Consider the following premises. If it is cloudy, then Sarah is an artist. If Sarah were an artist, then Charles is playing a game. If it snows, then it is cloudy. Charles is playing a game if and only if it is snowing. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Charles is playing a game if and only if Sarah is an artist.
 From the fact that Charles is playing a game if and only if it is snowing we can infer that if Charles plays a game, then it is snowing via biconditional elimination. From the fact that if it snows, then it is cloudy, and that if it is cloudy, then Sarah is an artist we can infer that if it snows, then Sarah is an artist via transitivity. From the fact that if Charles plays a game, then it is snowing, and that if it snows, then Sarah is an artist we can infer that if Charles plays a game, then Sarah is an artist via transitivity. Finally, from the fact that if Charles plays a game, then Sarah is an artist, and that if Sarah were an artist, then Charles is playing a game we can infer that Charles is playing a game if and only if Sarah is an artist via biconditional introduction, which contradicts that If is not true that Charles is playing a game if and only if Sarah is an artist. Therefore, the answer is no.