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Proofgold Asset
asset id
1b5fc92be7c8336586b63908e9e2c63a63c2593db8f2ee934b02c13c5fb4b6e5
asset hash
335a9ff07834c1943dee5361a8cae3e8abb95b1bd3fbe0a4a1c339bed316993a
bday / block
35138
tx
74f9b..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
c7a39..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 :
ι →
ι → ο
.
∀ x3 x4 :
ι →
ι → ι
.
∀ x5 :
ι → ι
.
∀ x6 x7 x8 :
ι → ο
.
∀ x9 x10 :
ι → ι
.
∀ x11 :
ι →
ι → ο
.
∀ x12 :
ι → ι
.
∀ x13 :
ι →
ι → ο
.
∀ x14 x15 :
ι → ι
.
∀ x16 x17 :
ι → ο
.
∀ x18 :
ι →
ι → ο
.
∀ x19 x20 :
ι → ι
.
∀ x21 .
∀ x22 :
ι → ο
.
∀ x23 x24 .
∀ x25 x26 :
ι →
ι → ι
.
∀ x27 :
ι →
ι → ο
.
∀ x28 x29 x30 x31 x32 .
∀ x33 :
ι →
ι → ι
.
∀ x34 :
ι → ι
.
∀ x35 x36 .
∀ x37 x38 :
ι → ι
.
∀ x39 :
ι →
ι → ο
.
∀ x40 :
ι → ο
.
∀ x41 .
∀ x42 :
ι →
ι → ι
.
∀ x43 :
ι →
ι →
ι → ο
.
∀ x44 :
ι →
ι →
ι → ι
.
∀ x45 :
ι →
ι →
ι →
ι → ι
.
∀ x46 :
ι → ο
.
∀ x47 .
∀ x48 :
ι →
ι → ο
.
∀ x49 :
ι →
ι → ι
.
∀ x50 :
ι → ι
.
∀ x51 x52 x53 :
ι → ο
.
∀ x54 :
ι →
ι → ο
.
∀ x55 :
ι →
ι →
ι → ι
.
∀ x56 x57 x58 :
ι →
ι → ι
.
∀ x59 :
ι →
ι → ο
.
∀ x60 x61 x62 x63 :
ι → ο
.
∀ x64 .
∀ x65 :
ι → ο
.
(
∀ x66 x67 .
x65
x67
⟶
(
x67
=
x66
⟶
False
)
⟶
x65
x66
⟶
False
)
⟶
(
∀ x66 x67 .
x0
x66
x67
⟶
x65
x67
⟶
False
)
⟶
(
∀ x66 .
x65
x66
⟶
(
x66
=
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 .
x0
x66
x67
⟶
x2
x67
(
x1
x68
)
⟶
x65
x68
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
x54
x66
x67
⟶
x0
(
x55
x67
(
x55
x67
(
x58
x66
x67
)
(
x57
x66
x67
)
)
(
x55
x67
(
x56
x66
x67
)
(
x57
x66
x67
)
)
)
x66
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
x54
x66
x67
⟶
(
x0
(
x55
x67
(
x55
x67
(
x58
x66
x67
)
(
x56
x66
x67
)
)
(
x57
x66
x67
)
)
x66
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
x54
x66
x67
⟶
(
x2
(
x57
x66
x67
)
(
x50
x67
)
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
x54
x66
x67
⟶
(
x2
(
x56
x66
x67
)
(
x50
x67
)
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
x54
x66
x67
⟶
(
x2
(
x58
x66
x67
)
(
x50
x67
)
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 x70 .
(
x63
x70
⟶
False
)
⟶
x51
x70
⟶
x62
x70
⟶
x52
x70
⟶
x61
x70
⟶
x53
x70
⟶
x60
x70
⟶
x54
x66
x70
⟶
x0
(
x55
x70
(
x3
x66
x70
)
(
x4
x66
x70
)
)
x66
⟶
x2
x67
(
x50
x70
)
⟶
x2
x69
(
x50
x70
)
⟶
x2
x68
(
x50
x70
)
⟶
x0
(
x55
x70
(
x55
x70
x67
x69
)
x68
)
x66
⟶
(
x0
(
x55
x70
(
x55
x70
x67
x68
)
(
x55
x70
x69
x68
)
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 x70 .
