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: For all x_7, x_7 will listen to a song if and only if x_7 is a carpenter. Robert is a carpenter if and only if Susan is happy. Robert is not listening to a song.
If Robert were a carpenter, then Susan is happy can be inferred via the biconditional elimination rule. If Susan were happy, then Robert is a carpenter can be inferred via the biconditional elimination rule. For all x_7, if x_7 listens to a song, then x_7 is a carpenter can be inferred via the universal biconditional elimination rule. For all x_7, if x_7 were a carpenter, then x_7 is listening to a song can be inferred via the universal biconditional elimination rule.