Consider the following premises. Mary is not running or it is overcast. If it rains, then Jessica is sleeping. Jessica is sleeping or it is not overcast. David is not playing squash or it is raining. It is not cold or David is playing squash. It is cold or Mary is running. Can we infer the following from them? If we can, name the inference rule being used: Jessica is sleeping.
 From the fact that it is cold or Mary is running, and that it is not cold or David is playing squash we can infer that Mary is running or David is playing squash via resolution. From the fact that Mary is running or David is playing squash, and that Mary is not running or it is overcast we can infer that David is playing squash or it is overcast via resolution. From the fact that Jessica is sleeping or it is not overcast we can infer that if it is overcast, then Jessica is sleeping via rewriting. From the fact that David is playing squash or it is overcast, and that David is not playing squash or it is raining we can infer that it is overcast or it is raining via resolution. Finally, from the fact that if it is overcast, then Jessica is sleeping, that if it rains, then Jessica is sleeping, and that it is overcast or it is raining we can infer that Jessica is sleeping via disjunction elimination. Therefore, the answer is yes.