如何将这句话转换成逻辑良好的一阶公式？

Question

I am trying to convert the following sentence to a well formed formula using first-order logic(Predicate logic).

All towers are of the same color.

I have defined the following predicates:

Tower(x) :: x is a tower.

Color(x, y) :: x is of color y

I am not able to convert the aforementioned sentence into a well formed formula using the above predicates. Is it possible to convert it using the above predicates or some new predicate should be required. Please advise.

EDIT: Forgot to add a detail. There are only three available colours in the world (red, green, blue). Can this detail be used. Does that make any difference to the solution?

Answer 1

存在一个Y1使得对于所有X Tower（X）都意味着Color（X，Y1）

Answer 2

我们不假定存在任何塔楼或颜色。

tower(x) ∧ tower(y) ∧ color(x,z) → color(y,z)

Answer 3

After posting this on StackOverflow, I realized that the problem is more suitable for Math . So I had reposted the problem there.

Although, Dave's solution is perfectly correct, the solution posted there seems more intuitive, so I am linking it here for reference of other users.