Consider the following premises. For all x_9, x_9 will not write a letter. There is at least one x_9 for which x_9 is a cashier. For all x_9, x_9 will write a letter or x_9 is not a cashier. Can we infer the following from them? There is at least one x_9 for which x_9 will work.
 From the fact that for all x_9, x_9 will write a letter or x_9 is not a cashier we can infer that for all x_9, if x_9 were a cashier, then x_9 is writing a letter. From the fact that there is at least one x_9 for which x_9 is a cashier we can infer that there is at least one x_9 for which x_9 is a cashier or x_9 will work. From the fact that for all x_9, if x_9 were a cashier, then x_9 is writing a letter, and that for all x_9, x_9 will not write a letter we can infer that for all x_9, x_9 is not a cashier. Finally, from the fact that there is at least one x_9 for which x_9 is a cashier or x_9 will work, and that for all x_9, x_9 is not a cashier we can infer that there is at least one x_9 for which x_9 will work. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.