Consider the following premises. For all x_14, x_14 will take a plane if and only if x_14 will drink water. For all x_14, x_14 is a writer or x_14 will make tea. For all x_14, if x_14 makes tea, then x_14 is taking a plane. For all x_14, x_14 is not a writer or x_14 is a server. For all x_14, x_14 will not drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which neither x_14 is a server nor x_14 will play a game.
 From the fact that for all x_14, x_14 will take a plane if and only if x_14 will drink water, and that for all x_14, x_14 will not drink water we can infer that for all x_14, x_14 will not take a plane via universal biconditional elimination. From the fact that for all x_14, if x_14 makes tea, then x_14 is taking a plane, and that for all x_14, x_14 will not take a plane we can infer that for all x_14, x_14 will not make tea via universal modus tollens. From the fact that for all x_14, x_14 is a writer or x_14 will make tea, and that for all x_14, x_14 is not a writer or x_14 is a server we can infer that for all x_14, x_14 will make tea or x_14 is a server via universal resolution. From the fact that for all x_14, x_14 will make tea or x_14 is a server, and that for all x_14, x_14 will not make tea we can infer that for all x_14, x_14 is a server via universal disjunctive syllogism. Finally, from the fact that for all x_14, x_14 is a server we can infer that for all x_14, x_14 is a server or x_14 will play a game via universal addition, which contradicts that There is at least one x_14 for which neither x_14 is a server nor x_14 will play a game. Therefore, the answer is no.