Consider the following premises. There is at least one x_7 for which x_7 is not rich or x_7 will work. For all x_7, x_7 is not sad. For all x_7, x_7 is rich or x_7 is excited. For all x_7, x_7 is excited if and only if x_7 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will work.
 From the fact that for all x_7, x_7 is excited if and only if x_7 is sad, and that for all x_7, x_7 is not sad we can infer that for all x_7, x_7 is not excited via universal biconditional elimination. From the fact that for all x_7, x_7 is rich or x_7 is excited, and that there is at least one x_7 for which x_7 is not rich or x_7 will work we can infer that there is at least one x_7 for which x_7 is excited or x_7 will work via existential resolution. Finally, from the fact that there is at least one x_7 for which x_7 is excited or x_7 will work, and that for all x_7, x_7 is not excited we can infer that there is at least one x_7 for which x_7 will work via existential disjunctive syllogism. Therefore, the answer is yes.