Consider the following premises. For all x_5, x_5 is not a doctor. For all x_5, x_5 is not a soldier or x_5 is a cashier. For all x_5, x_5 will not make tea or x_5 is a doctor. There is at least one x_5 for which x_5 will make tea or x_5 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is not a cashier.
 From the fact that there is at least one x_5 for which x_5 will make tea or x_5 is a soldier, and that for all x_5, x_5 will not make tea or x_5 is a doctor we can infer that there is at least one x_5 for which x_5 is a soldier or x_5 is a doctor via existential resolution. From the fact that there is at least one x_5 for which x_5 is a soldier or x_5 is a doctor, and that for all x_5, x_5 is not a soldier or x_5 is a cashier we can infer that there is at least one x_5 for which x_5 is a doctor or x_5 is a cashier via existential resolution. Finally, from the fact that there is at least one x_5 for which x_5 is a doctor or x_5 is a cashier, and that for all x_5, x_5 is not a doctor we can infer that there is at least one x_5 for which x_5 is a cashier via existential disjunctive syllogism, which contradicts that For all x_5, x_5 is not a cashier. Therefore, the answer is no.