(
x63
x70
⟶
False
)
⟶
x51
x70
⟶
x62
x70
⟶
x52
x70
⟶
x61
x70
⟶
x53
x70
⟶
x60
x70
⟶
x54
x66
x70
⟶
(
x0
(
x55
x70
(
x49
x66
x70
)
(
x4
x66
x70
)
)
x66
⟶
False
)
⟶
x2
x67
(
x50
x70
)
⟶
x2
x69
(
x50
x70
)
⟶
x2
x68
(
x50
x70
)
⟶
x0
(
x55
x70
(
x55
x70
x67
x69
)
x68
)
x66
⟶
(
x0
(
x55
x70
(
x55
x70
x67
x68
)
(
x55
x70
x69
x68
)
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 x70 .
(
x63
x70
⟶
False
)
⟶
x51
x70
⟶
x62
x70
⟶
x52
x70
⟶
x61
x70
⟶
x53
x70
⟶
x60
x70
⟶
x54
x66
x70
⟶
(
x0
(
x55
x70
(
x55
x70
(
x3
x66
x70
)
(
x49
x66
x70
)
)
(
x4
x66
x70
)
)
x66
⟶
False
)
⟶
x2
x67
(
x50
x70
)
⟶
x2
x69
(
x50
x70
)
⟶
x2
x68
(
x50
x70
)
⟶
x0
(
x55
x70
(
x55
x70
x67
x69
)
x68
)
x66
⟶
(
x0
(
x55
x70
(
x55
x70
x67
x68
)
(
x55
x70
x69
x68
)
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 x70 .
(
x63
x70
⟶
False
)
⟶
x51
x70
⟶
x62
x70
⟶
x52
x70
⟶
x61
x70
⟶
x53
x70
⟶
x60
x70
⟶
x54
x66
x70
⟶
(
x2
(
x4
x66
x70
)
(
x50
x70
)
⟶
False
)
⟶
x2
x67
(
x50
x70
)
⟶
x2
x69
(
x50
x70
)
⟶
x2
x68
(
x50
x70
)
⟶
x0
(
x55
x70
(
x55
x70
x67
x69
)
x68
)
x66
⟶
(
x0
(
x55
x70
(
x55
x70
x67
x68
)
(
x55
x70
x69
x68
)
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 x70 .
(
x63
x70
⟶
False
)
⟶
x51
x70
⟶
x62
x70
⟶
x52
x70
⟶
x61
x70
⟶
x53
x70
⟶
x60
x70
⟶
x54
x66
x70
⟶
(
x2
(
x49
x66
x70
)
(
x50
x70
)
⟶
False
)
⟶
x2
x67
(
x50
x70
)
⟶
x2
x69
(
x50
x70
)
⟶
x2
x68
(
x50
x70
)
⟶
x0
(
x55
x70
(
x55
x70
x67
x69
)
x68
)
x66
⟶
(
x0
(
x55
x70
(
x55
x70
x67
x68
)
(
x55
x70
x69
x68
)
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 x70 .
(
x63
x70
⟶
False
)
⟶
x51
x70
⟶
x62
x70
⟶
x52
x70
⟶
x61
x70
⟶
x53
x70
⟶
x60
x70
⟶
x54
x66
x70
⟶
(
x2
(
x3
x66
x70
)
(
x50
x70
)
⟶
False
)
⟶
x2
x67
(
x50
x70
)
⟶
x2
x69
(
x50
x70
)
⟶
x2
x68
(
x50
x70
)
⟶
x0
(
x55
x70
(
x55
x70
x67
x69
)
x68
)
x66
⟶
(
x0
(
x55
x70
(
x55
x70
x67
x68
)
(
x55
x70
x69
x68
)
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 .
x0
x67
x68
⟶
x2
x68
(
x1
x66
)
⟶
(
x2
x67
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
x48
x67
x66
⟶
(
x2
x67
(
x1
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
x2
x67
(
x1
x66
)
⟶
(
x48
x67
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
x2
x66
x67
⟶
(
x65
x67
⟶
False
)
⟶
(
x0
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
x0
x67
x66
⟶
(
x2
x67
x66
⟶
False
)
⟶
False
)
⟶
(
x65
x47
⟶
False
)
⟶
(
∀ x66 .
