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Proofgold Asset
asset id
8e057c9981fe871ae71ac1e727636fd38032281e2aff585c43f372ce9d8e3c72
asset hash
a51675906ceb45891bce93690808cf3f95c126e54c4e5597acd61560f62cc5be
bday / block
35125
tx
173db..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
cfb4a..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 x3 :
ι →
ι → ο
.
∀ x4 :
ι →
ι → ι
.
∀ x5 .
∀ x6 :
ι → ο
.
∀ x7 :
ι → ι
.
∀ x8 x9 x10 :
ι →
ι → ι
.
∀ x11 :
ι → ι
.
∀ x12 :
ι → ο
.
∀ x13 .
∀ x14 :
ι → ο
.
∀ x15 .
∀ x16 x17 :
ι → ο
.
∀ x18 x19 :
ι → ι
.
∀ x20 x21 :
ι →
ι →
ι → ι
.
∀ x22 x23 .
∀ x24 :
ι →
ι →
ι →
ι → ο
.
∀ x25 :
ι →
ι → ο
.
∀ x26 :
ι → ο
.
∀ x27 x28 x29 x30 x31 x32 .
∀ x33 :
ι →
ι →
ι →
ι → ι
.
∀ x34 x35 .
∀ x36 :
ι → ι
.
∀ x37 x38 :
ι → ο
.
∀ x39 :
ι →
ι →
ι →
ι → ι
.
∀ x40 .
∀ x41 :
ι → ο
.
∀ x42 .
∀ x43 x44 :
ι →
ι → ι
.
∀ x45 x46 x47 x48 :
ι → ο
.
∀ x49 :
ι →
ι →
ι → ι
.
∀ x50 :
ι →
ι →
ι →
ι →
ι →
ι → ι
.
∀ x51 :
ι →
ι →
ι →
ι → ο
.
∀ x52 :
ι → ι
.
∀ x53 x54 x55 x56 :
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 x61 x62 x63 x64 x65 x66 .
(
x56
x66
⟶
False
)
⟶
(
x45
x66
⟶
False
)
⟶
x55
x66
⟶
x46
x66
⟶
x54
x66
⟶
x47
x66
⟶
x53
x66
⟶
x48
x66
⟶
x2
x65
(
x52
x66
)
⟶
x2
x59
(
x52
x66
)
⟶
x2
x64
(
x52
x66
)
⟶
x2
x60
(
x52
x66
)
⟶
x51
x63
x66
x65
x59
⟶
x51
x61
x66
x59
x64
⟶
x51
x62
x66
x64
x60
⟶
(
x49
x66
x65
x59
=
x57
⟶
False
)
⟶
(
x49
x66
x59
x64
=
x57
⟶
False
)
⟶
(
x49
x66
x64
x60
=
x57
⟶
False
)
⟶
(
x50
x66
x65
x59
x60
x63
(
x50
x66
x59
x64
x60
x61
x62
)
=
x50
x66
x65
x64
x60
(
x50
x66
x65
x59
x64
x63
x61
)
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x55
x62
⟶
x46
x62
⟶
x54
x62
⟶
x47
x62
⟶
x53
x62
⟶
x48
x62
⟶
x2
x61
(
x52
x62
)
⟶
x2
x59
(
x52
x62
)
⟶
x2
x60
(
x52
x62
)
⟶
(
x49
x62
x61
x59
=
x57
⟶
False
)
⟶
(
x49
x62
x59
x60
=
x57
⟶
False
)
⟶
x49
x62
x61
x60
=
x57
⟶
False
)
⟶
(
∀ x59 x60 .
x0
x60
x59
⟶
(
x2
x60
x59
⟶
False
)
⟶
False
)
⟶
(
x58
x5
⟶
False
)
⟶
(
∀ x59 .
