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Proofgold Asset
asset id
e17a0275477821afaf969ac51399c1fe7eaee58e5c7b786b40664a7afeee75d0
asset hash
94caf3760ea30a8f97c1af075d70e5b325be5aa90dfad0069ed2d8e793fa267e
bday / block
37129
tx
2faaa..
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
b3861..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
372ed..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3b695..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f7c3d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
389f9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b1cc0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f3cdc..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e37d4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
230e1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
05e53..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c0878..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c2463..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9ea95..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b4c8a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7c528..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0b76b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5cb4b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6c725..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
84d5a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
615f5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fd1bb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0c647..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
99ce8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0b765..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1b190..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1b79b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
27059..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1c6d8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3a674..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cc0ce..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
60df6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d03a7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7676b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2bd9d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
db72f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c1515..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ccd93..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d5e1e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9a85f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
10481..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
afd75..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
29a16..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ac04a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7f9b0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6d3ff..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e1b03..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5c2af..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5f483..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1610e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d2827..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
da3f2..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5b060..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2cfca..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c148f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d7cce..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8b97c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
985a5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0314a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
aa9ff..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
dd0e6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
08a39..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cb63a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
79f22..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d8761..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
aa035..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
771b4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
11c17..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d98cb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
77ff4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
83424..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
49663..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0282b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
00e1f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
af16d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a5c5d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a6215..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c8b10..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5072f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
40e45..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fa72d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3b6e0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
662fb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fd83c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3da93..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
24019..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
04ae3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
45d70..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e4c05..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3b69b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6a4fb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
dbaa8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
599ac..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e7651..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
33dd8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3cc90..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a2a3d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f693b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fcfd2..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
bc1b4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e36fd..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
14b71..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fdf53..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0aba1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5ef43..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
85162..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
bddcc..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7c692..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
df54f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
303f2..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
983a2..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6647d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4a35f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4f557..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cbd9e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e643b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
242d1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e3246..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3c797..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
55a2d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cb670..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
dfcf9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
70101..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
26176..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b9708..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
164fa..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
83a9f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
830c6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
70e9a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
916cb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ec99f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6ea2b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9420c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
089ad..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
35e15..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
279d8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2158f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
aa8e6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0881d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
24054..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f0d5b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
11426..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
725c8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
81fa4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
89dbd..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
50d07..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
25f2f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
02262..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c5458..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3f579..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
14240..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
67161..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
110e1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
24aad..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3dc22..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7b2a6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
db744..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
80211..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0d9e0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
810e7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5d19f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b33d3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8f06c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
478f3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
bd6bc..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cb643..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6caef..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
97536..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7a491..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
86c47..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
04e02..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
737dc..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d7a9f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5c6e5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8df3f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d97a2..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
bc747..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c6cd1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1d96c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c2c18..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
70e38..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
2426f..
:=
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
⟶
372ed..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
3b695..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
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f7c3d..
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x7
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389f9..
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b1cc0..
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e37d4..
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230e1..
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05e53..
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c0878..
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c2463..
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9ea95..
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b4c8a..
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7c528..
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0b76b..
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5cb4b..
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6c725..
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84d5a..
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615f5..
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fd1bb..
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0c647..
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99ce8..
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0b765..
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1b190..
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1b79b..
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27059..
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x9
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1c6d8..
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3a674..
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cc0ce..
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60df6..
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d03a7..
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7676b..
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2bd9d..
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db72f..
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∈
x0
⟶
c1515..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
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x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
ccd93..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
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x4
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x0
⟶
∀ x5 .
x5
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x0
⟶
∀ x6 .
x6
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x0
⟶
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
d5e1e..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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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x8
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x0
⟶
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x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
9a85f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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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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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
∈
x0
⟶
10481..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x4
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x5
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x0
⟶
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x6
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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
⟶
afd75..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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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x0
⟶
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x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
29a16..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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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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
∈
x0
⟶
ac04a..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
7f9b0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
∈
x0
⟶
6d3ff..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
∈
x0
⟶
e1b03..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
∈
x0
⟶
5c2af..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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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
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
5f483..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
1610e..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
∈
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
⟶
d2827..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
da3f2..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
5b060..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
2cfca..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
c148f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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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
∈
x0
⟶
d7cce..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
∈
x0
⟶
8b97c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
∀ 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
⟶
985a5..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
∀ x7 .
x7
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x0
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
0314a..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
∀ x8 .
x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
∈
x0
⟶
aa9ff..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
∀ x7 .
