Vocabulary:
- $R(x)$ - "x is a river"
- $L(x)$ - "x is a lake"
- $S(x)$ - "x is a sea"
- $F(x, y)$ - "x flows into y"
The domain consists only of waterbodies (rivers, lakes and seas).
"Some lakes flow into other waterbodies, and some do not."
$ \exists x \exists y (x \ne y \wedge L(x) \wedge L(y) \wedge \exists z F(x, z) \wedge \neg \exists z F(y, z))$
Have I captured this correctly?
Yes... though you don’t have to point out that $x \neq y$ ... and in fact I would leave it out.
Given that $\exists z \ F(x,z)$ and $\neg \exists z \ F(y,z)$, it logically follows that $x \neq y$. Put differently, you can remove the $x \neq y$ and it will still be logically equivalent.
And, since the English sentence does not explicitly state that we are dealing with two different lakes, I think it is better to just leave it out.