%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU743^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:50 AM UTC 2026
% Result : Theorem 1.65s 1.38s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 19
% Syntax : Number of formulae : 97 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 1895 ( 536 equ; 0 cnn)
% Maximal formula atoms : 14 ( 19 avg)
% Number of connectives : 2806 ( 283 ~; 246 |; 152 &;2031 @)
% ( 10 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 24 con; 0-3 aty)
% Number of variables : 331 ( 0 ^; 244 !; 87 ?; 331 :)
% 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_11,type,
sK0: $i > $i > $i > $i ).
thf(f188,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f187,f68]) ).
thf(f68,plain,
( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( powersetTI1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true )
& ( $true
!= ( in @ ( binintersect @ sK8 @ sK9 ) @ ( powerset @ ( binintersect @ ( binunion @ sK8 @ sK10 ) @ ( binunion @ sK9 @ sK10 ) ) ) ) )
& ( $true
= ( in @ sK10 @ ( powerset @ sK7 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f37,f40,f39,f38]) ).
thf(f38,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) ) ) )
=> ( ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK7 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ sK8 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK8 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK7 ) )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK7 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ sK8 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK8 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK7 ) )
= $true ) ) )
=> ( ( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true )
& ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ sK8 @ sK9 ) @ ( powerset @ ( binintersect @ ( binunion @ sK8 @ X3 ) @ ( binunion @ sK9 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK7 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ sK8 @ sK9 ) @ ( powerset @ ( binintersect @ ( binunion @ sK8 @ X3 ) @ ( binunion @ sK9 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK7 ) )
= $true ) )
=> ( ( $true
!= ( in @ ( binintersect @ sK8 @ sK9 ) @ ( powerset @ ( binintersect @ ( binunion @ sK8 @ sK10 ) @ ( binunion @ sK9 @ sK10 ) ) ) ) )
& ( $true
= ( in @ sK10 @ ( powerset @ sK7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( powersetTI1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ( powersetTI1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) ) ) )
& ( inIntersectImpInIntersectUnions = $true )
& ( powersetTI1 = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetTI1 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetTI1
=> ( inIntersectImpInIntersectUnions
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetTI1
=> ( inIntersectImpInIntersectUnions
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X4 ) @ ( binunion @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( binintersectT_lem
=> ( binunionT_lem
=> ( powersetTI1
=> ( inIntersectImpInIntersectUnions
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X4 ) @ ( binunion @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',intersectInPowersetIntersectUnions) ).
thf(f187,plain,
( $true
!= ( in @ sK8 @ ( powerset @ sK7 ) ) ),
inference(subsumption_resolution,[status(thm)],[f186,f67]) ).
thf(f67,plain,
( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f186,plain,
( ( ( in @ sK9 @ ( powerset @ sK7 ) )
!= $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK7 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK7 ) ) )
| ( ( in @ sK9 @ ( powerset @ sK7 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f178,f65]) ).
thf(f65,plain,
( $true
= ( in @ sK10 @ ( powerset @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f178,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK10 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK9 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ X0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f177,f111]) ).
thf(f111,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f76,f70]) ).
thf(f70,plain,
binunionT_lem = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( binunionT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ( ( $true
!= ( in @ ( binunion @ sK12 @ sK13 ) @ ( powerset @ sK11 ) ) )
& ( $true
= ( in @ sK13 @ ( powerset @ sK11 ) ) )
& ( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f43,f45,f44]) ).
thf(f44,plain,
( ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( binunion @ X4 @ X5 ) @ ( powerset @ X3 ) )
!= $true )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) )
& ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) ) )
=> ( ? [X5: $i] :
( ( $true
!= ( in @ ( binunion @ sK12 @ X5 ) @ ( powerset @ sK11 ) ) )
& ( $true
= ( in @ X5 @ ( powerset @ sK11 ) ) ) )
& ( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ? [X5: $i] :
( ( $true
!= ( in @ ( binunion @ sK12 @ X5 ) @ ( powerset @ sK11 ) ) )
& ( $true
= ( in @ X5 @ ( powerset @ sK11 ) ) ) )
=> ( ( $true
!= ( in @ ( binunion @ sK12 @ sK13 ) @ ( powerset @ sK11 ) ) )
& ( $true
= ( in @ sK13 @ ( powerset @ sK11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( binunion @ X4 @ X5 ) @ ( powerset @ X3 ) )
!= $true )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) )
& ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( $true
!= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( binunionT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( $true
= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) )
<=> ( binunionT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) )
= binunionT_lem ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) )
= binunionT_lem ),
file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',binunionT_lem) ).
thf(f177,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK8 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK9 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( binunion @ sK9 @ sK10 ) @ ( powerset @ X0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f174,f111]) ).
thf(f174,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( binunion @ sK8 @ sK10 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK9 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( binunion @ sK9 @ sK10 ) @ ( powerset @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( binunion @ sK9 @ sK10 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK9 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( binunion @ sK8 @ sK10 ) @ ( powerset @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f162,f106]) ).
thf(f106,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)],[f91]) ).
thf(f91,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f64,f69]) ).
thf(f69,plain,
binintersectT_lem = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f64,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( binintersectT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,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 ) )
& ( ( binintersectT_lem = $true )
| ( ( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) )
& ( $true
= ( in @ sK6 @ ( powerset @ sK4 ) ) )
& ( ( in @ ( binintersect @ sK5 @ sK6 ) @ ( powerset @ sK4 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f33,f35,f34]) ).
thf(f34,plain,
( ? [X3: $i,X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) )
& ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
!= $true ) ) )
=> ( ( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ sK4 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK5 @ X5 ) @ ( powerset @ sK4 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ sK4 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK5 @ X5 ) @ ( powerset @ sK4 ) ) ) )
=> ( ( $true
= ( in @ sK6 @ ( powerset @ sK4 ) ) )
& ( ( in @ ( binintersect @ sK5 @ sK6 ) @ ( powerset @ sK4 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,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 ) )
& ( ( binintersectT_lem = $true )
| ? [X3: $i,X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) )
& ( ( in @ ( binintersect @ X4 @ X5 ) @ ( powerset @ X3 ) )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) )
| ( binintersectT_lem != $true ) )
& ( ( binintersectT_lem = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) )
<=> ( binintersectT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) )
<=> ( binintersectT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( binintersectT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binintersectT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',binintersectT_lem) ).
thf(f162,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( binintersect @ ( binunion @ sK8 @ sK10 ) @ ( binunion @ sK9 @ sK10 ) ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK9 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK9 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK10 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ sK8 @ sK10 ) @ ( binunion @ sK9 @ sK10 ) ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f66,f160]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X3 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f156,f106]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X3 ) )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X3 ) )
!= $true )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X3 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f153]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X3 ) )
!= $true )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) )
| ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) ) ),
inference(superposition,[status(thm)],[f137,f110]) ).
thf(f110,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f59,f72]) ).
thf(f72,plain,
powersetTI1 = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f59,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 ) )
| ( powersetTI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 ) )
& ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true ) ) ) )
| ( powersetTI1 != $true ) )
& ( ( powersetTI1 = $true )
| ( ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ sK2 @ ( powerset @ sK3 ) )
!= $true )
& ( ( in @ sK3 @ ( powerset @ sK1 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ sK2 ) )
| ( $true
!= ( in @ X7 @ sK1 ) )
| ( $true
= ( in @ X7 @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f27,f30,f29,f28]) ).
