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Proofgold Asset
asset id
903ef073c85a3dc8e1d935a390532b23562024bee6d90960bc3c64ca12fcbc5f
asset hash
38c5581c729b44579d8c750e5ababc10345465f61130f4030f2ee74b34487fe2
bday / block
35148
tx
f4933..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
6ae76..
:
∀ x0 x1 :
ι → ο
.
∀ x2 :
ι → ι
.
∀ x3 :
ι →
ι →
ι → ο
.
∀ x4 :
ι →
ι → ο
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι → ι
.
∀ x7 :
ι →
ι →
ι →
ι → ι
.
∀ x8 :
ι →
ι →
ι →
ι →
ι → ο
.
∀ x9 x10 x11 x12 :
ι →
ι → ι
.
∀ x13 :
ι →
ι → ο
.
∀ x14 :
ι →
ι →
ι → ο
.
∀ x15 x16 :
ι → ο
.
∀ x17 x18 :
ι →
ι → ο
.
∀ x19 .
∀ x20 :
ι →
ι → ι
.
∀ x21 :
ι →
ι → ο
.
∀ x22 x23 :
ι → ο
.
∀ x24 :
ι → ι
.
∀ x25 :
ι → ο
.
∀ x26 :
ι →
ι → ι
.
∀ x27 .
∀ x28 :
ι → ο
.
∀ x29 x30 :
ι → ι
.
∀ x31 x32 :
ι →
ι → ι
.
∀ x33 .
∀ x34 x35 :
ι → ο
.
∀ x36 .
∀ x37 :
ι →
ι →
ι →
ι → ο
.
∀ x38 :
ι →
ι → ο
.
∀ x39 x40 x41 x42 x43 .
∀ x44 :
ι →
ι → ο
.
∀ x45 .
∀ x46 :
ι → ι
.
∀ x47 :
ι →
ι → ι
.
∀ x48 x49 .
∀ x50 :
ι → ο
.
∀ x51 :
ι →
ι → ο
.
∀ x52 :
ι → ι
.
∀ x53 .
∀ x54 :
ι → ο
.
∀ x55 :
ι →
ι → ο
.
∀ x56 :
ι →
ι → ι
.
∀ x57 .
∀ x58 :
ι → ο
.
∀ x59 .
∀ x60 :
ι → ο
.
(
∀ x61 x62 .
x60
x62
⟶
(
x62
=
x61
⟶
False
)
⟶
x60
x61
⟶
False
)
⟶
(
∀ x61 x62 .
(
x0
x62
⟶
False
)
⟶
x16
x62
⟶
x1
x62
⟶
x15
x61
⟶
x3
x61
(
x2
x62
)
(
x2
x62
)
⟶
x14
x61
(
x2
x62
)
(
x2
x62
)
⟶
x4
x61
(
x6
(
x5
(
x2
x62
)
(
x2
x62
)
)
)
⟶
(
x8
x62
(
x7
(
x2
x62
)
(
x2
x62
)
x61
(
x9
x61
x62
)
)
(
x7
(
x2
x62
)
(
x2
x62
)
x61
(
x12
x61
x62
)
)
(
x7
(
x2
x62
)
(
x2
x62
)
x61
(
x11
x61
x62
)
)
(
x7
(
x2
x62
)
(
x2
x62
)
x61
(
x10
x61
x62
)
)
⟶
False
)
⟶
(
x8
x62
(
x9
x61
x62
)
(
x12
x61
x62
)
(
x11
x61
x62
)
(
x10
x61
x62
)
⟶
False
)
⟶
(
x13
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x0
x62
⟶
False
)
⟶
x16
x62
⟶
x1
x62
⟶
x15
x61
⟶
x3
x61
(
x2
x62
)
(
x2
x62
)
⟶
x14
x61
(
x2
x62
)
(
x2
x62
)
⟶
x4
x61
(
x6
(
x5
(
x2
x62
)
(
x2
x62
)
)
)
⟶
x8
x62
(
x9
x61
x62
)
(
x12
x61
x62
)
(
x11
x61
x62
)
(
x10
x61
x62
)
⟶
x8
x62
(
x7
(
x2
x62
)
(
x2
x62
)
x61
(
x9
x61
x62
)
)
(
x7
(
x2
x62
)
(
x2
x62
)
x61
(
x12
x61
x62
)
)
(
x7
(
x2
x62
)
(
x2
x62
)
x61
(
x11
x61
x62
)
)
(
x7
(
x2
x62
)
(
x2
x62
)
x61
(
x10
x61
x62
)
)
⟶
(
x13
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x0
x62
⟶
False
)
⟶
x16
x62
⟶
x1
x62
⟶
x15
x61
⟶
x3
x61
(
x2
x62
)
(
x2
x62
)
⟶
x14
x61
(
x2
x62
)
(
x2
x62
)
⟶
x4
x61
(
x6
(
x5
(
x2
x62
)
(
x2
x62
)
)
)
⟶
(
x4
(
x10
x61
x62
)
(
x2
x62
)
⟶
False
)
⟶
(
x13
