Consider the following premises. Barbara is not playing a game. For all x_3, x_3 will play a game or x_3 is an astronaut. Can we infer the following from them? Barbara is not an astronaut.
 From the fact that for all x_3, x_3 will play a game or x_3 is an astronaut we can infer that Barbara is playing a game or Barbara is an astronaut. Finally, from the fact that Barbara is playing a game or Barbara is an astronaut, and that Barbara is not playing a game we can infer that Barbara is an astronaut, which contradicts that Barbara is not an astronaut. Therefore, the answer is no.