Consider the following premises. For all x_3, x_3 will play a game if and only if x_3 is poor. For all x_3, if x_3 takes a plane, then x_3 is poor. For all x_3, x_3 will take a plane or x_3 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_3 for which x_3 is not poor.
 From the fact that for all x_3, x_3 will play a game if and only if x_3 is poor we can infer that for all x_3, if x_3 plays a game, then x_3 is poor via universal biconditional elimination. Finally, from the fact that for all x_3, if x_3 takes a plane, then x_3 is poor, that for all x_3, if x_3 plays a game, then x_3 is poor, and that for all x_3, x_3 will take a plane or x_3 will play a game we can infer that for all x_3, x_3 is poor via universal disjunction elimination, which contradicts that There is at least one x_3 for which x_3 is not poor. Therefore, the answer is no.