f120]) ).
thf(f333,plain,
( ( $true
!= ( in @ ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) ) @ ( powerset @ sK22 ) ) )
| ( ( in @ sK23 @ ( powerset @ sK22 ) )
!= $true )
| ( ( in @ ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) @ ( powerset @ sK22 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f328,f119]) ).
thf(f328,plain,
( ( ( in @ sK24 @ ( powerset @ sK22 ) )
!= $true )
| ( ( in @ ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) @ ( powerset @ sK22 ) )
!= $true )
| ( ( in @ sK23 @ ( powerset @ sK22 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) ) @ ( powerset @ sK22 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f287]) ).
thf(f287,plain,
( ( ( in @ sK23 @ ( powerset @ sK22 ) )
!= $true )
| ( ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) )
!= ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) ) )
| ( ( in @ sK24 @ ( powerset @ sK22 ) )
!= $true )
| ( ( in @ ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) @ ( powerset @ sK22 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) ) @ ( powerset @ sK22 ) ) ) ),
inference(superposition,[status(thm)],[f118,f286]) ).
thf(f286,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f283,f239]) ).
thf(f239,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X0 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f238]) ).
thf(f238,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X0 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f232]) ).
thf(f232,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X0 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
| ( $true != $true )
| ( ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X0 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f197,f78]) ).
thf(f78,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $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 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f38,f39]) ).
thf(f39,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
& ( $true
= ( in @ X4 @ X1 ) )
& ( ( in @ X4 @ X2 )
= $true ) )
=> ( ( ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X0 )
!= $true )
& ( ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
& ( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
& ( $true
= ( in @ X4 @ X1 ) )
& ( ( in @ X4 @ X2 )
= $true ) )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( $true
= ( sP0 @ X1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
& ( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( $true
!= ( sP0 @ X1 @ X0 @ X2 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sP0 @ X1 @ X0 @ X2 ) )
<=> ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f197,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK1 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) @ X0 )
!= $true )
| ( $true
!= ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f196]) ).
thf(f196,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK1 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) @ X0 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f192]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK1 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) @ X0 )
!= $true )
| ( $true
!= ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f177,f77]) ).
thf(f77,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ ( sK1 @ X0 @ X1 @ ( binunion @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ ( setminus @ X2 @ ( binintersect @ X3 @ X4 ) ) ) )
| ( ( sP0 @ X0 @ X1 @ ( binunion @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) )
!= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
!= ( in @ ( sK1 @ X0 @ X1 @ ( binunion @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ X2 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f173]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ ( sK1 @ X0 @ X1 @ ( binunion @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ X2 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X2 ) ) )
| ( $true
!= ( in @ ( sK1 @ X0 @ X1 @ ( binunion @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ ( setminus @ X2 @ ( binintersect @ X3 @ X4 ) ) ) )
| ( $true != $true )
| ( ( sP0 @ X0 @ X1 @ ( binunion @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) )
!= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f79,f158]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f98,f116]) ).
thf(f116,plain,
demorgan1a = $true,
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( demorgan1a != $true ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( demorgan1a != $true ) )
& ( ( demorgan1a = $true )
| ( ( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) )
& ( ( in @ sK12 @ ( binunion @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) )
!= $true )
& ( $true
= ( in @ sK12 @ sK10 ) )
& ( ( in @ sK12 @ ( setminus @ sK10 @ ( binintersect @ sK9 @ sK11 ) ) )
= $true )
& ( $true
= ( in @ sK11 @ ( powerset @ sK10 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f53,f56,f55,f54]) ).
thf(f54,plain,
( ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ ( binunion @ ( setminus @ X5 @ X4 ) @ ( setminus @ X5 @ X6 ) ) ) )
& ( $true
= ( in @ X7 @ X5 ) )
& ( ( in @ X7 @ ( setminus @ X5 @ ( binintersect @ X4 @ X6 ) ) )
= $true ) )
& ( ( in @ X6 @ ( powerset @ X5 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ ( binunion @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ X6 ) ) ) )
& ( $true
= ( in @ X7 @ sK10 ) )
& ( $true
= ( in @ X7 @ ( setminus @ sK10 @ ( binintersect @ sK9 @ X6 ) ) ) ) )
& ( ( in @ X6 @ ( powerset @ sK10 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f55,plain,
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ ( binunion @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ X6 ) ) ) )
& ( $true
= ( in @ X7 @ sK10 ) )
& ( $true
= ( in @ X7 @ ( setminus @ sK10 @ ( binintersect @ sK9 @ X6 ) ) ) ) )
& ( ( in @ X6 @ ( powerset @ sK10 ) )
= $true ) )
=> ( ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) )
!= $true )
& ( $true
= ( in @ X7 @ sK10 ) )
& ( ( in @ X7 @ ( setminus @ sK10 @ ( binintersect @ sK9 @ sK11 ) ) )
= $true ) )
& ( $true
= ( in @ sK11 @ ( powerset @ sK10 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f56,plain,
( ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) )
!= $true )
& ( $true
= ( in @ X7 @ sK10 ) )
& ( ( in @ X7 @ ( setminus @ sK10 @ ( binintersect @ sK9 @ sK11 ) ) )
= $true ) )
=> ( ( ( in @ sK12 @ ( binunion @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) )
!= $true )
& ( $true
= ( in @ sK12 @ sK10 ) )
& ( ( in @ sK12 @ ( setminus @ sK10 @ ( binintersect @ sK9 @ sK11 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f53,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( demorgan1a != $true ) )
& ( ( demorgan1a = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ ( binunion @ ( setminus @ X5 @ X4 ) @ ( setminus @ X5 @ X6 ) ) ) )
& ( $true
= ( in @ X7 @ X5 ) )
& ( ( in @ X7 @ ( setminus @ X5 @ ( binintersect @ X4 @ X6 ) ) )
= $true ) )
& ( ( in @ X6 @ ( powerset @ X5 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( demorgan1a != $true ) )
& ( ( demorgan1a = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
<=> ( demorgan1a = $true ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ( demorgan1a = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( demorgan1a = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) )
= demorgan1a ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) )
= demorgan1a ),
file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',demorgan1a) ).
thf(f79,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X0 )
!= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f283,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X0 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f282]) ).
thf(f282,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X0 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f278]) ).
thf(f278,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X0 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X0 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
| ( ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f219,f153]) ).
thf(f153,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( X0 = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f86,f115]) ).
thf(f115,plain,
setextT = $true,
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f86,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( X0 = X2 )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( setextT != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
& ( $true
!= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 ) )
& ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 )
= $true ) )
| ( X0 = X2 )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( setextT != $true ) )
& ( ( setextT = $true )
| ( ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ sK5 ) )
| ( ( in @ X7 @ sK3 )
= $true )
| ( ( in @ X7 @ sK4 )
!= $true ) )
& ( sK5 != sK3 )
& ( $true
!= ( sP0 @ sK3 @ sK4 @ sK5 ) )
& ( $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 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
=> ( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
& ( $true
!= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 ) )
& ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( ( in @ X7 @ X4 )
= $true )
| ( $true
!= ( in @ X7 @ X5 ) ) )
& ( X4 != X6 )
& ( $true
!= ( sP0 @ X4 @ X5 @ X6 ) ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) )
=> ( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ sK4 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( ( in @ X7 @ sK3 )
= $true )
| ( ( in @ X7 @ sK4 )
!= $true ) )
& ( sK3 != X6 )
& ( ( sP0 @ sK3 @ sK4 @ X6 )
!= $true ) )
& ( $true
= ( in @ sK3 @ ( powerset @ sK4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ sK4 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( ( in @ X7 @ sK3 )
= $true )
| ( ( in @ X7 @ sK4 )
!= $true ) )
& ( sK3 != X6 )
& ( ( sP0 @ sK3 @ sK4 @ X6 )
!= $true ) )
=> ( ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ sK5 ) )
| ( ( in @ X7 @ sK3 )
= $true )
| ( ( in @ X7 @ sK4 )
!= $true ) )
& ( sK5 != sK3 )
& ( $true
!= ( sP0 @ sK3 @ sK4 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( X0 = X2 )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( setextT != $true ) )
& ( ( setextT = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( ( in @ X7 @ X4 )
= $true )
| ( $true
!= ( in @ X7 @ X5 ) ) )
& ( X4 != X6 )
& ( $true
!= ( sP0 @ X4 @ X5 @ X6 ) ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ? [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
& ( $true
!= ( in @ X4 @ X1 ) )
& ( ( in @ X4 @ X0 )
= $true ) )
| ( X1 = X2 )
| ( $true
= ( sP0 @ X1 @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( setextT != $true ) )
& ( ( setextT = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ X2 )
!= $true )
| ( $true
= ( in @ X4 @ X1 ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( X1 != X2 )
& ( $true
!= ( sP0 @ X1 @ X0 @ X2 ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ? [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
& ( $true
!= ( in @ X4 @ X1 ) )
& ( ( in @ X4 @ X0 )
= $true ) )
| ( X1 = X2 )
| ( $true
= ( sP0 @ X1 @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( setextT = $true ) ),
inference(definition_folding,[status(thm)],[f30,f35]) ).
thf(f30,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ? [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
& ( $true
!= ( in @ X4 @ X1 ) )
& ( ( in @ X4 @ X0 )
= $true ) )
| ( X1 = X2 )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( setextT = $true ) ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( X1 = X2 )
| ? [X4: $i] :
( ( $true
!= ( in @ X4 @ X1 ) )
& ( ( in @ X4 @ X2 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( setextT = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,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 @ X1 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ X4 @ X2 )
= $true )
=> ( $true
= ( in @ X4 @ X1 ) ) ) )
=> ( X1 = X2 ) ) ) ) )
<=> ( setextT = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( setextT
= ( ! [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 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( setextT
= ( ! [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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',setextT) ).
thf(f219,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) @ X0 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
= ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f218]) ).
thf(f218,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK2 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) @ X0 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( $true
= ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f217]) ).
thf(f217,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
| ( $true
!= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ ( sK2 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) @ X0 )
!= $true )
| ( $true
= ( sP0 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f152,f171]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( sK2 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( $true
!= ( in @ ( sK2 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true )
| ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= X4 )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( sP0 @ X4 @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
| ( $true
!= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ ( sK2 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true )
| ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= X4 )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK2 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ X3 @ X4 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( sP0 @ X4 @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
| ( $true != $true )
| ( $true
!= ( in @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( powerset @ X3 ) ) ) ),
inference(superposition,[status(thm)],[f155,f154]) ).
