Search for blocks/addresses/...
Proofgold Signed Transaction
vin
Pr4wS..
/
38ae0..
PUJym..
/
b32bf..
vout
Pr4wS..
/
062a3..
0.03 bars
TMPJh..
/
abe10..
ownership of
e6fe7..
as prop with payaddr
PrGxv..
rights free controlledby
PrGxv..
upto 0
TMXMF..
/
8973f..
ownership of
edf53..
as prop with payaddr
PrGxv..
rights free controlledby
PrGxv..
upto 0
TMPKa..
/
903d0..
ownership of
652c9..
as prop with payaddr
PrGxv..
rights free controlledby
PrGxv..
upto 0
TMdE2..
/
664e0..
ownership of
3357d..
as prop with payaddr
PrGxv..
rights free controlledby
PrGxv..
upto 0
TMVvz..
/
adbe3..
ownership of
5224b..
as prop with payaddr
PrGxv..
rights free controlledby
PrGxv..
upto 0
TMaAZ..
/
8c37b..
ownership of
10769..
as prop with payaddr
PrGxv..
rights free controlledby
PrGxv..
upto 0
PUYqt..
/
5dc0d..
doc published by
PrGxv..
Param
62ee1..
:
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ο
) →
ο
Definition
and
:=
λ x0 x1 : ο .
∀ x2 : ο .
(
x0
⟶
x1
⟶
x2
)
⟶
x2
Param
3b429..
:
ι
→
(
ι
→
ι
) →
(
ι
→
ι
→
ο
) →
CT2
ι
Param
True
:
ο
Param
explicit_Field_minus
:
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
ι
→
ι
Known
dde2d..
:
∀ 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
)
)
)
)
)
)
Known
29eed..
:
∀ 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
)
⟶
(
x7
=
x6
x1
x1
⟶
∀ x8 : ο .
x8
)
⟶
∃ x8 .
and
(
prim1
x8
(
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
)
(
x8
=
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
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
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
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x8
=
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
)
(
x8
=
x6
x11
x12
)
)
)
)
)
)
=
x6
x2
x1
)
Known
04e39..
:
∀ 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
(
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
)
)
)
)
)
(
x3
(
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
)
)
)
)
=
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
(
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
)
)
)
)
)
(
x3
(
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
)
)
)
)
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x6
(
x3
(
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
)
)
)
)
)
(
x3
(
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
)
)
)
)
=
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
(
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
)
)
)
)
)
(
x3
(
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
)
)
)
)
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∃ x14 .
and
(
prim1
x14
x0
)
(
x6
(
x3
(
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
)
)
)
)
)
(
x3
(
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
)
)
)
)
=
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
(
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
)
)
)
)
)
(
x3
(
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
)
)
)
)
=
x6
x11
x12
)
)
)
)
)
)
=
x6
(
x3
(
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
)
(
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
)
(
x9
=
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
)
(
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
)
(
x7
=
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
)
(
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
)
(
x9
=
x6
x15
x16
)
)
)
)
)
)
=
x6
x11
x12
)
)
)
)
)
(
x3
(
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
)
(
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
)
(
x9
=
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
)
(
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
)
(
x7
=
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
)
(
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
)
(
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
)
(
x7
=
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
)
(
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
)
(
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
)
(
x7
=
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
)
(
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
)
(
x9
=
x6
x17
x18
)
)
)
)
)
)
=
x6
x13
x14
)
)
)
)
x11
)
)
)
)
Param
11fac..
:
ι
→
(
ι
→
ι
) →
(
ι
→
ι
) →
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
ο
Param
Subq
:
ι
→
ι
→
ο
Known
b1312..
:
∀ 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
⟶
∀ x11 : ο .
(
x7
=
x9
⟶
x8
=
x10
⟶
x11
)
⟶
x11
)
⟶
(
∀ 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 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x9
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x9
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
)
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x7
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x9
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x9
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
)
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x9
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x9
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x9
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x9
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
)
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x9
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x9
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
)
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x9
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x9
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x9
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x9
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
)
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x7
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x9
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x9
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
)
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
)
=
x6
(
x3
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x7
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x7
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
)
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x7
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x7
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x7
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x7
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
)
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x7
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x7
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x7
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x7
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
)
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x9
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x7
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x7
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
)
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x9
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x7
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x7
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x7
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x7
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
)
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x7
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x7
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x7
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x7
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
)
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
)
)
⟶
(
∀ x7 .
prim1
x7
(
3b429..
x0
(
λ x8 .
x0
)
(
λ x8 x9 .
True
)
x6
)
⟶
(
x7
=
x6
x1
x1
⟶
∀ x8 : ο .
x8
)
⟶
∃ x8 .
and
(
prim1
x8
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
)
(
x6
(
x3
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x7
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x8
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x8
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x7
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
)
=
x6
x2
x1
)
)
⟶
(
∀ 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 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
(
x3
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x9
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x7
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x6
(
x3
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
(
x3
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x9
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x6
(
x3
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
(
x3
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x9
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x9
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x6
(
x3
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
(
x3
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x9
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x6
(
x3
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
(
x3
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x9
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x9
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
(
x4
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x7
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
(
x3
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x9
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
)
=
x6
(
x3
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x7
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x8
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x7
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x8
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
)
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x7
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x9
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x7
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x9
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
)
(
x4
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
x7
=
x6
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
x16
⟶
x17
)
⟶
x17
)
)
(
prim0
(
λ x16 .
∀ x17 : ο .
