Consider the following premises. For all x_6, if x_6 were fast, then x_6 is running. For all x_6, if x_6 were a server, then x_6 is fast. David is a server. Can we infer the following from them? If we can, name the inference rule being used: David is not running.
 From the fact that for all x_6, if x_6 were a server, then x_6 is fast, and that for all x_6, if x_6 were fast, then x_6 is running we can infer that for all x_6, if x_6 were a server, then x_6 is running via universal transitivity. From the fact that for all x_6, if x_6 were a server, then x_6 is running we can infer that if David were a server, then David is running via universal instantiation. Finally, from the fact that if David were a server, then David is running, and that David is a server we can infer that David is running via modus ponens, which contradicts that David is not running. Therefore, the answer is no.