Consider the following premises. If Barbara reads a book, then Joseph is playing tennis. Barbara is reading a book or Joseph is running. For all x_8, x_8 will go running if and only if x_8 will play tennis. Can we infer the following from them? Joseph is playing tennis.
 From the fact that for all x_8, x_8 will go running if and only if x_8 will play tennis we can infer that for all x_8, if x_8 goes running, then x_8 is playing tennis. From the fact that for all x_8, if x_8 goes running, then x_8 is playing tennis we can infer that if Joseph goes running, then Joseph is playing tennis. Finally, from the fact that if Barbara reads a book, then Joseph is playing tennis, that if Joseph goes running, then Joseph is playing tennis, and that Barbara is reading a book or Joseph is running we can infer that Joseph is playing tennis. Therefore, the answer is yes.