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 ⟶ ∀ x9 . x1 x9 ⟶ x8 x9.
Assume H1: x0 x2.
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 H2:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x8 x11) x12).
Assume H3:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x8 x11) (ap (x8 x11) x12) = x12.
Assume H4:
∀ x11 . x0 x11 ⟶ ap (x8 x11) x2 = x3.
Assume H5:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x9 x11) x12).
Assume H6:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x9 x11) (ap (x9 x11) x12) = x12.
Assume H7:
∀ x11 . x0 x11 ⟶ ap (x9 x11) x2 = x4.
Assume H8:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ x0 (ap (x10 x11) x12).
Assume H9:
∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ap (x10 x11) (ap (x10 x11) x12) = x12.
Assume H10:
∀ x11 . x0 x11 ⟶ ap (x10 x11) x2 = x5.
Let x11 of type ι → ι → ι → ι → ο be given.
Assume H11:
∀ x12 x13 x14 x15 . x0 x12 ⟶ x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x11 x12 x13 x14 x15 ⟶ x11 x12 (ap (x8 x12) x13) x14 (ap (x8 x14) x15).
Assume H12:
∀ x12 x13 x14 x15 . x0 x12 ⟶ x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x11 x12 x13 x14 x15 ⟶ x11 x12 (ap (x9 x12) x13) x14 (ap (x9 x14) x15).
Assume H13:
∀ x12 x13 x14 x15 . x0 x12 ⟶ x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x11 x12 x13 x14 x15 ⟶ x11 x12 (ap (x10 x12) x13) x14 (ap (x10 x14) x15).
Assume H14:
∀ x12 . ... ⟶ ∀ x13 . ... ⟶ ∀ x14 . ... ⟶ ∀ x15 . ... ⟶ ∀ x16 . ... ⟶ ∀ x17 . ... ⟶ ∀ x18 . ... ⟶ ∀ x19 . ... ⟶ ∀ x20 . ... ⟶ ∀ x21 . ... ⟶ ∀ x22 . ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ not ... ⟶ not (x11 x15 x16 x17 x18) ⟶ not (x11 x15 x16 x19 x20) ⟶ not (x11 x15 x16 x21 x22) ⟶ not (x11 x17 x18 x19 x20) ⟶ not (x11 x17 x18 x21 x22) ⟶ not (x11 x19 x20 x21 x22) ⟶ False.