Consider the following premises. For all x_6, if x_6 were a cashier, then x_6 is playing squash. There is at least one x_6 for which if x_6 takes a plane, then x_6 is a cashier. For all x_6, if x_6 plays squash, then x_6 is taking a plane. For all x_6, if x_6 takes a plane, then x_6 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if is not true that x_6 will play squash if and only if x_6 will take a plane.
 From the fact that there is at least one x_6 for which if x_6 takes a plane, then x_6 is a cashier, and that for all x_6, if x_6 were a cashier, then x_6 is playing squash we can infer that there is at least one x_6 for which if x_6 takes a plane, then x_6 is playing squash via existential transitivity. Finally, from the fact that for all x_6, if x_6 plays squash, then x_6 is taking a plane, and that for all x_6, if x_6 takes a plane, then x_6 is playing squash we can infer that for all x_6, x_6 will play squash if and only if x_6 will take a plane via universal biconditional introduction, which contradicts that For all x_6, if is not true that x_6 will play squash if and only if x_6 will take a plane. Therefore, the answer is no.