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: Joseph is making tea or Barbara is running. It is overcast if and only if William is writing a letter. Joseph is not making tea. It is not overcast.
Barbara is running can be inferred via the disjunctive syllogism rule. Joseph is not making tea and it is not overcast can be inferred via the conjunction rule. It is not overcast and Joseph is not making tea can be inferred via the conjunction rule. If it is overcast, then William is writing a letter can be inferred via the biconditional elimination rule. If William writes a letter, then it is overcast can be inferred via the biconditional elimination rule. William is not writing a letter can be inferred via the biconditional elimination rule.