Consider the following premises. If it is cloudy, then Michael is sleeping. If David were a doctor, then it is cloudy. If it rains, then David is writing a letter. For all x_15, if x_15 writes a letter, then x_15 is a doctor. Can we infer the following from them? If it rains, then Michael is sleeping.
 From the fact that for all x_15, if x_15 writes a letter, then x_15 is a doctor we can infer that if David writes a letter, then David is a doctor. From the fact that if it rains, then David is writing a letter, and that if David writes a letter, then David is a doctor we can infer that if it rains, then David is a doctor. From the fact that if David were a doctor, then it is cloudy, and that if it is cloudy, then Michael is sleeping we can infer that if David were a doctor, then Michael is sleeping. Finally, from the fact that if it rains, then David is a doctor, and that if David were a doctor, then Michael is sleeping we can infer that if it rains, then Michael is sleeping. Therefore, the answer is yes.