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Note: This is a homework problem. I'm not asking for the full proof.

Consider the following paragraph of facts:

Anyone passing his/her AI exams and winning the PCH sweepstakes is happy. However, anyone who studies or is lucky can pass all of his/her exams (in all subjects). Sally did not study but she is lucky. Tom studied and so did Michelle. Anyone who is lucky wins the sweepstakes.

Use proof by resolution for predicate logic to answer the query: “Who is happy?” First, express this sentence using FOL and then apply proof by resolution.

My first goal query is the following: $$\forall p

eg Happy(p)$$

However, wouldn't this simply prove that there exists somebody that is happy rather than answer the question of whom is happy?

Would a goal query like the following also work?

$$

eg (Happy(Sally) \lor Happy(Tom) \lor Happy(Michelle))$$