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Proofgold Asset
asset id
aef2429ca6801ccc54e94bc4ee61f43864cd727fd47761a2a0ea3ede8ee8353d
asset hash
60077c9c47d12f15215c42388d490c25940a67c1c7bac6244855382906e962b2
bday / block
35134
tx
bca0e..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
3a9bd..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 x3 :
ι →
ι → ο
.
∀ x4 :
ι →
ι → ι
.
∀ x5 x6 :
ι → ο
.
∀ x7 :
ι →
ι → ο
.
∀ x8 :
ι →
ι →
ι → ι
.
∀ x9 :
ι →
ι → ι
.
∀ x10 :
ι →
ι →
ι → ι
.
∀ x11 x12 :
ι → ο
.
∀ x13 :
ι → ι
.
∀ x14 x15 :
ι →
ι →
ι →
ι → ι
.
∀ x16 :
ι → ι
.
∀ x17 :
ι → ο
.
∀ x18 x19 .
∀ x20 :
ι →
ι →
ι → ι
.
∀ x21 :
ι →
ι →
ι →
ι → ι
.
∀ x22 x23 :
ι → ο
.
∀ x24 :
ι →
ι → ο
.
∀ x25 x26 :
ι → ι
.
∀ x27 .
∀ x28 :
ι →
ι → ι
.
∀ x29 :
ι →
ι →
ι → ι
.
∀ x30 x31 x32 :
ι → ι
.
∀ x33 x34 x35 x36 .
∀ x37 :
ι →
ι → ο
.
∀ x38 :
ι → ο
.
∀ x39 :
ι →
ι → ι
.
∀ x40 x41 :
ι →
ι →
ι → ι
.
∀ x42 x43 .
∀ x44 :
ι → ι
.
∀ x45 :
ι →
ι →
ι →
ι → ι
.
∀ x46 :
ι →
ι → ι
.
∀ x47 x48 :
ι → ι
.
∀ x49 x50 :
ι → ο
.
∀ x51 :
ι → ι
.
∀ x52 :
ι →
ι → ι
.
∀ x53 .
∀ x54 :
ι →
ι →
ι → ι
.
∀ x55 x56 :
ι →
ι → ο
.
∀ x57 .
∀ x58 :
ι → ο
.
(
∀ x59 x60 .
x58
x60
⟶
(
x60
=
x59
⟶
False
)
⟶
x58
x59
⟶
False
)
⟶
(
∀ x59 x60 .
x0
x59
x60
⟶
x58
x60
⟶
False
)
⟶
(
∀ x59 .
x58
x59
⟶
(
x59
=
x57
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
x0
x59
x60
⟶
x2
x60
(
x1
x61
)
⟶
x58
x61
⟶
False
)
⟶
(
∀ x59 x60 x61 .
x0
x60
x61
⟶
x2
x61
(
x1
x59
)
⟶
(
x2
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x3
x60
x59
⟶
(
x2
x60
(
x1
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x2
x60
(
x1
x59
)
⟶
(
x3
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
x0
x60
x61
⟶
x0
x59
x61
⟶
x0
x59
(
x4
x61
x60
)
⟶
False
)
⟶
(
∀ x59 x60 .
x0
x60
x59
⟶
(
x0
(
x4
x59
x60
)
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x2
x59
x60
⟶
(
x58
x60
⟶
False
)
⟶
(
x0
x59
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x0
x60
x59
⟶
(
x2
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
x10
x60
x59
(
x9
x59
x60
)
=
x8
x60
x59
(
x9
x59
x60
)
⟶
(
x7
x59
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
x10
x60
x59
(
x9
x59
x60
)
=
x8
x60
x59
(
x9
x59
x60
)
⟶
(
x56
x59
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
(
x2
(
x9
x59
x60
)
(
x13
x60
)
⟶
False
)
⟶
(
x7
x59
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
(
x2
(
x9
x59
x60
)
(
x13
x60
)
⟶
False
)
⟶
(
x56
x59
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x12
x61
⟶
x6
x61
⟶
x11
x61
⟶
x7
x60
x61
⟶
x56
x60
x61
⟶
x7
x60
x61
⟶
x2
x59
(
x13
x61
)
⟶
(
x10
x61
x60
x59
=
x8
x61
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 x63 .
