Consider the following premises. For all x_13, if x_13 plays a game, then x_13 is a soldier. For all x_13, x_13 will go running or x_13 will read a book. For all x_13, x_13 will play a game if and only if x_13 will read a book. There is at least one x_13 for which if x_13 goes running, then x_13 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 is not a soldier.
 From the fact that for all x_13, x_13 will play a game if and only if x_13 will read a book we can infer that for all x_13, if x_13 reads a book, then x_13 is playing a game via universal biconditional elimination. From the fact that there is at least one x_13 for which if x_13 goes running, then x_13 is playing a game, that for all x_13, if x_13 reads a book, then x_13 is playing a game, and that for all x_13, x_13 will go running or x_13 will read a book we can infer that there is at least one x_13 for which x_13 will play a game via existential disjunction elimination. Finally, from the fact that for all x_13, if x_13 plays a game, then x_13 is a soldier, and that there is at least one x_13 for which x_13 will play a game we can infer that there is at least one x_13 for which x_13 is a soldier via existential modus ponens, which contradicts that For all x_13, x_13 is not a soldier. Therefore, the answer is no.