Search for blocks/addresses/...
Proofgold Asset
asset id
a6787ff35429f5ac6b9eed0564d26b0b834ff02a088c91afb97c8ef9fd6e7237
asset hash
fc34df12801ef133d82519aadc64d7f79e4099b3bcb6b161321c245607034293
bday / block
35145
tx
424ee..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
b6c37..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 :
ι →
ι → ο
.
∀ x3 :
ι →
ι → ι
.
∀ x4 :
ι → ο
.
∀ x5 :
ι →
ι → ι
.
∀ x6 :
ι →
ι →
ι →
ι → ο
.
∀ x7 x8 x9 :
ι →
ι →
ι → ο
.
∀ x10 :
ι →
ι → ο
.
∀ x11 :
ι → ι
.
∀ x12 :
ι →
ι →
ι → ι
.
∀ x13 .
∀ x14 :
ι →
ι → ι
.
∀ x15 x16 x17 x18 :
ι → ι
.
∀ x19 :
ι →
ι → ο
.
∀ x20 :
ι → ι
.
∀ x21 :
ι → ο
.
∀ x22 .
∀ x23 :
ι → ι
.
∀ x24 .
∀ x25 :
ι →
ι → ο
.
∀ x26 x27 :
ι → ι
.
∀ x28 :
ι →
ι → ι
.
∀ x29 .
∀ x30 x31 :
ι →
ι →
ι → ι
.
∀ x32 :
ι → ι
.
∀ x33 :
ι →
ι →
ι →
ι →
ι → ι
.
∀ x34 :
ι →
ι → ι
.
∀ x35 :
ι → ο
.
∀ x36 x37 x38 x39 .
∀ x40 :
ι → ο
.
∀ x41 x42 :
ι →
ι →
ι →
ι → ι
.
∀ x43 :
ι →
ι → ι
.
∀ x44 :
ι →
ι →
ι →
ι → ι
.
∀ x45 .
∀ x46 :
ι → ι
.
∀ x47 :
ι →
ι → ι
.
∀ x48 .
∀ x49 :
ι →
ι → ι
.
∀ x50 :
ι →
ι → ο
.
∀ x51 :
ι → ι
.
∀ x52 .
∀ x53 x54 :
ι → ο
.
∀ x55 .
∀ x56 :
ι → ο
.
∀ x57 x58 :
ι → ι
.
∀ x59 :
ι →
ι → ο
.
∀ x60 :
ι → ι
.
∀ x61 x62 :
ι →
ι →
ι → ι
.
∀ x63 :
ι →
ι → ι
.
∀ x64 :
ι →
ι →
ι →
ι → ι
.
∀ x65 x66 x67 x68 x69 x70 x71 .
∀ x72 :
ι →
ι → ο
.
∀ x73 .
∀ x74 :
ι → ο
.
(
∀ x75 x76 .
x74
x76
⟶
(
x76
=
x75
⟶
False
)
⟶
x74
x75
⟶
False
)
⟶
(
∀ x75 x76 .
x0
x75
x76
⟶
x74
x76
⟶
False
)
⟶
(
∀ x75 .
