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Proofgold Asset
asset id
5d352e2792e6d9a8eaf389d64c66c21a8c8a41dc34e9c99977dca17dab52475a
asset hash
f222343045bfc4f90f9949806f90866faaf62026a333be4995647d07603edf25
bday / block
35124
tx
7d0c5..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
a4380..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 :
ι →
ι → ο
.
∀ x3 x4 :
ι → ο
.
∀ x5 x6 :
ι → ι
.
∀ x7 :
ι →
ι → ι
.
∀ x8 x9 :
ι → ι
.
∀ x10 :
ι → ο
.
∀ x11 :
ι → ι
.
∀ x12 :
ι →
ι → ι
.
∀ x13 :
ι →
ι → ο
.
∀ x14 :
ι → ι
.
∀ x15 x16 :
ι → ο
.
∀ x17 .
∀ x18 :
ι → ο
.
∀ x19 :
ι → ι
.
∀ x20 :
ι →
ι → ι
.
∀ x21 x22 :
ι → ι
.
∀ x23 :
ι →
ι → ο
.
∀ x24 .
∀ x25 :
ι → ι
.
∀ x26 :
ι →
ι → ι
.
∀ x27 .
∀ x28 x29 :
ι → ο
.
∀ x30 .
∀ x31 :
ι → ι
.
∀ x32 :
ι →
ι → ι
.
∀ x33 :
ι →
ι →
ι → ο
.
∀ x34 :
ι →
ι → ι
.
∀ x35 .
∀ x36 :
ι → ι
.
∀ x37 :
ι → ο
.
∀ x38 x39 x40 x41 x42 .
∀ x43 :
ι → ο
.
∀ x44 :
ι →
ι → ι
.
∀ x45 x46 .
∀ x47 x48 :
ι → ο
.
∀ x49 :
ι → ι
.
∀ x50 :
ι →
ι → ο
.
∀ x51 .
∀ x52 :
ι → ι
.
∀ x53 .
∀ x54 :
ι →
ι → ι
.
∀ x55 .
∀ x56 :
ι → ο
.
∀ x57 :
ι →
ι →
ι →
ι →
ι →
ι → ι
.
∀ x58 :
ι →
ι → ο
.
∀ x59 :
ι →
ι → ι
.
∀ x60 :
ι →
ι →
ι →
ι → ο
.
∀ x61 :
ι →
ι → ι
.
∀ x62 :
ι →
ι → ο
.
∀ x63 .
∀ x64 :
ι → ο
.
(
∀ x65 x66 .
x64
x66
⟶
(
x66
=
x65
⟶
False
)
⟶
x64
x65
⟶
False
)
⟶
(
∀ x65 x66 .
x0
x65
x66
⟶
x64
x66
⟶
False
)
⟶
(
∀ x65 .
x64
x65
⟶
(
x65
=
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x0
x65
x66
⟶
x2
x66
(
x1
x67
)
⟶
x64
x67
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x0
x66
x67
⟶
x2
x67
(
x1
x65
)
⟶
(
x2
x66
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x10
x66
⟶
x3
x65
⟶
x10
x65
⟶
x4
x66
⟶
x8
x66
=
x9
x65
⟶
x7
x66
x65
=
x6
(
x9
x66
)
⟶
(
x65
=
x5
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x62
x66
x65
⟶
(
x2
x66
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x2
x66
(
x1
x65
)
⟶
(
x62
x66
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x2
x65
x66
⟶
(
x64
x66
⟶
False
)
⟶
(
x0
x65
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x0
x66
x65
⟶
(
x2
x66
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 .
x2
x68
(
x1
(
x61
x67
x66
)
)
⟶
x2
x65
(
x1
(
x61
x67
x66
)
)
⟶
x60
x67
x66
x68
x65
⟶
(
x60
x67
x66
x65
x68
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 .
x2
x68
(
x1
(
x61
x67
x66
)
)
⟶
x2
x65
(
x1
(
x61
x67
x66
)
)
⟶
(
x60
x67
x66
x68
x68
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x62
x65
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 .