thf(f28,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) )
=> ( ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 ) )
& ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ( ( in @ X5 @ ( powerset @ X6 ) )
!= $true )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( ( in @ X7 @ X6 )
= $true ) ) ) )
=> ( ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ? [X6: $i] :
( ( $true
!= ( in @ sK2 @ ( powerset @ X6 ) ) )
& ( ( in @ X6 @ ( powerset @ sK1 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ sK2 ) )
| ( $true
!= ( in @ X7 @ sK1 ) )
| ( ( in @ X7 @ X6 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ? [X6: $i] :
( ( $true
!= ( in @ sK2 @ ( powerset @ X6 ) ) )
& ( ( in @ X6 @ ( powerset @ sK1 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ sK2 ) )
| ( $true
!= ( in @ X7 @ sK1 ) )
| ( ( in @ X7 @ X6 )
= $true ) ) )
=> ( ( ( in @ sK2 @ ( powerset @ sK3 ) )
!= $true )
& ( ( in @ sK3 @ ( powerset @ sK1 ) )
= $true )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ sK2 ) )
| ( $true
!= ( in @ X7 @ sK1 ) )
| ( $true
= ( in @ X7 @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) ) ) )
| ( powersetTI1 != $true ) )
& ( ( powersetTI1 = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ( ( in @ X5 @ ( powerset @ X6 ) )
!= $true )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( ( in @ X7 @ X6 )
= $true ) ) ) ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) ) ) )
| ( powersetTI1 != $true ) )
& ( ( powersetTI1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) ) ) )
<=> ( powersetTI1 = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ( powersetTI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X2 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( powersetTI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( $true
= ( in @ X0 @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X0 @ ( powerset @ X2 ) ) ) ) )
= powersetTI1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X1 @ ( powerset @ X2 ) ) ) ) )
= powersetTI1 ),
file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',powersetTI1) ).
thf(f137,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( sK0 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( binintersect @ X0 @ X2 ) @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X3 ) ) )
| ( ( in @ X0 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f136]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( sK0 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( binintersect @ X0 @ X2 ) @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X4 ) ) )
| ( ( in @ X0 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) )
| ( $true != $true )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ X0 @ ( powerset @ X4 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) )
| ( $true
!= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X4 ) ) )
| ( ( in @ ( sK0 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( binintersect @ X0 @ X2 ) @ X3 ) @ X4 )
!= $true ) ),
inference(superposition,[status(thm)],[f129,f109]) ).
thf(f109,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f60,f72]) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( powersetTI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ ( sK0 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ X3 @ X4 ) @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ ( sK0 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ X3 @ X4 ) @ X5 ) )
| ( ( in @ X3 @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) )
| ( ( in @ X3 @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ) )
= $true )
| ( $true
!= ( in @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ ( sK0 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ X3 @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X5 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ ( sK0 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) @ X3 @ X4 ) @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X5 ) ) ) ),
inference(superposition,[status(thm)],[f108,f107]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( $true != $true )
| ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f83,f71]) ).
thf(f71,plain,
inIntersectImpInIntersectUnions = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( inIntersectImpInIntersectUnions != $true ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( inIntersectImpInIntersectUnions != $true ) )
& ( ( inIntersectImpInIntersectUnions = $true )
| ( ( ( in @ sK14 @ ( powerset @ sK15 ) )
= $true )
& ( $true
= ( in @ sK18 @ ( binintersect @ sK14 @ sK16 ) ) )
& ( $true
= ( in @ sK18 @ sK15 ) )
& ( $true
!= ( in @ sK18 @ ( binintersect @ ( binunion @ sK14 @ sK17 ) @ ( binunion @ sK16 @ sK17 ) ) ) )
& ( ( in @ sK17 @ ( powerset @ sK15 ) )
= $true )
& ( ( in @ sK16 @ ( powerset @ sK15 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18])],[f48,f52,f51,f50,f49]) ).
thf(f49,plain,
( ? [X5: $i,X6: $i] :
( ( ( in @ X5 @ ( powerset @ X6 ) )
= $true )
& ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) )
& ( $true
= ( in @ X9 @ X6 ) )
& ( ( in @ X9 @ ( binintersect @ ( binunion @ X5 @ X8 ) @ ( binunion @ X7 @ X8 ) ) )
!= $true ) )
& ( ( in @ X8 @ ( powerset @ X6 ) )
= $true ) )
& ( $true
= ( in @ X7 @ ( powerset @ X6 ) ) ) ) )
=> ( ( ( in @ sK14 @ ( powerset @ sK15 ) )
= $true )
& ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ ( binintersect @ sK14 @ X7 ) ) )
& ( $true
= ( in @ X9 @ sK15 ) )
& ( $true
!= ( in @ X9 @ ( binintersect @ ( binunion @ sK14 @ X8 ) @ ( binunion @ X7 @ X8 ) ) ) ) )
& ( ( in @ X8 @ ( powerset @ sK15 ) )
= $true ) )
& ( $true
= ( in @ X7 @ ( powerset @ sK15 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f50,plain,
( ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ ( binintersect @ sK14 @ X7 ) ) )
& ( $true
= ( in @ X9 @ sK15 ) )
& ( $true
!= ( in @ X9 @ ( binintersect @ ( binunion @ sK14 @ X8 ) @ ( binunion @ X7 @ X8 ) ) ) ) )
& ( ( in @ X8 @ ( powerset @ sK15 ) )
= $true ) )
& ( $true
= ( in @ X7 @ ( powerset @ sK15 ) ) ) )
=> ( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ ( binintersect @ sK14 @ sK16 ) ) )
& ( $true
= ( in @ X9 @ sK15 ) )
& ( $true
!= ( in @ X9 @ ( binintersect @ ( binunion @ sK14 @ X8 ) @ ( binunion @ sK16 @ X8 ) ) ) ) )
& ( ( in @ X8 @ ( powerset @ sK15 ) )
= $true ) )
& ( ( in @ sK16 @ ( powerset @ sK15 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ ( binintersect @ sK14 @ sK16 ) ) )
& ( $true
= ( in @ X9 @ sK15 ) )
& ( $true
!= ( in @ X9 @ ( binintersect @ ( binunion @ sK14 @ X8 ) @ ( binunion @ sK16 @ X8 ) ) ) ) )
& ( ( in @ X8 @ ( powerset @ sK15 ) )
= $true ) )
=> ( ? [X9: $i] :
( ( $true
= ( in @ X9 @ ( binintersect @ sK14 @ sK16 ) ) )
& ( $true
= ( in @ X9 @ sK15 ) )
& ( $true
!= ( in @ X9 @ ( binintersect @ ( binunion @ sK14 @ sK17 ) @ ( binunion @ sK16 @ sK17 ) ) ) ) )
& ( ( in @ sK17 @ ( powerset @ sK15 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f52,plain,
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ ( binintersect @ sK14 @ sK16 ) ) )
& ( $true
= ( in @ X9 @ sK15 ) )
& ( $true
!= ( in @ X9 @ ( binintersect @ ( binunion @ sK14 @ sK17 ) @ ( binunion @ sK16 @ sK17 ) ) ) ) )
=> ( ( $true
= ( in @ sK18 @ ( binintersect @ sK14 @ sK16 ) ) )
& ( $true
= ( in @ sK18 @ sK15 ) )
& ( $true
!= ( in @ sK18 @ ( binintersect @ ( binunion @ sK14 @ sK17 ) @ ( binunion @ sK16 @ sK17 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( inIntersectImpInIntersectUnions != $true ) )
& ( ( inIntersectImpInIntersectUnions = $true )
| ? [X5: $i,X6: $i] :
( ( ( in @ X5 @ ( powerset @ X6 ) )
= $true )
& ? [X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) )
& ( $true
= ( in @ X9 @ X6 ) )
& ( ( in @ X9 @ ( binintersect @ ( binunion @ X5 @ X8 ) @ ( binunion @ X7 @ X8 ) ) )
!= $true ) )
& ( ( in @ X8 @ ( powerset @ X6 ) )
= $true ) )
& ( $true
= ( in @ X7 @ ( powerset @ X6 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X1 @ X2 ) ) )
| ( ( in @ X4 @ X0 )
!= $true )
| ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( inIntersectImpInIntersectUnions != $true ) )
& ( ( inIntersectImpInIntersectUnions = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ ( binintersect @ X1 @ X2 ) ) )
& ( ( in @ X4 @ X0 )
= $true )
& ( $true
!= ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X1 @ X2 ) ) )
| ( ( in @ X4 @ X0 )
!= $true )
| ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
<=> ( inIntersectImpInIntersectUnions = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
| ( $true
!= ( in @ X4 @ ( binintersect @ X1 @ X2 ) ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( inIntersectImpInIntersectUnions = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( $true
= ( in @ X4 @ ( binintersect @ X1 @ X2 ) ) )
=> ( $true
= ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) )
<=> ( inIntersectImpInIntersectUnions = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( inIntersectImpInIntersectUnions
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( inIntersectImpInIntersectUnions
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ ( binintersect @ ( binunion @ X1 @ X4 ) @ ( binunion @ X2 @ X4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',inIntersectImpInIntersectUnions) ).
thf(f108,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f58,f72]) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( powersetTI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f66,plain,
( $true
!= ( in @ ( binintersect @ sK8 @ sK9 ) @ ( powerset @ ( binintersect @ ( binunion @ sK8 @ sK10 ) @ ( binunion @ sK9 @ sK10 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU743^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n007.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 12:32:08 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SEU743^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.39 % Domain : Set Theory
% 0.17/0.39 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.17/0.39 % Version : Especial > Reduced > Especial.
