Let x0 of type ι → ο be given.
Let x1 of type ι → ο be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Assume H0: ∀ x8 : ι → ο . x8 x2 ⟶ x8 x3 ⟶ x8 x4 ⟶ x8 x5 ⟶ x8 x6 ⟶ x8 x7 ⟶ ∀ x9 . x0 x9 ⟶ x8 x9.
Assume H1: ∀ x8 : ι → ο . x8 x2 ⟶ x8 x3 ⟶ x8 x4 ⟶ x8 x5 ⟶ ∀ x9 . x1 x9 ⟶ x8 x9.
Assume H2: x0 x2.
Assume H3: ∀ x8 . x0 x8 ⟶ ∀ x9 : ι → ο . (x1 x8 ⟶ x9 x8) ⟶ x9 x6 ⟶ x9 x7 ⟶ x9 x8.
Let x8 of type ι → ι be given.
Let x9 of type ι → ι be given.
Let x10 of type ι → ι be given.
Assume H4:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x8 x11) x12).
Assume H5:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x8 x11) (ap (x8 x11) x12) = x12.
Assume H6:
∀ x11 . x0 x11 ⟶ ap (x8 x11) x2 = x3.
Assume H7:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x9 x11) x12).
Assume H8:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x9 x11) (ap (x9 x11) x12) = x12.
Assume H9:
∀ x11 . x0 x11 ⟶ ap (x9 x11) x2 = x4.
Assume H10:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x10 x11) x12).
Assume H11:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x10 x11) (ap (x10 x11) x12) = x12.
Assume H12:
∀ x11 . x0 x11 ⟶ ap (x10 x11) x2 = x5.
Let x11 of type ι → ι → ι → ι → ο be given.
Assume H13:
∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x3 x13 x2).
Assume H14:
∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x4 x13 x2).
Assume H15:
∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x5 x13 x2).
Assume H16:
∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x6 x13 x2).
Assume H17:
∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ not (x11 x12 x7 x13 x2).
Let x12 of type ι → ι → ι → ι → ο be given.
Assume H18: ∀ x13 x14 x15 x16 . ... ⟶ ... ⟶ x0 x15 ⟶ x0 x16 ⟶ ∀ x17 : ο . (x11 x13 x14 x15 x16 ⟶ x17) ⟶ (x12 x13 x14 x15 x16 ⟶ x17) ⟶ (x11 x15 x16 x13 x14 ⟶ x17) ⟶ x17.