Consider the following premises. For all x_6, x_6 will not read a book. For all x_6, if x_6 cooks, then x_6 is listening to a song. For all x_6, x_6 will cook. For all x_6, x_6 will read a book or x_6 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will listen to a song.
We can infer this via the universal modus ponens rule. Therefore, the answer is yes.