x2
x68
(
x1
(
x61
x67
x66
)
)
⟶
x2
x65
(
x1
(
x61
x67
x66
)
)
⟶
x68
=
x65
⟶
(
x60
x67
x66
x68
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 .
x2
x68
(
x1
(
x61
x67
x66
)
)
⟶
x2
x65
(
x1
(
x61
x67
x66
)
)
⟶
x60
x67
x66
x68
x65
⟶
(
x68
=
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x11
x65
=
x6
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x58
x66
x65
⟶
(
x59
x65
x66
=
x8
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x13
x66
x65
⟶
(
x12
x65
x66
=
x9
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 x69 x70 .
x10
x70
⟶
x2
x70
(
x1
(
x61
x65
x66
)
)
⟶
x10
x69
⟶
x2
x69
(
x1
(
x61
x67
x68
)
)
⟶
(
x57
x65
x66
x67
x68
x70
x69
=
x7
x70
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x8
(
x6
x65
)
=
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x9
(
x6
x65
)
=
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x10
(
x14
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x13
(
x14
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x15
(
x14
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x3
(
x14
x65
)
⟶
False
)
⟶
False
)
⟶
(
(
x16
x17
⟶
False
)
⟶
False
)
⟶
(
x64
x17
⟶
False
)
⟶
(
∀ x65 .
(
x18
x65
⟶
False
)
⟶
x18
(
x19
x65
)
⟶
False
)
⟶
(
∀ x65 .
(
x18
x65
⟶
False
)
⟶
(
x2
(
x19
x65
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x10
(
x20
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x58
(
x20
x65
x66
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x13
(
x20
x66
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x3
(
x20
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
(
x18
(
x21
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
x64
(
x21
x65
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
(
x2
(
x21
x65
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
x56
x55
⟶
False
)
⟶
(
(
x10
x55
⟶
False
)
⟶
False
)
⟶
(
(
x3
x55
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
(
x23
(
x22
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
(
x2
(
x22
x65
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
(
x10
x24
⟶
False
)
⟶
False
)
⟶
(
(
x15
x24
⟶
False
)
⟶
False
)
⟶
(
(
x3
x24
⟶
False
)
⟶
False
)
⟶
(
x64
x24
⟶
False
)
⟶
(
∀ x65 .
x23
(
x25
x65
)
x65
⟶
False
)
⟶
(
∀ x65 .
(
x2
(
x25
x65
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x58
(
x26
x65
x66
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x13
(
x26
x66
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x3
(
x26
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x64
x66
⟶
False
)
⟶
(
x64
x65
⟶
False
)
⟶
x64
(
x54
x65
x66
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x64
x66
⟶
False
)
⟶
(
x64
x65
⟶
False
)
⟶
(
x10
(
x54
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x64
x66
⟶
False
)
⟶
(
x64
x65
⟶
False
)
⟶
(
x58
(
x54
x65
x66
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x64
x66
⟶
False
)
⟶
(
x64
x65
⟶
False
)
⟶
(
x13
(
x54
x65
x66
)
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x64
x66
⟶
False
)
⟶
(
x64
x65
⟶
False
)
⟶
(
x3
(
x54
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x64
x66
⟶
False
)
⟶
(
x64
x65
⟶
False
)
⟶
(
x2
(
x54
x65
x66
)
(
x1
(
x61
x66
x65
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x10
x53
⟶
False
)
⟶
False
)
⟶
(
(
x15
x53
⟶
False
)
⟶
False
)
⟶
(
(
x3
x53
⟶
False
)
⟶
False
)
⟶
(
x64
x27
⟶
False
)
⟶
(
∀ x65 .
