Consider the following premises. For all x_4, if x_4 cooks, then x_4 is climbing a mountain. There is at least one x_4 for which x_4 will make tea or x_4 is not a nurse. For all x_4, if x_4 climbs a mountain, then x_4 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, the fact that x_4 cooks does not imply that x_4 is making tea.
That contradicts the premises. Therefore the answer is no.