TSTP Solution File: SEU760^2 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU760^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 : Thu Aug 31 17:26:23 EDT 2023
% Result : Theorem 84.11s 84.30s
% Output : Proof 84.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_binintersect,type,
binintersect: $i > $i > $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( subset
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) )
=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) )
=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ ( binintersect
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) ) )
=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
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~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) )
=> ( subset
@ ( binintersect
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
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@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
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@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
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@ ( powerset
@ @+[X5: $i] :
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( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
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@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ ( binintersect
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) ) )
=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( in @ X2
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 ) )
=> ( in @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) )
=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X1 )
=> ( ( in @ X2
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( ( in
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) ) )
=> ( in @ X2 @ X1 ) )
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) ) )
=> ( in @ X2 @ X1 ) )
@ X1 ) )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( subset
@ ( binintersect
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ ( binintersect
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i,X2: $i] :
( ( ( in
@ @+[X3: $i] :
~ ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
@ X1 )
=> ( in
@ @+[X3: $i] :
~ ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
@ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( sP1
=> ( ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP16
=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) ) )
=> ( in @ X1
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) )
@ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset
@ ( binintersect
@ @+[X5: $i] :
~ ( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ! [X7: $i] :
( ( in @ X7
@ ( powerset
@ @+[X8: $i] :
~ ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X8 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X8 ) )
=> ! [X11: $i] :
( ( in @ X11 @ ( powerset @ X8 ) )
=> ( ( subset @ X10 @ X11 )
=> ( subset @ ( binintersect @ X9 @ X10 ) @ X11 ) ) ) ) ) ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) )
@ X3 )
@ X4 ) ) ) ) )
@ X2 ) ) ) ) )
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_subsetI1,definition,
( subsetI1
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) )
@ ( subset @ X1 @ X2 ) ) ) ) ).
thf(def_subsetE,definition,
( subsetE
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( subset @ X1 @ X2 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) ) ) ) ) ).
thf(def_binintersectER,definition,
( binintersectER
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
@ ( in @ X3 @ X2 ) ) ) ) ).
thf(woz13rule2,conjecture,
( ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) )
=> ( sP2
=> ( sP7
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) )
=> ( sP2
=> ( sP7
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[woz13rule2]) ).
thf(h1,assumption,
sP17,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP2
=> ( sP7
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( sP1
=> sP13 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP7
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( sP1
=> sP13 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP7,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( sP1
=> sP13 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( sP1
=> sP13 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset
@ ( binintersect
@ @+[X3: $i] :
~ ( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) )
@ X1 )
@ X2 ) ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) )
=> ( sP1
=> sP13 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
( in
@ @+[X1: $i] :
~ ( ( in @ X1
@ ( powerset
@ @+[X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X2 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) )
=> ( ( subset
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) )
@ X1 )
=> ( subset
@ ( binintersect
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) )
@ @+[X2: $i] :
~ ( ( in @ X2
@ ( powerset
@ @+[X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X3 ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3
@ ( powerset
@ @+[X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X7 )
=> ( subset @ ( binintersect @ X5 @ X6 ) @ X7 ) ) ) ) ) ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset
@ ( binintersect
@ @+[X4: $i] :
~ ( ( in @ X4
@ ( powerset
@ @+[X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X5 ) )
=> ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X5 ) )
=> ( ( subset @ X7 @ X8 )
=> ( subset @ ( binintersect @ X6 @ X7 ) @ X8 ) ) ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5
@ ( powerset
@ @+[X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ ( powerset @ X6 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X6 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X6 ) )
=> ( ( subset @ X8 @ X9 )
=> ( subset @ ( binintersect @ X7 @ X8 ) @ X9 ) ) ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( powerset
@ @+[X7: $i] :
~ ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X7 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X7 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X7 ) )
=> ( ( subset @ X9 @ X10 )
=> ( subset @ ( binintersect @ X8 @ X9 ) @ X10 ) ) ) ) ) ) )
=> ( ( subset @ X5 @ X6 )
=> ( subset @ ( binintersect @ X4 @ X5 ) @ X6 ) ) ) ) )
@ X2 )
@ X3 ) ) ) ) )
@ X1 ) ) )
@ ( powerset
@ @+[X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP1
=> sP13 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| ~ sP20
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP19
| ~ sP16
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP1
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP15 ),
inference(choice_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP18
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP6
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP6
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP5
| ~ sP6
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP12
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP11
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP17
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h1,h3,h5,h13,h14]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h13,h14])],[h12,17,h13,h14]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h11,h12])],[h10,18,h11,h12]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h9,h10])],[h8,19,h9,h10]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h7,h8])],[h6,20,h7,h8]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h5,h6])],[h4,21,h5,h6]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0,h0]),tab_negimp(discharge,[h3,h4])],[h2,22,h3,h4]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0,h0]),tab_negimp(discharge,[h1,h2])],[h0,23,h1,h2]) ).
thf(0,theorem,
( ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) )
=> ( sP2
=> ( sP7
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU760^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 00:00:06 EDT 2023
% 0.14/0.36 % CPUTime :
% 84.11/84.30 % SZS status Theorem
% 84.11/84.30 % Mode: cade22grackle2x4fb9
% 84.11/84.30 % Steps: 32319
% 84.11/84.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------