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b2a05../17422.. bday: 27924 doc published by Pr5Zc..Known 75b00.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 x7)))) = x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x2 x7))))Known 00235.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x7 (x1 x2 (x1 x5 (x1 x6 (x1 x8 (x1 x3 x9))))))Theorem 0a29c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x8 x4))))))...
Theorem 9665d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x8 x4))))))...
Known 48599.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x4 x9))))))Theorem b2313.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x4 x8))))))...
Theorem 69d03.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x4 x8))))))...
Known c0c54.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 x8))))) = x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x2 x8)))))Theorem 6e858.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x8 x3))))))...
Theorem 5bb23.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x8 x3))))))...
Known cf069.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x3 x9))))))Theorem a9ee0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x3 x8))))))...
Theorem 2bf49.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x3 x8))))))...
Known 1cc67.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x8 (x1 x2 (x1 x5 (x1 x6 (x1 x7 (x1 x3 x9))))))Theorem e7d0b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x8 (x1 x4 x3))))))...
Theorem 2929b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x8 (x1 x4 x3))))))...
Theorem bfe09.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x8 (x1 x3 x4))))))...
Theorem 103de.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x8 (x1 x3 x4))))))...
Known 97bd9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x7 x9))))))Theorem 17fab.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x8 x7))))))...
Theorem a618c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x8 x7))))))...
Theorem 11b25.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x7 x8))))))...
Theorem 7ffc2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x7 x8))))))...
Known 1f92a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x6 (x1 x2 (x1 x5 (x1 x7 (x1 x8 (x1 x3 x9))))))Theorem 2e744.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x8 x3))))))...
Theorem 1d6ea.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x8 x3))))))...
Known 4733e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x3 x9))))))Theorem 9b50f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x3 x8))))))...
Theorem aff7a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x3 x8))))))...
Known 80433.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x6 (x1 x2 (x1 x5 (x1 x8 (x1 x7 (x1 x3 x9))))))Theorem d0f88.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x8 (x1 x7 x3))))))...
Theorem d059f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x8 (x1 x7 x3))))))...
Theorem 217da.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x8 (x1 x3 x7))))))...
Theorem 16845.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x8 (x1 x3 x7))))))...
Known 475fb.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x7 x9))))))Theorem 92632.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x8 x7))))))...
Theorem 1ecd9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x8 x7))))))...
Theorem 72146.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x7 x8))))))...
Theorem cd0f6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x7 x8))))))...
Theorem 530a1.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x8 x4))))))...
Theorem cac63.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x8 x4))))))...
Known bd250.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x4 x9))))))Theorem 6432f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x4 x8))))))...
Theorem 94ad4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x4 x8))))))...
Theorem 23a00.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x7 x4))))))...
Theorem b3d3a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x7 x4))))))...
Theorem 67a86.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x4 x7))))))...
Theorem 522fc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x4 x7))))))...
Known 7a7f7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x7 (x1 x2 (x1 x8 (x1 x5 (x1 x6 (x1 x3 x9))))))Theorem aa522.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x3 (x1 x6 x4))))))...
Theorem 76a17.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x3 (x1 x6 x4))))))...
Known 45f87.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x1 x2 (x1 x3 (x1 x4 x5)) = x1 x3 (x1 x4 (x1 x2 x5))Theorem 1aa23.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x3 (x1 x4 x6))))))...
Theorem 7f2b7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x3 (x1 x4 x6))))))...
Theorem 98bec.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x4 (x1 x6 x3))))))...
Theorem 25190.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x4 (x1 x6 x3))))))...
Theorem 18806.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x4 (x1 x3 x6))))))...
Theorem b8578.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x4 (x1 x3 x6))))))...
Known 90f7b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x8 (x1 x2 (x1 x6 (x1 x7 (x1 x5 (x1 x3 x9))))))Theorem 6f0cd.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x6 (x1 x4 x3))))))...
Theorem 31941.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x6 (x1 x4 x3))))))...
Theorem 9fa47.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x6 (x1 x3 x4))))))...
Theorem c59a2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x6 (x1 x3 x4))))))...
Known f45b5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x7 (x1 x2 (x1 x6 (x1 x5 (x1 x8 (x1 x3 x9))))))Theorem 20bda.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x8 x4))))))...
Theorem 9c67a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x8 x4))))))...
