Consider the following premises. If David were a carpenter, then Elisabeth is an artist. Elisabeth is not an artist. For all x_7, x_7 is a carpenter if and only if x_7 will go running. Can we infer the following from them? If we can, name the inference rule being used: David is running.
 From the fact that for all x_7, x_7 is a carpenter if and only if x_7 will go running we can infer that David is a carpenter if and only if David is running via universal instantiation. From the fact that if David were a carpenter, then Elisabeth is an artist, and that Elisabeth is not an artist we can infer that David is not a carpenter via modus tollens. Finally, from the fact that David is a carpenter if and only if David is running, and that David is not a carpenter we can infer that David is not running via biconditional elimination, which contradicts that David is running. Therefore, the answer is no.