Consider the following premises. For all x_14, if x_14 listens to a song, then x_14 is taking a plane. For all x_14, if x_14 takes a plane, then x_14 is a carpenter. There is at least one x_14 for which x_14 will take a plane if and only if x_14 will play squash. For all x_14, x_14 will listen to a song or x_14 will play squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 is a carpenter.
 From the fact that there is at least one x_14 for which x_14 will take a plane if and only if x_14 will play squash we can infer that there is at least one x_14 for which if x_14 plays squash, then x_14 is taking a plane via existential biconditional elimination. From the fact that for all x_14, if x_14 listens to a song, then x_14 is taking a plane, that there is at least one x_14 for which if x_14 plays squash, then x_14 is taking a plane, and that for all x_14, x_14 will listen to a song or x_14 will play squash we can infer that there is at least one x_14 for which x_14 will take a plane via existential disjunction elimination. Finally, from the fact that for all x_14, if x_14 takes a plane, then x_14 is a carpenter, and that there is at least one x_14 for which x_14 will take a plane we can infer that there is at least one x_14 for which x_14 is a carpenter via existential modus ponens. Therefore, the answer is yes.