Consider the following premises. There is at least one x_5 for which x_5 will write a letter. For all x_5, if x_5 writes a letter, then x_5 is a server. For all x_5, if x_5 were fast, then x_5 is curious. For all x_5, if x_5 were a server, then x_5 is fast. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is curious.
 From the fact that for all x_5, if x_5 were a server, then x_5 is fast, and that for all x_5, if x_5 were fast, then x_5 is curious we can infer that for all x_5, if x_5 were a server, then x_5 is curious via universal transitivity. From the fact that for all x_5, if x_5 writes a letter, then x_5 is a server, and that for all x_5, if x_5 were a server, then x_5 is curious we can infer that for all x_5, if x_5 writes a letter, then x_5 is curious via universal transitivity. Finally, from the fact that for all x_5, if x_5 writes a letter, then x_5 is curious, and that there is at least one x_5 for which x_5 will write a letter we can infer that there is at least one x_5 for which x_5 is curious via existential modus ponens. Therefore, the answer is yes.