DRAT-trim: Efficient Checking and Trimming Using Expressive Clausal Proofs

Inspired by the success of the DRAT proof format for certification of boolean satisfiability (SAT), we argue that a similar goal of having unified automatically checkable proofs should be sought by the developers of automatic first-order theorem provers (ATPs). This would not only help to further increase assurance about the correctness of prover results, but would also be indispensable for tools which rely on ATPs, such as "hammers" employed within interactive theorem provers. The current situation, represented by the TSTP format, is unsatisfactory, because this format does not have a standardised semantics and thus cannot be checked automatically. Providing such semantics, however, is a challenging endeavour. One would ideally like to have a proof format which covers only-satisfiability-preserving operations such as Skolemisation and is versatile enough to encompass various proving methods (i.e. not just superposition) or is perhaps even open-ended towards yet to be conceived methods or at least easily extendable in principle. Going beyond pure first-order logic to theory reasoning in the style of SMT, or beyond proofs to certification of satisfiability are further interesting challenges. Although several projects have already provided partial solutions in this direction, we would like to use the opportunity of ARCADE to further promote the idea and gather critical mass needed for its satisfactory realisation. The challengeWe would like to propose to the first-order ATP community the challenge of designing, implementing and bringing into practice a unified mechanically checkable proof format along with an efficient proof checker. The format should support the whole reasoning pipeline including formula preprocessing, be sufficiently general to cover all the solving techniques currently employed by ATPs, and be open to future extensions for proof recording of techniques yet to be developed. In this paper, we summarise the current situation regarding proof output of ATPs, explain why we think striving for a mechanically checkable proof format is a worthy effort, list the main properties we believe an ideal format should satisfy, attempt to give an overview of work already done in the first-order ATP community and related areas, and, finally, suggest possible avenues and the next steps to be taken for meeting the challenge.At this point we add the disclaimer that other people have already examined this challenge in various ways. We attempt to present this previous work and do not claim that what we are suggesting is novel, but instead we are calling for further work in this area. Our main aim at ARCADE is to solicit opinions from experts on why the proposed idea has not yet made its way to practice and on how exactly should the community proceed to achieve the envisioned goal.

Section: Some Previous Work and Related Approachesmentioning

confidence: 99%

Checkable Proofs for First-Order Theorem Proving

Reger¹,

Suda²

“…In particular, RAT subsumes extended resolution [43,46], which allows to infer fresh variables. Heule et al developed the drat-trim [19,48] tool based on backward checking [18], which efficiently checks unsatisfiability proofs, as well as the mechanically verified checker written in the ACL2 theorem prover [49].…”

Section: A New Proof Format For Parallel Sat Portfoliosmentioning

confidence: 99%

Unsatisfiability Proofs for Parallel SAT Solver Portfolios with Clause Sharing and Inprocessing

Philipp¹

State-of-the-art SAT solvers are highly tuned systematic-search procedures augmented with formula simplification techniques. They emit unsatisfiability proofs in the DRAT format to guarantee correctness of their answers. However, the DRAT format is inadequate to model some parallel SAT solvers such as the award-winning system Plingeling. In Plingeling, each solver in the portfolio applies clause addition and elimination techniques. Clause sharing is restricted to clauses that do not contain melted literals. In this paper, we develop a transition system that models the computation of such parallel portfolio solvers. The transition system allows us to formally reason about portfolio solvers, and we show that the formalism is sound and complete. Based on the formalism, we derive a new proof format, called parallel DRAT, which can be used to certify UNSAT answers.

“…Due to concerns on reliability of SAT solvers because of possible undiscovered bugs [7,34,37], different proof formats for expressing unsatisfiability together with proof emitting solvers were developed to ensure the correctness of unsatisfiability results [15,14,5,51,35,13,25]. Efficiently generating and checking proofs required carefully designed proof systems and checkers [19].…”

Section: Introductionmentioning

confidence: 99%

Towards a Semantics of Unsatisfiability Proofs with Inprocessing

Philipp

Rebola-Pardo

Delete Resolution Asymmetric Tautology (DRAT) proofs have become a de facto standard to certify unsatisfiability results from SAT solvers with inprocessing. However, DRAT shows behaviors notably different from other proof systems: DRAT inferences are nonmonotonic, and clauses that are not consequences of the premises can be derived. In this paper, we clarify some discrepancies on the notions of reverse unit propagation (RUP) clauses and asymmetric tautologies (AT), and furthermore develop the concept of resolution consequences. This allows us to present an intuitive explanation of RAT in terms of permissive definitions. We prove that a formula derived using RATs can be stratified into clause sets depending on which definitions they require, which give a strong invariant along RAT proofs. We furthermore study its interaction with clause deletion, characterizing DRAT derivability as satisfiability-preservation.