Consider the following premises. For all x_11, if x_11 were excited, then x_11 is drinking water. There is at least one x_11 for which x_11 is excited. For all x_11, if x_11 writes a letter, then x_11 is not drinking water. For all x_11, x_11 will write a letter or x_11 will make tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 will make tea.
 From the fact that for all x_11, if x_11 were excited, then x_11 is drinking water, and that there is at least one x_11 for which x_11 is excited we can infer that there is at least one x_11 for which x_11 will drink water via existential modus ponens. From the fact that for all x_11, if x_11 writes a letter, then x_11 is not drinking water, and that there is at least one x_11 for which x_11 will drink water we can infer that there is at least one x_11 for which x_11 will not write a letter via existential modus tollens. Finally, from the fact that for all x_11, x_11 will write a letter or x_11 will make tea, and that there is at least one x_11 for which x_11 will not write a letter we can infer that there is at least one x_11 for which x_11 will make tea via existential disjunctive syllogism. Therefore, the answer is yes.