thf(f154,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) )
| ( $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] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true != $true )
| ( X0 = X2 ) ),
inference(definition_unfolding,[status(thm)],[f88,f115]) ).
thf(f88,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
| ( X0 = X2 )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( setextT != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f155,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( binunion @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f147]) ).
thf(f147,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ ( binunion @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true )
| ( $true != $true )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f102,f117]) ).
thf(f117,plain,
demorgan1b = $true,
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f102,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binunion @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( demorgan1b != $true ) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( demorgan1b = $true )
| ( ( ( in @ sK18 @ ( setminus @ sK15 @ ( binintersect @ sK16 @ sK17 ) ) )
!= $true )
& ( ( in @ sK18 @ sK15 )
= $true )
& ( $true
= ( in @ sK18 @ ( binunion @ ( setminus @ sK15 @ sK16 ) @ ( setminus @ sK15 @ sK17 ) ) ) )
& ( $true
= ( in @ sK17 @ ( powerset @ sK15 ) ) )
& ( $true
= ( in @ sK16 @ ( powerset @ sK15 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binunion @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( demorgan1b != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18])],[f63,f66,f65,f64]) ).
thf(f64,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK15 @ ( binintersect @ sK16 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ sK15 )
= $true )
& ( $true
= ( in @ X3 @ ( binunion @ ( setminus @ sK15 @ sK16 ) @ ( setminus @ sK15 @ X2 ) ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK15 ) ) ) )
& ( $true
= ( in @ sK16 @ ( powerset @ sK15 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f65,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK15 @ ( binintersect @ sK16 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ sK15 )
= $true )
& ( $true
= ( in @ X3 @ ( binunion @ ( setminus @ sK15 @ sK16 ) @ ( setminus @ sK15 @ X2 ) ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK15 ) ) ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK15 @ ( binintersect @ sK16 @ sK17 ) ) )
!= $true )
& ( ( in @ X3 @ sK15 )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ sK15 @ sK16 ) @ ( setminus @ sK15 @ sK17 ) ) )
= $true ) )
& ( $true
= ( in @ sK17 @ ( powerset @ sK15 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f66,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK15 @ ( binintersect @ sK16 @ sK17 ) ) )
!= $true )
& ( ( in @ X3 @ sK15 )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ sK15 @ sK16 ) @ ( setminus @ sK15 @ sK17 ) ) )
= $true ) )
=> ( ( ( in @ sK18 @ ( setminus @ sK15 @ ( binintersect @ sK16 @ sK17 ) ) )
!= $true )
& ( ( in @ sK18 @ sK15 )
= $true )
& ( $true
= ( in @ sK18 @ ( binunion @ ( setminus @ sK15 @ sK16 ) @ ( setminus @ sK15 @ sK17 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f63,plain,
( ( ( demorgan1b = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binunion @ ( setminus @ X4 @ X5 ) @ ( setminus @ X4 @ X6 ) ) )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( demorgan1b != $true ) ) ),
inference(rectify,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( demorgan1b = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( demorgan1b != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( demorgan1b = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( demorgan1b = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true ) ) ) ) )
<=> ( demorgan1b = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( demorgan1b
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( demorgan1b
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',demorgan1b) ).
thf(f152,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 ) )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( X0 = X2 )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( X0 = X2 )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f87,f115]) ).
thf(f87,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 ) )
| ( X0 = X2 )
| ( $true
= ( sP0 @ X0 @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( setextT != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f118,plain,
( ( setminus @ sK22 @ ( binintersect @ sK23 @ sK24 ) )
!= ( binunion @ ( setminus @ sK22 @ sK23 ) @ ( setminus @ sK22 @ sK24 ) ) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU753^2 : 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
% 0.17/0.34 % Computer : n013.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:32:53 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU753^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.28/0.46 % Version : Especial > Reduced > Especial.
% 0.28/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.28/0.46 % setminus A (binintersect X Y) = binunion (setminus A X) (setminus A Y)))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC255l [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % 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, 0.43 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
% 0.28/0.46 % Syntax : Number of formulae : 18 ( 6 unt; 11 typ; 6 def)
% 0.28/0.46 % Number of atoms : 48 ( 8 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 9 ( 6 avg)
% 0.28/0.46 % Number of connectives : 137 ( 0 ~; 0 |; 0 &; 108 @)
% 0.28/0.46 % ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 14 ( 3 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 12 ( 11 usr; 6 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=314
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(powerset_type,type,
% 0.28/0.46 powerset: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(binunion_type,type,
% 0.28/0.46 binunion: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(binintersect_type,type,
% 0.28/0.46 binintersect: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setminus_type,type,
% 0.28/0.46 setminus: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectT_lem_type,type,
% 0.28/0.46 binintersectT_lem: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectT_lem,definition,
% 0.28/0.46 ( binintersectT_lem
% 0.28/0.46 = ( ! [A: $i,X: $i] :
% 0.28/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.46 => ! [Y: $i] :
% 0.28/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binunionT_lem_type,type,
% 0.28/0.46 binunionT_lem: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binunionT_lem,definition,
% 0.28/0.46 ( binunionT_lem
% 0.28/0.46 = ( ! [A: $i,X: $i] :
% 0.28/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.46 => ! [Y: $i] :
% 0.28/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.46 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(complementT_lem_type,type,
% 0.28/0.46 complementT_lem: $o ).
% 0.28/0.46
% 0.28/0.46 thf(complementT_lem,definition,
% 0.28/0.46 ( complementT_lem
% 0.28/0.46 = ( ! [A: $i,X: $i] :
% 0.28/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setextT_type,type,
% 0.28/0.46 setextT: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setextT,definition,
% 0.28/0.46 ( setextT
% 0.28/0.46 = ( ! [A: $i,X: $i] :
% 0.28/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.46 => ! [Y: $i] :
% 0.28/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( in @ Xx @ X )
% 0.28/0.46 => ( in @ Xx @ Y ) ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( in @ Xx @ Y )
% 0.28/0.46 => ( in @ Xx @ X ) ) )
% 0.28/0.46 => ( X = Y ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(demorgan1a_type,type,
% 0.28/0.46 demorgan1a: $o ).
% 0.28/0.46
% 0.28/0.46 thf(demorgan1a,definition,
% 0.28/0.46 ( demorgan1a
% 0.28/0.46 = ( ! [A: $i,X: $i] :
% 0.28/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.46 => ! [Y: $i] :
% 0.28/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.28/0.46 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(demorgan1b_type,type,
% 0.28/0.46 demorgan1b: $o ).
% 0.28/0.46
% 0.28/0.46 thf(demorgan1b,definition,
% 0.28/0.46 ( demorgan1b
% 0.28/0.46 = ( ! [A: $i,X: $i] :
% 0.28/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.46 => ! [Y: $i] :
% 0.28/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.28/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(demorgan1,conjecture,
% 0.28/0.46 ( binintersectT_lem
% 0.28/0.46 => ( binunionT_lem
% 0.28/0.46 => ( complementT_lem
% 0.28/0.46 => ( setextT
% 0.28/0.46 => ( demorgan1a
% 0.28/0.46 => ( demorgan1b
% 0.28/0.46 => ! [A: $i,X: $i] :
% 0.28/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.46 => ! [Y: $i] :
% 0.28/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.46 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.28/0.46 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.70/1.32 ---- Embedded in THF ---
% 1.70/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.33 %%% Generated on Tue Feb 24 12:32:54 EST 2026
% 1.70/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.33 %%% Logic specification used:
% 1.70/1.33 %%% thf(spec, logic, $$dhol).
% 1.70/1.33
% 1.70/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2DTF8599.p
% See solution above
% 1.70/1.33 ------------------------
% 1.70/1.34 ---- Cleaned THF ---
% 1.70/1.34 thf(in_type,type,
% 1.70/1.34 in: $i > $i > $o ).
% 1.70/1.34
% 1.70/1.34 thf(powerset_type,type,
% 1.70/1.34 powerset: $i > $i ).
% 1.70/1.34
% 1.70/1.34 thf(binunion_type,type,
% 1.70/1.34 binunion: $i > $i > $i ).
% 1.70/1.34
% 1.70/1.34 thf(binintersect_type,type,
% 1.70/1.34 binintersect: $i > $i > $i ).
% 1.70/1.34
% 1.70/1.34 thf(setminus_type,type,
% 1.70/1.34 setminus: $i > $i > $i ).
% 1.70/1.34
% 1.70/1.34 thf(binintersectT_lem_type,type,
% 1.70/1.34 binintersectT_lem: $o ).
% 1.70/1.34
% 1.70/1.34 thf(binintersectT_lem,definition,
% 1.70/1.34 ( binintersectT_lem
% 1.70/1.34 = ( ! [A: $i,X: $i] :
% 1.70/1.34 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.34 => ! [Y: $i] :
% 1.70/1.34 ( ( in @ Y @ ( powerset @ A ) )
% 1.70/1.34 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.70/1.34
% 1.70/1.34 thf(binunionT_lem_type,type,
% 1.70/1.34 binunionT_lem: $o ).
% 1.70/1.34
% 1.70/1.34 thf(binunionT_lem,definition,
% 1.70/1.34 ( binunionT_lem
% 1.70/1.34 = ( ! [A: $i,X: $i] :
% 1.70/1.34 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.34 => ! [Y: $i] :
% 1.70/1.34 ( ( in @ Y @ ( powerset @ A ) )
% 1.70/1.34 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.70/1.34
% 1.70/1.34 thf(complementT_lem_type,type,
% 1.70/1.34 complementT_lem: $o ).
% 1.70/1.34
% 1.70/1.34 thf(complementT_lem,definition,
% 1.70/1.34 ( complementT_lem
% 1.70/1.34 = ( ! [A: $i,X: $i] :
% 1.70/1.34 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.34 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.70/1.34
% 1.70/1.34 thf(setextT_type,type,
% 1.70/1.34 setextT: $o ).
% 1.70/1.34
% 1.70/1.34 thf(setextT,definition,
% 1.70/1.34 ( setextT
% 1.70/1.34 = ( ! [A: $i,X: $i] :
% 1.70/1.34 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.34 => ! [Y: $i] :
% 1.70/1.34 ( ( in @ Y @ ( powerset @ A ) )
% 1.70/1.34 => ( ! [Xx: $i] :
% 1.70/1.34 ( ( in @ Xx @ A )
% 1.70/1.34 => ( ( in @ Xx @ X )
% 1.70/1.34 => ( in @ Xx @ Y ) ) )
% 1.70/1.34 => ( ! [Xx: $i] :
% 1.70/1.34 ( ( in @ Xx @ A )
% 1.70/1.34 => ( ( in @ Xx @ Y )
% 1.70/1.34 => ( in @ Xx @ X ) ) )
% 1.70/1.34 => ( X = Y ) ) ) ) ) ) ) ).