x74
x75
⟶
(
x75
=
x73
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x0
x75
x76
⟶
x2
x76
(
x1
x77
)
⟶
x74
x77
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x0
x76
x77
⟶
x2
x77
(
x1
x75
)
⟶
(
x2
x76
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x3
x73
x75
=
x73
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x72
x76
x75
⟶
(
x2
x76
(
x1
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x2
x76
(
x1
x75
)
⟶
(
x72
x76
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x3
x75
x73
=
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x2
x75
x76
⟶
(
x74
x76
⟶
False
)
⟶
(
x0
x75
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x0
x76
x75
⟶
(
x2
x76
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
x4
x78
⟶
x7
x78
x75
x76
⟶
x2
x78
(
x1
(
x5
x75
x76
)
)
⟶
x4
x77
⟶
x7
x77
x75
x76
⟶
x2
x77
(
x1
(
x5
x75
x76
)
)
⟶
x6
x75
x76
x78
x77
⟶
(
x6
x75
x76
x77
x78
⟶
False
)
⟶
False
)
⟶
(
x74
x71
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
x4
x78
⟶
x7
x78
x75
x76
⟶
x2
x78
(
x1
(
x5
x75
x76
)
)
⟶
x4
x77
⟶
x7
x77
x75
x76
⟶
x2
x77
(
x1
(
x5
x75
x76
)
)
⟶
(
x6
x75
x76
x78
x78
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x72
x75
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
x4
x78
⟶
x7
x78
x75
x76
⟶
x2
x78
(
x1
(
x5
x75
x76
)
)
⟶
x4
x77
⟶
x7
x77
x75
x76
⟶
x2
x77
(
x1
(
x5
x75
x76
)
)
⟶
x78
=
x77
⟶
(
x6
x75
x76
x78
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
x4
x78
⟶
x7
x78
x75
x76
⟶
x2
x78
(
x1
(
x5
x75
x76
)
)
⟶
x4
x77
⟶
x7
x77
x75
x76
⟶
x2
x77
(
x1
(
x5
x75
x76
)
)
⟶
x6
x75
x76
x78
x77
⟶
(
x78
=
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
(
x74
x75
⟶
False
)
⟶
x2
x75
(
x1
x77
)
⟶
x2
x76
x75
⟶
(
x8
x76
x77
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
(
x74
x75
⟶
False
)
⟶
x2
x75
(
x1
x77
)
⟶
x8
x76
x77
x75
⟶
(
x2
x76
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x10
x75
x77
⟶
x2
x76
x75
⟶
(
x9
x76
x77
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x10
x75
x77
⟶
x9
x76
x77
x75
⟶
(
x2
x76
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x11
x75
=
x1
x75
⟶
False
)
⟶
False
)
⟶
(
(
x70
=
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x2
x76
(
x1
x77
)
⟶
(
x12
x77
x76
x75
=
x3
x76
x75
⟶
False
)
⟶
False
)
⟶
(
(
x68
=
x67
⟶
False
)
⟶
False
)
⟶
(
(
x13
=
x73
⟶
False
)
⟶
False
)
⟶
(
(
x66
=
x65
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x10
x75
x76
⟶
(
x14
x76
x75
=
x15
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x77
⟶
x2
x75
(
x1
(
x5
x78
x77
)
)
⟶
x2
x76
x78
⟶
(
x64
x78
x77
x75
x76
=
x63
x75
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x16
x75
=
x17
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x2
x75
x77
⟶
x10
x76
x77
⟶
(
x61
x77
x75
x76
=
x62
x77
x75
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x19
(
x18
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x2
(
x18
x75
)
(
x1
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x21
(
x20
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
x74
(
x20
x75
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x10
(
x20
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
x19
(
x60
x75
)
x75
⟶
False
)
⟶
(
∀ x75 .
(
x2
(
x60
x75
)
(
x1
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x59
(
x58
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
x74
(
x58
x75
)
⟶
False
)
⟶
(
∀ x75 .
(
x2
(
x58
x75
)
(
x1
(
x1
(
x11
x75
)
)
)
⟶
False
)
⟶
False
)
⟶
(
x74
x22
⟶
False
)
⟶
(
∀ x75 .
(
x74
(
x57
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x2
(
x57
x75
)
(
x1
x75
)
⟶
False
)
⟶
False
)
⟶
(
(
x56
x55
⟶
False
)
⟶
False
)
⟶
(
(
x4
x55
⟶
False
)
⟶
False
)
⟶
(
(
x54
x55
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x21
(
x23
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
x74
(
x23
x75
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x10
(
x23
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
(
x53
x52
⟶
False
)
⟶
False
)
⟶
(
(
x74
x24
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
x74
(
x51
x75
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x2
(
x51
x75
)
(
x1
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x50
(
x49
x75
x76
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x25
(
x49
x76
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x54
(
x49
x75
x76
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
(
x49
x75
x76
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x2
(
x49
x75
x76
)
(
x1
(
x5
x76
x75
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x59
(
x26
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x2
(
x26
x75
)
(
x1
(
x1
(
x11
x75
)
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x54
x77
⟶
x50
x77
x75
⟶
x54
x76
⟶
(
x50
(
x3
x77
x76
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x54
x76
⟶
x4
x76
⟶
x56
x76
⟶
(
x53
(
x63
x76
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x54
x77
⟶
x25
x77
x75
⟶
x54
x76
⟶
(
x25
(
x3
x77
x76
)
x75
⟶
False
)
⟶
False
)
⟶
(
(
x53
x69
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
x74
(
x15
x75
)
⟶
False
)
⟶
(
x74
x48
⟶
False
)
⟶
(
(
x53
x67
⟶
False
)
⟶
False
)
⟶
(
(
x74
x73
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
x74
(
x1
x75
)
⟶
False
)
⟶
(
∀ x75 .
