Consider the following premises. It is raining or Michael is not bored. If it rains, then Charles is running. If Charles goes running, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: If Michael were bored, then it is cloudy.
 From the fact that it is raining or Michael is not bored we can infer that if Michael were bored, then it is raining via rewriting. From the fact that if Michael were bored, then it is raining, and that if it rains, then Charles is running we can infer that if Michael were bored, then Charles is running via transitivity. Finally, from the fact that if Michael were bored, then Charles is running, and that if Charles goes running, then it is cloudy we can infer that if Michael were bored, then it is cloudy via transitivity. Therefore, the answer is yes.