% 0.17/0.39 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.17/0.39 % (! Z:i.in Z (powerset A) -> in (binintersect X Y)
% 0.17/0.39 % (powerset (binintersect (binunion X Z) (binunion Y Z))))))
% 0.17/0.39
% 0.17/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.39 % Source : [Bro08]
% 0.17/0.39 % Names : ZFC245l [Bro08]
% 0.17/0.39 % : ZFC267l [Bro08]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % 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, 0.14 v6.0.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.17/0.39 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.17/0.39 % Number of atoms : 34 ( 4 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 8 ( 6 avg)
% 0.17/0.39 % Number of connectives : 101 ( 0 ~; 0 |; 0 &; 80 @)
% 0.17/0.39 % ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 18 ( 4 avg)
% 0.17/0.39 % Number of types : 2 ( 0 usr)
% 0.17/0.39 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.17/0.39 % Number of variables : 19 ( 0 ^; 19 !; 0 ?; 19 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : http://mathgate.info/detsetitem.php?id=305
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(in_type,type,
% 0.17/0.39 in: $i > $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(powerset_type,type,
% 0.17/0.39 powerset: $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(binunion_type,type,
% 0.17/0.39 binunion: $i > $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(binintersect_type,type,
% 0.17/0.39 binintersect: $i > $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(binintersectT_lem_type,type,
% 0.17/0.39 binintersectT_lem: $o ).
% 0.17/0.39
% 0.17/0.39 thf(binintersectT_lem,definition,
% 0.17/0.39 ( binintersectT_lem
% 0.17/0.39 = ( ! [A: $i,X: $i] :
% 0.17/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.39 => ! [Y: $i] :
% 0.17/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.39 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(binunionT_lem_type,type,
% 0.17/0.39 binunionT_lem: $o ).
% 0.17/0.39
% 0.17/0.39 thf(binunionT_lem,definition,
% 0.17/0.39 ( binunionT_lem
% 0.17/0.39 = ( ! [A: $i,X: $i] :
% 0.17/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.39 => ! [Y: $i] :
% 0.17/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.39 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(powersetTI1_type,type,
% 0.17/0.39 powersetTI1: $o ).
% 0.17/0.39
% 0.17/0.39 thf(powersetTI1,definition,
% 0.17/0.39 ( powersetTI1
% 0.17/0.39 = ( ! [A: $i,X: $i] :
% 0.17/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.39 => ! [Y: $i] :
% 0.17/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.39 => ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( ( in @ Xx @ X )
% 0.17/0.39 => ( in @ Xx @ Y ) ) )
% 0.17/0.39 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(inIntersectImpInIntersectUnions_type,type,
% 0.17/0.39 inIntersectImpInIntersectUnions: $o ).
% 0.17/0.39
% 0.17/0.39 thf(inIntersectImpInIntersectUnions,definition,
% 0.17/0.39 ( inIntersectImpInIntersectUnions
% 0.17/0.39 = ( ! [A: $i,X: $i] :
% 0.17/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.39 => ! [Y: $i] :
% 0.17/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.39 => ! [Z: $i] :
% 0.17/0.39 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.39 => ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.39 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(intersectInPowersetIntersectUnions,conjecture,
% 0.17/0.39 ( binintersectT_lem
% 0.17/0.39 => ( binunionT_lem
% 0.17/0.39 => ( powersetTI1
% 0.17/0.39 => ( inIntersectImpInIntersectUnions
% 0.17/0.39 => ! [A: $i,X: $i] :
% 0.17/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.39 => ! [Y: $i] :
% 0.17/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.39 => ! [Z: $i] :
% 0.17/0.39 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.39 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.65/1.32 ---- Embedded in THF ---
% 1.65/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.32 %%% Generated on Tue Feb 24 12:32:09 EST 2026
% 1.65/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.32 %%% Logic specification used:
% 1.65/1.32 %%% thf(spec, logic, $$dhol).
% 1.65/1.32
% 1.65/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2DTF13787.p
% See solution above
% 1.65/1.32 ------------------------
% 1.65/1.33 ---- Cleaned THF ---
% 1.65/1.33 thf(in_type,type,
% 1.65/1.33 in: $i > $i > $o ).
% 1.65/1.33
% 1.65/1.33 thf(powerset_type,type,
% 1.65/1.33 powerset: $i > $i ).
% 1.65/1.33
% 1.65/1.33 thf(binunion_type,type,
% 1.65/1.33 binunion: $i > $i > $i ).
% 1.65/1.33
% 1.65/1.33 thf(binintersect_type,type,
% 1.65/1.33 binintersect: $i > $i > $i ).
% 1.65/1.33
% 1.65/1.33 thf(binintersectT_lem_type,type,
% 1.65/1.33 binintersectT_lem: $o ).
% 1.65/1.33
% 1.65/1.33 thf(binintersectT_lem,definition,
% 1.65/1.33 ( binintersectT_lem
% 1.65/1.33 = ( ! [A: $i,X: $i] :
% 1.65/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.65/1.33 => ! [Y: $i] :
% 1.65/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.65/1.33 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.65/1.33
% 1.65/1.33 thf(binunionT_lem_type,type,
% 1.65/1.33 binunionT_lem: $o ).
% 1.65/1.33
% 1.65/1.33 thf(binunionT_lem,definition,
% 1.65/1.33 ( binunionT_lem
% 1.65/1.33 = ( ! [A: $i,X: $i] :
% 1.65/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.65/1.33 => ! [Y: $i] :
% 1.65/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.65/1.33 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.65/1.33
% 1.65/1.33 thf(powersetTI1_type,type,
% 1.65/1.33 powersetTI1: $o ).
% 1.65/1.33
% 1.65/1.33 thf(powersetTI1,definition,
% 1.65/1.33 ( powersetTI1
% 1.65/1.33 = ( ! [A: $i,X: $i] :
% 1.65/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.65/1.33 => ! [Y: $i] :
% 1.65/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.65/1.33 => ( ! [Xx: $i] :
% 1.65/1.33 ( ( in @ Xx @ A )
% 1.65/1.33 => ( ( in @ Xx @ X )
% 1.65/1.33 => ( in @ Xx @ Y ) ) )
% 1.65/1.33 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 1.65/1.33
% 1.65/1.33 thf(inIntersectImpInIntersectUnions_type,type,
% 1.65/1.33 inIntersectImpInIntersectUnions: $o ).
