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Proofgold Asset
asset id
49a2d393e315cb8f1fe65087a97fede259e144c05c3c8a43b378d353649e65ef
asset hash
9d6a0b27fb7c435f51b47eeee882cb8e75ccce13d4cf0b00690bf3ce06ecf649
bday / block
35118
tx
a623f..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
741e5..
:
∀ x0 :
ι → ο
.
∀ x1 :
ι →
ι → ο
.
∀ x2 .
∀ x3 :
ι →
ι → ο
.
∀ x4 .
∀ x5 :
ι → ο
.
∀ x6 .
∀ x7 x8 :
ι →
ι → ι
.
∀ x9 x10 .
∀ x11 :
ι →
ι →
ι → ο
.
∀ x12 :
ι → ο
.
∀ x13 :
ι →
ι → ι
.
∀ x14 x15 x16 :
ι → ι
.
∀ x17 x18 x19 x20 .
∀ x21 :
ι → ο
.
∀ x22 x23 x24 .
∀ x25 :
ι → ο
.
∀ x26 .
∀ x27 :
ι → ο
.
∀ x28 x29 x30 x31 .
∀ x32 :
ι →
ι → ι
.
∀ x33 x34 :
ι → ο
.
∀ x35 .
∀ x36 x37 x38 x39 :
ι → ο
.
∀ x40 :
ι → ι
.
∀ x41 x42 :
ι → ο
.
∀ x43 x44 x45 x46 x47 x48 .
∀ x49 :
ι → ο
.
∀ x50 .
∀ x51 :
ι → ο
.
∀ x52 .
∀ x53 :
ι → ο
.
∀ x54 x55 .
∀ x56 x57 :
ι →
ι → ι
.
∀ x58 x59 :
ι → ι
.
∀ x60 x61 :
ι →
ι → ι
.
∀ x62 .
∀ x63 :
ι →
ι → ι
.
∀ x64 .
∀ x65 :
ι → ο
.
∀ x66 :
ι →
ι → ι
.
∀ x67 :
ι → ο
.
∀ x68 .
∀ x69 :
ι → ι
.
∀ x70 :
ι →
ι → ο
.
∀ x71 :
ι → ι
.
∀ x72 x73 :
ι → ο
.
∀ x74 :
ι →
ι → ο
.
∀ x75 :
ι → ο
.
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
(
x74
x77
x76
⟶
False
)
⟶
(
x73
x76
⟶
False
)
⟶
(
x72
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x0
x77
⟶
(
x77
=
x76
⟶
False
)
⟶
x0
x76
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
(
x74
x77
x76
⟶
False
)
⟶
(
x72
x77
⟶
False
)
⟶
(
x73
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x1
x76
x77
⟶
x0
x77
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
x74
x77
x76
⟶
(
x0
x77
⟶
False
)
⟶
(
x72
x76
⟶
False
)
⟶
(
x73
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x0
x76
⟶
(
x76
=
x2
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 x78 .
x1
x76
x77
⟶
x70
x77
(
x71
x78
)
⟶
x0
x78
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
x74
x77
x76
⟶
(
x0
x76
⟶
False
)
⟶
(
x73
x77
⟶
False
)
⟶
(
x72
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x75
x76
⟶
(
x74
(
x69
x76
)
x68
⟶
False
)
⟶
x74
x68
x76
⟶
False
)
⟶
(
∀ x76 .
x75
x76
⟶
(
x74
x68
x76
⟶
False
)
⟶
x74
(
x69
x76
)
x68
⟶
False
)
⟶
(
∀ x76 x77 x78 .
x1
x77
x78
⟶
x70
x78
(
x71
x76
)
⟶
(
x70
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
x74
x77
x76
⟶
(
x72
x76
⟶
False
)
⟶
x72
x77
⟶
False
)
⟶
(
∀ x76 .
x67
x76
⟶
(
x66
x76
x68
=
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x3
x77
x76
⟶
(
x70
x77
(
x71
x76
)
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x70
x77
(
x71
x76
)
⟶
(
x3
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
x74
x77
x76
⟶
(
x73
x77
⟶
False
)
⟶
x73
x76
⟶
False
)
⟶
(
∀ x76 .
