Consider the following premises. For all x_7, x_7 will cook. For all x_7, if x_7 drives a car, then x_7 is happy. For all x_7, if x_7 drives a car, then x_7 is not fast. For all x_7, if x_7 cooks, then x_7 is fast. There is at least one x_7 for which if x_7 were happy, then x_7 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is happy.
 From the fact that for all x_7, if x_7 cooks, then x_7 is fast, and that for all x_7, x_7 will cook we can infer that for all x_7, x_7 is fast via universal modus ponens. From the fact that there is at least one x_7 for which if x_7 were happy, then x_7 is driving a car, and that for all x_7, if x_7 drives a car, then x_7 is happy we can infer that there is at least one x_7 for which x_7 is happy if and only if x_7 will drive a car via existential biconditional introduction. From the fact that for all x_7, if x_7 drives a car, then x_7 is not fast, and that for all x_7, x_7 is fast we can infer that for all x_7, x_7 will not drive a car via universal modus tollens. Finally, from the fact that there is at least one x_7 for which x_7 is happy if and only if x_7 will drive a car, and that for all x_7, x_7 will not drive a car we can infer that there is at least one x_7 for which x_7 is not happy via existential biconditional elimination, which contradicts that For all x_7, x_7 is happy. Therefore, the answer is no.