Consider the following premises. Susan is running. Elisabeth is not a politician. For all x_12, if x_12 sleeps, then x_12 is a politician. For all x_12, if x_12 were a politician, then x_12 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is sleeping.
 From the fact that for all x_12, if x_12 were a politician, then x_12 is sleeping, and that for all x_12, if x_12 sleeps, then x_12 is a politician we can infer that for all x_12, x_12 is a politician if and only if x_12 will sleep via universal biconditional introduction. From the fact that for all x_12, x_12 is a politician if and only if x_12 will sleep we can infer that Elisabeth is a politician if and only if Elisabeth is sleeping via universal instantiation. Finally, from the fact that Elisabeth is a politician if and only if Elisabeth is sleeping, and that Elisabeth is not a politician we can infer that Elisabeth is not sleeping via biconditional elimination, which contradicts that Elisabeth is sleeping. Therefore, the answer is no.