Consider the following premises. For all x_15, x_15 is an astronaut or x_15 is not a server. For all x_15, x_15 is a writer. For all x_15, if x_15 were a writer, then x_15 is a server. There is at least one x_15 for which x_15 will work if and only if x_15 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which x_15 will work.
 From the fact that for all x_15, x_15 is an astronaut or x_15 is not a server we can infer that for all x_15, if x_15 were a server, then x_15 is an astronaut via universal rewriting. From the fact that for all x_15, if x_15 were a writer, then x_15 is a server, and that for all x_15, if x_15 were a server, then x_15 is an astronaut we can infer that for all x_15, if x_15 were a writer, then x_15 is an astronaut via universal transitivity. From the fact that for all x_15, if x_15 were a writer, then x_15 is an astronaut, and that for all x_15, x_15 is a writer we can infer that for all x_15, x_15 is an astronaut via universal modus ponens. From the fact that there is at least one x_15 for which x_15 will work if and only if x_15 is an astronaut we can infer that there is at least one x_15 for which if x_15 were an astronaut, then x_15 is working via existential biconditional elimination. Finally, from the fact that there is at least one x_15 for which if x_15 were an astronaut, then x_15 is working, and that for all x_15, x_15 is an astronaut we can infer that there is at least one x_15 for which x_15 will work via existential modus ponens. Therefore, the answer is yes.