Consider the following premises. For all x, x will make tea. There is at least one x for which x will take a plane or x will not make tea. For all x, if x were a server, then x is taking a plane. For all x, if x reads a book, then x is a server. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will take a plane.
 From the fact that for all x, x will make tea we can infer that for all x, x will make tea or x will read a book via universal addition. From the fact that for all x, if x reads a book, then x is a server, and that for all x, if x were a server, then x is taking a plane we can infer that for all x, if x reads a book, then x is taking a plane via universal transitivity. From the fact that there is at least one x for which x will take a plane or x will not make tea we can infer that there is at least one x for which if x makes tea, then x is taking a plane via existential rewriting. Finally, from the fact that there is at least one x for which if x makes tea, then x is taking a plane, that for all x, if x reads a book, then x is taking a plane, and that for all x, x will make tea or x will read a book we can infer that there is at least one x for which x will take a plane via existential disjunction elimination. Therefore, the answer is yes.