Consider the following premises. There is at least one z_4 for which if z_4 writes a letter, then z_4 is poor. For all z_4, if z_4 cooks, then z_4 is climbing a mountain. For all z_4, if z_4 were poor, then z_4 is cooking. Can we infer the following from them? If we can, name the inference rule being used: For all z_4, the fact that z_4 writes a letter does not imply that z_4 is climbing a mountain.
That contradicts the premises. Therefore the answer is no.