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Proofgold Asset
asset id
92fff7d23617eb2e3f0ee95de516bd5eb989128f8cf12aa16b72020dfde6d69c
asset hash
38e03035ed214f3b25df34561b90dd42634b6c5966a28ddaeecd7f42d658989b
bday / block
35129
tx
31a5f..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
a3320..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 :
ι →
ι → ο
.
∀ x3 .
∀ x4 :
ι →
ι → ι
.
∀ x5 :
ι →
ι → ο
.
∀ x6 x7 :
ι → ο
.
∀ x8 :
ι → ι
.
∀ x9 :
ι → ο
.
∀ x10 :
ι →
ι → ι
.
∀ x11 .
∀ x12 :
ι → ο
.
∀ x13 x14 :
ι → ι
.
∀ x15 x16 :
ι →
ι → ι
.
∀ x17 .
∀ x18 x19 :
ι → ο
.
∀ x20 .
∀ x21 :
ι →
ι → ο
.
∀ x22 x23 x24 x25 x26 .
∀ x27 :
ι →
ι → ο
.
∀ x28 .
∀ x29 :
ι → ι
.
∀ x30 :
ι →
ι → ι
.
∀ x31 x32 .
∀ x33 :
ι → ο
.
∀ x34 :
ι →
ι → ο
.
∀ x35 :
ι → ι
.
∀ x36 .
∀ x37 :
ι → ο
.
∀ x38 :
ι →
ι → ο
.
∀ x39 :
ι →
ι → ι
.
∀ x40 .
∀ x41 :
ι → ο
.
∀ x42 :
ι →
ι →
ι → ι
.
∀ x43 :
ι →
ι → ο
.
∀ x44 :
ι → ο
.
∀ x45 :
ι → ι
.
∀ x46 :
ι →
ι →
ι → ο
.
∀ x47 :
ι →
ι → ι
.
∀ x48 :
ι →
ι →
ι →
ι → ι
.
∀ x49 x50 :
ι →
ι →
ι →
ι → ο
.
∀ x51 :
ι →
ι → ο
.
∀ x52 :
ι →
ι →
ι → ο
.
∀ x53 x54 x55 :
ι → ο
.
∀ x56 .
∀ x57 :
ι → ο
.
(
∀ x58 x59 .
x57
x59
⟶
(
x59
=
x58
⟶
False
)
⟶
x57
x58
⟶
False
)
⟶
(
∀ x58 x59 .
x0
x58
x59
⟶
x57
x59
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
(
x58
=
x56
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x0
x58
x59
⟶
x2
x59
(
x1
x60
)
⟶
x57
x60
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 x62 .
(
x55
x62
⟶
False
)
⟶
x44
x62
⟶
x54
x62
⟶
x2
x58
(
x45
x62
)
⟶
x2
x61
(
x45
x62
)
⟶
x2
x59
(
x45
x62
)
⟶
x53
x60
⟶
x46
x60
(
x45
x62
)
(
x45
x62
)
⟶
x52
x60
(
x45
x62
)
(
x45
x62
)
⟶
x2
x60
(
x1
(
x47
(
x45
x62
)
(
x45
x62
)
)
)
⟶
x51
x60
x62
⟶
x48
(
x45
x62
)
(
x45
x62
)
x60
x58
=
x58
⟶
x50
x62
x61
x58
(
x48
(
x45
x62
)
(
x45
x62
)
x60
x61
)
⟶
(
x49
x62
x58
x61
x59
⟶
False
)
⟶
(
x50
x62
x59
x58
(
x48
(
x45
x62
)
(
x45
x62
)
x60
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x0
x59
x60
⟶
x2
x60
(
x1
x58
)
⟶
(
x2
x59
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x43
x59
x58
⟶
(
x2
x59
(
x1
x58
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x2
x59
(
x1
x58
)
⟶
(
x43
x59
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x55
x60
⟶
False
)
⟶
x44
x60
⟶
x54
x60
⟶
x2
x58
(
x45
x60
)
⟶
x2
x59
(
x45
x60
)
⟶
(
x58
=
x59
⟶
False
)
⟶
x49
x60
x58
x59
(
x42
x59
x58
x60
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x55
x60
⟶
False
)
⟶
x44
x60
⟶
x54
x60
⟶
x2
x58
(
x45
x60
)
⟶
x2
x59
(
x45
x60
)
⟶
(
x58
=
x59
⟶
False
)
⟶
(
x2
(
x42
x59
x58
x60
)
(
x45
x60
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 x62 x63 .
