Consider the following premises. For all x_20, x_20 will sleep or x_20 is an astronaut. It is not snowing. It is snowing or William is a writer. For all x_20, x_20 will not sleep. Can we infer the following from them? If we can, name the inference rule being used: William is not a writer.
 From the fact that for all x_20, x_20 will sleep or x_20 is an astronaut, and that for all x_20, x_20 will not sleep we can infer that for all x_20, x_20 is an astronaut via universal disjunctive syllogism. Finally, from the fact that it is snowing or William is a writer, and that it is not snowing we can infer that William is a writer via disjunctive syllogism, which contradicts that William is not a writer. Therefore, the answer is no.