Consider the following premises. Michael is a doctor or Thomas is sleeping. For all x_10, if x_10 were a doctor, then x_10 is playing squash. Michael is not playing squash. Can we infer the following from them? Thomas is sleeping.
 From the fact that for all x_10, if x_10 were a doctor, then x_10 is playing squash we can infer that if Michael were a doctor, then Michael is playing squash. From the fact that if Michael were a doctor, then Michael is playing squash, and that Michael is not playing squash we can infer that Michael is not a doctor. Finally, from the fact that Michael is a doctor or Thomas is sleeping, and that Michael is not a doctor we can infer that Thomas is sleeping. Therefore, the answer is yes.