Consider the following premises. For all x_7, if x_7 were a cashier, then x_7 is not a politician. For all x_7, x_7 is a politician. Richard is sleeping if and only if Barbara is a cashier. Can we infer the following from them? Richard is sleeping.
 From the fact that for all x_7, if x_7 were a cashier, then x_7 is not a politician, and that for all x_7, x_7 is a politician we can infer that for all x_7, x_7 is not a cashier. From the fact that for all x_7, x_7 is not a cashier we can infer that Barbara is not a cashier. Finally, from the fact that Richard is sleeping if and only if Barbara is a cashier, and that Barbara is not a cashier we can infer that Richard is not sleeping, which contradicts that Richard is sleeping. Therefore, the answer is no.