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x0
x62
⟶
False
)
⟶
x16
x62
⟶
x1
x62
⟶
x15
x61
⟶
x3
x61
(
x2
x62
)
(
x2
x62
)
⟶
x14
x61
(
x2
x62
)
(
x2
x62
)
⟶
x4
x61
(
x6
(
x5
(
x2
x62
)
(
x2
x62
)
)
)
⟶
(
x4
(
x11
x61
x62
)
(
x2
x62
)
⟶
False
)
⟶
(
x13
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x0
x62
⟶
False
)
⟶
x16
x62
⟶
x1
x62
⟶
x15
x61
⟶
x3
x61
(
x2
x62
)
(
x2
x62
)
⟶
x14
x61
(
x2
x62
)
(
x2
x62
)
⟶
x4
x61
(
x6
(
x5
(
x2
x62
)
(
x2
x62
)
)
)
⟶
(
x4
(
x12
x61
x62
)
(
x2
x62
)
⟶
False
)
⟶
(
x13
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x0
x62
⟶
False
)
⟶
x16
x62
⟶
x1
x62
⟶
x15
x61
⟶
x3
x61
(
x2
x62
)
(
x2
x62
)
⟶
x14
x61
(
x2
x62
)
(
x2
x62
)
⟶
x4
x61
(
x6
(
x5
(
x2
x62
)
(
x2
x62
)
)
)
⟶
(
x4
(
x9
x61
x62
)
(
x2
x62
)
⟶
False
)
⟶
(
x13
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 x64 x65 x66 .
(
x0
x66
⟶
False
)
⟶
x16
x66
⟶
x1
x66
⟶
x15
x61
⟶
x3
x61
(
x2
x66
)
(
x2
x66
)
⟶
x14
x61
(
x2
x66
)
(
x2
x66
)
⟶
x4
x61
(
x6
(
x5
(
x2
x66
)
(
x2
x66
)
)
)
⟶
x13
x61
x66
⟶
x4
x65
(
x2
x66
)
⟶
x4
x62
(
x2
x66
)
⟶
x4
x64
(
x2
x66
)
⟶
x4
x63
(
x2
x66
)
⟶
x8
x66
(
x7
(
x2
x66
)
(
x2
x66
)
x61
x65
)
(
x7
(
x2
x66
)
(
x2
x66
)
x61
x62
)
(
x7
(
x2
x66
)
(
x2
x66
)
x61
x64
)
(
x7
(
x2
x66
)
(
x2
x66
)
x61
x63
)
⟶
(
x8
x66
x65
x62
x64
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 x64 x65 x66 .
(
x0
x66
⟶
False
)
⟶
x16
x66
⟶
x1
x66
⟶
x15
x61
⟶
x3
x61
(
x2
x66
)
(
x2
x66
)
⟶
x14
x61
(
x2
x66
)
(
x2
x66
)
⟶
x4
x61
(
x6
(
x5
(
x2
x66
)
(
x2
x66
)
)
)
⟶
x13
x61
x66
⟶
x4
x65
(
x2
x66
)
⟶
x4
x62
(
x2
x66
)
⟶
x4
x64
(
x2
x66
)
⟶
x4
x63
(
x2
x66
)
⟶
x8
x66
x65
x62
x64
x63
⟶
(
x8
x66
(
x7
(
x2
x66
)
(
x2
x66
)
x61
x65
)
(
x7
(
x2
x66
)
(
x2
x66
)
x61
x62
)
(
x7
(
x2
x66
)
(
x2
x66
)
x61
x64
)
(
x7
(
x2
x66
)
(
x2
x66
)
x61
x63
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x17
x61
x62
⟶
x60
x62
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x61
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x17
x61
x62
⟶
x4
x62
(
x6
x63
)
⟶
x60
x63
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x17
x62
x63
⟶
x4
x63
(
x6
x61
)
⟶
(
x4
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x18
x62
x61
⟶
(
x4
x62
(
x6
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x4
x62
(
x6
x61
)
⟶
(
x18
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x4
x61
x62
⟶
(
x60
x62
⟶
False
)
⟶
(
x17
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x17
x62
x61
⟶
(
x4
x62
x61
⟶
False
)
⟶
False
)
⟶
(
x60
x19
⟶
False
)
⟶
(
∀ x61 .