(
x64
(
x52
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x2
(
x52
x65
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
(
x15
x51
⟶
False
)
⟶
False
)
⟶
(
(
x3
x51
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x50
(
x49
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x28
(
x49
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x48
(
x49
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x29
(
x49
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x47
(
x49
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x58
(
x49
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x13
(
x49
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x3
(
x49
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x2
(
x49
x65
)
(
x1
(
x61
x65
x65
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x4
x30
⟶
False
)
⟶
False
)
⟶
(
(
x10
x30
⟶
False
)
⟶
False
)
⟶
(
(
x3
x30
⟶
False
)
⟶
False
)
⟶
(
(
x64
x46
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
x64
(
x31
x65
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
(
x2
(
x31
x65
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x58
(
x32
x65
x66
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x13
(
x32
x66
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x3
(
x32
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x64
(
x32
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x2
(
x32
x65
x66
)
(
x1
(
x61
x66
x65
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x3
x45
⟶
False
)
⟶
False
)
⟶
(
x64
x45
⟶
False
)
⟶
(
∀ x65 x66 .
(
x10
(
x44
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x58
(
x44
x65
x66
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x13
(
x44
x66
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x3
(
x44
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x2
(
x44
x65
x66
)
(
x1
(
x61
x66
x65
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x33
(
x34
x65
x66
)
x66
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x10
(
x34
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x58
(
x34
x65
x66
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x13
(
x34
x66
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x3
(
x34
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x2
(
x34
x65
x66
)
(
x1
(
x61
x66
x65
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x10
x35
⟶
False
)
⟶
False
)
⟶
(
(
x3
x35
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 .
x2
x68
(
x1
(
x61
x67
(
x61
x65
x66
)
)
)
⟶
(
x3
(
x8
x68
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
x3
x65
⟶
x64
(
x8
x65
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 .
x2
x68
(
x1
(
x61
(
x61
x66
x65
)
x67
)
)
⟶
(
x3
(
x9
x68
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
x3
x65
⟶
x64
(
x9
x65
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
(
x3
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x64
x65
⟶
False
)
⟶
x64
(
x6
x65
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x10
x66
⟶
x4
x66
⟶
x3
x65
⟶
x10
x65
⟶
x4
x65
⟶
(
x4
(
x7
x66
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x10
x66
⟶
x4
x66
⟶
x3
x65
⟶
x10
x65
⟶
x4
x65
⟶
(
x3
(
x7
x66
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x3
(
x61
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
x4
x65
⟶
(
x4
(
x5
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
x4
x65
⟶
(
x10
(
x5
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
x4
x65
⟶
(
x3
(
x5
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x64
x65
⟶
(
x64
(
x8
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x64
x65
⟶
(
x64
(
x9
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x4
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x3
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x28
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x48
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x29
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x3
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x10
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x3
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x3
x67
⟶
x13
x67
x65
⟶
x3
x66
⟶
(
x13
(
x7
x67
x66
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x3
x67
⟶
x13
x67
x66
⟶
x3
x65
⟶
(
x3
(
x7
x67
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x10
x66
⟶
x3
x65
⟶
x10
x65
⟶
(
x10
(
x7
x66
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x10
x66
⟶
x3
x65
⟶
x10
x65
⟶
(
x3
(
x7
x66
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x3
x67
⟶
x58
x67
x65
⟶
x3
x66
⟶
(
x58
(
x7
x66
x67
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x3
x67
⟶
x58
x67
x66
⟶
x3
x65
⟶
(
x3
(
x7
x65
x67
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x58
(
x6
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x13
(
x6
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x3
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x18
x65
⟶
x3
x65
⟶
(
x18
(
x8
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x18
x65
⟶
x3
x65
⟶
(
x18
(
x9
x65
)
⟶
False
)
⟶
False
)
⟶
(
(
x64
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x64
(
x1
x65
)
⟶
False
)
⟶
(
∀ x65 .
(
x18
x65
⟶
False
)
⟶
x3
x65
⟶
x10
x65
⟶
x18
(
x9
x65
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x3
x65
⟶
x15
x65
⟶
(
x15
(
x7
x66
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x3
x65
⟶
x15
x65
⟶
(
x3
(
x7
x66
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
(
x3
(
x7
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
(
x64
(
x7
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
(
x56
x65
⟶
False
)
⟶
x18
(
x8
x65
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
(
x3
(
x7
x66
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
(
x64
(
x7
x66
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
x56
x65
⟶
(
x18
(
x8
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x64
x65
⟶
(
x64
(
x8
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x64
x66
⟶
False
)
⟶
(
x64
x65
⟶
False
)
⟶
x64
(
x61
x66
x65
)
⟶
False
)
⟶
(
∀ x65 .