(
x3
x59
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x56
x60
⟶
False
)
⟶
(
x45
x60
⟶
False
)
⟶
x6
x60
⟶
x2
x59
(
x7
x60
)
⟶
(
x9
x60
x59
=
x8
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x56
x60
⟶
False
)
⟶
(
x45
x60
⟶
False
)
⟶
x6
x60
⟶
x2
x59
(
x7
x60
)
⟶
(
x43
x60
x59
=
x44
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x56
x60
⟶
False
)
⟶
(
x45
x60
⟶
False
)
⟶
x55
x60
⟶
x46
x60
⟶
x54
x60
⟶
x47
x60
⟶
x53
x60
⟶
x48
x60
⟶
x2
x59
(
x52
x60
)
⟶
(
x9
x60
(
x10
x60
x59
)
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x56
x60
⟶
False
)
⟶
(
x45
x60
⟶
False
)
⟶
x55
x60
⟶
x46
x60
⟶
x54
x60
⟶
x47
x60
⟶
x53
x60
⟶
x48
x60
⟶
x2
x59
(
x52
x60
)
⟶
(
x43
x60
(
x10
x60
x59
)
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x56
x61
⟶
False
)
⟶
(
x45
x61
⟶
False
)
⟶
x55
x61
⟶
x46
x61
⟶
x54
x61
⟶
x47
x61
⟶
x53
x61
⟶
x48
x61
⟶
x2
x60
(
x52
x61
)
⟶
x51
x59
x61
x60
x60
⟶
(
x50
x61
x60
x60
x60
x59
(
x10
x61
x60
)
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x56
x61
⟶
False
)
⟶
(
x45
x61
⟶
False
)
⟶
x55
x61
⟶
x46
x61
⟶
x54
x61
⟶
x47
x61
⟶
x53
x61
⟶
x48
x61
⟶
x2
x60
(
x52
x61
)
⟶
x51
x59
x61
x60
x60
⟶
(
x50
x61
x60
x60
x60
(
x10
x61
x60
)
x59
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x56
x59
⟶
False
)
⟶
x12
x59
⟶
x58
(
x11
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x56
x59
⟶
False
)
⟶
x12
x59
⟶
(
x2
(
x11
x59
)
(
x1
(
x52
x59
)
)
⟶
False
)
⟶
False
)
⟶
(
x58
x13
⟶
False
)
⟶
(
x45
x42
⟶
False
)
⟶
(
x56
x42
⟶
False
)
⟶
(
(
x48
x42
⟶
False
)
⟶
False
)
⟶
(
x14
x15
⟶
False
)
⟶
(
(
x41
x15
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x16
x59
⟶
False
)
⟶
x12
x59
⟶
x17
(
x18
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x16
x59
⟶
False
)
⟶
x12
x59
⟶
(
x2
(
x18
x59
)
(
x1
(
x52
x59
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x56
x59
⟶
False
)
⟶
x12
x59
⟶
(
x17
(
x19
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x56
x59
⟶
False
)
⟶
x12
x59
⟶
x58
(
x19
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x56
x59
⟶
False
)
⟶
x12
x59
⟶
(
x2
(
x19
x59
)
(
x1
(
x52
x59
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x58
x40
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 x63 .
(
x56
x63
⟶
False
)
⟶
(
x45
x63
⟶
False
)
⟶
x48
x63
⟶
x2
x59
(
x52
x63
)
⟶
x2
x62
(
x52
x63
)
⟶
x2
x60
(
x7
x63
)
⟶
x61
=
x60
⟶
x43
x63
x60
=
x59
⟶
x9
x63
x60
=
x62
⟶
(
x0
x61
(
x20
x63
x59
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x48
x62
⟶
x2
x59
(
x52
x62
)
⟶
x2
x61
(
x52
x62
)
⟶
x0
x60
(
x20
x62
x59
x61
)
⟶
(
x9
x62
(
x39
x61
x59
x62
x60
)
=
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x48
x62
⟶
x2
x59
(
x52
x62
)
⟶
x2
x61
(
x52
x62
)
⟶
x0
x60
(
x20
x62
x59
x61
)
⟶
(
x43
x62
(
x39
x61
x59
x62
x60
)
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x48
x62
⟶
x2
x59
(
x52
x62
)
⟶
x2
x61
(
x52
x62
)
⟶
x0
x60
(
x20
x62
x59
x61
)
⟶
(
x60
=
x39
x61
x59
x62
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x48
x62
⟶
x2
x59
(
x52
x62
)
⟶
x2
x61
(
x52
x62
)
⟶
x0
x60
(
x20
x62
x59
x61
)
⟶
(
x2
(
x39
x61
x59
x62
x60
)
(
x7
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x38
x59
⟶
False
)
⟶
x12
x59
⟶
x37
(
x52
x59
)
⟶
False
)
⟶
(
∀ x59 .
