Consider the following premises. For all x, if x were an electrician, then x is listening to a song. For all x, if x listens to a song, then x is an electrician. For all x, x will listen to a song or x is not an electrician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which if is not true that x is an electrician if and only if x will listen to a song.
 From the fact that for all x, if x were an electrician, then x is listening to a song, and that for all x, if x listens to a song, then x is an electrician we can infer that for all x, x is an electrician if and only if x will listen to a song via universal biconditional introduction. From the fact that for all x, x will listen to a song or x is not an electrician we can infer that for all x, if x were an electrician, then x is listening to a song via universal rewriting. From the fact that for all x, x is an electrician if and only if x will listen to a song we can infer that for all x, if x listens to a song, then x is an electrician via universal biconditional elimination. Finally, from the fact that for all x, if x were an electrician, then x is listening to a song, and that for all x, if x listens to a song, then x is an electrician we can infer that for all x, x is an electrician if and only if x will listen to a song via universal biconditional introduction, which contradicts that There is at least one x for which if is not true that x is an electrician if and only if x will listen to a song. Therefore, the answer is no.