Labelled Splitting

We define a superposition calculus with explicit splitting and an explicit, new backtracking rule on the basis of labelled clauses. For the first time we show a superposition calculus with explicit backtracking rule sound and complete. The new backtracking rule advances backtracking with branch condensing known from Spass . An experimental evaluation of an implementation of the new rule shows that it improves considerably the previous Spass splitting implementation. Finally, we discuss the relationship between labelled first-order splitting and DPLL style splitting with intelligent backtracking and clause learning.