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Proofgold Asset
asset id
4906078f69609222bd6d41bcdaaaca9037756158f302140b19abd3b9470466f9
asset hash
60fb8879eb44e55e292a0aa647401125eddd62cd521aed4898e0048becca892f
bday / block
48587
tx
ae626..
preasset
doc published by
Pr3KZ..
Param
2f869..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ο
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Definition
5a3b5..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 .
∀ x6 : ο .
(
2f869..
x0
x1
x2
x3
x4
⟶
(
x1
=
x5
⟶
∀ x7 : ο .
x7
)
⟶
(
x2
=
x5
⟶
∀ x7 : ο .
x7
)
⟶
(
x3
=
x5
⟶
∀ x7 : ο .
x7
)
⟶
(
x4
=
x5
⟶
∀ x7 : ο .
x7
)
⟶
not
(
x0
x1
x5
)
⟶
x0
x2
x5
⟶
not
(
x0
x3
x5
)
⟶
not
(
x0
x4
x5
)
⟶
x6
)
⟶
x6
Definition
247da..
:=
λ x0 :
ι →
ι → ο
.
λ x1 x2 x3 x4 x5 x6 .
∀ x7 : ο .
(
5a3b5..
x0
x1
x2
x3
x4
x5
⟶
(
x1
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x2
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x3
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x4
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
(
x5
=
x6
⟶
∀ x8 : ο .
x8
)
⟶
x0
x1
x6
⟶
not
(
x0
x2
x6
)
⟶
not
(
x0
x3
x6
)
⟶
not
(
x0
x4
x6
)
⟶
x0
x5
x6
⟶
x7
)
⟶
x7
Param
e643b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
86706..
:
ι
→
(
ι
→
ι
→
ο
) →
ο
Param
35fb6..
:
ι
→
(
ι
→
ι
→
ο
) →
ο
Known
1e947..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x15
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
(
x0
x2
x9
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x8
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x10
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x5
x10
⟶
x0
x3
x13
⟶
not
(
x0
x4
x10
)
⟶
False
)
⟶
(
x0
x3
x9
⟶
x0
x3
x13
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
x0
x3
x13
⟶
x0
x3
x15
⟶
False
Known
7f382..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x15
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
(
x0
x2
x9
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x8
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x10
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x5
x10
⟶
x0
x3
x13
⟶
not
(
x0
x4
x10
)
⟶
False
)
⟶
(
x0
x3
x9
⟶
x0
x3
x13
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
x0
x3
x13
⟶
not
(
x0
x3
x15
)
⟶
x0
x3
x14
⟶
False
Known
dcb1a..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x15
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
(
x0
x2
x9
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x8
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x10
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x5
x10
⟶
x0
x3
x13
⟶
not
(
x0
x4
x10
)
⟶
False
)
⟶
(
x0
x3
x9
⟶
x0
x3
x13
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
x0
x3
x13
⟶
not
(
x0
x3
x15
)
⟶
not
(
x0
x3
x14
)
⟶
False
Known
60237..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x15
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
(
x0
x2
x9
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x8
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x10
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x5
x10
⟶
x0
x3
x13
⟶
not
(
x0
x4
x10
)
⟶
False
)
⟶
(
x0
x3
x9
⟶
x0
x3
x13
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
not
(
x0
x3
x13
)
⟶
False
Definition
or
or
:=
λ x0 x1 : ο .
∀ x2 : ο .
(
x0
⟶
x2
)
⟶
(
x1
⟶
x2
)
⟶
x2
Known
xm
xm
:
∀ x0 : ο .
or
x0
(
not
x0
)
Theorem
429de..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x15
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
(
x0
x2
x9
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x8
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x10
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x5
x10
⟶
x0
x3
x13
⟶
not
(
x0
x4
x10
)
⟶
False
)
⟶
(
x0
x3
x9
⟶
x0
x3
x13
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
False
...
Definition
and
and
:=
λ x0 x1 : ο .
∀ x2 : ο .
(
x0
⟶
x1
⟶
x2
)
⟶
x2
Known
dneg
dneg
:
∀ x0 : ο .
not
(
not
x0
)
⟶
x0
Known
636a9..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
e643b..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
e643b..
x1
x6
x8
x4
x9
x2
x7
x3
x5
Known
andI
andI
:
∀ x0 x1 : ο .
x0
⟶
x1
⟶
and
x0
x1
Theorem
13d61..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x11
⟶
not
(
x0
x3
x9
)
⟶
False
)
⟶
(
x0
x2
x14
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x12
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x10
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x5
x10
⟶
x0
x3
x13
⟶
not
(
x0
x4
x10
)
⟶
False
)
⟶
False
...