% 1.70/1.34
% 1.70/1.34 thf(demorgan1a_type,type,
% 1.70/1.34 demorgan1a: $o ).
% 1.70/1.34
% 1.70/1.34 thf(demorgan1a,definition,
% 1.70/1.34 ( demorgan1a
% 1.70/1.34 = ( ! [A: $i,X: $i] :
% 1.70/1.34 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.34 => ! [Y: $i] :
% 1.70/1.34 ( ( in @ Y @ ( powerset @ A ) )
% 1.70/1.34 => ! [Xx: $i] :
% 1.70/1.34 ( ( in @ Xx @ A )
% 1.70/1.34 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 1.70/1.34 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 1.70/1.34
% 1.70/1.34 thf(demorgan1b_type,type,
% 1.70/1.34 demorgan1b: $o ).
% 1.70/1.34
% 1.70/1.34 thf(demorgan1b,definition,
% 1.70/1.34 ( demorgan1b
% 1.70/1.34 = ( ! [A: $i,X: $i] :
% 1.70/1.34 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.34 => ! [Y: $i] :
% 1.70/1.34 ( ( in @ Y @ ( powerset @ A ) )
% 1.70/1.34 => ! [Xx: $i] :
% 1.70/1.34 ( ( in @ Xx @ A )
% 1.70/1.34 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 1.70/1.34 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 1.70/1.34
% 1.70/1.34 thf(demorgan1,conjecture,
% 1.70/1.34 ( binintersectT_lem
% 1.70/1.34 => ( binunionT_lem
% 1.70/1.34 => ( complementT_lem
% 1.70/1.34 => ( setextT
% 1.70/1.34 => ( demorgan1a
% 1.70/1.34 => ( demorgan1b
% 1.70/1.34 => ! [A: $i,X: $i] :
% 1.70/1.34 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.34 => ! [Y: $i] :
% 1.70/1.34 ( ( in @ Y @ ( powerset @ A ) )
% 1.70/1.34 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 1.70/1.34 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 1.70/1.34 ------------------------
% 1.70/1.35 % (8791)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/183Mi)
% 1.70/1.35 % (8793)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_8599 for (2999ds/27Mi)
% 1.70/1.36 % (8797)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/18Mi)
% 1.70/1.36 % (8792)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_8599 for (2999ds/4Mi)
% 1.70/1.36 % (8795)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_8599 for (2999ds/2Mi)
% 1.70/1.36 % (8794)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/2Mi)
% 1.70/1.36 % (8792)Instruction limit reached!
% 1.70/1.36 % (8792)------------------------------
% 1.70/1.36 % (8792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (8792)Termination reason: Unknown
% 1.70/1.36 % (8792)Termination phase: Preprocessing 3
% 1.70/1.36
% 1.70/1.36 % (8792)Memory used [KB]: 1023
% 1.70/1.36 % (8792)Time elapsed: 0.003 s
% 1.70/1.36 % (8792)Instructions burned: 4 (million)
% 1.70/1.36 % (8792)------------------------------
% 1.70/1.36 % (8792)------------------------------
% 1.70/1.36 % (8795)Instruction limit reached!
% 1.70/1.36 % (8795)------------------------------
% 1.70/1.36 % (8795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (8795)Termination reason: Unknown
% 1.70/1.36 % (8795)Termination phase: Property scanning
% 1.70/1.36
% 1.70/1.36 % (8795)Memory used [KB]: 1023
% 1.70/1.36 % (8795)Time elapsed: 0.003 s
% 1.70/1.36 % (8795)Instructions burned: 3 (million)
% 1.70/1.36 % (8795)------------------------------
% 1.70/1.36 % (8795)------------------------------
% 1.70/1.36 % (8794)Instruction limit reached!
% 1.70/1.36 % (8794)------------------------------
% 1.70/1.36 % (8794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (8794)Termination reason: Unknown
% 1.70/1.36 % (8794)Termination phase: Property scanning
% 1.70/1.36
% 1.70/1.36 % (8794)Memory used [KB]: 1023
% 1.70/1.36 % (8794)Time elapsed: 0.004 s
% 1.70/1.36 % (8794)Instructions burned: 3 (million)
% 1.70/1.36 % (8794)------------------------------
% 1.70/1.36 % (8794)------------------------------
% 1.70/1.36 % (8793)Instruction limit reached!
% 1.70/1.36 % (8793)------------------------------
% 1.70/1.36 % (8793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (8793)Termination reason: Unknown
% 1.70/1.36 % (8793)Termination phase: Saturation
% 1.70/1.36
% 1.70/1.36 % (8793)Memory used [KB]: 5628
% 1.70/1.36 % (8793)Time elapsed: 0.011 s
% 1.70/1.36 % (8793)Instructions burned: 29 (million)
% 1.70/1.36 % (8793)------------------------------
% 1.70/1.36 % (8793)------------------------------
% 1.70/1.37 % (8796)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_8599 for (2999ds/275Mi)
% 1.70/1.37 % (8797)Instruction limit reached!
% 1.70/1.37 % (8797)------------------------------
% 1.70/1.37 % (8797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (8797)Termination reason: Unknown
% 1.70/1.37 % (8797)Termination phase: Saturation
% 1.70/1.37
% 1.70/1.37 % (8797)Memory used [KB]: 5628
% 1.70/1.37 % (8797)Time elapsed: 0.011 s
% 1.70/1.37 % (8797)Instructions burned: 18 (million)
% 1.70/1.37 % (8797)------------------------------
% 1.70/1.37 % (8797)------------------------------
% 1.70/1.37 % (8798)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/3Mi)
% 1.70/1.37 % (8801)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_8599 for (2999ds/3Mi)
% 1.70/1.37 % (8798)Instruction limit reached!
% 1.70/1.37 % (8798)------------------------------
% 1.70/1.37 % (8798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (8798)Termination reason: Unknown
% 1.70/1.37 % (8798)Termination phase: Property scanning
% 1.70/1.37
% 1.70/1.37 % (8798)Memory used [KB]: 1023
% 1.70/1.37 % (8798)Time elapsed: 0.003 s
% 1.70/1.37 % (8798)Instructions burned: 3 (million)
% 1.70/1.37 % (8798)------------------------------
% 1.70/1.37 % (8798)------------------------------
% 1.70/1.38 % (8801)Instruction limit reached!
% 1.70/1.38 % (8801)------------------------------
% 1.70/1.38 % (8801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (8801)Termination reason: Unknown
% 1.70/1.38 % (8801)Termination phase: Preprocessing 3
% 1.70/1.38
% 1.70/1.38 % (8801)Memory used [KB]: 1023
% 1.70/1.38 % (8801)Time elapsed: 0.003 s
% 1.70/1.38 % (8801)Instructions burned: 4 (million)
% 1.70/1.38 % (8801)------------------------------
% 1.70/1.38 % (8801)------------------------------
% 1.70/1.38 % (8799)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_8599 for (2999ds/37Mi)
% 1.70/1.38 % (8800)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_8599 for (2999ds/15Mi)
% 1.70/1.38 % (8802)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_8599 for (2999ds/1041Mi)
% 1.70/1.39 % (8803)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/7Mi)
% 1.70/1.39 % (8804)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/16Mi)
% 1.70/1.39 % (8800)Instruction limit reached!
% 1.70/1.39 % (8800)------------------------------
% 1.70/1.39 % (8800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (8800)Termination reason: Unknown
% 1.70/1.39 % (8800)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (8800)Memory used [KB]: 5628
% 1.70/1.39 % (8800)Time elapsed: 0.010 s
% 1.70/1.39 % (8800)Instructions burned: 15 (million)
% 1.70/1.39 % (8800)------------------------------
% 1.70/1.39 % (8800)------------------------------
% 1.70/1.39 % (8803)Instruction limit reached!
% 1.70/1.39 % (8803)------------------------------
% 1.70/1.39 % (8803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (8803)Termination reason: Unknown
% 1.70/1.39 % (8803)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (8803)Memory used [KB]: 1023
% 1.70/1.39 % (8803)Time elapsed: 0.004 s
% 1.70/1.39 % (8803)Instructions burned: 9 (million)
% 1.70/1.39 % (8803)------------------------------
% 1.70/1.39 % (8803)------------------------------
% 1.70/1.39 % (8804)Instruction limit reached!
% 1.70/1.39 % (8804)------------------------------
% 1.70/1.39 % (8804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (8804)Termination reason: Unknown
% 1.70/1.39 % (8804)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (8804)Memory used [KB]: 5884
% 1.70/1.39 % (8804)Time elapsed: 0.008 s
% 1.70/1.39 % (8804)Instructions burned: 18 (million)
% 1.70/1.39 % (8804)------------------------------
% 1.70/1.39 % (8804)------------------------------
% 1.70/1.39 % (8799)Instruction limit reached!
% 1.70/1.39 % (8799)------------------------------
% 1.70/1.39 % (8799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (8799)Termination reason: Unknown
% 1.70/1.39 % (8799)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (8799)Memory used [KB]: 5628
% 1.70/1.39 % (8799)Time elapsed: 0.019 s
% 1.70/1.39 % (8799)Instructions burned: 37 (million)
% 1.70/1.39 % (8799)------------------------------
% 1.70/1.39 % (8799)------------------------------
% 1.77/1.40 % (8805)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_8599 for (2999ds/3Mi)
% 1.77/1.40 % (8807)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/7Mi)
% 1.77/1.40 % (8805)Instruction limit reached!
% 1.77/1.40 % (8805)------------------------------
% 1.77/1.40 % (8805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.40 % (8805)Termination reason: Unknown
% 1.77/1.40 % (8805)Termination phase: Preprocessing 3
% 1.77/1.40
% 1.77/1.40 % (8805)Memory used [KB]: 1023
% 1.77/1.40 % (8805)Time elapsed: 0.003 s
% 1.77/1.40 % (8805)Instructions burned: 4 (million)
% 1.77/1.40 % (8805)------------------------------
% 1.77/1.40 % (8805)------------------------------
% 1.77/1.40 % (8806)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_8599 for (2999ds/3Mi)
% 1.77/1.40 % (8807)Instruction limit reached!