% 1.65/1.33
% 1.65/1.33 thf(inIntersectImpInIntersectUnions,definition,
% 1.65/1.33 ( inIntersectImpInIntersectUnions
% 1.65/1.33 = ( ! [A: $i,X: $i] :
% 1.65/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.65/1.33 => ! [Y: $i] :
% 1.65/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.65/1.33 => ! [Z: $i] :
% 1.65/1.33 ( ( in @ Z @ ( powerset @ A ) )
% 1.65/1.33 => ! [Xx: $i] :
% 1.65/1.33 ( ( in @ Xx @ A )
% 1.65/1.33 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 1.65/1.33 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 1.65/1.33
% 1.65/1.33 thf(intersectInPowersetIntersectUnions,conjecture,
% 1.65/1.33 ( binintersectT_lem
% 1.65/1.33 => ( binunionT_lem
% 1.65/1.33 => ( powersetTI1
% 1.65/1.33 => ( inIntersectImpInIntersectUnions
% 1.65/1.33 => ! [A: $i,X: $i] :
% 1.65/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.65/1.33 => ! [Y: $i] :
% 1.65/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.65/1.33 => ! [Z: $i] :
% 1.65/1.33 ( ( in @ Z @ ( powerset @ A ) )
% 1.65/1.33 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 1.65/1.33 ------------------------
% 1.65/1.35 % (13885)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13787 for (2999ds/183Mi)
% 1.65/1.35 % (13887)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_13787 for (2999ds/27Mi)
% 1.65/1.35 % (13886)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_13787 for (2999ds/4Mi)
% 1.65/1.35 % (13889)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_13787 for (2999ds/2Mi)
% 1.65/1.35 % (13891)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13787 for (2999ds/18Mi)
% 1.65/1.35 % (13888)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13787 for (2999ds/2Mi)
% 1.65/1.35 % (13890)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_13787 for (2999ds/275Mi)
% 1.65/1.35 % (13888)Instruction limit reached!
% 1.65/1.35 % (13888)------------------------------
% 1.65/1.35 % (13888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (13888)Termination reason: Unknown
% 1.65/1.35 % (13889)Instruction limit reached!
% 1.65/1.35 % (13889)------------------------------
% 1.65/1.35 % (13889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (13888)Termination phase: Preprocessing 3
% 1.65/1.35
% 1.65/1.35 % (13888)Memory used [KB]: 1023
% 1.65/1.35 % (13888)Time elapsed: 0.003 s
% 1.65/1.35 % (13888)Instructions burned: 3 (million)
% 1.65/1.35 % (13888)------------------------------
% 1.65/1.35 % (13888)------------------------------
% 1.65/1.35 % (13889)Termination reason: Unknown
% 1.65/1.35 % (13889)Termination phase: Property scanning
% 1.65/1.35
% 1.65/1.35 % (13889)Memory used [KB]: 1023
% 1.65/1.35 % (13889)Time elapsed: 0.003 s
% 1.65/1.35 % (13889)Instructions burned: 3 (million)
% 1.65/1.35 % (13889)------------------------------
% 1.65/1.35 % (13889)------------------------------
% 1.65/1.35 % (13886)Instruction limit reached!
% 1.65/1.35 % (13886)------------------------------
% 1.65/1.35 % (13886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (13886)Termination reason: Unknown
% 1.65/1.35 % (13886)Termination phase: Saturation
% 1.65/1.35
% 1.65/1.35 % (13886)Memory used [KB]: 1023
% 1.65/1.35 % (13886)Time elapsed: 0.004 s
% 1.65/1.35 % (13886)Instructions burned: 5 (million)
% 1.65/1.35 % (13886)------------------------------
% 1.65/1.35 % (13886)------------------------------
% 1.65/1.36 % (13891)Instruction limit reached!
% 1.65/1.36 % (13891)------------------------------
% 1.65/1.36 % (13891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (13891)Termination reason: Unknown
% 1.65/1.36 % (13891)Termination phase: Saturation
% 1.65/1.36
% 1.65/1.36 % (13891)Memory used [KB]: 5628
% 1.65/1.36 % (13891)Time elapsed: 0.011 s
% 1.65/1.36 % (13891)Instructions burned: 18 (million)
% 1.65/1.36 % (13891)------------------------------
% 1.65/1.36 % (13891)------------------------------
% 1.65/1.36 % (13887)Instruction limit reached!
% 1.65/1.36 % (13887)------------------------------
% 1.65/1.36 % (13887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (13887)Termination reason: Unknown
% 1.65/1.36 % (13887)Termination phase: Saturation
% 1.65/1.36
% 1.65/1.36 % (13887)Memory used [KB]: 5628
% 1.65/1.36 % (13887)Time elapsed: 0.016 s
% 1.65/1.36 % (13887)Instructions burned: 29 (million)
% 1.65/1.36 % (13887)------------------------------
% 1.65/1.36 % (13887)------------------------------
% 1.65/1.36 % (13892)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13787 for (2999ds/3Mi)
% 1.65/1.36 % (13893)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_13787 for (2999ds/37Mi)
% 1.65/1.37 % (13894)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_13787 for (2999ds/15Mi)
% 1.65/1.37 % (13892)Instruction limit reached!
% 1.65/1.37 % (13892)------------------------------
% 1.65/1.37 % (13892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (13892)Termination reason: Unknown
% 1.65/1.37 % (13892)Termination phase: Preprocessing 3
% 1.65/1.37
% 1.65/1.37 % (13892)Memory used [KB]: 1023
% 1.65/1.37 % (13892)Time elapsed: 0.003 s
% 1.65/1.37 % (13892)Instructions burned: 3 (million)
% 1.65/1.37 % (13892)------------------------------
% 1.65/1.37 % (13892)------------------------------
% 1.65/1.37 % (13895)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_13787 for (2999ds/3Mi)
% 1.65/1.37 % (13894)Instruction limit reached!
% 1.65/1.37 % (13894)------------------------------
% 1.65/1.37 % (13894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (13894)Termination reason: Unknown
% 1.65/1.37 % (13894)Termination phase: Saturation
% 1.65/1.37
% 1.65/1.37 % (13894)Memory used [KB]: 5628
% 1.65/1.37 % (13894)Time elapsed: 0.009 s
% 1.65/1.37 % (13894)Instructions burned: 15 (million)
% 1.65/1.37 % (13894)------------------------------
% 1.65/1.37 % (13894)------------------------------
% 1.65/1.37 % (13895)Instruction limit reached!
% 1.65/1.37 % (13895)------------------------------
% 1.65/1.37 % (13895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (13895)Termination reason: Unknown
% 1.65/1.37 % (13895)Termination phase: Property scanning
% 1.65/1.37
% 1.65/1.37 % (13895)Memory used [KB]: 1023
% 1.65/1.37 % (13895)Time elapsed: 0.004 s
% 1.65/1.37 % (13895)Instructions burned: 5 (million)
% 1.65/1.37 % (13895)------------------------------
% 1.65/1.37 % (13895)------------------------------
% 1.65/1.37 % (13890)First to succeed.
% 1.65/1.38 % (13896)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_13787 for (2999ds/1041Mi)
% 1.65/1.38 % (13890)Refutation found. Thanks to Tanya!
% 1.65/1.38 % SZS status Theorem for DTF2THF_13787
% 1.65/1.38 % SZS output start Proof for DTF2THF_13787
% 1.65/1.38 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.38 thf(func_def_1, type, powerset: $i > $i).
% 1.65/1.38 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.65/1.38 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.65/1.38 thf(func_def_11, type, sK0: $i > $i > $i > $i).
% 1.65/1.38 thf(f188,plain,(
% 1.65/1.38 $false),
% 1.65/1.38 inference(subsumption_resolution,[status(thm)],[f187,f68])).
% 1.65/1.38 thf(f68,plain,(
% 1.65/1.38 ($true = (in @ sK8 @ (powerset @ sK7)))),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f41])).
% 1.65/1.38 thf(f41,plain,(
% 1.65/1.38 (powersetTI1 = $true) & (inIntersectImpInIntersectUnions = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (($true = (in @ sK8 @ (powerset @ sK7))) & (((in @ sK9 @ (powerset @ sK7)) = $true) & (($true != (in @ (binintersect @ sK8 @ sK9) @ (powerset @ (binintersect @ (binunion @ sK8 @ sK10) @ (binunion @ sK9 @ sK10))))) & ($true = (in @ sK10 @ (powerset @ sK7))))))),
% 1.65/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f37,f40,f39,f38])).
