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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.
Let x3 of type ι be given.
Assume H0: 74e69.. x0.
Assume H1: 762f0.. x3 x1 x2.
Let x4 of type ιιιο be given.
Assume H2: ∀ x5 . 74e69.. x5x4 c4def.. x5 x5.
Assume H3: ∀ x5 x6 x7 x8 x9 . x4 x8 x5 x6x4 x9 x6 x7x4 (6b90c.. x8 x9) x5 x7.
Assume H4: ∀ x5 . 74e69.. x5x4 c9248.. x5 5e331...
Assume H5: ∀ x5 x6 x7 x8 . 74e69.. x7x4 x8 x5 x6x4 (a6e19.. x8) x5 (a3eb9.. x6 x7).
Assume H6: ∀ x5 x6 x7 x8 . 74e69.. x6x4 x8 x5 x7x4 (2fe34.. x8) x5 (a3eb9.. x6 x7).
Assume H7: ∀ x5 x6 x7 x8 x9 x10 . x4 x9 (bf68c.. x5 x7) x8x4 x10 (bf68c.. x6 x7) x8x4 (3e00e.. x9 x10) (bf68c.. (a3eb9.. x5 x6) x7) x8.
Assume H8: ∀ x5 x6 x7 x8 x9 . x4 x8 x5 x6x4 x9 x5 x7x4 (f9341.. x8 x9) x5 (bf68c.. x6 x7).
Assume H9: ∀ x5 x6 x7 x8 . 74e69.. x6x4 x8 x5 x7x4 (1fa6d.. x8) (bf68c.. x5 x6) x7.
Assume H10: ∀ x5 x6 x7 x8 . 74e69.. x5x4 x8 x6 x7x4 (3a365.. x8) (bf68c.. x5 x6) x7.
Apply H10 with x0, x1, x2, x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H1 with x4 leaving 9 subgoals.
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.