Consider the following premises. For all x_12, x_12 is not a police officer. For all x_12, x_12 is a taxi driver or x_12 will play squash. For all x_12, x_12 is an artist. For all x_12, x_12 is a police officer if and only if x_12 is a taxi driver. For all x_12, if x_12 plays squash, then x_12 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 is not an artist.
 From the fact that for all x_12, x_12 is a police officer if and only if x_12 is a taxi driver, and that for all x_12, x_12 is not a police officer we can infer that for all x_12, x_12 is not a taxi driver via universal biconditional elimination. From the fact that for all x_12, x_12 is a taxi driver or x_12 will play squash, and that for all x_12, x_12 is not a taxi driver we can infer that for all x_12, x_12 will play squash via universal disjunctive syllogism. From the fact that for all x_12, if x_12 plays squash, then x_12 is driving a car, and that for all x_12, x_12 will play squash we can infer that for all x_12, x_12 will drive a car via universal modus ponens. From the fact that for all x_12, x_12 is an artist, and that for all x_12, x_12 will drive a car we can infer that for all x_12, x_12 is an artist and x_12 will drive a car via universal conjunction. Finally, from the fact that for all x_12, x_12 is an artist and x_12 will drive a car we can infer that for all x_12, x_12 is an artist via universal simplification, which contradicts that There is at least one x_12 for which x_12 is not an artist. Therefore, the answer is no.