Consider the following premises. For all x_10, x_10 will drink water or x_10 will work. For all x_10, x_10 will play a game if and only if x_10 is happy. For all x_10, x_10 will not play a game. For all x_10, if x_10 works, then x_10 is happy. For all x_10, if x_10 were happy, then x_10 is working. For all x_10, x_10 will not drink water or x_10 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_10 for which x_10 is not a server.
 From the fact that for all x_10, x_10 will play a game if and only if x_10 is happy, and that for all x_10, x_10 will not play a game we can infer that for all x_10, x_10 is not happy via universal biconditional elimination. From the fact that for all x_10, x_10 will drink water or x_10 will work, and that for all x_10, x_10 will not drink water or x_10 is a server we can infer that for all x_10, x_10 will work or x_10 is a server via universal resolution. From the fact that for all x_10, if x_10 were happy, then x_10 is working, and that for all x_10, if x_10 works, then x_10 is happy we can infer that for all x_10, x_10 is happy if and only if x_10 will work via universal biconditional introduction. From the fact that for all x_10, x_10 is happy if and only if x_10 will work, and that for all x_10, x_10 is not happy we can infer that for all x_10, x_10 will not work via universal biconditional elimination. Finally, from the fact that for all x_10, x_10 will work or x_10 is a server, and that for all x_10, x_10 will not work we can infer that for all x_10, x_10 is a server via universal disjunctive syllogism, which contradicts that There is at least one x_10 for which x_10 is not a server. Therefore, the answer is no.