Consider the following premises. For all x_10, if x_10 plays a game, then x_10 is an astronaut. If it is sunny, then William is an astronaut. If it is cold, then it is sunny. It is cold or William is playing a game. Can we infer the following from them? William is not an astronaut.
 From the fact that for all x_10, if x_10 plays a game, then x_10 is an astronaut we can infer that if William plays a game, then William is an astronaut. From the fact that if it is cold, then it is sunny, and that if it is sunny, then William is an astronaut we can infer that if it is cold, then William is an astronaut. Finally, from the fact that if it is cold, then William is an astronaut, that if William plays a game, then William is an astronaut, and that it is cold or William is playing a game we can infer that William is an astronaut, which contradicts that William is not an astronaut. Therefore, the answer is no.