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Proofgold Asset
asset id
7381b660ff8e8eab1f56f74de954d100b92c0a1e3a95c0d13135b1434eb3a247
asset hash
07a0f565978fe2e22fe4cb2c84e1e0c51d46abf326cf26392f79a25321de2cb0
bday / block
35121
tx
a5255..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
9e379..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 x3 :
ι →
ι → ο
.
∀ x4 :
ι → ο
.
∀ x5 :
ι →
ι → ο
.
∀ x6 x7 :
ι → ι
.
∀ x8 :
ι → ο
.
∀ x9 :
ι → ι
.
∀ x10 :
ι →
ι → ο
.
∀ x11 :
ι → ο
.
∀ x12 x13 .
∀ x14 :
ι →
ι → ο
.
∀ x15 :
ι → ι
.
∀ x16 .
∀ x17 :
ι → ο
.
∀ x18 .
∀ x19 :
ι → ο
.
∀ x20 :
ι → ι
.
∀ x21 x22 .
∀ x23 :
ι →
ι → ι
.
∀ x24 :
ι →
ι →
ι →
ι → ι
.
∀ x25 :
ι →
ι → ο
.
∀ x26 x27 x28 x29 :
ι → ο
.
∀ x30 x31 .
∀ x32 x33 :
ι → ο
.
∀ x34 :
ι →
ι → ο
.
∀ x35 x36 x37 :
ι → ο
.
∀ x38 :
ι →
ι → ι
.
∀ x39 :
ι →
ι →
ι → ο
.
∀ x40 x41 x42 :
ι →
ι → ι
.
∀ x43 :
ι →
ι → ο
.
∀ x44 x45 :
ι → ι
.
∀ x46 .
∀ x47 :
ι → ι
.
∀ x48 x49 :
ι → ο
.
∀ x50 :
ι → ι
.
∀ x51 :
ι → ο
.
∀ x52 x53 x54 :
ι →
ι → ι
.
∀ x55 x56 :
ι → ι
.
∀ x57 x58 :
ι → ο
.
∀ x59 .
∀ x60 x61 :
ι → ο
.
∀ x62 :
ι →
ι → ο
.
∀ x63 :
ι → ι
.
∀ x64 :
ι → ο
.
∀ x65 .
∀ x66 :
ι → ο
.
∀ x67 :
ι →
ι → ο
.
∀ x68 :
ι →
ι → ι
.
∀ x69 :
ι → ο
.
∀ x70 .
∀ x71 :
ι → ο
.
∀ x72 .
∀ x73 :
ι →
ι → ο
.
∀ x74 :
ι → ο
.
∀ x75 :
ι →
ι → ο
.
∀ x76 :
ι → ι
.
∀ x77 :
ι → ο
.
∀ x78 .
∀ x79 :
ι → ο
.
(
∀ x80 x81 .
x79
x81
⟶
(
x81
=
x80
⟶
False
)
⟶
x79
x80
⟶
False
)
⟶
(
∀ x80 x81 .
x0
x80
x81
⟶
x79
x81
⟶
False
)
⟶
(
∀ x80 .
x79
x80
⟶
(
x80
=
x78
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x0
x80
x81
⟶
x2
x81
(
x1
x82
)
⟶
x79
x82
⟶
False
)
⟶
(
∀ x80 x81 x82 .
(
x77
x82
⟶
False
)
⟶
x74
x82
⟶
(
x77
x81
⟶
False
)
⟶
x75
x81
x82
⟶
x2
x80
(
x76
x81
)
⟶
(
x2
x80
(
x76
x82
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x0
x81
x82
⟶
x2
x82
(
x1
x80
)
⟶
(
x2
x81
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x73
x81
x80
⟶
(
x2
x81
(
x1
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x2
x81
(
x1
x80
)
⟶
(
x73
x81
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x2
x80
x81
⟶
(
x79
x81
⟶
False
)
⟶
(
x0
x80
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x0
x81
x80
⟶
(
x2
x81
x80
⟶
False
)
⟶
False
)
⟶
(
x79
x72
⟶
False
)
⟶
(
∀ x80 .
(
x73
x80
x80
⟶
False
)
⟶
False
)
⟶
(
(
x71
x70
⟶
False
)
⟶
False
)
⟶
(
x79
x70
⟶
False
)
⟶
(
∀ x80 x81 .
