%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU734^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:46 AM UTC 2026
% Result : Theorem 1.60s 1.38s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 1584 ( 451 equ; 0 cnn)
% Maximal formula atoms : 14 ( 17 avg)
% Number of connectives : 2201 ( 238 ~; 208 |; 116 &;1558 @)
% ( 10 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 21 con; 0-3 aty)
% Number of variables : 266 ( 0 ^; 204 !; 62 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
binintersect: $i > $i > $i ).
thf(func_def_4,type,
setminus: $i > $i > $i ).
thf(func_def_22,type,
sK10: $i > $i > $i > $i ).
thf(f189,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f188,f61]) ).
thf(f61,plain,
( ( in @ sK8 @ ( powerset @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( complementT_lem = $true )
& ( complementImpComplementIntersect = $true )
& ( subsetTI = $true )
& ( ( subset @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) )
!= $true )
& ( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true )
& ( ( in @ sK8 @ ( powerset @ sK7 ) )
= $true )
& ( binintersectT_lem = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f23,f38,f37]) ).
thf(f37,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( subset @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ ( binintersect @ sK8 @ X2 ) ) )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ sK7 ) ) ) )
& ( ( in @ sK8 @ ( powerset @ sK7 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ? [X2: $i] :
( ( ( subset @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ ( binintersect @ sK8 @ X2 ) ) )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ sK7 ) ) ) )
=> ( ( ( subset @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) )
!= $true )
& ( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( complementT_lem = $true )
& ( complementImpComplementIntersect = $true )
& ( subsetTI = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectT_lem = $true ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( complementImpComplementIntersect = $true )
& ( subsetTI = $true )
& ( complementT_lem = $true )
& ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( binintersectT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( subsetTI = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( binintersectT_lem
=> ( complementT_lem
=> ( subsetTI
=> ( complementImpComplementIntersect
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( binintersectT_lem
=> ( complementT_lem
=> ( subsetTI
=> ( complementImpComplementIntersect
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( binintersectT_lem
=> ( complementT_lem
=> ( subsetTI
=> ( complementImpComplementIntersect
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',complementSubsetComplementIntersect) ).
thf(f188,plain,
( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f187,f62]) ).
thf(f62,plain,
( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f187,plain,
( ( ( in @ sK9 @ ( powerset @ sK7 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f186]) ).
thf(f186,plain,
( ( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true )
| ( ( in @ sK9 @ ( powerset @ sK7 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f175,f99]) ).
thf(f99,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f53,f60]) ).
thf(f60,plain,
binintersectT_lem = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( binintersectT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ sK1 ) )
!= $true )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f29,f28]) ).
thf(f28,plain,
( ? [X3: $i,X4: $i] :
( ( ( in @ X3 @ ( powerset @ X4 ) )
= $true )
& ? [X5: $i] :
( ( $true
!= ( in @ ( binintersect @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
& ( ( in @ X5 @ ( powerset @ X4 ) )
= $true ) ) )
=> ( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ? [X5: $i] :
( ( $true
!= ( in @ ( binintersect @ sK0 @ X5 ) @ ( powerset @ sK1 ) ) )
& ( ( in @ X5 @ ( powerset @ sK1 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X5: $i] :
( ( $true
!= ( in @ ( binintersect @ sK0 @ X5 ) @ ( powerset @ sK1 ) ) )
& ( ( in @ X5 @ ( powerset @ sK1 ) )
= $true ) )
=> ( ( ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ sK1 ) )
!= $true )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ? [X3: $i,X4: $i] :
( ( ( in @ X3 @ ( powerset @ X4 ) )
= $true )
& ? [X5: $i] :
( ( $true
!= ( in @ ( binintersect @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
& ( ( in @ X5 @ ( powerset @ X4 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ! [X1: $i,X0: $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 )
| ? [X1: $i,X0: $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)],[f19]) ).
thf(f19,plain,
( ! [X1: $i,X0: $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)],[f15]) ).
thf(f15,plain,
( ( binintersectT_lem = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( binintersectT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binintersectT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',binintersectT_lem) ).
thf(f175,plain,
( ( in @ ( binintersect @ sK8 @ sK9 ) @ ( powerset @ sK7 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f174]) ).
thf(f174,plain,
( ( ( in @ ( binintersect @ sK8 @ sK9 ) @ ( powerset @ sK7 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f168,f102]) ).
thf(f102,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f76,f66]) ).
thf(f66,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f76,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( complementT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ( ( ( in @ sK14 @ ( powerset @ sK15 ) )
= $true )
& ( $true
!= ( in @ ( setminus @ sK15 @ sK14 ) @ ( powerset @ sK15 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f47,f48]) ).
thf(f48,plain,
( ? [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
& ( ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) )
!= $true ) )
=> ( ( ( in @ sK14 @ ( powerset @ sK15 ) )
= $true )
& ( $true
!= ( in @ ( setminus @ sK15 @ sK14 ) @ ( powerset @ sK15 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
& ( ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
<=> ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
<=> ( complementT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',complementT_lem) ).
thf(f168,plain,
( $true
!= ( in @ ( setminus @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) @ ( powerset @ sK7 ) ) ),
inference(subsumption_resolution,[status(thm)],[f167,f61]) ).
thf(f167,plain,
( ( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) @ ( powerset @ sK7 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f166,f62]) ).
thf(f166,plain,
( ( ( in @ sK9 @ ( powerset @ sK7 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) @ ( powerset @ sK7 ) ) )
| ( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $true
!= ( in @ ( setminus @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) @ ( powerset @ sK7 ) ) )
| ( ( in @ sK9 @ ( powerset @ sK7 ) )
!= $true )
| ( $true != $true )
| ( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f63,f164]) ).
thf(f164,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f162,f102]) ).
thf(f162,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f160]) ).
thf(f160,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f155,f98]) ).
thf(f98,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X2 )
= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f71,f64]) ).
thf(f64,plain,
subsetTI = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f71,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( subset @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
& ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( ( subset @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ( ( ( in @ sK12 @ ( powerset @ sK11 ) )
= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ sK12 )
!= $true )
| ( ( in @ X7 @ sK13 )
= $true )
| ( ( in @ X7 @ sK11 )
!= $true ) )
& ( ( subset @ sK12 @ sK13 )
!= $true )
& ( ( in @ sK13 @ ( powerset @ sK11 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f41,f44,f43,f42]) ).
