Consider the following premises. For all x_17, if x_17 makes tea, then x_17 is happy. For all x_17, x_17 will read a book or x_17 is a sailor. For all x_17, if x_17 were happy, then x_17 is making tea. There is at least one x_17 for which if x_17 makes tea, then x_17 is not a sailor. For all x_17, x_17 will not read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_17 for which x_17 is not happy.
 From the fact that for all x_17, if x_17 were happy, then x_17 is making tea, and that for all x_17, if x_17 makes tea, then x_17 is happy we can infer that for all x_17, x_17 is happy if and only if x_17 will make tea via universal biconditional introduction. From the fact that for all x_17, x_17 will read a book or x_17 is a sailor, and that for all x_17, x_17 will not read a book we can infer that for all x_17, x_17 is a sailor via universal disjunctive syllogism. From the fact that for all x_17, x_17 is happy if and only if x_17 will make tea we can infer that for all x_17, if x_17 were happy, then x_17 is making tea via universal biconditional elimination. From the fact that there is at least one x_17 for which if x_17 makes tea, then x_17 is not a sailor, and that for all x_17, x_17 is a sailor we can infer that there is at least one x_17 for which x_17 will not make tea via existential modus tollens. Finally, from the fact that for all x_17, if x_17 were happy, then x_17 is making tea, and that there is at least one x_17 for which x_17 will not make tea we can infer that there is at least one x_17 for which x_17 is not happy via existential modus tollens. Therefore, the answer is yes.