CD Tools -- Condensed Detachment and Structure Generating Theorem Proving (System Description)

Abstract

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.

Learning from Łukasiewicz and Meredith: Investigations into Proof Structures

“…This work extends the results presented at CADE 2021 [72]. The concepts and techniques described here are backed by an implemented system, CD Tools [70,71], a library for experimenting with CD and related techniques, which is written in SWI Prolog [74] and available as free software. CD Tools includes two provers, SGCD (the name suggesting Structure-Generating proving for Condensed Detachment) for CD problems, and CCS (the name suggesting Compressed Combinatory Structures) for CD problems and first-order Horn problems.…”

“…19 As a further source of "names" we took Thesis 1-68 from a textbook by Łukasiewicz [35]. These were often used for experiments in ATP [76,41,77,78,70]. If the MGT of a subproof is a named formula in this sense, this is indicated as property NN, whose value points to the respective row of Table 3.…”

“…These values may be hard to determine such that they often can only be narrowed down to an integer interval. Values of these properties were found with the provers CCS [71] and SGCD [70] in configurations that exhaustively search for proofs with a given compacted size or tree size, respectively.…”

“…In the paper we will discuss particular features of these provers and report experimental results obtained with them. For more details on SGCD and CCS we refer to [70] and [71], respectively. 1 The contributions of the paper can be summarized as follows.…”

“…7. Providing the basis for an implemented system to experiment with CD problems and their proof structures [70,71]. It includes two provers, each addressing a specific main aspect.…”