Linearity and regularity with negation normal form

Proving completeness of NC-resolution under a linear restriction has been elusive; it is proved here for formulas in negation normal form. The proof uses a generalization of the AndersonBledsoe excess literal argument, which was developed for resolution. That result is extended to NC-resolution with partial replacement. A simple proof of the completeness of regular, connected tableaux for formulas in conjunctive normal form is also presented. These techniques are then used to establish the completeness of regular, connected tableaux for formulas in negation normal form