thf(f42,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
=> ( ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
& ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
( ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) )
& ( ( subset @ X5 @ X6 )
!= $true )
& ( ( in @ X6 @ ( powerset @ X4 ) )
= $true ) ) )
=> ( ( ( in @ sK12 @ ( powerset @ sK11 ) )
= $true )
& ? [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ sK12 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ sK11 )
!= $true ) )
& ( ( subset @ sK12 @ X6 )
!= $true )
& ( ( in @ X6 @ ( powerset @ sK11 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ sK12 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ sK11 )
!= $true ) )
& ( ( subset @ sK12 @ X6 )
!= $true )
& ( ( in @ X6 @ ( powerset @ sK11 ) )
= $true ) )
=> ( ! [X7: $i] :
( ( ( in @ X7 @ sK12 )
!= $true )
| ( ( in @ X7 @ sK13 )
= $true )
| ( ( in @ X7 @ sK11 )
!= $true ) )
& ( ( subset @ sK12 @ sK13 )
!= $true )
& ( ( in @ sK13 @ ( powerset @ sK11 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( subset @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) )
& ( ( subset @ X5 @ X6 )
!= $true )
& ( ( in @ X6 @ ( powerset @ X4 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( subset @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( ( subset @ X1 @ X2 )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( subset @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
<=> ( subsetTI = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ( subsetTI = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( subset @ X1 @ X2 )
= $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 ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( subsetTI = $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 @ X1 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ( subset @ X1 @ X2 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ) )
= subsetTI ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ) )
= subsetTI ),
file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',subsetTI) ).
thf(f155,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( setminus @ X0 @ X1 ) @ X3 ) @ X0 )
!= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X3 ) ) )
| ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( setminus @ X0 @ X1 ) @ X3 ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f150]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X3 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ ( sK10 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( setminus @ X0 @ X1 ) @ X3 ) @ X0 )
!= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X3 ) ) )
| ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( subset @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f122,f97]) ).
thf(f97,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f73,f64]) ).
thf(f73,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( subset @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( sK10 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ X4 ) @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ ( sK10 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 )
!= $true )
| ( ( subset @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( sK10 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ ( powerset @ X4 ) )
!= $true )
| ( ( subset @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK10 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) @ X3 @ X4 ) @ ( setminus @ X0 @ X1 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f101,f100]) ).
thf(f100,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( setminus @ X4 @ X5 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ ( setminus @ X4 @ X5 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f54,f65]) ).
thf(f65,plain,
complementImpComplementIntersect = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f54,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( setminus @ X4 @ X5 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( complementImpComplementIntersect != $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( complementImpComplementIntersect = $true )
| ( ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ sK5 ) ) ) )
& ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binintersect @ X5 @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( setminus @ X4 @ X5 ) )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( complementImpComplementIntersect != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f32,f35,f34,f33]) ).
thf(f33,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ sK3 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK3 @ sK4 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK3 ) )
= $true ) )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ sK3 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK3 @ sK4 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK3 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ sK5 ) ) )
!= $true )
& ( ( in @ X3 @ sK3 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK3 @ sK4 ) )
= $true ) )
& ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ sK5 ) ) )
!= $true )
& ( ( in @ X3 @ sK3 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK3 @ sK4 ) )
= $true ) )
=> ( ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ sK5 ) ) ) )
& ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ( complementImpComplementIntersect = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $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 @ ( setminus @ X4 @ X5 ) )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( complementImpComplementIntersect != $true ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( complementImpComplementIntersect = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $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 @ ( setminus @ X1 @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementImpComplementIntersect != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( complementImpComplementIntersect = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ( complementImpComplementIntersect = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( complementImpComplementIntersect = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
=> ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) )
= complementImpComplementIntersect ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) )
= complementImpComplementIntersect ),
file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',complementImpComplementIntersect) ).
thf(f101,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f72,f64]) ).
thf(f72,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK10 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( subset @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f63,plain,
( ( subset @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ ( binintersect @ sK8 @ sK9 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU734^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n028.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:32:27 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.39 ---- Original DTF file ---
% 0.15/0.39 thf(spec,logic,$$dhol).
% 0.15/0.39 %------------------------------------------------------------------------------
% 0.15/0.39 % File : SEU734^2 : TPTP v9.2.1. Released v3.7.0.
% 0.15/0.39 % Domain : Set Theory
% 0.15/0.39 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.15/0.39 % Version : Especial > Reduced > Especial.
% 0.15/0.39 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.15/0.39 % subset (setminus A X) (setminus A (binintersect X Y))))
% 0.15/0.39
% 0.15/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.15/0.39 % Source : [Bro08]
% 0.15/0.39 % Names : ZFC236l [Bro08]
% 0.15/0.39
% 0.15/0.39 % Status : Theorem
% 0.15/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.15/0.39 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.15/0.39 % Number of atoms : 31 ( 4 equ; 0 cnn)
% 0.15/0.39 % Maximal formula atoms : 7 ( 6 avg)
% 0.15/0.39 % Number of connectives : 83 ( 0 ~; 0 |; 0 &; 65 @)
% 0.15/0.39 % ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% 0.15/0.39 % Maximal formula depth : 14 ( 4 avg)
% 0.15/0.39 % Number of types : 2 ( 0 usr)
% 0.15/0.39 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.15/0.39 % Number of symbols : 10 ( 9 usr; 4 con; 0-2 aty)
% 0.15/0.39 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 0.15/0.39 % SPC : TH0_THM_EQU_NAR
% 0.15/0.39
% 0.15/0.39 % Comments : http://mathgate.info/detsetitem.php?id=296
% 0.15/0.39 %------------------------------------------------------------------------------
% 0.15/0.39 thf(in_type,type,
% 0.15/0.39 in: $i > $i > $o ).
% 0.15/0.39
% 0.15/0.39 thf(powerset_type,type,
% 0.15/0.39 powerset: $i > $i ).
% 0.15/0.39
% 0.15/0.39 thf(subset_type,type,
% 0.15/0.39 subset: $i > $i > $o ).
% 0.15/0.39
% 0.15/0.39 thf(binintersect_type,type,
% 0.15/0.39 binintersect: $i > $i > $i ).
% 0.15/0.39
% 0.15/0.39 thf(setminus_type,type,
% 0.15/0.39 setminus: $i > $i > $i ).
