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: If Sarah were a carpenter, then it is raining. Patricia is a cashier. For all x_28, if x_28 were a cashier, then x_28 is bored. Elisabeth is a politician if and only if it is raining. Elisabeth is not a politician.
Patricia is a cashier and Elisabeth is not a politician can be inferred via the conjunction rule. Elisabeth is not a politician and Patricia is a cashier can be inferred via the conjunction rule. If Elisabeth were a politician, then it is raining can be inferred via the biconditional elimination rule. If it rains, then Elisabeth is a politician can be inferred via the biconditional elimination rule. It is not raining can be inferred via the biconditional elimination rule. There is at least one x for which x is a cashier can be inferred via the existential generalization rule.