% 1.77/1.40 % (8807)------------------------------
% 1.77/1.40 % (8807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.40 % (8807)Termination reason: Unknown
% 1.77/1.40 % (8807)Termination phase: Saturation
% 1.77/1.40
% 1.77/1.40 % (8807)Memory used [KB]: 5500
% 1.77/1.40 % (8807)Time elapsed: 0.004 s
% 1.77/1.40 % (8807)Instructions burned: 7 (million)
% 1.77/1.40 % (8807)------------------------------
% 1.77/1.40 % (8807)------------------------------
% 1.77/1.41 % (8806)Instruction limit reached!
% 1.77/1.41 % (8806)------------------------------
% 1.77/1.41 % (8806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.41 % (8806)Termination reason: Unknown
% 1.77/1.41 % (8806)Termination phase: Property scanning
% 1.77/1.41
% 1.77/1.41 % (8806)Memory used [KB]: 1023
% 1.77/1.41 % (8806)Time elapsed: 0.004 s
% 1.77/1.41 % (8806)Instructions burned: 4 (million)
% 1.77/1.41 % (8806)------------------------------
% 1.77/1.41 % (8806)------------------------------
% 1.77/1.41 % (8808)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/3Mi)
% 1.77/1.41 % (8808)Instruction limit reached!
% 1.77/1.41 % (8808)------------------------------
% 1.77/1.41 % (8808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.41 % (8808)Termination reason: Unknown
% 1.77/1.41 % (8808)Termination phase: Property scanning
% 1.77/1.41
% 1.77/1.41 % (8808)Memory used [KB]: 1023
% 1.77/1.41 % (8808)Time elapsed: 0.003 s
% 1.77/1.41 % (8808)Instructions burned: 5 (million)
% 1.77/1.41 % (8808)------------------------------
% 1.77/1.41 % (8808)------------------------------
% 1.77/1.41 % (8791)Instruction limit reached!
% 1.77/1.41 % (8791)------------------------------
% 1.77/1.41 % (8791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.41 % (8791)Termination reason: Unknown
% 1.77/1.41 % (8791)Termination phase: Saturation
% 1.77/1.41
% 1.77/1.41 % (8791)Memory used [KB]: 6140
% 1.77/1.41 % (8791)Time elapsed: 0.059 s
% 1.77/1.41 % (8791)Instructions burned: 185 (million)
% 1.77/1.41 % (8791)------------------------------
% 1.77/1.41 % (8791)------------------------------
% 1.77/1.41 % (8810)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/18Mi)
% 1.77/1.42 % (8812)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/6Mi)
% 1.77/1.42 % (8809)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/4Mi)
% 1.77/1.42 % (8812)Instruction limit reached!
% 1.77/1.42 % (8812)------------------------------
% 1.77/1.42 % (8812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.42 % (8812)Termination reason: Unknown
% 1.77/1.42 % (8812)Termination phase: Saturation
% 1.77/1.42
% 1.77/1.42 % (8812)Memory used [KB]: 5500
% 1.77/1.42 % (8812)Time elapsed: 0.003 s
% 1.77/1.42 % (8812)Instructions burned: 7 (million)
% 1.77/1.42 % (8812)------------------------------
% 1.77/1.42 % (8812)------------------------------
% 1.77/1.42 % (8810)Instruction limit reached!
% 1.77/1.42 % (8810)------------------------------
% 1.77/1.42 % (8810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.42 % (8810)Termination reason: Unknown
% 1.77/1.42 % (8810)Termination phase: Saturation
% 1.77/1.42
% 1.77/1.42 % (8810)Memory used [KB]: 5628
% 1.77/1.42 % (8810)Time elapsed: 0.008 s
% 1.77/1.42 % (8810)Instructions burned: 18 (million)
% 1.77/1.42 % (8810)------------------------------
% 1.77/1.42 % (8810)------------------------------
% 1.77/1.42 % (8809)Instruction limit reached!
% 1.77/1.42 % (8809)------------------------------
% 1.77/1.42 % (8809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.42 % (8809)Termination reason: Unknown
% 1.77/1.42 % (8809)Termination phase: Property scanning
% 1.77/1.42
% 1.77/1.42 % (8809)Memory used [KB]: 1023
% 1.77/1.42 % (8809)Time elapsed: 0.003 s
% 1.77/1.42 % (8809)Instructions burned: 5 (million)
% 1.77/1.42 % (8809)------------------------------
% 1.77/1.42 % (8809)------------------------------
% 1.77/1.42 % (8813)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_8599 for (2999ds/902Mi)
% 1.77/1.42 % (8811)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/710Mi)
% 1.77/1.42 % (8813)Refutation not found, incomplete strategy
% 1.77/1.42 % (8813)------------------------------
% 1.77/1.42 % (8813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.42 % (8813)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.42
% 1.77/1.42
% 1.77/1.42 % (8813)Memory used [KB]: 5628
% 1.77/1.42 % (8813)Time elapsed: 0.005 s
% 1.77/1.42 % (8813)Instructions burned: 9 (million)
% 1.77/1.42 % (8813)------------------------------
% 1.77/1.42 % (8813)------------------------------
% 1.77/1.43 % (8814)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_8599 for (2999ds/21Mi)
% 1.77/1.43 % (8815)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/5Mi)
% 1.77/1.43 % (8815)Instruction limit reached!
% 1.77/1.43 % (8815)------------------------------
% 1.77/1.43 % (8815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.43 % (8815)Termination reason: Unknown
% 1.77/1.43 % (8815)Termination phase: Saturation
% 1.77/1.43
% 1.77/1.43 % (8815)Memory used [KB]: 5500
% 1.77/1.43 % (8815)Time elapsed: 0.004 s
% 1.77/1.43 % (8815)Instructions burned: 7 (million)
% 1.77/1.43 % (8815)------------------------------
% 1.77/1.43 % (8815)------------------------------
% 1.77/1.43 % (8817)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/377Mi)
% 1.77/1.44 % (8814)Instruction limit reached!
% 1.77/1.44 % (8814)------------------------------
% 1.77/1.44 % (8814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.44 % (8814)Termination reason: Unknown
% 1.77/1.44 % (8814)Termination phase: Saturation
% 1.77/1.44
% 1.77/1.44 % (8814)Memory used [KB]: 5628
% 1.77/1.44 % (8814)Time elapsed: 0.008 s
% 1.77/1.44 % (8814)Instructions burned: 22 (million)
% 1.77/1.44 % (8814)------------------------------
% 1.77/1.44 % (8814)------------------------------
% 1.77/1.44 % (8816)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/6Mi)
% 1.77/1.44 % (8816)Instruction limit reached!
% 1.77/1.44 % (8816)------------------------------
% 1.77/1.44 % (8816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.44 % (8816)Termination reason: Unknown
% 1.77/1.44 % (8816)Termination phase: Function definition elimination
% 1.77/1.44
% 1.77/1.44 % (8816)Memory used [KB]: 1023
% 1.77/1.44 % (8816)Time elapsed: 0.004 s
% 1.77/1.44 % (8816)Instructions burned: 6 (million)
% 1.77/1.44 % (8816)------------------------------
% 1.77/1.44 % (8816)------------------------------
% 1.77/1.44 % (8818)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/779Mi)
% 1.77/1.45 % (8819)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/19Mi)
% 1.77/1.45 % (8819)Instruction limit reached!
% 1.77/1.45 % (8819)------------------------------
% 1.77/1.45 % (8819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.45 % (8819)Termination reason: Unknown
% 1.77/1.45 % (8819)Termination phase: Saturation
% 1.77/1.45
% 1.77/1.45 % (8819)Memory used [KB]: 5500
% 1.77/1.45 % (8819)Time elapsed: 0.006 s
% 1.77/1.45 % (8819)Instructions burned: 19 (million)
% 1.77/1.45 % (8819)------------------------------
% 1.77/1.45 % (8819)------------------------------
% 1.77/1.46 % (8820)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/879Mi)
% 1.77/1.46 % (8821)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8599 for (2999ds/17Mi)
% 1.77/1.46 % (8796)First to succeed.
% 1.77/1.47 % (8821)Instruction limit reached!
% 1.77/1.47 % (8821)------------------------------
% 1.77/1.47 % (8821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.47 % (8821)Termination reason: Unknown
% 1.77/1.47 % (8821)Termination phase: Saturation
% 1.77/1.47
% 1.77/1.47 % (8821)Memory used [KB]: 5628
% 1.77/1.47 % (8821)Time elapsed: 0.006 s
% 1.77/1.47 % (8821)Instructions burned: 17 (million)
% 1.77/1.47 % (8821)------------------------------
% 1.77/1.47 % (8821)------------------------------
% 1.77/1.47 % (8796)Refutation found. Thanks to Tanya!
% 1.77/1.47 % SZS status Theorem for DTF2THF_8599
% 1.77/1.47 % SZS output start Proof for DTF2THF_8599
% 1.77/1.47 thf(func_def_0, type, in: $i > $i > $o).
% 1.77/1.47 thf(func_def_1, type, powerset: $i > $i).
% 1.77/1.47 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.77/1.47 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.77/1.47 thf(func_def_4, type, setminus: $i > $i > $i).
% 1.77/1.47 thf(func_def_14, type, sP0: $i > $i > $i > $o).
% 1.77/1.47 thf(func_def_15, type, sK1: $i > $i > $i > $i).
% 1.77/1.47 thf(func_def_16, type, sK2: $i > $i > $i > $i).
% 1.77/1.47 thf(f413,plain,(
% 1.77/1.47 $false),
% 1.77/1.47 inference(avatar_sat_refutation,[status(thm)],[f343,f369,f386,f396,f412])).
% 1.77/1.47 thf(f412,plain,(
% 1.77/1.47 spl25_4),
% 1.77/1.47 inference(avatar_contradiction_clause,[status(thm)],[f411])).
% 1.77/1.47 thf(f411,plain,(
% 1.77/1.47 $false | spl25_4),
% 1.77/1.47 inference(subsumption_resolution,[status(thm)],[f410,f119])).
% 1.77/1.47 thf(f119,plain,(
% 1.77/1.47 ((in @ sK24 @ (powerset @ sK22)) = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 thf(f76,plain,(
% 1.77/1.47 (((in @ sK23 @ (powerset @ sK22)) = $true) & (((in @ sK24 @ (powerset @ sK22)) = $true) & ((setminus @ sK22 @ (binintersect @ sK23 @ sK24)) != (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24))))) & (demorgan1b = $true) & (demorgan1a = $true) & (setextT = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (complementT_lem = $true)),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24])],[f73,f75,f74])).
