Proofgold Asset

Known 93eac.. : ∀ 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 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x0 x6 ⟶ x1 x2 (x1 x3 (x1 x4 (x1 x5 x6))) = x1 x3 (x1 x4 (x1 x5 (x1 x2 x6)))
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 3bd71.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x4 x5)))))) (proof)
Theorem 3a262.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x4 x5)))))) (proof)
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 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 0985b.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x5 x4)))))) (proof)
Theorem 40b9a.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x5 x4)))))) (proof)
Theorem beac9.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x4 x5)))))) (proof)
Theorem cf17e.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x4 x5)))))) (proof)
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 a0820.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x5 x3)))))) (proof)
Theorem 64d28.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x5 x3)))))) (proof)
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 02d79.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x3 x5)))))) (proof)
Theorem e9d51.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x3 x5)))))) (proof)
Theorem 6c995.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x5 (x1 x4 x3)))))) (proof)
Theorem b2d1a.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x5 (x1 x4 x3)))))) (proof)
Theorem e111b.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x5 (x1 x3 x4)))))) (proof)
Theorem 41bed.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x5 (x1 x3 x4)))))) (proof)
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 9612e.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x3 (x1 x7 x4)))))) (proof)
Theorem 562cb.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x3 (x1 x7 x4)))))) (proof)
Known 21e70.. : ∀ 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 x6 (x1 x8 (x1 x2 (x1 x7 (x1 x5 (x1 x3 (x1 x4 x9))))))
Theorem d0eb7.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x3 (x1 x4 x7)))))) (proof)
Theorem 5cf10.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x3 (x1 x4 x7)))))) (proof)
Theorem eb36a.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x4 (x1 x7 x3)))))) (proof)
Theorem f86b7.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x4 (x1 x7 x3)))))) (proof)
Known 09638.. : ∀ 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 x6 (x1 x8 (x1 x2 (x1 x7 (x1 x5 (x1 x4 (x1 x3 x9))))))
Theorem 369ca.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x4 (x1 x3 x7)))))) (proof)
Theorem 2d5b4.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x4 (x1 x3 x7)))))) (proof)
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 62402.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x7 (x1 x4 x3)))))) (proof)
Theorem 50715.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x7 (x1 x4 x3)))))) (proof)
Theorem 9c867.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x7 (x1 x3 x4)))))) (proof)
Theorem b7428.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x5 (x1 x7 (x1 x3 x4)))))) (proof)
Theorem ed885.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x3 (x1 x7 x5)))))) (proof)
Theorem c4483.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x3 (x1 x7 x5)))))) (proof)
Known 493fa.. : ∀ 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 x6 (x1 x8 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x5 x9))))))
Theorem 19c01.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x3 (x1 x5 x7)))))) (proof)
Theorem 02c4e.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x3 (x1 x5 x7)))))) (proof)
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 b6bc8.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x5 (x1 x7 x3)))))) (proof)
Theorem 13cf3.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x5 (x1 x7 x3)))))) (proof)
Known 3b0bb.. : ∀ 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 x6 (x1 x8 (x1 x2 (x1 x7 (x1 x4 (x1 x5 (x1 x3 x9))))))
Theorem 36cb6.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x5 (x1 x3 x7)))))) (proof)
Theorem 029d6.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x5 (x1 x3 x7)))))) (proof)
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 c7df7.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x7 (x1 x5 x3)))))) (proof)
Theorem b33ca.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x7 (x1 x5 x3)))))) (proof)
Theorem 5abce.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x7 (x1 x3 x5)))))) (proof)
Theorem 72277.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x4 (x1 x7 (x1 x3 x5)))))) (proof)
Theorem 16281.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x4 (x1 x7 x5)))))) (proof)
Theorem f26ed.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x4 (x1 x7 x5)))))) (proof)
Known bedad.. : ∀ 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 x6 (x1 x8 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x5 x9))))))
Theorem 644af.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x4 (x1 x5 x7)))))) (proof)
Theorem d8d6a.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x4 (x1 x5 x7)))))) (proof)
Theorem 8652a.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x5 (x1 x7 x4)))))) (proof)
Theorem eb99a.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x5 (x1 x7 x4)))))) (proof)
Known bfc06.. : ∀ 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 x6 (x1 x8 (x1 x2 (x1 x7 (x1 x3 (x1 x5 (x1 x4 x9))))))
Theorem a23aa.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x5 (x1 x4 x7)))))) (proof)
Theorem 29b33.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x5 (x1 x4 x7)))))) (proof)
Theorem e6fa7.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x7 (x1 x5 x4)))))) (proof)
Theorem fc180.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x7 (x1 x5 x4)))))) (proof)
Theorem a2a08.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x7 (x1 x4 x5)))))) (proof)
Theorem 37f36.. : ∀ 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 x6 (x1 x9 (x1 x2 (x1 x8 (x1 x3 (x1 x7 (x1 x4 x5)))))) (proof)
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))
Known 9a069.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x7 (x1 x4 (x1 x6 x9))))))
Theorem 09345.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x4 (x1 x7 x6)))))) (proof)
Theorem 493c4.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x4 (x1 x7 x6)))))) (proof)
Theorem df0a7.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x4 (x1 x6 x7)))))) (proof)
