Consider the following premises. For all x_16, x_16 is a musician if and only if x_16 is poor. For all x_16, x_16 will play a game if and only if x_16 is a musician. For all x_16, if x_16 were a politician, then x_16 is poor. There is at least one x_16 for which x_16 is an artist if and only if x_16 is a politician. For all x_16, x_16 will not play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_16, x_16 is an artist.
 From the fact that for all x_16, x_16 will play a game if and only if x_16 is a musician, and that for all x_16, x_16 will not play a game we can infer that for all x_16, x_16 is not a musician via universal biconditional elimination. From the fact that for all x_16, x_16 is a musician if and only if x_16 is poor, and that for all x_16, x_16 is not a musician we can infer that for all x_16, x_16 is not poor via universal biconditional elimination. From the fact that for all x_16, if x_16 were a politician, then x_16 is poor, and that for all x_16, x_16 is not poor we can infer that for all x_16, x_16 is not a politician via universal modus tollens. From the fact that there is at least one x_16 for which x_16 is an artist if and only if x_16 is a politician we can infer that there is at least one x_16 for which if x_16 were an artist, then x_16 is a politician via existential biconditional elimination. Finally, from the fact that there is at least one x_16 for which if x_16 were an artist, then x_16 is a politician, and that for all x_16, x_16 is not a politician we can infer that there is at least one x_16 for which x_16 is not an artist via existential modus tollens, which contradicts that For all x_16, x_16 is an artist. Therefore, the answer is no.