Consider the following premises. For all x_5, x_5 is not a scientist. For all x_5, if x_5 were poor, then x_5 is a scientist. There is at least one x_5 for which x_5 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will play a game.
 From the fact that there is at least one x_5 for which x_5 is poor we can infer that there is at least one x_5 for which x_5 is poor or x_5 will play a game via existential addition. From the fact that for all x_5, if x_5 were poor, then x_5 is a scientist, and that for all x_5, x_5 is not a scientist we can infer that for all x_5, x_5 is not poor via universal modus tollens. Finally, from the fact that there is at least one x_5 for which x_5 is poor or x_5 will play a game, and that for all x_5, x_5 is not poor we can infer that there is at least one x_5 for which x_5 will play a game via existential disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.