Comments

Efficiency Rule 1:    Don't branch until you have to.

Efficiency Rule 2:    Apply the rules generally in the order

                                1.    Non quantifiers

                                2.    QN

                                3.    EI

                                4.    UI

Decision Problem

Truth trees are not a solution to the decision problem for validity on 1st order logic.

If A is not logically valid then the tree constructed on ØA may have an open branch of infinite length. There is no procedure to tell us at some point that all barnches at some later point will be closed.