x65
x76
⟶
x74
x68
x76
⟶
(
x1
x76
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x70
x76
x77
⟶
(
x0
x77
⟶
False
)
⟶
(
x1
x76
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
x74
x77
x76
⟶
x73
x76
⟶
(
x73
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x1
x77
x76
⟶
(
x70
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
x74
x77
x76
⟶
x72
x77
⟶
(
x72
x76
⟶
False
)
⟶
False
)
⟶
(
(
x70
x2
x4
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x67
x76
⟶
(
x63
x76
x68
=
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x5
x77
⟶
x5
x76
⟶
x74
x77
x76
⟶
x74
(
x7
x76
x6
)
x77
⟶
False
)
⟶
(
∀ x76 x77 .
x5
x77
⟶
x5
x76
⟶
(
x74
(
x7
x76
x6
)
x77
⟶
False
)
⟶
(
x74
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x5
x76
⟶
x74
x6
x76
⟶
(
x8
x68
x76
=
x68
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x67
x77
⟶
x67
x76
⟶
(
x66
(
x69
x77
)
(
x69
x76
)
=
x66
x76
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x67
x77
⟶
x67
x76
⟶
(
x63
(
x69
x77
)
(
x69
x76
)
=
x69
(
x63
x77
x76
)
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 x78 .
x67
x78
⟶
x67
x76
⟶
x67
x77
⟶
(
x63
(
x63
x78
x76
)
x77
=
x63
x78
(
x63
x76
x77
)
⟶
False
)
⟶
False
)
⟶
(
(
x70
x10
x9
⟶
False
)
⟶
False
)
⟶
(
(
x70
x10
x64
⟶
False
)
⟶
False
)
⟶
(
(
x11
x10
x9
x64
⟶
False
)
⟶
False
)
⟶
(
(
x72
x10
⟶
False
)
⟶
False
)
⟶
(
x0
x10
⟶
False
)
⟶
(
(
x70
x6
x9
⟶
False
)
⟶
False
)
⟶
(
(
x70
x6
x64
⟶
False
)
⟶
False
)
⟶
(
(
x11
x6
x9
x64
⟶
False
)
⟶
False
)
⟶
(
(
x72
x6
⟶
False
)
⟶
False
)
⟶
(
x0
x6
⟶
False
)
⟶
(
∀ x76 x77 .
x67
x77
⟶
x67
x76
⟶
(
x63
x77
(
x69
x76
)
=
x66
x77
x76
⟶
False
)
⟶
False
)
⟶
(
(
x70
x62
x9
⟶
False
)
⟶
False
)
⟶
(
(
x70
x62
x64
⟶
False
)
⟶
False
)
⟶
(
(
x11
x62
x9
x64
⟶
False
)
⟶
False
)
⟶
(
(
x0
x62
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x69
x10
)
=
x10
⟶
False
)
⟶
False
)
⟶
(
(
x69
(
x69
x6
)
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x69
x10
=
x69
x10
⟶
False
)
⟶
False
)
⟶
(
(
x69
x6
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x69
x62
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x66
(
x69
x10
)
(
x69
x10
)
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x66
(
x69
x10
)
(
x69
x6
)
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x66
(
x69
x10
)
x62
=
x69
x10
⟶
False
)
⟶
False
)
⟶
(
(
x66
(
x69
x6
)
(
x69
x10
)
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x66
(
x69
x6
)
(
x69
x6
)
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x66
(
x69
x6
)
x6
=
x69
x10
⟶
False
)
⟶
False
)
⟶
(
(
x66
(
x69
x6
)
x62
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x66
x10
x10
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x66
x10
x6
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x66
x10
x62
=
x10
⟶
False
)
⟶
False
)
⟶
(
(
x66
x6
(
x69
x6
)
=
x10
⟶
False
)
⟶
False
)
⟶
(
(
x66
x6
x10
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x66
x6
x6
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x66
x6
x62
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x66
x62
(
x69
x10
)
=
x10
⟶
False
)
⟶
False
)
⟶
(
(
x66
x62
(
x69
x6
)
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x66
x62