(
x5
x63
⟶
False
)
⟶
x12
x63
⟶
x6
x63
⟶
x11
x63
⟶
x2
x62
(
x13
x63
)
⟶
x7
x59
x63
⟶
x2
x61
(
x13
x63
)
⟶
x60
=
x54
x63
x61
x62
⟶
x55
x59
x61
⟶
(
x0
x60
(
x8
x63
x59
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x12
x62
⟶
x6
x62
⟶
x11
x62
⟶
x2
x61
(
x13
x62
)
⟶
x7
x59
x62
⟶
x0
x60
(
x8
x62
x59
x61
)
⟶
(
x55
x59
(
x14
x59
x61
x62
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x12
x62
⟶
x6
x62
⟶
x11
x62
⟶
x2
x61
(
x13
x62
)
⟶
x7
x59
x62
⟶
x0
x60
(
x8
x62
x59
x61
)
⟶
(
x60
=
x54
x62
(
x14
x59
x61
x62
x60
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x12
x62
⟶
x6
x62
⟶
x11
x62
⟶
x2
x61
(
x13
x62
)
⟶
x7
x59
x62
⟶
x0
x60
(
x8
x62
x59
x61
)
⟶
(
x2
(
x14
x59
x61
x62
x60
)
(
x13
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 x63 .
(
x5
x63
⟶
False
)
⟶
x12
x63
⟶
x6
x63
⟶
x11
x63
⟶
x2
x62
(
x13
x63
)
⟶
x7
x59
x63
⟶
x2
x61
(
x13
x63
)
⟶
x60
=
x54
x63
x62
x61
⟶
x55
x59
x61
⟶
(
x0
x60
(
x10
x63
x59
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x12
x62
⟶
x6
x62
⟶
x11
x62
⟶
x2
x61
(
x13
x62
)
⟶
x7
x59
x62
⟶
x0
x60
(
x10
x62
x59
x61
)
⟶
(
x55
x59
(
x15
x59
x61
x62
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x12
x62
⟶
x6
x62
⟶
x11
x62
⟶
x2
x61
(
x13
x62
)
⟶
x7
x59
x62
⟶
x0
x60
(
x10
x62
x59
x61
)
⟶
(
x60
=
x54
x62
x61
(
x15
x59
x61
x62
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x12
x62
⟶
x6
x62
⟶
x11
x62
⟶
x2
x61
(
x13
x62
)
⟶
x7
x59
x62
⟶
x0
x60
(
x10
x62
x59
x61
)
⟶
(
x2
(
x15
x59
x61
x62
x60
)
(
x13
x62
)
⟶
False
)
⟶
False
)
⟶
(
x58
x53
⟶
False
)
⟶
(
∀ x59 .
(
x3
x59
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x58
x60
⟶
False
)
⟶
x2
x59
x60
⟶
(
x52
x60
x59
=
x51
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x5
x59
⟶
False
)
⟶
x17
x59
⟶
x58
(
x16
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x5
x59
⟶
False
)
⟶
x17
x59
⟶
(
x2
(
x16
x59
)
(
x1
(
x13
x59
)
)
⟶
False
)
⟶
False
)
⟶
(
x58
x18
⟶
False
)
⟶
(
∀ x59 .
(
x50
x59
⟶
False
)
⟶
x17
x59
⟶
x49
(
x48
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x50
x59
⟶
False
)
⟶
x17
x59
⟶
(
x2
(
x48
x59
)
(
x1
(
x13
x59
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x5
x59
⟶
False
)
⟶
x17
x59
⟶
(
x49
(
x47
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x5
x59
⟶
False
)
⟶
x17
x59
⟶
x58
(
x47
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x5
x59
⟶
False
)
⟶
x17
x59
⟶
(
x2
(
x47
x59
)
(
x1
(
x13
x59
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x58
x19
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x2
x59
(
x13
x60
)
⟶
(
x46
x60
(
x46
x60
x59
)
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 x63 x64 .
