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Proofgold Asset
asset id
c0b7b7cb2f73f222579f810eb87683f40f4d585dabd20f651fb19f336c3f31b6
asset hash
ca930d260277c59ff940348f5317bd7db477bc29ff9437bf8562521b62d59fcb
bday / block
9425
tx
ec764..
preasset
doc published by
PrGxv..
Definition
and
and
:=
λ x0 x1 : ο .
∀ x2 : ο .
(
x0
⟶
x1
⟶
x2
)
⟶
x2
Definition
f3993..
:=
λ x0 :
ι → ο
.
λ x1 :
(
ι → ο
)
→ ο
.
λ x2 :
(
ι →
ι → ο
)
→ ο
.
λ x3 .
λ x4 x5 :
ι →
ι → ι
.
and
(
and
(
and
(
and
(
and
(
x2
(
λ x6 x7 .
x0
(
x4
x6
x7
)
)
)
(
x1
(
λ x6 .
x1
(
λ x7 .
x0
(
x5
x6
x7
)
)
)
)
)
(
x1
(
λ x6 .
x4
x6
x3
=
x6
)
)
)
(
x2
(
λ x6 x7 .
x4
x6
x7
=
x4
x7
x6
)
)
)
(
x1
(
λ x6 .
x1
(
λ x7 .
x4
(
x5
x6
x7
)
x7
=
x6
)
)
)
)
(
x1
(
λ x6 .
x1
(
λ x7 .
x5
(
x4
x6
x7
)
x7
=
x6
)
)
)
Definition
c1ee3..
:=
λ x0 :
ι → ο
.
λ x1 :
(
ι → ο
)
→ ο
.
λ x2 :
(
ι →
ι → ο
)
→ ο
.
λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
λ x17 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
λ x18 :
ι →
ι → ι
.
λ x19 .
x18
(
x18
(
x17
(
x17
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
)
(
x17
x4
x11
x3
x16
x12
x13
x8
x14
x15
x7
x10
x6
x5
x9
)
(
x17
x5
x3
x15
x14
x13
x9
x11
x7
x6
x10
x4
x8
x16
x12
)
(
x17
x6
x16
x14
x3
x9
x10
x7
x4
x5
x11
x8
x12
x13
x15
)
(
x17
x7
x12
x13
x9
x15
x3
x6
x16
x8
x5
x14
x10
x11
x4
)
(
x17
x8
x13
x9
x10
x3
x5
x4
x11
x12
x15
x7
x16
x14
x6
)
(
x17
x9
x8
x11
x7
x6
x4
x13
x12
x14
x16
x15
x5
x3
x10
)
(
x17
x10
x14
x7
x4
x16
x11
x12
x13
x3
x8
x6
x15
x9
x5
)
(
x17
x11
x15
x6
x5
x8
x12
x14
x3
x10
x13
x16
x9
x4
x7
)
(
x17
x12
x7
x10
x11
x5
x15
x16
x8
x13
x3
x9
x4
x6
x14
)
(
x17
x13
x10
x4
x8
x14
x7
x15
x6
x16
x9
x5
x11
x12
x3
)
(
x17
x14
x6
x8
x12
x10
x16
x5
x15
x9
x4
x11
x3
x7
x13
)
(
x17
x15
x5
x16
x13
x11
x14
x3
x9
x4
x6
x12
x7
x10
x8
)
(
x17
x16
x9
x12
x15
x4
x6
x10
x5
x7
x14
x3
x13
x8
x11
)
)
x19
)
Definition
f5650..
:=
λ x0 :
ι → ο
.
λ x1 :
(
ι → ο
)
→ ο
.
λ x2 :
(
ι →
ι → ο
)
→ ο
.
λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
λ x17 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
λ x18 :
ι →
ι → ι
.