(
x69
(
x68
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x3
(
x68
x80
x81
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x67
(
x68
x81
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x4
(
x68
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
x66
x65
⟶
False
)
⟶
(
(
x69
x65
⟶
False
)
⟶
False
)
⟶
(
(
x4
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x74
x80
⟶
(
x5
(
x6
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x74
x80
⟶
(
x64
(
x6
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x74
x80
⟶
x77
(
x6
x80
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x74
x80
⟶
(
x75
(
x6
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x8
x80
⟶
x79
(
x7
x80
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x8
x80
⟶
(
x2
(
x7
x80
)
(
x1
(
x76
x80
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x5
(
x9
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x64
(
x9
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x75
(
x9
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x61
x80
⟶
x74
x80
⟶
(
x62
(
x63
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x61
x80
⟶
x74
x80
⟶
(
x10
(
x63
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x61
x80
⟶
x74
x80
⟶
(
x60
(
x63
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x61
x80
⟶
x74
x80
⟶
x79
(
x63
x80
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x61
x80
⟶
x74
x80
⟶
(
x2
(
x63
x80
)
(
x1
(
x76
x80
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x11
x12
⟶
False
)
⟶
False
)
⟶
(
(
x69
x12
⟶
False
)
⟶
False
)
⟶
(
(
x4
x12
⟶
False
)
⟶
False
)
⟶
(
x79
x59
⟶
False
)
⟶
(
(
x66
x59
⟶
False
)
⟶
False
)
⟶
(
(
x69
x59
⟶
False
)
⟶
False
)
⟶
(
(
x4
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x58
x80
⟶
False
)
⟶
x8
x80
⟶
x57
(
x56
x80
)
⟶
False
)
⟶
(
∀ x80 .
(
x58
x80
⟶
False
)
⟶
x8
x80
⟶
(
x2
(
x56
x80
)
(
x1
(
x76
x80
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x8
x80
⟶
(
x57
(
x55
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x8
x80
⟶
x79
(
x55
x80
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x8
x80
⟶
(
x2
(
x55
x80
)
(
x1
(
x76
x80
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x61
x13
⟶
False
)
⟶
False
)
⟶
(
(
x64
x13
⟶
False
)
⟶
False
)
⟶
(
(
x14
x13
x72
⟶
False
)
⟶
False
)
⟶
(
(
x74
x13
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x62
(
x15
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x10
(
x15
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x2
(
x15
x80
)
(
x1
(
x76
x80
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x3
(
x54
x80
x81
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x67
(
x54
x81
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x4
(
x54
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x79
(
x54
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x2
(
x54
x80
x81
)
(
x1
(
x53
x81
x80
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x69
x16
⟶
False
)
⟶
False
)
⟶
(
(
x4
x16
⟶
False
)
⟶
False
)
⟶
(
(
x17
x18
⟶
False
)
⟶
False
)
⟶
(
(
x69
x18
⟶
False
)
⟶
False
)
⟶
(
(
x4
x18
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 x83 .
x2
x82
(
x1
(
x53
x83
x83
)
)
⟶
x52
x83
x82
=
x52
x81
x80
⟶
(
x82
=
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 x83 .
x2
x82
(
x1
(
x53
x83
x83
)
)
⟶
x52
x83
x82
=
x52
x80
x81
⟶
(
x83
=
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x51
x80
⟶
False
)
⟶
x8
x80
⟶
x60
(
x76
x80
)
⟶
False
)
⟶
(
∀ x80 .
x51
x80
⟶
x8
x80
⟶
(
x60
(
x76
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x49
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x64
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x77
(
x50
x80
)
⟶
False
)
⟶
(
∀ x80 .
x58
x80
⟶
x8
x80
⟶
(
x57
(
x76
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x48
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x19
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x61
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x64
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x77
(
x50
x80
)
⟶
False
)
⟶
(
∀ x80 .
(
x58
x80
⟶
False
)
⟶
x8
x80
⟶
x57
(
x76
x80
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x8
x80
⟶
x79
(
x76
x80
)
⟶
False
)
⟶
(
∀ x80 .
x77
x80
⟶
x8
x80
⟶
(
x79
(
x76
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x75
(
x47
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x2
(
x20
x80
)
x80
⟶
False
)
⟶
False
)
⟶
(
(
x8
x46
⟶
False
)
⟶
False
)
⟶
(
(
x74
x21
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x2
(
x45
x80
)
(
x1
(
x53
(
x76
x80
)
(
x76
x80
)
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x79
x22
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
x75
x80
x81
⟶
(
x74
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x8
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x74
x80
⟶
(
x75
(
x44
x80
)
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x74
x80
⟶
(
x5
(
x44
x80
)
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x74
x80
⟶
(
x64
(
x44
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
(
x77
x80
⟶
False
)
⟶
x74
x80
⟶
x77
(
x44
x80
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x74
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x64
(
x50
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x77
(
x50
x80
)
⟶
False
)
⟶
(
∀ x80 x81 .
