Consider the following premises. For all x_8, if x_8 plays a game, then x_8 is writing a letter. For all x_8, if x_8 were a nurse, then x_8 is running. For all x_8, if x_8 writes a letter, then x_8 is a nurse. For all x_8, if x_8 goes running, then x_8 is playing a game. Can we infer the following from them? If Barbara writes a letter, then Barbara is running.
 From the fact that for all x_8, if x_8 goes running, then x_8 is playing a game, and that for all x_8, if x_8 plays a game, then x_8 is writing a letter we can infer that for all x_8, if x_8 goes running, then x_8 is writing a letter. From the fact that for all x_8, if x_8 writes a letter, then x_8 is a nurse, and that for all x_8, if x_8 were a nurse, then x_8 is running we can infer that for all x_8, if x_8 writes a letter, then x_8 is running. From the fact that for all x_8, if x_8 goes running, then x_8 is writing a letter, and that for all x_8, if x_8 writes a letter, then x_8 is running we can infer that for all x_8, x_8 will go running if and only if x_8 will write a letter. From the fact that for all x_8, x_8 will go running if and only if x_8 will write a letter we can infer that Barbara is running if and only if Barbara is writing a letter. Finally, from the fact that Barbara is running if and only if Barbara is writing a letter we can infer that if Barbara writes a letter, then Barbara is running. Therefore, the answer is yes.