(
x48
x66
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 .
x46
x69
⟶
x43
x69
(
x42
x66
x66
)
x66
⟶
x2
x69
(
x1
(
x42
(
x42
x66
x66
)
x66
)
)
⟶
x2
x67
x66
⟶
x2
x68
x66
⟶
(
x45
x66
x69
x67
x68
=
x44
x69
x67
x68
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x6
x66
⟶
x65
(
x5
x66
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x6
x66
⟶
(
x2
(
x5
x66
)
(
x1
(
x50
x66
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x7
x66
⟶
False
)
⟶
x6
x66
⟶
x8
(
x9
x66
)
⟶
False
)
⟶
(
∀ x66 .
(
x7
x66
⟶
False
)
⟶
x6
x66
⟶
(
x2
(
x9
x66
)
(
x1
(
x50
x66
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x6
x66
⟶
(
x8
(
x10
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x6
x66
⟶
x65
(
x10
x66
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x6
x66
⟶
(
x2
(
x10
x66
)
(
x1
(
x50
x66
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x7
x41
⟶
False
)
⟶
False
)
⟶
(
x63
x41
⟶
False
)
⟶
(
(
x40
x41
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x51
x66
⟶
x62
x66
⟶
x52
x66
⟶
x61
x66
⟶
x60
x66
⟶
(
x11
(
x12
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x51
x66
⟶
x62
x66
⟶
x52
x66
⟶
x61
x66
⟶
x60
x66
⟶
(
x2
(
x12
x66
)
(
x50
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x7
x66
⟶
False
)
⟶
x40
x66
⟶
x13
(
x14
x66
)
x66
⟶
False
)
⟶
(
∀ x66 .
(
x7
x66
⟶
False
)
⟶
x40
x66
⟶
(
x2
(
x14
x66
)
(
x50
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x40
x66
⟶
(
x13
(
x15
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x40
x66
⟶
(
x2
(
x15
x66
)
(
x50
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x16
x66
⟶
False
)
⟶
x6
x66
⟶
x17
(
x50
x66
)
⟶
False
)
⟶
(
∀ x66 .
x16
x66
⟶
x6
x66
⟶
(
x17
(
x50
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x7
x66
⟶
x6
x66
⟶
(
x8
(
x50
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x7
x66
⟶
False
)
⟶
x6
x66
⟶
x8
(
x50
x66
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x6
x66
⟶
x65
(
x50
x66
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x51
x66
⟶
x62
x66
⟶
x52
x66
⟶
x61
x66
⟶
x60
x66
⟶
(
x39
(
x38
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x63
x66
⟶
x6
x66
⟶
(
x65
(
x50
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x51
x66
⟶
x62
x66
⟶
x52
x66
⟶
x61
x66
⟶
x60
x66
⟶
(
x11
(
x38
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x51
x66
⟶
x62
x66
⟶
x52
x66
⟶
x61
x66
⟶
x60
x66
⟶
(
x18
(
x38
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x40
x66
⟶
(
x13
(
x38
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x51
x66
⟶
x62
x66
⟶
x52
x66
⟶
x61
x66
⟶
x53
x66
⟶
x60
x66
⟶
(
x59
(
x19
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x63
x66
⟶
False
)
⟶
x51
x66
⟶
x62
x66
⟶
x52
x66
⟶
x61
x66
⟶
x60
x66
⟶
(
x54
(
x37
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
(
x2
(
x20
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
(
x40
x36
⟶
False
)
⟶
False
)
⟶
(
(
x60
x21
⟶
False
)
⟶
False
)
⟶
(
(
x6
x35
⟶
False
)
⟶
False
)
⟶
(
(
x22
x23
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x22
x66
⟶
(
x2
(
x34
x66
)
(
x1
(
x42
(
x42
(
x50
x66
)
(
x50
x66
)
)
(
x50
x66
)
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x22
x66
⟶
(
x43
(
x34
x66
)
(
x42
(
x50
x66
)
(
x50
x66
)
)
(
x50
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x22
x66
⟶
(
x46
(
x34
x66
)
⟶
False
)
⟶
False
)
⟶
(
(
x65
x24
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
x59
x66
x67
⟶
(
x2
x66
(
x1
(
x50
x67
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
x59
x66
x67
⟶
x65
x66
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x60
x67
⟶
x54
x66
x67
⟶
(
x2
x66
(
x1
(
x50
x67
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x60
x67
⟶
x54
x66
x67
⟶
x65
x66
⟶
False
)
⟶
(
∀ x66 .
