Consider the following premises. For all x_15, if x_15 were an artist, then x_15 is an electrician. For all x_15, x_15 is an astronaut and x_15 will sleep. For all x_15, if x_15 works, then x_15 is a writer. For all x_15, if x_15 were a writer, then x_15 is not an electrician. For all x_15, if x_15 were an astronaut, then x_15 is an artist. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 will not work.
 From the fact that for all x_15, x_15 is an astronaut and x_15 will sleep we can infer that for all x_15, x_15 is an astronaut via universal simplification. From the fact that for all x_15, if x_15 were an astronaut, then x_15 is an artist, and that for all x_15, if x_15 were an artist, then x_15 is an electrician we can infer that for all x_15, if x_15 were an astronaut, then x_15 is an electrician via universal transitivity. From the fact that for all x_15, if x_15 were an astronaut, then x_15 is an electrician, and that for all x_15, x_15 is an astronaut we can infer that for all x_15, x_15 is an electrician via universal modus ponens. From the fact that for all x_15, if x_15 were a writer, then x_15 is not an electrician, and that for all x_15, x_15 is an electrician we can infer that for all x_15, x_15 is not a writer via universal modus tollens. Finally, from the fact that for all x_15, if x_15 works, then x_15 is a writer, and that for all x_15, x_15 is not a writer we can infer that for all x_15, x_15 will not work via universal modus tollens. Therefore, the answer is yes.