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_15, if x_15 were sad, then x_15 is cooking. For all x_15, x_15 is a politician or x_15 is not a poet. For all x_15, if x_15 were sad, then x_15 is a politician. There is at least one x_15 for which if x_15 were a politician, then x_15 is sad.
There is at least one x_15 for which if x_15 were a politician, then x_15 is cooking can be inferred via the existential transitivity rule. For all x_15, if x_15 were a poet, then x_15 is a politician can be inferred via the universal rewriting rule. There is at least one x_15 for which x_15 is a politician if and only if x_15 is sad can be inferred via the existential biconditional introduction rule. There is at least one x_15 for which x_15 is sad if and only if x_15 is a politician can be inferred via the existential biconditional introduction rule.