% 0.15/0.39
% 0.15/0.39 thf(binintersectT_lem_type,type,
% 0.15/0.39 binintersectT_lem: $o ).
% 0.15/0.39
% 0.15/0.39 thf(binintersectT_lem,definition,
% 0.15/0.39 ( binintersectT_lem
% 0.15/0.39 = ( ! [A: $i,X: $i] :
% 0.15/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.39 => ! [Y: $i] :
% 0.15/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.39 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 thf(complementT_lem_type,type,
% 0.15/0.39 complementT_lem: $o ).
% 0.15/0.39
% 0.15/0.39 thf(complementT_lem,definition,
% 0.15/0.39 ( complementT_lem
% 0.15/0.39 = ( ! [A: $i,X: $i] :
% 0.15/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.39 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 thf(subsetTI_type,type,
% 0.15/0.39 subsetTI: $o ).
% 0.15/0.39
% 0.15/0.39 thf(subsetTI,definition,
% 0.15/0.39 ( subsetTI
% 0.15/0.39 = ( ! [A: $i,X: $i] :
% 0.15/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.39 => ! [Y: $i] :
% 0.15/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.39 => ( ! [Xx: $i] :
% 0.15/0.39 ( ( in @ Xx @ A )
% 0.15/0.39 => ( ( in @ Xx @ X )
% 0.15/0.39 => ( in @ Xx @ Y ) ) )
% 0.15/0.39 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 thf(complementImpComplementIntersect_type,type,
% 0.15/0.39 complementImpComplementIntersect: $o ).
% 0.15/0.39
% 0.15/0.39 thf(complementImpComplementIntersect,definition,
% 0.15/0.39 ( complementImpComplementIntersect
% 0.15/0.39 = ( ! [A: $i,X: $i] :
% 0.15/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.39 => ! [Y: $i] :
% 0.15/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.39 => ! [Xx: $i] :
% 0.15/0.39 ( ( in @ Xx @ A )
% 0.15/0.39 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.15/0.39 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 thf(complementSubsetComplementIntersect,conjecture,
% 0.15/0.39 ( binintersectT_lem
% 0.15/0.39 => ( complementT_lem
% 0.15/0.39 => ( subsetTI
% 0.15/0.39 => ( complementImpComplementIntersect
% 0.15/0.39 => ! [A: $i,X: $i] :
% 0.15/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.39 => ! [Y: $i] :
% 0.15/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.39 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 %------------------------------------------------------------------------------
% 0.15/0.39 ------------------------
% 1.60/1.32 ---- Embedded in THF ---
% 1.60/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.32 %%% Generated on Tue Feb 24 12:32:27 EST 2026
% 1.60/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.32 %%% Logic specification used:
% 1.60/1.32 %%% thf(spec, logic, $$dhol).
% 1.60/1.32
% 1.60/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2DTF25614.p
% See solution above
% 1.60/1.32 ------------------------
% 1.60/1.33 ---- Cleaned THF ---
% 1.60/1.33 thf(in_type,type,
% 1.60/1.33 in: $i > $i > $o ).
% 1.60/1.33
% 1.60/1.33 thf(powerset_type,type,
% 1.60/1.33 powerset: $i > $i ).
% 1.60/1.33
% 1.60/1.33 thf(subset_type,type,
% 1.60/1.33 subset: $i > $i > $o ).
% 1.60/1.33
% 1.60/1.33 thf(binintersect_type,type,
% 1.60/1.33 binintersect: $i > $i > $i ).
% 1.60/1.33
% 1.60/1.33 thf(setminus_type,type,
% 1.60/1.33 setminus: $i > $i > $i ).
% 1.60/1.33
% 1.60/1.33 thf(binintersectT_lem_type,type,
% 1.60/1.33 binintersectT_lem: $o ).
% 1.60/1.33
% 1.60/1.33 thf(binintersectT_lem,definition,
% 1.60/1.33 ( binintersectT_lem
% 1.60/1.33 = ( ! [A: $i,X: $i] :
% 1.60/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.60/1.33 => ! [Y: $i] :
% 1.60/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.60/1.33 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.60/1.33
% 1.60/1.33 thf(complementT_lem_type,type,
% 1.60/1.33 complementT_lem: $o ).
% 1.60/1.33
% 1.60/1.33 thf(complementT_lem,definition,
% 1.60/1.33 ( complementT_lem
% 1.60/1.33 = ( ! [A: $i,X: $i] :
% 1.60/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.60/1.33 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.60/1.33
% 1.60/1.33 thf(subsetTI_type,type,
% 1.60/1.33 subsetTI: $o ).
% 1.60/1.33
% 1.60/1.33 thf(subsetTI,definition,
% 1.60/1.33 ( subsetTI
% 1.60/1.33 = ( ! [A: $i,X: $i] :
% 1.60/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.60/1.33 => ! [Y: $i] :
% 1.60/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.60/1.33 => ( ! [Xx: $i] :
% 1.60/1.33 ( ( in @ Xx @ A )
% 1.60/1.33 => ( ( in @ Xx @ X )
% 1.60/1.33 => ( in @ Xx @ Y ) ) )
% 1.60/1.33 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 1.60/1.33
% 1.60/1.33 thf(complementImpComplementIntersect_type,type,
% 1.60/1.33 complementImpComplementIntersect: $o ).
% 1.60/1.33
% 1.60/1.33 thf(complementImpComplementIntersect,definition,
% 1.60/1.33 ( complementImpComplementIntersect
% 1.60/1.33 = ( ! [A: $i,X: $i] :
% 1.60/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.60/1.33 => ! [Y: $i] :
% 1.60/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.60/1.33 => ! [Xx: $i] :
% 1.60/1.33 ( ( in @ Xx @ A )
% 1.60/1.33 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 1.60/1.33 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 1.60/1.33
% 1.60/1.33 thf(complementSubsetComplementIntersect,conjecture,
% 1.60/1.33 ( binintersectT_lem
% 1.60/1.33 => ( complementT_lem
% 1.60/1.33 => ( subsetTI
% 1.60/1.33 => ( complementImpComplementIntersect
% 1.60/1.33 => ! [A: $i,X: $i] :
% 1.60/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.60/1.33 => ! [Y: $i] :
% 1.60/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.60/1.33 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 1.60/1.33 ------------------------
% 1.60/1.36 % (25714)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25614 for (2999ds/2Mi)
% 1.60/1.36 % (25717)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25614 for (2999ds/18Mi)
% 1.60/1.36 % (25712)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_25614 for (2999ds/4Mi)
% 1.60/1.36 % (25716)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_25614 for (2999ds/275Mi)
% 1.60/1.36 % (25713)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_25614 for (2999ds/27Mi)
% 1.60/1.36 % (25711)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25614 for (2999ds/183Mi)
% 1.60/1.36 % (25715)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_25614 for (2999ds/2Mi)
% 1.60/1.36 % (25714)Instruction limit reached!
