Consider the following premises. For all x_6, x_6 is curious or x_6 will not play a game. For all x_6, x_6 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_6 for which neither x_6 is curious nor x_6 is a doctor.
 From the fact that for all x_6, x_6 is curious or x_6 will not play a game we can infer that for all x_6, if x_6 plays a game, then x_6 is curious via universal rewriting. From the fact that for all x_6, if x_6 plays a game, then x_6 is curious, and that for all x_6, x_6 will play a game we can infer that for all x_6, x_6 is curious via universal modus ponens. Finally, from the fact that for all x_6, x_6 is curious we can infer that for all x_6, x_6 is curious or x_6 is a doctor via universal addition, which contradicts that There is at least one x_6 for which neither x_6 is curious nor x_6 is a doctor. Therefore, the answer is no.