% 1.77/1.47 thf(f74,plain,(
% 1.77/1.47 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((setminus @ X0 @ (binintersect @ X1 @ X2)) != (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) => (((in @ sK23 @ (powerset @ sK22)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ sK22)) = $true) & ((binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ X2)) != (setminus @ sK22 @ (binintersect @ sK23 @ X2)))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f75,plain,(
% 1.77/1.47 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK22)) = $true) & ((binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ X2)) != (setminus @ sK22 @ (binintersect @ sK23 @ X2)))) => (((in @ sK24 @ (powerset @ sK22)) = $true) & ((setminus @ sK22 @ (binintersect @ sK23 @ sK24)) != (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f73,plain,(
% 1.77/1.47 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((setminus @ X0 @ (binintersect @ X1 @ X2)) != (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) & (demorgan1b = $true) & (demorgan1a = $true) & (setextT = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (complementT_lem = $true)),
% 1.77/1.47 inference(rectify,[status(thm)],[f25])).
% 1.77/1.47 thf(f25,plain,(
% 1.77/1.47 ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((setminus @ X1 @ (binintersect @ X0 @ X2)) != (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))))) & (demorgan1b = $true) & (demorgan1a = $true) & (setextT = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (complementT_lem = $true)),
% 1.77/1.47 inference(flattening,[status(thm)],[f24])).
% 1.77/1.47 thf(f24,plain,(
% 1.77/1.47 (((((? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((setminus @ X1 @ (binintersect @ X0 @ X2)) != (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))))) & (demorgan1b = $true)) & (demorgan1a = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f23])).
% 1.77/1.47 thf(f23,plain,(
% 1.77/1.47 ~((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ((setminus @ X1 @ (binintersect @ X0 @ X2)) = (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))))))))))),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f22])).
% 1.77/1.47 thf(f22,plain,(
% 1.77/1.47 ~(binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan1a => (demorgan1b => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((setminus @ X1 @ (binintersect @ X0 @ X2)) = (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))))))))))),
% 1.77/1.47 inference(rectify,[status(thm)],[f8])).
% 1.77/1.47 thf(f8,negated_conjecture,(
% 1.77/1.47 ~(binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan1a => (demorgan1b => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))))))),
% 1.77/1.47 inference(negated_conjecture,[status(cth)],[f7])).
% 1.77/1.47 thf(f7,conjecture,(
% 1.77/1.47 binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan1a => (demorgan1b => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))))))),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',demorgan1)).
% 1.77/1.47 thf(f410,plain,(
% 1.77/1.47 ((in @ sK24 @ (powerset @ sK22)) != $true) | spl25_4),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f409])).
% 1.77/1.47 thf(f409,plain,(
% 1.77/1.47 ((in @ sK24 @ (powerset @ sK22)) != $true) | ($true != $true) | spl25_4),
% 1.77/1.47 inference(superposition,[status(thm)],[f385,f157])).
% 1.77/1.47 thf(f157,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i] : (($true = (in @ (setminus @ X3 @ X2) @ (powerset @ X3))) | ($true != (in @ X2 @ (powerset @ X3)))) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f141])).
% 1.77/1.47 thf(f141,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ($true != (in @ X2 @ (powerset @ X3))) | ($true = (in @ (setminus @ X3 @ X2) @ (powerset @ X3)))) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f99,f112])).
% 1.77/1.47 thf(f112,plain,(
% 1.77/1.47 (complementT_lem = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 thf(f99,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i] : (($true = (in @ (setminus @ X3 @ X2) @ (powerset @ X3))) | ($true != (in @ X2 @ (powerset @ X3))) | (complementT_lem != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f61])).
% 1.77/1.47 thf(f61,plain,(
% 1.77/1.47 ((complementT_lem = $true) | (((in @ (setminus @ sK14 @ sK13) @ (powerset @ sK14)) != $true) & ($true = (in @ sK13 @ (powerset @ sK14))))) & (! [X2 : $i,X3 : $i] : (($true = (in @ (setminus @ X3 @ X2) @ (powerset @ X3))) | ($true != (in @ X2 @ (powerset @ X3)))) | (complementT_lem != $true))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f59,f60])).
% 1.77/1.47 thf(f60,plain,(
% 1.77/1.47 ? [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) != $true) & ($true = (in @ X0 @ (powerset @ X1)))) => (((in @ (setminus @ sK14 @ sK13) @ (powerset @ sK14)) != $true) & ($true = (in @ sK13 @ (powerset @ sK14))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f59,plain,(
% 1.77/1.47 ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) != $true) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X2 : $i,X3 : $i] : (($true = (in @ (setminus @ X3 @ X2) @ (powerset @ X3))) | ($true != (in @ X2 @ (powerset @ X3)))) | (complementT_lem != $true))),
% 1.77/1.47 inference(rectify,[status(thm)],[f58])).
% 1.77/1.47 thf(f58,plain,(
% 1.77/1.47 ((complementT_lem = $true) | ? [X1 : $i,X0 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X1 : $i,X0 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) | (complementT_lem != $true))),
% 1.77/1.47 inference(nnf_transformation,[status(thm)],[f31])).
% 1.77/1.47 thf(f31,plain,(
% 1.77/1.47 (complementT_lem = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f19])).
% 1.77/1.47 thf(f19,plain,(
% 1.77/1.47 (complementT_lem = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true))),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f18])).
% 1.77/1.47 thf(f18,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 1.77/1.47 inference(rectify,[status(thm)],[f3])).
% 1.77/1.47 thf(f3,axiom,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',complementT_lem)).
% 1.77/1.47 thf(f385,plain,(
% 1.77/1.47 ((in @ (setminus @ sK22 @ sK24) @ (powerset @ sK22)) != $true) | spl25_4),
% 1.77/1.47 inference(avatar_component_clause,[status(thm)],[f383])).
% 1.77/1.47 thf(f383,definition,(
% 1.77/1.47 spl25_4 <=> ((in @ (setminus @ sK22 @ sK24) @ (powerset @ sK22)) = $true)),
% 1.77/1.47 introduced(definition,[new_symbols(naming,[spl25_4])],[avatar_definition])).
% 1.77/1.47 thf(f396,plain,(
% 1.77/1.47 spl25_3),
% 1.77/1.47 inference(avatar_contradiction_clause,[status(thm)],[f395])).
% 1.77/1.47 thf(f395,plain,(
% 1.77/1.47 $false | spl25_3),
% 1.77/1.47 inference(subsumption_resolution,[status(thm)],[f394,f120])).
% 1.77/1.47 thf(f120,plain,(
% 1.77/1.47 ((in @ sK23 @ (powerset @ sK22)) = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 thf(f394,plain,(
% 1.77/1.47 ((in @ sK23 @ (powerset @ sK22)) != $true) | spl25_3),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f393])).
% 1.77/1.47 thf(f393,plain,(
% 1.77/1.47 ($true != $true) | ((in @ sK23 @ (powerset @ sK22)) != $true) | spl25_3),
% 1.77/1.47 inference(superposition,[status(thm)],[f381,f157])).
% 1.77/1.47 thf(f381,plain,(
% 1.77/1.47 ($true != (in @ (setminus @ sK22 @ sK23) @ (powerset @ sK22))) | spl25_3),
% 1.77/1.47 inference(avatar_component_clause,[status(thm)],[f379])).
% 1.77/1.47 thf(f379,definition,(
% 1.77/1.47 spl25_3 <=> ($true = (in @ (setminus @ sK22 @ sK23) @ (powerset @ sK22)))),
% 1.77/1.47 introduced(definition,[new_symbols(naming,[spl25_3])],[avatar_definition])).
% 1.77/1.47 thf(f386,plain,(
% 1.77/1.47 ~spl25_3 | ~spl25_4 | spl25_2),
% 1.77/1.47 inference(avatar_split_clause,[status(thm)],[f377,f340,f383,f379])).
% 1.77/1.47 thf(f340,definition,(
% 1.77/1.47 spl25_2 <=> ((in @ (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24)) @ (powerset @ sK22)) = $true)),
% 1.77/1.47 introduced(definition,[new_symbols(naming,[spl25_2])],[avatar_definition])).
% 1.77/1.47 thf(f377,plain,(
% 1.77/1.47 ((in @ (setminus @ sK22 @ sK24) @ (powerset @ sK22)) != $true) | ($true != (in @ (setminus @ sK22 @ sK23) @ (powerset @ sK22))) | spl25_2),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f375])).
% 1.77/1.47 thf(f375,plain,(
% 1.77/1.47 ($true != $true) | ((in @ (setminus @ sK22 @ sK24) @ (powerset @ sK22)) != $true) | ($true != (in @ (setminus @ sK22 @ sK23) @ (powerset @ sK22))) | spl25_2),
% 1.77/1.47 inference(superposition,[status(thm)],[f342,f159])).
% 1.77/1.47 thf(f159,plain,(
% 1.77/1.47 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ (binunion @ X3 @ X5) @ (powerset @ X4)) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X3 @ (powerset @ X4)) != $true)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.77/1.47 thf(f132,plain,(
% 1.77/1.47 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X3 @ (powerset @ X4)) != $true) | ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)) = $true)) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f89,f114])).
% 1.77/1.47 thf(f114,plain,(
% 1.77/1.47 (binunionT_lem = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 thf(f89,plain,(
% 1.77/1.47 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)) = $true) | (binunionT_lem != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f51])).
% 1.77/1.47 thf(f51,plain,(
% 1.77/1.47 ((binunionT_lem = $true) | (($true = (in @ sK6 @ (powerset @ sK7))) & (((in @ sK8 @ (powerset @ sK7)) = $true) & ($true != (in @ (binunion @ sK6 @ sK8) @ (powerset @ sK7)))))) & (! [X3 : $i,X4 : $i] : (((in @ X3 @ (powerset @ X4)) != $true) | ! [X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)) = $true))) | (binunionT_lem != $true))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f48,f50,f49])).
% 1.77/1.47 thf(f49,plain,(
% 1.77/1.47 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) != $true))) => (($true = (in @ sK6 @ (powerset @ sK7))) & ? [X2 : $i] : (((in @ X2 @ (powerset @ sK7)) = $true) & ((in @ (binunion @ sK6 @ X2) @ (powerset @ sK7)) != $true)))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f50,plain,(
% 1.77/1.47 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK7)) = $true) & ((in @ (binunion @ sK6 @ X2) @ (powerset @ sK7)) != $true)) => (((in @ sK8 @ (powerset @ sK7)) = $true) & ($true != (in @ (binunion @ sK6 @ sK8) @ (powerset @ sK7))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f48,plain,(
% 1.77/1.47 ((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)))) & (! [X3 : $i,X4 : $i] : (((in @ X3 @ (powerset @ X4)) != $true) | ! [X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)) = $true))) | (binunionT_lem != $true))),
% 1.77/1.47 inference(rectify,[status(thm)],[f47])).
