Consider the following premises. If Robert plays tennis, then Jennifer is listening to a song. Robert is not a cashier or Charles is a carpenter. For all x_6, x_6 is a cashier or x_6 will play tennis. If Charles were a carpenter, then Jennifer is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not listening to a song.
 From the fact that for all x_6, x_6 is a cashier or x_6 will play tennis we can infer that Robert is a cashier or Robert is playing tennis via universal instantiation. From the fact that Robert is a cashier or Robert is playing tennis, and that Robert is not a cashier or Charles is a carpenter we can infer that Robert is playing tennis or Charles is a carpenter via resolution. Finally, from the fact that if Robert plays tennis, then Jennifer is listening to a song, that if Charles were a carpenter, then Jennifer is listening to a song, and that Robert is playing tennis or Charles is a carpenter we can infer that Jennifer is listening to a song via disjunction elimination, which contradicts that Jennifer is not listening to a song. Therefore, the answer is no.