(
x55
x63
⟶
False
)
⟶
x44
x63
⟶
x54
x63
⟶
x2
x58
(
x45
x63
)
⟶
x2
x62
(
x45
x63
)
⟶
x2
x59
(
x45
x63
)
⟶
x2
x61
(
x45
x63
)
⟶
x2
x60
(
x45
x63
)
⟶
x49
x63
x58
x62
x59
⟶
x49
x63
x58
x62
x61
⟶
x49
x63
x58
x62
x60
⟶
(
x58
=
x62
⟶
False
)
⟶
(
x49
x63
x59
x61
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x55
x60
⟶
False
)
⟶
x44
x60
⟶
x54
x60
⟶
x2
x58
(
x45
x60
)
⟶
x2
x59
(
x45
x60
)
⟶
(
x49
x60
x58
x59
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x55
x60
⟶
False
)
⟶
x44
x60
⟶
x54
x60
⟶
x2
x58
(
x45
x60
)
⟶
x2
x59
(
x45
x60
)
⟶
(
x49
x60
x58
x59
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x55
x60
⟶
False
)
⟶
x44
x60
⟶
x54
x60
⟶
x2
x58
(
x45
x60
)
⟶
x2
x59
(
x45
x60
)
⟶
(
x49
x60
x58
x58
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 .
(
x55
x61
⟶
False
)
⟶
x44
x61
⟶
x54
x61
⟶
x2
x58
(
x45
x61
)
⟶
x2
x60
(
x45
x61
)
⟶
x2
x59
(
x45
x61
)
⟶
x49
x61
x58
x60
x59
⟶
(
x49
x61
x59
x60
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 .
(
x55
x61
⟶
False
)
⟶
x44
x61
⟶
x54
x61
⟶
x2
x58
(
x45
x61
)
⟶
x2
x60
(
x45
x61
)
⟶
x2
x59
(
x45
x61
)
⟶
x49
x61
x58
x60
x59
⟶
(
x49
x61
x59
x58
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 .
(
x55
x61
⟶
False
)
⟶
x44
x61
⟶
x54
x61
⟶
x2
x58
(
x45
x61
)
⟶
x2
x60
(
x45
x61
)
⟶
x2
x59
(
x45
x61
)
⟶
x49
x61
x58
x60
x59
⟶
(
x49
x61
x60
x59
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 .
(
x55
x61
⟶
False
)
⟶
x44
x61
⟶
x54
x61
⟶
x2
x58
(
x45
x61
)
⟶
x2
x60
(
x45
x61
)
⟶
x2
x59
(
x45
x61
)
⟶
x49
x61
x58
x60
x59
⟶
(
x49
x61
x60
x58
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 .
(
x55
x61
⟶
False
)
⟶
x44
x61
⟶
x54
x61
⟶
x2
x58
(
x45
x61
)
⟶
x2
x60
(
x45
x61
)
⟶
x2
x59
(
x45
x61
)
⟶
x49
x61
x58
x60
x59
⟶
(
x49
x61
x58
x59
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x2
x58
x59
⟶
(
x57
x59
⟶
False
)
⟶
(
x0
x58
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x0
x59
x58
⟶
(
x2
x59
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x55
x60
⟶
False
)
⟶
x44
x60
⟶
x54
x60
⟶
x2
x58
(
x45
x60
)
⟶
x2
x59
(
x45
x60
)
⟶
(
x50
x60
x58
x59
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x55
x60
⟶
False
)
⟶
x44
x60
⟶
x54
x60
⟶
x2
x58
(
x45
x60
)
⟶
x2
x59
(
x45
x60
)
⟶
(
x50
x60
x58
x58
x59
⟶
False
)
⟶
False
)
⟶
(
x57
x3
⟶
False
)
⟶
(
∀ x58 .
