Consider the following premises. There is at least one y for which if y goes running, then y is listening to a song. For all y, if y goes running, then y is a cashier. For all y, if y were a cashier, then y is running. Can we infer the following from them? For all y, the fact that y were a cashier does not imply that y is listening to a song.
That contradicts the premises. Therefore the answer is no.