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Proofgold Asset
asset id
e1ada920faaf9e708c6c451cf37f88374c3f0a216d3fb8383ec56b0d801e4c22
asset hash
cb7349f8b558060de06da6a79fd403e1f69c0c76c96debf818e54b855457a5b2
bday / block
20423
tx
e477e..
preasset
doc published by
Pr4zB..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Known
FalseE
FalseE
:
False
⟶
∀ x0 : ο .
x0
Theorem
41280..
:
∀ x0 x1 :
ι → ο
.
∀ x2 x3 x4 x5 x6 x7 .
(
∀ x8 :
ι → ο
.
x8
x2
⟶
x8
x3
⟶
x8
x4
⟶
x8
x5
⟶
x8
x6
⟶
x8
x7
⟶
∀ x9 .
x0
x9
⟶
x8
x9
)
⟶
x0
x2
⟶
x0
x3
⟶
x0
x4
⟶
x0
x5
⟶
x0
x6
⟶
x0
x7
⟶
x1
x2
⟶
x1
x3
⟶
x1
x4
⟶
x1
x5
⟶
∀ x8 x9 x10 :
ι → ι
.
x8
x2
=
x3
⟶
x8
x3
=
x2
⟶
x8
x4
=
x5
⟶
x8
x5
=
x4
⟶
x9
x2
=
x4
⟶
x9
x3
=
x5
⟶
x9
x4
=
x2
⟶
x9
x5
=
x3
⟶
x10
x2
=
x5
⟶
x10
x3
=
x4
⟶
x10
x4
=
x3
⟶
x10
x5
=
x2
⟶
∀ x11 :
ι →
ι →
ι →
ι → ο
.
(
∀ x12 x13 .
x0
x12
⟶
x0
x13
⟶
not
(
x11
x12
x13
x12
x13
)
)
⟶
(
∀ x12 x13 x14 x15 .
x11
x12
x13
x14
x15
⟶
x11
x14
x15
x12
x13
)
⟶
(
∀ x12 x13 .
x0
x12
⟶
x0
x13
⟶
not
(
x11
x12
x13
x7
x7
)
)
⟶
(
∀ x12 x13 x14 x15 .
x0
x12
⟶
x1
x13
⟶
x0
x14
⟶
x1
x15
⟶
not
(
x11
x12
x13
x14
x15
)
⟶
not
(
x11
x12
(
x8
x13
)
x14
(
x8
x15
)
)
)
⟶
(
∀ x12 x13 x14 x15 .
x0
x12
⟶
x1
x13
⟶
x0
x14
⟶
x1
x15
⟶
not
(
x11
x12
x13
x14
x15
)
⟶
not
(
x11
x12
(
x9
x13
)
x14
(
x9
x15
)
)
)
⟶
(
∀ x12 x13 x14 x15 .
x0
x12
⟶
x1
x13
⟶
x0
x14
⟶
x1
x15
⟶
not
(
x11
x12
x13
x14
x15
)
⟶
not
(
x11
x12
(
x10
x13
)
x14
(
x10
x15
)
)
)
⟶
(
∀ x12 .
x0
x12
⟶
not
(
x11
x4
x7
x5
x12
)
)
⟶
(
∀ x12 .