x38
x59
⟶
x12
x59
⟶
(
x37
(
x52
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x16
x59
⟶
x12
x59
⟶
(
x17
(
x52
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x16
x59
⟶
False
)
⟶
x12
x59
⟶
x17
(
x52
x59
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x56
x60
⟶
False
)
⟶
(
x45
x60
⟶
False
)
⟶
x47
x60
⟶
x48
x60
⟶
x2
x59
(
x52
x60
)
⟶
x58
(
x49
x60
x59
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x56
x59
⟶
False
)
⟶
x12
x59
⟶
x58
(
x52
x59
)
⟶
False
)
⟶
(
∀ x59 .
(
x14
x59
⟶
False
)
⟶
x41
x59
⟶
x17
(
x7
x59
)
⟶
False
)
⟶
(
∀ x59 .
x14
x59
⟶
x41
x59
⟶
(
x17
(
x7
x59
)
⟶
False
)
⟶
False
)
⟶
(
(
x58
x57
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x56
x59
⟶
x12
x59
⟶
(
x58
(
x52
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x45
x59
⟶
False
)
⟶
x41
x59
⟶
x58
(
x7
x59
)
⟶
False
)
⟶
(
∀ x59 .
x45
x59
⟶
x41
x59
⟶
(
x58
(
x7
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
(
x2
(
x36
x59
)
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x56
x61
⟶
False
)
⟶
(
x45
x61
⟶
False
)
⟶
x48
x61
⟶
x2
x59
(
x52
x61
)
⟶
x2
x60
(
x52
x61
)
⟶
(
x51
(
x21
x60
x59
x61
)
x61
x59
x60
⟶
False
)
⟶
False
)
⟶
(
(
x41
x35
⟶
False
)
⟶
False
)
⟶
(
(
x12
x22
⟶
False
)
⟶
False
)
⟶
(
(
x6
x34
⟶
False
)
⟶
False
)
⟶
(
(
x48
x23
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x48
x62
⟶
x2
x59
(
x52
x62
)
⟶
x2
x61
(
x52
x62
)
⟶
x51
x60
x62
x59
x61
⟶
(
x2
x60
(
x7
x62
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x41
x59
⟶
(
x12
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x6
x59
⟶
(
x41
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x6
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 x63 x64 .
(
x56
x64
⟶
False
)
⟶
(
x45
x64
⟶
False
)
⟶
x55
x64
⟶
x46
x64
⟶
x54
x64
⟶
x47
x64
⟶
x53
x64
⟶
x48
x64
⟶
x2
x63
(
x52
x64
)
⟶
x2
x59
(
x52
x64
)
⟶
x2
x62
(
x52
x64
)
⟶
x51
x60
x64
x63
x59
⟶
x51
x61
x64
x59
x62
⟶
(
x51
(
x50
x64
x63
x59
x62
x60
x61
)
x64
x63
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x56
x60
⟶
False
)
⟶
(
x45
x60
⟶
False
)
⟶
x6
x60
⟶
x2
x59
(
x7
x60
)
⟶
(
x2
(
x9
x60
x59
)
(
x52
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x56
x60
⟶
False
)
⟶
(
x45
x60
⟶
False
)
⟶
x47
x60
⟶
x53
x60
⟶
x48
x60
⟶
x2
x59
(
x52
x60
)
⟶
(
x51
(
x10
x60
x59
)
x60
x59
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
(
x56
x60
⟶
False
)
⟶
(
x45
x60
⟶
False
)
⟶
x6
x60
⟶
x2
x59
(
x7
x60
)
⟶
(
x2
(
x43
x60
x59
)
(
x52
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x6
x60
⟶
x2
x59
(
x7
x60
)
⟶
(
x2
(
x8
x60
x59
)
(
x52
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x56
x61
⟶
False
)
⟶
(
x45
x61
⟶
False
)
⟶
x48
x61
⟶
x2
x59
(
x52
x61
)
⟶
x2
x60
(
x52
x61
)
⟶
(
x2
(
x49
x61
x59
x60
)
(
x1
(
x7
x61
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x6
x60
⟶
x2
x59
(
x7
x60
)
⟶
(
x2
(
x44
x60
x59
)
(
x52
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 x63 .
