Consider the following premises. For all x_13, if x_13 were fast, then x_13 is running. For all x_13, x_13 is an electrician. For all x_13, if x_13 were a mechanic, then x_13 is running. There is at least one x_13 for which if x_13 were an electrician, then x_13 is a writer. For all x_13, x_13 is a mechanic or x_13 is fast. Can we infer the following from them? If we can, name the inference rule being used: Some writers will go running.
 From the fact that for all x_13, if x_13 were a mechanic, then x_13 is running, that for all x_13, if x_13 were fast, then x_13 is running, and that for all x_13, x_13 is a mechanic or x_13 is fast we can infer that for all x_13, x_13 will go running via universal disjunction elimination. From the fact that there is at least one x_13 for which if x_13 were an electrician, then x_13 is a writer, and that for all x_13, x_13 is an electrician we can infer that there is at least one x_13 for which x_13 is a writer via existential modus ponens. Finally, from the fact that there is at least one x_13 for which x_13 is a writer, and that for all x_13, x_13 will go running we can infer that some writers will go running via existential conjunction. Therefore, the answer is yes.