(
x18
x61
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 x64 .
(
x60
x64
⟶
False
)
⟶
x15
x61
⟶
x3
x61
x64
x63
⟶
x4
x61
(
x6
(
x5
x64
x63
)
)
⟶
x4
x62
x64
⟶
(
x7
x64
x63
x61
x62
=
x20
x61
x62
⟶
False
)
⟶
False
)
⟶
(
(
x58
x57
⟶
False
)
⟶
False
)
⟶
(
x60
x57
⟶
False
)
⟶
(
∀ x61 x62 .
(
x15
(
x56
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x21
(
x56
x61
x62
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x55
(
x56
x62
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x22
(
x56
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
x54
x53
⟶
False
)
⟶
(
(
x15
x53
⟶
False
)
⟶
False
)
⟶
(
(
x22
x53
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x23
x61
⟶
False
)
⟶
x25
x61
⟶
x60
(
x24
x61
)
⟶
False
)
⟶
(
∀ x61 .
(
x23
x61
⟶
False
)
⟶
x25
x61
⟶
(
x4
(
x24
x61
)
(
x6
(
x2
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
x62
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
x60
(
x26
x61
x62
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
x62
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
(
x15
(
x26
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
x62
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
(
x21
(
x26
x61
x62
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
x62
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
(
x55
(
x26
x61
x62
)
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
x62
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
(
x22
(
x26
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
x62
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
(
x4
(
x26
x61
x62
)
(
x6
(
x5
x62
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
x60
x27
⟶
False
)
⟶
(
∀ x61 .
(
x14
(
x52
x61
)
x61
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x3
(
x52
x61
)
x61
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x51
(
x52
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x15
(
x52
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x21
(
x52
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x55
(
x52
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x22
(
x52
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x4
(
x52
x61
)
(
x6
(
x5
x61
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x50
x49
⟶
False
)
⟶
False
)
⟶
(
(
x15
x49
⟶
False
)
⟶
False
)
⟶
(
(
x22
x49
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x0
x61
⟶
False
)
⟶
x25
x61
⟶
x28
(
x29
x61
)
⟶
False
)
⟶
(
∀ x61 .
(
x0
x61
⟶
False
)
⟶
x25
x61
⟶
(
x4
(
x29
x61
)
(
x6
(
x2
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x23
x61
⟶
False
)
⟶
x25
x61
⟶
(
x28
(
x30
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x23
x61
⟶
False
)
⟶
x25
x61
⟶
x60
(
x30
x61
)
⟶
False
)
⟶
(
∀ x61 .
(
x23
x61
⟶
False
)
⟶
x25
x61
⟶
(
x4
(
x30
x61
)
(
x6
(
x2
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x60
x48
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x21
(
x31
x61
x62
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x55
(
x31
x62
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x22
(
x31
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
(
x31
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x4
(
x31
x61
x62
)
(
x6
(
x5
x62
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x15
(
x47
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x21
(
x47
x61
x62
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x55
(
x47
x62
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x22
(
x47
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x4
(
x47
x61
x62
)
(
x6
(
x5
x62
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x3
(
x32
x61
x62
)
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x15
(
x32
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x21
(
x32
x61
x62
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x55
(
x32
x62
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x22
(
x32
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x4
(
x32
x61
x62
)
(
x6
(
x5
x62
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x15
x33
⟶
False
)
⟶
False
)
⟶
(
(
x22
x33
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x34
x61
⟶
False
)
⟶
x25
x61
⟶
x35
(
x2
x61
)
⟶
False
)
⟶
(
∀ x61 .
x34
x61
⟶
x25
x61
⟶
(
x35
(
x2
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x0
x61
⟶
x25
x61
⟶
(
x28
(
x2
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x0
x61
⟶
False
)
⟶
x25
x61
⟶
x28
(
x2
x61
)
⟶
False
)
⟶
(
∀ x61 .
