VFR: A Verified Filter for Sliding-Window 3-CNF — Research Artifact for the paper "Formal Verification of Romanov's Triplet Logic: A Verified Filter for Sliding-window 3-CNF with Application to Structured Formulas"

This archive contains the complete research artifact for the paper

"Formal Verification of Romanov's Triplet Logic: A Verified Filter for

Sliding-Window 3-CNF with Application to Structured Formulas" (2026).

CONTENTS

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- theories/ — Coq/Rocq formalization (17 .v files, 427 lemmas and theorems, 0 admits)

  * Theorem 1 (weak & compat), Theorem 2 (systemic aligned)

  * Algorithm.v — verified path-building and effective procedure

  * FormulaTranslation.v — CNF ↔ CTF soundness

  * Complexity.v — polynomial cost model (O(n⁴) generic, O(n²) single-forbidden)

  * Structured.v — verified grouped sliding CNF solver

  * Counterexample.v — formalized incompleteness proofs

- OCaml extraction — vfr_solver (JSON bridge to verified code)

- Swansea RUP checker — Coq/Rocq-extracted UNSAT proof verifier

- Python reference implementation — solver, CTF/CTS, hyperstructures, tests

- Docker — fully reproducible multi-stage build

- 175 pytest tests + 3 empirical verification scripts

- TLA+ specifications (17 modules)

VERIFIED COMPONENTS

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- Sliding-window CNF → OCaml vfr_solver (extracted)

- Grouped sliding CNF → OCaml solve_grouped_sliding (extracted)

- Overlapping single-group CNF → OCaml solve_overlapping_single_group (extracted)

- UNSAT proofs → Swansea RUP checker (Coq-extracted)

REPRODUCIBILITY

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See DEPLOY.md for artifact evaluation instructions:

  docker build -t vfr . && docker run --rm vfr

THIRD-PARTY COMPONENTS

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The Docker image includes third-party tools and libraries (Z3, Rocq/Coq, OCaml,

Python packages, Ubuntu system packages, and the Swansea RUP checker). Their

licenses are summarized in THIRD_PARTY_LICENSES.md. The VFR project itself is

released under the MIT License.