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Proofgold Asset
asset id
90e0d13c9cc484ac48fe356af938499d27a5206b9ff830013f6b45b1b1c9c285
asset hash
6b2dd26d0e34c65cb4e5e53d2c9bbf3ceab8509d13cfc5d2c492c7176d7fe6a1
bday / block
35122
tx
a35aa..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
44fca..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 x3 :
ι →
ι → ο
.
∀ x4 :
ι → ι
.
∀ x5 :
ι → ο
.
∀ x6 x7 x8 :
ι →
ι → ι
.
∀ x9 :
ι →
ι →
ι → ι
.
∀ x10 :
ι →
ι → ο
.
∀ x11 :
ι → ο
.
∀ x12 .
∀ x13 :
ι →
ι → ο
.
∀ x14 x15 x16 x17 :
ι → ι
.
∀ x18 :
ι →
ι → ο
.
∀ x19 :
ι → ι
.
∀ x20 :
ι → ο
.
∀ x21 x22 :
ι → ι
.
∀ x23 .
∀ x24 :
ι → ι
.
∀ x25 :
ι →
ι → ο
.
∀ x26 :
ι → ο
.
∀ x27 x28 :
ι → ι
.
∀ x29 :
ι →
ι → ο
.
∀ x30 :
ι → ι
.
∀ x31 x32 .
∀ x33 :
ι → ι
.
∀ x34 x35 x36 x37 x38 .
∀ x39 x40 :
ι → ο
.
∀ x41 x42 .
∀ x43 :
ι → ο
.
∀ x44 :
ι →
ι → ο
.
∀ x45 x46 x47 x48 :
ι → ι
.
∀ x49 :
ι → ο
.
∀ x50 :
ι → ι
.
∀ x51 x52 :
ι → ο
.
∀ x53 .
∀ x54 :
ι → ο
.
∀ x55 :
ι →
ι → ο
.
∀ x56 x57 :
ι → ι
.
∀ x58 :
ι →
ι → ι
.
∀ x59 x60 :
ι → ο
.
∀ x61 .
∀ x62 :
ι → ο
.
(
∀ x63 x64 .
x62
x64
⟶
(
x64
=
x63
⟶
False
)
⟶
x62
x63
⟶
False
)
⟶
(
∀ x63 x64 .
x0
x63
x64
⟶
x62
x64
⟶
False
)
⟶
(
∀ x63 .
x62
x63
⟶
(
x63
=
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 x65 .
x0
x63
x64
⟶
x2
x64
(
x1
x65
)
⟶
x62
x65
⟶
False
)
⟶
(
∀ x63 x64 x65 .
x0
x64
x65
⟶
x2
x65
(
x1
x63
)
⟶
(
x2
x64
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x3
x64
x63
⟶
(
x2
x64
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x2
x64
(
x1
x63
)
⟶
(
x3
x64
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x2
x63
x64
⟶
(
x62
x64
⟶
False
)
⟶
(
x0
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x60
x63
⟶
x54
x63
⟶
x55
x63
(
x58
(
x57
x63
)
(
x56
x63
)
)
⟶
(
x59
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x60
x63
⟶
x54
x63
⟶
(
x2
(
x56
x63
)
(
x4
x63
)
⟶
False
)
⟶
(
x59
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x60
x63
⟶
x54
x63
⟶
(
x2
(
x57
x63
)
(
x4
x63
)
⟶
False
)
⟶
(
x59
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 x65 .