x2
x81
(
x1
(
x53
x80
x80
)
)
⟶
(
x74
(
x52
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x2
x81
(
x1
(
x53
x80
x80
)
)
⟶
(
x64
(
x52
x80
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x77
x81
⟶
False
)
⟶
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x5
x80
(
x50
x81
)
⟶
x75
x80
(
x50
x81
)
⟶
(
x5
(
x23
x80
x81
)
x81
⟶
False
)
⟶
(
x2
(
x23
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x80
=
x44
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x77
x81
⟶
False
)
⟶
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x5
x80
(
x50
x81
)
⟶
x75
x80
(
x50
x81
)
⟶
(
x43
(
x23
x80
x81
)
x81
⟶
False
)
⟶
(
x2
(
x23
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x80
=
x44
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x77
x81
⟶
False
)
⟶
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x5
x80
(
x50
x81
)
⟶
x75
x80
(
x50
x81
)
⟶
x2
(
x23
x80
x81
)
(
x76
x80
)
⟶
x43
(
x23
x80
x81
)
x81
⟶
x5
(
x23
x80
x81
)
x81
⟶
(
x80
=
x44
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x77
x81
⟶
False
)
⟶
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x5
x80
(
x50
x81
)
⟶
x75
x80
(
x50
x81
)
⟶
(
x75
(
x23
x80
x81
)
x81
⟶
False
)
⟶
(
x80
=
x44
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x77
x81
⟶
False
)
⟶
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x5
x80
(
x50
x81
)
⟶
x75
x80
(
x50
x81
)
⟶
(
x64
(
x23
x80
x81
)
⟶
False
)
⟶
(
x80
=
x44
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
(
x77
x82
⟶
False
)
⟶
x74
x82
⟶
(
x77
x81
⟶
False
)
⟶
x64
x81
⟶
x5
x81
(
x50
x82
)
⟶
x75
x81
(
x50
x82
)
⟶
x81
=
x44
x82
⟶
x64
x80
⟶
x75
x80
x82
⟶
x43
x80
x82
⟶
x5
x80
x82
⟶
(
x2
x80
(
x76
x81
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
(
x77
x82
⟶
False
)
⟶
x74
x82
⟶
(
x77
x81
⟶
False
)
⟶
x64
x81
⟶
x5
x81
(
x50
x82
)
⟶
x75
x81
(
x50
x82
)
⟶
x81
=
x44
x82
⟶
x64
x80
⟶
x75
x80
x82
⟶
x2
x80
(
x76
x81
)
⟶
(
x5
x80
x82
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
(
x77
x82
⟶
False
)
⟶
x74
x82
⟶
(
x77
x81
⟶
False
)
⟶
x64
x81
⟶
x5
x81
(
x50
x82
)
⟶
x75
x81
(
x50
x82
)
⟶
x81
=
x44
x82
⟶
x64
x80
⟶
x75
x80
x82
⟶
x2
x80
(
x76
x81
)
⟶
(
x43
x80
x82
⟶
False
)
⟶
False
)
⟶
(
(
x78
=
x22
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x75
(
x42
x80
x81
)
x81
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x75
(
x41
x80
x81
)
(
x40
x80
x81
)
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x75
(
x42
x80
x81
)
x81
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x38
x80
x81
=
x40
x80
x81
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x75
(
x42
x80
x81
)
x81
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x74
(
x40
x80
x81
)
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x74
x82
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x75
(
x42
x80
x82
)
x82
⟶
False
)
⟶
(
x2
(
x42
x80
x82
)
(
x76
x80
)
⟶
False
)
⟶
x39
x80
(
x41
x80
x82
)
(
x38
x80
x82
)
⟶
x74
x81
⟶
x38
x80
x82
=
x81
⟶
x75
(
x41
x80
x82
)
x81
⟶
(
x80
=
x50
x82
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x75
(
x42
x80
x81
)
x81
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x2
(
x38
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x75
(
x42
x80
x81
)
x81
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x2
(
x41
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x64
(
x42
x80
x81
)
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x75
(
x41
x80
x81
)
(
x40
x80
x81
)
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x64
(
x42
x80
x81
)
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x38
x80
x81
=
x40
x80
x81
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x64
(
x42
x80
x81
)
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x74
(
x40
x80
x81
)
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x74
x82
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x64
(
x42
x80
x82
)
⟶
False
)
⟶
(
x2
(
x42
x80
x82
)
(
x76
x80
)
⟶
False
)
⟶
x39
x80
(
x41
x80
x82
)
(
x38
x80
x82
)
⟶
x74
x81
⟶
x38
x80
x82
=
x81
⟶