% 1.65/1.38 thf(f38,plain,(
% 1.65/1.38 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true) & ((in @ X3 @ (powerset @ X0)) = $true)))) => (($true = (in @ sK8 @ (powerset @ sK7))) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK7))) & ? [X3 : $i] : (($true != (in @ (binintersect @ sK8 @ X2) @ (powerset @ (binintersect @ (binunion @ sK8 @ X3) @ (binunion @ X2 @ X3))))) & ((in @ X3 @ (powerset @ sK7)) = $true))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f39,plain,(
% 1.65/1.38 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK7))) & ? [X3 : $i] : (($true != (in @ (binintersect @ sK8 @ X2) @ (powerset @ (binintersect @ (binunion @ sK8 @ X3) @ (binunion @ X2 @ X3))))) & ((in @ X3 @ (powerset @ sK7)) = $true))) => (((in @ sK9 @ (powerset @ sK7)) = $true) & ? [X3 : $i] : (($true != (in @ (binintersect @ sK8 @ sK9) @ (powerset @ (binintersect @ (binunion @ sK8 @ X3) @ (binunion @ sK9 @ X3))))) & ((in @ X3 @ (powerset @ sK7)) = $true)))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f40,plain,(
% 1.65/1.38 ? [X3 : $i] : (($true != (in @ (binintersect @ sK8 @ sK9) @ (powerset @ (binintersect @ (binunion @ sK8 @ X3) @ (binunion @ sK9 @ X3))))) & ((in @ X3 @ (powerset @ sK7)) = $true)) => (($true != (in @ (binintersect @ sK8 @ sK9) @ (powerset @ (binintersect @ (binunion @ sK8 @ sK10) @ (binunion @ sK9 @ sK10))))) & ($true = (in @ sK10 @ (powerset @ sK7))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f37,plain,(
% 1.65/1.38 (powersetTI1 = $true) & (inIntersectImpInIntersectUnions = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true) & ((in @ X3 @ (powerset @ X0)) = $true))))),
% 1.65/1.38 inference(rectify,[status(thm)],[f22])).
% 1.65/1.38 thf(f22,plain,(
% 1.65/1.38 (powersetTI1 = $true) & (inIntersectImpInIntersectUnions = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & ? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) != $true) & ((in @ X3 @ (powerset @ X1)) = $true))))),
% 1.65/1.38 inference(flattening,[status(thm)],[f21])).
% 1.65/1.38 thf(f21,plain,(
% 1.65/1.38 (((? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) != $true) & ((in @ X3 @ (powerset @ X1)) = $true)))) & (inIntersectImpInIntersectUnions = $true)) & (powersetTI1 = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)),
% 1.65/1.38 inference(ennf_transformation,[status(thm)],[f15])).
% 1.65/1.38 thf(f15,plain,(
% 1.65/1.38 ~((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetTI1 = $true) => ((inIntersectImpInIntersectUnions = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => ((in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) = $true))))))))),
% 1.65/1.38 inference(fool_elimination,[status(thm)],[f14])).
% 1.65/1.38 thf(f14,plain,(
% 1.65/1.38 ~(binintersectT_lem => (binunionT_lem => (powersetTI1 => (inIntersectImpInIntersectUnions => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))))))))))),
% 1.65/1.38 inference(rectify,[status(thm)],[f6])).
% 1.65/1.38 thf(f6,negated_conjecture,(
% 1.65/1.38 ~(binintersectT_lem => (binunionT_lem => (powersetTI1 => (inIntersectImpInIntersectUnions => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X4) @ (binunion @ X2 @ X4)))))))))))),
% 1.65/1.38 inference(negated_conjecture,[status(cth)],[f5])).
% 1.65/1.38 thf(f5,conjecture,(
% 1.65/1.38 binintersectT_lem => (binunionT_lem => (powersetTI1 => (inIntersectImpInIntersectUnions => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X4) @ (binunion @ X2 @ X4))))))))))),
% 1.65/1.38 file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',intersectInPowersetIntersectUnions)).
% 1.65/1.38 thf(f187,plain,(
% 1.65/1.38 ($true != (in @ sK8 @ (powerset @ sK7)))),
% 1.65/1.38 inference(subsumption_resolution,[status(thm)],[f186,f67])).
% 1.65/1.38 thf(f67,plain,(
% 1.65/1.38 ((in @ sK9 @ (powerset @ sK7)) = $true)),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f41])).
% 1.65/1.38 thf(f186,plain,(
% 1.65/1.38 ((in @ sK9 @ (powerset @ sK7)) != $true) | ($true != (in @ sK8 @ (powerset @ sK7)))),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.65/1.38 thf(f184,plain,(
% 1.65/1.38 ($true != $true) | ($true != (in @ sK8 @ (powerset @ sK7))) | ((in @ sK9 @ (powerset @ sK7)) != $true)),
% 1.65/1.38 inference(superposition,[status(thm)],[f178,f65])).
% 1.65/1.38 thf(f65,plain,(
% 1.65/1.38 ($true = (in @ sK10 @ (powerset @ sK7)))),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f41])).
% 1.65/1.38 thf(f178,plain,(
% 1.65/1.38 ( ! [X0 : $i] : (($true != (in @ sK10 @ (powerset @ X0))) | ($true != (in @ sK9 @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0)))) )),
% 1.65/1.38 inference(subsumption_resolution,[status(thm)],[f177,f111])).
% 1.65/1.38 thf(f111,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.65/1.38 thf(f95,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true)) )),
% 1.65/1.38 inference(definition_unfolding,[status(thm)],[f76,f70])).
% 1.65/1.38 thf(f70,plain,(
% 1.65/1.38 (binunionT_lem = $true)),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f41])).
% 1.65/1.38 thf(f76,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | (binunionT_lem != $true)) )),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f46])).
% 1.65/1.38 thf(f46,plain,(
% 1.65/1.38 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ((($true != (in @ (binunion @ sK12 @ sK13) @ (powerset @ sK11))) & ($true = (in @ sK13 @ (powerset @ sK11)))) & ($true = (in @ sK12 @ (powerset @ sK11)))))),
% 1.65/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f43,f45,f44])).
% 1.65/1.38 thf(f44,plain,(
% 1.65/1.38 ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ (binunion @ X4 @ X5) @ (powerset @ X3)) != $true) & ($true = (in @ X5 @ (powerset @ X3)))) & ($true = (in @ X4 @ (powerset @ X3)))) => (? [X5 : $i] : (($true != (in @ (binunion @ sK12 @ X5) @ (powerset @ sK11))) & ($true = (in @ X5 @ (powerset @ sK11)))) & ($true = (in @ sK12 @ (powerset @ sK11))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f45,plain,(
% 1.65/1.38 ? [X5 : $i] : (($true != (in @ (binunion @ sK12 @ X5) @ (powerset @ sK11))) & ($true = (in @ X5 @ (powerset @ sK11)))) => (($true != (in @ (binunion @ sK12 @ sK13) @ (powerset @ sK11))) & ($true = (in @ sK13 @ (powerset @ sK11))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f43,plain,(
% 1.65/1.38 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ (binunion @ X4 @ X5) @ (powerset @ X3)) != $true) & ($true = (in @ X5 @ (powerset @ X3)))) & ($true = (in @ X4 @ (powerset @ X3)))))),
% 1.65/1.38 inference(rectify,[status(thm)],[f42])).
% 1.65/1.38 thf(f42,plain,(
% 1.65/1.38 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (($true = (in @ (binunion @ X0 @ X2) @ (powerset @ X1))) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true)) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (($true != (in @ (binunion @ X0 @ X2) @ (powerset @ X1))) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)))),
% 1.65/1.38 inference(nnf_transformation,[status(thm)],[f20])).
% 1.65/1.38 thf(f20,plain,(
% 1.65/1.38 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (($true = (in @ (binunion @ X0 @ X2) @ (powerset @ X1))) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true)) <=> (binunionT_lem = $true)),
% 1.65/1.38 inference(ennf_transformation,[status(thm)],[f11])).
% 1.65/1.38 thf(f11,plain,(
% 1.65/1.38 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ($true = (in @ (binunion @ X0 @ X2) @ (powerset @ X1))))) <=> (binunionT_lem = $true)),
% 1.65/1.38 inference(fool_elimination,[status(thm)],[f10])).
% 1.65/1.38 thf(f10,plain,(
% 1.65/1.38 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))) = binunionT_lem)),
% 1.65/1.38 inference(rectify,[status(thm)],[f2])).
% 1.65/1.38 thf(f2,axiom,(
% 1.65/1.38 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
% 1.65/1.38 file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',binunionT_lem)).
