Consider the following premises. For all x_6, if x_6 plays squash, then x_6 is making tea. For all x_6, if x_6 plays squash, then x_6 is a poet. For all x_6, x_6 is not a poet. For all x_6, if x_6 takes a plane, then x_6 is playing squash. For all x_6, if x_6 makes tea, then x_6 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will take a plane.
 From the fact that for all x_6, if x_6 plays squash, then x_6 is a poet, and that for all x_6, x_6 is not a poet we can infer that for all x_6, x_6 will not play squash via universal modus tollens. From the fact that for all x_6, if x_6 plays squash, then x_6 is making tea, and that for all x_6, if x_6 makes tea, then x_6 is taking a plane we can infer that for all x_6, if x_6 plays squash, then x_6 is taking a plane via universal transitivity. From the fact that for all x_6, if x_6 plays squash, then x_6 is taking a plane, and that for all x_6, if x_6 takes a plane, then x_6 is playing squash we can infer that for all x_6, x_6 will play squash if and only if x_6 will take a plane via universal biconditional introduction. Finally, from the fact that for all x_6, x_6 will play squash if and only if x_6 will take a plane, and that for all x_6, x_6 will not play squash we can infer that for all x_6, x_6 will not take a plane via universal biconditional elimination, which contradicts that There is at least one x_6 for which x_6 will take a plane. Therefore, the answer is no.