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Proofgold Asset

asset id
bde19a0d7ff2406950d12616646d7ae51c77f2126ed4b9475d8b6d3b32dd31a7
asset hash
6b9b69a04a942abd9e93d37828578edfd44fad6aa152ed87c2f79d45d41350b3
bday / block
26893
tx
27f78..
preasset
doc published by Pr5Zc..
Known cbdc2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x2 x9))))))
Known f4647.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x3 (x1 x2 (x1 x4 (x1 x6 x9))))))
Theorem 0360c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x3 (x1 x5 (x1 x7 x2))))))
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Theorem 5fc58.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x3 (x1 x5 (x1 x7 x2))))))
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Known cdeba.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x4 (x1 x3 (x1 x5 (x1 x2 x9))))))
Theorem 711ec.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x3 (x1 x5 (x1 x2 x7))))))
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Theorem 25302.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x3 (x1 x5 (x1 x2 x7))))))
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Known 9567f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x3 (x1 x2 (x1 x6 (x1 x4 x9))))))
Theorem 13e7d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x3 (x1 x7 (x1 x5 x2))))))
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Theorem 840b3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x3 (x1 x7 (x1 x5 x2))))))
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Known 93eac.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 . x0 x2x0 x3x0 x4x0 x5x0 x6x1 x2 (x1 x3 (x1 x4 (x1 x5 x6))) = x1 x3 (x1 x4 (x1 x5 (x1 x2 x6)))
Known dd4b8.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x3 (x1 x6 (x1 x2 x9))))))
Theorem 8bef3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x3 (x1 x7 (x1 x2 x5))))))
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Theorem 48a6c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x3 (x1 x7 (x1 x2 x5))))))
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Known a7e77.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x2 (x1 x3 (x1 x6 x9))))))
Theorem ab7a0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 x5))))))
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Theorem 4f20b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x7 x5))))))
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Known 9e514.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x4 (x1 x2 (x1 x3 (x1 x5 x9))))))
Theorem c419e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 x7))))))
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Theorem 56165.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x3 (x1 x5 x7))))))
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Known c0c54.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x1 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 87efc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 x3))))))
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Theorem 42767.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x7 x3))))))
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Known 02c51.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x4 (x1 x2 (x1 x5 (x1 x3 x9))))))
Theorem af301.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 x7))))))
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Theorem 9af63.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x5 (x1 x3 x7))))))
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Theorem bcf4b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x7 (x1 x5 x3))))))
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Theorem 1d383.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x7 (x1 x5 x3))))))
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Known dc941.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x2 (x1 x6 (x1 x3 x9))))))
Theorem 88c40.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x7 (x1 x3 x5))))))
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Theorem f8b3e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x4 (x1 x2 (x1 x7 (x1 x3 x5))))))
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Known e52fe.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x6 (x1 x2 (x1 x3 x9))))))
Theorem 3fc43.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x2 (x1 x4 x3))))))
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Theorem 6563e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x2 (x1 x4 x3))))))
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Known 75b00.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 x7)))) = x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x2 x7))))
Theorem c906d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x2 (x1 x3 x4))))))
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Theorem bb18d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x2 (x1 x3 x4))))))
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Theorem 5f2f0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x3 (x1 x4 x2))))))
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Theorem 1afdd.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x3 (x1 x4 x2))))))
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Known 6015f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x6 (x1 x3 (x1 x2 x9))))))
Theorem eedee.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x3 (x1 x2 x4))))))
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Theorem e5ad0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x3 (x1 x2 x4))))))
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Theorem 054b9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x3 x2))))))
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Theorem 2618e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x3 x2))))))
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Theorem 9ab20.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x2 x3))))))
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Theorem 184f1.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x2 x3))))))
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Known 4da10.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x4 (x1 x3 (x1 x2 (x1 x6 x9))))))
Theorem 6bff2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x2 (x1 x7 x3))))))
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Theorem 2ea86.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x2 (x1 x7 x3))))))
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Known 450b1.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x5 (x1 x4 (x1 x2 (x1 x3 x9))))))
Theorem 68295.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x2 (x1 x3 x7))))))
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Theorem 5d644.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x2 (x1 x3 x7))))))
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Theorem 93271.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x3 (x1 x7 x2))))))
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Theorem f64f1.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x3 (x1 x7 x2))))))
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Known d30db.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x5 (x1 x4 (x1 x3 (x1 x2 x9))))))
Theorem 967d5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x3 (x1 x2 x7))))))
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Theorem 2dd42.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x3 (x1 x2 x7))))))
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Theorem 06233.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x7 (x1 x3 x2))))))
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Theorem b1b95.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x7 (x1 x3 x2))))))
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Theorem 2268e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x7 (x1 x2 x3))))))
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Theorem 7e9e7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x4 (x1 x7 (x1 x2 x3))))))
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Theorem 47810.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x2 (x1 x7 x4))))))
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Theorem d3667.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x2 (x1 x7 x4))))))
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Known 7d35f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x5 (x1 x3 (x1 x2 (x1 x4 x9))))))
Theorem fc248.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x2 (x1 x4 x7))))))
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Theorem 0c36f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x2 (x1 x4 x7))))))
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Theorem 4ca75.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x4 (x1 x7 x2))))))
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Theorem 1a329.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x4 (x1 x7 x2))))))