(
prim1
x16
x0
⟶
(
∃ x18 .
and
(
prim1
x18
x0
)
(
x9
=
x6
x16
x18
)
)
⟶
x17
)
⟶
x17
)
)
)
)
=
x6
x11
x13
)
)
⟶
x12
)
⟶
x12
)
)
)
(
x3
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x7
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x7
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x8
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x7
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x7
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x8
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
)
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x7
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x7
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x8
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x8
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x7
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x7
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
)
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
(
prim0
(
λ x11 .
∀ x12 : ο .
(
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x7
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x7
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x9
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x7
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x9
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
)
(
x4
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
x7
=
x6
(
prim0
(
λ x17 .
∀ x18 : ο .
(
prim1
x17
x0
⟶
(
∃ x19 .
and
(
prim1
x19
x0
)
(
x7
=
x6
x17
x19
)
)
⟶
x18
)
⟶
x18
)
)
x14
⟶
x15
)
⟶
x15
)
)
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x9
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
)
)
=
x6
(
prim0
(
λ x14 .
∀ x15 : ο .
(
prim1
x14
x0
⟶
(
∃ x16 .
and
(
prim1
x16
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x7
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x7
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x9
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x9
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x7
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x9
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x9
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
)
(
x4
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
x7
=
x6
(
prim0
(
λ x22 .
∀ x23 : ο .
(
prim1
x22
x0
⟶
(
∃ x24 .
and
(
prim1
x24
x0
)
(
x7
=
x6
x22
x24
)
)
⟶
x23
)
⟶
x23
)
)
x19
⟶
x20
)
⟶
x20
)
)
(
prim0
(
λ x19 .
∀ x20 : ο .
(
prim1
x19
x0
⟶
(
∃ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
)
⟶
x20
)
⟶
x20
)
)
)
)
=
x6
x14
x16
)
)
⟶
x15
)
⟶
x15
)
)
x11
⟶
x12
)
⟶
x12
)
)
)
)
⟶
and
(
11fac..
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
∃ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
x8
x9
)
)
)
)
x1
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
x7
=
x6
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
x8
)
)
)
x1
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
x6
x1
x2
)
(
λ x7 x8 .
x6
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
)
(
λ x7 x8 .
x6
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
)
)
)
(
(
∀ x7 .
prim1
x7
x0
⟶
x6
x7
x1
=
x7
)
⟶
and
(
and
(
and
(
and
(
and
(
Subq
x0
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
)
(
∀ x7 .
prim1
x7
x0
⟶
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
=
x7
)
)
(
x6
x1
x1
=
x1
)
)
(
x6
x2
x1
=
x2
)
)
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
=
x3
x7
x8
)
)
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
)
=
x4
x7
x8
)
)
Theorem
5224b..
:
∀ 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
)
)
⟶
and
(
11fac..
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
∃ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
x8
x9
)
)
)
)
x1
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
x7
=
x6
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
x8
)
)
)
x1
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
x6
x1
x2
)
(
λ x7 x8 .
x6
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
)
(
λ x7 x8 .
x6
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
)
)
)
(
(
∀ x7 .
prim1
x7
x0
⟶
x6
x7
x1
=
x7
)
⟶
and
(
and
(
and
(
and
(
and
(
Subq
x0
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
)
(
∀ x7 .
prim1
x7
x0
⟶
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
=
x7
)
)
(
x6
x1
x1
=
x1
)
)
(
x6
x2
x1
=
x2
)
)
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
=
x3
x7
x8
)
)
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
)
=
x4
x7
x8
)
)
...
Theorem
652c9..
:
∀ 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
)
)
⟶
11fac..
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
∃ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
x8
x9
)
)
)
)
x1
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
x7
=
x6
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
x8
)
)
)
x1
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
x6
x1
x2
)
(
λ x7 x8 .
x6
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
)
(
λ x7 x8 .
x6
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
)
)
...
Known
and6E
:
∀ x0 x1 x2 x3 x4 x5 : ο .
and
(
and
(
and
(
and
(
and
x0
x1
)
x2
)
x3
)
x4
)
x5
⟶
∀ x6 : ο .
(
x0
⟶
x1
⟶
x2
⟶
x3
⟶
x4
⟶
x5
⟶
x6
)
⟶
x6
Known
and7I
:
∀ x0 x1 x2 x3 x4 x5 x6 : ο .
x0
⟶
x1
⟶
x2
⟶
x3
⟶
x4
⟶
x5
⟶
x6
⟶
and
(
and
(
and
(
and
(
and
(
and
x0
x1
)
x2
)
x3
)
x4
)
x5
)
x6
Theorem
e6fe7..
:
∀ 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
x0
⟶
x6
x7
x1
=
x7
)
⟶
and
(
and
(
and
(
and
(
and
(
and
(
11fac..
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
∃ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
x8
x9
)
)
)
)
x1
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
x7
=
x6
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
x8
)
)
)
x1
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
x6
x1
x2
)
(
λ x7 x8 .
x6
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
)
(
λ x7 x8 .
x6
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x11
x12
)
)
)
)
x9
)
)
)
)
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∃ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x11
x12
)
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
x9
x10
)
)
)
)
)
)
)
)
(
Subq
x0
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
)
)
(
∀ x7 .
prim1
x7
x0
⟶
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∃ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x9
x10
)
)
)
=
x7
)
)
(
x6
x1
x1
=
x1
)
)
(
x6
x2
x1
=
x2
)
)
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
=
x3
x7
x8
)
)
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x10
x11
)
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x12
x13
)
)
)
)
x10
)
)
)
)
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∃ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x12
x13
)
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∃ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x10
x11
)
)
)
)
)
)
=
x4
x7
x8
)
...