Consider the following premises. Charles is cooking. If David were a janitor, then Robert is a police officer. Mary is a writer or David is a janitor. If Mary were sad, then Robert is a police officer. Mary is not a writer or Mary is sad. Can we infer the following from them? Robert is a police officer.
 From the fact that Mary is a writer or David is a janitor, and that Mary is not a writer or Mary is sad we can infer that David is a janitor or Mary is sad. Finally, from the fact that if David were a janitor, then Robert is a police officer, that if Mary were sad, then Robert is a police officer, and that David is a janitor or Mary is sad we can infer that Robert is a police officer. Therefore, the answer is yes.