CD Tools -- Condensed Detachment and Structure Generating Theorem Proving (System Description)
This work addresses automated theorem proving for researchers in logic and AI, offering incremental improvements in proof search flexibility and efficiency.
The authors tackled the problem of automated theorem proving by developing CD Tools, a Prolog library for condensed detachment that includes the SGCD prover, which blends goal- and axiom-driven search to achieve performance close to state-of-the-art provers and produced a new, much shorter proof for a historic problem.
CD Tools is a Prolog library for experimenting with condensed detachment in first-order ATP, which puts a recent formal view centered around proof structures into practice. From the viewpoint of first-order ATP, condensed detachment offers a setting that is relatively simple but with essential features and serious applications, making it attractive as a basis for developing and evaluating novel techniques. CD Tools includes specialized provers based on the enumeration of proof structures. We focus here on one of these, SGCD, which permits to blend goal- and axiom-driven proof search in particularly flexible ways. In purely goal-driven configurations it acts similarly to a prover of the clausal tableaux or connection method family. In blended configurations its performance is much stronger, close to state-of-the-art provers, while emitting relatively short proofs. Experiments show characteristics and application possibilities of the structure generating approach realized by that prover. For a historic problem often studied in ATP it produced a new proof that is much shorter than any known one.