x0
x12
⟶
not
(
x11
x6
x6
x4
x12
)
)
⟶
not
(
x11
x2
x2
x2
x2
)
⟶
not
(
x11
x2
x2
x2
x3
)
⟶
not
(
x11
x2
x2
x2
x4
)
⟶
not
(
x11
x2
x2
x2
x5
)
⟶
not
(
x11
x2
x2
x2
x6
)
⟶
not
(
x11
x2
x2
x2
x7
)
⟶
not
(
x11
x2
x2
x3
x2
)
⟶
not
(
x11
x2
x2
x3
x3
)
⟶
not
(
x11
x2
x2
x3
x4
)
⟶
not
(
x11
x2
x2
x3
x5
)
⟶
not
(
x11
x2
x2
x3
x6
)
⟶
not
(
x11
x2
x2
x3
x7
)
⟶
not
(
x11
x2
x2
x4
x2
)
⟶
not
(
x11
x2
x2
x4
x3
)
⟶
not
(
x11
x2
x2
x4
x4
)
⟶
not
(
x11
x2
x2
x4
x5
)
⟶
not
(
x11
x2
x2
x4
x6
)
⟶
not
(
x11
x2
x2
x4
x7
)
⟶
not
(
x11
x2
x2
x5
x2
)
⟶
not
(
x11
x2
x2
x5
x3
)
⟶
not
(
x11
x2
x2
x5
x4
)
⟶
not
(
x11
x2
x2
x5
x5
)
⟶
not
(
x11
x2
x2
x5
x6
)
⟶
not
(
x11
x2
x2
x5
x7
)
⟶
not
(
x11
x2
x2
x6
x2
)
⟶
not
(
x11
x2
x2
x6
x3
)
⟶
not
(
x11
x2
x2
x6
x4
)
⟶
not
(
x11
x2
x2
x6
x5
)
⟶
not
(
x11
x2
x2
x6
x6
)
⟶
not
(
x11
x2
x2
x6
x7
)
⟶
not
(
x11
x2
x2
x7
x2
)
⟶
not
(
x11
x2
x2
x7
x3
)
⟶
not
(
x11
x2
x2
x7
x4
)
⟶
not
(
x11
x2
x2
x7
x5
)
⟶
not
(
x11
x2
x2
x7
x6
)
⟶
not
(
x11
x2
x2
x7
x7
)
⟶
not
(
x11
x2
x3
x2
x2
)
⟶
not
(
x11
x2
x3
x2
x3
)
⟶
not
(
x11
x2
x3
x2
x4
)
⟶
not
(
x11
x2
x3
x2
x5
)
⟶
not
(
x11
x2
x3
x2
x6
)
⟶
not
(
x11
x2
x3
x2
x7
)
⟶
not
(
x11
x2
x3
x3
x2
)
⟶
not
(
x11
x2
x3
x3
x3
)
⟶
not
(
x11
x2
x3
x3
x4
)
⟶
not
(
x11
x2
x3
x3
x5
)
⟶
not
(
x11
x2
x3
x3
x6
)
⟶
not
(
x11
x2
x3
x3
x7
)
⟶
not
(
x11
x2
x3
x4
x2
)
⟶
not
(
x11
x2
x3
x4
x3
)
⟶
not
(
x11
x2
x3
x4
x4
)
⟶
not
(
x11
x2
x3
x4
x5
)
⟶
not
(
x11
x2
x3
x4
x6
)
⟶
not
(
x11
x2
x3
x4
x7
)
⟶
not
(
x11
x2
x3
x5
x2
)
⟶
not
(
x11
x2
x3
x5
x3
)
⟶
not
(
x11
x2
x3
x5
x4
)
⟶
not
(
x11
x2
x3
x5
x5
)
⟶
not
(
x11
x2
x3
x5
x6
)
⟶
not
(
x11
x2
x3
x5
x7
)
⟶
not
(
x11
x2
x3
x6
x2
)
⟶
not
(
x11
x2
x3
x6
x3
)
⟶
not
(
x11
x2
x3
x6
x4
)
⟶
not
(
x11
x2
x3
x6
x5
)
⟶
not
(
x11
x2
x3
x6
x6
)
⟶
not
(
x11
x2
x3
x6
x7
)
⟶
not
(
x11
x2
x3
x7
x2
)
⟶
not
(
x11