x10
=
x69
x10
⟶
False
)
⟶
False
)
⟶
(
(
x66
x62
x6
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x66
x62
x62
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x69
x10
)
x10
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x69
x10
)
x6
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x69
x6
)
(
x69
x6
)
=
x69
x10
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x69
x6
)
x10
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x69
x6
)
x6
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x63
(
x69
x6
)
x62
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
x10
(
x69
x10
)
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x63
x10
(
x69
x6
)
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
x10
x62
=
x10
⟶
False
)
⟶
False
)
⟶
(
(
x63
x6
(
x69
x10
)
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
x6
(
x69
x6
)
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x63
x6
x6
=
x10
⟶
False
)
⟶
False
)
⟶
(
(
x63
x6
x62
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
x62
(
x69
x10
)
=
x69
x10
⟶
False
)
⟶
False
)
⟶
(
(
x63
x62
(
x69
x6
)
=
x69
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
x62
x10
=
x10
⟶
False
)
⟶
False
)
⟶
(
(
x63
x62
x6
=
x6
⟶
False
)
⟶
False
)
⟶
(
(
x63
x62
x62
=
x62
⟶
False
)
⟶
False
)
⟶
(
(
x74
(
x69
x10
)
(
x69
x10
)
⟶
False
)
⟶
False
)
⟶
(
(
x74
(
x69
x10
)
(
x69
x6
)
⟶
False
)
⟶
False
)
⟶
(
(
x74
(
x69
x10
)
x10
⟶
False
)
⟶
False
)
⟶
(
(
x74
(
x69
x10
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x74
(
x69
x10
)
x62
⟶
False
)
⟶
False
)
⟶
(
x74
(
x69
x6
)
(
x69
x10
)
⟶
False
)
⟶
(
(
x74
(
x69
x6
)
(
x69
x6
)
⟶
False
)
⟶
False
)
⟶
(
(
x74
(
x69
x6
)
x10
⟶
False
)
⟶
False
)
⟶
(
(
x74
(
x69
x6
)
x6
⟶
False
)
⟶
False
)
⟶
(
(
x74
(
x69
x6
)
x62
⟶
False
)
⟶
False
)
⟶
(
x74
x10
(
x69
x10
)
⟶
False
)
⟶
(
x74
x10
(
x69
x6
)
⟶
False
)
⟶
(
(
x74
x10
x10
⟶
False
)
⟶
False
)
⟶
(
x74
x10
x6
⟶
False
)
⟶
(
x74
x10
x62
⟶
False
)
⟶
(
x74
x6
(
x69
x10
)
⟶
False
)
⟶
(
x74
x6
(
x69
x6
)
⟶
False
)
⟶
(
(
x74
x6
x10
⟶
False
)
⟶
False
)
⟶
(
(
x74
x6
x6
⟶
False
)
⟶
False
)
⟶
(
x74
x6
x62
⟶
False
)
⟶
(
x74
x62
(
x69
x10
)
⟶
False
)
⟶
(
x74
x62
(
x69
x6
)
⟶
False
)
⟶
(
(
x74
x62
x10
⟶
False
)
⟶
False
)
⟶
(
(
x74
x62
x6
⟶
False
)
⟶
False
)
⟶
(
(
x74
x62
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x12
x77
⟶
x12
x76
⟶
(
x74
x77
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
(
x3
x76
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 x78 .
(
x0
x78
⟶
False
)
⟶
(
x0
x76
⟶
False
)
⟶
x70
x76
(
x71
x78
)
⟶
x70
x77
x76
⟶
(
x11
x77
x78
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 x78 .
(
x0
x78
⟶
False
)
⟶
(
x0
x76
⟶
False
)
⟶
x70
x76
(
x71
x78
)
⟶
x11
x77
x78
x76
⟶
(
x70
x77
x76
⟶
False
)
⟶
False
)
⟶
(
(
x68
=
x2
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x70
x77
x9
⟶
x65
x76
⟶
(
x61
x77
x76
=
x60
x77
x76
⟶
False
)
⟶
False
)
⟶
(
(
x64
=
x4
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x70
x76
x9
⟶
(
x59
x76
=
x58
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x70
x77
x9
⟶
x5
x76
⟶
(
x8
x77
x76
=
x13
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x70
x77
x64
⟶
x5
