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: It is windy or it is cloudy. William is not a bartender. William is a bartender if and only if William is a scientist. If it is cloudy, then Barbara is writing a letter. If it is windy, then Barbara is writing a letter.
Barbara is writing a letter can be inferred via the disjunction elimination rule. If William were a bartender, then William is a scientist can be inferred via the biconditional elimination rule. If William were a scientist, then William is a bartender can be inferred via the biconditional elimination rule. William is not a scientist can be inferred via the biconditional elimination rule.