(
x23
x61
⟶
False
)
⟶
x25
x61
⟶
x60
(
x2
x61
)
⟶
False
)
⟶
(
(
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x23
x61
⟶
x25
x61
⟶
(
x60
(
x2
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x58
x63
⟶
x22
x61
⟶
x21
x61
x63
⟶
x15
x61
⟶
(
x15
(
x20
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x58
x63
⟶
x22
x61
⟶
x21
x61
x63
⟶
x15
x61
⟶
(
x22
(
x20
x61
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x4
(
x46
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
(
x25
x36
⟶
False
)
⟶
False
)
⟶
(
(
x1
x45
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x1
x61
⟶
(
x25
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 x64 .
(
x60
x64
⟶
False
)
⟶
x15
x61
⟶
x3
x61
x64
x63
⟶
x4
x61
(
x6
(
x5
x64
x63
)
)
⟶
x4
x62
x64
⟶
(
x4
(
x7
x64
x63
x61
x62
)
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 x64 .
(
x0
x64
⟶
False
)
⟶
x16
x64
⟶
x1
x64
⟶
x4
x61
(
x2
x64
)
⟶
x4
x63
(
x2
x64
)
⟶
x4
x62
(
x2
x64
)
⟶
x8
x64
x61
x63
x61
x62
⟶
(
x37
x64
x61
x63
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 x64 .
(
x0
x64
⟶
False
)
⟶
x16
x64
⟶
x1
x64
⟶
x4
x61
(
x2
x64
)
⟶
x4
x63
(
x2
x64
)
⟶
x4
x62
(
x2
x64
)
⟶
x37
x64
x61
x63
x62
⟶
(
x8
x64
x61
x63
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
x38
x61
x59
⟶
(
x23
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x58
x62
⟶
x4
x61
(
x6
x62
)
⟶
(
x58
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
x23
x61
⟶
(
x38
x61
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
(
x60
x63
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
x4
x62
(
x6
(
x5
x63
x61
)
)
⟶
x15
x62
⟶
x3
x62
x63
x61
⟶
(
x3
x62
x63
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
(
x60
x63
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
x4
x62
(
x6
(
x5
x63
x61
)
)
⟶
x15
x62
⟶
x3
x62
x63
x61
⟶
x60
x62
⟶
False
)
⟶
(
∀ x61 x62 x63 .
(
x60
x63
⟶
False
)
⟶
(
x60
x61
⟶
False
)
⟶
x4
x62
(
x6
(
x5
x63
x61
)
)
⟶
x15
x62
⟶
x3
x62
x63
x61
⟶
(
x15
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x58
x62
⟶
x4
x61
x62
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x58
x62
⟶
x4
x61
x62
⟶
(
x22
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
(
x34
x61
⟶
False
)
⟶
x0
x61
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x58
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
x0
x61
⟶
(
x34
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x63
(
x6
(
x5
x61
x62
)
)
⟶
x15
x63
⟶
x50
x63
⟶
x44
x63
x62
⟶
(
x14
x63
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x63
(
x6
(
x5
x61
x62
)
)
⟶
x15
x63
⟶
x50
x63
⟶
x44
x63
x62
⟶
(
x15
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x28
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x54
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x28
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x28
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x22
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
(
x34
x61
⟶
False
)
⟶
x34
x61
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
(
x34
x61
⟶
False
)
⟶
x23
x61
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x63
(
x6
(
x5
x62
x61
)
)
⟶
x15
x63
⟶
x14
x63
x62
x61
⟶
(
x44
x63
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x63
(
x6
(
x5
x62
x61
)
)
⟶
x15
x63
⟶
x14
x63
x62
x61
⟶
(
x50
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x63
(
x6
(
x5
x62
x61
)
)
⟶
x15
x63
⟶
x14
x63
x62
x61
⟶
(
x15
