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Proofgold Proof

pf
Let x0 of type (ιο) → ο be given.
Let x1 of type (ιιο) → ο be given.
Let x2 of type ι be given.
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 be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Let x10 of type ι be given.
Let x11 of type ι be given.
Assume H0: ∀ x12 : ι → ο . x12 x2x12 x3x12 x4x12 x5x12 x6x12 x7x12 x8x12 x9x12 x10x12 x11x0 x12.
Assume H1: ∀ x12 : ι → ι → ο . .......................................................................................x12 x4 x11x12 x5 x2x12 x5 x3x12 x5 x4x12 x5 x5x12 x5 x6x12 x5 x7x12 x5 x8x12 x5 x9x12 x5 x10x12 x5 x11x12 x6 x2x12 x6 x3x12 x6 x4x12 x6 x5x12 x6 x6x12 x6 x7x12 x6 x8x12 x6 x9x12 x6 x10x12 x6 x11x12 x7 x2x12 x7 x3x12 x7 x4x12 x7 x5x12 x7 x6x12 x7 x7x12 x7 x8x12 x7 x9x12 x7 x10x12 x7 x11x12 x8 x2x12 x8 x3x12 x8 x4x12 x8 x5x12 x8 x6x12 x8 x7x12 x8 x8x12 x8 x9x12 x8 x10x12 x8 x11x12 x9 x2x12 x9 x3x12 x9 x4x12 x9 x5x12 x9 x6x12 x9 x7x12 x9 x8x12 x9 x9x12 x9 x10x12 x9 x11x12 x10 x2x12 x10 x3x12 x10 x4x12 x10 x5x12 x10 x6x12 x10 x7x12 x10 x8x12 x10 x9x12 x10 x10x12 x10 x11x12 x11 x2x12 x11 x3x12 x11 x4x12 x11 x5x12 x11 x6x12 x11 x7x12 x11 x8x12 x11 x9x12 x11 x10x12 x11 x11x0 (λ x13 . x0 (λ x14 . x12 x13 x14)).
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