Consider the following premises. For all x_15, x_15 will sleep or x_15 will play a game. For all x_15, if x_15 sleeps, then x_15 is a musician. For all x_15, if x_15 were a scientist, then x_15 is a soldier. For all x_15, x_15 is a scientist if and only if x_15 is a musician. For all x_15, x_15 will play a game if and only if x_15 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 is a soldier.
 From the fact that for all x_15, x_15 will play a game if and only if x_15 is a musician we can infer that for all x_15, if x_15 plays a game, then x_15 is a musician via universal biconditional elimination. From the fact that for all x_15, if x_15 sleeps, then x_15 is a musician, that for all x_15, if x_15 plays a game, then x_15 is a musician, and that for all x_15, x_15 will sleep or x_15 will play a game we can infer that for all x_15, x_15 is a musician via universal disjunction elimination. From the fact that for all x_15, x_15 is a scientist if and only if x_15 is a musician we can infer that for all x_15, if x_15 were a musician, then x_15 is a scientist via universal biconditional elimination. From the fact that for all x_15, if x_15 were a musician, then x_15 is a scientist, and that for all x_15, if x_15 were a scientist, then x_15 is a soldier we can infer that for all x_15, if x_15 were a musician, then x_15 is a soldier via universal transitivity. Finally, from the fact that for all x_15, if x_15 were a musician, then x_15 is a soldier, and that for all x_15, x_15 is a musician we can infer that for all x_15, x_15 is a soldier via universal modus ponens. Therefore, the answer is yes.