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Proofgold Proposition
∀ x0 x1 x2 .
∀ x3 x4 :
ι →
ι → ι
.
∀ x5 :
ι →
ι → ο
.
∀ x6 :
ι →
ι → ι
.
62ee1..
x0
x1
x2
x3
x4
x5
⟶
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
x6
x7
x8
=
x6
x9
x10
⟶
and
(
x7
=
x9
)
(
x8
=
x10
)
)
⟶
∀ x7 .
prim1
x7
(
3b429..
x0
(
λ x8 .
x0
)
(
λ x8 x9 .
True
)
x6
)
⟶
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
x6
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x15
x16
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x17
x18
)
)
)
)
x15
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x17
x18
)
)
)
)
x15
)
)
)
)
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x15
x16
)
)
)
)
)
)
=
x6
x11
x12
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x13
x14
)
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x13
x14
)
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x13
x14
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x15
x16
)
)
)
)
x13
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x13
x14
)
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x15
x16
)
)
)
)
x13
)
)
)
)
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x13
x14
)
)
)
)
)
)
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x17
x18
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x8
=
x6
x19
x20
)
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x9
=
x6
x19
x20
)
)
)
)
x17
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x9
=
x6
x19
x20
)
)
)
)
x17
)
)
)
)
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x8
=
x6
x19
x20
)
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x17
x18
)
)
)
)
)
)
=
x6
x13
x14
)
)
)
)
x11
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x13
x14
)
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x13
x14
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x15
x16
)
)
)
)
x13
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x13
x14
)
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x15
x16
)
)
)
)
x13
)
)
)
)
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x13
x14
)
)
)
)
)
)
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x17
x18
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x8
=
x6
x19
x20
)
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x9
=
x6
x19
x20
)
)
)
)
x17
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x9
=
x6
x19
x20
)
)
)
)
x17
)
)
)
)
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x8
=
x6
x19
x20
)
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x17
x18
)
)
)
)
)
)
=
x6
x13
x14
)
)
)
)
x11
)
)
)
)
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x13
x14
)
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x15
x16
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x17
x18
)
)
)
)
x15
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x17
x18
)
)
)
)
x15
)
)
)
)
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x15
x16
)
)
)
)
)
)
=
x6
x11
x12
)
)
)
)
)
)
=
x6
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x15
x16
)
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x7
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x17
x18
)
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
x15
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x15
x16
)
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
x15
)
)
)
)
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x7
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x17
x18
)
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
)
)
=
x6
x11
x12
)
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x11
x12
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x13
x14
)
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x13
x14
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x15
x16
)
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
x13
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x13
x14
)
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
x13
)
)
)
)
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x15
x16
)
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x13
x14
)
)
)
)
)
)
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x17
x18
)
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x7
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x7
=
x6
x19
x20
)
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x8
=
x6
x19
x20
)
)
)
)
x17
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x17
x18
)
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x8
=
x6
x19
x20
)
)
)
)
x17
)
)
)
)
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x7
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x7
=
x6
x19
x20
)
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
)
)
=
x6
x13
x14
)
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x13
x14
)
)
)
)
x11
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x15
x16
)
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x7
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x17
x18
)
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
x15
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x15
x16
)
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
x15
)
)
)
)
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x7
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x17
x18
)
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
)
)
=
x6
x11
x12
)
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x13
x14
)
)
)
)
x11
)
)
)
)
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x13
x14
)
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x13
x14
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x15
x16
)
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
x13
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x13
x14
)
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x15
x16
)
)
)
)
x13
)
)
)
)
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x15
x16
)
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x13
x14
)
)
)
)
)
)
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x17
x18
)
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x7
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x7
=
x6
x19
x20
)
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x8
=
x6
x19
x20
)
)
)
)
x17
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x17
x18
)
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x8
=
x6
x19
x20
)
)
)
)
x17
)
)
)
)
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x7
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∃ x20 .
and
(
prim1
x20
x0
)
(
x7
=
x6
x19
x20
)
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x17
x18
)
)
)
)
)
)
=
x6
x13
x14
)
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x11
x12
)
)
)
)
)
)
type
prop
theory
HoTg
name
-
proof
PUaTF..
Megalodon
-
proofgold address
TMFkr..
creator
3881
PrGxv..
/
1d796..
owner
3881
PrGxv..
/
1d796..
term root
24a53..