Consider the following premises. For all x_6, x_6 is an astronaut or x_6 is a cashier. For all x_6, x_6 is not an astronaut. For all x_6, if x_6 were a cashier, then x_6 is a writer. For all x_6, if x_6 were a writer, then x_6 is cooking. Can we infer the following from them? There is at least one x_6 for which x_6 will not cook.
 From the fact that for all x_6, x_6 is an astronaut or x_6 is a cashier, and that for all x_6, x_6 is not an astronaut we can infer that for all x_6, x_6 is a cashier. From the fact that for all x_6, if x_6 were a cashier, then x_6 is a writer, and that for all x_6, x_6 is a cashier we can infer that for all x_6, x_6 is a writer. Finally, from the fact that for all x_6, if x_6 were a writer, then x_6 is cooking, and that for all x_6, x_6 is a writer we can infer that for all x_6, x_6 will cook, which contradicts that There is at least one x_6 for which x_6 will not cook. Therefore, the answer is no.