x76
⟶
(
x57
x77
x76
=
x63
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x70
x76
x9
⟶
(
x14
x76
=
x69
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x5
x77
⟶
x70
x76
x64
⟶
(
x7
x77
x76
=
x63
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x65
x76
⟶
(
x16
x76
=
x15
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x70
x77
x64
⟶
x70
x76
x64
⟶
(
x56
x77
x76
=
x13
x77
x76
⟶
False
)
⟶
False
)
⟶
(
(
x5
x17
⟶
False
)
⟶
False
)
⟶
(
x0
x17
⟶
False
)
⟶
(
(
x12
x18
⟶
False
)
⟶
False
)
⟶
(
(
x0
x18
⟶
False
)
⟶
False
)
⟶
(
(
x75
x19
⟶
False
)
⟶
False
)
⟶
(
(
x12
x19
⟶
False
)
⟶
False
)
⟶
(
(
x67
x19
⟶
False
)
⟶
False
)
⟶
(
(
x0
x19
⟶
False
)
⟶
False
)
⟶
(
(
x5
x20
⟶
False
)
⟶
False
)
⟶
(
(
x73
x55
⟶
False
)
⟶
False
)
⟶
(
(
x12
x55
⟶
False
)
⟶
False
)
⟶
(
(
x75
x54
⟶
False
)
⟶
False
)
⟶
(
(
x73
x54
⟶
False
)
⟶
False
)
⟶
(
(
x12
x54
⟶
False
)
⟶
False
)
⟶
(
(
x67
x54
⟶
False
)
⟶
False
)
⟶
(
(
x53
x52
⟶
False
)
⟶
False
)
⟶
(
(
x21
x52
⟶
False
)
⟶
False
)
⟶
(
x0
x52
⟶
False
)
⟶
(
(
x72
x22
⟶
False
)
⟶
False
)
⟶
(
(
x12
x22
⟶
False
)
⟶
False
)
⟶
(
(
x75
x23
⟶
False
)
⟶
False
)
⟶
(
(
x72
x23
⟶
False
)
⟶
False
)
⟶
(
(
x12
x23
⟶
False
)
⟶
False
)
⟶
(
(
x67
x23
⟶
False
)
⟶
False
)
⟶
(
x0
x24
⟶
False
)
⟶
(
(
x51
x50
⟶
False
)
⟶
False
)
⟶
(
(
x25
x26
⟶
False
)
⟶
False
)
⟶
(
(
x49
x26
⟶
False
)
⟶
False
)
⟶
(
(
x27
x26
⟶
False
)
⟶
False
)
⟶
(
x0
x26
⟶
False
)
⟶
(
(
x25
x28
⟶
False
)
⟶
False
)
⟶
(
x0
x28
⟶
False
)
⟶
(
(
x70
x28
(
x71
x9
)
⟶
False
)
⟶
False
)
⟶
(
(
x21
x48
⟶
False
)
⟶
False
)
⟶
(
x0
x48
⟶
False
)
⟶
(
(
x65
x47
⟶
False
)
⟶
False
)
⟶
(
(
x12
x29
⟶
False
)
⟶
False
)
⟶
(
(
x75
x46
⟶
False
)
⟶
False
)
⟶
(
(
x0
x30
⟶
False
)
⟶
False
)
⟶
(
(
x51
x45
⟶
False
)
⟶
False
)
⟶
(
(
x75
x45
⟶
False
)
⟶
False
)
⟶
(
(
x67
x45
⟶
False
)
⟶
False
)
⟶
(
(
x12
x45
⟶
False
)
⟶
False
)
⟶
(
(
x70
x45
x9
⟶
False
)
⟶
False
)
⟶
(
(
x25
x31
⟶
False
)
⟶
False
)
⟶
(
(
x21
x44
⟶
False
)
⟶
False
)
⟶
(
x0
x44
⟶
False
)
⟶
(
(
x65
x43
⟶
False
)
⟶
False
)
⟶
(
(
x75
x43
⟶
False
)
⟶
False
)
⟶
(
(
x67
x43
⟶
False
)
⟶
False
)
⟶
(
(
x12
x43
⟶
False
)
⟶
False
)
⟶
(
(
x70
x43
x9
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x65
x76
⟶
(
x16
(
x16
x76
)
=
x16
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x67
x76
⟶
(
x15
(
x15
x76
)
=
x15
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x67
x76
⟶
(
x58
(
x58
x76
)
=
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x67
x76
⟶
(
x69
(
x69
x76
)
=
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x70
x76
x9
⟶
(
x59
(
x59
x76
)
=
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x70
x76
x9
⟶
(
x14
(
x14
x76
)
=
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
(
x73
x77
⟶
False
)
⟶
x75
x77
⟶
(
x73
x76
⟶
False
)
⟶
x75
x76
⟶
x73
(
x63
x77
x76
)
⟶
False
)
⟶
(
x42
x9
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
(
x75
(
x66
x77
x76
)
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x51
x76
⟶
(
x51
(
x58
x76
)
⟶
False
)
⟶
False
)
⟶
(
∀ x76 .
x51
x76
⟶
(
x67
(
x58
x76
)
⟶
False
)
⟶
False
)
⟶
(
(
x25
x4
⟶
False
)
⟶
False
)
⟶
(
x0
x4
⟶
False
)
⟶
(
(
x21
x4
⟶
False
)
⟶
False
)
⟶
(
∀ x76 x77 .
x75
x77
⟶
x75
x76
⟶
(