Consider the following premises. For all x_14, x_14 is a bartender if and only if x_14 will cook. For all x_14, x_14 will not write a letter. For all x_14, if x_14 were a bartender, then x_14 is not driving a car. For all x_14, x_14 will write a letter. Can we infer the following from them? For all x_14, x_14 will not cook.
 From the fact that for all x_14, x_14 is a bartender if and only if x_14 will cook we can infer that for all x_14, if x_14 cooks, then x_14 is a bartender. From the fact that for all x_14, x_14 will write a letter we can infer that for all x_14, x_14 will write a letter or x_14 will drive a car. From the fact that for all x_14, x_14 will write a letter or x_14 will drive a car, and that for all x_14, x_14 will not write a letter we can infer that for all x_14, x_14 will drive a car. From the fact that for all x_14, if x_14 were a bartender, then x_14 is not driving a car, and that for all x_14, x_14 will drive a car we can infer that for all x_14, x_14 is not a bartender. Finally, from the fact that for all x_14, if x_14 cooks, then x_14 is a bartender, and that for all x_14, x_14 is not a bartender we can infer that for all x_14, x_14 will not cook. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.