Consider the following premises. There is at least one x_5 for which x_5 is not curious or x_5 is excited. For all x_5, x_5 will take a plane or x_5 is curious. For all x_5, x_5 will not take a plane or x_5 will work. For all x_5, if x_5 were excited, then x_5 is a doctor. For all x_5, if x_5 works, then x_5 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is a doctor.
 From the fact that for all x_5, x_5 will take a plane or x_5 is curious, and that for all x_5, x_5 will not take a plane or x_5 will work we can infer that for all x_5, x_5 is curious or x_5 will work via universal resolution. From the fact that for all x_5, x_5 is curious or x_5 will work, and that there is at least one x_5 for which x_5 is not curious or x_5 is excited we can infer that there is at least one x_5 for which x_5 will work or x_5 is excited via existential resolution. Finally, from the fact that for all x_5, if x_5 works, then x_5 is a doctor, that for all x_5, if x_5 were excited, then x_5 is a doctor, and that there is at least one x_5 for which x_5 will work or x_5 is excited we can infer that there is at least one x_5 for which x_5 is a doctor via existential disjunction elimination. Therefore, the answer is yes.