Consider the following premises. For all x_18, if x_18 were a taxi driver, then x_18 is playing a game. For all x_18, x_18 is a doctor. There is at least one x_18 for which if x_18 writes a letter, then x_18 is playing a game. For all x_18, x_18 will write a letter or x_18 is a taxi driver. Can we infer the following from them? For all x_18, neither x_18 will play a game nor x_18 is a bartender.
That contradicts the premises. Therefore the answer is no.