Consider the following premises. There is at least one x_18 for which if x_18 takes a plane, then x_18 is cooking. For all x_18, x_18 is not rich. For all x_18, x_18 is fast if and only if x_18 will cook. For all x_18, x_18 is rich if and only if x_18 will take a plane. For all x_18, if x_18 cooks, then x_18 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_18 for which x_18 is not fast.
 From the fact that for all x_18, x_18 is rich if and only if x_18 will take a plane we can infer that for all x_18, if x_18 takes a plane, then x_18 is rich via universal biconditional elimination. From the fact that there is at least one x_18 for which if x_18 takes a plane, then x_18 is cooking, and that for all x_18, if x_18 cooks, then x_18 is taking a plane we can infer that there is at least one x_18 for which x_18 will take a plane if and only if x_18 will cook via existential biconditional introduction. From the fact that for all x_18, if x_18 takes a plane, then x_18 is rich, and that for all x_18, x_18 is not rich we can infer that for all x_18, x_18 will not take a plane via universal modus tollens. From the fact that there is at least one x_18 for which x_18 will take a plane if and only if x_18 will cook, and that for all x_18, x_18 will not take a plane we can infer that there is at least one x_18 for which x_18 will not cook via existential biconditional elimination. Finally, from the fact that for all x_18, x_18 is fast if and only if x_18 will cook, and that there is at least one x_18 for which x_18 will not cook we can infer that there is at least one x_18 for which x_18 is not fast via existential biconditional elimination. Therefore, the answer is yes.