Consider the following premises. For all x_10, x_10 will not listen to a song or x_10 is an electrician. There is at least one x_10 for which if x_10 plays tennis, then x_10 is not sad. For all x_10, x_10 is sad if and only if x_10 is an electrician. For all x_10, x_10 will listen to a song or x_10 is a sailor. For all x_10, if x_10 were a sailor, then x_10 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will not play tennis.
 From the fact that for all x_10, x_10 is sad if and only if x_10 is an electrician we can infer that for all x_10, if x_10 were an electrician, then x_10 is sad via universal biconditional elimination. From the fact that for all x_10, x_10 will listen to a song or x_10 is a sailor, and that for all x_10, x_10 will not listen to a song or x_10 is an electrician we can infer that for all x_10, x_10 is a sailor or x_10 is an electrician via universal resolution. From the fact that for all x_10, if x_10 were a sailor, then x_10 is sad, that for all x_10, if x_10 were an electrician, then x_10 is sad, and that for all x_10, x_10 is a sailor or x_10 is an electrician we can infer that for all x_10, x_10 is sad via universal disjunction elimination. Finally, from the fact that there is at least one x_10 for which if x_10 plays tennis, then x_10 is not sad, and that for all x_10, x_10 is sad we can infer that there is at least one x_10 for which x_10 will not play tennis via existential modus tollens. Therefore, the answer is yes.