x2
x3
x7
x3
)
⟶
not
(
x11
x2
x3
x7
x4
)
⟶
not
(
x11
x2
x3
x7
x5
)
⟶
not
(
x11
x2
x3
x7
x6
)
⟶
not
(
x11
x2
x3
x7
x7
)
⟶
not
(
x11
x2
x4
x2
x2
)
⟶
not
(
x11
x2
x4
x2
x3
)
⟶
not
(
x11
x2
x4
x2
x4
)
⟶
not
(
x11
x2
x4
x2
x5
)
⟶
not
(
x11
x2
x4
x2
x6
)
⟶
not
(
x11
x2
x4
x2
x7
)
⟶
not
(
x11
x2
x4
x3
x2
)
⟶
not
(
x11
x2
x4
x3
x3
)
⟶
not
(
x11
x2
x4
x3
x4
)
⟶
not
(
x11
x2
x4
x3
x5
)
⟶
not
(
x11
x2
x4
x3
x6
)
⟶
not
(
x11
x2
x4
x3
x7
)
⟶
not
(
x11
x2
x4
x4
x2
)
⟶
not
(
x11
x2
x4
x4
x3
)
⟶
not
(
x11
x2
x4
x4
x4
)
⟶
not
(
x11
x2
x4
x4
x5
)
⟶
not
(
x11
x2
x4
x4
x6
)
⟶
not
(
x11
x2
x4
x4
x7
)
⟶
not
(
x11
x2
x4
x5
x2
)
⟶
not
(
x11
x2
x4
x5
x3
)
⟶
not
(
x11
x2
x4
x5
x4
)
⟶
not
(
x11
x2
x4
x5
x5
)
⟶
not
(
x11
x2
x4
x5
x6
)
⟶
not
(
x11
x2
x4
x5
x7
)
⟶
not
(
x11
x2
x4
x6
x2
)
⟶
not
(
x11
x2
x4
x6
x3
)
⟶
not
(
x11
x2
x4
x6
x4
)
⟶
not
(
x11
x2
x4
x6
x5
)
⟶
not
(
x11
x2
x4
x6
x6
)
⟶
not
(
x11
x2
x4
x6
x7
)
⟶
not
(
x11
x2
x4
x7
x2
)
⟶
not
(
x11
x2
x4
x7
x3
)
⟶
not
(
x11
x2
x4
x7
x4
)
⟶
not
(
x11
x2
x4
x7
x5
)
⟶
not
(
x11
x2
x4
x7
x6
)
⟶
not
(
x11
x2
x4
x7
x7
)
⟶
not
(
x11
x2
x5
x2
x2
)
⟶
not
(
x11
x2
x5
x2
x3
)
⟶
not
(
x11
x2
x5
x2
x4
)
⟶
not
(
x11
x2
x5
x2
x5
)
⟶
not
(
x11
x2
x5
x2
x6
)
⟶
not
(
x11
x2
x5
x2
x7
)
⟶
not
(
x11
x2
x5
x3
x2
)
⟶
not
(
x11
x2
x5
x3
x3
)
⟶
not
(
x11
x2
x5
x3
x4
)
⟶
not
(
x11
x2
x5
x3
x5
)
⟶
not
(
x11
x2
x5
x3
x6
)
⟶
not
(
x11
x2
x5
x3
x7
)
⟶
not
(
x11
x2
x5
x4
x2
)
⟶
not
(
x11
x2
x5
x4
x3
)
⟶
not
(
x11
x2
x5
x4
x4
)
⟶
not
(
x11
x2
x5
x4
x5
)
⟶
not
(
x11
x2
x5
x4
x6
)
⟶
not
(
x11
x2
x5
x4
x7
)
⟶
not
(
x11
x2
x5
x5
x2
)
⟶
not
(
x11
x2
x5
x5
x3
)
⟶
not
(
x11
x2
x5
x5
x4
)
⟶
not
(
x11
x2
x5
x5
x5
)
⟶
not
(
x11
x2
x5
x5
x6
)
⟶
not
(
x11
x2
x5
x5
x7
)
⟶
not
(
x11
x2
x5
x6
x2
)
⟶
not
(
x11
x2
x5
x6
x3
)
⟶
not
(
x11
x2
x5
x6
x4
)
⟶
not
(
x11
x2
x5
x6
x5
)
⟶
not
(