% 1.60/1.36 % (25714)------------------------------
% 1.60/1.36 % (25714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (25714)Termination reason: Unknown
% 1.60/1.36 % (25714)Termination phase: Property scanning
% 1.60/1.36
% 1.60/1.36 % (25714)Memory used [KB]: 1023
% 1.60/1.36 % (25714)Time elapsed: 0.003 s
% 1.60/1.36 % (25714)Instructions burned: 2 (million)
% 1.60/1.36 % (25714)------------------------------
% 1.60/1.36 % (25714)------------------------------
% 1.60/1.36 % (25715)Instruction limit reached!
% 1.60/1.36 % (25715)------------------------------
% 1.60/1.36 % (25715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (25715)Termination reason: Unknown
% 1.60/1.36 % (25715)Termination phase: Property scanning
% 1.60/1.36
% 1.60/1.36 % (25715)Memory used [KB]: 1023
% 1.60/1.36 % (25715)Time elapsed: 0.003 s
% 1.60/1.36 % (25715)Instructions burned: 3 (million)
% 1.60/1.36 % (25715)------------------------------
% 1.60/1.36 % (25715)------------------------------
% 1.60/1.36 % (25712)Instruction limit reached!
% 1.60/1.36 % (25712)------------------------------
% 1.60/1.36 % (25712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (25712)Termination reason: Unknown
% 1.60/1.36 % (25712)Termination phase: Saturation
% 1.60/1.36
% 1.60/1.36 % (25712)Memory used [KB]: 1023
% 1.60/1.36 % (25712)Time elapsed: 0.004 s
% 1.60/1.36 % (25712)Instructions burned: 4 (million)
% 1.60/1.36 % (25712)------------------------------
% 1.60/1.36 % (25712)------------------------------
% 1.60/1.36 % (25717)Instruction limit reached!
% 1.60/1.36 % (25717)------------------------------
% 1.60/1.36 % (25717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (25717)Termination reason: Unknown
% 1.60/1.36 % (25717)Termination phase: Saturation
% 1.60/1.36
% 1.60/1.36 % (25717)Memory used [KB]: 5628
% 1.60/1.36 % (25717)Time elapsed: 0.011 s
% 1.60/1.36 % (25717)Instructions burned: 18 (million)
% 1.60/1.36 % (25717)------------------------------
% 1.60/1.36 % (25717)------------------------------
% 1.60/1.37 % (25713)Instruction limit reached!
% 1.60/1.37 % (25713)------------------------------
% 1.60/1.37 % (25713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.37 % (25713)Termination reason: Unknown
% 1.60/1.37 % (25713)Termination phase: Saturation
% 1.60/1.37
% 1.60/1.37 % (25713)Memory used [KB]: 5628
% 1.60/1.37 % (25713)Time elapsed: 0.016 s
% 1.60/1.37 % (25713)Instructions burned: 27 (million)
% 1.60/1.37 % (25713)------------------------------
% 1.60/1.37 % (25713)------------------------------
% 1.60/1.37 % (25719)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_25614 for (2999ds/37Mi)
% 1.60/1.37 % (25718)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25614 for (2999ds/3Mi)
% 1.60/1.37 % (25720)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_25614 for (2999ds/15Mi)
% 1.60/1.37 % (25718)Instruction limit reached!
% 1.60/1.37 % (25718)------------------------------
% 1.60/1.37 % (25718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.37 % (25718)Termination reason: Unknown
% 1.60/1.37 % (25718)Termination phase: Property scanning
% 1.60/1.37
% 1.60/1.37 % (25718)Memory used [KB]: 1023
% 1.60/1.37 % (25718)Time elapsed: 0.003 s
% 1.60/1.37 % (25718)Instructions burned: 3 (million)
% 1.60/1.37 % (25718)------------------------------
% 1.60/1.37 % (25718)------------------------------
% 1.60/1.38 % (25716)First to succeed.
% 1.60/1.38 % (25720)Instruction limit reached!
% 1.60/1.38 % (25720)------------------------------
% 1.60/1.38 % (25720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.38 % (25720)Termination reason: Unknown
% 1.60/1.38 % (25721)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_25614 for (2999ds/3Mi)
% 1.60/1.38 % (25720)Termination phase: Saturation
% 1.60/1.38
% 1.60/1.38 % (25720)Memory used [KB]: 5628
% 1.60/1.38 % (25720)Time elapsed: 0.009 s
% 1.60/1.38 % (25720)Instructions burned: 15 (million)
% 1.60/1.38 % (25720)------------------------------
% 1.60/1.38 % (25720)------------------------------
% 1.60/1.38 % (25721)Instruction limit reached!
% 1.60/1.38 % (25721)------------------------------
% 1.60/1.38 % (25721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.38 % (25721)Termination reason: Unknown
% 1.60/1.38 % (25721)Termination phase: Function definition elimination
% 1.60/1.38
% 1.60/1.38 % (25721)Memory used [KB]: 1023
% 1.60/1.38 % (25721)Time elapsed: 0.003 s
% 1.60/1.38 % (25721)Instructions burned: 4 (million)
% 1.60/1.38 % (25721)------------------------------
% 1.60/1.38 % (25721)------------------------------
% 1.60/1.38 % (25716)Refutation found. Thanks to Tanya!
% 1.60/1.38 % SZS status Theorem for DTF2THF_25614
% 1.60/1.38 % SZS output start Proof for DTF2THF_25614
% 1.60/1.38 thf(func_def_0, type, in: $i > $i > $o).
% 1.60/1.38 thf(func_def_1, type, powerset: $i > $i).
% 1.60/1.38 thf(func_def_2, type, subset: $i > $i > $o).
% 1.60/1.38 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.60/1.38 thf(func_def_4, type, setminus: $i > $i > $i).