(
x5
x64
⟶
False
)
⟶
x11
x64
⟶
x2
x63
(
x1
(
x13
x64
)
)
⟶
x2
x59
(
x1
(
x13
x64
)
)
⟶
x2
x62
(
x13
x64
)
⟶
x2
x60
(
x13
x64
)
⟶
x61
=
x54
x64
x62
x60
⟶
x0
x62
x63
⟶
x0
x60
x59
⟶
(
x0
x61
(
x20
x64
x63
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x11
x62
⟶
x2
x61
(
x1
(
x13
x62
)
)
⟶
x2
x59
(
x1
(
x13
x62
)
)
⟶
x0
x60
(
x20
x62
x61
x59
)
⟶
(
x0
(
x45
x59
x61
x62
x60
)
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x11
x62
⟶
x2
x61
(
x1
(
x13
x62
)
)
⟶
x2
x59
(
x1
(
x13
x62
)
)
⟶
x0
x60
(
x20
x62
x61
x59
)
⟶
(
x0
(
x21
x59
x61
x62
x60
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x11
x62
⟶
x2
x61
(
x1
(
x13
x62
)
)
⟶
x2
x59
(
x1
(
x13
x62
)
)
⟶
x0
x60
(
x20
x62
x61
x59
)
⟶
(
x60
=
x54
x62
(
x21
x59
x61
x62
x60
)
(
x45
x59
x61
x62
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x11
x62
⟶
x2
x61
(
x1
(
x13
x62
)
)
⟶
x2
x59
(
x1
(
x13
x62
)
)
⟶
x0
x60
(
x20
x62
x61
x59
)
⟶
(
x2
(
x45
x59
x61
x62
x60
)
(
x13
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x5
x62
⟶
False
)
⟶
x11
x62
⟶
x2
x61
(
x1
(
x13
x62
)
)
⟶
x2
x59
(
x1
(
x13
x62
)
)
⟶
x0
x60
(
x20
x62
x61
x59
)
⟶
(
x2
(
x21
x59
x61
x62
x60
)
(
x13
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x22
x59
⟶
False
)
⟶
x17
x59
⟶
x23
(
x13
x59
)
⟶
False
)
⟶
(
∀ x59 .
x22
x59
⟶
x17
x59
⟶
(
x23
(
x13
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x50
x59
⟶
x17
x59
⟶
(
x49
(
x13
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x50
x59
⟶
False
)
⟶
x17
x59
⟶
x49
(
x13
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x5
x59
⟶
False
)
⟶
x12
x59
⟶
x6
x59
⟶
x11
x59
⟶
x24
(
x25
x59
)
x59
⟶
False
)
⟶
(
∀ x59 .
x58
(
x51
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x5
x59
⟶
False
)
⟶
x17
x59
⟶
x58
(
x13
x59
)
⟶
False
)
⟶
(
(
x58
x57
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x5
x59
⟶
x17
x59
⟶
(
x58
(
x13
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x2
(
x44
x59
)
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x5
x59
⟶
False
)
⟶
x12
x59
⟶
x11
x59
⟶
(
x7
(
x26
x59
)
x59
⟶
False
)
⟶
False
)
⟶
(
(
x11
x43
⟶
False
)
⟶
False
)
⟶
(
(
x17
x27
⟶
False
)
⟶
False
)
⟶
(
(
x58
x42
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
(
x11
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
(
x12
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
x5
x59
⟶
False
)
⟶
(
∀ x59 .
