Consider the following premises. If Mary were a janitor, then Susan is playing squash. For all x_16, x_16 will cook if and only if x_16 is a janitor. If it is late, then Mary is a janitor. It is late or Mary is cooking. Can we infer the following from them? If we can, name the inference rule being used: Susan is not playing squash.
 From the fact that for all x_16, x_16 will cook if and only if x_16 is a janitor we can infer that Mary is cooking if and only if Mary is a janitor via universal instantiation. From the fact that Mary is cooking if and only if Mary is a janitor we can infer that if Mary cooks, then Mary is a janitor via biconditional elimination. From the fact that if it is late, then Mary is a janitor, that if Mary cooks, then Mary is a janitor, and that it is late or Mary is cooking we can infer that Mary is a janitor via disjunction elimination. Finally, from the fact that if Mary were a janitor, then Susan is playing squash, and that Mary is a janitor we can infer that Susan is playing squash via modus ponens, which contradicts that Susan is not playing squash. Therefore, the answer is no.