Consider the following premises. For all x_12, x_12 will listen to a song or x_12 will make tea. For all x_12, x_12 will make tea if and only if x_12 is a taxi driver. For all x_12, if x_12 were a taxi driver, then x_12 is an electrician. For all x_12, if x_12 were an office clerk, then x_12 is an electrician. For all x_12, x_12 will not 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_12 for which x_12 is not an electrician.
 From the fact that for all x_12, x_12 will listen to a song or x_12 will make tea, and that for all x_12, x_12 will not listen to a song we can infer that for all x_12, x_12 will make tea via universal disjunctive syllogism. From the fact that for all x_12, x_12 will make tea we can infer that for all x_12, x_12 will make tea or x_12 is an office clerk via universal addition. From the fact that for all x_12, x_12 will make tea if and only if x_12 is a taxi driver we can infer that for all x_12, if x_12 makes tea, then x_12 is a taxi driver via universal biconditional elimination. From the fact that for all x_12, if x_12 makes tea, then x_12 is a taxi driver, and that for all x_12, if x_12 were a taxi driver, then x_12 is an electrician we can infer that for all x_12, if x_12 makes tea, then x_12 is an electrician via universal transitivity. Finally, from the fact that for all x_12, if x_12 makes tea, then x_12 is an electrician, that for all x_12, if x_12 were an office clerk, then x_12 is an electrician, and that for all x_12, x_12 will make tea or x_12 is an office clerk we can infer that for all x_12, x_12 is an electrician via universal disjunction elimination, which contradicts that There is at least one x_12 for which x_12 is not an electrician. Therefore, the answer is no.