Let x0 of type ι → ι → ι → ι → ο be given.
Let x1 of type ι → ι → ι → ι → ο be given.
Assume H0: ∀ x2 x3 x4 x5 . x0 x2 x3 x4 x5 ⟶ x0 x4 x5 x2 x3.
Assume H1:
∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ not (x0 x2 x3 x2 x3).
Assume H2:
∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ x1 x2 x3 x2 x3.
Assume H3:
∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ ∀ x4 . x4 ∈ u6 ⟶ ∀ x5 . x5 ∈ u6 ⟶ (x2 = u5 ⟶ x3 = u5 ⟶ False) ⟶ (x4 = u5 ⟶ x5 = u5 ⟶ False) ⟶ x0 x2 x3 x4 x5 ⟶ x1 x2 x3 x4 x5.
Assume H4:
∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ ∀ x4 . x4 ∈ u6 ⟶ ∀ x5 . x5 ∈ u6 ⟶ (x2 = u5 ⟶ x3 = u5 ⟶ False) ⟶ (x4 = u5 ⟶ x5 = u5 ⟶ False) ⟶ (x2 = x4 ⟶ x3 = x5 ⟶ False) ⟶ x1 x2 x3 x4 x5 ⟶ x0 x2 x3 x4 x5.
Assume H5:
∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ ∀ x4 . x4 ∈ u6 ⟶ ∀ x5 . x5 ∈ u6 ⟶ ∀ x6 . x6 ∈ u6 ⟶ ∀ x7 . x7 ∈ u6 ⟶ ∀ x8 . x8 ∈ u6 ⟶ ∀ x9 . x9 ∈ u6 ⟶ x0 x2 x3 x4 x5 ⟶ x0 x2 x3 x6 x7 ⟶ x0 x2 x3 x8 x9 ⟶ x0 x4 x5 x6 x7 ⟶ x0 x4 x5 x8 x9 ⟶ x0 x6 x7 x8 x9 ⟶ False.
Assume H6:
∀ x2 . ... ⟶ ∀ x3 . ... ⟶ ∀ x4 . ... ⟶ ∀ x5 . ... ⟶ ∀ x6 . ... ⟶ ∀ x7 . ... ⟶ ∀ x8 . ... ⟶ ∀ x9 . ... ⟶ ∀ x10 . ... ⟶ ∀ x11 . ... ⟶ ∀ x12 . ... ⟶ ∀ x13 . ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ not (x1 x2 x3 x12 x13) ⟶ not (x1 x4 x5 x6 x7) ⟶ not (x1 x4 x5 x8 x9) ⟶ not (x1 x4 x5 x10 x11) ⟶ not (x1 x4 x5 x12 x13) ⟶ not (x1 x6 x7 x8 x9) ⟶ not (x1 x6 x7 x10 x11) ⟶ not (x1 x6 x7 x12 x13) ⟶ not (x1 x8 x9 x10 x11) ⟶ not (x1 x8 x9 x12 x13) ⟶ not (x1 x10 x11 x12 x13) ⟶ False.