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PURmgSRaTMrF1S7xUzVP6yAS3PSeg6i2Tuu
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b2a05../17422.. bday: 27924 doc published by Pr5Zc..
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))))
Known 00235.. : ∀ 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 x4 (x1 x7 (x1 x2 (x1 x5 (x1 x6 (x1 x8 (x1 x3 x9))))))
Theorem 0a29c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x8 x4))))))
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Theorem 9665d.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x8 x4))))))
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Known 48599.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x4 x9))))))
Theorem b2313.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x4 x8))))))
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Theorem 69d03.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x3 (x1 x4 x8))))))
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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 6e858.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x8 x3))))))
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Theorem 5bb23.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x8 x3))))))
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Known cf069.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x3 x9))))))
Theorem a9ee0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x3 x8))))))
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Theorem 2bf49.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x4 (x1 x3 x8))))))
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Known 1cc67.. : ∀ 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 x4 (x1 x8 (x1 x2 (x1 x5 (x1 x6 (x1 x7 (x1 x3 x9))))))
Theorem e7d0b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x8 (x1 x4 x3))))))
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Theorem 2929b.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x8 (x1 x4 x3))))))
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Theorem bfe09.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x8 (x1 x3 x4))))))
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Theorem 103de.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x7 (x1 x8 (x1 x3 x4))))))
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Known 97bd9.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x7 x9))))))
Theorem 17fab.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x8 x7))))))
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Theorem a618c.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x8 x7))))))
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Theorem 11b25.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x7 x8))))))
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Theorem 7ffc2.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x3 (x1 x7 x8))))))
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Known 1f92a.. : ∀ 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 x4 (x1 x6 (x1 x2 (x1 x5 (x1 x7 (x1 x8 (x1 x3 x9))))))
Theorem 2e744.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x8 x3))))))
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Theorem 1d6ea.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x8 x3))))))
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Known 4733e.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x3 x9))))))
Theorem 9b50f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x3 x8))))))
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Theorem aff7a.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x7 (x1 x3 x8))))))
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Known 80433.. : ∀ 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 x4 (x1 x6 (x1 x2 (x1 x5 (x1 x8 (x1 x7 (x1 x3 x9))))))
Theorem d0f88.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x8 (x1 x7 x3))))))
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Theorem d059f.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x8 (x1 x7 x3))))))
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Theorem 217da.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x8 (x1 x3 x7))))))
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Theorem 16845.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x4 (x1 x8 (x1 x3 x7))))))
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Known 475fb.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x7 x9))))))
Theorem 92632.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x8 x7))))))
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Theorem 1ecd9.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x8 x7))))))
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Theorem 72146.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x7 x8))))))
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Theorem cd0f6.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x4 (x1 x7 x8))))))
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Theorem 530a1.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x8 x4))))))
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Theorem cac63.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x8 x4))))))
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Known bd250.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x4 x9))))))
Theorem 6432f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x4 x8))))))
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Theorem 94ad4.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x7 (x1 x4 x8))))))
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Theorem 23a00.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x7 x4))))))
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Theorem b3d3a.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x7 x4))))))
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Theorem 67a86.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x4 x7))))))
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Theorem 522fc.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x6 (x1 x3 (x1 x8 (x1 x4 x7))))))
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Known 7a7f7.. : ∀ 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 x4 (x1 x7 (x1 x2 (x1 x8 (x1 x5 (x1 x6 (x1 x3 x9))))))
Theorem aa522.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x3 (x1 x6 x4))))))
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Theorem 76a17.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x3 (x1 x6 x4))))))
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Known 45f87.. : ∀ 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 . x0 x2x0 x3x0 x4x0 x5x1 x2 (x1 x3 (x1 x4 x5)) = x1 x3 (x1 x4 (x1 x2 x5))
Theorem 1aa23.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x3 (x1 x4 x6))))))
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Theorem 7f2b7.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x3 (x1 x4 x6))))))
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Theorem 98bec.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x4 (x1 x6 x3))))))
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Theorem 25190.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x4 (x1 x6 x3))))))
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Theorem 18806.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x4 (x1 x3 x6))))))
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Theorem b8578.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x4 (x1 x3 x6))))))
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Known 90f7b.. : ∀ 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 x4 (x1 x8 (x1 x2 (x1 x6 (x1 x7 (x1 x5 (x1 x3 x9))))))
Theorem 6f0cd.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x6 (x1 x4 x3))))))
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Theorem 31941.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x6 (x1 x4 x3))))))
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Theorem 9fa47.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x6 (x1 x3 x4))))))
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Theorem c59a2.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x8 (x1 x6 (x1 x3 x4))))))
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Known f45b5.. : ∀ 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 x4 (x1 x7 (x1 x2 (x1 x6 (x1 x5 (x1 x8 (x1 x3 x9))))))
Theorem 20bda.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x8 x4))))))
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Theorem 9c67a.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x8 x4))))))
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Known e64b6.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x4 x9))))))
Theorem 9749c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x4 x8))))))