x11
x2
x5
x6
x6
)
⟶
not
(
x11
x2
x5
x6
x7
)
⟶
not
(
x11
x2
x5
x7
x2
)
⟶
not
(
x11
x2
x5
x7
x3
)
⟶
not
(
x11
x2
x5
x7
x4
)
⟶
not
(
x11
x2
x5
x7
x5
)
⟶
not
(
x11
x2
x5
x7
x6
)
⟶
not
(
x11
x2
x5
x7
x7
)
⟶
not
(
x11
x2
x6
x2
x2
)
⟶
not
(
x11
x2
x6
x2
x3
)
⟶
not
(
x11
x2
x6
x2
x4
)
⟶
not
(
x11
x2
x6
x2
x5
)
⟶
not
(
x11
x2
x6
x2
x6
)
⟶
not
(
x11
x2
x6
x2
x7
)
⟶
not
(
x11
x2
x6
x3
x2
)
⟶
not
(
x11
x2
x6
x3
x3
)
⟶
not
(
x11
x2
x6
x3
x4
)
⟶
not
(
x11
x2
x6
x3
x5
)
⟶
not
(
x11
x2
x6
x3
x6
)
⟶
not
(
x11
x2
x6
x3
x7
)
⟶
not
(
x11
x2
x6
x4
x2
)
⟶
not
(
x11
x2
x6
x4
x3
)
⟶
not
(
x11
x2
x6
x4
x4
)
⟶
not
(
x11
x2
x6
x4
x5
)
⟶
not
(
x11
x2
x6
x4
x6
)
⟶
not
(
x11
x2
x6
x4
x7
)
⟶
not
(
x11
x2
x6
x5
x2
)
⟶
not
(
x11
x2
x6
x5
x3
)
⟶
not
(
x11
x2
x6
x5
x4
)
⟶
not
(
x11
x2
x6
x5
x5
)
⟶
not
(
x11
x2
x6
x5
x6
)
⟶
not
(
x11
x2
x6
x5
x7
)
⟶
not
(
x11
x2
x6
x6
x2
)
⟶
not
(
x11
x2
x6
x6
x3
)
⟶
not
(
x11
x2
x6
x6
x4
)
⟶
not
(
x11
x2
x6
x6
x5
)
⟶
not
(
x11
x2
x6
x6
x6
)
⟶
not
(
x11
x2
x6
x6
x7
)
⟶
not
(
x11
x2
x6
x7
x2
)
⟶
not
(
x11
x2
x6
x7
x3
)
⟶
not
(
x11
x2
x6
x7
x4
)
⟶
not
(
x11
x2
x6
x7
x5
)
⟶
not
(
x11
x2
x6
x7
x6
)
⟶
not
(
x11
x2
x6
x7
x7
)
⟶
not
(
x11
x2
x7
x2
x2
)
⟶
not
(
x11
x2
x7
x2
x3
)
⟶
not
(
x11
x2
x7
x2
x4
)
⟶
not
(
x11
x2
x7
x2
x5
)
⟶
not
(
x11
x2
x7
x2
x6
)
⟶
not
(
x11
x2
x7
x2
x7
)
⟶
not
(
x11
x2
x7
x3
x2
)
⟶
not
(
x11
x2
x7
x3
x3
)
⟶
not
(
x11
x2
x7
x3
x4
)
⟶
not
(
x11
x2
x7
x3
x5
)
⟶
not
(
x11
x2
x7
x3
x6
)
⟶
not
(
x11
x2
x7
x3
x7
)
⟶
not
(
x11
x2
x7
x4
x2
)
⟶
not
(
x11
x2
x7
x4
x3
)
⟶
not
(
x11
x2
x7
x4
x4
)
⟶
not
(
x11
x2
x7
x4
x5
)
⟶
not
(
x11
x2
x7
x4
x6
)
⟶
not
(
x11
x2
x7
x4
x7
)
⟶
not
(
x11
x2
x7
x5
x2
)
⟶
not
(
x11
x2
x7
x5
x3
)
⟶
not
(
x11
x2
x7
x5
x4
)
⟶
not
(
x11
x2
x7
x5
x5
)
⟶
not
(
x11
x2
x7
x5
x6
)
⟶
not
(
x11
x2
x7
x5
x7
)
⟶
not
(
x11
x2
x7
x6
x2
)
⟶
not
(