Consider the following premises. For all x_11, if x_11 goes running, then x_11 is a nurse. There is at least one x_11 for which x_11 will go running. For all x_11, if x_11 writes a letter, then x_11 is not a nurse. For all x_11, x_11 will write a letter or x_11 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_11 for which x_11 is a writer.
 From the fact that for all x_11, if x_11 goes running, then x_11 is a nurse, and that there is at least one x_11 for which x_11 will go running we can infer that there is at least one x_11 for which x_11 is a nurse via existential modus ponens. From the fact that for all x_11, if x_11 writes a letter, then x_11 is not a nurse, and that there is at least one x_11 for which x_11 is a nurse we can infer that there is at least one x_11 for which x_11 will not write a letter via existential modus tollens. Finally, from the fact that for all x_11, x_11 will write a letter or x_11 is a writer, and that there is at least one x_11 for which x_11 will not write a letter we can infer that there is at least one x_11 for which x_11 is a writer via existential disjunctive syllogism. Therefore, the answer is yes.