Consider the following premises. For all x_11, x_11 is a politician if and only if x_11 is a server. If Barbara were not a politician, then Sarah is playing squash. Barbara is not a server. Can we infer the following from them? If we can, name the inference rule being used: Sarah is not playing squash.
 From the fact that for all x_11, x_11 is a politician if and only if x_11 is a server we can infer that Barbara is a politician if and only if Barbara is a server via universal instantiation. From the fact that Barbara is a politician if and only if Barbara is a server, and that Barbara is not a server we can infer that Barbara is not a politician via biconditional elimination. Finally, from the fact that if Barbara were not a politician, then Sarah is playing squash, and that Barbara is not a politician we can infer that Sarah is playing squash via modus ponens, which contradicts that Sarah is not playing squash. Therefore, the answer is no.