Consider the following premises. There is at least one x_15 for which if x_15 takes a plane, then x_15 is playing a game. For all x_15, if x_15 writes a letter, then x_15 is playing a game. For all x_15, x_15 will take a plane or x_15 will write a letter. For all x_15, x_15 is a cashier or x_15 will go running. For all x_15, if x_15 goes running, then x_15 is a writer. For all x_15, if x_15 were a cashier, then x_15 is a writer. 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 is a writer.
 From the fact that for all x_15, if x_15 were a cashier, then x_15 is a writer, that for all x_15, if x_15 goes running, then x_15 is a writer, and that for all x_15, x_15 is a cashier or x_15 will go running we can infer that for all x_15, x_15 is a writer via universal disjunction elimination. From the fact that there is at least one x_15 for which if x_15 takes a plane, then x_15 is playing a game, that for all x_15, if x_15 writes a letter, then x_15 is playing a game, and that for all x_15, x_15 will take a plane or x_15 will write a letter we can infer that there is at least one x_15 for which x_15 will play a game via existential disjunction elimination. From the fact that for all x_15, x_15 is a writer, and that there is at least one x_15 for which x_15 will play a game we can infer that some writers will play a game via existential conjunction. Finally, from the fact that some writers will play a game we can infer that there is at least one x_15 for which x_15 is a writer via existential simplification. Therefore, the answer is yes.