Consider the following premises. For all x_7, x_7 will go running if and only if x_7 will play a game. For all x_7, if x_7 were excited, then x_7 is playing a game. There is at least one x_7 for which x_7 will play squash. For all x_7, x_7 will go running or x_7 is excited. Can we infer the following from them? For all x_7, either x_7 will play a game or x_7 will play squash are not true.
 From the fact that for all x_7, x_7 will go running if and only if x_7 will play a game we can infer that for all x_7, if x_7 goes running, then x_7 is playing a game. From the fact that for all x_7, if x_7 goes running, then x_7 is playing a game, that for all x_7, if x_7 were excited, then x_7 is playing a game, and that for all x_7, x_7 will go running or x_7 is excited we can infer that for all x_7, x_7 will play a game. Finally, from the fact that for all x_7, x_7 will play a game, and that there is at least one x_7 for which x_7 will play squash we can infer that there is at least one x_7 for which x_7 will play a game and x_7 will play squash, which contradicts that For all x_7, either x_7 will play a game or x_7 will play squash are not true. Therefore, the answer is no.