Consider the following premises. For all x_11, x_11 is not a musician. There is at least one x_11 for which if x_11 were a politician, then x_11 is writing a letter. For all x_11, x_11 is a politician. For all x_11, x_11 is a musician or x_11 is a cashier. Can we infer the following from them? For all x_11, x_11 is not a musician.
That is one of the premises. Therefore, the answer is yes.