(Solution Verification) How should I move forward with these compound propositions?

Question

The question is the following :

Let $P(x)$, $Q(x)$, $R(x)$ and $S(x)$ be the statements "x is a duck", "x is one of my poultries", "x is an officer", "x is willing to waltz". Now consider the following 4 statements,

1. No ducks are willing to waltz.
2. No officers ever decline to waltz.
3. All my poultries are ducks.
4. My poultries are not officers.

Does (4) follow (1), (2), and (3)? If not, is here a correct conclusion?

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Now if I attempt to solve this with reasoning, 1 and 2 imply ducks are not officers (a). 1 and 3 are kind of tricky, "All my poultries are ducks" doesn't mean "all ducks are poultries", which means these two imply "At least one of my ducks is poultry" (b). Now from (a) and (b), we can conclude "at least one of my ducks are not officers".

So to answer the initial question, No, 4 doesn't follow 1, 2, and 3. And the correct conclusion is "at least one of my ducks are not officers". Is this the correct solution?

Now if I try to do the same mathematically with quantifiers and connectives, The four statements can be represented as the following :

1. $\forall x \bigl(\lnot P(x) \land S(x) \bigr)$
2. $\forall x \bigl( R(x) \land S(x) \bigr)$
3. $\forall x \bigl( Q(x) \to P(x) \bigr)$
4. $\forall x \bigl( Q(x) \land \lnot R(x) \bigr)$

The domain is all ducks, poultries and officers.

This is where I'm stuck. How can I move forward with this now? Considering (If) the solution via reasoning was correct, using quantifiers and connectives, the answer should be $$\exists x\bigl( P(x) \to R(x) \bigr)$$I might just be totally wrong in every sense here, I'll appreciate any help on this. Thank you.