% 1.60/1.38 thf(func_def_22, type, sK10: $i > $i > $i > $i).
% 1.60/1.38 thf(f189,plain,(
% 1.60/1.38 $false),
% 1.60/1.38 inference(subsumption_resolution,[status(thm)],[f188,f61])).
% 1.60/1.38 thf(f61,plain,(
% 1.60/1.38 ((in @ sK8 @ (powerset @ sK7)) = $true)),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f39])).
% 1.60/1.38 thf(f39,plain,(
% 1.60/1.38 (complementT_lem = $true) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & ((((subset @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ (binintersect @ sK8 @ sK9))) != $true) & ((in @ sK9 @ (powerset @ sK7)) = $true)) & ((in @ sK8 @ (powerset @ sK7)) = $true)) & (binintersectT_lem = $true)),
% 1.60/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f23,f38,f37])).
% 1.60/1.38 thf(f37,plain,(
% 1.60/1.38 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (((subset @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ (binintersect @ sK8 @ X2))) != $true) & ($true = (in @ X2 @ (powerset @ sK7)))) & ((in @ sK8 @ (powerset @ sK7)) = $true))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f38,plain,(
% 1.60/1.38 ? [X2 : $i] : (((subset @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ (binintersect @ sK8 @ X2))) != $true) & ($true = (in @ X2 @ (powerset @ sK7)))) => (((subset @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ (binintersect @ sK8 @ sK9))) != $true) & ((in @ sK9 @ (powerset @ sK7)) = $true))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f23,plain,(
% 1.60/1.38 (complementT_lem = $true) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binintersectT_lem = $true)),
% 1.60/1.38 inference(flattening,[status(thm)],[f22])).
% 1.60/1.38 thf(f22,plain,(
% 1.60/1.38 (((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (complementImpComplementIntersect = $true)) & (subsetTI = $true)) & (complementT_lem = $true)) & (binintersectT_lem = $true)),
% 1.60/1.38 inference(ennf_transformation,[status(thm)],[f11])).
% 1.60/1.38 thf(f11,plain,(
% 1.60/1.38 ~((binintersectT_lem = $true) => ((complementT_lem = $true) => ((subsetTI = $true) => ((complementImpComplementIntersect = $true) => ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)))))))),
% 1.60/1.38 inference(fool_elimination,[status(thm)],[f10])).
% 1.60/1.38 thf(f10,plain,(
% 1.60/1.38 ~(binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))))),
% 1.60/1.38 inference(rectify,[status(thm)],[f6])).
% 1.60/1.38 thf(f6,negated_conjecture,(
% 1.60/1.38 ~(binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))))),
% 1.60/1.38 inference(negated_conjecture,[status(cth)],[f5])).
% 1.60/1.38 thf(f5,conjecture,(
% 1.60/1.38 binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 1.60/1.38 file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',complementSubsetComplementIntersect)).
% 1.60/1.38 thf(f188,plain,(
% 1.60/1.38 ((in @ sK8 @ (powerset @ sK7)) != $true)),
% 1.60/1.38 inference(subsumption_resolution,[status(thm)],[f187,f62])).
% 1.60/1.38 thf(f62,plain,(
% 1.60/1.38 ((in @ sK9 @ (powerset @ sK7)) = $true)),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f39])).
% 1.60/1.38 thf(f187,plain,(
% 1.60/1.38 ((in @ sK9 @ (powerset @ sK7)) != $true) | ((in @ sK8 @ (powerset @ sK7)) != $true)),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f186])).
% 1.60/1.38 thf(f186,plain,(
% 1.60/1.38 ((in @ sK8 @ (powerset @ sK7)) != $true) | ((in @ sK9 @ (powerset @ sK7)) != $true) | ($true != $true)),
% 1.60/1.38 inference(superposition,[status(thm)],[f175,f99])).
% 1.60/1.38 thf(f99,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.60/1.38 thf(f77,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true) | ($true != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.60/1.38 inference(definition_unfolding,[status(thm)],[f53,f60])).
% 1.60/1.38 thf(f60,plain,(
% 1.60/1.38 (binintersectT_lem = $true)),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f39])).
% 1.60/1.38 thf(f53,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | (binintersectT_lem != $true)) )),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f30])).
% 1.60/1.38 thf(f30,plain,(
% 1.60/1.38 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true))) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | (((in @ sK0 @ (powerset @ sK1)) = $true) & (((in @ (binintersect @ sK0 @ sK2) @ (powerset @ sK1)) != $true) & ((in @ sK2 @ (powerset @ sK1)) = $true))))),
% 1.60/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f29,f28])).
% 1.60/1.38 thf(f28,plain,(
% 1.60/1.38 ? [X3 : $i,X4 : $i] : (((in @ X3 @ (powerset @ X4)) = $true) & ? [X5 : $i] : (($true != (in @ (binintersect @ X3 @ X5) @ (powerset @ X4))) & ((in @ X5 @ (powerset @ X4)) = $true))) => (((in @ sK0 @ (powerset @ sK1)) = $true) & ? [X5 : $i] : (($true != (in @ (binintersect @ sK0 @ X5) @ (powerset @ sK1))) & ((in @ X5 @ (powerset @ sK1)) = $true)))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f29,plain,(
% 1.60/1.38 ? [X5 : $i] : (($true != (in @ (binintersect @ sK0 @ X5) @ (powerset @ sK1))) & ((in @ X5 @ (powerset @ sK1)) = $true)) => (((in @ (binintersect @ sK0 @ sK2) @ (powerset @ sK1)) != $true) & ((in @ sK2 @ (powerset @ sK1)) = $true))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f27,plain,(
% 1.60/1.38 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true))) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | ? [X3 : $i,X4 : $i] : (((in @ X3 @ (powerset @ X4)) = $true) & ? [X5 : $i] : (($true != (in @ (binintersect @ X3 @ X5) @ (powerset @ X4))) & ((in @ X5 @ (powerset @ X4)) = $true))))),
% 1.60/1.38 inference(rectify,[status(thm)],[f26])).
% 1.60/1.38 thf(f26,plain,(
% 1.60/1.38 (! [X1 : $i,X0 : $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) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true))))),
% 1.60/1.38 inference(nnf_transformation,[status(thm)],[f19])).
% 1.60/1.38 thf(f19,plain,(
% 1.60/1.38 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) <=> (binintersectT_lem = $true)),
% 1.60/1.38 inference(ennf_transformation,[status(thm)],[f15])).