x75
(
x41
x80
x82
)
x81
⟶
(
x80
=
x50
x82
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x64
(
x42
x80
x81
)
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x2
(
x38
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
(
x64
(
x42
x80
x81
)
⟶
False
)
⟶
(
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x2
(
x41
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
x64
(
x42
x80
x81
)
⟶
x75
(
x42
x80
x81
)
x81
⟶
(
x75
(
x41
x80
x81
)
(
x40
x80
x81
)
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
x64
(
x42
x80
x81
)
⟶
x75
(
x42
x80
x81
)
x81
⟶
(
x38
x80
x81
=
x40
x80
x81
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
x64
(
x42
x80
x81
)
⟶
x75
(
x42
x80
x81
)
x81
⟶
(
x74
(
x40
x80
x81
)
⟶
False
)
⟶
(
x39
x80
(
x41
x80
x81
)
(
x38
x80
x81
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x74
x82
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x2
(
x42
x80
x82
)
(
x76
x80
)
⟶
x64
(
x42
x80
x82
)
⟶
x75
(
x42
x80
x82
)
x82
⟶
x39
x80
(
x41
x80
x82
)
(
x38
x80
x82
)
⟶
x74
x81
⟶
x38
x80
x82
=
x81
⟶
x75
(
x41
x80
x82
)
x81
⟶
(
x80
=
x50
x82
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
x64
(
x42
x80
x81
)
⟶
x75
(
x42
x80
x81
)
x81
⟶
(
x2
(
x38
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x74
x81
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x2
(
x42
x80
x81
)
(
x76
x80
)
⟶
x64
(
x42
x80
x81
)
⟶
x75
(
x42
x80
x81
)
x81
⟶
(
x2
(
x41
x80
x81
)
(
x76
x80
)
⟶
False
)
⟶
(
x80
=
x50
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 x83 x84 .
x74
x84
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x80
=
x50
x84
⟶
x2
x81
(
x76
x80
)
⟶
x2
x83
(
x76
x80
)
⟶
x74
x82
⟶
x83
=
x82
⟶
x75
x81
x82
⟶
(
x39
x80
x81
x83
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 x83 .
x74
x83
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x80
=
x50
x83
⟶
x2
x81
(
x76
x80
)
⟶
x2
x82
(
x76
x80
)
⟶
x39
x80
x81
x82
⟶
(
x75
x81
(
x24
x82
x81
x80
x83
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 x83 .
x74
x83
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x80
=
x50
x83
⟶
x2
x81
(
x76
x80
)
⟶
x2
x82
(
x76
x80
)
⟶
x39
x80
x81
x82
⟶
(
x82
=
x24
x82
x81
x80
x83
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 x83 .
x74
x83
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x80
=
x50
x83
⟶
x2
x81
(
x76
x80
)
⟶
x2
x82
(
x76
x80
)
⟶
x39
x80
x81
x82
⟶
(
x74
(
x24
x82
x81
x80
x83
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x74
x82
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x80
=
x50
x82
⟶
x64
x81
⟶
x75
x81
x82
⟶
(
x2
x81
(
x76
x80
)
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x74
x82
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x80
=
x50
x82
⟶
x2
x81
(
x76
x80
)
⟶
(
x75
x81
x82
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x74
x82
⟶
(
x77
x80
⟶
False
)
⟶
x64
x80
⟶
x74
x80
⟶
x80
=
x50
x82
⟶
x2
x81
(
x76
x80
)
⟶
(
x64
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
(
x77
x81
⟶
False
)
⟶
x74
x81
⟶
x75
x80
x81
⟶
x43
x80
x81
⟶
(
x25
x80
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x8
x80
⟶
x14
x80
x78
⟶
(
x77
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x71
x81
⟶
x2
x80
(
x1
x81
)
⟶
(
x71
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x48
x81
⟶
x74
x81
⟶
x75
x80
x81
⟶
x5
x80
x81
⟶
(
x5
x80
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x48
x81
⟶
x74
x81
⟶
x75
x80
x81
⟶
x5
x80
x81
⟶
(
x48
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x8
x80
⟶
x77
x80
⟶
(
x14
x80
x78
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x71
x81
⟶
x2
x80
x81
⟶
(
x69
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x71
x81
⟶
x2
x80
x81
⟶
(
x4
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x19
x81
⟶
x74
x81
⟶
x75
x80
x81
⟶
x5
x80
x81
⟶
(
x5
x80
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x19
x81
⟶
x74
x81
⟶
x75
x80
x81
⟶
x5
x80
x81
⟶
(
x19
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x8
x80
⟶
(
x51
x80
⟶
False
)
⟶
x58
x80
⟶
False
)
⟶
(
∀ x80 .