% 1.65/1.38 thf(f177,plain,(
% 1.65/1.38 ( ! [X0 : $i] : (($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK9 @ (powerset @ X0))) | ($true != (in @ sK10 @ (powerset @ X0))) | ($true != (in @ (binunion @ sK9 @ sK10) @ (powerset @ X0)))) )),
% 1.65/1.38 inference(subsumption_resolution,[status(thm)],[f174,f111])).
% 1.65/1.38 thf(f174,plain,(
% 1.65/1.38 ( ! [X0 : $i] : (($true != (in @ (binunion @ sK8 @ sK10) @ (powerset @ X0))) | ($true != (in @ sK10 @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK9 @ (powerset @ X0))) | ($true != (in @ (binunion @ sK9 @ sK10) @ (powerset @ X0)))) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.65/1.38 thf(f172,plain,(
% 1.65/1.38 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ (binunion @ sK9 @ sK10) @ (powerset @ X0))) | ($true != (in @ sK10 @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK9 @ (powerset @ X0))) | ($true != (in @ (binunion @ sK8 @ sK10) @ (powerset @ X0)))) )),
% 1.65/1.38 inference(superposition,[status(thm)],[f162,f106])).
% 1.65/1.38 thf(f106,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.65/1.38 thf(f91,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.65/1.38 inference(definition_unfolding,[status(thm)],[f64,f69])).
% 1.65/1.38 thf(f69,plain,(
% 1.65/1.38 (binintersectT_lem = $true)),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f41])).
% 1.65/1.38 thf(f64,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | (binintersectT_lem != $true)) )),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f36])).
% 1.65/1.38 thf(f36,plain,(
% 1.65/1.38 (! [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)) & ((binintersectT_lem = $true) | (($true = (in @ sK5 @ (powerset @ sK4))) & (($true = (in @ sK6 @ (powerset @ sK4))) & ((in @ (binintersect @ sK5 @ sK6) @ (powerset @ sK4)) != $true))))),
% 1.65/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f33,f35,f34])).
% 1.65/1.38 thf(f34,plain,(
% 1.65/1.38 ? [X3 : $i,X4 : $i] : (($true = (in @ X4 @ (powerset @ X3))) & ? [X5 : $i] : (($true = (in @ X5 @ (powerset @ X3))) & ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) != $true))) => (($true = (in @ sK5 @ (powerset @ sK4))) & ? [X5 : $i] : (($true = (in @ X5 @ (powerset @ sK4))) & ($true != (in @ (binintersect @ sK5 @ X5) @ (powerset @ sK4)))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f35,plain,(
% 1.65/1.38 ? [X5 : $i] : (($true = (in @ X5 @ (powerset @ sK4))) & ($true != (in @ (binintersect @ sK5 @ X5) @ (powerset @ sK4)))) => (($true = (in @ sK6 @ (powerset @ sK4))) & ((in @ (binintersect @ sK5 @ sK6) @ (powerset @ sK4)) != $true))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f33,plain,(
% 1.65/1.38 (! [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)) & ((binintersectT_lem = $true) | ? [X3 : $i,X4 : $i] : (($true = (in @ X4 @ (powerset @ X3))) & ? [X5 : $i] : (($true = (in @ X5 @ (powerset @ X3))) & ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) != $true))))),
% 1.65/1.38 inference(rectify,[status(thm)],[f32])).
% 1.65/1.38 thf(f32,plain,(
% 1.65/1.38 (! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ X1))))) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | ? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X1))))))),
% 1.65/1.38 inference(nnf_transformation,[status(thm)],[f23])).
% 1.65/1.38 thf(f23,plain,(
% 1.65/1.38 ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ X1))))) <=> (binintersectT_lem = $true)),
% 1.65/1.38 inference(ennf_transformation,[status(thm)],[f9])).
% 1.65/1.38 thf(f9,plain,(
% 1.65/1.38 ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ X1))))) <=> (binintersectT_lem = $true)),
% 1.65/1.38 inference(fool_elimination,[status(thm)],[f8])).
% 1.65/1.38 thf(f8,plain,(
% 1.65/1.38 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))),
% 1.65/1.38 inference(rectify,[status(thm)],[f1])).
% 1.65/1.38 thf(f1,axiom,(
% 1.65/1.38 (binintersectT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 1.65/1.38 file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',binintersectT_lem)).
% 1.65/1.38 thf(f162,plain,(
% 1.65/1.38 ( ! [X0 : $i] : (($true != (in @ (binintersect @ (binunion @ sK8 @ sK10) @ (binunion @ sK9 @ sK10)) @ (powerset @ X0))) | ($true != (in @ sK10 @ (powerset @ X0))) | ($true != (in @ sK9 @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0)))) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.65/1.38 thf(f161,plain,(
% 1.65/1.38 ( ! [X0 : $i] : (($true != (in @ sK9 @ (powerset @ X0))) | ($true != (in @ sK10 @ (powerset @ X0))) | ($true != (in @ (binintersect @ (binunion @ sK8 @ sK10) @ (binunion @ sK9 @ sK10)) @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0))) | ($true != $true)) )),
% 1.65/1.38 inference(superposition,[status(thm)],[f66,f160])).
% 1.65/1.38 thf(f160,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1))))) | ($true != (in @ X2 @ (powerset @ X3))) | ($true != (in @ X0 @ (powerset @ X3))) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3))) | ((in @ X1 @ (powerset @ X3)) != $true)) )),
% 1.65/1.38 inference(subsumption_resolution,[status(thm)],[f156,f106])).
% 1.65/1.38 thf(f156,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X3))) | ((in @ X1 @ (powerset @ X3)) != $true) | ($true != (in @ X2 @ (powerset @ X3))) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1))))) | ($true != (in @ X0 @ (powerset @ X3))) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3)))) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 1.65/1.38 thf(f155,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3))) | ($true != $true) | ($true != (in @ X0 @ (powerset @ X3))) | ((in @ X1 @ (powerset @ X3)) != $true) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1))))) | ($true != (in @ X2 @ (powerset @ X3))) | ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X3)))) )),
% 1.65/1.38 inference(duplicate_literal_removal,[status(thm)],[f153])).
% 1.65/1.38 thf(f153,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X3)) != $true) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1))))) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3))) | ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X3))) | ($true != $true) | ($true != (in @ X2 @ (powerset @ X3))) | ($true != (in @ X0 @ (powerset @ X3))) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1))))) | ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X3))) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3)))) )),
% 1.65/1.38 inference(superposition,[status(thm)],[f137,f110])).
% 1.65/1.38 thf(f110,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X0)) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X2)) = $true)) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.65/1.38 thf(f85,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X0)) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X2)) = $true) | ($true != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.65/1.38 inference(definition_unfolding,[status(thm)],[f59,f72])).
% 1.65/1.38 thf(f72,plain,(
% 1.65/1.38 (powersetTI1 = $true)),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f41])).
% 1.65/1.38 thf(f59,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X2)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X0)) | (powersetTI1 != $true)) )),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f31])).
% 1.65/1.38 thf(f31,plain,(
% 1.65/1.38 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X1 @ (powerset @ X2)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) & ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X0)) & ((in @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true)))) | (powersetTI1 != $true)) & ((powersetTI1 = $true) | (((in @ sK2 @ (powerset @ sK1)) = $true) & (((in @ sK2 @ (powerset @ sK3)) != $true) & ((in @ sK3 @ (powerset @ sK1)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ sK2)) | ($true != (in @ X7 @ sK1)) | ($true = (in @ X7 @ sK3))))))),
% 1.65/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f27,f30,f29,f28])).
