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Proofgold Asset

asset id
00d40abe9d6b41f409690e110a318f0045f0504be2720c10a145c0185854354d
asset hash
b1241a7b1dbd87eb9a443dbdb2a6a21b51bf6208494310f7b5b804cd350c18e5
bday / block
24253
tx
c2f26..
preasset
doc published by Pr5Zc..
Known 2c5ad.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13)))))))))))
Theorem ea7b1.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))))))))) (proof)
Theorem 6cd80.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15))))))))))))) (proof)
Theorem 855a7.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16)))))))))))))) (proof)
Theorem 20d59.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x0 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17))))))))))))))) (proof)
Known 98924.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13))))))))))) x14 = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))))))))
Theorem 6c527.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))))))))) x15 = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem ce587.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15))))))))))))) x16 = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 58626.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16)))))))))))))) x17 = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Theorem 5e801.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x0 x18x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17))))))))))))))) x18 = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 (x1 x17 x18))))))))))))))) (proof)
Known 6d3cf.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x1 (x1 x2 x3) (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 x11))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 x11))))))))
Theorem b1a4d.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x1 (x1 x2 x3) (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12)))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12))))))))) (proof)
Theorem d42d0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x1 (x1 x2 x3) (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13)))))))))) (proof)
Theorem 1de7f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x1 (x1 x2 x3) (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14))))))))))) (proof)
Theorem 8c174.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 x3) (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15))))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem 07c5e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 x3) (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16)))))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem f6743.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 x3) (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17))))))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Known d3054.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x1 (x1 x2 (x1 x3 x4)) (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12)))))))))
Theorem 51365.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x1 (x1 x2 (x1 x3 x4)) (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13)))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13)))))))))) (proof)
Theorem cdcaf.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x1 (x1 x2 (x1 x3 x4)) (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14))))))))))) (proof)
Theorem 2dce9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 x4)) (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem 216d3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 x4)) (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 7ff40.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 x4)) (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Known 443d0.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x1 (x1 x2 (x1 x3 (x1 x4 x5))) (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13))))))))))
Theorem bd67e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x1 (x1 x2 (x1 x3 (x1 x4 x5))) (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14))))))))))) (proof)
Theorem 31d91.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 (x1 x4 x5))) (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem c3115.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 x5))) (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16)))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 91b03.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 x5))) (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17))))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Known 65945.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 x6)))) (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))))))))
Theorem f3234.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 x6)))) (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem c5f8f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 x6)))) (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 09f1f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 x6)))) (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Known 3e472.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 x7))))) (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15))))))))))))
Theorem 03232.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 x7))))) (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16)))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 99928.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 x7))))) (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17))))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Known e06ed.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 x8)))))) (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16)))))))))))))
Theorem 6b05b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 x8)))))) (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Known a871b.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 x9))))))) (x1 x10 x11) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 x11))))))))
Known 3e03a.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 . x0 x2x0 x3x0 x4x0 x5x1 (x1 x2 x3) (x1 x4 x5) = x1 x2 (x1 x3 (x1 x4 x5))
Theorem 693ec.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 x10)))))))) (x1 x11 x12) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12))))))))) (proof)
Theorem 02361.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 x10)))))))) (x1 x11 (x1 x12 x13)) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13)))))))))) (proof)
Theorem cbdd8.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 x10)))))))) (x1 x11 (x1 x12 (x1 x13 x14))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14))))))))))) (proof)
Theorem d2cdc.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 x10)))))))) (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem fbfe3.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 x10)))))))) (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 00001.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 x10)))))))) (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Theorem f3ec9.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 x11))))))))) (x1 x12 x13) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13)))))))))) (proof)
Theorem 2e619.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 x11))))))))) (x1 x12 (x1 x13 x14)) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14))))))))))) (proof)
Theorem 841f4.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 x11))))))))) (x1 x12 (x1 x13 (x1 x14 x15))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem b3115.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 x11))))))))) (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16)))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem e54de.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 x11))))))))) (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17))))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Theorem cd854.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12)))))))))) (x1 x13 x14) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14))))))))))) (proof)
Theorem 84b1f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12)))))))))) (x1 x13 (x1 x14 x15)) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem 4b6df.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12)))))))))) (x1 x13 (x1 x14 (x1 x15 x16))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 11a48.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 x12)))))))))) (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Theorem 8c836.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13))))))))))) (x1 x14 x15) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))))) (proof)
Theorem 17484.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13))))))))))) (x1 x14 (x1 x15 x16)) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 5b69c.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 x13))))))))))) (x1 x14 (x1 x15 (x1 x16 x17))) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Theorem 2052e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))))))))) (x1 x15 x16) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 x16))))))))))))) (proof)
Theorem 73cc8.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))))))))) (x1 x15 (x1 x16 x17)) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)
Theorem 9a64e.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι . (∀ x2 x3 . x0 x2x0 x3x0 (x1 x2 x3))(∀ x2 x3 x4 . x0 x2x0 x3x0 x4x1 (x1 x2 x3) x4 = x1 x2 (x1 x3 x4))∀ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x1 (x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15))))))))))))) (x1 x16 x17) = x1 x2 (x1 x3 (x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 (x1 x15 (x1 x16 x17)))))))))))))) (proof)