Consider the following premises. There is at least one x_6 for which x_6 is not a soldier or x_6 will play tennis. For all x_6, x_6 will not cook or x_6 is a mechanic. For all x_6, if x_6 plays tennis, then x_6 is a police officer. For all x_6, if x_6 were a mechanic, then x_6 is a police officer. For all x_6, x_6 is a soldier or x_6 will cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is a police officer.
 From the fact that for all x_6, x_6 is a soldier or x_6 will cook, and that there is at least one x_6 for which x_6 is not a soldier or x_6 will play tennis we can infer that there is at least one x_6 for which x_6 will cook or x_6 will play tennis via existential resolution. From the fact that there is at least one x_6 for which x_6 will cook or x_6 will play tennis, and that for all x_6, x_6 will not cook or x_6 is a mechanic we can infer that there is at least one x_6 for which x_6 will play tennis or x_6 is a mechanic via existential resolution. Finally, from the fact that for all x_6, if x_6 plays tennis, then x_6 is a police officer, that for all x_6, if x_6 were a mechanic, then x_6 is a police officer, and that there is at least one x_6 for which x_6 will play tennis or x_6 is a mechanic we can infer that there is at least one x_6 for which x_6 is a police officer via existential disjunction elimination. Therefore, the answer is yes.