Consider the following premises. If Richard plays a game, then Richard is a scientist. For all x_7, x_7 will play a game or x_7 is not a scientist. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Richard is a scientist if and only if Richard is playing a game.
 From the fact that for all x_7, x_7 will play a game or x_7 is not a scientist we can infer that for all x_7, if x_7 were a scientist, then x_7 is playing a game via universal rewriting. From the fact that for all x_7, if x_7 were a scientist, then x_7 is playing a game we can infer that if Richard were a scientist, then Richard is playing a game via universal instantiation. Finally, from the fact that if Richard were a scientist, then Richard is playing a game, and that if Richard plays a game, then Richard is a scientist we can infer that Richard is a scientist if and only if Richard is playing a game via biconditional introduction, which contradicts that If is not true that Richard is a scientist if and only if Richard is playing a game. Therefore, the answer is no.