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Proofgold Asset
asset id
8619e148ad058d8056568ccbe672506661859ad43cd476e21ef43ebaa36b3ae4
asset hash
ca1744a657e11b279856511bd6094f57a26504d62522e9846f8b04d41582ca6c
bday / block
35128
tx
57369..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
8c099..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ο
.
∀ x2 :
ι →
ι → ο
.
∀ x3 x4 x5 :
ι → ι
.
∀ x6 x7 :
ι →
ι → ο
.
∀ x8 x9 :
ι →
ι → ι
.
∀ x10 :
ι →
ι → ο
.
∀ x11 x12 x13 :
ι → ο
.
∀ x14 .
∀ x15 :
ι → ο
.
∀ x16 x17 :
ι → ι
.
∀ x18 :
ι → ο
.
∀ x19 .
∀ x20 :
ι → ι
.
∀ x21 :
ι → ο
.
∀ x22 .
∀ x23 :
ι → ι
.
∀ x24 :
ι →
ι → ο
.
∀ x25 x26 :
ι → ι
.
∀ x27 :
ι → ο
.
∀ x28 x29 .
∀ x30 :
ι → ο
.
∀ x31 .
∀ x32 :
ι → ι
.
∀ x33 :
ι → ο
.
∀ x34 :
ι → ι
.
∀ x35 x36 .
∀ x37 :
ι → ο
.
∀ x38 x39 .
∀ x40 x41 :
ι → ο
.
∀ x42 :
ι →
ι → ι
.
∀ x43 .
∀ x44 :
ι → ο
.
∀ x45 x46 .
∀ x47 :
ι → ο
.
∀ x48 x49 .
∀ x50 :
ι → ι
.
∀ x51 x52 x53 .
∀ x54 :
ι → ι
.
∀ x55 :
ι →
ι → ο
.
∀ x56 :
ι → ι
.
∀ x57 .
∀ x58 :
ι → ο
.
∀ x59 .
∀ x60 :
ι → ι
.
∀ x61 .
∀ x62 x63 :
ι → ο
.
∀ x64 .
∀ x65 :
ι → ο
.
∀ x66 :
ι →
ι → ι
.
∀ x67 .
∀ x68 :
ι → ο
.
(
∀ x69 x70 .
x68
x70
⟶
(
x70
=
x69
⟶
False
)
⟶
x68
x69
⟶
False
)
⟶
(
∀ x69 x70 .
x0
x69
x70
⟶
x68
x70
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
(
x69
=
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x6
x69
(
x5
x70
)
⟶
(
x7
x69
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x7
x69
x70
⟶
(
x6
x69
(
x5
x70
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 x71 .
x0
x69
x70
⟶
x2
x70
(
x4
x71
)
⟶
x68
x71
⟶
False
)
⟶
(
∀ x69 x70 x71 .
x0
x70
x71
⟶
x2
x71
(
x4
x69
)
⟶
(
x2
x70
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x69
(
x4
(
x4
x70
)
)
⟶
(
x6
x69
(
x8
x70
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x6
x70
x69
⟶
(
x2
x70
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x70
(
x4
x69
)
⟶
(
x6
x70
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x69
x70
⟶
(
x68
x70
⟶
False
)
⟶
(
x0
x69
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 x71 .
x6
x70
x71
⟶
x6
x71
x69
⟶
(
x6
x70
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x0
x70
x69
⟶
(
x2
x70
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x69
(
x4
(
x4
x70
)
)
⟶
(
x6
x69
(
x9
x70
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
(
x68
x70
⟶
False
)
⟶
x2
x69
(
x4
(
x4
x70
)
)
⟶
(
x2
x69
(
x4
(
x4
(
x3
(
x66
x70
(
x9
x70
x69
)
)
)
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
(
x68
x70
⟶
False
)
⟶
x2
x69
(
x4
(
x4
x70
)
)
⟶
(
x10
x69
(
x66
x70
(
x9
x70
x69
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
(
x68
x70
⟶
False
)
⟶
x2
x69
(
x4
(
x4
x70
)
)
⟶
(
x7
x69
(
x66
x70
(
x9
x70
x69
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x6
x69
x69
⟶
False
)
⟶
False
)
⟶
(
(
x65
x64
⟶
False
)
⟶
False
)
⟶
(
(
x11
x64
⟶
False
)
⟶
False
)
⟶
(
(
x63
x64
⟶
False
)
⟶
False
)
⟶
(
x68
x64
⟶
False
)
⟶
(
(
x62
x61
⟶
False
)
⟶
False
)
⟶
(
(
x12
x61
⟶
False
)
⟶
False
)
⟶
(
x68
x61
⟶
False
)
⟶
(
(
x13
x14
⟶
False
)
⟶
False
)
⟶
(
x68
x14
⟶
False
)
⟶
(
∀ x69 .
(
x15
x69
⟶
False
)
⟶
(
x12
(
x16
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x15
x69
⟶
False
)
⟶
x15
(
x16
x69
)
⟶
False
)
⟶
(
∀ x69 .
