Let x0 of type ι be given.
Let x1 of type ι → ι → ι → ι be given.
Assume H0:
∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ In (x1 x2 x3 x4) x0.
Let x2 of type ι → ι → ι be given.
Assume H1:
∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ In (x2 x3 x4) x0.
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 → ι → ι be given.
Assume H5:
∀ x7 . In x7 x0 ⟶ ∀ x8 . In x8 x0 ⟶ In (x6 x7 x8) x0.
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 be given.
Let x9 of type ι → ι → ι be given.
Assume H8:
∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ In (x9 x10 x11) x0.
Assume H9:
∀ x10 . In x10 x0 ⟶ (x9 x8 x10 = x10 ⟶ False) ⟶ False.
Assume H10:
∀ x10 . In x10 x0 ⟶ (x9 x10 x8 = x10 ⟶ False) ⟶ False.
Assume H11:
∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x7 (x9 x11 x10) x10 = x11 ⟶ False) ⟶ False.
Assume H12:
∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ (x9 (x7 x11 x10) x10 = x11 ⟶ False) ⟶ False.
Assume H13:
∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ x9 x11 x10 = x9 x12 x10 ⟶ (x11 = x12 ⟶ False) ⟶ False.
Assume H14:
∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ ∀ x12 . In x12 x0 ⟶ (x1 x10 x11 x12 = x7 (x9 (x9 x12 x10) x11) (x9 x10 x11) ⟶ False) ⟶ False.
Assume H15:
∀ x10 . In x10 x0 ⟶ (x6 x8 x10 = x10 ⟶ False) ⟶ False.
Assume H16:
∀ x10 . In x10 x0 ⟶ (x2 x8 x10 = x10 ⟶ False) ⟶ False.
Assume H17:
∀ x10 . ... ⟶ ∀ x11 . ... ⟶ ∀ x12 . In x12 ... ⟶ (x1 x10 x11 (x2 x10 (x2 x11 (x1 x10 x11 (x2 x10 (x2 x11 (x1 x10 x11 (x2 x10 (x2 x11 x12)))))))) = x12 ⟶ False) ⟶ False.