What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: Barbara is running if and only if Patricia is sleeping. It is cold if and only if David is a scientist. Barbara is not running. David is not a scientist.
Barbara is not running and David is not a scientist can be inferred via the conjunction rule. David is not a scientist and Barbara is not running can be inferred via the conjunction rule. If Barbara goes running, then Patricia is sleeping can be inferred via the biconditional elimination rule. If it is cold, then David is a scientist can be inferred via the biconditional elimination rule. If Patricia sleeps, then Barbara is running can be inferred via the biconditional elimination rule. If David were a scientist, then it is cold can be inferred via the biconditional elimination rule. Patricia is not sleeping can be inferred via the biconditional elimination rule. It is not cold can be inferred via the biconditional elimination rule.