λ x19 .
x18
(
x18
(
x17
(
x17
x3
x5
x4
x6
x8
x7
x15
x11
x10
x12
x16
x14
x9
x13
)
(
x17
x4
x3
x13
x10
x16
x9
x8
x6
x15
x14
x5
x12
x11
x7
)
(
x17
x5
x15
x3
x11
x12
x8
x14
x16
x6
x7
x13
x9
x4
x10
)
(
x17
x6
x14
x11
x3
x9
x16
x7
x13
x5
x15
x10
x4
x12
x8
)
(
x17
x7
x12
x10
x9
x3
x13
x6
x5
x16
x4
x8
x15
x14
x11
)
(
x17
x8
x9
x14
x13
x11
x3
x4
x12
x7
x10
x6
x5
x16
x15
)
(
x17
x9
x16
x8
x7
x6
x5
x3
x15
x14
x13
x12
x11
x10
x4
)
(
x17
x10
x13
x12
x8
x14
x6
x16
x3
x11
x5
x4
x7
x15
x9
)
(
x17
x11
x4
x9
x12
x15
x10
x5
x8
x3
x6
x14
x13
x7
x16
)
(
x17
x12
x7
x16
x14
x4
x11
x10
x9
x8
x3
x15
x6
x13
x5
)
(
x17
x13
x8
x7
x15
x5
x4
x9
x10
x12
x11
x3
x16
x6
x14
)
(
x17
x14
x10
x6
x5
x13
x15
x11
x4
x9
x16
x7
x3
x8
x12
)
(
x17
x15
x11
x5
x16
x7
x12
x13
x14
x4
x8
x9
x10
x3
x6
)
(
x17
x16
x6
x15
x4
x10
x14
x12
x7
x13
x9
x11
x8
x5
x3
)
)
x19
)
Definition
2e6fa..
:=
λ x0 :
ι → ο
.
λ x1 :
(
ι → ο
)
→ ο
.
λ x2 :
(
ι →
ι → ο
)
→ ο
.
λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
λ x17 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
λ x18 x19 x20 :
ι →
ι → ι
.
λ x21 x22 x23 .
x20
(
x19
(
x19
x23
x21
)
x22
)
(
x19
x21
x22
)
Known
andI
andI
:
∀ x0 x1 : ο .
x0
⟶
x1
⟶
and
x0
x1
Known
and6I
and6I
:
∀ x0 x1 x2 x3 x4 x5 : ο .
x0
⟶
x1
⟶
x2
⟶
x3
⟶
x4
⟶
x5
⟶
and
(
and
(
and
(
and
(
and
x0
x1
)
x2
)
x3
)
x4
)
x5
Known
and3I
and3I
:
∀ x0 x1 x2 : ο .
x0
⟶
x1
⟶
x2
⟶
and
(
and
x0
x1
)
x2
Known
and5I
and5I
:
∀ x0 x1 x2 x3 x4 : ο .
x0
⟶
x1
⟶
x2
⟶
x3
⟶
x4
⟶
and
(
and
(
and
(
and
x0
x1
)
x2
)
x3
)
x4
Theorem
eeafe..
:
∀ x0 :
ι → ο
.
∀ x1 :
(
ι → ο
)
→ ο
.
∀ x2 :
(
ι →
ι → ο
)
→ ο
.
∀ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 .
x0
x3
⟶
x0
x4
⟶
x0
x5
⟶
x0
x6
⟶
x0
x7
⟶
x0
x8
⟶
x0
x9
⟶
x0
x10
⟶
x0
x11
⟶
x0
x12
⟶
x0
x13
⟶
x0
x14
⟶
x0
x15
⟶
x0
x16
⟶
(
∀ x17 :
ι → ο
.
x17
x3
⟶
x17
x4
⟶
x17
x5
⟶
x17
x6
⟶
x17
x7
⟶
x17
x8
⟶
x17
x9
⟶
x17
x10
⟶
x17
x11
⟶
x17
x12
⟶
x17
x13
⟶
x17
x14
⟶
x17
x15
⟶
x17
x16
⟶
x1
x17
)
⟶
(
∀ x17 :
ι →
ι → ο
.
