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 Elisabeth is making tea. If Susan writes a letter, then Patricia is taking a plane. It is not overcast. If Patricia takes a plane, then Elisabeth is making tea. Susan is writing a letter if and only if Patricia is a soldier.
If Susan writes a letter, then Elisabeth is making tea can be inferred via the transitivity rule. If it is overcast, then Elisabeth is making tea can be inferred via the biconditional elimination rule. If Susan writes a letter, then Patricia is a soldier can be inferred via the biconditional elimination rule. If Elisabeth makes tea, then it is overcast can be inferred via the biconditional elimination rule. If Patricia were a soldier, then Susan is writing a letter can be inferred via the biconditional elimination rule. Elisabeth is not making tea can be inferred via the biconditional elimination rule.