% 1.65/1.38 thf(f28,plain,(
% 1.65/1.38 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) != $true)) => (($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) & ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X0)) & ((in @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true)))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f29,plain,(
% 1.65/1.38 ? [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6 : $i] : (((in @ X5 @ (powerset @ X6)) != $true) & ($true = (in @ X6 @ (powerset @ X4))) & ! [X7 : $i] : (($true != (in @ X7 @ X5)) | ($true != (in @ X7 @ X4)) | ((in @ X7 @ X6) = $true)))) => (((in @ sK2 @ (powerset @ sK1)) = $true) & ? [X6 : $i] : (($true != (in @ sK2 @ (powerset @ X6))) & ((in @ X6 @ (powerset @ sK1)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ sK2)) | ($true != (in @ X7 @ sK1)) | ((in @ X7 @ X6) = $true))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f30,plain,(
% 1.65/1.38 ? [X6 : $i] : (($true != (in @ sK2 @ (powerset @ X6))) & ((in @ X6 @ (powerset @ sK1)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ sK2)) | ($true != (in @ X7 @ sK1)) | ((in @ X7 @ X6) = $true))) => (((in @ sK2 @ (powerset @ sK3)) != $true) & ((in @ sK3 @ (powerset @ sK1)) = $true) & ! [X7 : $i] : (($true != (in @ X7 @ sK2)) | ($true != (in @ X7 @ sK1)) | ($true = (in @ X7 @ sK3))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f27,plain,(
% 1.65/1.38 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X1 @ (powerset @ X2)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) != $true)))) | (powersetTI1 != $true)) & ((powersetTI1 = $true) | ? [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6 : $i] : (((in @ X5 @ (powerset @ X6)) != $true) & ($true = (in @ X6 @ (powerset @ X4))) & ! [X7 : $i] : (($true != (in @ X7 @ X5)) | ($true != (in @ X7 @ X4)) | ((in @ X7 @ X6) = $true)))))),
% 1.65/1.38 inference(rectify,[status(thm)],[f26])).
% 1.65/1.38 thf(f26,plain,(
% 1.65/1.38 (! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (($true = (in @ X0 @ (powerset @ X2))) | ($true != (in @ X2 @ (powerset @ X1))) | ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true)))) | (powersetTI1 != $true)) & ((powersetTI1 = $true) | ? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (($true != (in @ X0 @ (powerset @ X2))) & ($true = (in @ X2 @ (powerset @ X1))) & ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true)))))),
% 1.65/1.38 inference(nnf_transformation,[status(thm)],[f19])).
% 1.65/1.38 thf(f19,plain,(
% 1.65/1.38 ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (($true = (in @ X0 @ (powerset @ X2))) | ($true != (in @ X2 @ (powerset @ X1))) | ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) != $true)))) <=> (powersetTI1 = $true)),
% 1.65/1.38 inference(flattening,[status(thm)],[f18])).
% 1.65/1.38 thf(f18,plain,(
% 1.65/1.38 (powersetTI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((($true = (in @ X0 @ (powerset @ X2))) | ? [X3 : $i] : ((((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X3 @ X1) = $true))) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 1.65/1.38 inference(ennf_transformation,[status(thm)],[f13])).
% 1.65/1.38 thf(f13,plain,(
% 1.65/1.38 (powersetTI1 = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ((in @ X3 @ X2) = $true))) => ($true = (in @ X0 @ (powerset @ X2))))))),
% 1.65/1.38 inference(fool_elimination,[status(thm)],[f12])).
% 1.65/1.38 thf(f12,plain,(
% 1.65/1.38 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (in @ X0 @ (powerset @ X2))))) = powersetTI1)),
% 1.65/1.38 inference(rectify,[status(thm)],[f3])).
% 1.65/1.38 thf(f3,axiom,(
% 1.65/1.38 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))) = powersetTI1)),
% 1.65/1.38 file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',powersetTI1)).
% 1.65/1.38 thf(f137,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (sK0 @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (binintersect @ X0 @ X2) @ X3) @ X4) != $true) | ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X3))) | ((in @ X0 @ (powerset @ X4)) != $true) | ($true != (in @ X2 @ (powerset @ X4))) | ($true != (in @ X1 @ (powerset @ X4))) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3))) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)))))) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f136])).
% 1.65/1.38 thf(f136,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (sK0 @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (binintersect @ X0 @ X2) @ X3) @ X4) != $true) | ($true != (in @ X2 @ (powerset @ X4))) | ((in @ X0 @ (powerset @ X4)) != $true) | ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X3))) | ($true != (in @ X1 @ (powerset @ X4))) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1))))) | ($true != $true) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3)))) )),
% 1.65/1.38 inference(duplicate_literal_removal,[status(thm)],[f131])).
% 1.65/1.38 thf(f131,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X0 @ (powerset @ X4)) != $true) | ($true != $true) | ($true != (in @ X1 @ (powerset @ X4))) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3))) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X3))) | ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X3))) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1))))) | ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X3))) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1))))) | ($true != (in @ X2 @ (powerset @ X4))) | ((in @ (sK0 @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (binintersect @ X0 @ X2) @ X3) @ X4) != $true)) )),
% 1.65/1.38 inference(superposition,[status(thm)],[f129,f109])).
% 1.65/1.38 thf(f109,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X2)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.65/1.38 thf(f84,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) | ((in @ X1 @ (powerset @ X2)) = $true) | ($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.65/1.38 inference(definition_unfolding,[status(thm)],[f60,f72])).
% 1.65/1.38 thf(f60,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X2)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) | (powersetTI1 != $true)) )),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f31])).
% 1.65/1.38 thf(f129,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (in @ (sK0 @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ X3 @ X4) @ (binintersect @ X0 @ X2))) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X4))) | ($true != (in @ X0 @ (powerset @ X5))) | ($true != (in @ X1 @ (powerset @ X5))) | ($true != (in @ X3 @ (powerset @ X4))) | ($true != (in @ X2 @ (powerset @ X5))) | ($true != (in @ (sK0 @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ X3 @ X4) @ X5)) | ((in @ X3 @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)))) = $true)) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.65/1.38 thf(f128,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (powerset @ X4))) | ((in @ X3 @ (powerset @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)))) = $true) | ($true != (in @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ (powerset @ X4))) | ($true != (in @ (sK0 @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ X3 @ X4) @ X5)) | ($true != (in @ X2 @ (powerset @ X5))) | ($true != $true) | ($true != (in @ (sK0 @ (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)) @ X3 @ X4) @ (binintersect @ X0 @ X2))) | ($true != (in @ X1 @ (powerset @ X5))) | ($true != (in @ X0 @ (powerset @ X5)))) )),
% 1.65/1.38 inference(superposition,[status(thm)],[f108,f107])).
% 1.65/1.38 thf(f107,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true = (in @ X4 @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) | ((in @ X4 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ($true != (in @ X2 @ (powerset @ X1))) | ((in @ X3 @ (powerset @ X1)) != $true) | ($true != (in @ X4 @ (binintersect @ X0 @ X2)))) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.65/1.38 thf(f99,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X4 @ X1) != $true) | ((in @ X3 @ (powerset @ X1)) != $true) | ($true != $true) | ($true = (in @ X4 @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) | ($true != (in @ X4 @ (binintersect @ X0 @ X2))) | ($true != (in @ X2 @ (powerset @ X1)))) )),
% 1.65/1.38 inference(definition_unfolding,[status(thm)],[f83,f71])).
% 1.65/1.38 thf(f71,plain,(
% 1.65/1.38 (inIntersectImpInIntersectUnions = $true)),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f41])).
% 1.65/1.38 thf(f83,plain,(
% 1.65/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ($true != (in @ X4 @ (binintersect @ X0 @ X2))) | ((in @ X4 @ X1) != $true) | ($true = (in @ X4 @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) | ((in @ X3 @ (powerset @ X1)) != $true) | ($true != (in @ X2 @ (powerset @ X1))) | (inIntersectImpInIntersectUnions != $true)) )),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f53])).
% 1.65/1.38 thf(f53,plain,(
% 1.65/1.38 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ (binintersect @ X0 @ X2))) | ((in @ X4 @ X1) != $true) | ($true = (in @ X4 @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3))))) | ((in @ X3 @ (powerset @ X1)) != $true)) | ($true != (in @ X2 @ (powerset @ X1))))) | (inIntersectImpInIntersectUnions != $true)) & ((inIntersectImpInIntersectUnions = $true) | (((in @ sK14 @ (powerset @ sK15)) = $true) & (((($true = (in @ sK18 @ (binintersect @ sK14 @ sK16))) & ($true = (in @ sK18 @ sK15)) & ($true != (in @ sK18 @ (binintersect @ (binunion @ sK14 @ sK17) @ (binunion @ sK16 @ sK17))))) & ((in @ sK17 @ (powerset @ sK15)) = $true)) & ((in @ sK16 @ (powerset @ sK15)) = $true))))),
% 1.65/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18])],[f48,f52,f51,f50,f49])).