(
x56
x63
⟶
False
)
⟶
(
x45
x63
⟶
False
)
⟶
x55
x63
⟶
x46
x63
⟶
x54
x63
⟶
x47
x63
⟶
x53
x63
⟶
x48
x63
⟶
x2
x62
(
x52
x63
)
⟶
x2
x59
(
x52
x63
)
⟶
x51
x61
x63
x62
x59
⟶
(
x49
x63
x62
x59
=
x57
⟶
False
)
⟶
(
x49
x63
x59
x62
=
x57
⟶
False
)
⟶
x51
x60
x63
x59
x62
⟶
x50
x63
x62
x59
x62
x61
x60
=
x10
x63
x62
⟶
(
x24
x61
x63
x62
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x55
x62
⟶
x46
x62
⟶
x54
x62
⟶
x47
x62
⟶
x53
x62
⟶
x48
x62
⟶
x2
x61
(
x52
x62
)
⟶
x2
x59
(
x52
x62
)
⟶
x51
x60
x62
x61
x59
⟶
x24
x60
x62
x61
x59
⟶
(
x50
x62
x61
x59
x61
x60
(
x33
x60
x59
x61
x62
)
=
x10
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x55
x62
⟶
x46
x62
⟶
x54
x62
⟶
x47
x62
⟶
x53
x62
⟶
x48
x62
⟶
x2
x61
(
x52
x62
)
⟶
x2
x59
(
x52
x62
)
⟶
x51
x60
x62
x61
x59
⟶
x24
x60
x62
x61
x59
⟶
(
x51
(
x33
x60
x59
x61
x62
)
x62
x59
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x55
x62
⟶
x46
x62
⟶
x54
x62
⟶
x47
x62
⟶
x53
x62
⟶
x48
x62
⟶
x2
x61
(
x52
x62
)
⟶
x2
x59
(
x52
x62
)
⟶
x51
x60
x62
x61
x59
⟶
x24
x60
x62
x61
x59
⟶
x49
x62
x59
x61
=
x57
⟶
False
)
⟶
(
∀ x59 x60 x61 x62 .
(
x56
x62
⟶
False
)
⟶
(
x45
x62
⟶
False
)
⟶
x55
x62
⟶
x46
x62
⟶
x54
x62
⟶
x47
x62
⟶
x53
x62
⟶
x48
x62
⟶
x2
x61
(
x52
x62
)
⟶
x2
x59
(
x52
x62
)
⟶
x51
x60
x62
x61
x59
⟶
x24
x60
x62
x61
x59
⟶
x49
x62
x61
x59
=
x57
⟶
False
)
⟶
(
∀ x59 x60 x61 .
