Consider the following premises. If it is overcast, then William is a bartender. If Richard listens to a song, then it is overcast. If William were a bartender, then it is snowing. William is not a bartender. If it snows, then Richard is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: Richard is listening to a song.
 From the fact that if Richard listens to a song, then it is overcast, and that if it is overcast, then William is a bartender we can infer that if Richard listens to a song, then William is a bartender via transitivity. From the fact that if William were a bartender, then it is snowing, and that if it snows, then Richard is listening to a song we can infer that if William were a bartender, then Richard is listening to a song via transitivity. From the fact that if William were a bartender, then Richard is listening to a song, and that if Richard listens to a song, then William is a bartender we can infer that William is a bartender if and only if Richard is listening to a song via biconditional introduction. Finally, from the fact that William is a bartender if and only if Richard is listening to a song, and that William is not a bartender we can infer that Richard is not listening to a song via biconditional elimination, which contradicts that Richard is listening to a song. Therefore, the answer is no.