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 overcast if and only if Thomas is listening to a song. Thomas is not listening to a song. For all z, z will climb a mountain and z is a janitor.
If it is overcast, then Thomas is listening to a song can be inferred via the biconditional elimination rule. If Thomas listens to a song, then it is overcast can be inferred via the biconditional elimination rule. It is not overcast can be inferred via the biconditional elimination rule. For all z, z will climb a mountain can be inferred via the universal simplification rule. For all z, z is a janitor can be inferred via the universal simplification rule.