Consider the following premises. There is at least one x_6 for which if x_6 were bored, then x_6 is taking a plane. For all x_6, x_6 will write a letter or x_6 is bored. For all x_6, if x_6 takes a plane, then x_6 is bored. For all x_6, if x_6 writes a letter, then x_6 is taking a plane. Can we infer the following from them? There is at least one x_6 for which x_6 will take a plane.
 From the fact that there is at least one x_6 for which if x_6 were bored, then x_6 is taking a plane, and that for all x_6, if x_6 takes a plane, then x_6 is bored we can infer that there is at least one x_6 for which x_6 is bored if and only if x_6 will take a plane. From the fact that there is at least one x_6 for which x_6 is bored if and only if x_6 will take a plane we can infer that there is at least one x_6 for which if x_6 were bored, then x_6 is taking a plane. Finally, from the fact that for all x_6, if x_6 writes a letter, then x_6 is taking a plane, that there is at least one x_6 for which if x_6 were bored, then x_6 is taking a plane, and that for all x_6, x_6 will write a letter or x_6 is bored we can infer that there is at least one x_6 for which x_6 will take a plane. Therefore, the answer is yes.