x60
x65
⟶
x54
x65
⟶
x59
x65
⟶
x2
x63
(
x4
x65
)
⟶
x2
x64
(
x4
x65
)
⟶
(
x55
x65
(
x58
x63
x64
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x0
x64
x63
⟶
(
x2
x64
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x5
x64
⟶
False
)
⟶
x54
x64
⟶
x2
x63
(
x1
(
x4
x64
)
)
⟶
x0
(
x6
x64
(
x9
(
x4
x64
)
(
x7
x63
x64
)
(
x8
x63
x64
)
)
)
x63
⟶
(
x10
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x5
x64
⟶
False
)
⟶
x54
x64
⟶
x2
x63
(
x1
(
x4
x64
)
)
⟶
(
x55
x64
(
x9
(
x4
x64
)
(
x7
x63
x64
)
(
x8
x63
x64
)
)
⟶
False
)
⟶
(
x10
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x5
x64
⟶
False
)
⟶
x54
x64
⟶
x2
x63
(
x1
(
x4
x64
)
)
⟶
(
x0
(
x8
x63
x64
)
x63
⟶
False
)
⟶
(
x10
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x5
x64
⟶
False
)
⟶
x54
x64
⟶
x2
x63
(
x1
(
x4
x64
)
)
⟶
(
x0
(
x7
x63
x64
)
x63
⟶
False
)
⟶
(
x10
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x5
x64
⟶
False
)
⟶
x54
x64
⟶
x2
x63
(
x1
(
x4
x64
)
)
⟶
(
x2
(
x8
x63
x64
)
(
x4
x64
)
⟶
False
)
⟶
(
x10
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x5
x64
⟶
False
)
⟶
x54
x64
⟶
x2
x63
(
x1
(
x4
x64
)
)
⟶
(
x2
(
x7
x63
x64
)
(
x4
x64
)
⟶
False
)
⟶
(
x10
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 x65 x66 .
(
x5
x66
⟶
False
)
⟶
x54
x66
⟶
x2
x65
(
x1
(
x4
x66
)
)
⟶
x10
x65
x66
⟶
x2
x64
(
x4
x66
)
⟶
x2
x63
(
x4
x66
)
⟶
x0
x64
x65
⟶
x0
x63
x65
⟶
x55
x66
(
x9
(
x4
x66
)
x64
x63
)
⟶
(
x0
(
x6
x66
(
x9
(
x4
x66
)
x64
x63
)
)
x65
⟶
False
)
⟶
False
)
⟶
(
x62
x53
⟶
False
)
⟶
(
∀ x63 .
(
x3
x63
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 x65 .
(
x62
x65
⟶
False
)
⟶
x2
x63
x65
⟶
x2
x64
x65
⟶
(
x9
x65
x63
x64
=
x58
x63
x64
⟶
False
)
⟶
False
)
⟶
(
(
x11
x12
⟶
False
)
⟶
False
)
⟶
(
(
x52
x12
⟶
False
)
⟶
False
)
⟶
(
x62
x12
⟶
False
)
⟶
(
∀ x63 .
(
x51
x63
⟶
False
)
⟶
(
x52
(
x50
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x51
x63
⟶
False
)
⟶
x51
(
x50
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x51
x63
⟶
False
)
⟶
(
x2
(
x50
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x13
(
x14
x63
)
x53
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x2
(
x14
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x51
x63
⟶
False
)
⟶
x51
(
x15
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x51
x63
⟶
False
)
⟶
(
x2
(
x15
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x51
(
x16
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
x62
(
x16
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x2
(
x16
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x49
x63
⟶
(
x13
(
x48
x63
)
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x18
(
x17
x63
)
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x2
(
x17
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x5
x63
⟶
False
)
⟶
x20
x63
⟶
x62
(
x19
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x5
x63
⟶
False
)
⟶
x20
x63
⟶
(
x2
(
x19
x63
)
(
x1
(
x4
x63
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x52
x63
⟶
False
)
⟶
x52
(
x21
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x52
x63
⟶
False
)
⟶
(
x2
(
x21
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x18
(
x22
x63
)
x63
⟶
False
)
⟶
(
∀ x63 .
(
x2
(
x22
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
x52
x23
⟶
False
)
⟶
(
∀ x63 .
