Consider the following premises. For all x_9, if x_9 were a politician, then x_9 is not a cashier. There is at least one x_9 for which x_9 is a cashier. For all x_9, x_9 is a politician. Can we infer the following from them? For all x_9, x_9 will not write a letter.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.