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 → ο be given.

Let x1 of type ι → ι → ο be given.

Let x2 of type ι → ο be given.

Let x3 of type ι be given.

Let x4 of type ι → ο be given.

Let x5 of type ι be given.

Let x6 of type ι → ο be given.

Let x7 of type ι → ο be given.

Let x8 of type ι be given.

Let x9 of type ι → ο be given.

Let x10 of type ι be given.

Let x11 of type ι be given.

Let x12 of type ι be given.

Let x13 of type ι → ι be given.

Let x14 of type ι → ι → ι be given.

Let x15 of type ι → ο be given.

Let x16 of type ι → ι be given.

Let x17 of type ι → ι → ι be given.

Let x18 of type ι → ι → ι be given.

Let x19 of type ι → ι → ι be given.

Let x20 of type ι → ι → ι be given.

Let x21 of type ι be given.

Let x22 of type ι be given.

Let x23 of type ι → ο be given.

Let x24 of type ι → ι → ι → ι be given.

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

Let x26 of type ι be given.

Let x27 of type ι → ι be given.

Let x28 of type ι → ο be given.

Let x29 of type ι → ι be given.

Let x30 of type ι → ι be given.

Let x31 of type ι be given.

Let x32 of type ι be given.

Let x33 of type ι → ο be given.

Let x34 of type ι be given.

Let x35 of type ι be given.

Let x36 of type ι be given.

Let x37 of type ι → ο be given.

Let x38 of type ι → ι → ι be given.

Let x39 of type ι → ι → ο be given.

Let x40 of type ι → ι → ι be given.

Let x41 of type ι be given.

Assume H5: ∀ x42 x43 . x43 = x41 ⟶ (x40 x42 x43 = x41 ⟶ False) ⟶ False.

Assume H6: ∀ x42 x43 . x43 = x41 ⟶ (x40 x43 x42 = x41 ⟶ False) ⟶ False.

Assume H7: ∀ x42 x43 . x40 x42 x43 = x41 ⟶ (x42 = x41 ⟶ False) ⟶ (x43 = x41 ⟶ False) ⟶ False.

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

Assume H9: ∀ x42 x43 x44 x45 . x39 x44 x45 ⟶ x39 x43 x42 ⟶ (x39 (x38 x44 x43) (x40 x45 x42) ⟶ False) ⟶ False.

Assume H10: ∀ x42 x43 x44 x45 . x39 (x38 x43 x45) (x40 x42 x44) ⟶ (x39 x45 x44 ⟶ False) ⟶ False.

Assume H11: ∀ x42 x43 x44 x45 . x39 (x38 x45 x43) (x40 x44 x42) ⟶ (x39 x45 x44 ⟶ False) ⟶ False.

Assume H12: ∀ x42 x43 . x39 x42 x43 ⟶ x0 x43 ⟶ False.

Assume H13: ∀ x42 . x0 x42 ⟶ (x42 = x41 ⟶ False) ⟶ False.

Assume H14: ∀ x42 x43 . x1 x42 x43 ⟶ (x0 x43 ⟶ False) ⟶ (x39 x42 x43 ⟶ False) ⟶ False.

Assume H15: ∀ x42 x43 . x39 x43 x42 ⟶ (x1 x43 x42 ⟶ False) ⟶ False.

Assume H16: (x2 x3 ⟶ False) ⟶ False.

Assume H17: x0 x3 ⟶ False.

Assume H18: x4 x5 ⟶ False.

Assume H19: (x37 x5 ⟶ False) ⟶ False.

Assume H20: (x6 x5 ⟶ False) ⟶ False.

Assume H21: (x37 x36 ⟶ False) ⟶ False.

Assume H22: (x7 x36 ⟶ False) ⟶ False.

Assume H23: (x6 x36 ⟶ False) ⟶ False.

Assume H24: x0 x36 ⟶ False.

Assume H25: (x37 x35 ⟶ False) ⟶ False.

Assume H26: (x7 x35 ⟶ False) ⟶ False.

Assume H27: (x6 x35 ⟶ False) ⟶ False.

Assume H28: x0 x8 ⟶ False.

Assume H29: (x7 x34 ⟶ False) ⟶ False.

Assume H30: (x6 x34 ⟶ False) ⟶ False.

Assume H31: (x33 x32 ⟶ False) ⟶ False.

Assume H32: (x37 x32 ⟶ False) ⟶ False.

Assume H33: (x6 x32 ⟶ False) ⟶ False.

Assume H34: (x9 x10 ⟶ False) ⟶ False.

Assume H35: (x0 x31 ⟶ False) ⟶ False.

Assume H36: (x6 x11 ⟶ False) ⟶ False.

Assume H37: x0 x11 ⟶ False.

Assume H38: (x37 x12 ⟶ False) ⟶ False.

Assume H39: (x6 x12 ⟶ False) ⟶ False.

...

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Proofgold Proof