% 1.77/1.47 thf(f47,plain,(
% 1.77/1.47 ((binunionT_lem = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) != $true)))) & (! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true))) | (binunionT_lem != $true))),
% 1.77/1.47 inference(nnf_transformation,[status(thm)],[f26])).
% 1.77/1.47 thf(f26,plain,(
% 1.77/1.47 (binunionT_lem = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true)))),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f13])).
% 1.77/1.47 thf(f13,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true))) <=> (binunionT_lem = $true)),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f12])).
% 1.77/1.47 thf(f12,plain,(
% 1.77/1.47 (binunionT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))))),
% 1.77/1.47 inference(rectify,[status(thm)],[f2])).
% 1.77/1.47 thf(f2,axiom,(
% 1.77/1.47 (binunionT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))))),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',binunionT_lem)).
% 1.77/1.47 thf(f342,plain,(
% 1.77/1.47 ((in @ (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24)) @ (powerset @ sK22)) != $true) | spl25_2),
% 1.77/1.47 inference(avatar_component_clause,[status(thm)],[f340])).
% 1.77/1.47 thf(f369,plain,(
% 1.77/1.47 spl25_1),
% 1.77/1.47 inference(avatar_contradiction_clause,[status(thm)],[f368])).
% 1.77/1.47 thf(f368,plain,(
% 1.77/1.47 $false | spl25_1),
% 1.77/1.47 inference(subsumption_resolution,[status(thm)],[f367,f119])).
% 1.77/1.47 thf(f367,plain,(
% 1.77/1.47 ((in @ sK24 @ (powerset @ sK22)) != $true) | spl25_1),
% 1.77/1.47 inference(subsumption_resolution,[status(thm)],[f366,f120])).
% 1.77/1.47 thf(f366,plain,(
% 1.77/1.47 ((in @ sK23 @ (powerset @ sK22)) != $true) | ((in @ sK24 @ (powerset @ sK22)) != $true) | spl25_1),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f365])).
% 1.77/1.47 thf(f365,plain,(
% 1.77/1.47 ((in @ sK24 @ (powerset @ sK22)) != $true) | ($true != $true) | ((in @ sK23 @ (powerset @ sK22)) != $true) | spl25_1),
% 1.77/1.47 inference(superposition,[status(thm)],[f355,f156])).
% 1.77/1.47 thf(f156,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.77/1.47 thf(f148,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f111,f113])).
% 1.77/1.47 thf(f113,plain,(
% 1.77/1.47 (binintersectT_lem = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 thf(f111,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (binintersectT_lem != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f72])).
% 1.77/1.47 thf(f72,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | (((in @ sK20 @ (powerset @ sK19)) = $true) & (((in @ (binintersect @ sK20 @ sK21) @ (powerset @ sK19)) != $true) & ((in @ sK21 @ (powerset @ sK19)) = $true))))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21])],[f69,f71,f70])).
% 1.77/1.47 thf(f70,plain,(
% 1.77/1.47 ? [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) & ? [X5 : $i] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) != $true) & ($true = (in @ X5 @ (powerset @ X3))))) => (((in @ sK20 @ (powerset @ sK19)) = $true) & ? [X5 : $i] : (($true != (in @ (binintersect @ sK20 @ X5) @ (powerset @ sK19))) & ((in @ X5 @ (powerset @ sK19)) = $true)))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f71,plain,(
% 1.77/1.47 ? [X5 : $i] : (($true != (in @ (binintersect @ sK20 @ X5) @ (powerset @ sK19))) & ((in @ X5 @ (powerset @ sK19)) = $true)) => (((in @ (binintersect @ sK20 @ sK21) @ (powerset @ sK19)) != $true) & ((in @ sK21 @ (powerset @ sK19)) = $true))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f69,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | ? [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) & ? [X5 : $i] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) != $true) & ($true = (in @ X5 @ (powerset @ X3))))))),
% 1.77/1.47 inference(rectify,[status(thm)],[f68])).
% 1.77/1.47 thf(f68,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true))))),
% 1.77/1.47 inference(nnf_transformation,[status(thm)],[f32])).
% 1.77/1.47 thf(f32,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) <=> (binintersectT_lem = $true)),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f21])).
% 1.77/1.47 thf(f21,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true))) <=> (binintersectT_lem = $true)),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f20])).
% 1.77/1.47 thf(f20,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))) = binintersectT_lem)),
% 1.77/1.47 inference(rectify,[status(thm)],[f1])).
% 1.77/1.47 thf(f1,axiom,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))) = binintersectT_lem)),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',binintersectT_lem)).
% 1.77/1.47 thf(f355,plain,(
% 1.77/1.47 ((in @ (binintersect @ sK23 @ sK24) @ (powerset @ sK22)) != $true) | spl25_1),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f354])).
% 1.77/1.47 thf(f354,plain,(
% 1.77/1.47 ($true != $true) | ((in @ (binintersect @ sK23 @ sK24) @ (powerset @ sK22)) != $true) | spl25_1),
% 1.77/1.47 inference(superposition,[status(thm)],[f338,f157])).
% 1.77/1.47 thf(f338,plain,(
% 1.77/1.47 ($true != (in @ (setminus @ sK22 @ (binintersect @ sK23 @ sK24)) @ (powerset @ sK22))) | spl25_1),
% 1.77/1.47 inference(avatar_component_clause,[status(thm)],[f336])).
% 1.77/1.47 thf(f336,definition,(
% 1.77/1.47 spl25_1 <=> ($true = (in @ (setminus @ sK22 @ (binintersect @ sK23 @ sK24)) @ (powerset @ sK22)))),
% 1.77/1.47 introduced(definition,[new_symbols(naming,[spl25_1])],[avatar_definition])).
% 1.77/1.47 thf(f343,plain,(
% 1.77/1.47 ~spl25_1 | ~spl25_2),
% 1.77/1.47 inference(avatar_split_clause,[status(thm)],[f334,f340,f336])).
% 1.77/1.47 thf(f334,plain,(
% 1.77/1.47 ($true != (in @ (setminus @ sK22 @ (binintersect @ sK23 @ sK24)) @ (powerset @ sK22))) | ((in @ (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24)) @ (powerset @ sK22)) != $true)),
% 1.77/1.47 inference(subsumption_resolution,[status(thm)],[f333,f120])).
% 1.77/1.47 thf(f333,plain,(
% 1.77/1.47 ($true != (in @ (setminus @ sK22 @ (binintersect @ sK23 @ sK24)) @ (powerset @ sK22))) | ((in @ sK23 @ (powerset @ sK22)) != $true) | ((in @ (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24)) @ (powerset @ sK22)) != $true)),
% 1.77/1.47 inference(subsumption_resolution,[status(thm)],[f328,f119])).
% 1.77/1.47 thf(f328,plain,(
% 1.77/1.47 ((in @ sK24 @ (powerset @ sK22)) != $true) | ((in @ (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24)) @ (powerset @ sK22)) != $true) | ((in @ sK23 @ (powerset @ sK22)) != $true) | ($true != (in @ (setminus @ sK22 @ (binintersect @ sK23 @ sK24)) @ (powerset @ sK22)))),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f287])).
% 1.77/1.47 thf(f287,plain,(
% 1.77/1.47 ((in @ sK23 @ (powerset @ sK22)) != $true) | ((setminus @ sK22 @ (binintersect @ sK23 @ sK24)) != (setminus @ sK22 @ (binintersect @ sK23 @ sK24))) | ((in @ sK24 @ (powerset @ sK22)) != $true) | ((in @ (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24)) @ (powerset @ sK22)) != $true) | ($true != (in @ (setminus @ sK22 @ (binintersect @ sK23 @ sK24)) @ (powerset @ sK22)))),
% 1.77/1.47 inference(superposition,[status(thm)],[f118,f286])).
% 1.77/1.47 thf(f286,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(subsumption_resolution,[status(thm)],[f283,f239])).
% 1.77/1.47 thf(f239,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X0 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.77/1.47 thf(f238,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X0 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) != $true) | ($true != $true)) )),
% 1.77/1.47 inference(duplicate_literal_removal,[status(thm)],[f232])).
% 1.77/1.47 thf(f232,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X0 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) != $true) | ($true != $true) | ((sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X0 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(superposition,[status(thm)],[f197,f78])).
% 1.77/1.47 thf(f78,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK1 @ X2 @ X1 @ X0) @ X1) = $true) | ((sP0 @ X2 @ X1 @ X0) != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f40])).
% 1.77/1.47 thf(f40,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i,X2 : $i] : ((((sP0 @ X2 @ X1 @ X0) = $true) | ! [X3 : $i] : (((in @ X3 @ X0) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) != $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) != $true)))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f38,f39])).
% 1.77/1.47 thf(f39,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X4 : $i] : (((in @ X4 @ X0) != $true) & ($true = (in @ X4 @ X1)) & ((in @ X4 @ X2) = $true)) => (((in @ (sK1 @ X2 @ X1 @ X0) @ X0) != $true) & ((in @ (sK1 @ X2 @ X1 @ X0) @ X1) = $true) & ((in @ (sK1 @ X2 @ X1 @ X0) @ X2) = $true)))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f38,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i,X2 : $i] : ((((sP0 @ X2 @ X1 @ X0) = $true) | ! [X3 : $i] : (((in @ X3 @ X0) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) != $true))) & (? [X4 : $i] : (((in @ X4 @ X0) != $true) & ($true = (in @ X4 @ X1)) & ((in @ X4 @ X2) = $true)) | ((sP0 @ X2 @ X1 @ X0) != $true)))),
% 1.77/1.47 inference(rectify,[status(thm)],[f37])).
% 1.77/1.47 thf(f37,plain,(
% 1.77/1.47 ! [X2 : $i,X0 : $i,X1 : $i] : ((($true = (sP0 @ X1 @ X0 @ X2)) | ! [X3 : $i] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true))) & (? [X3 : $i] : (((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true)) | ($true != (sP0 @ X1 @ X0 @ X2))))),
% 1.77/1.47 inference(nnf_transformation,[status(thm)],[f35])).
% 1.77/1.47 thf(f35,plain,(
% 1.77/1.47 ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (sP0 @ X1 @ X0 @ X2)) <=> ? [X3 : $i] : (((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true)))),
% 1.77/1.47 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.77/1.47 thf(f197,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK1 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) @ X0) != $true) | ($true != (sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f196])).
