Consider the following premises. If John were a writer, then Richard is sleeping. Richard is not a cashier. For all x_20, x_20 will sleep if and only if x_20 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: John is a writer.
 From the fact that for all x_20, x_20 will sleep if and only if x_20 is a cashier we can infer that Richard is sleeping if and only if Richard is a cashier via universal instantiation. From the fact that Richard is sleeping if and only if Richard is a cashier, and that Richard is not a cashier we can infer that Richard is not sleeping via biconditional elimination. Finally, from the fact that if John were a writer, then Richard is sleeping, and that Richard is not sleeping we can infer that John is not a writer via modus tollens, which contradicts that John is a writer. Therefore, the answer is no.