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 it rains, then Richard is a writer. If Karen were an astronaut, then Richard is not a writer. For all x_32, if x_32 were an office clerk, then x_32 is a writer. Sarah is sad if and only if it is cloudy. Sarah is not sad. Richard is an office clerk or it is raining.
If Sarah were sad, then it is cloudy can be inferred via the biconditional elimination rule. If it is cloudy, then Sarah is sad can be inferred via the biconditional elimination rule. It is not cloudy can be inferred via the biconditional elimination rule.