% 1.60/1.38 thf(f15,plain,(
% 1.60/1.38 (binintersectT_lem = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true)))),
% 1.60/1.38 inference(fool_elimination,[status(thm)],[f14])).
% 1.60/1.38 thf(f14,plain,(
% 1.60/1.38 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 1.60/1.38 inference(rectify,[status(thm)],[f1])).
% 1.60/1.38 thf(f1,axiom,(
% 1.60/1.38 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 1.60/1.38 file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',binintersectT_lem)).
% 1.60/1.38 thf(f175,plain,(
% 1.60/1.38 ((in @ (binintersect @ sK8 @ sK9) @ (powerset @ sK7)) != $true)),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f174])).
% 1.60/1.38 thf(f174,plain,(
% 1.60/1.38 ((in @ (binintersect @ sK8 @ sK9) @ (powerset @ sK7)) != $true) | ($true != $true)),
% 1.60/1.38 inference(superposition,[status(thm)],[f168,f102])).
% 1.60/1.38 thf(f102,plain,(
% 1.60/1.38 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.60/1.38 thf(f94,plain,(
% 1.60/1.38 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != $true)) )),
% 1.60/1.38 inference(definition_unfolding,[status(thm)],[f76,f66])).
% 1.60/1.38 thf(f66,plain,(
% 1.60/1.38 (complementT_lem = $true)),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f39])).
% 1.60/1.38 thf(f76,plain,(
% 1.60/1.38 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | (complementT_lem != $true)) )),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f49])).
% 1.60/1.38 thf(f49,plain,(
% 1.60/1.38 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | (((in @ sK14 @ (powerset @ sK15)) = $true) & ($true != (in @ (setminus @ sK15 @ sK14) @ (powerset @ sK15)))))),
% 1.60/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f47,f48])).
% 1.60/1.38 thf(f48,plain,(
% 1.60/1.38 ? [X2 : $i,X3 : $i] : (((in @ X2 @ (powerset @ X3)) = $true) & ((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) != $true)) => (((in @ sK14 @ (powerset @ sK15)) = $true) & ($true != (in @ (setminus @ sK15 @ sK14) @ (powerset @ sK15))))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f47,plain,(
% 1.60/1.38 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : (((in @ X2 @ (powerset @ X3)) = $true) & ((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) != $true)))),
% 1.60/1.38 inference(rectify,[status(thm)],[f46])).
% 1.60/1.38 thf(f46,plain,(
% 1.60/1.38 (! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true)))),
% 1.60/1.38 inference(nnf_transformation,[status(thm)],[f18])).
% 1.60/1.38 thf(f18,plain,(
% 1.60/1.38 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) <=> (complementT_lem = $true)),
% 1.60/1.38 inference(ennf_transformation,[status(thm)],[f13])).
% 1.60/1.38 thf(f13,plain,(
% 1.60/1.38 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) <=> (complementT_lem = $true)),
% 1.60/1.38 inference(fool_elimination,[status(thm)],[f12])).
% 1.60/1.38 thf(f12,plain,(
% 1.60/1.38 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.60/1.38 inference(rectify,[status(thm)],[f2])).
% 1.60/1.38 thf(f2,axiom,(
% 1.60/1.38 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.60/1.38 file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',complementT_lem)).
% 1.60/1.38 thf(f168,plain,(
% 1.60/1.38 ($true != (in @ (setminus @ sK7 @ (binintersect @ sK8 @ sK9)) @ (powerset @ sK7)))),
% 1.60/1.38 inference(subsumption_resolution,[status(thm)],[f167,f61])).
% 1.60/1.38 thf(f167,plain,(
% 1.60/1.38 ((in @ sK8 @ (powerset @ sK7)) != $true) | ($true != (in @ (setminus @ sK7 @ (binintersect @ sK8 @ sK9)) @ (powerset @ sK7)))),
% 1.60/1.38 inference(subsumption_resolution,[status(thm)],[f166,f62])).
% 1.60/1.38 thf(f166,plain,(
% 1.60/1.38 ((in @ sK9 @ (powerset @ sK7)) != $true) | ($true != (in @ (setminus @ sK7 @ (binintersect @ sK8 @ sK9)) @ (powerset @ sK7))) | ((in @ sK8 @ (powerset @ sK7)) != $true)),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.60/1.38 thf(f165,plain,(
% 1.60/1.38 ($true != (in @ (setminus @ sK7 @ (binintersect @ sK8 @ sK9)) @ (powerset @ sK7))) | ((in @ sK9 @ (powerset @ sK7)) != $true) | ($true != $true) | ((in @ sK8 @ (powerset @ sK7)) != $true)),
% 1.60/1.38 inference(superposition,[status(thm)],[f63,f164])).
% 1.60/1.38 thf(f164,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(subsumption_resolution,[status(thm)],[f162,f102])).
% 1.60/1.38 thf(f162,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.60/1.38 thf(f161,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(duplicate_literal_removal,[status(thm)],[f160])).
% 1.60/1.38 thf(f160,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ($true != $true)) )),
% 1.60/1.38 inference(superposition,[status(thm)],[f155,f98])).
% 1.60/1.38 thf(f98,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK10 @ X2 @ X1 @ X0) @ X0) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((subset @ X1 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.60/1.38 thf(f89,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK10 @ X2 @ X1 @ X0) @ X0) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((subset @ X1 @ X2) = $true) | ($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(definition_unfolding,[status(thm)],[f71,f64])).
% 1.60/1.38 thf(f64,plain,(
% 1.60/1.38 (subsetTI = $true)),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f39])).
% 1.60/1.38 thf(f71,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (sK10 @ X2 @ X1 @ X0) @ X0) = $true) | ((subset @ X1 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (subsetTI != $true)) )),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f45])).
% 1.60/1.38 thf(f45,plain,(
% 1.60/1.38 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : ((((in @ (sK10 @ X2 @ X1 @ X0) @ X1) = $true) & ((in @ (sK10 @ X2 @ X1 @ X0) @ X2) != $true) & ((in @ (sK10 @ X2 @ X1 @ X0) @ X0) = $true)) | ((subset @ X1 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) | (subsetTI != $true)) & ((subsetTI = $true) | (((in @ sK12 @ (powerset @ sK11)) = $true) & (! [X7 : $i] : (((in @ X7 @ sK12) != $true) | ((in @ X7 @ sK13) = $true) | ((in @ X7 @ sK11) != $true)) & ((subset @ sK12 @ sK13) != $true) & ((in @ sK13 @ (powerset @ sK11)) = $true))))),
% 1.60/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f41,f44,f43,f42])).