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Known 26999.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x5 (x1 x3 (x1 x4 (x1 x2 x9))))))
Theorem 0c267.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x4 (x1 x2 x7))))))
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Theorem fe331.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x4 (x1 x2 x7))))))
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Theorem 109af.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x7 (x1 x4 x2))))))
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Theorem 60a32.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x7 (x1 x4 x2))))))
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Theorem 72c96.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x7 (x1 x2 x4))))))
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Theorem c6190.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x3 (x1 x7 (x1 x2 x4))))))
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Theorem 6ac44.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x3 (x1 x7 x4))))))
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Theorem 932b8.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x3 (x1 x7 x4))))))
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Known f01f7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x5 (x1 x2 (x1 x3 (x1 x4 x9))))))
Theorem 9863a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x3 (x1 x4 x7))))))
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Theorem 8bc38.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x3 (x1 x4 x7))))))
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Theorem 24db4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x4 (x1 x7 x3))))))
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Theorem a7f76.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x4 (x1 x7 x3))))))
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Known a380d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x6 (x1 x7 (x1 x5 (x1 x2 (x1 x4 (x1 x3 x9))))))
Theorem e2bf1.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x4 (x1 x3 x7))))))
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Theorem de538.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x4 (x1 x3 x7))))))
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Theorem 82756.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x7 (x1 x4 x3))))))
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Theorem 99cc6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x7 (x1 x4 x3))))))
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Theorem 4efa3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x7 (x1 x3 x4))))))
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Theorem beb26.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x5 (x1 x2 (x1 x7 (x1 x3 x4))))))
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Known 5c72d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x6 (x1 x4 (x1 x2 (x1 x3 x9))))))
Theorem af013.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x2 (x1 x4 x3))))))
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Theorem ba33c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x2 (x1 x4 x3))))))
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Theorem 5e2c7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x2 (x1 x3 x4))))))
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Theorem c8f17.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x2 (x1 x3 x4))))))
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Theorem 89942.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x3 (x1 x4 x2))))))
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Theorem d94f0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x3 (x1 x4 x2))))))
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Known f60a4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x6 (x1 x4 (x1 x3 (x1 x2 x9))))))
Theorem 11c37.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x3 (x1 x2 x4))))))
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Theorem ad057.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x3 (x1 x2 x4))))))
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Theorem ea6b2.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x4 (x1 x3 x2))))))
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Theorem 32610.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x4 (x1 x3 x2))))))
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Theorem 1f311.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x4 (x1 x2 x3))))))
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Theorem da8c8.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x5 (x1 x4 (x1 x2 x3))))))
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Known a8925.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x6 (x1 x3 (x1 x2 (x1 x4 x9))))))
Theorem 4bd15.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x2 (x1 x5 x3))))))
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Theorem a8c05.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x2 (x1 x5 x3))))))
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Theorem 809b9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x2 (x1 x3 x5))))))
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Theorem 6553c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x2 (x1 x3 x5))))))
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Theorem c71e7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x3 (x1 x5 x2))))))
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Theorem 81f7f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x3 (x1 x5 x2))))))
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Theorem ebd2c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x3 (x1 x2 x5))))))
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Theorem 76f34.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x3 (x1 x2 x5))))))
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Known 07a54.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x6 (x1 x3 (x1 x4 (x1 x2 x9))))))
Theorem 8d725.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x5 (x1 x3 x2))))))
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Theorem db40b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x5 (x1 x3 x2))))))
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Theorem 539a9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x5 (x1 x2 x3))))))
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Theorem 40223.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x4 (x1 x5 (x1 x2 x3))))))
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Theorem 97bc5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x2 (x1 x5 x4))))))
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Theorem 54eab.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x2 (x1 x5 x4))))))
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Theorem 5cca6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x2 (x1 x4 x5))))))
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Theorem 55ac6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x2 (x1 x4 x5))))))
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Known b6723.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x6 (x1 x2 (x1 x3 (x1 x4 x9))))))
Theorem af4bd.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x4 (x1 x5 x2))))))
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Theorem 44f2b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x4 (x1 x5 x2))))))
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Theorem 0cb1f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x4 (x1 x2 x5))))))
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Theorem d4485.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x4 (x1 x2 x5))))))
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Known 3c860.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x8 (x1 x5 (x1 x7 (x1 x6 (x1 x2 (x1 x4 (x1 x3 x9))))))
Theorem 62730.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x5 (x1 x4 x2))))))
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Theorem 14632.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x5 (x1 x4 x2))))))
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Theorem a67e5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x5 (x1 x2 x4))))))
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Theorem 9b37b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x3 (x1 x5 (x1 x2 x4))))))
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Theorem 84e2d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4))(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x2 (x1 x3 (x1 x5 x4))))))
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Theorem 4f920.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4)(∀ x2 x3 . x0 x2x0 x3x1 x2 x3 = x1 x3 x2)∀ x2 x3 x4 x5 x6 x7 x8 x9 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9)))))) = x1 x9 (x1 x6 (x1 x8 (x1 x7 (x1 x2 (x1 x3 (x1 x5 x4))))))
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