Consider the following premises. For all x_13, x_13 will cook if and only if x_13 is a carpenter. There is at least one x_13 for which if x_13 were a scientist, then x_13 is cooking. For all x_13, x_13 is a carpenter or x_13 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, neither x_13 will cook nor x_13 will climb a mountain.
That contradicts the premises. Therefore the answer is no.