% 1.77/1.47 thf(f196,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK1 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) @ X0) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != (sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) )),
% 1.77/1.47 inference(duplicate_literal_removal,[status(thm)],[f192])).
% 1.77/1.47 thf(f192,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK1 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) @ X0) != $true) | ($true != (sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true) | ($true != (sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(superposition,[status(thm)],[f177,f77])).
% 1.77/1.47 thf(f77,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK1 @ X2 @ X1 @ X0) @ X2) = $true) | ((sP0 @ X2 @ X1 @ X0) != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f40])).
% 1.77/1.47 thf(f177,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (sK1 @ X0 @ X1 @ (binunion @ (setminus @ X2 @ X3) @ (setminus @ X2 @ X4))) @ (setminus @ X2 @ (binintersect @ X3 @ X4)))) | ((sP0 @ X0 @ X1 @ (binunion @ (setminus @ X2 @ X3) @ (setminus @ X2 @ X4))) != $true) | ($true != (in @ X3 @ (powerset @ X2))) | ($true != (in @ (sK1 @ X0 @ X1 @ (binunion @ (setminus @ X2 @ X3) @ (setminus @ X2 @ X4))) @ X2)) | ($true != (in @ X4 @ (powerset @ X2)))) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f173])).
% 1.77/1.47 thf(f173,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (sK1 @ X0 @ X1 @ (binunion @ (setminus @ X2 @ X3) @ (setminus @ X2 @ X4))) @ X2)) | ($true != (in @ X4 @ (powerset @ X2))) | ($true != (in @ (sK1 @ X0 @ X1 @ (binunion @ (setminus @ X2 @ X3) @ (setminus @ X2 @ X4))) @ (setminus @ X2 @ (binintersect @ X3 @ X4)))) | ($true != $true) | ((sP0 @ X0 @ X1 @ (binunion @ (setminus @ X2 @ X3) @ (setminus @ X2 @ X4))) != $true) | ($true != (in @ X3 @ (powerset @ X2)))) )),
% 1.77/1.47 inference(superposition,[status(thm)],[f79,f158])).
% 1.77/1.47 thf(f158,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true) | ((in @ X3 @ X1) != $true)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.77/1.47 thf(f133,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f98,f116])).
% 1.77/1.47 thf(f116,plain,(
% 1.77/1.47 (demorgan1a = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 thf(f98,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | (demorgan1a != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f57])).
% 1.77/1.47 thf(f57,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true))) | (demorgan1a != $true)) & ((demorgan1a = $true) | (($true = (in @ sK9 @ (powerset @ sK10))) & ((((in @ sK12 @ (binunion @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11))) != $true) & ($true = (in @ sK12 @ sK10)) & ((in @ sK12 @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11))) = $true)) & ($true = (in @ sK11 @ (powerset @ sK10))))))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f53,f56,f55,f54])).
% 1.77/1.47 thf(f54,plain,(
% 1.77/1.47 ? [X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X5)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (($true != (in @ X7 @ (binunion @ (setminus @ X5 @ X4) @ (setminus @ X5 @ X6)))) & ($true = (in @ X7 @ X5)) & ((in @ X7 @ (setminus @ X5 @ (binintersect @ X4 @ X6))) = $true)) & ((in @ X6 @ (powerset @ X5)) = $true))) => (($true = (in @ sK9 @ (powerset @ sK10))) & ? [X6 : $i] : (? [X7 : $i] : (($true != (in @ X7 @ (binunion @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ X6)))) & ($true = (in @ X7 @ sK10)) & ($true = (in @ X7 @ (setminus @ sK10 @ (binintersect @ sK9 @ X6))))) & ((in @ X6 @ (powerset @ sK10)) = $true)))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f55,plain,(
% 1.77/1.47 ? [X6 : $i] : (? [X7 : $i] : (($true != (in @ X7 @ (binunion @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ X6)))) & ($true = (in @ X7 @ sK10)) & ($true = (in @ X7 @ (setminus @ sK10 @ (binintersect @ sK9 @ X6))))) & ((in @ X6 @ (powerset @ sK10)) = $true)) => (? [X7 : $i] : (((in @ X7 @ (binunion @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11))) != $true) & ($true = (in @ X7 @ sK10)) & ((in @ X7 @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11))) = $true)) & ($true = (in @ sK11 @ (powerset @ sK10))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f56,plain,(
% 1.77/1.47 ? [X7 : $i] : (((in @ X7 @ (binunion @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11))) != $true) & ($true = (in @ X7 @ sK10)) & ((in @ X7 @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11))) = $true)) => (((in @ sK12 @ (binunion @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11))) != $true) & ($true = (in @ sK12 @ sK10)) & ((in @ sK12 @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11))) = $true))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f53,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true))) | (demorgan1a != $true)) & ((demorgan1a = $true) | ? [X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X5)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (($true != (in @ X7 @ (binunion @ (setminus @ X5 @ X4) @ (setminus @ X5 @ X6)))) & ($true = (in @ X7 @ X5)) & ((in @ X7 @ (setminus @ X5 @ (binintersect @ X4 @ X6))) = $true)) & ((in @ X6 @ (powerset @ X5)) = $true))))),
% 1.77/1.47 inference(rectify,[status(thm)],[f52])).
% 1.77/1.47 thf(f52,plain,(
% 1.77/1.47 (! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (demorgan1a != $true)) & ((demorgan1a = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))))),
% 1.77/1.47 inference(nnf_transformation,[status(thm)],[f28])).
% 1.77/1.47 thf(f28,plain,(
% 1.77/1.47 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) <=> (demorgan1a = $true)),
% 1.77/1.47 inference(flattening,[status(thm)],[f27])).
% 1.77/1.47 thf(f27,plain,(
% 1.77/1.47 (demorgan1a = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true)) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f15])).
% 1.77/1.47 thf(f15,plain,(
% 1.77/1.47 (demorgan1a = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) => ((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true)))))),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f14])).
% 1.77/1.47 thf(f14,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))) = demorgan1a)),
% 1.77/1.47 inference(rectify,[status(thm)],[f5])).
% 1.77/1.47 thf(f5,axiom,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))) = demorgan1a)),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',demorgan1a)).
% 1.77/1.47 thf(f79,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK1 @ X2 @ X1 @ X0) @ X0) != $true) | ((sP0 @ X2 @ X1 @ X0) != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f40])).
% 1.77/1.47 thf(f283,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X0 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f282])).
% 1.77/1.47 thf(f282,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X0 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(duplicate_literal_removal,[status(thm)],[f278])).
% 1.77/1.47 thf(f278,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)) != $true) | ((sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X0 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X0 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true) | ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.77/1.47 inference(superposition,[status(thm)],[f219,f153])).
% 1.77/1.47 thf(f153,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X2 @ X1 @ X0) @ X1) = $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true = (sP0 @ X0 @ X1 @ X2)) | ((in @ X2 @ (powerset @ X1)) != $true) | (X0 = X2)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.77/1.47 thf(f123,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true = (sP0 @ X0 @ X1 @ X2)) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X1) = $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != $true)) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f86,f115])).
% 1.77/1.47 thf(f115,plain,(
% 1.77/1.47 (setextT = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 thf(f86,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X1) = $true) | (X0 = X2) | ($true = (sP0 @ X0 @ X1 @ X2)) | ($true != (in @ X0 @ (powerset @ X1))) | (setextT != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f46])).
% 1.77/1.47 thf(f46,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | (((in @ (sK2 @ X2 @ X1 @ X0) @ X2) = $true) & ($true != (in @ (sK2 @ X2 @ X1 @ X0) @ X0)) & ((in @ (sK2 @ X2 @ X1 @ X0) @ X1) = $true)) | (X0 = X2) | ($true = (sP0 @ X0 @ X1 @ X2))) | ($true != (in @ X0 @ (powerset @ X1)))) | (setextT != $true)) & ((setextT = $true) | ((((in @ sK5 @ (powerset @ sK4)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ sK5)) | ((in @ X7 @ sK3) = $true) | ((in @ X7 @ sK4) != $true)) & (sK5 != sK3) & ($true != (sP0 @ sK3 @ sK4 @ sK5))) & ($true = (in @ sK3 @ (powerset @ sK4)))))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f42,f45,f44,f43])).
% 1.77/1.47 thf(f43,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true)) => (((in @ (sK2 @ X2 @ X1 @ X0) @ X2) = $true) & ($true != (in @ (sK2 @ X2 @ X1 @ X0) @ X0)) & ((in @ (sK2 @ X2 @ X1 @ X0) @ X1) = $true)))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f44,plain,(
% 1.77/1.47 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ (powerset @ X5)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ X6)) | ((in @ X7 @ X4) = $true) | ($true != (in @ X7 @ X5))) & (X4 != X6) & ($true != (sP0 @ X4 @ X5 @ X6))) & ((in @ X4 @ (powerset @ X5)) = $true)) => (? [X6 : $i] : (((in @ X6 @ (powerset @ sK4)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ X6)) | ((in @ X7 @ sK3) = $true) | ((in @ X7 @ sK4) != $true)) & (sK3 != X6) & ((sP0 @ sK3 @ sK4 @ X6) != $true)) & ($true = (in @ sK3 @ (powerset @ sK4))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f45,plain,(
% 1.77/1.47 ? [X6 : $i] : (((in @ X6 @ (powerset @ sK4)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ X6)) | ((in @ X7 @ sK3) = $true) | ((in @ X7 @ sK4) != $true)) & (sK3 != X6) & ((sP0 @ sK3 @ sK4 @ X6) != $true)) => (((in @ sK5 @ (powerset @ sK4)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ sK5)) | ((in @ X7 @ sK3) = $true) | ((in @ X7 @ sK4) != $true)) & (sK5 != sK3) & ($true != (sP0 @ sK3 @ sK4 @ sK5)))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f42,plain,(
% 1.77/1.47 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ X3 @ X0) != $true) & ((in @ X3 @ X1) = $true)) | (X0 = X2) | ($true = (sP0 @ X0 @ X1 @ X2))) | ($true != (in @ X0 @ (powerset @ X1)))) | (setextT != $true)) & ((setextT = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ (powerset @ X5)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ X6)) | ((in @ X7 @ X4) = $true) | ($true != (in @ X7 @ X5))) & (X4 != X6) & ($true != (sP0 @ X4 @ X5 @ X6))) & ((in @ X4 @ (powerset @ X5)) = $true)))),
% 1.77/1.47 inference(rectify,[status(thm)],[f41])).
