Claim L0: ...

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Claim L1: ...

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Claim L2: ...

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Claim L3: ...

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Claim L4: ...

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Let x0 of type ι → ι → ο be given.

Let x1 of type ι → ι → ο be given.

Let x2 of type ι → ι → ι be given.

Let x3 of type ι → ο 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 → ο 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 → ι be given.

Let x12 of type ι → ο be given.

Let x13 of type ι → ι be given.

Let x14 of type ι → ι → ι → ι be given.

Let x15 of type ι → ι → ι → ι be given.

Let x16 of type ι be given.

Let x17 of type ι be given.

Let x18 of type ι be given.

Let x19 of type ι be given.

Let x20 of type ι → ο be given.

Let x21 of type ι → ι → ι be given.

Let x22 of type ι → ι → ι be given.

Let x23 of type ι → ι → ι be given.

Let x24 of type ι → ι → ι be given.

Let x25 of type ι → ι → ι → ι be given.

Let x26 of type ι → ι be given.

Let x27 of type ι → ο be given.

Let x28 of type ι → ι be given.

Let x29 of type ι → ι → ι be given.

Let x30 of type ι → ι → ι be given.

Let x31 of type ι → ι be given.

Let x32 of type ι be given.

Let x33 of type ι be given.

Let x34 of type ι → ο be given.

Let x35 of type ι → ο be given.

Let x36 of type ι be given.

Let x37 of type ι → ο be given.

Let x38 of type ι be given.

Let x39 of type ι → ο be given.

Let x40 of type ι be given.

Let x41 of type ι → ο be given.

Assume H5: ∀ x42 x43 . x41 x43 ⟶ (x43 = x42 ⟶ False) ⟶ x41 x42 ⟶ False.

Assume H6: ∀ x42 x43 . x0 x42 x43 ⟶ x41 x43 ⟶ False.

Assume H7: ∀ x42 . x41 x42 ⟶ (x42 = x40 ⟶ False) ⟶ False.

Assume H8: ∀ x42 x43 . x1 x42 x43 ⟶ (x41 x43 ⟶ False) ⟶ (x0 x42 x43 ⟶ False) ⟶ False.

Assume H9: ∀ x42 x43 . x0 x43 x42 ⟶ (x1 x43 x42 ⟶ False) ⟶ False.

Assume H10: ∀ x42 . (x2 x42 x40 = x42 ⟶ False) ⟶ False.

Assume H11: (x39 x38 ⟶ False) ⟶ False.

Assume H12: x41 x38 ⟶ False.

Assume H13: x37 x36 ⟶ False.

Assume H14: (x3 x36 ⟶ False) ⟶ False.

Assume H15: (x35 x36 ⟶ False) ⟶ False.

Assume H16: (x3 x4 ⟶ False) ⟶ False.

Assume H17: (x34 x4 ⟶ False) ⟶ False.

Assume H18: (x35 x4 ⟶ False) ⟶ False.

Assume H19: x41 x4 ⟶ False.

Assume H20: (x3 x5 ⟶ False) ⟶ False.

Assume H21: (x34 x5 ⟶ False) ⟶ False.

Assume H22: (x35 x5 ⟶ False) ⟶ False.

Assume H23: x41 x33 ⟶ False.

Assume H24: (x34 x6 ⟶ False) ⟶ False.

Assume H25: (x35 x6 ⟶ False) ⟶ False.

Assume H26: (x7 x8 ⟶ False) ⟶ False.

Assume H27: (x3 x8 ⟶ False) ⟶ False.

Assume H28: (x35 x8 ⟶ False) ⟶ False.

Assume H29: (x41 x32 ⟶ False) ⟶ False.

Assume H30: (x35 x9 ⟶ False) ⟶ False.

Assume H31: x41 x9 ⟶ False.

Assume H32: (x3 x10 ⟶ False) ⟶ False.

Assume H33: (x35 x10 ⟶ False) ⟶ False.

Assume H34: ∀ x42 . (x2 x42 x42 = x42 ⟶ False) ⟶ False.

Assume H35: ∀ x42 . (x41 x42 ⟶ False) ⟶ x35 x42 ⟶ x41 (x31 x42) ⟶ False.

Assume H36: ∀ x42 . (x41 x42 ⟶ False) ⟶ x35 x42 ⟶ x41 (x11 x42) ⟶ False.

Assume H37: ∀ x42 x43 x44 x45 . (x35 (x30 (x29 x43 x42) (x29 x45 x44)) ⟶ False) ⟶ False.

Assume H38: ∀ x42 x43 . (x41 x43 ⟶ False) ⟶ x41 (x2 x42 x43) ⟶ False.

Assume H39: ∀ x42 x43 . (x35 (x28 (x29 x43 x42)) ⟶ False) ⟶ False.

Assume H40: ∀ x42 x43 . (x41 x43 ⟶ False) ⟶ x41 (x2 x43 x42) ⟶ False.

Assume H41: ∀ x42 x43 . x41 (x30 x42 x43) ⟶ False.

Assume H42: ....

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Proofgold Proof