Consider the following premises. There is at least one x_12 for which x_12 is not a mechanic or x_12 will climb a mountain. For all x_12, x_12 is a mechanic or x_12 will read a book. For all x_12, if x_12 reads a book, then x_12 is a politician. For all x_12, if x_12 were a politician, then x_12 is reading a book. For all x_12, x_12 is a politician if and only if x_12 will climb a mountain. 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 a politician.
 From the fact that for all x_12, x_12 is a politician if and only if x_12 will climb a mountain we can infer that for all x_12, if x_12 climbs a mountain, then x_12 is a politician via universal biconditional elimination. From the fact that for all x_12, x_12 is a mechanic or x_12 will read a book, and that there is at least one x_12 for which x_12 is not a mechanic or x_12 will climb a mountain we can infer that there is at least one x_12 for which x_12 will read a book or x_12 will climb a mountain via existential resolution. From the fact that for all x_12, if x_12 were a politician, then x_12 is reading a book, and that for all x_12, if x_12 reads a book, then x_12 is a politician we can infer that for all x_12, x_12 is a politician if and only if x_12 will read a book via universal biconditional introduction. From the fact that for all x_12, x_12 is a politician if and only if x_12 will read a book we can infer that for all x_12, if x_12 reads a book, then x_12 is a politician via universal biconditional elimination. Finally, from the fact that for all x_12, if x_12 reads a book, then x_12 is a politician, that for all x_12, if x_12 climbs a mountain, then x_12 is a politician, and that there is at least one x_12 for which x_12 will read a book or x_12 will climb a mountain we can infer that there is at least one x_12 for which x_12 is a politician via existential disjunction elimination. Therefore, the answer is yes.