Consider the following premises. For all x, if x makes tea, then x is writing a letter. For all x, x will make tea if and only if x will play a game. For all x, x will not write a letter. There is at least one x for which if x writes a letter, then x is making tea. Can we infer the following from them? There is at least one x for which x will not play a game.
 From the fact that there is at least one x for which if x writes a letter, then x is making tea, and that for all x, if x makes tea, then x is writing a letter we can infer that there is at least one x for which x will write a letter if and only if x will make tea. From the fact that there is at least one x for which x will write a letter if and only if x will make tea, and that for all x, x will not write a letter we can infer that there is at least one x for which x will not make tea. Finally, from the fact that for all x, x will make tea if and only if x will play a game, and that there is at least one x for which x will not make tea we can infer that there is at least one x for which x will not play a game. Therefore, the answer is yes.