(
x43
x58
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 .
(
x57
x61
⟶
False
)
⟶
x53
x58
⟶
x46
x58
x61
x60
⟶
x2
x58
(
x1
(
x47
x61
x60
)
)
⟶
x2
x59
x61
⟶
(
x48
x61
x60
x58
x59
=
x4
x58
x59
⟶
False
)
⟶
False
)
⟶
(
(
x41
x40
⟶
False
)
⟶
False
)
⟶
(
x57
x40
⟶
False
)
⟶
(
∀ x58 x59 .
(
x53
(
x39
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x5
(
x39
x58
x59
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x38
(
x39
x59
x58
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x6
(
x39
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
x37
x36
⟶
False
)
⟶
(
(
x53
x36
⟶
False
)
⟶
False
)
⟶
(
(
x6
x36
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x7
x58
⟶
False
)
⟶
x9
x58
⟶
x57
(
x8
x58
)
⟶
False
)
⟶
(
∀ x58 .
(
x7
x58
⟶
False
)
⟶
x9
x58
⟶
(
x2
(
x8
x58
)
(
x1
(
x45
x58
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x57
x59
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
x57
(
x10
x58
x59
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x57
x59
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
(
x53
(
x10
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x57
x59
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
(
x5
(
x10
x58
x59
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x57
x59
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
(
x38
(
x10
x58
x59
)
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x57
x59
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
(
x6
(
x10
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x57
x59
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
(
x2
(
x10
x58
x59
)
(
x1
(
x47
x59
x58
)
)
⟶
False
)
⟶
False
)
⟶
(
x57
x11
⟶
False
)
⟶
(
∀ x58 .
(
x52
(
x35
x58
)
x58
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x46
(
x35
x58
)
x58
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x34
(
x35
x58
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x53
(
x35
x58
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x5
(
x35
x58
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x38
(
x35
x58
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x6
(
x35
x58
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x2
(
x35
x58
)
(
x1
(
x47
x58
x58
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x33
x32
⟶
False
)
⟶
False
)
⟶
(
(
x53
x32
⟶
False
)
⟶
False
)
⟶
(
(
x6
x32
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x55
x58
⟶
False
)
⟶
x9
x58
⟶
x12
(
x13
x58
)
⟶
False
)
⟶
(
∀ x58 .
(
x55
x58
⟶
False
)
⟶
x9
x58
⟶
(
x2
(
x13
x58
)
(
x1
(
x45
x58
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x7
x58
⟶
False
)
⟶
x9
x58
⟶
(
x12
(
x14
x58
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x7
x58
⟶
False
)
⟶
x9
x58
⟶
x57
(
x14
x58
)
⟶
False
)
⟶
(
∀ x58 .
(
x7
x58
⟶
False
)
⟶
x9
x58
⟶
(
x2
(
x14
x58
)
(
x1
(
x45
x58
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x57
x31
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x5
(
x15
x58
x59
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x38
(
x15
x59
x58
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x6
(
x15
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x57
(
x15
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x2
(
x15
x58
x59
)
(
x1
(
x47
x59
x58
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x53
(
x30
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x5
(
x30
x58
x59
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x38
(
x30
x59
x58
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x6
(
x30
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x2
(
x30
x58
x59
)
(
x1
(
x47
x59
x58
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x46
(
x16
x58
x59
)
x59
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x53
(
x16
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x5
(
x16
x58
x59
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x38
(
x16
x59
x58
)
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x6
(
x16
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
(
x2
(
x16
x58
x59
)
(
x1
(
x47
x59
x58
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x53
x17
⟶
False
)
⟶
False
)
⟶
(
(
x6
x17
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x18
x58
⟶
False
)
⟶
x9
x58
⟶
x19
(
x45
x58
)
⟶
False
)
⟶
(
∀ x58 .
x18
x58
⟶
x9
x58
⟶
(
x19
(
x45
x58
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x55
x58
⟶
x9
x58
⟶
(
x12
(
x45
x58
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x55
x58
⟶
False
)
⟶
x9
x58
⟶
x12
(
x45
x58
)
⟶
False
)
⟶
(
∀ x58 .
