Consider the following premises. If it is cloudy, then Mary is a doctor. It is late or Charles is a police officer. It is not late or Charles is making tea. If Charles makes tea, then Mary is a doctor. If Charles were a police officer, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: Mary is not a doctor.
 From the fact that if Charles were a police officer, then it is cloudy, and that if it is cloudy, then Mary is a doctor we can infer that if Charles were a police officer, then Mary is a doctor via transitivity. From the fact that it is late or Charles is a police officer, and that it is not late or Charles is making tea we can infer that Charles is a police officer or Charles is making tea via resolution. Finally, from the fact that if Charles were a police officer, then Mary is a doctor, that if Charles makes tea, then Mary is a doctor, and that Charles is a police officer or Charles is making tea we can infer that Mary is a doctor via disjunction elimination, which contradicts that Mary is not a doctor. Therefore, the answer is no.