Let x0 of type ι → ο be given.
Let x1 of type ι 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.
Assume H0: x0 x1.
Let x7 of type ι → ι be given.
Assume H1:
∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ x0 (ap (x7 x8) x9).
Assume H2:
∀ x8 . x0 x8 ⟶ ∀ x9 . x0 x9 ⟶ ap (x7 x8) (ap (x7 x8) x9) = x9.
Assume H3:
∀ x8 . x0 x8 ⟶ ap (x7 x8) x1 = x4.
Let x8 of type ι → ι → ι → ι → ο be given.
Assume H4:
∀ x9 x10 x11 x12 . x0 x9 ⟶ x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x8 x9 x10 x11 x12 ⟶ x8 x9 (ap (x7 x9) x10) x11 (ap (x7 x11) x12).
Assume H5:
∀ x9 . x0 x9 ⟶ ∀ x10 . x0 x10 ⟶ ∀ x11 . x0 x11 ⟶ ∀ x12 . x0 x12 ⟶ ∀ x13 . x0 x13 ⟶ ∀ x14 . x0 x14 ⟶ ∀ x15 . x0 x15 ⟶ ∀ x16 . x0 x16 ⟶ ∀ x17 . x0 x17 ⟶ ∀ x18 . x0 x18 ⟶ ∀ x19 . x0 x19 ⟶ not (x8 x9 x1 x10 x11) ⟶ not (x8 x9 x1 x12 x13) ⟶ not (x8 x9 x1 x14 x15) ⟶ not (x8 x9 x1 x16 x17) ⟶ not (x8 x9 x1 x18 x19) ⟶ not (x8 x10 x11 x12 x13) ⟶ not (x8 x10 x11 x14 x15) ⟶ not (x8 x10 x11 x16 x17) ⟶ not (x8 x10 x11 x18 x19) ⟶ not (x8 x12 x13 x14 x15) ⟶ not (x8 x12 x13 x16 x17) ⟶ not (x8 x12 x13 x18 x19) ⟶ not (x8 x14 x15 x16 x17) ⟶ not (x8 x14 x15 x18 x19) ⟶ not (x8 x16 x17 x18 x19) ⟶ False.
Let x9 of type ι be given.
Assume H6: x0 x9.
Let x10 of type ι be given.
Assume H7: x0 x10.
Let x11 of type ι be given.
Assume H8: x0 x11.
Let x12 of type ι be given.
Assume H9: x0 x12.
Let x13 of type ι be given.
Assume H10: x0 x13.
Let x14 of type ι be given.
Assume H11: x0 x14.
Let x15 of type ι be given.
Assume H12: x0 x15.
Let x16 of type ι be given.
Assume H13: x0 x16.
Let x17 of type ι be given.
Assume H14: x0 x17.
Let x18 of type ι be given.
Assume H15: x0 x18.
Let x19 of type ι be given.
Assume H16: x0 x19.
Apply H3 with
x9,
λ x20 x21 . ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ not (x8 x12 x13 ... ...) ⟶ not (x8 x14 x15 x16 x17) ⟶ not (x8 x14 x15 x18 x19) ⟶ not (x8 x16 x17 x18 x19) ⟶ False leaving 2 subgoals.