Let x0 of type ι be given.

Let x1 of type ι → ι → ο be given.

Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2.

Assume H1: 4402e.. x0 x1.

Assume H2: cf2df.. x0 x1.

Let x2 of type ι be given.

Assume H3: x2 ∈ x0.

Let x3 of type ι be given.

Assume H4: x3 ⊆ setminus x0 (Sing x2).

Claim L5: ...

...

Let x4 of type ι be given.

Assume H6: x4 ∈ x3.

Let x5 of type ι be given.

Assume H7: x5 ∈ x3.

Let x6 of type ι be given.

Assume H8: x6 ∈ x3.

Let x7 of type ι be given.

Assume H9: x7 ∈ x3.

Let x8 of type ι be given.

Assume H10: x8 ∈ x3.

Let x9 of type ι be given.

Assume H11: x9 ∈ x3.

Let x10 of type ι be given.

Assume H12: x10 ∈ x3.

Let x11 of type ι be given.

Assume H13: x11 ∈ x3.

Let x12 of type ι be given.

Assume H14: x12 ∈ x3.

Assume H15: e37fb.. x1 x4 x5 x6 x7 x8 x9 x10 x11 x12.

Let x13 of type ο be given.

Assume H16: ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ 68d0b.. x1 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 ⟶ x13.

Assume H17: ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ f4564.. x1 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 ⟶ x13.

Assume H18: ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ 4ff4c.. x1 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 ⟶ x13.

Assume H19: ∀ x14 . ... ⟶ ∀ x15 . ... ⟶ ∀ x16 . ... ⟶ ∀ x17 . ... ⟶ ∀ x18 . ... ⟶ ∀ x19 . ... ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ b0a38.. x1 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 ⟶ x13.

...

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Proofgold Proof