Consider the following premises. If it is cloudy, then Mary is listening to a song. Barbara is playing tennis. For all x_17, if x_17 listens to a song, then x_17 is writing a letter. Mary is writing a letter or it is cloudy. For all x_17, if x_17 writes a letter, then x_17 is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not playing tennis.
That contradicts the premises. Therefore the answer is no.