x11
x59
⟶
(
x17
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
(
x2
(
x28
x60
x59
)
(
x1
(
x13
x60
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x58
x60
⟶
False
)
⟶
x2
x59
x60
⟶
(
x2
(
x52
x60
x59
)
(
x1
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
x11
x61
⟶
x2
x59
(
x13
x61
)
⟶
x2
x60
(
x13
x61
)
⟶
(
x2
(
x54
x61
x59
x60
)
(
x13
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x11
x61
⟶
x2
x60
(
x13
x61
)
⟶
x2
x59
(
x1
(
x13
x61
)
)
⟶
(
x2
(
x41
x61
x60
x59
)
(
x1
(
x13
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x11
x61
⟶
x2
x60
(
x13
x61
)
⟶
x2
x59
(
x1
(
x13
x61
)
)
⟶
(
x2
(
x29
x61
x60
x59
)
(
x1
(
x13
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x11
x61
⟶
x2
x60
(
x1
(
x13
x61
)
)
⟶
x2
x59
(
x1
(
x13
x61
)
)
⟶
(
x2
(
x40
x61
x60
x59
)
(
x1
(
x13
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x2
x59
(
x13
x60
)
⟶
(
x2
(
x46
x60
x59
)
(
x13
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x11
x59
⟶
(
x2
(
x25
x59
)
(
x13
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x12
x61
⟶
x6
x61
⟶
x11
x61
⟶
x7
x60
x61
⟶
x2
x59
(
x13
x61
)
⟶
(
x2
(
x8
x61
x60
x59
)
(
x1
(
x13
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x12
x61
⟶
x6
x61
⟶
x11
x61
⟶
x7
x60
x61
⟶
x2
x59
(
x13
x61
)
⟶
(
x2
(
x10
x61
x60
x59
)
(
x1
(
x13
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
(
x28
x60
x59
=
x13
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x12
x61
⟶
x6
x61
⟶
x11
x61
⟶
x2
x60
(
x13
x61
)
⟶
x2
x59
(
x13
x61
)
⟶
x54
x61
x60
x59
=
x25
x61
⟶
x54
x61
x59
x60
=
x25
x61
⟶
(
x59
=
x46
x61
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x12
x61
⟶
x6
x61
⟶
x11
x61
⟶
x2
x60
(
x13
x61
)
⟶
x2
x59
(
x13
x61
)
⟶
x59
=
x46
x61
x60
⟶
(
x54
x61
x59
x60
=
x25
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x12
x61
⟶
x6
x61
⟶
x11
x61
⟶
x2
x60
(
x13
x61
)
⟶
x2
x59
(
x13
x61
)
⟶
x59
=
x46
x61
x60
⟶
(
x54
x61
x60
x59
=
x25
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x11
x61
⟶
x2
x60
(
x13
x61
)
⟶
x2
x59
(
x1
(
x13
x61
)
)
⟶
(
x41
x61
x60
x59
=
x40
x61
x59
(
x52
(
x13
x61
)
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x11
x60
⟶
x38
x60
⟶
x2
x59
(
x13
x60
)
⟶
x54
x60
(
x39
x59
x60
)
x59
=
x39
x59
x60
⟶
x54
x60
x59
(
x39
x59
x60
)
=
x39
x59
x60
⟶
(
x59
=
x25
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x11
x60
⟶
x38
x60
⟶
x2
x59
(
x13
x60
)
⟶
(
x2
(
x39
x59
x60
)
(
x13
x60
)
⟶
False
)
⟶
(
x59
=
x25
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
x11
x61
⟶
x38
x61
⟶
x2
x60
(
x13
x61
)
⟶
x60
=
x25
x61
⟶
x2
x59
(
x13
x61
)
⟶
(
x54
x61
x60
x59
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
x11
x61
⟶
x38
x61
⟶
x2
x60
(
x13
x61
)
⟶
x60
=
x25
x61
⟶
x2
x59
(
x13
x61
)
⟶
(
x54
x61
x59
x60
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x11
x61
⟶
x2
x60
(
x13
x61
)
⟶
x2
x59
(
x1
(
x13
x61
)
)
⟶
(
x29
x61
x60
x59
=
x40
x61
(
x52
(
x13
x61
)
x60
)
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x11
x59
⟶
x54
x59
(
x54
x59
(
x32
x59
)
(
x30
x59
)
)
(
x31
x59
)
=
x54
x59
(
