Consider the following premises. For all x_3, x_3 will play tennis. There is at least one x_3 for which x_3 is not rich or x_3 is a scientist. For all x_3, x_3 will not play tennis or x_3 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, neither x_3 will write a letter nor x_3 is a scientist.
That contradicts the premises. Therefore the answer is no.