Consider the following premises. There is at least one x_6 for which x_6 will listen to a song if and only if x_6 is bored. For all x_6, if x_6 were bored, then x_6 is listening to a song. Can we infer the following from them? For all x_6, the fact that x_6 were bored does not imply that x_6 is listening to a song.
That contradicts the premises. Therefore the answer is no.