Consider the following premises. For all x_6, x_6 is not a police officer or x_6 is a carpenter. There is at least one x_6 for which if x_6 were a carpenter, then x_6 is fast. For all x_6, x_6 is a police officer or x_6 will play a game. For all x_6, x_6 will not 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 x_6 is fast.
 From the fact that for all x_6, x_6 is a police officer or x_6 will play a game, and that for all x_6, x_6 is not a police officer or x_6 is a carpenter we can infer that for all x_6, x_6 will play a game or x_6 is a carpenter via universal resolution. From the fact that for all x_6, x_6 will play a game or x_6 is a carpenter, and that for all x_6, x_6 will not play a game we can infer that for all x_6, x_6 is a carpenter via universal disjunctive syllogism. Finally, from the fact that there is at least one x_6 for which if x_6 were a carpenter, then x_6 is fast, and that for all x_6, x_6 is a carpenter we can infer that there is at least one x_6 for which x_6 is fast via existential modus ponens. Therefore, the answer is yes.