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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: d7d78.. x0 x1 x2.
Let x3 of type ιιιο be given.
Assume H1: ∀ x4 . x3 c4def.. x4 x4.
Assume H2: ∀ x4 x5 x6 x7 x8 . x3 x4 x6 x7x3 x5 x7 x8x3 (6b90c.. x4 x5) x6 x8.
Assume H3: ∀ x4 . x3 c9248.. x4 236c6...
Assume H4: ∀ x4 x5 x6 . x3 x4 x5 x6x3 (a6e19.. x4) x5 (0b8ef.. x6).
Assume H5: ∀ x4 x5 x6 . x3 x4 x5 x6x3 (2fe34.. x4) x5 (6c5f4.. x6).
Assume H6: ∀ x4 x5 x6 x7 x8 . e05e6.. x5x3 x4 (cfc98.. x6 x7) x8x3 (3e00e.. x4 x5) (cfc98.. (0b8ef.. x6) x7) x8.
Assume H7: ∀ x4 x5 x6 x7 x8 . e05e6.. x4x3 x5 (cfc98.. x6 x7) x8x3 (3e00e.. x4 x5) (cfc98.. (6c5f4.. x6) x7) x8.
Assume H8: ∀ x4 x5 x6 x7 x8 . x3 x4 x6 x7x3 x5 x6 x8x3 (f9341.. x4 x5) x6 (cfc98.. x7 x8).
Assume H9: ∀ x4 x5 x6 x7 . x3 x4 x5 x7x3 (1fa6d.. x4) (cfc98.. x5 x6) x7.
Assume H10: ∀ x4 x5 x6 x7 . x3 x4 x6 x7x3 (3a365.. x4) (cfc98.. x5 x6) x7.
Apply H5 with x0, x1, x2.
Apply H0 with x3 leaving 10 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H10.