Consider the following premises. William is an artist or William is not a police officer. Jennifer is not an astronaut. For all x_17, if x_17 were an artist, then x_17 is a police officer. Jennifer is an astronaut if and only if William is a police officer. Can we infer the following from them? If we can, name the inference rule being used: William is an artist.
 From the fact that for all x_17, if x_17 were an artist, then x_17 is a police officer we can infer that if William were an artist, then William is a police officer via universal instantiation. From the fact that William is an artist or William is not a police officer we can infer that if William were a police officer, then William is an artist via rewriting. From the fact that Jennifer is an astronaut if and only if William is a police officer, and that Jennifer is not an astronaut we can infer that William is not a police officer via biconditional elimination. From the fact that if William were a police officer, then William is an artist, and that if William were an artist, then William is a police officer we can infer that William is a police officer if and only if William is an artist via biconditional introduction. Finally, from the fact that William is a police officer if and only if William is an artist, and that William is not a police officer we can infer that William is not an artist via biconditional elimination, which contradicts that William is an artist. Therefore, the answer is no.