x79
x80
⟶
(
x71
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x61
x81
⟶
x74
x81
⟶
x75
x80
x81
⟶
x5
x80
x81
⟶
(
x5
x80
x81
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x61
x81
⟶
x74
x81
⟶
x75
x80
x81
⟶
x5
x80
x81
⟶
(
x61
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x77
x80
⟶
False
)
⟶
x58
x80
⟶
x61
x80
⟶
(
x26
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x77
x80
⟶
False
)
⟶
x58
x80
⟶
x61
x80
⟶
(
x61
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x77
x80
⟶
False
)
⟶
x58
x80
⟶
x61
x80
⟶
x77
x80
⟶
False
)
⟶
(
∀ x80 .
x8
x80
⟶
x58
x80
⟶
(
x51
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x57
x80
⟶
x4
x80
⟶
x69
x80
⟶
(
x66
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x57
x80
⟶
x4
x80
⟶
x69
x80
⟶
(
x69
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x57
x80
⟶
x4
x80
⟶
x69
x80
⟶
(
x4
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x35
x80
⟶
x36
x80
⟶
(
x37
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x8
x80
⟶
(
x51
x80
⟶
False
)
⟶
x51
x80
⟶
False
)
⟶
(
∀ x80 .
x8
x80
⟶
(
x51
x80
⟶
False
)
⟶
x77
x80
⟶
False
)
⟶
(
∀ x80 .
x4
x80
⟶
x69
x80
⟶
(
x66
x80
⟶
False
)
⟶
(
x69
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x4
x80
⟶
x69
x80
⟶
(
x66
x80
⟶
False
)
⟶
(
x4
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x4
x80
⟶
x69
x80
⟶
(
x66
x80
⟶
False
)
⟶
x57
x80
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x37
x80
⟶
(
x36
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x37
x80
⟶
(
x35
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x8
x80
⟶
x77
x80
⟶
(
x51
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x8
x80
⟶
x77
x80
⟶
(
x77
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x79
x82
⟶
x2
x80
(
x1
(
x53
x81
x82
)
)
⟶
(
x79
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x79
x80
⟶
x4
x80
⟶
x69
x80
⟶
(
x66
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x79
x80
⟶
x4
x80
⟶
x69
x80
⟶
(
x69
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x79
x80
⟶
x4
x80
⟶
x69
x80
⟶
(
x4
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x77
x80
⟶
False
)
⟶
x49
x80
⟶
(
x37
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
(
x77
x80
⟶
False
)
⟶
x49
x80
⟶
x77
x80
⟶
False
)
⟶
(
∀ x80 x81 x82 .
x79
x82
⟶
x2
x80
(
x1
(
x53
x82
x81
)
)
⟶
(
x79
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 x81 .
x4
x81
⟶
x69
x81
⟶
x2
x80
(
x1
x81
)
⟶
(
x69
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x4
x80
⟶
x69
x80
⟶
x79
x80
⟶
(
x17
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x4
x80
⟶
x69
x80
⟶
x79
x80
⟶
(
x69
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x4
x80
⟶
x69
x80
⟶
x79
x80
⟶
(
x4
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x14
x80
x72
⟶
x61
x80
⟶
(
x49
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x14
x80
x72
⟶
x61
x80
⟶
(
x48
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x14
x80
x72
⟶
x61
x80
⟶
(
x19
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x14
x80
x72
⟶
x61
x80
⟶
(
x61
x80
⟶
False
)
⟶
False
)
⟶
(
∀ x80 .
x74
x80
⟶
x14
x80
x72
⟶
x61
x80
⟶
(