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fcbc2.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMcPY../4d42e.. ownership of bdce7.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMSPQ../f679c.. ownership of 8081c.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMFN2../b729a.. ownership of c29e7.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMWHv../e4fcc.. ownership of b36b8.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMRUq../e254b.. ownership of e78fb.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMXQx../39118.. ownership of 46e85.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMMDN../fb315.. ownership of 356a9.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMa8A../b3e7a.. ownership of 40e68.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMNbY../ad3a1.. ownership of c49c3.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMM2g../b9c73.. ownership of 37c00.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMHZB../36a0c.. ownership of 62118.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0TMUqA../3d531.. ownership of f38ff.. as prop with payaddr Pr5Zc.. rights free controlledby Pr5Zc.. upto 0PUX2k../de8d0.. doc published by Pr5Zc..Known 02adf.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x3 (x1 x8 (x1 x5 (x1 x6 x9))))))Theorem 62118.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x5 (x1 x6 x7)))))) (proof)Theorem c49c3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x5 (x1 x6 x7)))))) (proof)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)))Theorem 356a9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x6 (x1 x7 x5)))))) (proof)Theorem e78fb.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x6 (x1 x7 x5)))))) (proof)Known b514c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x3 (x1 x8 (x1 x6 (x1 x5 x9))))))Theorem c29e7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x6 (x1 x5 x7)))))) (proof)Theorem bdce7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x6 (x1 x5 x7)))))) (proof)Theorem b5ff4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x7 (x1 x6 x5)))))) (proof)Theorem b7485.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x7 (x1 x6 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))Theorem a661c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x7 (x1 x5 x6)))))) (proof)Theorem 4ef3a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x9 (x1 x7 (x1 x5 x6)))))) (proof)Known e21d3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x5 x8)))))Theorem 4c588.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 (x1 x5 (x1 x9 x6)))))) (proof)Theorem 80796.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 (x1 x5 (x1 x9 x6)))))) (proof)Theorem 9d2ac.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 (x1 x6 (x1 x9 x5)))))) (proof)Theorem 4d2e5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 (x1 x6 (x1 x9 x5)))))) (proof)Known 6e27c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x8 (x1 x5 x9))))))Theorem e0c47.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 (x1 x9 (x1 x6 x5)))))) (proof)Theorem 55fa7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 (x1 x9 (x1 x6 x5)))))) (proof)Theorem 0ecb7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 (x1 x9 (x1 x5 x6)))))) (proof)Theorem 3ba46.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 (x1 x9 (x1 x5 x6)))))) (proof)Theorem 1e91a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x5 (x1 x9 x7)))))) (proof)Theorem 729c0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x5 (x1 x9 x7)))))) (proof)Known 0c0cb.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x6 x8)))))Theorem 137b6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x7 (x1 x9 x5)))))) (proof)Theorem 86c97.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x7 (x1 x9 x5)))))) (proof)Known a3f08.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x8 (x1 x6 x9))))))Theorem cd1f3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x9 (x1 x7 x5)))))) (proof)Theorem 06b77.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x9 (x1 x7 x5)))))) (proof)Theorem c28cc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x9 (x1 x5 x7)))))) (proof)Theorem 42270.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x6 (x1 x9 (x1 x5 x7)))))) (proof)Theorem ec060.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x6 (x1 x9 x7)))))) (proof)Theorem ed083.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x6 (x1 x9 x7)))))) (proof)Theorem 6c746.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x7 (x1 x9 x6)))))) (proof)Theorem 985c0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x7 (x1 x9 x6)))))) (proof)Theorem 18c35.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x9 (x1 x7 x6)))))) (proof)Theorem 55efd.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x9 (x1 x7 x6)))))) (proof)Theorem 675fa.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x9 (x1 x6 x7)))))) (proof)Theorem 1986f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 (x1 x9 (x1 x6 x7)))))) (proof)Known c79b2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x5 (x1 x8 (x1 x3 (x1 x6 x9))))))Theorem 39fbc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x3 (x1 x7 x6)))))) (proof)Theorem 6037a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x3 (x1 x7 x6)))))) (proof)Theorem 8b1ba.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x3 (x1 x6 x7)))))) (proof)Theorem 00053.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x3 (x1 x6 x7)))))) (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)))))Known 544eb.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x4 (x1 x8 (x1 x5 (x1 x6 x9))))))Theorem 61c5c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x6 (x1 x7 x3)))))) (proof)Theorem acb76.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x6 (x1 x7 x3)))))) (proof)Known e7e34.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x5 (x1 x8 (x1 x6 (x1 x3 x9))))))Theorem 3085b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x6 (x1 x3 x7)))))) (proof)Theorem 31d9d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x6 (x1 x3 x7)))))) (proof)Known 40d8d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x4 (x1 x8 (x1 x6 (x1 x5 x9))))))Theorem 55d1d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x7 (x1 x6 x3)))))) (proof)Theorem dc780.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x7 (x1 x6 x3)))))) (proof)Theorem 126b0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x7 (x1 x3 x6)))))) (proof)Theorem b456d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x9 (x1 x7 (x1 x3 x6)))))) (proof)Known fe87a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x3 x8)))))Theorem be4a0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 (x1 x3 (x1 x9 x6)))))) (proof)Theorem 9c404.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 (x1 x3 (x1 x9 x6)))))) (proof)Known a4992.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x4 (x1 x6 (x1 x5 x8)))))Theorem a069e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 (x1 x6 (x1 x9 x3)))))) (proof)Theorem ddb89.