x64
x65
⟶
(
x64
(
x9
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x15
x65
⟶
x10
x65
⟶
(
x43
(
x8
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x2
(
x36
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
(
x64
x42
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x2
(
x11
x65
)
(
x1
(
x61
x65
x65
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x50
(
x11
x65
)
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
(
x3
(
x6
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
(
x3
(
x7
x65
x66
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x58
x66
x65
⟶
(
x2
(
x59
x65
x66
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
(
x10
(
x5
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
(
x3
(
x5
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x3
x66
⟶
x13
x66
x65
⟶
(
x2
(
x12
x65
x66
)
(
x1
x65
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 x69 x70 .
x10
x70
⟶
x2
x70
(
x1
(
x61
x65
x66
)
)
⟶
x10
x69
⟶
x2
x69
(
x1
(
x61
x67
x68
)
)
⟶
(
x2
(
x57
x65
x66
x67
x68
x70
x69
)
(
x1
(
x61
x65
x68
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 x68 x69 x70 .
x10
x70
⟶
x2
x70
(
x1
(
x61
x65
x66
)
)
⟶
x10
x69
⟶
x2
x69
(
x1
(
x61
x67
x68
)
)
⟶
(
x10
(
x57
x65
x66
x67
x68
x70
x69
)
⟶
False
)
⟶
False
)
⟶
(
(
x63
=
x42
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x2
x65
(
x1
(
x61
x66
x67
)
)
⟶
x67
=
x63
⟶
x65
=
x63
⟶
(
x33
x65
x66
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x2
x65
(
x1
(
x61
x66
x67
)
)
⟶
x67
=
x63
⟶
x33
x65
x66
x67
⟶
(
x65
=
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x2
x66
(
x1
(
x61
x65
x67
)
)
⟶
(
x67
=
x63
⟶
False
)
⟶
x65
=
x12
x65
x66
⟶
(
x33
x66
x65
x67
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x2
x65
(
x1
(
x61
x66
x67
)
)
⟶
(
x67
=
x63
⟶
False
)
⟶
x33
x65
x66
x67
⟶
(
x66
=
x12
x66
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x16
x66
⟶
x2
x65
(
x1
x66
)
⟶
(
x16
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
x58
x65
x66
⟶
(
x58
x65
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
x58
x65
x66
⟶
(
x3
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
x58
x65
x66
⟶
(
x64
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x16
x66
⟶
x2
x65
x66
⟶
(
x10
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x16
x66
⟶
x2
x65
x66
⟶
(
x3
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
x13
x65
x66
⟶
(
x13
x65
x66
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
x13
x65
x66
⟶
(
x3
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x3
x65
⟶
x13
x65
x66
⟶
(
x64
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x64
x65
⟶
(
x16
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x3
x67
⟶
x58
x67
x65
⟶
x2
x66
(
x1
x67
)
⟶
(
x58
x66
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x18
x65
⟶
x3
x65
⟶
x10
x65
⟶
(
x56
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x18
x65
⟶
x3
x65
⟶
x10
x65
⟶
(
x10
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x18
x65
⟶
x3
x65
⟶
x10
x65
⟶
(
x3
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 .
x18
x66
⟶
x2
x65
(
x1
x66
)
⟶
(
x18
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x3
x67
⟶
x13
x67
x65
⟶
x2
x66
(
x1
x67
)
⟶
(
x13
x66
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
(
x56
x65
⟶
False
)
⟶
(
x10
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
(
x56
x65
⟶
False
)
⟶
(
x3
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x65 .
x3
x65
⟶
x10
x65
⟶
(
x56
x65
⟶
False
)
⟶
x18
x65
⟶
False
)
⟶
(
∀ x65 x66 .
x64
x66
⟶
x2
x65
(
x1
x66
)
⟶
x23
x65
x66
⟶
False
)
⟶
(
∀ x65 x66 x67 .
x64
x67
⟶
x2
x65
(
x1
(