| ∀ x0 : ι → ο . ∀ x1 x2 : ι → ι → ι . (∀ x3 x4 . x0 x3 ⟶ x0 x4 ⟶ x0 (x1 x3 x4)) ⟶ (∀ x3 x4 . x0 x3 ⟶ x0 x4 ⟶ x0 (x2 x3 x4)) ⟶ (∀ x3 x4 x5 . x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x1 x3 (x1 x4 x5) = x1 x4 (x1 x3 x5)) ⟶ (∀ x3 x4 x5 . x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x1 (x1 x3 x4) x5 = x1 x3 (x1 x4 x5)) ⟶ (∀ x3 x4 x5 . x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x2 x3 (x1 x4 x5) = x1 (x2 x3 x4) (x2 x3 x5)) ⟶ (∀ x3 x4 x5 . x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x2 (x1 x3 x4) x5 = x1 (x2 x3 x5) (x2 x4 x5)) ⟶ ∀ x3 : ι → ι . (∀ x4 . x0 x4 ⟶ x3 x4 = x2 x4 x4) ⟶ ∀ x4 : ι → ι . (∀ x5 . x0 x5 ⟶ x0 (x4 x5)) ⟶ (∀ x5 . x0 x5 ⟶ x4 (x4 x5) = x5) ⟶ (∀ x5 x6 . x0 x5 ⟶ x0 x6 ⟶ x1 (x4 x5) (x1 x5 x6) = x6) ⟶ (∀ x5 x6 . x0 x5 ⟶ x0 x6 ⟶ x1 x5 (x1 (x4 x5) x6) = x6) ⟶ (∀ x5 x6 . x0 x5 ⟶ x0 x6 ⟶ x2 (x4 x5) x6 = x4 (x2 x5 x6)) ⟶ (∀ x5 x6 . x0 x5 ⟶ x0 x6 ⟶ x2 x5 (x4 x6) = x4 (x2 x5 x6)) ⟶ (∀ x5 x6 . x0 x5 ⟶ x0 x6 ⟶ x2 x5 x6 = x2 x6 x5) ⟶ (∀ x5 x6 x7 x8 . x0 x5 ⟶ x0 x6 ⟶ x0 x7 ⟶ x0 x8 ⟶ x2 (x2 x5 x6) (x2 x7 x8) = x2 (x2 x5 x7) (x2 x6 x8)) ⟶ ∀ x5 : ι → ο . (∀ x6 . x0 x6 ⟶ ∀ x7 : ο . (∀ x8 . and (x5 x8) (x3 x8 = x3 x6) ⟶ x7) ⟶ x7) ⟶ ∀ x6 x7 . x0 x6 ⟶ x0 x7 ⟶ ∀ x8 x9 x10 x11 . x0 x8 ⟶ x0 x9 ⟶ x0 x10 ⟶ x0 x11 ⟶ x6 = x1 (x3 x8) (x1 (x3 x9) (x1 (x3 x10) (x3 x11))) ⟶ ∀ x12 x13 x14 x15 . x0 x12 ⟶ x0 x13 ⟶ x0 x14 ⟶ x0 x15 ⟶ x7 = x1 (x3 x12) (x1 (x3 x13) (x1 (x3 x14) (x3 x15))) ⟶ ∀ x16 : ο . (∀ x17 x18 x19 x20 . x5 x17 ⟶ x5 x18 ⟶ x5 x19 ⟶ x5 x20 ⟶ x2 x6 x7 = x1 (x3 x17) (x1 (x3 x18) (x1 (x3 x19) (x3 x20))) ⟶ x16) ⟶ x16 |
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