% 1.60/1.38 thf(f42,plain,(
% 1.60/1.38 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) => (((in @ (sK10 @ X2 @ X1 @ X0) @ X1) = $true) & ((in @ (sK10 @ X2 @ X1 @ X0) @ X2) != $true) & ((in @ (sK10 @ X2 @ X1 @ X0) @ X0) = $true)))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f43,plain,(
% 1.60/1.38 ? [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ X5) != $true) | ((in @ X7 @ X6) = $true) | ((in @ X7 @ X4) != $true)) & ((subset @ X5 @ X6) != $true) & ((in @ X6 @ (powerset @ X4)) = $true))) => (((in @ sK12 @ (powerset @ sK11)) = $true) & ? [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ sK12) != $true) | ((in @ X7 @ X6) = $true) | ((in @ X7 @ sK11) != $true)) & ((subset @ sK12 @ X6) != $true) & ((in @ X6 @ (powerset @ sK11)) = $true)))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f44,plain,(
% 1.60/1.38 ? [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ sK12) != $true) | ((in @ X7 @ X6) = $true) | ((in @ X7 @ sK11) != $true)) & ((subset @ sK12 @ X6) != $true) & ((in @ X6 @ (powerset @ sK11)) = $true)) => (! [X7 : $i] : (((in @ X7 @ sK12) != $true) | ((in @ X7 @ sK13) = $true) | ((in @ X7 @ sK11) != $true)) & ((subset @ sK12 @ sK13) != $true) & ((in @ sK13 @ (powerset @ sK11)) = $true))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f41,plain,(
% 1.60/1.38 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) | ((subset @ X1 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ X5) != $true) | ((in @ X7 @ X6) = $true) | ((in @ X7 @ X4) != $true)) & ((subset @ X5 @ X6) != $true) & ((in @ X6 @ (powerset @ X4)) = $true))))),
% 1.60/1.38 inference(rectify,[status(thm)],[f40])).
% 1.60/1.38 thf(f40,plain,(
% 1.60/1.38 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) | ((subset @ X1 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true)) & ((subset @ X1 @ X2) != $true) & ((in @ X2 @ (powerset @ X0)) = $true))))),
% 1.60/1.38 inference(nnf_transformation,[status(thm)],[f25])).
% 1.60/1.38 thf(f25,plain,(
% 1.60/1.38 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) | ((subset @ X1 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) <=> (subsetTI = $true)),
% 1.60/1.38 inference(flattening,[status(thm)],[f24])).
% 1.60/1.38 thf(f24,plain,(
% 1.60/1.38 (subsetTI = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((subset @ X1 @ X2) = $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))),
% 1.60/1.38 inference(ennf_transformation,[status(thm)],[f17])).
% 1.60/1.38 thf(f17,plain,(
% 1.60/1.38 (subsetTI = $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 @ X1) = $true) => ((in @ X3 @ X2) = $true))) => ((subset @ X1 @ X2) = $true))))),
% 1.60/1.38 inference(fool_elimination,[status(thm)],[f16])).
% 1.60/1.38 thf(f16,plain,(
% 1.60/1.38 (! [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))) => (subset @ X1 @ X2)))) = subsetTI)),
% 1.60/1.38 inference(rectify,[status(thm)],[f3])).
% 1.60/1.38 thf(f3,axiom,(
% 1.60/1.38 (! [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))) => (subset @ X1 @ X2)))) = subsetTI)),
% 1.60/1.38 file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',subsetTI)).
% 1.60/1.38 thf(f155,plain,(
% 1.60/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK10 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0) != $true) | ($true != (in @ (setminus @ X0 @ X1) @ (powerset @ X3))) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ($true != (in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.60/1.38 thf(f154,plain,(
% 1.60/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK10 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0) != $true) | ($true != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))) | ($true != (in @ (setminus @ X0 @ X1) @ (powerset @ X3))) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(duplicate_literal_removal,[status(thm)],[f150])).
% 1.60/1.38 thf(f150,plain,(
% 1.60/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ (setminus @ X0 @ X1) @ (powerset @ X3))) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))) | ((in @ (sK10 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0) != $true) | ($true != (in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ($true != (in @ (setminus @ X0 @ X1) @ (powerset @ X3))) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(superposition,[status(thm)],[f122,f97])).
% 1.60/1.38 thf(f97,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK10 @ X2 @ X1 @ X0) @ X1) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((subset @ X1 @ X2) = $true)) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.60/1.38 thf(f87,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X1 @ X2) = $true) | ($true != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (sK10 @ X2 @ X1 @ X0) @ X1) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.60/1.38 inference(definition_unfolding,[status(thm)],[f73,f64])).
% 1.60/1.38 thf(f73,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (sK10 @ X2 @ X1 @ X0) @ X1) = $true) | ((subset @ X1 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (subsetTI != $true)) )),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f45])).
% 1.60/1.38 thf(f122,plain,(
% 1.60/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (sK10 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ X1)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X4)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X3 @ (powerset @ X4)) != $true) | ((in @ (sK10 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ X0) != $true) | ((subset @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.60/1.38 thf(f121,plain,(
% 1.60/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (sK10 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ X0) != $true) | ($true != $true) | ((in @ X3 @ (powerset @ X4)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X4)) != $true) | ((subset @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (sK10 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ X1)) != $true)) )),
% 1.60/1.38 inference(superposition,[status(thm)],[f101,f100])).
% 1.60/1.38 thf(f100,plain,(
% 1.60/1.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (setminus @ X4 @ X5)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true)) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.60/1.38 thf(f86,plain,(
% 1.60/1.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X7 @ X4) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ($true != $true) | ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true) | ((in @ X7 @ (setminus @ X4 @ X5)) != $true)) )),
% 1.60/1.38 inference(definition_unfolding,[status(thm)],[f54,f65])).
% 1.60/1.38 thf(f65,plain,(
% 1.60/1.38 (complementImpComplementIntersect = $true)),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f39])).
% 1.60/1.38 thf(f54,plain,(
% 1.60/1.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (setminus @ X4 @ X5)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (complementImpComplementIntersect != $true)) )),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f36])).
