Consider the following premises. For all x_12, if x_12 were a soldier, then x_12 is a nurse. For all x_12, if x_12 were a nurse, then x_12 is sad. For all x_12, x_12 will read a book. For all x_12, if x_12 drinks water, then x_12 is sad. There is at least one x_12 for which x_12 will drink water or x_12 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will read a book.
 From the fact that for all x_12, if x_12 were a soldier, then x_12 is a nurse, and that for all x_12, if x_12 were a nurse, then x_12 is sad we can infer that for all x_12, if x_12 were a soldier, then x_12 is sad via universal transitivity. From the fact that for all x_12, if x_12 drinks water, then x_12 is sad, that for all x_12, if x_12 were a soldier, then x_12 is sad, and that there is at least one x_12 for which x_12 will drink water or x_12 is a soldier we can infer that there is at least one x_12 for which x_12 is sad via existential disjunction elimination. From the fact that for all x_12, x_12 will read a book, and that there is at least one x_12 for which x_12 is sad we can infer that there is at least one x_12 for which x_12 will read a book and x_12 is sad via existential conjunction. Finally, from the fact that there is at least one x_12 for which x_12 will read a book and x_12 is sad we can infer that there is at least one x_12 for which x_12 will read a book via existential simplification. Therefore, the answer is yes.