Consider the following premises. For all x_11, x_11 is a cashier if and only if x_11 is an electrician. For all x_11, x_11 is a cashier if and only if x_11 will listen to a song. For all x_11, if x_11 were an electrician, then x_11 is listening 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_11 for which if is not true that x_11 is a cashier if and only if x_11 is an electrician.
 From the fact that for all x_11, x_11 is a cashier if and only if x_11 is an electrician we can infer that for all x_11, if x_11 were a cashier, then x_11 is an electrician via universal biconditional elimination. From the fact that for all x_11, x_11 is a cashier if and only if x_11 will listen to a song we can infer that for all x_11, if x_11 listens to a song, then x_11 is a cashier via universal biconditional elimination. From the fact that for all x_11, if x_11 were an electrician, then x_11 is listening to a song, and that for all x_11, if x_11 listens to a song, then x_11 is a cashier we can infer that for all x_11, if x_11 were an electrician, then x_11 is a cashier via universal transitivity. Finally, from the fact that for all x_11, if x_11 were a cashier, then x_11 is an electrician, and that for all x_11, if x_11 were an electrician, then x_11 is a cashier we can infer that for all x_11, x_11 is a cashier if and only if x_11 is an electrician via universal biconditional introduction, which contradicts that There is at least one x_11 for which if is not true that x_11 is a cashier if and only if x_11 is an electrician. Therefore, the answer is no.