(
x15
x69
⟶
False
)
⟶
(
x2
(
x16
x69
)
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x15
x69
⟶
False
)
⟶
x15
(
x60
x69
)
⟶
False
)
⟶
(
∀ x69 .
(
x15
x69
⟶
False
)
⟶
(
x2
(
x60
x69
)
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
x12
x59
⟶
False
)
⟶
(
(
x11
x59
⟶
False
)
⟶
False
)
⟶
(
(
x63
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
(
x15
(
x17
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
x68
(
x17
x69
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
(
x2
(
x17
x69
)
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
x58
x57
⟶
False
)
⟶
(
(
x11
x57
⟶
False
)
⟶
False
)
⟶
(
(
x63
x57
⟶
False
)
⟶
False
)
⟶
(
(
x18
x19
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
(
x55
(
x56
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
(
x2
(
x56
x69
)
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x55
(
x54
x69
)
x69
⟶
False
)
⟶
(
∀ x69 .
(
x2
(
x54
x69
)
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
(
x12
x53
⟶
False
)
⟶
False
)
⟶
(
(
x11
x53
⟶
False
)
⟶
False
)
⟶
(
(
x63
x53
⟶
False
)
⟶
False
)
⟶
(
x68
x53
⟶
False
)
⟶
(
x68
x52
⟶
False
)
⟶
(
∀ x69 .
(
x68
(
x20
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x2
(
x20
x69
)
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
(
x21
x22
⟶
False
)
⟶
False
)
⟶
(
(
x11
x22
⟶
False
)
⟶
False
)
⟶
(
(
x63
x22
⟶
False
)
⟶
False
)
⟶
(
x68
x51
⟶
False
)
⟶
(
(
x58
x51
⟶
False
)
⟶
False
)
⟶
(
(
x11
x51
⟶
False
)
⟶
False
)
⟶
(
(
x63
x51
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
(
x12
(
x50
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
x68
(
x50
x69
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
(
x2
(
x50
x69
)
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x24
(
x23
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x7
(
x23
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x2
(
x23
x69
)
(
x4
(
x4
(
x3
x69
)
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x68
x49
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x7
(
x25
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x2
(
x25
x69
)
(
x4
(
x4
(
x3
x69
)
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
x68
(
x26
x69
)
⟶
False
)
⟶
(
∀ x69 .
(
x68
x69
⟶
False
)
⟶
(
x2
(
x26
x69
)
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
(
x27
x28
⟶
False
)
⟶
False
)
⟶
(
(
x1
x28
⟶
False
)
⟶
False
)
⟶
(
(
x11
x29
⟶
False
)
⟶
False
)
⟶
(
(
x63
x29
⟶
False
)
⟶
False
)
⟶
(
(
x30
x31
⟶
False
)
⟶
False
)
⟶
(
(
x11
x31
⟶
False
)
⟶
False
)
⟶
(
(
x63
x31
⟶
False
)
⟶
False
)
⟶
(
(
x12
x48
⟶
False
)
⟶
False
)
⟶
(
x68
x48
⟶
False
)
⟶
(
(
x47
x46
⟶
False
)
⟶
False
)
⟶
(
(
x11
x46
⟶
False
)
⟶
False
)
⟶
(
(
x63
x46
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x10
(
x32
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x7
(
x32
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x2
(
x32
x69
)
(
x4
(
x4
(
x3
x69
)
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x27
x45
⟶
False
)
⟶
False
)
⟶
(
(
x33
x45
⟶
False
)
⟶
False
)
⟶
(
(
x1
x45
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 x71 x72 .
x2
x71
(
x4
(
x4
x72
)
)
⟶
x66
x72
x71
=
x66
x70
x69
⟶
(
x71
=
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 x71 x72 .
x2
x71
(
x4
(
x4
x72
)
)
⟶
x66
x72
x71
=
x66
x69
x70
⟶
(
x72
=
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
(
x68
x70
⟶
False
)
⟶
x2
x69
(
x4
(
x4
x70
)
)
⟶
(
x27
(
x66
x70
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
(
x68
x70
⟶
False
)
⟶
x2
x69
(
x4
(
x4
x70
)
)
⟶
x33
(
x66
x70
x69
)
⟶
False
)
⟶
(
∀ x69 .
(
x33
x69
⟶
False
)
⟶
x1
x69
⟶
(
x27
(
x66
(
x3
x69
)
(
x5
x69
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x33
x69
⟶
False
)
⟶
x1
x69
⟶
x33
(
x66
(
x3
x69
)
(
x5
x69
)
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x24
(
x5
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x12
x69
⟶
(
x62
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x70
(
x4
(
x4
x69
)
)
⟶
x68
(
x8
x69
x70
)
⟶
False
)
⟶
(
(
x68
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x7
(
x5
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
(
x4
x69
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x10
(
x5
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x12
x69
⟶
(
x12
(
x4
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
(
x2
(
x34
x69
)
x69
⟶
False
)
⟶
False
)
⟶
(
(
x44
x43
⟶
False
)
⟶
False
)
⟶
(
(
x1
x35
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x2
(
x5
x69
)
(
x4
(
x4
(
x3
x69
)
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x68
x36
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
(
x44
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x70
(
x4
(
x4
x69
)
)
⟶
(
x2
(
x8
x69
x70
)
(
x4
(
x4
x69
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x70
(
x4
(
x4
x69
)
)
⟶
(
x2
(
x9
x69
x70
)
(
x4
(
x4
x69
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x70
(
x4
(
x4
x69
)
)
⟶
(
x1
(
x66
x69
x70
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x2
x70
(
x4
(
x4
x69
)
)
⟶
(
x27
(
x66
x69
x70
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 x71 .
