Consider the following premises. There is at least one x for which x will play a game or x will play tennis. For all x, x is not a soldier. For all x, if x plays a game, then x is a soldier. For all x, x is a soldier if and only if x will play a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will play tennis.
 From the fact that for all x, x is a soldier if and only if x will play a game we can infer that for all x, if x were a soldier, then x is playing a game via universal biconditional elimination. From the fact that for all x, if x were a soldier, then x is playing a game, and that for all x, if x plays a game, then x is a soldier we can infer that for all x, x is a soldier if and only if x will play a game via universal biconditional introduction. From the fact that for all x, x is a soldier if and only if x will play a game, and that for all x, x is not a soldier we can infer that for all x, x will not play a game via universal biconditional elimination. Finally, from the fact that there is at least one x for which x will play a game or x will play tennis, and that for all x, x will not play a game we can infer that there is at least one x for which x will play tennis via existential disjunctive syllogism. Therefore, the answer is yes.