x32
x59
)
(
x54
x59
(
x30
x59
)
(
x31
x59
)
)
⟶
(
x6
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x11
x59
⟶
(
x2
(
x31
x59
)
(
x13
x59
)
⟶
False
)
⟶
(
x6
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x11
x59
⟶
(
x2
(
x30
x59
)
(
x13
x59
)
⟶
False
)
⟶
(
x6
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x11
x59
⟶
(
x2
(
x32
x59
)
(
x13
x59
)
⟶
False
)
⟶
(
x6
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
x11
x62
⟶
x6
x62
⟶
x2
x61
(
x13
x62
)
⟶
x2
x59
(
x13
x62
)
⟶
x2
x60
(
x13
x62
)
⟶
(
x54
x62
(
x54
x62
x61
x59
)
x60
=
x54
x62
x61
(
x54
x62
x59
x60
)
⟶
False
)
⟶
False
)
⟶
(
(
x57
=
x42
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x11
x61
⟶
x2
x60
(
x1
(
x13
x61
)
)
⟶
x2
x59
(
x1
(
x13
x61
)
)
⟶
(
x40
x61
x60
x59
=
x20
x61
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x12
x61
⟶
x6
x61
⟶
x11
x61
⟶
x7
x60
x61
⟶
x2
x59
(
x13
x61
)
⟶
(
x8
x61
x60
x59
=
x41
x61
x59
(
x28
x61
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x5
x61
⟶
False
)
⟶
x12
x61
⟶
x6
x61
⟶
x11
x61
⟶
x7
x60
x61
⟶
x2
x59
(
x13
x61
)
⟶
(
x10
x61
x60
x59
=
x29
x61
x59
(
x28
x61
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
x37
x59
x57
⟶
(
x5
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
x5
x59
⟶
(
x37
x59
x57
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
(
x22
x59
⟶
False
)
⟶
x50
x59
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
x50
x59
⟶
(
x22
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
(
x22
x59
⟶
False
)
⟶
x22
x59
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
(
x22
x59
⟶
False
)
⟶
x5
x59
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
x5
x59
⟶
(
x22
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
x5
x59
⟶
(
x5
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x22
x60
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
(
x22
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
(
x50
x59
⟶
False
)
⟶
x5
x59
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
x5
x59
⟶
(
x50
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x5
x60
⟶
False
)
⟶
x12
x60
⟶
x6
x60
⟶
x11
x60
⟶
x7
x59
x60
⟶
(
x6
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x11
x59
⟶
x12
x59
⟶
(
x38
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
(
x50
x59
⟶
False
)
⟶
x5
x59
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
x37
x59
x53
⟶
(
x50
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
x37
x59
x53
⟶
x5
x59
⟶
False
)
⟶
(
∀ x59 .
x17
x59
⟶
(
x5
x59
⟶
False
)
⟶
x50
x59
⟶
(
x37
x59
x53
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x0
x59
x60
⟶
x0
x60
x59
⟶
False
)
⟶
(
x55
x36
(
x54
x33
(
x54
x33
x35
x34
)
(
x46
x33
x35
)
)
⟶
False
)
⟶
(
(
x55
x36
x34
⟶
False
)
⟶
False
)
⟶
(
(
x7
x36
x33
⟶
False
)
⟶
False
)
⟶
(
(
x56
x36
x33
⟶
False
)
⟶
False
)
⟶
(
(
x2
x34
(
x13
x33
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x35
(
x13
x33
)
⟶
False
)
⟶
False
)
⟶
(
(
x11
x33
⟶
False
)
⟶
False
)
⟶
(
(
x6
x33
⟶
False
)
⟶
False
)
⟶
(
(
x12
x33
⟶
False
)
⟶
False
)
⟶
(
x5
x33
⟶
False
)
⟶
False
(proof)