(
x7
x58
⟶
False
)
⟶
x9
x58
⟶
x57
(
x45
x58
)
⟶
False
)
⟶
(
(
x57
x56
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x7
x58
⟶
x9
x58
⟶
(
x57
(
x45
x58
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x41
x60
⟶
x6
x58
⟶
x5
x58
x60
⟶
x53
x58
⟶
(
x53
(
x4
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x41
x60
⟶
x6
x58
⟶
x5
x58
x60
⟶
x53
x58
⟶
(
x6
(
x4
x58
x59
)
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
(
x2
(
x29
x58
)
x58
⟶
False
)
⟶
False
)
⟶
(
(
x9
x20
⟶
False
)
⟶
False
)
⟶
(
(
x54
x28
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x54
x58
⟶
(
x9
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 x61 .
(
x57
x61
⟶
False
)
⟶
x53
x58
⟶
x46
x58
x61
x60
⟶
x2
x58
(
x1
(
x47
x61
x60
)
)
⟶
x2
x59
x61
⟶
(
x2
(
x48
x61
x60
x58
x59
)
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
x21
x58
x56
⟶
(
x7
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x41
x59
⟶
x2
x58
(
x1
x59
)
⟶
(
x41
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
x7
x58
⟶
(
x21
x58
x56
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x57
x60
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
x2
x59
(
x1
(
x47
x60
x58
)
)
⟶
x53
x59
⟶
x46
x59
x60
x58
⟶
(
x46
x59
x60
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x57
x60
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
x2
x59
(
x1
(
x47
x60
x58
)
)
⟶
x53
x59
⟶
x46
x59
x60
x58
⟶
x57
x59
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x57
x60
⟶
False
)
⟶
(
x57
x58
⟶
False
)
⟶
x2
x59
(
x1
(
x47
x60
x58
)
)
⟶
x53
x59
⟶
x46
x59
x60
x58
⟶
(
x53
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x41
x59
⟶
x2
x58
x59
⟶
(
x53
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x41
x59
⟶
x2
x58
x59
⟶
(
x6
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
(
x18
x58
⟶
False
)
⟶
x55
x58
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
(
x41
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
x55
x58
⟶
(
x18
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x60
(
x1
(
x47
x58
x59
)
)
⟶
x53
x60
⟶
x33
x60
⟶
x27
x60
x59
⟶
(
x52
x60
x58
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x60
(
x1
(
x47
x58
x59
)
)
⟶
x53
x60
⟶
x33
x60
⟶
x27
x60
x59
⟶
(
x53
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x12
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x37
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x12
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x53
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x12
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x6
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
(
x18
x58
⟶
False
)
⟶
x18
x58
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
(
x18
x58
⟶
False
)
⟶
x7
x58
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x60
(
x1
(
x47
x59
x58
)
)
⟶
x53
x60
⟶
x52
x60
x59
x58
⟶
(
x27
x60
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x60
(
x1
(
x47
x59
x58
)
)
⟶
x53
x60
⟶
x52
x60
x59
x58
⟶
(
x33
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x60
(
x1
(
x47
x59
x58
)
)
⟶
x53
x60
⟶
x52
x60
x59
x58
⟶
(
x53
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x6
x58
⟶
x53
x58
⟶
(
x37
x58
⟶
False
)
⟶
(
x53
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x6
x58
⟶
x53
x58
⟶
(
x37
x58
⟶
False
)
⟶
(
x6
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x6
