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_12, if x_12 writes a letter, then x_12 is taking a plane. For all x_12, if x_12 were excited, then x_12 is not a politician. There is at least one x_12 for which x_12 will write a letter. For all x_12, if x_12 takes a plane, then x_12 is a politician.
There is at least one x_12 for which x_12 will take a plane can be inferred via the existential modus ponens rule. For all x_12, if x_12 writes a letter, then x_12 is a politician can be inferred via the universal transitivity rule.