Consider the following premises. For all x_9, x_9 is not a soldier. For all x_9, if x_9 were a soldier, then x_9 is sad. For all x_9, x_9 is sad or x_9 will play a game. There is at least one x_9 for which if x_9 were sad, then x_9 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will not play a game.
 From the fact that there is at least one x_9 for which if x_9 were sad, then x_9 is a soldier, and that for all x_9, if x_9 were a soldier, then x_9 is sad we can infer that there is at least one x_9 for which x_9 is sad if and only if x_9 is a soldier via existential biconditional introduction. From the fact that there is at least one x_9 for which x_9 is sad if and only if x_9 is a soldier, and that for all x_9, x_9 is not a soldier we can infer that there is at least one x_9 for which x_9 is not sad via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 is sad or x_9 will play a game, and that there is at least one x_9 for which x_9 is not sad we can infer that there is at least one x_9 for which x_9 will play a game via existential disjunctive syllogism, which contradicts that For all x_9, x_9 will not play a game. Therefore, the answer is no.