Consider the following premises. For all x_6, if x_6 writes a letter, then x_6 is a janitor. There is at least one x_6 for which if x_6 were a janitor, then x_6 is a writer. For all x_6, if x_6 were a mechanic, then x_6 is writing a letter. For all x_6, x_6 is not a writer. Can we infer the following from them? For all x_6, x_6 is not a writer.
That is one of the premises. Therefore, the answer is yes.