Consider the following premises. It is sunny if and only if James is a poet. For all y_4, if y_4 were a poet, then y_4 is not running. For all y_4, y_4 will go running. Can we infer the following from them? If we can, name the inference rule being used: It is sunny.
 From the fact that for all y_4, if y_4 were a poet, then y_4 is not running, and that for all y_4, y_4 will go running we can infer that for all y_4, y_4 is not a poet via universal modus tollens. From the fact that for all y_4, y_4 is not a poet we can infer that James is not a poet via universal instantiation. From the fact that it is sunny if and only if James is a poet we can infer that if it is sunny, then James is a poet via biconditional elimination. Finally, from the fact that if it is sunny, then James is a poet, and that James is not a poet we can infer that it is not sunny via modus tollens, which contradicts that It is sunny. Therefore, the answer is no.