Consider the following premises. There is at least one x_6 for which if x_6 were poor, then x_6 is drinking water. For all x_6, x_6 will play a game. For all x_6, if x_6 drinks water, then x_6 is playing squash. For all x_6, if x_6 plays squash, then x_6 is not playing a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not poor.
 From the fact that for all x_6, if x_6 plays squash, then x_6 is not playing a game, and that for all x_6, x_6 will play a game we can infer that for all x_6, x_6 will not play squash via universal modus tollens. From the fact that for all x_6, if x_6 drinks water, then x_6 is playing squash, and that for all x_6, x_6 will not play squash we can infer that for all x_6, x_6 will not drink water via universal modus tollens. Finally, from the fact that there is at least one x_6 for which if x_6 were poor, then x_6 is drinking water, and that for all x_6, x_6 will not drink water we can infer that there is at least one x_6 for which x_6 is not poor via existential modus tollens. Therefore, the answer is yes.