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 (x1 x6 (x1 x9 x3)))))) (proof)Known ec6fe.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x4 (x1 x6 (x1 x8 (x1 x5 x9))))))Theorem e7895.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 (x1 x9 (x1 x6 x3)))))) (proof)Theorem 4c5fd.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 (x1 x9 (x1 x6 x3)))))) (proof)Known 4294d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x8 (x1 x3 x9))))))Theorem 839cf.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 (x1 x9 (x1 x3 x6)))))) (proof)Theorem db6e5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 (x1 x9 (x1 x3 x6)))))) (proof)Theorem c171b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x3 (x1 x9 x7)))))) (proof)Theorem 2b2d3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x3 (x1 x9 x7)))))) (proof)Known 59a9e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x4 (x1 x5 (x1 x6 x8)))))Theorem 9b673.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x7 (x1 x9 x3)))))) (proof)Theorem 3871f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x7 (x1 x9 x3)))))) (proof)Known fab97.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x4 (x1 x5 (x1 x8 (x1 x6 x9))))))Theorem 28c14.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x9 (x1 x7 x3)))))) (proof)Theorem 25d80.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x9 (x1 x7 x3)))))) (proof)Theorem 78554.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x9 (x1 x3 x7)))))) (proof)Theorem cd6e8.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x6 (x1 x9 (x1 x3 x7)))))) (proof)Known 52cf5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x6 x8)))))Theorem ff9a0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x6 (x1 x9 x7)))))) (proof)Theorem 178d4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x6 (x1 x9 x7)))))) (proof)Theorem d963d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x7 (x1 x9 x6)))))) (proof)Theorem 2b82a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x7 (x1 x9 x6)))))) (proof)Known f7c9a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x8 (x1 x6 x9))))))Theorem 43fcf.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x9 (x1 x7 x6)))))) (proof)Theorem d65f7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x9 (x1 x7 x6)))))) (proof)Theorem e3e0c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x9 (x1 x6 x7)))))) (proof)Theorem c6668.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 (x1 x9 (x1 x6 x7)))))) (proof)Theorem 42c1a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x3 (x1 x7 x5)))))) (proof)Theorem bb3a9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x3 (x1 x7 x5)))))) (proof)Known 03523.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x6 (x1 x8 (x1 x3 (x1 x5 x9))))))Theorem afbf4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x3 (x1 x5 x7)))))) (proof)Theorem d96b6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x3 (x1 x5 x7)))))) (proof)Known 4074c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x5 (x1 x8 (x1 x4 (x1 x6 x9))))))Theorem 6711c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x5 (x1 x7 x3)))))) (proof)Theorem 53687.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x5 (x1 x7 x3)))))) (proof)Known 4e1c3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x6 (x1 x8 (x1 x5 (x1 x3 x9))))))Theorem 3c7f2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x5 (x1 x3 x7)))))) (proof)Theorem 0e8c3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x5 (x1 x3 x7)))))) (proof)Known 1dee2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x5 (x1 x8 (x1 x6 (x1 x4 x9))))))Theorem 044da.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x7 (x1 x5 x3)))))) (proof)Theorem 217dc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x7 (x1 x5 x3)))))) (proof)Theorem e0a29.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x7 (x1 x3 x5)))))) (proof)Theorem fa835.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x9 (x1 x7 (x1 x3 x5)))))) (proof)Theorem 59aa0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x9 x5)))))) (proof)Theorem f4922.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x9 x5)))))) (proof)Known dcffd.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x5 (x1 x6 (x1 x4 x8)))))Theorem dc1c4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x7 (x1 x5 (x1 x9 x3)))))) (proof)Theorem dbcac.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x7 (x1 x5 (x1 x9 x3)))))) (proof)Known b393b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x5 (x1 x6 (x1 x8 (x1 x4 x9))))))Theorem ea207.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x7 (x1 x9 (x1 x5 x3)))))) (proof)Theorem 85292.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x7 (x1 x9 (x1 x5 x3)))))) (proof)Theorem cd941.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x7 (x1 x9 (x1 x3 x5)))))) (proof)Theorem 3d044.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x7 (x1 x9 (x1 x3 x5)))))) (proof)Known 6f1b5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x3 x8)))))Theorem 3bca8.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x3 (x1 x9 x7)))))) (proof)Theorem 284bc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x3 (x1 x9 x7)))))) (proof)Known a88f6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x5 (x1 x4 (x1 x6 x8)))))Theorem 9a8db.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x7 (x1 x9 x3)))))) (proof)Theorem 2a27c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x7 (x1 x9 x3)))))) (proof)Known c9a83.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x3 (x1 x2 (x1 x5 (x1 x4 (x1 x8 (x1 x6 x9))))))Theorem 45834.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x9 (x1 x7 x3)))))) (proof)Theorem acfaa.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x9 (x1 x7 x3)))))) (proof)Known 4fda7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x8 (x1 x3 x9))))))Theorem 21de4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x9 (x1 x3 x7)))))) (proof)Theorem f8225.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x5 (x1 x9 (x1 x3 x7)))))) (proof)Known 7f03c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x5 x8)))))Theorem d6239.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x5 (x1 x9 x7)))))) (proof)Theorem 91125.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x5 (x1 x9 x7)))))) (proof)Theorem 0434b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x9 x5)))))) (proof)Theorem 09aae.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x9 x5)))))) (proof)Theorem 69f8a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x9 (x1 x7 x5)))))) (proof)Theorem 2e4e2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x9 (x1 x7 x5)))))) (proof)Known f5ab0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x7 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x5 x9))))))Theorem 2fca2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x9 (x1 x5 x7)))))) (proof)Theorem fff32.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 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 x8 (x1 x4 (x1 x2 (x1 x6 (x1 x3 (x1 x9 (x1 x5 x7)))))) (proof) |
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