Consider the following premises. For all x_8, x_8 will go running if and only if x_8 will listen to a song. For all x_8, if x_8 were an astronaut, then x_8 is running. There is at least one x_8 for which if x_8 listens to a song, then x_8 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, if is not true that x_8 will listen to a song if and only if x_8 will go running.
That contradicts the premises. Therefore the answer is no.