Consider the following premises. It is cloudy or Elisabeth is not running. Elisabeth is running or Thomas is a mechanic. If William plays tennis, then it is cloudy. Thomas is a mechanic if and only if William is playing tennis. Can we infer the following from them? It is cloudy.
 From the fact that Thomas is a mechanic if and only if William is playing tennis we can infer that if Thomas were a mechanic, then William is playing tennis. From the fact that it is cloudy or Elisabeth is not running we can infer that if Elisabeth goes running, then it is cloudy. From the fact that if Thomas were a mechanic, then William is playing tennis, and that if William plays tennis, then it is cloudy we can infer that if Thomas were a mechanic, then it is cloudy. Finally, from the fact that if Elisabeth goes running, then it is cloudy, that if Thomas were a mechanic, then it is cloudy, and that Elisabeth is running or Thomas is a mechanic we can infer that it is cloudy. Therefore, the answer is yes.