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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιιι be given.
Assume H0: ∀ x2 . In x2 x0∀ x3 . In x3 x0In (x1 x2 x3) x0.
Let x2 of type ιιιι be given.
Assume H1: ∀ x3 . In x3 x0∀ x4 . In x4 x0∀ x5 . In x5 x0In (x2 x3 x4 x5) x0.
Let x3 of type ι be given.
Assume H2: In x3 x0.
Let x4 of type ι be given.
Assume H3: In x4 x0.
Let x5 of type ιιιι be given.
Assume H4: ∀ x6 . In x6 x0∀ x7 . In x7 x0∀ x8 . In x8 x0In (x5 x6 x7 x8) x0.
Let x6 of type ιιι be given.
Assume H5: ∀ x7 . In x7 x0∀ x8 . In x8 x0In (x6 x7 x8) x0.
Let x7 of type ιιι be given.
Assume H6: ∀ x8 . In x8 x0∀ x9 . In x9 x0In (x7 x8 x9) x0.
Let x8 of type ι be given.
Assume H7: In x8 x0.
Let x9 of type ιιι be given.
Assume H8: ∀ x10 . In x10 x0∀ x11 . In x11 x0In (x9 x10 x11) x0.
Assume H9: ∀ x10 . In x10 x0(x9 x8 x10 = x10False)False.
Assume H10: ∀ x10 . In x10 x0(x9 x10 x8 = x10False)False.
Assume H11: ∀ x10 . In x10 x0∀ x11 . In x11 x0(x7 (x9 x11 x10) x10 = x11False)False.
Assume H12: ∀ x10 . In x10 x0∀ x11 . In x11 x0(x1 x10 x11 = x9 (x7 x8 (x7 x8 x10)) (x7 x11 x10)False)False.
Assume H13: ∀ x10 . In x10 x0(x7 x10 x8 = x10False)False.
Assume H14: ∀ x10 . In x10 x0(x7 x10 x10 = x8False)False.
Assume H15: ∀ x10 . In x10 x0(x6 x8 x10 = x10False)False.
Assume H16: ∀ x10 . In x10 x0∀ x11 . In x11 x0(x2 x8 x10 x11 = x11False)False.
Assume H17: ∀ x10 . In x10 x0∀ x11 . In x11 x0(x5 x8 x10 x11 = x11False)False.
Assume H18: ∀ x10 . ...∀ x11 . ...∀ x12 . ...(x5 x10 x11 (x6 x10 (x1 x11 (x5 x10 x11 (x6 x10 ...)))) = ...False)False.
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