Depth-first proof search without backtracking for free-variable clausal tableaux

We analyse the problem of constructing a deterministic proof procedure for free-variable clausal tableaux that performs depth-first proof search without backtracking; and we present a solution based on a fairness strategy. That strategy uses weight orderings and a notion of tableau subsumption to avoid proof cycles and it employs reconstruction steps to handle the destructiveness of free-variable calculi.