Consider the following premises. There is at least one x_6 for which x_6 is a police officer or x_6 will cook. For all x_6, x_6 will cook if and only if x_6 will write a letter. For all x_6, if x_6 were a cashier, then x_6 is writing a letter. For all x_6, x_6 is not a police officer or x_6 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not write a letter.
 From the fact that for all x_6, x_6 will cook if and only if x_6 will write a letter we can infer that for all x_6, if x_6 cooks, then x_6 is writing a letter via universal biconditional elimination. From the fact that there is at least one x_6 for which x_6 is a police officer or x_6 will cook, and that for all x_6, x_6 is not a police officer or x_6 is a cashier we can infer that there is at least one x_6 for which x_6 will cook or x_6 is a cashier via existential resolution. Finally, from the fact that for all x_6, if x_6 cooks, then x_6 is writing a letter, that for all x_6, if x_6 were a cashier, then x_6 is writing a letter, and that there is at least one x_6 for which x_6 will cook or x_6 is a cashier we can infer that there is at least one x_6 for which x_6 will write a letter via existential disjunction elimination, which contradicts that For all x_6, x_6 will not write a letter. Therefore, the answer is no.