x74
(
x17
x75
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
(
x74
x75
⟶
False
)
⟶
x74
(
x5
x76
x75
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
(
x74
x75
⟶
False
)
⟶
x2
x75
(
x1
x76
)
⟶
(
x8
(
x47
x75
x76
)
x76
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x2
(
x27
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x10
(
x46
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x10
x75
x76
⟶
(
x9
(
x28
x75
x76
)
x76
x75
⟶
False
)
⟶
False
)
⟶
(
(
x74
x45
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
(
x74
x75
⟶
False
)
⟶
x2
x75
(
x1
x77
)
⟶
x8
x76
x77
x75
⟶
(
x2
x76
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x10
x76
x75
⟶
(
x2
x76
(
x1
(
x1
x75
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x10
x75
x77
⟶
x9
x76
x77
x75
⟶
(
x2
x76
(
x1
x77
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x2
(
x11
x75
)
(
x1
(
x1
x75
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x70
x48
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x2
x76
(
x1
x77
)
⟶
(
x2
(
x12
x77
x76
x75
)
(
x1
x77
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x68
x48
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x2
x77
(
x1
(
x16
x78
)
)
⟶
x10
x76
x78
⟶
(
x2
(
x44
x78
x75
x77
x76
)
(
x1
(
x5
x78
x48
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x2
x77
(
x1
(
x16
x78
)
)
⟶
x10
x76
x78
⟶
(
x7
(
x44
x78
x75
x77
x76
)
x78
x48
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x2
x77
(
x1
(
x16
x78
)
)
⟶
x10
x76
x78
⟶
(
x4
(
x44
x78
x75
x77
x76
)
⟶
False
)
⟶
False
)
⟶
(
(
x8
x13
x29
x66
⟶
False
)
⟶
False
)
⟶
(
(
x2
x66
(
x1
x29
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x10
x75
x77
⟶
x2
x76
(
x1
(
x16
x77
)
)
⟶
(
x10
(
x30
x77
x75
x76
)
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x10
x75
x76
⟶
(
x2
(
x14
x76
x75
)
(
x1
(
x16
x76
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x77
⟶
x2
x75
(
x1
(
x5
x78
x77
)
)
⟶
x2
x76
x78
⟶
(
x2
(
x64
x78
x77
x75
x76
)
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x2
x75
(
x1
(
x16
x76
)
)
⟶
(
x10
(
x43
x76
x75
)
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x2
(
x16
x75
)
(
x1
(
x1
(
x11
x75
)
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x59
(
x16
x75
)
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x77
x48
⟶
x2
x75
(
x1
(
x5
x77
x48
)
)
⟶
x10
x76
x77
⟶
(
x2
(
x31
x77
x75
x76
)
(
x1
(
x5
x77
x48
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x77
x48
⟶
x2
x75
(
x1
(
x5
x77
x48
)
)
⟶
x10
x76
x77
⟶
(
x7
(
x31
x77
x75
x76
)
x77
x48
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x77
x48
⟶
x2
x75
(
x1
(
x5
x77
x48
)
)
⟶
x10
x76
x77
⟶
(
x4
(
x31
x77
x75
x76
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x2
x75
x77
⟶
x10
x76
x77
