How can I convert this sentence to propositional logic (semantic and resolution)?

Question

There were 3 people J, P, A. Only 2 people brought gifts to the party. If J brought a gift to the party, proof that P or A did not brought the gift.

What I can think about this sentence is: $ J, P \rightarrow ¬A, A \rightarrow ¬P \vDash ¬A \lor ¬P $

But with these premises and conclusion, I can't proof it in semantic way or proof theory by applying CNF to derive empty clause. I would like to ask for help that what should be the right premises and conclusion?

Thank you very much for any helps that you may provide.

Updated from suggestions:

$J, ¬(J\land P \land A) \vDash ¬A \lor ¬P $

$J, ¬(J \land (P \land A)) \vDash ¬A \lor ¬P $

$J, ¬J \lor ¬(P \land A) \vDash ¬A \lor ¬P $

$J, ¬J \lor ¬P \lor ¬A \vDash ¬A \lor ¬P $

Apply resolution to derive empty clause.

$J, ¬J \lor ¬P \lor ¬A, ¬(¬A \lor ¬P) \vdash $ Empty Clause

$J, ¬J \lor ¬P \lor ¬A, A \land P \vdash $ Empty Clause

Empty Clause $ \vdash $ Empty Clause

Thank you for all helps.

Answer 1

There were 3 people J, P, A. Only 2 people brought gifts to the party. If J brought a gift to the party, proof that P or A did not brought the gift.

We need the following axioms :

1) $J$ --- expressing the fact that "J brought a gift"

2) $\lnot (J \land P \land A)$ --- expressing the fact that "Only 2 people brought gifts", i.e. that ""Not all three...".

Then we have to transform 2) in clause form and apply Resolution.

Answer 2

Can you use the equivalence $A\to B \equiv \neg A \vee B$, to transform the goal $\neg A\vee\neg P$ into $A\to\neg P$?

If you are allowed to do that, things become quite easy afterwards.