(
x62
(
x47
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x2
(
x47
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x52
(
x46
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
x62
(
x46
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x2
(
x46
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x49
x63
⟶
(
x25
(
x24
x63
)
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x49
x63
⟶
(
x20
(
x24
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x26
x63
⟶
False
)
⟶
x20
x63
⟶
x51
(
x27
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x26
x63
⟶
False
)
⟶
x20
x63
⟶
(
x2
(
x27
x63
)
(
x1
(
x4
x63
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x5
x63
⟶
False
)
⟶
x20
x63
⟶
(
x51
(
x28
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x5
x63
⟶
False
)
⟶
x20
x63
⟶
x62
(
x28
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x5
x63
⟶
False
)
⟶
x20
x63
⟶
(
x2
(
x28
x63
)
(
x1
(
x4
x63
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x54
x63
⟶
(
x44
(
x45
x63
)
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x54
x63
⟶
(
x29
(
x45
x63
)
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x54
x63
⟶
(
x2
(
x45
x63
)
(
x1
(
x4
x63
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
x62
(
x30
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
(
x2
(
x30
x63
)
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
(
x52
x31
⟶
False
)
⟶
False
)
⟶
(
x62
x31
⟶
False
)
⟶
(
(
x49
x32
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x43
x63
⟶
False
)
⟶
x20
x63
⟶
x52
(
x4
x63
)
⟶
False
)
⟶
(
∀ x63 .
(
x52
x63
⟶
False
)
⟶
x52
(
x1
x63
)
⟶
False
)
⟶
(
∀ x63 .
x43
x63
⟶
x20
x63
⟶
(
x52
(
x4
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x26
x63
⟶
x20
x63
⟶
(
x51
(
x4
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x26
x63
⟶
False
)
⟶
x20
x63
⟶
x51
(
x4
x63
)
⟶
False
)
⟶
(
∀ x63 x64 .
x52
x64
⟶
x52
x63
⟶
(
x11
(
x58
x64
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x52
x63
⟶
(
x11
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x5
x63
⟶
False
)
⟶
x20
x63
⟶
x62
(
x4
x63
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x52
(
x58
x63
x64
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x62
(
x1
x63
)
⟶
False
)
⟶
(
∀ x63 .
x5
x63
⟶
x20
x63
⟶
(
x62
(
x4
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x49
x64
⟶
x25
x63
x64
⟶
x20
x63
⟶
(
x13
(
x4
x63
)
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x52
x63
⟶
(
x52
(
x1
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x2
(
x33
x63
)
x63
⟶
False
)
⟶
False
)
⟶
(
(
x20
x42
⟶
False
)
⟶
False
)
⟶
(
(
x54
x34
⟶
False
)
⟶
False
)
⟶
(
(
x62
x41
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x54
x63
⟶
(
x20
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 x65 .
(
x62
x65
⟶
False
)
⟶
x2
x63
x65
⟶
x2
x64
x65
⟶
(
x2
(
x9
x65
x63
x64
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x54
x64
⟶
(
x2
(
x6
x64
x63
)
(
x4
x64
)
⟶
False
)
⟶
False
)
⟶
(
(
x61
=
x41
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 x65 .
(
x62
x65
⟶
False
)
⟶
x2
x63
x65
⟶
x2
x64
x65
⟶
(
x9
x65
x63
x64
=
x9
x65
x64
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x58
x64
x63
=
x58
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
x25
x63
x61
⟶
(
x5
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x13
x63
x53
⟶
(
x51
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x13
x63
x53
⟶
x62
x63
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
x5
x63
⟶
(
x25
x63
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x11
x64
⟶
x2
x63
(
x1
x64
)
⟶
(
x11
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x62
x63
⟶
(
x13
x63
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
(
x43
x63
⟶
False
)
⟶
x26
x63
⟶
False
)
⟶
(
∀ x63 x64 .
x11
x64
⟶
x2
x63
x64
⟶
(
x52
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x13
x63
x61
⟶
(
x62
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
x26
x63
⟶
(
x43
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x62
x63
⟶
(
x11
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x40
x63
⟶
x52
x63
⟶
(
x39
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x51
x64
⟶
x2
x63
(
x1
x64
)
⟶
(
x51
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
(
x43
x63
⟶
False
)
⟶
x43
x63
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
(
x43
x63
⟶
False
)
⟶
x5
x63
⟶
False
)
⟶
(
∀ x63 .
