Consider the following premises. Elisabeth is a scientist or Jennifer is playing squash. For all x_7, x_7 will go running if and only if x_7 is a scientist. If Jennifer plays squash, then Elisabeth is running. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not running.
 From the fact that for all x_7, x_7 will go running if and only if x_7 is a scientist we can infer that Elisabeth is running if and only if Elisabeth is a scientist via universal instantiation. From the fact that Elisabeth is running if and only if Elisabeth is a scientist we can infer that if Elisabeth were a scientist, then Elisabeth is running via biconditional elimination. Finally, from the fact that if Elisabeth were a scientist, then Elisabeth is running, that if Jennifer plays squash, then Elisabeth is running, and that Elisabeth is a scientist or Jennifer is playing squash we can infer that Elisabeth is running via disjunction elimination, which contradicts that Elisabeth is not running. Therefore, the answer is no.