Known
66a94..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
5a3b5..
x1
x2
x3
x4
x5
x6
⟶
5a3b5..
x1
x2
x3
x5
x4
x6
Theorem
9759f..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
247da..
x1
x2
x3
x4
x5
x6
x7
⟶
247da..
x1
x2
x3
x5
x4
x6
x7
...
Theorem
f325d..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x14
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x12
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x10
⟶
not
(
x0
x3
x13
)
⟶
False
)
⟶
(
x0
x2
x11
⟶
not
(
x0
x3
x9
)
⟶
False
)
⟶
False
...
Known
33ada..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
2f869..
x1
x2
x3
x4
x5
⟶
2f869..
x1
x3
x2
x5
x4
Known
neq_i_sym
neq_i_sym
:
∀ x0 x1 .
(
x0
=
x1
⟶
∀ x2 : ο .
x2
)
⟶
x1
=
x0
⟶
∀ x2 : ο .
x2
Theorem
38647..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
247da..
x1
x2
x3
x4
x5
x6
x7
⟶
247da..
x1
x3
x2
x5
x4
x7
x6
...
Known
174e8..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
e643b..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
e643b..
x1
x5
x3
x7
x2
x9
x4
x8
x6
Known
cc783..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
e643b..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
e643b..
x1
x7
x5
x9
x3
x8
x2
x6
x4
Theorem
8ef0f..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
e643b..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
e643b..
x1
x3
x5
x2
x7
x4
x9
x6
x8
...
Theorem
95448..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x3
x12
⟶
not
(
x0
x2
x15
)
⟶
False
)
⟶
(
x0
x3
x10
⟶
not
(
x0
x2
x15
)
⟶
False
)
⟶
(
x0
x3
x8
⟶
not
(
x0
x2
x15
)
⟶
False
)
⟶
False
...
Known
f8e2e..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
e643b..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
e643b..
x1
x3
x2
x5
x4
x7
x6
x9
x8
Theorem
2f0fc..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x13
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
(
x0
x2
x11
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
(
x0
x2
x9
⟶
not
(
x0
x3
x14
)
⟶
False
)
⟶
False
...
Known
42c8f..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
e643b..
x1
x2
x3
x4
x5
x6
x7
x8
x9
⟶
e643b..
x1
x2
x4
x3
x6
x5
x8
x7
x9
Theorem
1267d..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x3
x12
⟶
not
(
x0
x2
x13
)
⟶
False
)
⟶
(
x0
x3
x10
⟶
not
(
x0
x2
x13
)
⟶
False
)
⟶
False
...
Theorem
e0bf3..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
(
x0
x2
x11
⟶
not
(
x0
x3
x12
)
⟶
False
)
⟶
False
...
Theorem
d4066..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 .
x2
∈
x1
⟶
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
∀ x5 .
x5
∈
x1
⟶
∀ x6 .
x6
∈
x1
⟶
∀ x7 .
x7
∈
x1
⟶
∀ x8 .
x8
∈
x1
⟶
∀ x9 .
x9
∈
x1
⟶
∀ x10 .
x10
∈
x1
⟶
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x1
⟶
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x1
⟶
∀ x15 .
x15
∈
x1
⟶
(
∀ x16 .
x16
∈
x1
⟶
∀ x17 .
x17
∈
x1
⟶
x0
x16
x17
⟶
x0
x17
x16
)
⟶
(
x2
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x8
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x9
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x10
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x11
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x12
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x13
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x14
⟶
∀ x16 : ο .
x16
)
⟶
(
x2
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x3
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x4
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x5
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x6
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
(
x7
=
x15
⟶
∀ x16 : ο .
x16
)
⟶
247da..
x0
x2
x3
x4
x5
x6
x7
⟶
e643b..
(
λ x16 x17 .
not
(
x0
x16
x17
)
)
x8
x9
x10
x11
x12
x13
x14
x15
⟶
86706..
x1
x0
⟶
35fb6..
x1
x0
⟶
False
...