⟶
(
x9
(
x61
x77
x75
x76
)
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x2
(
x32
x75
)
(
x1
(
x5
x75
x48
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x7
(
x32
x75
)
x75
x48
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
(
x74
x75
⟶
False
)
⟶
(
x4
(
x32
x75
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x2
x75
x77
⟶
x10
x76
x77
⟶
(
x2
(
x62
x77
x75
x76
)
(
x1
x77
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x10
x75
x77
⟶
x2
x76
(
x1
(
x16
x77
)
)
⟶
(
x30
x77
x75
x76
=
x43
x77
(
x12
(
x16
x77
)
x76
(
x14
x77
x75
)
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x2
x75
x78
⟶
x10
x77
x78
⟶
x2
x76
(
x1
x78
)
⟶
x0
x75
x76
⟶
x0
x76
x77
⟶
(
x76
=
x62
x78
x75
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x2
x75
x78
⟶
x10
x77
x78
⟶
x2
x76
(
x1
x78
)
⟶
x76
=
x62
x78
x75
x77
⟶
(
x0
x76
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x2
x75
x78
⟶
x10
x77
x78
⟶
x2
x76
(
x1
x78
)
⟶
x76
=
x62
x78
x75
x77
⟶
(
x0
x75
x76
⟶
False
)
⟶
False
)
⟶
(
(
x69
=
x71
⟶
False
)
⟶
False
)
⟶
(
(
x73
=
x45
⟶
False
)
⟶
False
)
⟶
(
(
x67
=
x13
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x10
x77
x78
⟶
x4
x76
⟶
x7
x76
x78
x48
⟶
x2
x76
(
x1
(
x5
x78
x48
)
)
⟶
x64
x78
x48
x76
(
x42
x76
x77
x75
x78
)
=
x70
⟶
x64
x78
x48
x76
(
x42
x76
x77
x75
x78
)
=
x68
⟶
(
x76
=
x31
x78
x75
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 x79 .
(
x74
x79
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x79
x48
⟶
x2
x75
(
x1
(
x5
x79
x48
)
)
⟶
x10
x78
x79
⟶
x4
x76
⟶
x7
x76
x79
x48
⟶
x2
x76
(
x1
(
x5
x79
x48
)
)
⟶
x64
x79
x48
x76
(
x42
x76
x78
x75
x79
)
=
x70
⟶
x2
x77
x79
⟶
x0
x77
(
x61
x79
(
x42
x76
x78
x75
x79
)
x78
)
⟶
x64
x79
x48
x75
x77
=
x70
⟶
(
x76
=
x31
x79
x75
x78
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x10
x77
x78
⟶
x4
x76
⟶
x7
x76
x78
x48
⟶
x2
x76
(
x1
(
x5
x78
x48
)
)
⟶
(
x64
x78
x48
x75
(
x41
x76
x77
x75
x78
)
=
x70
⟶
False
)
⟶
x64
x78
x48
x76
(
x42
x76
x77
x75
x78
)
=
x68
⟶
(
x76
=
x31
x78
x75
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 x79 .
(
x74
x79
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x79
x48
⟶
x2
x75
(
x1
(
x5
x79
x48
)
)
⟶
x10
x78
x79
⟶
x4
x76
⟶
x7
x76
x79
x48
⟶
x2
x76
(
x1
(
x5
x79
x48
)
)
⟶
(
x64
x79
x48
x75
(
x41
x76
x78
x75
x79
)
=
x70
⟶
False
)
⟶
x2
x77
x79
⟶
x0
x77
(
x61
x79
(
x42
x76
x78
x75
x79
)
x78
)
⟶
x64
x79
x48
x75
x77
=
x70
⟶
(
x76
=
x31
x79
x75
x78
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x10
x77
x78
⟶
x4
x76
⟶
x7
x76
x78
x48
⟶
x2
x76
(
x1
(
x5
x78
x48
)
)
⟶
(
x0
(
x41
x76
x77
x75
x78
)
(
x61
x78
(
x42
x76
x77
x75
x78
)
x77
)
⟶
False
)
⟶
x64
x78
x48
x76
(
x42
x76
x77
x75
x78
)
=
x68
⟶
(
x76
=
x31
x78
x75
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 x79 .
