Equation 677 Database

Can we find a finite magma M that satisfies

∀ x y : M,   x = y ◇ (x ◇ ((y ◇ x) ◇ y)) (Equation 677)

but does not satisfy

∀ x : M,   x = ((x ◇ x) ◇ x) ◇ x  ? (Equation 255)