x40
x66
⟶
(
x6
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x60
x66
⟶
(
x40
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x60
x66
⟶
(
x22
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x22
x66
⟶
(
x6
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 .
x46
x69
⟶
x43
x69
(
x42
x66
x66
)
x66
⟶
x2
x69
(
x1
(
x42
(
x42
x66
x66
)
x66
)
)
⟶
x2
x67
x66
⟶
x2
x68
x66
⟶
(
x2
(
x45
x66
x69
x67
x68
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x40
x66
⟶
(
x2
(
x38
x66
)
(
x50
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 .
x22
x68
⟶
x2
x66
(
x50
x68
)
⟶
x2
x67
(
x50
x68
)
⟶
(
x2
(
x55
x68
x66
x67
)
(
x50
x68
)
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
(
x65
x66
⟶
False
)
⟶
x2
x66
(
x1
(
x50
x67
)
)
⟶
x0
(
x38
x67
)
x66
⟶
x0
(
x55
x67
(
x25
x66
x67
)
(
x26
x66
x67
)
)
x66
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
(
x65
x66
⟶
False
)
⟶
x2
x66
(
x1
(
x50
x67
)
)
⟶
x0
(
x38
x67
)
x66
⟶
(
x0
(
x55
x67
(
x33
x66
x67
)
(
x26
x66
x67
)
)
x66
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
(
x65
x66
⟶
False
)
⟶
x2
x66
(
x1
(
x50
x67
)
)
⟶
x0
(
x38
x67
)
x66
⟶
(
x0
(
x55
x67
(
x55
x67
(
x25
x66
x67
)
(
x33
x66
x67
)
)
(
x26
x66
x67
)
)
x66
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
(
x65
x66
⟶
False
)
⟶
x2
x66
(
x1
(
x50
x67
)
)
⟶
x0
(
x38
x67
)
x66
⟶
(
x2
(
x26
x66
x67
)
(
x50
x67
)
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
(
x65
x66
⟶
False
)
⟶
x2
x66
(
x1
(
x50
x67
)
)
⟶
x0
(
x38
x67
)
x66
⟶
(
x2
(
x33
x66
x67
)
(
x50
x67
)
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
(
x65
x66
⟶
False
)
⟶
x2
x66
(
x1
(
x50
x67
)
)
⟶
x0
(
x38
x67
)
x66
⟶
(
x2
(
x25
x66
x67
)
(
x50
x67
)
⟶
False
)
⟶
(
x59
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 x69 x70 .
