Consider the following premises. For all x_11, if x_11 were a nurse, then x_11 is cooking. There is at least one x_11 for which if x_11 climbs a mountain, then x_11 is cooking. For all x_11, x_11 is a soldier or x_11 is a nurse. For all x_11, if x_11 were a soldier, then x_11 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, neither x_11 will cook nor x_11 is a politician.
That contradicts the premises. Therefore the answer is no.