Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι be given.
Let x5 of type ι → ι → ι be given.
Let x6 of type ι → ι → ι → ι be given.
Let x7 of type ι → ι → ι be given.
Let x8 of type ι → ι → ι → ι be given.
Let x9 of type ι → ι → ι → ι be given.
Let x10 of type ι → ι → ι be given.
Let x11 of type ι → ι → ι be given.
Let x12 of type ι → ι → ι be given.
Let x13 of type ι → ι → ι be given.
Assume H2:
∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x7 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x7 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x7 x14 (x9 x15 x16 x17))))))))))))))) = x17.
Assume H3:
∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x7 x14 (x7 x15 (x9 x14 x15 (x7 x14 (x7 x15 (x9 x14 x15 (x7 x14 (x7 x15 x16)))))))) = x16.
Assume H4:
∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x7 x15 (x13 x16 x17)) = x7 x15 (x13 x16 (x10 x14 x17)).
Assume H5:
∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 x18)) = x7 x16 (x12 x17 (x9 x14 x15 x18)).
Assume H6:
∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x12 x15 x18))).
Assume H7:
∀ x14 . ... ⟶ ∀ x15 . ... ⟶ ∀ x16 . ... ⟶ ∀ x17 . ... ⟶ ∀ x18 . In ... ... ⟶ x13 x14 (x12 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x13 x14 (x12 x15 x18))).