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
∈
x0
⟶
dd0e6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
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x4
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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
∈
x0
⟶
08a39..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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⟶
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x5
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x0
⟶
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x6
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x0
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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
⟶
cb63a..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
79f22..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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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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
⟶
d8761..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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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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
⟶
aa035..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
771b4..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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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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
⟶
11c17..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x0
⟶
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x4
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x0
⟶
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x0
⟶
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x6
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x0
⟶
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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
⟶
d98cb..
x1
x3
x4
x5
x6
x7
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77ff4..
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83424..
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49663..
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a5c5d..
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a6215..
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c8b10..
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5072f..
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40e45..
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fa72d..
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3b6e0..
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662fb..
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3da93..
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24019..
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04ae3..
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45d70..
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e4c05..
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3b69b..
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6a4fb..
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599ac..
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33dd8..
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3cc90..
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a2a3d..
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f693b..
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fcfd2..
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bc1b4..
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e36fd..
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x8
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x9
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⟶
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x10
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14b71..
x1
x3
x4
x5
x6
x7
x8
x9
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⟶
x2
)
⟶
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∀ x3 .
x3
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x0
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fdf53..
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x3
x4
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x7
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x9
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⟶
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⟶
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0aba1..
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⟶
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5ef43..
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x3
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x7
x8
x9
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⟶
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⟶
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x8
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x10
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85162..
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x3
x4
x5
x6
x7
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x9
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⟶
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⟶
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x8
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x10
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bddcc..
x1
x3
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x6
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x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
x3
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x8
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x10
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7c692..
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x3
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x5
x6
x7
x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
x3
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x8
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x9
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x10
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df54f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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⟶
(
∀ x3 .
x3
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x8
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x9
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x10
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303f2..
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x3
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x9
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⟶
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⟶
(
∀ x3 .
x3
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x8
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x9
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x10
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983a2..
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x3
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x9
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⟶
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⟶
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x3
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x8
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⟶
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x9
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x0
⟶
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x10
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x0
⟶
6647d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x4
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x0
⟶
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x6
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x8
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x0
⟶
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x9
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x0
⟶
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x10
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x0
⟶
4a35f..
x1
x3
x4
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x6
x7
x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
x3
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x4
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x6
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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
⟶
4f557..
x1
x3
x4
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x6
x7
x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
x3
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x4
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x6
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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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x0
⟶
cbd9e..
x1
x3
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x6
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x8
x9
x10
⟶
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⟶
(
∀ x3 .
x3
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x4
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x6
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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
⟶
e643b..
x1
x3
x4
x5
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x7
x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
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x6
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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
⟶
242d1..
x1
x3
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x5
x6
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x8
x9
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⟶
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)
⟶
(
∀ x3 .
x3
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x8
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x9
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x0
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∀ x10 .
x10
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⟶
e3246..
x1
x3
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x6
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x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
x3
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x4
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x6
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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
⟶
3c797..
x1
x3
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x5
x6
x7
x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
x3
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x4
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x6
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x8
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x9
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x10
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x0
⟶
55a2d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
x3
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x4
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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
⟶
cb670..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x4
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⟶
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x6
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x8
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x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
dfcf9..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x4
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x0
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⟶
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x6
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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
⟶
70101..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x4
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x0
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⟶
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x6
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x7
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⟶
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x8
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x0
⟶
∀ x9 .
x9
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x0
⟶
∀ x10 .
x10
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x0
⟶
26176..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x4
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x6
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x7
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x8
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x9
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x0
⟶
∀ x10 .
x10
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⟶
b9708..
x1
x3
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x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x6
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x8
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x9
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x0
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x10
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⟶
164fa..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x8
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x9
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x0
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x10
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⟶
83a9f..
x1
x3
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x5
x6
x7
x8
x9
x10
⟶
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⟶
(
∀ x3 .
x3
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x6
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x8
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x0
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x10
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⟶
830c6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x8
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x9
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x0
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∀ x10 .
x10
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x0
⟶
70e9a..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x10
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916cb..
x1
x3
x4
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x6
x7
x8
x9
x10
⟶
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)
⟶
(
∀ x3 .
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x9
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x10
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⟶
ec99f..
x1
x3
x4
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x6
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x8
x9
x10
⟶
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⟶
(
∀ x3 .
x3
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x8
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x9
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⟶
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x10
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⟶
6ea2b..
x1
x3
x4
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x6
x7
x8
x9
x10
⟶
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⟶
(
∀ x3 .
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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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⟶
9420c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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)
⟶
(
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∀ x10 .
x10
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089ad..
x1
x3
x4
x5
x6
x7
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x9
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⟶
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)
⟶
(
∀ x3 .
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x4
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x10
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35e15..
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x5
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x7
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x9
x10
⟶
x2
)
⟶
(
∀ x3 .
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279d8..
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2158f..