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Theorem f302d.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x3 (x1 x4 x8))))))
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Theorem 1c443.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x8 x3))))))
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Theorem d96f9.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x8 x3))))))
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Known c6482.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x3 x9))))))
Theorem dfaeb.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x3 x8))))))
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Theorem 24446.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x4 (x1 x3 x8))))))
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Known 196dd.. : ∀ 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 x4 (x1 x8 (x1 x2 (x1 x6 (x1 x5 (x1 x7 (x1 x3 x9))))))
Theorem c18e4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x8 (x1 x4 x3))))))
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Theorem 90151.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x8 (x1 x4 x3))))))
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Theorem 8dbee.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x8 (x1 x3 x4))))))
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Theorem 45128.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x6 (x1 x8 (x1 x3 x4))))))
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Theorem 4f7e6.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x8 x6))))))
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Theorem c9231.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x8 x6))))))
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Known 47d38.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x6 x9))))))
Theorem 4f524.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x6 x8))))))
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Theorem 7c1aa.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x3 (x1 x6 x8))))))
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Known 89a50.. : ∀ 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 x4 (x1 x6 (x1 x2 (x1 x7 (x1 x5 (x1 x8 (x1 x3 x9))))))
Theorem e9e79.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x8 x3))))))
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Theorem 54d94.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x8 x3))))))
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Known cfc03.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x3 x9))))))
Theorem b8eb5.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x3 x8))))))
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Theorem 9fcd7.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x6 (x1 x3 x8))))))
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Known cd2ee.. : ∀ 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 x4 (x1 x6 (x1 x2 (x1 x8 (x1 x5 (x1 x7 (x1 x3 x9))))))
Theorem 5d727.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x8 (x1 x6 x3))))))
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Theorem 57035.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x8 (x1 x6 x3))))))
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Theorem 28fd2.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x8 (x1 x3 x6))))))
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Theorem a40fc.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x4 (x1 x8 (x1 x3 x6))))))
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Theorem 2fd6f.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x8 x6))))))
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Theorem 87247.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x8 x6))))))
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Known 02dcc.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x6 x9))))))
Theorem 88e25.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x6 x8))))))
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Theorem 0ede9.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x4 (x1 x6 x8))))))
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Theorem c0e86.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x8 x4))))))
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Theorem 4f0ca.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x8 x4))))))
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Known df8da.. : ∀ 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 x5 (x1 x8 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x4 x9))))))
Theorem c46d6.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x4 x8))))))
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Theorem 1daff.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x6 (x1 x4 x8))))))
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Theorem c5657.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x6 x4))))))
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Theorem 5e527.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x6 x4))))))
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Theorem 4db0d.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x4 x6))))))
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Theorem d6e5a.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x7 (x1 x3 (x1 x8 (x1 x4 x6))))))
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Known c40bc.. : ∀ 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 x4 (x1 x7 (x1 x2 (x1 x8 (x1 x6 (x1 x5 (x1 x3 x9))))))
Theorem f0452.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x6 x4))))))
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Theorem 20739.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x6 x4))))))
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Theorem e10b6.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x4 x6))))))
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Theorem 50882.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x3 (x1 x4 x6))))))
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Theorem 6083c.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x6 x3))))))
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Theorem aed5b.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x6 x3))))))
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Theorem 21500.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x3 x6))))))
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Theorem fe3e3.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x4 (x1 x3 x6))))))
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Known a52a5.. : ∀ 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 x4 (x1 x8 (x1 x2 (x1 x7 (x1 x6 (x1 x5 (x1 x3 x9))))))
Theorem 56937.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x6 (x1 x4 x3))))))
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Theorem db7c0.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x6 (x1 x4 x3))))))
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Theorem 703fe.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x6 (x1 x3 x4))))))
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Theorem 85a3d.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x7 (x1 x6 (x1 x3 x4))))))
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Known 65d27.. : ∀ 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 x4 (x1 x7 (x1 x2 (x1 x6 (x1 x8 (x1 x5 (x1 x3 x9))))))
Theorem 1b768.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x3 (x1 x7 x4))))))
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Theorem 38ac1.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x3 (x1 x7 x4))))))
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Theorem 3efa7.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x3 (x1 x4 x7))))))
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Theorem 3ab57.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x3 (x1 x4 x7))))))
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Theorem e6d82.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x4 (x1 x7 x3))))))
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Theorem 41885.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x4 (x1 x7 x3))))))
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Theorem 02f69.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x4 (x1 x3 x7))))))
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Theorem d2454.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x4 (x1 x3 x7))))))
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Theorem 7ab7e.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x7 (x1 x4 x3))))))
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Theorem 98d13.. : ∀ 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 x5 (x1 x9 (x1 x2 (x1 x8 (x1 x6 (x1 x7 (x1 x4 x3))))))
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