Consider the following premises. William is not a soldier. Sarah is playing a game if and only if William is a taxi driver. For all z, z is a soldier if and only if z is a taxi driver. Can we infer the following from them? Sarah is playing a game.
 From the fact that for all z, z is a soldier if and only if z is a taxi driver we can infer that William is a soldier if and only if William is a taxi driver. From the fact that William is a soldier if and only if William is a taxi driver, and that William is not a soldier we can infer that William is not a taxi driver. Finally, from the fact that Sarah is playing a game if and only if William is a taxi driver, and that William is not a taxi driver we can infer that Sarah is not playing a game, which contradicts that Sarah is playing a game. Therefore, the answer is no.