Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Assume H0:
∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0.
Let x2 of type ι → ι → ι → ι be given.
Assume H1:
∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ ∀ x5 . In x5 x0 ⟶ In (x2 x3 x4 x5) x0.
Let x3 of type ι → ι → ι be given.
Assume H2:
∀ x4 . In x4 x0 ⟶ ∀ x5 . In x5 x0 ⟶ In (x3 x4 x5) x0.
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 → ι → ι be given.
Assume H6:
∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ In (x7 x8 x9) x0.
Let x8 of type ι → ι → ι be given.
Assume H7:
∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ In (x8 x9 x10) x0.
Let x9 of type ι be given.
Let x10 of type ι → ι → ι be given.
Assume H9:
∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ In (x10 x11 x12) x0.
Assume H10:
∀ x11 . In x11 x0 ⟶ (x10 x9 x11 = x11 ⟶ False) ⟶ False.
Assume H11:
∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x1 x11 (x10 x11 x12) = x12 ⟶ False) ⟶ False.
Assume H12:
∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x10 x11 (x1 x11 x12) = x12 ⟶ False) ⟶ False.
Assume H13:
∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ (x2 x11 x12 x13 = x1 (x10 x12 x11) (x10 x12 (x10 x11 x13)) ⟶ False) ⟶ False.
Assume H14:
∀ x11 . In x11 x0 ⟶ (x8 x9 x11 = x11 ⟶ False) ⟶ False.
Assume H15:
∀ x11 . In x11 x0 ⟶ (x3 x9 x11 = x11 ⟶ False) ⟶ False.
Assume H16:
∀ x11 . In x11 ... ⟶ ∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ ∀ x14 . In x14 x0 ⟶ (x2 x11 x13 (x8 x12 (x7 x11 (x2 x13 x12 (x2 x11 x13 (x8 x12 (x7 x11 (x2 x13 x12 (x2 x11 x13 (x8 x12 (x7 x11 (x2 x13 x12 x14))))))))))) = x14 ⟶ False) ⟶ False.