Theorem 954a7.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x4 (x1 x6 x7)))))) (proof)
Known 90996.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x7 (x1 x5 (x1 x6 x9))))))
Theorem 5afb0.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x6 (x1 x7 x4)))))) (proof)
Theorem a5291.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x6 (x1 x7 x4)))))) (proof)
Known b0409.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x7 (x1 x6 (x1 x4 x9))))))
Theorem b94ce.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x6 (x1 x4 x7)))))) (proof)
Theorem 07760.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x6 (x1 x4 x7)))))) (proof)
Known 3b506.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x7 (x1 x6 (x1 x5 x9))))))
Theorem 9120b.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x7 (x1 x6 x4)))))) (proof)
Theorem 7ce28.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x7 (x1 x6 x4)))))) (proof)
Theorem 09b6b.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x7 (x1 x4 x6)))))) (proof)
Theorem f0f61.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x8 (x1 x7 (x1 x4 x6)))))) (proof)
Known 41f0c.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x6 (x1 x4 (x1 x7 x9))))))
Theorem 63e9e.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x4 (x1 x8 x6)))))) (proof)
Theorem 4070a.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x4 (x1 x8 x6)))))) (proof)
Theorem 15ab9.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x4 (x1 x6 x8)))))) (proof)
Theorem 1a658.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x4 (x1 x6 x8)))))) (proof)
Known 90d48.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x6 (x1 x5 (x1 x7 x9))))))
Theorem bc508.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x6 (x1 x8 x4)))))) (proof)
Theorem a6dbb.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x6 (x1 x8 x4)))))) (proof)
Theorem cc376.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x6 (x1 x4 x8)))))) (proof)
Theorem 2eeba.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x6 (x1 x4 x8)))))) (proof)
Known 83cbf.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x6 (x1 x7 (x1 x5 x9))))))
Theorem 0b31e.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x8 (x1 x6 x4)))))) (proof)
Theorem 7e31b.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x8 (x1 x6 x4)))))) (proof)
Known 28a45.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x6 (x1 x7 (x1 x4 x9))))))
Theorem 891ec.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x8 (x1 x4 x6)))))) (proof)
Theorem 544a1.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x7 (x1 x8 (x1 x4 x6)))))) (proof)
Theorem e8302.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x4 (x1 x8 x7)))))) (proof)
Theorem 5283c.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x4 (x1 x8 x7)))))) (proof)
Theorem cf9b8.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x4 (x1 x7 x8)))))) (proof)
Theorem 6f835.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x4 (x1 x7 x8)))))) (proof)
Known b1c4c.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x5 (x1 x6 (x1 x7 x9))))))
Theorem df430.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x7 (x1 x8 x4)))))) (proof)
Theorem 75865.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x7 (x1 x8 x4)))))) (proof)
Theorem 98f7a.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x7 (x1 x4 x8)))))) (proof)
Theorem b042d.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x7 (x1 x4 x8)))))) (proof)
Known 3e08f.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x5 (x1 x7 (x1 x6 x9))))))
Theorem d799f.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x8 (x1 x7 x4)))))) (proof)
Theorem e7448.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x8 (x1 x7 x4)))))) (proof)
Theorem 7561d.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x8 (x1 x4 x7)))))) (proof)
Theorem b510a.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x6 (x1 x8 (x1 x4 x7)))))) (proof)
Known 9eafc.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x4 (x1 x6 (x1 x7 x9))))))
Theorem dfe02.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x6 (x1 x8 x7)))))) (proof)
Theorem bd6e6.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x6 (x1 x8 x7)))))) (proof)
Theorem cc07c.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x6 (x1 x7 x8)))))) (proof)
Theorem b2602.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x6 (x1 x7 x8)))))) (proof)
Theorem 9899d.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x7 (x1 x8 x6)))))) (proof)
Theorem 43bf1.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x7 (x1 x8 x6)))))) (proof)
Known 9e5b5.. : ∀ 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 x2 (x1 x8 (x1 x3 (x1 x4 (x1 x7 (x1 x6 x9))))))
Theorem ada68.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x7 (x1 x6 x8)))))) (proof)
Theorem 6cf56.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x7 (x1 x6 x8)))))) (proof)
Theorem 778bf.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x8 (x1 x7 x6)))))) (proof)
Theorem 05f91.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x8 (x1 x7 x6)))))) (proof)
Theorem 760f9.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x8 (x1 x6 x7)))))) (proof)
Theorem 06bcd.. : ∀ 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 x2 (x1 x9 (x1 x3 (x1 x4 (x1 x8 (x1 x6 x7)))))) (proof)
Known 7c026.. : ∀ 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 x2 (x1 x8 (x1 x4 (x1 x7 (x1 x3 (x1 x6 x9))))))
Theorem 2c075.. : ∀ 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 x2 (x1 x9 (x1 x4 (x1 x8 (x1 x3 (x1 x7 x6)))))) (proof)
Theorem 31ce4.. : ∀ 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 x2 (x1 x9 (x1 x4 (x1 x8 (x1 x3 (x1 x7 x6)))))) (proof)
Theorem cf5ac.. : ∀ 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 x2 (x1 x9 (x1 x4 (x1 x8 (x1 x3 (x1 x6 x7)))))) (proof)
Theorem 53f22.. : ∀ 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 x2 (x1 x9 (x1 x4 (x1 x8 (x1 x3 (x1 x6 x7)))))) (proof)
Theorem 092e2.. : ∀ 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 x2 (x1 x9 (x1 x4 (x1 x8 (x1 x6 (x1 x7 x3)))))) (proof)
Theorem 63fe0.. : ∀ 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 x2 (x1 x9 (x1 x4 (x1 x8 (x1 x6 (x1 x7 x3)))))) (proof)
Known a8331.. : ∀ 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 x2 (x1 x8 (x1 x4 (x1 x7 (x1 x6 (x1 x3 x9))))))
Theorem bf5b5.. : ∀ 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 x2 (x1 x9 (x1 x4 (x1 x8 (x1 x6 (x1 x3 x7)))))) (proof)
Theorem 70d6f.. : ∀ 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 x2 (x1 x9 (x1 x4 (x1 x8 (x1 x6 (x1 x3 x7)))))) (proof)