(
x56
x61
⟶
False
)
⟶
(
x45
x61
⟶
False
)
⟶
x48
x61
⟶
x2
x59
(
x52
x61
)
⟶
x2
x60
(
x52
x61
)
⟶
(
x49
x61
x59
x60
=
x20
x61
x59
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
x25
x59
x57
⟶
(
x56
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
x56
x59
⟶
(
x25
x59
x57
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
(
x38
x59
⟶
False
)
⟶
x16
x59
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
x16
x59
⟶
(
x38
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
(
x38
x59
⟶
False
)
⟶
x38
x59
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
(
x38
x59
⟶
False
)
⟶
x56
x59
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
x56
x59
⟶
(
x38
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
x56
x59
⟶
(
x56
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
(
x16
x59
⟶
False
)
⟶
x56
x59
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x56
x59
⟶
False
)
⟶
(
x45
x59
⟶
False
)
⟶
x14
x59
⟶
(
x53
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x56
x59
⟶
False
)
⟶
(
x45
x59
⟶
False
)
⟶
x14
x59
⟶
(
x54
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x56
x59
⟶
False
)
⟶
(
x45
x59
⟶
False
)
⟶
x14
x59
⟶
x45
x59
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x56
x59
⟶
False
)
⟶
(
x45
x59
⟶
False
)
⟶
x14
x59
⟶
x56
x59
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
x56
x59
⟶
(
x16
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x56
x59
⟶
False
)
⟶
x16
x59
⟶
(
x45
x59
⟶
False
)
⟶
(
x47
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x56
x59
⟶
False
)
⟶
x16
x59
⟶
(
x45
x59
⟶
False
)
⟶
(
x46
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x56
x59
⟶
False
)
⟶
x16
x59
⟶
(
x45
x59
⟶
False
)
⟶
x45
x59
⟶
False
)
⟶
(
∀ x59 .
x48
x59
⟶
(
x56
x59
⟶
False
)
⟶
x16
x59
⟶
(
x45
x59
⟶
False
)
⟶
x56
x59
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
(
x16
x59
⟶
False
)
⟶
x56
x59
⟶
False
)
⟶
(
∀ x59 .
x41
x59
⟶
x45
x59
⟶
(
x14
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x41
x59
⟶
(
x45
x59
⟶
False
)
⟶
x26
x59
⟶
x56
x59
⟶
False
)
⟶
(
∀ x59 .
x41
x59
⟶
x56
x59
⟶
x26
x59
⟶
(
x45
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x41
x59
⟶
x45
x59
⟶
(
x26
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x41
x59
⟶
(
x56
x59
⟶
False
)
⟶
(
x26
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
x25
x59
x5
⟶
(
x16
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
x25
x59
x5
⟶
x56
x59
⟶
False
)
⟶
(
∀ x59 .
x12
x59
⟶
(
x56
x59
⟶
False
)
⟶
x16
x59
⟶
(
x25
x59
x5
⟶
False
)
⟶
False
)
⟶
(
∀ x59 x60 .
x0
x59
x60
⟶
x0
x60
x59
⟶
False
)
⟶
(
x24
x27
x30
x29
x28
⟶
False
)
⟶
(
x49
x30
x32
x28
=
x57
⟶
False
)
⟶
(
x49
x30
x28
x32
=
x57
⟶
False
)
⟶
(
(
x24
(
x50
x30
x29
x28
x32
x27
x31
)
x30
x29
x32
⟶
False
)
⟶
False
)
⟶
(
(
x51
x31
x30
x28
x32
⟶
False
)
⟶
False
)
⟶
(
(
x51
x27
x30
x29
x28
⟶
False
)
⟶
False
)
⟶
(
(
x2
x32
(
x52
x30
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x28
(
x52
x30
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x29
(
x52
x30
)
⟶
False
)
⟶
False
)
⟶
(
(
x48
x30
⟶
False
)
⟶
False
)
⟶
(
(
x53
x30
⟶
False
)
⟶
False
)
⟶
(
(
x47
x30
⟶
False
)
⟶
False
)
⟶
(
(
x54
x30
⟶
False
)
⟶
False
)
⟶
(
(
x46
x30
⟶
False
)
⟶
False
)
⟶
(
(
x55
x30
⟶
False
)
⟶
False
)
⟶
(
x45
x30
⟶
False
)
⟶
(
x56
x30
⟶
False
)
⟶
False
(proof)