(
x52
x63
⟶
False
)
⟶
x51
x63
⟶
False
)
⟶
(
∀ x63 .
x39
x63
⟶
(
x52
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x62
x64
⟶
x2
x63
(
x1
x64
)
⟶
x18
x63
x64
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
x5
x63
⟶
(
x43
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
x5
x63
⟶
(
x5
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x51
x63
⟶
(
x52
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x62
x64
⟶
False
)
⟶
x2
x63
(
x1
x64
)
⟶
x62
x63
⟶
(
x18
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x39
x63
⟶
(
x49
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
(
x62
x64
⟶
False
)
⟶
x2
x63
(
x1
x64
)
⟶
(
x18
x63
x64
⟶
False
)
⟶
x62
x63
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
(
x26
x63
⟶
False
)
⟶
x5
x63
⟶
False
)
⟶
(
∀ x63 x64 .
x52
x64
⟶
x2
x63
(
x1
x64
)
⟶
(
x52
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x62
x63
⟶
(
x49
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x54
x64
⟶
x2
x63
(
x1
(
x4
x64
)
)
⟶
x62
x63
⟶
(
x44
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x54
x64
⟶
x2
x63
(
x1
(
x4
x64
)
)
⟶
x62
x63
⟶
(
x29
x63
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x62
x64
⟶
x2
x63
(
x1
x64
)
⟶
(
x62
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
x5
x63
⟶
(
x26
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x54
x63
⟶
x59
x63
⟶
x5
x63
⟶
False
)
⟶
(
∀ x63 .
x62
x63
⟶
(
x52
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x49
x63
⟶
(
x40
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
(
x26
x63
⟶
False
)
⟶
x5
x63
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
x25
x63
x53
⟶
(
x26
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
x25
x63
x53
⟶
x5
x63
⟶
False
)
⟶
(
∀ x63 .
x20
x63
⟶
(
x5
x63
⟶
False
)
⟶
x26
x63
⟶
(
x25
x63
x53
⟶
False
)
⟶
False
)
⟶
(
∀ x63 .
(
x62
x63
⟶
False
)
⟶
x51
x63
⟶
(
x13
x63
x53
⟶
False
)
⟶
False
)
⟶
(
∀ x63 x64 .
x0
x63
x64
⟶
x0
x64
x63
⟶
False
)
⟶
(
∀ x63 x64 .
x2
x64
(
x4
x35
)
⟶
x2
x63
(
x4
x35
)
⟶
x0
x64
x36
⟶
x0
x63
x36
⟶
(
x0
(
x6
x35
(
x9
(
x4
x35
)
x64
x63
)
)
x36
⟶
False
)
⟶
(
x10
x36
x35
⟶
False
)
⟶
False
)
⟶
(
x10
x36
x35
⟶
x0
(
x6
x35
(
x9
(
x4
x35
)
x37
x38
)
)
x36
⟶
False
)
⟶
(
x10
x36
x35
⟶
(
x0
x38
x36
⟶
False
)
⟶
False
)
⟶
(
x10
x36
x35
⟶
(
x0
x37
x36
⟶
False
)
⟶
False
)
⟶
(
x10
x36
x35
⟶
(
x2
x38
(
x4
x35
)
⟶
False
)
⟶
False
)
⟶
(
x10
x36
x35
⟶
(
x2
x37
(
x4
x35
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x36
(
x1
(
x4
x35
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x54
x35
⟶
False
)
⟶
False
)
⟶
(
(
x59
x35
⟶
False
)
⟶
False
)
⟶
(
(
x60
x35
⟶
False
)
⟶
False
)
⟶
False
(proof)