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: Sarah is an office clerk if and only if it is overcast. It is not overcast. If Sarah were not an office clerk, then Thomas is happy. Joseph is a cashier.
It is not overcast and Joseph is a cashier can be inferred via the conjunction rule. Joseph is a cashier and it is not overcast can be inferred via the conjunction rule. If Sarah were an office clerk, then it is overcast can be inferred via the biconditional elimination rule. If it is overcast, then Sarah is an office clerk can be inferred via the biconditional elimination rule. Sarah is not an office clerk can be inferred via the biconditional elimination rule.