Consider the following premises. For all x_9, x_9 will play a game if and only if x_9 is a sailor. For all x_9, if x_9 plays a game, then x_9 is a sailor. For all x_9, x_9 will not work. For all x_9, x_9 will play a game if and only if x_9 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is not a sailor.
 From the fact that for all x_9, x_9 will play a game if and only if x_9 is a sailor we can infer that for all x_9, if x_9 were a sailor, then x_9 is playing a game via universal biconditional elimination. From the fact that for all x_9, if x_9 plays a game, then x_9 is a sailor, and that for all x_9, if x_9 were a sailor, then x_9 is playing a game we can infer that for all x_9, x_9 will play a game if and only if x_9 is a sailor via universal biconditional introduction. From the fact that for all x_9, x_9 will play a game if and only if x_9 will work, and that for all x_9, x_9 will not work we can infer that for all x_9, x_9 will not play a game via universal biconditional elimination. Finally, from the fact that for all x_9, x_9 will play a game if and only if x_9 is a sailor, and that for all x_9, x_9 will not play a game we can infer that for all x_9, x_9 is not a sailor via universal biconditional elimination. Therefore, the answer is yes.