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x22
x61
⟶
x15
x61
⟶
(
x54
x61
⟶
False
)
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x22
x61
⟶
x15
x61
⟶
(
x54
x61
⟶
False
)
⟶
(
x22
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x22
x61
⟶
x15
x61
⟶
(
x54
x61
⟶
False
)
⟶
x28
x61
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
x23
x61
⟶
(
x34
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
x23
x61
⟶
(
x23
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x60
x63
⟶
x4
x61
(
x6
(
x5
x62
x63
)
)
⟶
(
x60
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x4
x62
(
x6
(
x5
x61
x61
)
)
⟶
x3
x62
x61
x61
⟶
(
x51
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x54
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x22
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x60
x63
⟶
x4
x61
(
x6
(
x5
x63
x62
)
)
⟶
(
x60
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
(
x60
x63
⟶
False
)
⟶
x4
x61
(
x6
(
x5
x62
x63
)
)
⟶
x3
x61
x62
x63
⟶
(
x51
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x22
x62
⟶
x15
x62
⟶
x4
x61
(
x6
x62
)
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
(
x0
x61
⟶
False
)
⟶
x23
x61
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x63
(
x6
(
x5
x61
x62
)
)
⟶
(
x21
x63
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x63
(
x6
(
x5
x62
x61
)
)
⟶
(
x55
x63
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
(
x60
x63
⟶
False
)
⟶
x60
x61
⟶
x4
x62
(
x6
(
x5
x63
x61
)
)
⟶
x51
x62
x63
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x60
x63
⟶
x4
x61
(
x6
(
x5
x63
x62
)
)
⟶
x3
x61
x63
x62
⟶
(
x51
x61
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x50
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x22
x61
⟶
x15
x61
⟶
(
x22
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
x23
x61
⟶
(
x0
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x63
(
x6
(
x5
x61
x62
)
)
⟶
(
x22
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x60
x63
⟶
x4
x61
(
x6
(
x5
x63
x62
)
)
⟶
(
x51
x61
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x4
x62
(
x6
(
x5
x63
x61
)
)
⟶
x51
x62
x63
⟶
(
x3
x62
x63
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
(
x0
x61
⟶
False
)
⟶
x23
x61
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
x38
x61
x19
⟶
(
x0
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
x38
x61
x19
⟶
x23
x61
⟶
False
)
⟶
(
∀ x61 .
x25
x61
⟶
(
x23
x61
⟶
False
)
⟶
x0
x61
⟶
(
x38
x61
x19
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x17
x61
x62
⟶
x17
x62
x61
⟶
False
)
⟶
(
(
x37
x39
(
x7
(
x2
x39
)
(
x2
x39
)
x43
x42
)
(
x7
(
x2
x39
)
(
x2
x39
)
x43
x41
)
(
x7
(
x2
x39
)
(
x2
x39
)
x43
x40
)
⟶
False
)
⟶
(
x37
x39
x42
x41
x40
⟶
False
)
⟶
False
)
⟶
(
x37
x39
x42
x41
x40
⟶
x37
x39
(
x7
(
x2
x39
)
(
x2
x39
)
x43
x42
)
(
x7
(
x2
x39
)
(
x2
x39
)
x43
x41
)
(
x7
(
x2
x39
)
(
x2
x39
)
x43
x40
)
⟶
False
)
⟶
(
(
x13
x43
x39
⟶
False
)
⟶
False
)
⟶
(
(
x4
x43
(
x6
(
x5
(
x2
x39
)
(
x2
x39
)
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x14
x43
(
x2
x39
)
(
x2
x39
)
⟶
False
)
⟶
False
)
⟶
(
(
x3
x43
(
x2
x39
)
(
x2
x39
)
⟶
False
)
⟶
False
)
⟶
(
(
x15
x43
⟶
False
)
⟶
False
)
⟶
(
(
x4
x40
(
x2
x39
)
⟶
False
)
⟶
False
)
⟶
(
(
x4
x41
(
x2
x39
)
⟶
False
)
⟶
False
)
⟶
(
(
x4
x42
(
x2
x39
)
⟶
False
)
⟶
False
)
⟶
(
(
x1
x39
⟶
False
)
⟶
False
)
⟶
(
(
x16
x39
⟶
False
)
⟶
False
)
⟶
(
x0
x39
⟶
False
)
⟶
False
(proof)