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Proofgold Asset
asset id
249f8782ea8e840bd497468aebc7ae01f4c2c70c2b88b0e52b803da934dd1d30
asset hash
77d65ae965f7f97987638458c81c1e1ee2c51721a258fdd651dc708d4aa4ea45
bday / block
35144
tx
b386a..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
939ca..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 x2 :
ι →
ι → ι
.
∀ x3 x4 x5 .
∀ x6 x7 x8 x9 :
ι → ι
.
∀ x10 x11 x12 x13 :
ι →
ι → ι
.
∀ x14 x15 .
∀ x16 :
ι → ο
.
∀ x17 x18 :
ι →
ι →
ι → ι
.
∀ x19 .
∀ x20 :
ι →
ι → ι
.
∀ x21 :
ι → ι
.
∀ x22 .
∀ x23 :
ι → ο
.
∀ x24 .
∀ x25 :
ι → ο
.
∀ x26 x27 .
∀ x28 :
ι → ο
.
∀ x29 :
ι →
ι → ο
.
∀ x30 :
ι → ο
.
(
∀ x31 x32 .
x30
x32
⟶
(
x32
=
x31
⟶
False
)
⟶
x30
x31
⟶
False
)
⟶
(
∀ x31 x32 x33 x34 .
x0
x33
x34
⟶
x0
x32
x31
⟶
(
x0
(
x2
x33
x32
)
(
x1
x34
x31
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 x33 x34 .
x0
(
x2
x32
x34
)
(
x1
x31
x33
)
⟶
(
x0
x34
x33
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 x33 x34 .
x0
(
x2
x34
x32
)
(
x1
x33
x31
)
⟶
(
x0
x34
x33
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
x0
x31
x32
⟶
x30
x32
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
(
x31
=
x3
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
x29
x31
x32
⟶
(
x30
x32
⟶
False
)
⟶
(
x0
x31
x32
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
x0
x32
x31
⟶
(
x29
x32
x31
⟶
False
)
⟶
False
)
⟶
(
x28
x27
⟶
False
)
⟶
(
x30
x4
⟶
False
)
⟶
(
(
x28
x26
⟶
False
)
⟶
False
)
⟶
(
x30
x26
⟶
False
)
⟶
(
(
x25
x24
⟶
False
)
⟶
False
)
⟶
(
(
x30
x5
⟶
False
)
⟶
False
)
⟶
(
(
x23
x22
⟶
False
)
⟶
False
)
⟶
(
x30
x22
⟶
False
)
⟶
(
∀ x31 .
(
x30
x31
⟶
False
)
⟶
x23
x31
⟶
x30
(
x21
x31
)
⟶
False
)
⟶
(
∀ x31 .
(
x30
x31
⟶
False
)
⟶
x23
x31
⟶
x30
(
x6
x31
)
⟶
False
)
⟶
(
∀ x31 x32 x33 x34 .
(
x23
(
x20
(
x2
x32
x31
)
(
x2
x34
x33
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
(
x23
(
x1
x31
x32
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
(
x30
(
x21
x31
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
(
x23
(
x7
(
x2
x32
x31
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
x30
x32
⟶
(
x30
(
x1
x32
x31
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
(
x30
(
x6
x31
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
x30
x32
⟶
(
x30
(
x1
x31
x32
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
x30
(
x20
x31
x32
)
⟶
False
)
⟶
(
∀ x31 .
(
x28
(
x7
x31
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
x30
(
x7
x31
)
⟶
False
)
⟶
(
∀ x31 x32 .
x30
(
x2
x31
x32
)
⟶
False
)
⟶
(
∀ x31 x32 .
(
x25
(
x2
x31
x32
)
⟶
False
)
⟶
False
)
⟶
(
(
x30
x3
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
(
x30
(
x21
x31
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
(
x30
(
x6
x31
)
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
(
x29
(
x8
x31
)
x31
⟶
False
)
⟶
False
)
⟶
(
(
x30
x19
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
(
x2
x32
x31
=
x20
(
x20
x32
x31
)
(
x7
x32
)
⟶
False
)
⟶
False
)
⟶
(
(
x3
=
x19
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
(
x0
(
x9
x31
)
x31
⟶
False
)
⟶
(
x30
x31
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
x30
x32
⟶
x0
x31
x32
⟶
False
)
⟶
(
∀ x31 x32 .
(
x0
(
x2
(
x11
x32
x31
)
(
x10
x32
x31
)
)
x31
⟶
False
)
⟶
(
x0
(
x10
x32
x31
)
x32
⟶
False
)
⟶
(
x32
=
x21
x31
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 x33 .
x0
(
x10
x33
x32
)
x33
⟶
x0
(
x2
x31
(
x10
x33
x32
)
)
x32
⟶
(
x33
=
x21
x32
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 x33 x34 .
x33
=
x21
x34
⟶
x0
(
x2
x32
x31
)
x34
⟶
(
x0
x31
x33
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 x33 .
x32
=
x21
x33
⟶
x0
x31
x32
⟶
(
x0
(
x2
(
x18
x31
x32
x33
)
x31
)
x33
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
(
x0
(
x2
(
x12
x32
x31
)
(
x13
x32
x31
)
)
x31
⟶
False
)
⟶
(
x0
(
x12
x32
x31
)
x32
⟶
False
)
⟶
(
x32
=
x6
x31
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 x33 .
x0
(
x12
x33
x32
)
x33
⟶
x0
(
x2
(
x12
x33
x32
)
x31
)
x32
⟶
(
x33
=
x6
x32
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 x33 x34 .
x33
=
x6
x34
⟶
x0
(
x2
x31
x32
)
x34
⟶
(
x0
x31
x33
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 x33 .
x32
=
x6
x33
⟶
x0
x31
x32
⟶
(
x0
(
x2
x31
(
x17
x31
x32
x33
)
)
x33
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
(
x20
x32
x31
=
x20
x31
x32
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
x23
x31
⟶
(
x16
x31
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
x23
x31
⟶
(
x23
x31
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
(
x28
x31
⟶
False
)
⟶
x30
x31
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
(
x28
x31
⟶
False
)
⟶
False
)
⟶
(
∀ x31 .
x30
x31
⟶
(
x23
x31
⟶
False
)
⟶
False
)
⟶
(
∀ x31 x32 .
x0
x31
x32
⟶
x0
x32
x31
⟶
False
)
⟶
(
x6
(
x1
x15
x14
)
=
x15
⟶
x21
(
x1
x15
x14
)
=
x14
⟶
False
)
⟶
(
x14
=
x3
⟶
False
)
⟶
(
x15
=
x3
⟶
False
)
⟶
False
(proof)