Consider the following premises. For all x_5, if x_5 plays squash, then x_5 is drinking water. For all x_5, if x_5 drinks water, then x_5 is taking a plane. For all x_5, if x_5 takes a plane, then x_5 is writing a letter. There is at least one x_5 for which x_5 will play squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not write a letter.
 From the fact that for all x_5, if x_5 drinks water, then x_5 is taking a plane, and that for all x_5, if x_5 takes a plane, then x_5 is writing a letter we can infer that for all x_5, if x_5 drinks water, then x_5 is writing a letter via universal transitivity. From the fact that for all x_5, if x_5 plays squash, then x_5 is drinking water, and that for all x_5, if x_5 drinks water, then x_5 is writing a letter we can infer that for all x_5, if x_5 plays squash, then x_5 is writing a letter via universal transitivity. Finally, from the fact that for all x_5, if x_5 plays squash, then x_5 is writing a letter, and that there is at least one x_5 for which x_5 will play squash we can infer that there is at least one x_5 for which x_5 will write a letter via existential modus ponens, which contradicts that For all x_5, x_5 will not write a letter. Therefore, the answer is no.