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Proofgold Asset
asset id
fecc8ecbe5d2becb32977a727804926848d4fb97cadd2b8e0ca676c183fa096f
asset hash
324bb5b389f2b2230e62e9d37157e8446545b67de7c0cfcd3c024d16ea734c59
bday / block
37675
tx
ec379..
preasset
doc published by
Pr4zB..
Param
4402e..
:
ι
→
(
ι
→
ι
→
ο
) →
ο
Param
cf2df..
:
ι
→
(
ι
→
ι
→
ο
) →
ο
Definition
Subq
Subq
:=
λ x0 x1 .
∀ x2 .
x2
∈
x0
⟶
x2
∈
x1
Param
setminus
setminus
:
ι
→
ι
→
ι
Param
Sing
Sing
:
ι
→
ι
Param
77953..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
40920..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d17b7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ed6d2..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
59d98..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0dd76..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f7297..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
940a6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
580d8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
04c7a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8e334..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7c6aa..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
38607..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
077c6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6a2c7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
01042..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6d769..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0c718..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
25ef3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fa706..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e5296..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
36e22..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b8ed0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
44299..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e9a2b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7e591..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
aa284..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ba6f3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
dafd9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
546aa..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1f676..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0a50a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
380c0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9e687..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4cf61..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6c968..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6fe5f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fd9fb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7aa0e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0e688..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c1824..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
df3c6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c7c61..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e5b9c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ea5d0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7f80f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f1399..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0a04b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
aec6c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b50f9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cc1e8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ade95..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5ed8e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
efc7e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8fef1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
418c9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f3a4c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8dc75..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
36e27..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8dbd3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0ed40..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
76168..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
df932..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8aed1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9f9d1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
be6eb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
913ca..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e1ecf..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c6073..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d10a3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e1502..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cb091..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e4d18..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e9c3a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c34cb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
805ab..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4d434..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
42ad9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fe1c4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
61a95..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5f61d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b5d0d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
01336..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d6df6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
92541..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
672d9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7fb8b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
92a6c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
54502..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ce66c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
28caf..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5a896..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
27efe..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6e10f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
244e1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
10c44..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cac90..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f45e1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9a447..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d09d5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6c310..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
59ef4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6157c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6a2f1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d246f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a81fb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
a0244..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
40920..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
d17b7..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
ed6d2..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
59d98..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
0dd76..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
f7297..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
940a6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
580d8..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
04c7a..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
8e334..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
7c6aa..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
38607..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
077c6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
6a2c7..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
01042..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
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⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
⟶
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x5
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x0
⟶
∀ x6 .
x6
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⟶
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x7
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x0
⟶
∀ x8 .
x8
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⟶
∀ x9 .
x9
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⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
6d769..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
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x0
⟶
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x5
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x0
⟶
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x6
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x0
⟶
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x7
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x0
⟶
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x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
0c718..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
⟶
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x5
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x0
⟶
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x6
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⟶
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x0
⟶
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x8
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⟶
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x9
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⟶
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x10
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⟶
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x11
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x0
⟶
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x12
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x0
⟶
∀ x13 .
x13
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x0
⟶
25ef3..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
⟶
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x5
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x0
⟶
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x6
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x0
⟶
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x7
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x0
⟶
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x8
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x0
⟶
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x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
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x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
fa706..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
⟶
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x5
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x0
⟶
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x6
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x0
⟶
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x7
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x0
⟶
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x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
e5296..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
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x5
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x0
⟶
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x6
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x0
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x7
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x0
⟶
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x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
36e22..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
⟶
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x5
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x0
⟶
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x6
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x0
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x7
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x0
⟶
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x8
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⟶
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x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
b8ed0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
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x0
⟶
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x5
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x0
⟶
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x6
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x0
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x7
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x0
⟶
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x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
44299..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
⟶
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x5
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x0
⟶
∀ x6 .
x6
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x0
⟶
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x7
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x0
⟶
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x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
e9a2b..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
⟶
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x5
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x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
7e591..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
∈
x0
⟶
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x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
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x7
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x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
aa284..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
ba6f3..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
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x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
dafd9..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
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x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
546aa..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
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x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
1f676..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
0a50a..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
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x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
380c0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
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x0
⟶
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x5
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x0
⟶
∀ x6 .
x6
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x0
⟶
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x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
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x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
9e687..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
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x0
⟶
∀ x5 .
x5
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x0
⟶
∀ x6 .
x6
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x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
4cf61..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
6c968..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
6fe5f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
fd9fb..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
7aa0e..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
0e688..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
c1824..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
df3c6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
c7c61..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
e5b9c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
ea5d0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
7f80f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
f1399..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
0a04b..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
aec6c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
b50f9..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
cc1e8..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
ade95..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
5ed8e..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
efc7e..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
8fef1..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
418c9..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
f3a4c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
8dc75..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
36e27..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
8dbd3..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
0ed40..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
76168..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
df932..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
8aed1..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
9f9d1..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
be6eb..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
913ca..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
e1ecf..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
c6073..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
d10a3..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
e1502..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
cb091..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
e4d18..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
e9c3a..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
c34cb..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
805ab..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
4d434..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
42ad9..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
fe1c4..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
61a95..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
5f61d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
b5d0d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
01336..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
d6df6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
92541..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
672d9..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
7fb8b..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
92a6c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
54502..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
ce66c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
28caf..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
5a896..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
27efe..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
6e10f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
244e1..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
10c44..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
cac90..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
f45e1..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
9a447..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
d09d5..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
6c310..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
59ef4..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
6157c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
6a2f1..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
d246f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
a81fb..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
x2
)
⟶
x2
Known
77204..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
77953..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
∀ x14 : ο .
(
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
∀ x19 .
x19
∈
x0
⟶
∀ x20 .
x20
∈
x0
⟶
∀ x21 .
x21
∈
x0
⟶
∀ x22 .
x22
∈
x0
⟶
∀ x23 .
x23
∈
x0
⟶
∀ x24 .
x24
∈
x0
⟶
cb091..
x2
x15
x16
x17
x18
x19
x20
x21
x22
x3
x23
x24
⟶
x14
)
⟶
(
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
∀ x19 .
x19
∈
x0
⟶
∀ x20 .
x20
∈
x0
⟶
∀ x21 .
x21
∈
x0
⟶
∀ x22 .
x22
∈
x0
⟶
∀ x23 .
x23
∈
x0
⟶
∀ x24 .
x24
∈
x0
⟶
5f61d..
x2
x15
x16
x17
x18
x19
x3
x20
x21
x22
x23
x24
⟶
x14
)
⟶
x14
Known
Subq_tra
Subq_tra
:
∀ x0 x1 x2 .
x0
⊆
x1
⟶
x1
⊆
x2
⟶
x0
⊆
x2
Known
setminus_Subq
setminus_Subq
:
∀ x0 x1 .
setminus
x0
x1
⊆
x0
Theorem
9af4b..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
∀ x13 .
x13
∈
x3
⟶
77953..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
⟶
a0244..
x0
x1
(proof)