Consider the following premises. For all x_13, if x_13 were a cashier, then x_13 is taking a plane. Karen is taking a plane. If Karen takes a plane, then Karen is playing squash. For all x_13, if x_13 plays squash, then x_13 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: Karen is playing squash.
 From the fact that for all x_13, if x_13 plays squash, then x_13 is a cashier, and that for all x_13, if x_13 were a cashier, then x_13 is taking a plane we can infer that for all x_13, if x_13 plays squash, then x_13 is taking a plane via universal transitivity. From the fact that for all x_13, if x_13 plays squash, then x_13 is taking a plane we can infer that if Karen plays squash, then Karen is taking a plane via universal instantiation. From the fact that if Karen takes a plane, then Karen is playing squash, and that if Karen plays squash, then Karen is taking a plane we can infer that Karen is taking a plane if and only if Karen is playing squash via biconditional introduction. From the fact that Karen is taking a plane if and only if Karen is playing squash we can infer that if Karen takes a plane, then Karen is playing squash via biconditional elimination. Finally, from the fact that if Karen takes a plane, then Karen is playing squash, and that Karen is taking a plane we can infer that Karen is playing squash via modus ponens. Therefore, the answer is yes.