Consider the following premises. For all x_4, if x_4 were a writer, then x_4 is a carpenter. There is at least one x_4 for which if x_4 plays a game, then x_4 is a writer. For all x_4, if x_4 were a carpenter, then x_4 is playing a game. 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 were a writer does not imply that x_4 is a carpenter.
That contradicts the premises. Therefore the answer is no.