Known e64b6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x4 x9))))))Theorem 9749c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x4 x8))))))...
Theorem f302d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x4 x8))))))...
Theorem 1c443.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x8 x3))))))...
Theorem d96f9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x8 x3))))))...
Known c6482.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x3 x9))))))Theorem dfaeb.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x3 x8))))))...
Theorem 24446.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x3 x8))))))...
Known 196dd.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x8 (x1 x2 (x1 x6 (x1 x5 (x1 x7 (x1 x3 x9))))))Theorem c18e4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x8 (x1 x4 x3))))))...
Theorem 90151.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x8 (x1 x4 x3))))))...
Theorem 8dbee.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x8 (x1 x3 x4))))))...
Theorem 45128.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x8 (x1 x3 x4))))))...
Theorem 4f7e6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x8 x6))))))...
Theorem c9231.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x8 x6))))))...
Known 47d38.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x6 x9))))))Theorem 4f524.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x6 x8))))))...
Theorem 7c1aa.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x6 x8))))))...
Known 89a50.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x6 (x1 x2 (x1 x7 (x1 x5 (x1 x8 (x1 x3 x9))))))Theorem e9e79.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x8 x3))))))...
Theorem 54d94.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x8 x3))))))...
Known cfc03.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x3 x9))))))Theorem b8eb5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x3 x8))))))...
Theorem 9fcd7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x3 x8))))))...
Known cd2ee.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x6 (x1 x2 (x1 x8 (x1 x5 (x1 x7 (x1 x3 x9))))))Theorem 5d727.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x8 (x1 x6 x3))))))...
Theorem 57035.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x8 (x1 x6 x3))))))...
Theorem 28fd2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x8 (x1 x3 x6))))))...
Theorem a40fc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x8 (x1 x3 x6))))))...
Theorem 2fd6f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x8 x6))))))...
Theorem 87247.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x8 x6))))))...
Known 02dcc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x6 x9))))))Theorem 88e25.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x6 x8))))))...
Theorem 0ede9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x6 x8))))))...
Theorem c0e86.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x8 x4))))))...
Theorem 4f0ca.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x8 x4))))))...
Known df8da.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x4 x9))))))Theorem c46d6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x4 x8))))))...
Theorem 1daff.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x4 x8))))))...
Theorem c5657.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x6 x4))))))...
Theorem 5e527.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x6 x4))))))...
Theorem 4db0d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x4 x6))))))...
Theorem d6e5a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x4 x6))))))...
Known c40bc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x7 (x1 x2 (x1 x8 (x1 x6 (x1 x5 (x1 x3 x9))))))Theorem f0452.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x6 x4))))))...
Theorem 20739.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x6 x4))))))...
Theorem e10b6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x4 x6))))))...
Theorem 50882.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x4 x6))))))...
Theorem 6083c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x6 x3))))))...
Theorem aed5b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x6 x3))))))...
Theorem 21500.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x3 x6))))))...
Theorem fe3e3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x3 x6))))))...
Known a52a5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x8 (x1 x2 (x1 x7 (x1 x6 (x1 x5 (x1 x3 x9))))))Theorem 56937.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x6 (x1 x4 x3))))))...
Theorem db7c0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x6 (x1 x4 x3))))))...
Theorem 703fe.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x6 (x1 x3 x4))))))...
Theorem 85a3d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x6 (x1 x3 x4))))))...
Known 65d27.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x4 (x1 x7 (x1 x2 (x1 x6 (x1 x8 (x1 x5 (x1 x3 x9))))))Theorem 1b768.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x3 (x1 x7 x4))))))...
Theorem 38ac1.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x3 (x1 x7 x4))))))...
Theorem 3efa7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x3 (x1 x4 x7))))))...
Theorem 3ab57.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x3 (x1 x4 x7))))))...
Theorem e6d82.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x4 (x1 x7 x3))))))...
Theorem 41885.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x4 (x1 x7 x3))))))...
Theorem 02f69.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x4 (x1 x3 x7))))))...
Theorem d2454.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x4 (x1 x3 x7))))))...
Theorem 7ab7e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4)) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x7 (x1 x4 x3))))))...
Theorem 98d13.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3)) ⟶ (∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4) ⟶ (∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x1 x2 x3 = x1 x3 x2) ⟶ ∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x0 x9 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x7 (x1 x4 x3))))))...
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