Consider the following premises. John is not curious or it is cloudy. For all y, y will play tennis or y is curious. Thomas is not poor. John is not playing tennis or Thomas is poor. Can we infer the following from them? If we can, name the inference rule being used: It is cloudy.
 From the fact that for all y, y will play tennis or y is curious we can infer that John is playing tennis or John is curious via universal instantiation. From the fact that John is playing tennis or John is curious, and that John is not playing tennis or Thomas is poor we can infer that John is curious or Thomas is poor via resolution. From the fact that John is curious or Thomas is poor, and that John is not curious or it is cloudy we can infer that Thomas is poor or it is cloudy via resolution. Finally, from the fact that Thomas is poor or it is cloudy, and that Thomas is not poor we can infer that it is cloudy via disjunctive syllogism. Therefore, the answer is yes.