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