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aa8e6..
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0881d..
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⟶
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⟶
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24054..
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x3
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x9
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⟶
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⟶
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f0d5b..
x1
x3
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⟶
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⟶
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x8
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x9
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x10
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11426..
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x3
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x9
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⟶
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⟶
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x8
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x10
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725c8..
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x3
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x9
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⟶
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⟶
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x3
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x4
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x8
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x9
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x10
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81fa4..
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x3
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x9
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⟶
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⟶
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x8
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x10
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89dbd..
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x3
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⟶
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x8
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x10
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50d07..
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x3
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x9
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⟶
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⟶
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x8
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x10
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25f2f..
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x3
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⟶
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x8
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x9
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x0
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x10
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02262..
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x3
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x9
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⟶
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⟶
(
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x10
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c5458..
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x3
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x9
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⟶
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⟶
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x10
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3f579..
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⟶
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⟶
(
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x3
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x8
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x9
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x10
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⟶
14240..
x1
x3
x4
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x6
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x9
x10
⟶
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)
⟶
(
∀ x3 .
x3
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x4
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x8
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x10
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⟶
67161..
x1
x3
x4
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x6
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x9
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⟶
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)
⟶
(
∀ x3 .
x3
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x4
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x8
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x9
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x10
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⟶
110e1..
x1
x3
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x7
x8
x9
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⟶
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)
⟶
(
∀ x3 .
x3
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x4
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x8
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x10
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⟶
24aad..
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x3
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x9
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⟶
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⟶
(
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x3
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x8
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x9
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x0
⟶
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x10
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⟶
3dc22..
x1
x3
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x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x4
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x8
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x9
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x0
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x10
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x0
⟶
7b2a6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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⟶
(
∀ x3 .
x3
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x8
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x9
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x10
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⟶
db744..
x1
x3
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x6
x7
x8
x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x8
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x9
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x0
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∀ x10 .
x10
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80211..
x1
x3
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x8
x9
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⟶
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⟶
(
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x3
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x8
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x9
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x10
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0d9e0..
x1
x3
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x6
x7
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x9
x10
⟶
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⟶
(
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x3
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x8
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x9
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x10
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810e7..
x1
x3
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x5
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x9
x10
⟶
x2
)
⟶
(
∀ x3 .
x3
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x9
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x10
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5d19f..
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x3
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x10
⟶
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⟶
(
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x10
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b33d3..
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x3
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x9
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⟶
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⟶
(
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x10
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8f06c..
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x3
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x7
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x9
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⟶
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⟶
(
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x3
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x10
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478f3..
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x3
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x8
x9
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⟶
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⟶
(
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x10
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bd6bc..
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x3
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x8
x9
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⟶
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⟶
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∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
cb643..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
6caef..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
97536..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
7a491..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
86c47..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
04e02..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
737dc..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
d7a9f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
5c6e5..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
8df3f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
d97a2..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
bc747..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
c6cd1..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
1d96c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
c2c18..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
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
⟶
70e38..
x1
x3
x4
x5
x6
x7
x8
x9
x10
⟶
x2
)
⟶
x2
Known
13304..
:
∀ 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
⟶
b3861..
x2
x4
x5
x6
x7
x8
x9
x10
⟶
∀ x11 : ο .
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
83424..
x2
x12
x13
x3
x14
x15
x16
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
af16d..
x2
x12
x13
x3
x14
x15
x16
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
fa72d..
x2
x12
x13
x3
x14
x15
x16
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
242d1..
x2
x12
x13
x14
x15
x16
x17
x3
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
0881d..
x2
x12
x13
x14
x15
x3
x16
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
24054..
x2
x12
x13
x14
x15
x3
x16
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
25f2f..
x2
x12
x13
x14
x15
x16
x3
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
7b2a6..
x2
x12
x13
x14
x15
x3
x16
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
80211..
x2
x12
x13
x14
x15
x3
x16
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
0d9e0..
x2
x12
x13
x14
x15
x3
x16
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
478f3..
x2
x12
x13
x14
x15
x16
x3
x17
x18
⟶
x11
)
⟶
(
∀ x12 .
x12
∈
x0
⟶
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x0
⟶
∀ x15 .
x15
∈
x0
⟶
∀ x16 .
x16
∈
x0
⟶
∀ x17 .
x17
∈
x0
⟶
∀ x18 .
x18
∈
x0
⟶
1d96c..
x2
x12
x13
x14
x15
x16
x17
x3
x18
⟶
x11
)
⟶
x11
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
4e529..
:
∀ 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
⟶
b3861..
x1
x4
x5
x6
x7
x8
x9
x10
⟶
2426f..
x0
x1
(proof)