% 1.60/1.38 thf(f36,plain,(
% 1.60/1.38 ((complementImpComplementIntersect = $true) | (((($true != (in @ sK6 @ (setminus @ sK3 @ (binintersect @ sK4 @ sK5)))) & ((in @ sK6 @ sK3) = $true) & ((in @ sK6 @ (setminus @ sK3 @ sK4)) = $true)) & ((in @ sK5 @ (powerset @ sK3)) = $true)) & ((in @ sK4 @ (powerset @ sK3)) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))) = $true) | ((in @ X7 @ X4) != $true) | ((in @ X7 @ (setminus @ X4 @ X5)) != $true)) | ((in @ X6 @ (powerset @ X4)) != $true)) | ((in @ X5 @ (powerset @ X4)) != $true)) | (complementImpComplementIntersect != $true))),
% 1.60/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f32,f35,f34,f33])).
% 1.60/1.38 thf(f33,plain,(
% 1.60/1.38 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (setminus @ X0 @ X1)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ sK3 @ (binintersect @ sK4 @ X2))) != $true) & ((in @ X3 @ sK3) = $true) & ((in @ X3 @ (setminus @ sK3 @ sK4)) = $true)) & ((in @ X2 @ (powerset @ sK3)) = $true)) & ((in @ sK4 @ (powerset @ sK3)) = $true))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f34,plain,(
% 1.60/1.38 ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ sK3 @ (binintersect @ sK4 @ X2))) != $true) & ((in @ X3 @ sK3) = $true) & ((in @ X3 @ (setminus @ sK3 @ sK4)) = $true)) & ((in @ X2 @ (powerset @ sK3)) = $true)) => (? [X3 : $i] : (((in @ X3 @ (setminus @ sK3 @ (binintersect @ sK4 @ sK5))) != $true) & ((in @ X3 @ sK3) = $true) & ((in @ X3 @ (setminus @ sK3 @ sK4)) = $true)) & ((in @ sK5 @ (powerset @ sK3)) = $true))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f35,plain,(
% 1.60/1.38 ? [X3 : $i] : (((in @ X3 @ (setminus @ sK3 @ (binintersect @ sK4 @ sK5))) != $true) & ((in @ X3 @ sK3) = $true) & ((in @ X3 @ (setminus @ sK3 @ sK4)) = $true)) => (($true != (in @ sK6 @ (setminus @ sK3 @ (binintersect @ sK4 @ sK5)))) & ((in @ sK6 @ sK3) = $true) & ((in @ sK6 @ (setminus @ sK3 @ sK4)) = $true))),
% 1.60/1.38 introduced(definition,[],[choice_axiom])).
% 1.60/1.38 thf(f32,plain,(
% 1.60/1.38 ((complementImpComplementIntersect = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (setminus @ X0 @ X1)) = $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 @ (setminus @ X4 @ X5)) != $true)) | ((in @ X6 @ (powerset @ X4)) != $true)) | ((in @ X5 @ (powerset @ X4)) != $true)) | (complementImpComplementIntersect != $true))),
% 1.60/1.38 inference(rectify,[status(thm)],[f31])).
% 1.60/1.38 thf(f31,plain,(
% 1.60/1.38 ((complementImpComplementIntersect = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ (setminus @ X1 @ X0)) = $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 @ (setminus @ X1 @ X0)) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementImpComplementIntersect != $true))),
% 1.60/1.38 inference(nnf_transformation,[status(thm)],[f21])).
% 1.60/1.38 thf(f21,plain,(
% 1.60/1.38 (complementImpComplementIntersect = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ (setminus @ X1 @ X0)) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.60/1.38 inference(flattening,[status(thm)],[f20])).
% 1.60/1.38 thf(f20,plain,(
% 1.60/1.38 (complementImpComplementIntersect = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) = $true) | ((in @ X3 @ (setminus @ X1 @ X0)) != $true)) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.60/1.38 inference(ennf_transformation,[status(thm)],[f9])).
% 1.60/1.38 thf(f9,plain,(
% 1.60/1.38 (complementImpComplementIntersect = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (setminus @ X1 @ X0)) = $true) => ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) = $true)))))),
% 1.60/1.38 inference(fool_elimination,[status(thm)],[f8])).
% 1.60/1.38 thf(f8,plain,(
% 1.60/1.38 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ X0)) => (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))))))) = complementImpComplementIntersect)),
% 1.60/1.38 inference(rectify,[status(thm)],[f4])).
% 1.60/1.38 thf(f4,axiom,(
% 1.60/1.38 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = complementImpComplementIntersect)),
% 1.60/1.38 file('/export/starexec/sandbox2/tmp/tmp.GQWWWhHSz1/DTF2THF_25614.p',complementImpComplementIntersect)).
% 1.60/1.38 thf(f101,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK10 @ X2 @ X1 @ X0) @ X2) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((subset @ X1 @ X2) = $true)) )),
% 1.60/1.38 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.60/1.38 thf(f88,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (sK10 @ X2 @ X1 @ X0) @ X2) != $true) | ((subset @ X1 @ X2) = $true)) )),
% 1.60/1.38 inference(definition_unfolding,[status(thm)],[f72,f64])).
% 1.60/1.38 thf(f72,plain,(
% 1.60/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (sK10 @ X2 @ X1 @ X0) @ X2) != $true) | ((subset @ X1 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (subsetTI != $true)) )),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f45])).
% 1.60/1.38 thf(f63,plain,(
% 1.60/1.38 ((subset @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ (binintersect @ sK8 @ sK9))) != $true)),
% 1.60/1.38 inference(cnf_transformation,[status(thm)],[f39])).
% 1.60/1.38 % SZS output end Proof for DTF2THF_25614
% 1.60/1.38 % (25716)------------------------------
% 1.60/1.38 % (25716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.38 % (25716)Termination reason: Refutation
% 1.60/1.38
% 1.60/1.38 % (25716)Memory used [KB]: 5756
% 1.60/1.38 % (25716)Time elapsed: 0.028 s
% 1.60/1.38 % (25716)Instructions burned: 43 (million)
% 1.60/1.38 % (25716)------------------------------
% 1.60/1.38 % (25716)------------------------------
% 1.60/1.38 % (25710)Success in time 0.04 s
%------------------------------------------------------------------------------