Consider the following premises. For all x_4, x_4 will not play a game. For all x_4, x_4 will play a game or x_4 will cook. There is at least one x_4 for which x_4 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will listen to a song.
That is one of the premises. Therefore, the answer is yes.