Consider the following premises. For all x_6, if x_6 plays squash, then x_6 is playing a game. For all x_6, if x_6 plays a game, then x_6 is playing squash. For all x_6, if x_6 plays squash, then x_6 is playing a game. 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 the fact that x_6 plays squash does not imply that x_6 is playing a game.
 From the fact that for all x_6, if x_6 plays a game, then x_6 is playing squash, and that for all x_6, if x_6 plays squash, then x_6 is playing a game we can infer that for all x_6, x_6 will play a game if and only if x_6 will play squash via universal biconditional introduction. From the fact that for all x_6, x_6 will play a game if and only if x_6 will play squash we can infer that for all x_6, if x_6 plays a game, then x_6 is playing squash via universal biconditional elimination. From the fact that for all x_6, if x_6 plays a game, then x_6 is playing squash, and that for all x_6, if x_6 plays squash, then x_6 is playing a game we can infer that for all x_6, x_6 will play a game if and only if x_6 will play squash via universal biconditional introduction. Finally, from the fact that for all x_6, x_6 will play a game if and only if x_6 will play squash we can infer that for all x_6, if x_6 plays squash, then x_6 is playing a game via universal biconditional elimination, which contradicts that There is at least one x_6 for which the fact that x_6 plays squash does not imply that x_6 is playing a game. Therefore, the answer is no.