% 1.65/1.38 thf(f49,plain,(
% 1.65/1.38 ? [X5 : $i,X6 : $i] : (((in @ X5 @ (powerset @ X6)) = $true) & ? [X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ (binintersect @ X5 @ X7))) & ($true = (in @ X9 @ X6)) & ((in @ X9 @ (binintersect @ (binunion @ X5 @ X8) @ (binunion @ X7 @ X8))) != $true)) & ((in @ X8 @ (powerset @ X6)) = $true)) & ($true = (in @ X7 @ (powerset @ X6))))) => (((in @ sK14 @ (powerset @ sK15)) = $true) & ? [X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ (binintersect @ sK14 @ X7))) & ($true = (in @ X9 @ sK15)) & ($true != (in @ X9 @ (binintersect @ (binunion @ sK14 @ X8) @ (binunion @ X7 @ X8))))) & ((in @ X8 @ (powerset @ sK15)) = $true)) & ($true = (in @ X7 @ (powerset @ sK15)))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f50,plain,(
% 1.65/1.38 ? [X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ (binintersect @ sK14 @ X7))) & ($true = (in @ X9 @ sK15)) & ($true != (in @ X9 @ (binintersect @ (binunion @ sK14 @ X8) @ (binunion @ X7 @ X8))))) & ((in @ X8 @ (powerset @ sK15)) = $true)) & ($true = (in @ X7 @ (powerset @ sK15)))) => (? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ (binintersect @ sK14 @ sK16))) & ($true = (in @ X9 @ sK15)) & ($true != (in @ X9 @ (binintersect @ (binunion @ sK14 @ X8) @ (binunion @ sK16 @ X8))))) & ((in @ X8 @ (powerset @ sK15)) = $true)) & ((in @ sK16 @ (powerset @ sK15)) = $true))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f51,plain,(
% 1.65/1.38 ? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ (binintersect @ sK14 @ sK16))) & ($true = (in @ X9 @ sK15)) & ($true != (in @ X9 @ (binintersect @ (binunion @ sK14 @ X8) @ (binunion @ sK16 @ X8))))) & ((in @ X8 @ (powerset @ sK15)) = $true)) => (? [X9 : $i] : (($true = (in @ X9 @ (binintersect @ sK14 @ sK16))) & ($true = (in @ X9 @ sK15)) & ($true != (in @ X9 @ (binintersect @ (binunion @ sK14 @ sK17) @ (binunion @ sK16 @ sK17))))) & ((in @ sK17 @ (powerset @ sK15)) = $true))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f52,plain,(
% 1.65/1.38 ? [X9 : $i] : (($true = (in @ X9 @ (binintersect @ sK14 @ sK16))) & ($true = (in @ X9 @ sK15)) & ($true != (in @ X9 @ (binintersect @ (binunion @ sK14 @ sK17) @ (binunion @ sK16 @ sK17))))) => (($true = (in @ sK18 @ (binintersect @ sK14 @ sK16))) & ($true = (in @ sK18 @ sK15)) & ($true != (in @ sK18 @ (binintersect @ (binunion @ sK14 @ sK17) @ (binunion @ sK16 @ sK17)))))),
% 1.65/1.38 introduced(definition,[],[choice_axiom])).
% 1.65/1.38 thf(f48,plain,(
% 1.65/1.38 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ (binintersect @ X0 @ X2))) | ((in @ X4 @ X1) != $true) | ($true = (in @ X4 @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3))))) | ((in @ X3 @ (powerset @ X1)) != $true)) | ($true != (in @ X2 @ (powerset @ X1))))) | (inIntersectImpInIntersectUnions != $true)) & ((inIntersectImpInIntersectUnions = $true) | ? [X5 : $i,X6 : $i] : (((in @ X5 @ (powerset @ X6)) = $true) & ? [X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ (binintersect @ X5 @ X7))) & ($true = (in @ X9 @ X6)) & ((in @ X9 @ (binintersect @ (binunion @ X5 @ X8) @ (binunion @ X7 @ X8))) != $true)) & ((in @ X8 @ (powerset @ X6)) = $true)) & ($true = (in @ X7 @ (powerset @ X6))))))),
% 1.65/1.38 inference(rectify,[status(thm)],[f47])).
% 1.65/1.38 thf(f47,plain,(
% 1.65/1.38 (! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ (binintersect @ X1 @ X2))) | ((in @ X4 @ X0) != $true) | ($true = (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (inIntersectImpInIntersectUnions != $true)) & ((inIntersectImpInIntersectUnions = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ (binintersect @ X1 @ X2))) & ((in @ X4 @ X0) = $true) & ($true != (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))) & ((in @ X3 @ (powerset @ X0)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))))),
% 1.65/1.38 inference(nnf_transformation,[status(thm)],[f25])).
% 1.65/1.38 thf(f25,plain,(
% 1.65/1.38 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ (binintersect @ X1 @ X2))) | ((in @ X4 @ X0) != $true) | ($true = (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) <=> (inIntersectImpInIntersectUnions = $true)),
% 1.65/1.38 inference(flattening,[status(thm)],[f24])).
% 1.65/1.38 thf(f24,plain,(
% 1.65/1.38 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((($true = (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) | ($true != (in @ X4 @ (binintersect @ X1 @ X2)))) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (inIntersectImpInIntersectUnions = $true)),
% 1.65/1.38 inference(ennf_transformation,[status(thm)],[f17])).
% 1.65/1.38 thf(f17,plain,(
% 1.65/1.38 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) => ! [X4 : $i] : (((in @ X4 @ X0) = $true) => (($true = (in @ X4 @ (binintersect @ X1 @ X2))) => ($true = (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))))) <=> (inIntersectImpInIntersectUnions = $true)),
% 1.65/1.38 inference(fool_elimination,[status(thm)],[f16])).
% 1.65/1.38 thf(f16,plain,(
% 1.65/1.38 (inIntersectImpInIntersectUnions = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))))))))),
% 1.65/1.38 inference(rectify,[status(thm)],[f4])).
% 1.65/1.38 thf(f4,axiom,(
% 1.65/1.38 (inIntersectImpInIntersectUnions = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (binintersect @ X1 @ X2)) => (in @ X3 @ (binintersect @ (binunion @ X1 @ X4) @ (binunion @ X2 @ X4)))))))))),
% 1.65/1.38 file('/export/starexec/sandbox/tmp/tmp.Q5hxdiKJV3/DTF2THF_13787.p',inIntersectImpInIntersectUnions)).
% 1.65/1.38 thf(f108,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X2)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.65/1.38 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.65/1.38 thf(f86,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X2)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.65/1.38 inference(definition_unfolding,[status(thm)],[f58,f72])).
% 1.65/1.38 thf(f58,plain,(
% 1.65/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X2)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true) | (powersetTI1 != $true)) )),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f31])).
% 1.65/1.38 thf(f66,plain,(
% 1.65/1.38 ($true != (in @ (binintersect @ sK8 @ sK9) @ (powerset @ (binintersect @ (binunion @ sK8 @ sK10) @ (binunion @ sK9 @ sK10)))))),
% 1.65/1.38 inference(cnf_transformation,[status(thm)],[f41])).
% 1.65/1.38 % SZS output end Proof for DTF2THF_13787
% 1.65/1.38 % (13890)------------------------------
% 1.65/1.38 % (13890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (13890)Termination reason: Refutation
% 1.65/1.38
% 1.65/1.38 % (13890)Memory used [KB]: 5756
% 1.65/1.38 % (13890)Time elapsed: 0.035 s
% 1.65/1.38 % (13890)Instructions burned: 57 (million)
% 1.65/1.38 % (13890)------------------------------
% 1.65/1.38 % (13890)------------------------------
% 1.65/1.38 % (13884)Success in time 0.048 s
%------------------------------------------------------------------------------