Consider the following premises. For all x_22, x_22 will drink water if and only if x_22 will listen to a song. Elisabeth is not listening to a song. It is cloudy. Can we infer the following from them? If we can, name the inference rule being used: It is cloudy or James is working.
 From the fact that for all x_22, x_22 will drink water if and only if x_22 will listen to a song we can infer that Elisabeth is drinking water if and only if Elisabeth is listening to a song via universal instantiation. From the fact that Elisabeth is drinking water if and only if Elisabeth is listening to a song, and that Elisabeth is not listening to a song we can infer that Elisabeth is not drinking water via biconditional elimination. From the fact that it is cloudy, and that Elisabeth is not drinking water we can infer that it is cloudy and Elisabeth is not drinking water via conjunction. From the fact that it is cloudy and Elisabeth is not drinking water we can infer that it is cloudy via simplification. Finally, from the fact that it is cloudy we can infer that it is cloudy or James is working via addition. Therefore, the answer is yes.