x17
x3
x3
⟶
x17
x3
x4
⟶
x17
x3
x5
⟶
x17
x3
x6
⟶
x17
x3
x7
⟶
x17
x3
x8
⟶
x17
x3
x9
⟶
x17
x3
x10
⟶
x17
x3
x11
⟶
x17
x3
x12
⟶
x17
x3
x13
⟶
x17
x3
x14
⟶
x17
x3
x15
⟶
x17
x3
x16
⟶
x17
x4
x3
⟶
x17
x4
x4
⟶
x17
x4
x5
⟶
x17
x4
x6
⟶
x17
x4
x7
⟶
x17
x4
x8
⟶
x17
x4
x9
⟶
x17
x4
x10
⟶
x17
x4
x11
⟶
x17
x4
x12
⟶
x17
x4
x13
⟶
x17
x4
x14
⟶
x17
x4
x15
⟶
x17
x4
x16
⟶
x17
x5
x3
⟶
x17
x5
x4
⟶
x17
x5
x5
⟶
x17
x5
x6
⟶
x17
x5
x7
⟶
x17
x5
x8
⟶
x17
x5
x9
⟶
x17
x5
x10
⟶
x17
x5
x11
⟶
x17
x5
x12
⟶
x17
x5
x13
⟶
x17
x5
x14
⟶
x17
x5
x15
⟶
x17
x5
x16
⟶
x17
x6
x3
⟶
x17
x6
x4
⟶
x17
x6
x5
⟶
x17
x6
x6
⟶
x17
x6
x7
⟶
x17
x6
x8
⟶
x17
x6
x9
⟶
x17
x6
x10
⟶
x17
x6
x11
⟶
x17
x6
x12
⟶
x17
x6
x13
⟶
x17
x6
x14
⟶
x17
x6
x15
⟶
x17
x6
x16
⟶
x17
x7
x3
⟶
x17
x7
x4
⟶
x17
x7
x5
⟶
x17
x7
x6
⟶
x17
x7
x7
⟶
x17
x7
x8
⟶
x17
x7
x9
⟶
x17
x7
x10
⟶
x17
x7
x11
⟶
x17
x7
x12
⟶
x17
x7
x13
⟶
x17
x7
x14
⟶
x17
x7
x15
⟶
x17
x7
x16
⟶
x17
x8
x3
⟶
x17
x8
x4
⟶
x17
x8
x5
⟶
x17
x8
x6
⟶
x17
x8
x7
⟶
x17
x8
x8
⟶
x17
x8
x9
⟶
x17
x8
x10
⟶
x17
x8
x11
⟶
x17
x8
x12
⟶
x17
x8
x13
⟶
x17
x8
x14
⟶
x17
x8
x15
⟶
x17
x8
x16
⟶
x17
x9
x3
⟶
x17
x9
x4
⟶
x17
x9
x5
⟶
x17
x9
x6
⟶
x17
x9
x7
⟶
x17
x9
x8
⟶
x17
x9
x9
⟶
x17
x9
x10
⟶
x17
x9
x11
⟶
x17
x9
x12
⟶
x17
x9
x13
⟶
x17
x9
x14
⟶
x17
x9
x15
⟶
x17
x9
x16
⟶
x17
x10
x3
⟶
x17
x10
x4
⟶
x17
x10
x5
⟶
x17
x10
x6
⟶
x17
x10
x7
⟶
x17
x10
x8
⟶
x17
x10
x9
⟶
x17
x10
x10
⟶
x17
x10
x11
⟶
x17
x10
x12
⟶
x17
x10
x13
⟶
x17
x10
x14
⟶
x17
x10
x15
⟶
x17
x10
x16
⟶
x17
x11
x3
⟶
x17
x11
x4
⟶
x17
x11
x5
⟶
x17
x11
x6
⟶
x17
x11
x7
⟶
x17
x11
x8
⟶
x17
x11
x9
⟶
x17
x11
x10
⟶
x17
x11
x11
⟶
x17
x11
x12
⟶
x17
x11
x13
⟶
x17
x11
x14
⟶
x17
x11
x15
⟶
x17
x11
x16
⟶
x17
x12
x3
⟶
x17
x12
x4
⟶
x17
x12
x5
⟶
x17
x12
x6
⟶
x17
x12
x7
⟶
x17
x12
x8
⟶
x17
x12
x9
⟶
x17
x12
x10
⟶
x17
x12
x11
⟶
x17
x12
x12
⟶
x17
x12
x13
⟶
x17
x12
x14
⟶
x17
x12
x15
⟶
x17
x12
x16
⟶
x17
x13
x3
⟶
x17
x13
x4
⟶
x17
x13
x5
⟶
x17
x13
x6
⟶
x17
x13
x7
⟶
x17
x13
x8
⟶
x17
x13
x9
⟶
x17
x13
x10
⟶
x17
x13
x11
⟶
x17
x13
x12
⟶
x17
x13
x13
⟶