(
x63
x70
⟶
False
)
⟶
x51
x70
⟶
x62
x70
⟶
x52
x70
⟶
x61
x70
⟶
x53
x70
⟶
x60
x70
⟶
(
x65
x66
⟶
False
)
⟶
x2
x66
(
x1
(
x50
x70
)
)
⟶
x59
x66
x70
⟶
x2
x69
(
x50
x70
)
⟶
x2
x67
(
x50
x70
)
⟶
x2
x68
(
x50
x70
)
⟶
x0
(
x55
x70
(
x55
x70
x69
x67
)
x68
)
x66
⟶
x0
(
x55
x70
x67
x68
)
x66
⟶
(
x0
(
x55
x70
x69
x68
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
(
x63
x67
⟶
False
)
⟶
x51
x67
⟶
x62
x67
⟶
x52
x67
⟶
x61
x67
⟶
x53
x67
⟶
x60
x67
⟶
(
x65
x66
⟶
False
)
⟶
x2
x66
(
x1
(
x50
x67
)
)
⟶
x59
x66
x67
⟶
(
x0
(
x38
x67
)
x66
⟶
False
)
⟶
False
)
⟶
(
(
x64
=
x24
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 x68 .
x22
x68
⟶
x2
x66
(
x50
x68
)
⟶
x2
x67
(
x50
x68
)
⟶
(
x55
x68
x66
x67
=
x45
(
x50
x68
)
(
x34
x68
)
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
x27
x66
x64
⟶
(
x63
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
x63
x66
⟶
(
x27
x66
x64
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
(
x16
x66
⟶
False
)
⟶
x7
x66
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
x7
x66
⟶
(
x16
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
(
x16
x66
⟶
False
)
⟶
x16
x66
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
(
x16
x66
⟶
False
)
⟶
x63
x66
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
x63
x66
⟶
(
x16
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
x63
x66
⟶
(
x63
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
(
x7
x66
⟶
False
)
⟶
x63
x66
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
x63
x66
⟶
(
x7
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
(
x7
x66
⟶
False
)
⟶
x63
x66
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
x27
x66
x47
⟶
(
x7
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
x27
x66
x47
⟶
x63
x66
⟶
False
)
⟶
(
∀ x66 .
x6
x66
⟶
(
x63
x66
⟶
False
)
⟶
x7
x66
⟶
(
x27
x66
x47
⟶
False
)
⟶
False
)
⟶
(
∀ x66 x67 .
x0
x66
x67
⟶
x0
x67
x66
⟶
False
)
⟶
(
∀ x66 x67 x68 .
x2
x68
(
x50
x32
)
⟶
x2
x66
(
x50
x32
)
⟶
x2
x67
(
x50
x32
)
⟶
x0
(
x55
x32
(
x55
x32
x68
x66
)
x67
)
x31
⟶
(
x0
(
x55
x32
(
x55
x32
x68
x67
)
(
x55
x32
x66
x67
)
)
x31
⟶
False
)
⟶
(
x59
x31
x32
⟶
False
)
⟶
False
)
⟶
(
x59
x31
x32
⟶
x0
(
x55
x32
(
x55
x32
x30
x29
)
(
x55
x32
x28
x29
)
)
x31
⟶
False
)
⟶
(
x59
x31
x32
⟶
(
x0
(
x55
x32
(
x55
x32
x30
x28
)
x29
)
x31
⟶
False
)
⟶
False
)
⟶
(
x59
x31
x32
⟶
(
x2
x29
(
x50
x32
)
⟶
False
)
⟶
False
)
⟶
(
x59
x31
x32
⟶
(
x2
x28
(
x50
x32
)
⟶
False
)
⟶
False
)
⟶
(
x59
x31
x32
⟶
(
x2
x30
(
x50
x32
)
⟶
False
)
⟶
False
)
⟶
(
(
x54
x31
x32
⟶
False
)
⟶
False
)
⟶
(
(
x60
x32
⟶
False
)
⟶
False
)
⟶
(
(
x53
x32
⟶
False
)
⟶
False
)
⟶
(
(
x61
x32
⟶
False
)
⟶
False
)
⟶
(
(
x52
x32
⟶
False
)
⟶
False
)
⟶
(
(
x62
x32
⟶
False
)
⟶
False
)
⟶
(
(
x51
x32
⟶
False
)
⟶
False
)
⟶
(
x63
x32
⟶
False
)
⟶
False
(proof)