Consider the following premises. There is at least one x for which if x plays squash, then x is a mechanic. For all x, x will play squash or x will write a letter. For all x, if x writes a letter, then x is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x, x is not a mechanic.
That contradicts the premises. Therefore the answer is no.