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Proofgold Asset
asset id
fb65bb87df0c57b7200e1957f60c7c9267f1663a40254c9ccc5fc9c245e7e3f5
asset hash
ed364648a423371263dffe56baaefe618c39f204b649b5e55b9c6b2941fd3f8c
bday / block
35128
tx
9121f..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
71e57..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ο
.
∀ x2 :
ι →
ι → ι
.
∀ x3 x4 .
∀ x5 :
ι →
ι → ι
.
∀ x6 .
∀ x7 :
ι →
ι →
ι → ι
.
∀ x8 :
ι →
ι → ι
.
∀ x9 x10 .
∀ x11 :
ι →
ι → ι
.
∀ x12 :
ι → ο
.
∀ x13 .
∀ x14 :
ι → ο
.
∀ x15 .
∀ x16 :
ι → ο
.
∀ x17 .
∀ x18 :
ι → ο
.
∀ x19 .
∀ x20 :
ι → ι
.
∀ x21 :
ι →
ι → ο
.
∀ x22 .
∀ x23 :
ι → ο
.
∀ x24 x25 x26 x27 .
∀ x28 :
ι → ο
.
∀ x29 x30 x31 .
∀ x32 :
ι → ι
.
∀ x33 .
∀ x34 :
ι → ι
.
∀ x35 x36 x37 x38 x39 :
ι → ο
.
∀ x40 .
∀ x41 x42 x43 :
ι → ο
.
∀ x44 :
ι →
ι → ι
.
∀ x45 :
ι → ο
.
∀ x46 x47 x48 x49 .
∀ x50 :
ι → ο
.
∀ x51 .
∀ x52 :
ι → ο
.
∀ x53 :
ι → ι
.
∀ x54 .
∀ x55 :
ι → ο
.
∀ x56 :
ι → ι
.
∀ x57 x58 .
∀ x59 :
ι → ο
.
∀ x60 :
ι →
ι →
ι → ο
.
∀ x61 .
∀ x62 :
ι →
ι → ι
.
∀ x63 x64 :
ι → ι
.
∀ x65 :
ι →
ι → ι
.
∀ x66 x67 :
ι →
ι → ο
.
∀ x68 :
ι → ι
.
∀ x69 .
∀ x70 :
ι → ο
.
(
∀ x71 x72 .
x70
x72
⟶
(
x72
=
x71
⟶
False
)
⟶
x70
x71
⟶
False
)
⟶
(
∀ x71 x72 .
x0
x71
x72
⟶
x70
x72
⟶
False
)
⟶
(
∀ x71 .
x70
x71
⟶
(
x71
=
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x71 .
x1
x71
⟶
(
x2
x71
x3
=
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x0
x71
x72
⟶
x67
x72
(
x68
x73
)
⟶
x70
x73
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x0
x72
x73
⟶
x67
x73
(
x68
x71
)
⟶
(
x67
x72
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x66
x72
x71
⟶
(
x67
x72
(
x68
x71
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x67
x72
(
x68
x71
)
⟶
(
x66
x72
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 .
x1
x71
⟶
(
x65
x3
x71
=
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x67
x73
x4
⟶
x67
x71
x4
⟶
x67
x72
x4
⟶
(
x5
(
x7
x73
x71
x72
)
(
x7
x73
x71
(
x5
x72
x6
)
)
=
x8
x9
(
x7
x73
x71
(
x5
x72
x9
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 .
x67
x71
x4
⟶
(
x7
x9
x3
x71
=
x64
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x67
x71
x72
⟶
(
x70
x72
⟶
False
)
⟶
(
x0
x71
x72
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x0
x72
x71
⟶
(
x67
x72
x71
⟶
False
)
⟶
False
)
⟶
(
(
x67
x69
x10
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x1
x72
⟶
x1
x71
⟶
(
x62
(
x63
x72
)
(
x63
x71
)
=
x62
x71
x72
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 .
x1
x72
⟶
x1
x71
⟶
(
x11
(
x63
x72
)
(
x63
x71
)
=
x63
(
x11
x72
x71
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x1
x73
⟶
x1
x71
⟶
x1
x72
⟶
(
x65
(
x65
x73
x71
)
x72
=
x65
x73
(
x65
x71
x72
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x1
x73
⟶
x1
x71
⟶
x1
x72
⟶
(
x11
(
x11
x73
x71
)
x72
=
x11
x73
(
x11
x71
x72
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x1
x73
⟶
x1
x71
⟶
x1
x72
⟶
(
x65
(
x11
x73
x71
)
x72
=
x11
(
x65
x73
x72
)
(
x65
x71
x72
)
⟶
False
)
⟶
False
)
⟶
(
∀ x71 x72 x73 .