(
x74
x79
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x79
x48
⟶
x2
x75
(
x1
(
x5
x79
x48
)
)
⟶
x10
x78
x79
⟶
x4
x76
⟶
x7
x76
x79
x48
⟶
x2
x76
(
x1
(
x5
x79
x48
)
)
⟶
(
x0
(
x41
x76
x78
x75
x79
)
(
x61
x79
(
x42
x76
x78
x75
x79
)
x78
)
⟶
False
)
⟶
x2
x77
x79
⟶
x0
x77
(
x61
x79
(
x42
x76
x78
x75
x79
)
x78
)
⟶
x64
x79
x48
x75
x77
=
x70
⟶
(
x76
=
x31
x79
x75
x78
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x10
x77
x78
⟶
x4
x76
⟶
x7
x76
x78
x48
⟶
x2
x76
(
x1
(
x5
x78
x48
)
)
⟶
(
x2
(
x41
x76
x77
x75
x78
)
x78
⟶
False
)
⟶
x64
x78
x48
x76
(
x42
x76
x77
x75
x78
)
=
x68
⟶
(
x76
=
x31
x78
x75
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 x79 .
(
x74
x79
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x79
x48
⟶
x2
x75
(
x1
(
x5
x79
x48
)
)
⟶
x10
x78
x79
⟶
x4
x76
⟶
x7
x76
x79
x48
⟶
x2
x76
(
x1
(
x5
x79
x48
)
)
⟶
(
x2
(
x41
x76
x78
x75
x79
)
x79
⟶
False
)
⟶
x2
x77
x79
⟶
x0
x77
(
x61
x79
(
x42
x76
x78
x75
x79
)
x78
)
⟶
x64
x79
x48
x75
x77
=
x70
⟶
(
x76
=
x31
x79
x75
x78
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x10
x77
x78
⟶
x4
x76
⟶
x7
x76
x78
x48
⟶
x2
x76
(
x1
(
x5
x78
x48
)
)
⟶
(
x2
(
x42
x76
x77
x75
x78
)
x78
⟶
False
)
⟶
(
x76
=
x31
x78
x75
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 x79 .
(
x74
x79
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x79
x48
⟶
x2
x75
(
x1
(
x5
x79
x48
)
)
⟶
x10
x78
x79
⟶
x4
x76
⟶
x7
x76
x79
x48
⟶
x2
x76
(
x1
(
x5
x79
x48
)
)
⟶
x76
=
x31
x79
x75
x78
⟶
x2
x77
x79
⟶
(
x64
x79
x48
x75
(
x33
x77
x76
x78
x75
x79
)
=
x70
⟶
False
)
⟶
(
x64
x79
x48
x76
x77
=
x68
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 x79 .
(
x74
x79
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x79
x48
⟶
x2
x75
(
x1
(
x5
x79
x48
)
)
⟶
x10
x78
x79
⟶
x4
x76
⟶
x7
x76
x79
x48
⟶
x2
x76
(
x1
(
x5
x79
x48
)
)
⟶
x76
=
x31
x79
x75
x78
⟶
x2
x77
x79
⟶
(
x0
(
x33
x77
x76
x78
x75
x79
)
(
x61
x79
x77
x78
)
⟶
False
)
⟶
(
x64
x79
x48
x76
x77
=
x68
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 x79 .
(
x74
x79
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x79
x48
⟶
x2
x75
(
x1
(
x5
x79
x48
)
)
⟶
x10
x78
x79
⟶
x4
x76
⟶
x7
x76
x79
x48
⟶
x2
x76
(
x1
(
x5
x79
x48
)
)
⟶
x76
=
x31
x79
x75
x78
⟶
x2
x77
x79
⟶
(
x2
(
x33
x77
x76
x78
x75
x79
)
x79
⟶
False
)
⟶
(
x64
x79
x48
x76
x77
=
x68
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 x79 x80 .
