Consider the following premises. For all x_10, x_10 will not read a book. For all x_10, if x_10 were a musician, then x_10 is playing tennis. For all x_10, if x_10 were a doctor, then x_10 is a musician. For all x_10, x_10 will read a book or x_10 will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is a doctor.
 From the fact that for all x_10, x_10 will read a book or x_10 will not play tennis we can infer that for all x_10, if x_10 plays tennis, then x_10 is reading a book via universal rewriting. From the fact that for all x_10, if x_10 plays tennis, then x_10 is reading a book, and that for all x_10, x_10 will not read a book we can infer that for all x_10, x_10 will not play tennis via universal modus tollens. From the fact that for all x_10, if x_10 were a musician, then x_10 is playing tennis, and that for all x_10, x_10 will not play tennis we can infer that for all x_10, x_10 is not a musician via universal modus tollens. Finally, from the fact that for all x_10, if x_10 were a doctor, then x_10 is a musician, and that for all x_10, x_10 is not a musician we can infer that for all x_10, x_10 is not a doctor via universal modus tollens, which contradicts that There is at least one x_10 for which x_10 is a doctor. Therefore, the answer is no.