x1
x73
⟶
x1
x71
⟶
x1
x72
⟶
(
x65
x73
(
x2
x71
x72
)
=
x2
(
x65
x73
x71
)
x72
⟶
False
)
⟶
False
)
⟶
(
(
x67
x6
x61
⟶
False
)
⟶
False
)
⟶
(
(
x67
x6
x4
⟶
False
)
⟶
False
)
⟶
(
(
x60
x6
x61
x4
⟶
False
)
⟶
False
)
⟶
(
(
x12
x6
⟶
False
)
⟶
False
)
⟶
(
x70
x6
⟶
False
)
⟶
(
(
x67
x9
x61
⟶
False
)
⟶
False
)
⟶
(
(
x67
x9
x4
⟶
False
)
⟶
False
)
⟶
(
(
x60
x9
x61
x4
⟶
False
)
⟶
False
)
⟶
(
(
x12
x9
⟶
False
)
⟶
False
)
⟶
(
x70
x9
⟶
False
)
⟶
(
∀ x71 .
x1
x71
⟶
(
x65
x71
(
x63
x3
)
=
x63
x71
⟶
False
)
⟶
False
)
⟶
(
(
x67
x3
x61
⟶
False
)
⟶
False
)
⟶
(
(
x67
x3
x4
⟶
False
)
⟶
False
)
⟶
(
(
x60
x3
x61
x4
⟶
False
)
⟶
False
)
⟶
(
(
x12
x3
⟶
False
)
⟶
False
)
⟶
(
x70
x3
⟶
False
)
⟶
(
∀ x71 x72 .
x1
x72
⟶
x1
x71
⟶
(
x11
x72
(
x63
x71
)
=
x62
x72
x71
⟶
False
)
⟶
False
)
⟶
(
(
x67
x13
x61
⟶
False
)
⟶
False
)
⟶
(
(
x67
x13
x4
⟶
False
)
⟶
False
)
⟶
(
(
x60
x13
x61
x4
⟶
False
)
⟶
False
)
⟶
(
(
x70
x13
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x2
(
x63
x6
)
x9
)
=
x2
x6
x9
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x2
(
x63
x9
)
x6
)
=
x2
x9
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x2
(
x63
x3
)
x6
)
=
x2
x3
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x2
(
x63
x3
)
x9
)
=
x2
x3
x9
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x2
x6
x9
)
=
x2
(
x63
x6
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x2
x9
x6
)
=
x2
(
x63
x9
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x2
x3
x6
)
=
x2
(
x63
x3
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x2
x3
x9
)
=
x2
(
x63
x3
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x63
x6
)
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x63
x9
)
=
x9
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x63
x3
)
=
x3
⟶
False
)
⟶
False
)
⟶
(
(
x63
x6
=
x63
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
x9
=
x63
x9
⟶
False
)
⟶
False
)
⟶
(
(
x63
x3
=
x63
x3
⟶
False
)
⟶
False
)
⟶
(
(
x63
x13
=
x13
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x6
)
x9
)
(
x2
(
x63
x9
)
x6
)
=
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x6
)
x9
)
(
x2
(
x63
x3
)
x6
)
=
x2
x3
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x6
)
x9
)
(
x2
x9
x6
)
=
x63
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x6
)
x9
)
(
x2
x3
x6
)
=
x2
(
x63
x3
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x6
)
x9
)
(
x63
x9
)
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x6
)
x9
)
x9
=
x63
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x6
)
x9
)
x3
=
x2
(
x63
x6
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x9
)
x6
)
(
x2
(
x63
x6
)
x9
)
=
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x9
)
x6
)
(
x2
(
x63
x3
)
x9
)
=
x2
x3
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x9
)
x6
)
(
x2
x6
x9
)
=
x63
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x9
)
x6
)
(
x2
x3
x9
)
=
x2
(
x63
x3
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x9
)
x6
)
(
x63
x6
)
=
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x9
)
x6
)
x6
=
x63
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x9
)
x6
)
x3
=
x2
(
x63
x9
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x6
)
(
x2
(
x63
x6
)
x9
)
=
x2
x3
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x6
)
(
x2
x6
x9
)
=
x2
(
x63
x3
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x6
)
(
x63
x6
)
=
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x6
)
(
x63
x9
)
=
x2
x9
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x6
)
x6
=
x63
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x6
)
x9
=
x2
(
x63
x9
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x6
)
x3
=
x2
(
x63
x3
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x9
)
(
x2
x9
x6
)
=
x2
(
x63
x3
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x9
)
(
x63
x6
)
=
x2
x6
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x9
)
(
x63
x9
)
=
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x9
)
x6
=
x2
(
x63
x6
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x9
)
x9
=
x63
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
(
x63
x3
)
x9
)
x3
=
x2
(
x63
x3
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
x6
x9
)
(
x2
(
x63
x9
)
x6
)
=
x63
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
x6
x9
)
(
x2
(
x63
x3
)
x6
)
=
x2
(
x63
x3
)
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
x6
x9
)
(
x2
x9
x6
)
=
x3
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
x6
x9
)
(
x2
x3
x6
)
=
x2
x3
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
x6
x9
)
(
x63
x9
)
=
x63
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
x6
x9
)
x9
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
x6
x9
)
x3
=
x2
x6
x9
⟶
False
)
⟶
False
)
⟶
(
(
x65
(
x2
x9
x6
)
(
x2
(
x63
x6
)
x9
)
=
x63
x3
⟶
False
)
⟶
False
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