(
x74
x80
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x80
x48
⟶
x2
x75
(
x1
(
x5
x80
x48
)
)
⟶
x10
x79
x80
⟶
x4
x76
⟶
x7
x76
x80
x48
⟶
x2
x76
(
x1
(
x5
x80
x48
)
)
⟶
x76
=
x31
x80
x75
x79
⟶
x2
x77
x80
⟶
x2
x78
x80
⟶
x0
x78
(
x61
x80
x77
x79
)
⟶
x64
x80
x48
x75
x78
=
x70
⟶
(
x64
x80
x48
x76
x77
=
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x76
x48
⟶
x2
x75
(
x1
(
x5
x76
x48
)
)
⟶
x64
x76
x48
x75
(
x34
x75
x76
)
=
x70
⟶
(
x75
=
x32
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x76
x48
⟶
x2
x75
(
x1
(
x5
x76
x48
)
)
⟶
(
x2
(
x34
x75
x76
)
x76
⟶
False
)
⟶
(
x75
=
x32
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
(
x74
x77
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x77
x48
⟶
x2
x75
(
x1
(
x5
x77
x48
)
)
⟶
x75
=
x32
x77
⟶
x2
x76
x77
⟶
(
x64
x77
x48
x75
x76
=
x70
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 x78 .
(
x74
x78
⟶
False
)
⟶
x4
x75
⟶
x7
x75
x78
x48
⟶
x2
x75
(
x1
(
x5
x78
x48
)
)
⟶
x2
x77
(
x1
(
x16
x78
)
)
⟶
x10
x76
x78
⟶
(
x44
x78
x75
x77
x76
=
x31
x78
x75
(
x30
x78
x76
x77
)
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x74
x76
⟶
x2
x75
(
x1
x76
)
⟶
x19
x75
x76
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x74
x77
⟶
x2
x75
(
x1
(
x5
x76
x77
)
)
⟶
(
x74
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x2
x75
(
x1
x76
)
⟶
x74
x75
⟶
(
x19
x75
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x74
x77
⟶
x2
x75
(
x1
(
x5
x77
x76
)
)
⟶
(
x74
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x2
x76
(
x1
(
x5
x75
x48
)
)
⟶
x4
x76
⟶
x7
x76
x75
x48
⟶
(
x56
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x2
x76
(
x1
(
x5
x75
x48
)
)
⟶
x4
x76
⟶
x7
x76
x75
x48
⟶
(
x7
x76
x75
x48
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x2
x76
(
x1
(
x5
x75
x48
)
)
⟶
x4
x76
⟶
x7
x76
x75
x48
⟶
(
x4
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x2
x75
(
x1
x76
)
⟶
(
x19
x75
x76
⟶
False
)
⟶
x74
x75
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x2
x77
(
x1
(
x5
x75
x76
)
)
⟶
(
x50
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x2
x77
(
x1
(
x5
x76
x75
)
)
⟶
(
x25
x77
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
x2
x75
x48
⟶
(
x53
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x10
x76
x75
⟶
(
x21
x76
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
x53
x75
⟶
(
x35
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
x74
x76
⟶
x2
x75
(
x1
x76
)
⟶
(
x74
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 x77 .
x2
x77
(
x1
(
x5
x75
x76
)
)
⟶
(
x54
x77
⟶
False
)
⟶
False
)
⟶
(
∀ x75 .
x74
x75
⟶
(
x40
x75
⟶
False
)
⟶
False
)
⟶
(
∀ x75 x76 .
(
x74
x76
⟶
False
)
⟶
x10
x75
x76
⟶
x74
x75
⟶
False
)
⟶
(
∀ x75 x76 .
x0
x75
x76
⟶
x0
x76
x75
⟶
False
)
⟶
(
x6
x36
x48
(
x44
x36
(
x32
x36
)
x37
x38
)
(
x32
x36
)
⟶
False
)
⟶
(
(
x10
x38
x36
⟶
False
)
⟶
False
)
⟶
(
(
x2
x39
(
x1
(
x5
x36
x48
)
)
⟶
False
)
⟶
False
)
⟶
(
(
x7
x39
x36
x48
⟶
False
)
⟶
False
)
⟶
(
(
x4
x39
⟶
False
)
⟶
False
)
⟶
(
(
x2
x37
(
x1
(
x17
x36
)
)
⟶
False
)
⟶
False
)
⟶
(
x74
x36
⟶
False
)
⟶
False
(proof)