x17
x13
x14
⟶
x17
x13
x15
⟶
x17
x13
x16
⟶
x17
x14
x3
⟶
x17
x14
x4
⟶
x17
x14
x5
⟶
x17
x14
x6
⟶
x17
x14
x7
⟶
x17
x14
x8
⟶
x17
x14
x9
⟶
x17
x14
x10
⟶
x17
x14
x11
⟶
x17
x14
x12
⟶
x17
x14
x13
⟶
x17
x14
x14
⟶
x17
x14
x15
⟶
x17
x14
x16
⟶
x17
x15
x3
⟶
x17
x15
x4
⟶
x17
x15
x5
⟶
x17
x15
x6
⟶
x17
x15
x7
⟶
x17
x15
x8
⟶
x17
x15
x9
⟶
x17
x15
x10
⟶
x17
x15
x11
⟶
x17
x15
x12
⟶
x17
x15
x13
⟶
x17
x15
x14
⟶
x17
x15
x15
⟶
x17
x15
x16
⟶
x17
x16
x3
⟶
x17
x16
x4
⟶
x17
x16
x5
⟶
x17
x16
x6
⟶
x17
x16
x7
⟶
x17
x16
x8
⟶
x17
x16
x9
⟶
x17
x16
x10
⟶
x17
x16
x11
⟶
x17
x16
x12
⟶
x17
x16
x13
⟶
x17
x16
x14
⟶
x17
x16
x15
⟶
x17
x16
x16
⟶
x1
(
λ x18 .
x1
(
x17
x18
)
)
)
⟶
(
∀ x17 :
ι →
ι → ο
.
x17
x3
x4
⟶
x17
x3
x5
⟶
x17
x4
x5
⟶
x17
x3
x6
⟶
x17
x4
x6
⟶
x17
x5
x6
⟶
x17
x3
x7
⟶
x17
x4
x7
⟶
x17
x5
x7
⟶
x17
x6
x7
⟶
x17
x3
x8
⟶
x17
x4
x8
⟶
x17
x5
x8
⟶
x17
x6
x8
⟶
x17
x7
x8
⟶
x17
x3
x9
⟶
x17
x4
x9
⟶
x17
x5
x9
⟶
x17
x6
x9
⟶
x17
x7
x9
⟶
x17
x8
x9
⟶
x17
x3
x10
⟶
x17
x4
x10
⟶
x17
x5
x10
⟶
x17
x6
x10
⟶
x17
x7
x10
⟶
x17
x8
x10
⟶
x17
x9
x10
⟶
x17
x3
x11
⟶
x17
x4
x11
⟶
x17
x5
x11
⟶
x17
x6
x11
⟶
x17
x7
x11
⟶
x17
x8
x11
⟶
x17
x9
x11
⟶
x17
x10
x11
⟶
x17
x3
x12
⟶
x17
x4
x12
⟶
x17
x5
x12
⟶
x17
x6
x12
⟶
x17
x7
x12
⟶
x17
x8
x12
⟶
x17
x9
x12
⟶
x17
x10
x12
⟶
x17
x11
x12
⟶
x17
x3
x13
⟶
x17
x4
x13
⟶
x17
x5
x13
⟶
x17
x6
x13
⟶
x17
x7
x13
⟶
x17
x8
x13
⟶
x17
x9
x13
⟶
x17
x10
x13
⟶
x17
x11
x13
⟶
x17
x12
x13
⟶
x17
x3
x14
⟶
x17
x4
x14
⟶
x17
x5
x14
⟶
x17
x6
x14
⟶
x17
x7
x14
⟶
x17
x8
x14
⟶
x17
x9
x14
⟶
x17
x10
x14
⟶
x17
x11
x14
⟶
x17
x12
x14
⟶
x17
x13
x14
⟶
x17
x3
x15
⟶
x17
x4
x15
⟶
x17
x5
x15
⟶
x17
x6
x15
⟶
x17
x7
x15
⟶
x17
x8
x15
⟶
x17
x9
x15
⟶
x17
x10
x15
⟶
x17
x11
x15
⟶
x17
x12
x15
⟶
x17
x13
x15
⟶
x17
x14
x15
⟶
x17
x3
x16
⟶
x17
x4
x16
⟶
x17
x5
x16
⟶
x17
x6
x16
⟶
x17
x7
x16
⟶
x17
x8
x16
⟶
x17
x9
x16
⟶
x17
x10
x16
⟶
x17
x11
x16
⟶
x17
x12
x16
⟶
x17
x13
x16
⟶
x17
x14
x16
⟶
x17
x15
x16
⟶
x2
x17
)
⟶
∀ x17 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
∀ x18 :
ι →
ι → ι
.
