Consider the following premises. For all x_12, x_12 is a lawyer if and only if x_12 will play a game. Sarah is not a taxi driver. If Patricia plays a game, then Sarah is a taxi driver. Patricia is running if and only if Patricia is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not running.
 From the fact that for all x_12, x_12 is a lawyer if and only if x_12 will play a game we can infer that Patricia is a lawyer if and only if Patricia is playing a game via universal instantiation. From the fact that if Patricia plays a game, then Sarah is a taxi driver, and that Sarah is not a taxi driver we can infer that Patricia is not playing a game via modus tollens. From the fact that Patricia is a lawyer if and only if Patricia is playing a game, and that Patricia is not playing a game we can infer that Patricia is not a lawyer via biconditional elimination. Finally, from the fact that Patricia is running if and only if Patricia is a lawyer, and that Patricia is not a lawyer we can infer that Patricia is not running via biconditional elimination. Therefore, the answer is yes.