% 1.77/1.47 thf(f41,plain,(
% 1.77/1.47 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ? [X4 : $i] : (((in @ X4 @ X2) = $true) & ($true != (in @ X4 @ X1)) & ((in @ X4 @ X0) = $true)) | (X1 = X2) | ($true = (sP0 @ X1 @ X0 @ X2))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (setextT != $true)) & ((setextT = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ! [X4 : $i] : (((in @ X4 @ X2) != $true) | ($true = (in @ X4 @ X1)) | ((in @ X4 @ X0) != $true)) & (X1 != X2) & ($true != (sP0 @ X1 @ X0 @ X2))) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.77/1.47 inference(nnf_transformation,[status(thm)],[f36])).
% 1.77/1.47 thf(f36,plain,(
% 1.77/1.47 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ? [X4 : $i] : (((in @ X4 @ X2) = $true) & ($true != (in @ X4 @ X1)) & ((in @ X4 @ X0) = $true)) | (X1 = X2) | ($true = (sP0 @ X1 @ X0 @ X2))) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (setextT = $true)),
% 1.77/1.47 inference(definition_folding,[status(thm)],[f30,f35])).
% 1.77/1.47 thf(f30,plain,(
% 1.77/1.47 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ? [X4 : $i] : (((in @ X4 @ X2) = $true) & ($true != (in @ X4 @ X1)) & ((in @ X4 @ X0) = $true)) | (X1 = X2) | ? [X3 : $i] : (((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true))) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (setextT = $true)),
% 1.77/1.47 inference(flattening,[status(thm)],[f29])).
% 1.77/1.47 thf(f29,plain,(
% 1.77/1.47 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((X1 = X2) | ? [X4 : $i] : ((($true != (in @ X4 @ X1)) & ((in @ X4 @ X2) = $true)) & ((in @ X4 @ X0) = $true))) | ? [X3 : $i] : ((((in @ X3 @ X2) != $true) & ((in @ X3 @ X1) = $true)) & ((in @ X3 @ X0) = $true))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (setextT = $true)),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f11])).
% 1.77/1.47 thf(f11,plain,(
% 1.77/1.47 ! [X1 : $i,X0 : $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] : (((in @ X4 @ X0) = $true) => (((in @ X4 @ X2) = $true) => ($true = (in @ X4 @ X1)))) => (X1 = X2))))) <=> (setextT = $true)),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f10])).
% 1.77/1.47 thf(f10,plain,(
% 1.77/1.47 (setextT = ! [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))))))),
% 1.77/1.47 inference(rectify,[status(thm)],[f4])).
% 1.77/1.47 thf(f4,axiom,(
% 1.77/1.47 (setextT = ! [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))))))),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',setextT)).
% 1.77/1.47 thf(f219,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ($true != (in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))) | ($true = (sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f218])).
% 1.77/1.47 thf(f218,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ (sK2 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ($true != (in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ($true = (sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) )),
% 1.77/1.47 inference(duplicate_literal_removal,[status(thm)],[f217])).
% 1.77/1.47 thf(f217,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != (in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ($true != (in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))) | ($true != (in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))) | ((in @ (sK2 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0) != $true) | ($true = (sP0 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != (in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))) | ($true != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.77/1.47 inference(superposition,[status(thm)],[f152,f171])).
% 1.77/1.47 thf(f171,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (sK2 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ($true != (in @ (sK2 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0)) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X4 @ (powerset @ X3)) != $true) | ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = X4) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (sP0 @ X4 @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != (in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.77/1.47 thf(f167,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (sK2 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0)) | ((in @ X4 @ (powerset @ X3)) != $true) | ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = X4) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (sK2 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (sP0 @ X4 @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != $true) | ($true != (in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) )),
% 1.77/1.47 inference(superposition,[status(thm)],[f155,f154])).
% 1.77/1.47 thf(f154,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X2 @ X1 @ X0) @ X2) = $true) | ($true = (sP0 @ X0 @ X1 @ X2)) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true) | (X0 = X2)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.77/1.47 thf(f121,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X2) = $true) | ($true = (sP0 @ X0 @ X1 @ X2)) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != $true) | (X0 = X2)) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f88,f115])).
% 1.77/1.47 thf(f88,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X2) = $true) | (X0 = X2) | ($true = (sP0 @ X0 @ X1 @ X2)) | ($true != (in @ X0 @ (powerset @ X1))) | (setextT != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f46])).
% 1.77/1.47 thf(f155,plain,(
% 1.77/1.47 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true) | ((in @ X7 @ X4) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f147])).
% 1.77/1.47 thf(f147,plain,(
% 1.77/1.47 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true) | ($true != $true) | ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true)) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f102,f117])).
% 1.77/1.47 thf(f117,plain,(
% 1.77/1.47 (demorgan1b = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 thf(f102,plain,(
% 1.77/1.47 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (demorgan1b != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f67])).
% 1.77/1.47 thf(f67,plain,(
% 1.77/1.47 ((demorgan1b = $true) | (((((in @ sK18 @ (setminus @ sK15 @ (binintersect @ sK16 @ sK17))) != $true) & ((in @ sK18 @ sK15) = $true) & ($true = (in @ sK18 @ (binunion @ (setminus @ sK15 @ sK16) @ (setminus @ sK15 @ sK17))))) & ($true = (in @ sK17 @ (powerset @ sK15)))) & ($true = (in @ sK16 @ (powerset @ sK15))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true)) | ((in @ X6 @ (powerset @ X4)) != $true)) | ((in @ X5 @ (powerset @ X4)) != $true)) | (demorgan1b != $true))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18])],[f63,f66,f65,f64])).
% 1.77/1.47 thf(f64,plain,(
% 1.77/1.47 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ sK15 @ (binintersect @ sK16 @ X2))) != $true) & ((in @ X3 @ sK15) = $true) & ($true = (in @ X3 @ (binunion @ (setminus @ sK15 @ sK16) @ (setminus @ sK15 @ X2))))) & ($true = (in @ X2 @ (powerset @ sK15)))) & ($true = (in @ sK16 @ (powerset @ sK15))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f65,plain,(
% 1.77/1.47 ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ sK15 @ (binintersect @ sK16 @ X2))) != $true) & ((in @ X3 @ sK15) = $true) & ($true = (in @ X3 @ (binunion @ (setminus @ sK15 @ sK16) @ (setminus @ sK15 @ X2))))) & ($true = (in @ X2 @ (powerset @ sK15)))) => (? [X3 : $i] : (((in @ X3 @ (setminus @ sK15 @ (binintersect @ sK16 @ sK17))) != $true) & ((in @ X3 @ sK15) = $true) & ((in @ X3 @ (binunion @ (setminus @ sK15 @ sK16) @ (setminus @ sK15 @ sK17))) = $true)) & ($true = (in @ sK17 @ (powerset @ sK15))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f66,plain,(
% 1.77/1.47 ? [X3 : $i] : (((in @ X3 @ (setminus @ sK15 @ (binintersect @ sK16 @ sK17))) != $true) & ((in @ X3 @ sK15) = $true) & ((in @ X3 @ (binunion @ (setminus @ sK15 @ sK16) @ (setminus @ sK15 @ sK17))) = $true)) => (((in @ sK18 @ (setminus @ sK15 @ (binintersect @ sK16 @ sK17))) != $true) & ((in @ sK18 @ sK15) = $true) & ($true = (in @ sK18 @ (binunion @ (setminus @ sK15 @ sK16) @ (setminus @ sK15 @ sK17)))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f63,plain,(
% 1.77/1.47 ((demorgan1b = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6))) != $true)) | ((in @ X6 @ (powerset @ X4)) != $true)) | ((in @ X5 @ (powerset @ X4)) != $true)) | (demorgan1b != $true))),
% 1.77/1.47 inference(rectify,[status(thm)],[f62])).
% 1.77/1.47 thf(f62,plain,(
% 1.77/1.47 ((demorgan1b = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) | (demorgan1b != $true))),
% 1.77/1.47 inference(nnf_transformation,[status(thm)],[f34])).
% 1.77/1.47 thf(f34,plain,(
% 1.77/1.47 (demorgan1b = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.77/1.47 inference(flattening,[status(thm)],[f33])).
% 1.77/1.47 thf(f33,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) = $true) | ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) != $true)) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (demorgan1b = $true)),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f17])).
% 1.77/1.47 thf(f17,plain,(
% 1.77/1.47 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) => ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) = $true))))) <=> (demorgan1b = $true)),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f16])).
% 1.77/1.47 thf(f16,plain,(
% 1.77/1.47 (demorgan1b = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) => (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))))))))),
% 1.77/1.47 inference(rectify,[status(thm)],[f6])).
% 1.77/1.47 thf(f6,axiom,(
% 1.77/1.47 (demorgan1b = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.HsoFkBrQ2u/DTF2THF_8599.p',demorgan1b)).
% 1.77/1.47 thf(f152,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK2 @ X2 @ X1 @ X0) @ X0)) | ($true = (sP0 @ X0 @ X1 @ X2)) | ($true != (in @ X0 @ (powerset @ X1))) | (X0 = X2) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.77/1.47 thf(f122,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK2 @ X2 @ X1 @ X0) @ X0)) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != $true) | ($true != (in @ X0 @ (powerset @ X1))) | (X0 = X2) | ($true = (sP0 @ X0 @ X1 @ X2))) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f87,f115])).
% 1.77/1.47 thf(f87,plain,(
% 1.77/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ (sK2 @ X2 @ X1 @ X0) @ X0)) | (X0 = X2) | ($true = (sP0 @ X0 @ X1 @ X2)) | ($true != (in @ X0 @ (powerset @ X1))) | (setextT != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f46])).
% 1.77/1.47 thf(f118,plain,(
% 1.77/1.47 ((setminus @ sK22 @ (binintersect @ sK23 @ sK24)) != (binunion @ (setminus @ sK22 @ sK23) @ (setminus @ sK22 @ sK24)))),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f76])).
% 1.77/1.47 % SZS output end Proof for DTF2THF_8599
% 1.77/1.47 % (8796)------------------------------
% 1.77/1.47 % (8796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.47 % (8796)Termination reason: Refutation
% 1.77/1.47
% 1.77/1.47 % (8796)Memory used [KB]: 6140
% 1.77/1.47 % (8796)Time elapsed: 0.106 s
% 1.77/1.47 % (8796)Instructions burned: 186 (million)
% 1.77/1.47 % (8796)------------------------------
% 1.77/1.47 % (8796)------------------------------
% 1.77/1.47 % (8790)Success in time 0.114 s
%------------------------------------------------------------------------------