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x3
=
x19
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x4
=
x20
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x5
=
x21
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x6
=
x22
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x7
=
x23
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x8
=
x24
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x9
=
x25
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x10
=
x26
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x11
=
x27
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x12
=
x28
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x13
=
x29
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x14
=
x30
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x15
=
x31
)
⟶
(
∀ x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 .
x18
(
x17
x19
x20
x21
x22
x23
x24
x25
x26
x27
x28
x29
x30
x31
x32
)
x16
=
x32
)
⟶
∀ x19 : ο .
(
∀ x20 :
ι →
ι → ι
.
(
∀ x21 : ο .
(
∀ x22 :
ι →
ι → ι
.
and
(
f3993..
x0
x1
x2
x3
x20
x22
)
(
∀ x23 : ο .
(
∀ x24 .
(
∀ x25 : ο .
(
∀ x26 .
(
∀ x27 : ο .
(
∀ x28 .
(
∀ x29 : ο .
(
∀ x30 .
(
∀ x31 : ο .
(
∀ x32 .
and
(
and
(
and
(
and
(
and
(
and
(
x0
x24
)
(
x0
x26
)
)
(
x0
x28
)
)
(
x0
x30
)
)
(
x0
x32
)
)
(
and
(
and
(
and
(
and
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x20
x24
(
x22
x3
x28
)
)
(
x22
x3
x30
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x22
x3
x32
)
x28
(
x20
x24
(
x22
x3
x28
)
)
)
=
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x22
x3
x32
)
x28
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x20
x24
(
x22
x3
x28
)
)
(
x22
x3
x30
)
(
x20
x24
(
x22
x3
x28
)
)
)
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x32
x24
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x28
(
x22
x3
x32
)
x28
)
=
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x28
(
x22
x3
x32
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x32
x24
x28
)
)
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x20
x24
(
x22
x3
x28
)
)
(
x20
x24
(
x22
x3
x28
)
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x22
x24
x26
)
x26
x26
)
=
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x22
x24
x26
)
x26
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x20
x24
(
x22
x3
x28
)
)
(
x20
x24
(
x22
x3
x28
)
)
x26
)
)
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x24
x32
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x22
x24
x26
)
(
x20
x24
(
x22
x3
x28
)
)
(
x22
x3
x32
)
)
=
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
(
x22
x24
x26
)
(
x20
x24
(
x22
x3
x28
)
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x24
x32
(
x22
x3
x32
)
)
)
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x32
(
x22
x3
x32
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x32
(
x22
x3
x30
)
x26
)
=
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x32
(
x22
x3
x30
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x32
(
x22
x3
x32
)
x26
)
)
)
)
(
and
(
x20
x30
(
x20
(
x20
(
x22
x3
x28
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x24
x26
x28
)
)
x32
)
=
x4
)
(
x20
(
x20
x30
(
x20
(
x22
x3
x28
)
(
2e6fa..
x0
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x20
x22
x24
x26
x28
)
)
)
x32
=
x5
)
)
⟶
x31
)
⟶
x31
)
⟶
x29
)
⟶
x29
)
⟶
x27
)
⟶
x27
)
⟶
x25
)
⟶
x25
)
⟶
x23
)
⟶
x23
)
⟶
x21
)
⟶
x21
)
⟶
x19
)
⟶
x19
(proof)