x58
⟶
x53
x58
⟶
(
x37
x58
⟶
False
)
⟶
x12
x58
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
x7
x58
⟶
(
x18
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
x7
x58
⟶
(
x7
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x57
x60
⟶
x2
x58
(
x1
(
x47
x59
x60
)
)
⟶
(
x57
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x2
x59
(
x1
(
x47
x58
x58
)
)
⟶
x46
x59
x58
x58
⟶
(
x34
x59
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x37
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x53
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x6
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x57
x60
⟶
x2
x58
(
x1
(
x47
x60
x59
)
)
⟶
(
x57
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x57
x60
⟶
False
)
⟶
x2
x58
(
x1
(
x47
x59
x60
)
)
⟶
x46
x58
x59
x60
⟶
(
x34
x58
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x6
x59
⟶
x53
x59
⟶
x2
x58
(
x1
x59
)
⟶
(
x53
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
(
x55
x58
⟶
False
)
⟶
x7
x58
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x60
(
x1
(
x47
x58
x59
)
)
⟶
(
x5
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x60
(
x1
(
x47
x59
x58
)
)
⟶
(
x38
x60
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
(
x57
x60
⟶
False
)
⟶
x57
x58
⟶
x2
x59
(
x1
(
x47
x60
x58
)
)
⟶
x34
x59
x60
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x57
x60
⟶
x2
x58
(
x1
(
x47
x60
x59
)
)
⟶
x46
x58
x60
x59
⟶
(
x34
x58
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x33
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x53
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
x6
x58
⟶
x53
x58
⟶
(
x6
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
x7
x58
⟶
(
x55
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x60
(
x1
(
x47
x58
x59
)
)
⟶
(
x6
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x57
x60
⟶
x2
x58
(
x1
(
x47
x60
x59
)
)
⟶
(
x34
x58
x60
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 x60 .
x2
x59
(
x1
(
x47
x60
x58
)
)
⟶
x34
x59
x60
⟶
(
x46
x59
x60
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x57
x58
⟶
(
x53
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
(
x55
x58
⟶
False
)
⟶
x7
x58
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
x21
x58
x3
⟶
(
x55
x58
⟶
False
)
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
x21
x58
x3
⟶
x7
x58
⟶
False
)
⟶
(
∀ x58 .
x9
x58
⟶
(
x7
x58
⟶
False
)
⟶
x55
x58
⟶
(
x21
x58
x3
⟶
False
)
⟶
False
)
⟶
(
∀ x58 x59 .
x0
x58
x59
⟶
x0
x59
x58
⟶
False
)
⟶
(
x50
x22
x25
x23
(
x48
(
x45
x22
)
(
x45
x22
)
x24
x25
)
⟶
False
)
⟶
(
x26
=
x23
⟶
False
)
⟶
(
(
x50
x22
x26
x23
(
x48
(
x45
x22
)
(
x45
x22
)
x24
x26
)
⟶
False
)
⟶
False
)
⟶
(
(
x48
(
x45
x22
)
(
x45
x22
)
x24
x23
=
x23
⟶
False
)
⟶
False
)
⟶
(
(
x51
x24
x22
⟶
False
)
⟶
False
)
⟶
(
(
x2
x24
(
x1
(
x47
(
x45
x22
)
(
x45
x22
)
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x52
x24
(
x45
x22
)
(
x45
x22
)
⟶
False
)
⟶
False
)
⟶
(
(
x46
x24
(
x45
x22
)
(
x45
x22
)
⟶
False
)
⟶
False
)
⟶
(
(
x53
x24
⟶
False
)
⟶
False
)
⟶
(
(
x2
x25
(
x45
x22
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x26
(
x45
x22
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x23
(
x45
x22
)
⟶
False
)
⟶
False
)
⟶
(
(
x54
x22
⟶
False
)
⟶
False
)
⟶
(
(
x44
x22
⟶
False
)
⟶
False
)
⟶
(
x55
x22
⟶
False
)
⟶
False
(proof)