x1
x71
⟶
x2
x69
(
x4
(
x4
(
x3
x71
)
)
)
⟶
x7
x70
x71
⟶
x10
x70
x71
⟶
x2
x70
(
x4
(
x4
(
x3
x71
)
)
)
⟶
x6
x70
(
x8
(
x3
x71
)
x69
)
⟶
(
x24
x69
x71
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x24
x69
x70
⟶
(
x6
(
x42
x69
x70
)
(
x8
(
x3
x70
)
x69
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x24
x69
x70
⟶
(
x2
(
x42
x69
x70
)
(
x4
(
x4
(
x3
x70
)
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x24
x69
x70
⟶
(
x10
(
x42
x69
x70
)
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x24
x69
x70
⟶
(
x7
(
x42
x69
x70
)
x70
⟶
False
)
⟶
False
)
⟶
(
(
x67
=
x36
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
x33
x69
⟶
(
x37
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x13
x70
⟶
x2
x69
(
x4
x70
)
⟶
(
x13
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
(
x65
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x13
x70
⟶
x2
x69
x70
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x13
x70
⟶
x2
x69
x70
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x62
x70
⟶
x2
x69
(
x4
x70
)
⟶
(
x62
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
(
x13
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x62
x70
⟶
x2
x69
x70
⟶
(
x12
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x41
x70
⟶
x2
x69
(
x4
x70
)
⟶
(
x41
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x15
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x58
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x15
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x15
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
(
x62
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x12
x69
⟶
(
x41
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x15
x70
⟶
x2
x69
(
x4
x70
)
⟶
(
x15
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
(
x58
x69
⟶
False
)
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
(
x58
x69
⟶
False
)
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
(
x58
x69
⟶
False
)
⟶
x15
x69
⟶
False
)
⟶
(
∀ x69 .
(
x12
x69
⟶
False
)
⟶
x15
x69
⟶
False
)
⟶
(
∀ x69 .
(
x12
x69
⟶
False
)
⟶
x41
x69
⟶
(
x18
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x68
x70
⟶
x2
x69
(
x4
x70
)
⟶
x55
x69
x70
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x58
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x15
x69
⟶
(
x12
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x18
x69
⟶
(
x41
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x18
x69
⟶
x12
x69
⟶
False
)
⟶
(
∀ x69 x70 .
(
x68
x70
⟶
False
)
⟶
x2
x69
(
x4
x70
)
⟶
x68
x69
⟶
(
x55
x69
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x63
x70
⟶
x11
x70
⟶
x2
x69
(
x4
x70
)
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
x68
x69
⟶
(
x30
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
x68
x69
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
x68
x69
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
(
x68
x70
⟶
False
)
⟶
x2
x69
(
x4
x70
)
⟶
(
x55
x69
x70
⟶
False
)
⟶
x68
x69
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x21
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
x30
x69
⟶
(
x40
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
x30
x69
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x63
x69
⟶
x11
x69
⟶
x30
x69
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x12
x70
⟶
x2
x69
(
x4
x70
)
⟶
(
x12
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x68
x70
⟶
x2
x69
(
x4
x70
)
⟶
(
x68
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
(
x12
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x47
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x11
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 .
x68
x69
⟶
x63
x69
⟶
x11
x69
⟶
(
x63
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x7
x69
x70
⟶
x10
x69
x70
⟶
(
x24
x69
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x7
x69
x70
⟶
x10
x69
x70
⟶
(
x10
x69
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x1
x70
⟶
x2
x69
(
x4
(
x4
(
x3
x70
)
)
)
⟶
x7
x69
x70
⟶
x10
x69
x70
⟶
(
x7
x69
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x69 x70 .
x0
x69
x70
⟶
x0
x70
x69
⟶
False
)
⟶
(
∀ x69 .
x1
x69
⟶
x27
x69
⟶
(
x69
=
x66
(
x3
x69
)
(
x5
x69
)
⟶
False
)
⟶
False
)
⟶
(
x7
x39
(
x66
x38
(
x9
x38
(
x8
x38
x39
)
)
)
⟶
x24
x39
(
x66
x38
(
x9
x38
(
x8
x38
x39
)
)
)
⟶
x2
x39
(
x4
(
x4
(
x3
(
x66
x38
(
x9
x38
(
x8
x38
x39
)
)
)
)
)
)
⟶
False
)
⟶
(
(
x2
x39
(
x4
(
x4
x38
)
)
⟶
False
)
⟶
False
)
⟶
(
x68
x38
⟶
False
)
⟶
False
(proof)