Consider the following premises. There is at least one x_12 for which if x_12 plays a game, then x_12 is an artist. For all x_12, x_12 is an electrician or x_12 will listen to a song. For all x_12, x_12 is not an electrician. For all x_12, x_12 is a mechanic or x_12 will play a game. For all x_12, if x_12 were a mechanic, then x_12 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will listen to a song and x_12 is an artist.
 From the fact that for all x_12, if x_12 were a mechanic, then x_12 is an artist, that there is at least one x_12 for which if x_12 plays a game, then x_12 is an artist, and that for all x_12, x_12 is a mechanic or x_12 will play a game we can infer that there is at least one x_12 for which x_12 is an artist via existential disjunction elimination. From the fact that for all x_12, x_12 is an electrician or x_12 will listen to a song, and that for all x_12, x_12 is not an electrician we can infer that for all x_12, x_12 will listen to a song via universal disjunctive syllogism. Finally, from the fact that for all x_12, x_12 will listen to a song, and that there is at least one x_12 for which x_12 is an artist we can infer that there is at least one x_12 for which x_12 will listen to a song and x_12 is an artist via existential conjunction. Therefore, the answer is yes.