Consider the following premises. For all x_7, x_7 is not a taxi driver. There is at least one x_7 for which x_7 will play a game if and only if x_7 is a nurse. For all x_7, if x_7 were a nurse, then x_7 is a sailor. For all x_7, x_7 is a taxi driver if and only if x_7 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will play a game.
 From the fact that for all x_7, x_7 is a taxi driver if and only if x_7 is a sailor, and that for all x_7, x_7 is not a taxi driver we can infer that for all x_7, x_7 is not a sailor via universal biconditional elimination. From the fact that for all x_7, if x_7 were a nurse, then x_7 is a sailor, and that for all x_7, x_7 is not a sailor we can infer that for all x_7, x_7 is not a nurse via universal modus tollens. Finally, from the fact that there is at least one x_7 for which x_7 will play a game if and only if x_7 is a nurse, and that for all x_7, x_7 is not a nurse we can infer that there is at least one x_7 for which x_7 will not play a game via existential biconditional elimination, which contradicts that For all x_7, x_7 will play a game. Therefore, the answer is no.