16 research outputs found
Extending SMTCoq, a Certified Checker for SMT (Extended Abstract)
This extended abstract reports on current progress of SMTCoq, a communication
tool between the Coq proof assistant and external SAT and SMT solvers. Based on
a checker for generic first-order certificates implemented and proved correct
in Coq, SMTCoq offers facilities both to check external SAT and SMT answers and
to improve Coq's automation using such solvers, in a safe way. Currently
supporting the SAT solver zChaff, and the SMT solver veriT for the combination
of the theories of congruence closure and linear integer arithmetic, SMTCoq is
meant to be extendable with a reasonable amount of effort: we present work in
progress to support the SMT solver CVC4 and the theory of bit vectors.Comment: In Proceedings HaTT 2016, arXiv:1606.0542
REFACTOR: Learning to Extract Theorems from Proofs
Human mathematicians are often good at recognizing modular and reusable
theorems that make complex mathematical results within reach. In this paper, we
propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for
training neural networks to mimic this ability in formal mathematical theorem
proving. We show on a set of unseen proofs, REFACTOR is able to extract 19.6%
of the theorems that humans would use to write the proofs. When applying the
model to the existing Metamath library, REFACTOR extracted 16 new theorems.
With newly extracted theorems, we show that the existing proofs in the MetaMath
database can be refactored. The new theorems are used very frequently after
refactoring, with an average usage of 733.5 times, and help shorten the proof
lengths. Lastly, we demonstrate that the prover trained on the new-theorem
refactored dataset proves more test theorems and outperforms state-of-the-art
baselines by frequently leveraging a diverse set of newly extracted theorems.
Code can be found at https://github.com/jinpz/refactor.Comment: ICLR 202
Even shorter proofs without new variables
Proof formats for SAT solvers have diversified over the last decade, enabling
new features such as extended resolution-like capabilities, very general
extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning.
Interference-based methods have been proven effective, and some theoretical
work has been undertaken to better explain their limits and semantics. In this
work, we combine the subsumption redundancy notion from (Buss, Thapen 2019) and
the overwrite logic framework from (Rebola-Pardo, Suda 2018). Natural
generalizations then become apparent, enabling even shorter proofs of the
pigeonhole principle (compared to those from (Heule, Kiesl, Biere 2017)) and
smaller unsatisfiable core generation.Comment: 21 page