---
license: cc-by-4.0
task_categories:
- reinforcement-learning
- text-generation
- tabular-classification
language:
- en
pretty_name: LeanWordBench
size_categories:
- 10K<n<100K
tags:
- benchmark
- formal-verification
- theorem-proving
- algebra
- reinforcement-learning
- word-problems
- lean
configs:
- config_name: default
  data_files:
  - split: train
    path: data/leanwordbench_instances.jsonl
---

# Dataset Card: LeanWordBench

## Summary

LeanWordBench is a benchmark suite for verifiable certificate search over
algebraic word problems. Instances are grouped into families such as free-group
word equality, subgroup membership, word equations, braid rewriting, exact
planning, Andrews--Curtis frontier search, knot move traces, Gröbner reduction,
and group-ring witness search.

## Intended Use

The benchmark is intended for evaluating systems that produce explicit
mathematical certificates: rewrite traces, witnesses, substitutions, action
sequences, collision candidates, or algebraic objects. Scores should be reported
only after exact replay by the family verifier.

## Not Intended For

- Treating frontier timeouts as mathematical negative labels.
- Ranking systems by natural-language explanations that do not include accepted
  certificates.
- Claiming that classical exact procedures solve frontier regimes merely because
  they audit released closed slices.

## Data Sources

Most rows are generated from standard mathematical presentations and exact
verifiers. External sources are referenced in `data/manifest.json` and include
SMT-LIB/StringFuzz style word-equation resources, AC-Solver/Miller--Schupp
Andrews--Curtis instances, SymbolicData-inspired Gröbner systems, Regina/knot
diagram resources, and Gardam/Soelberg group-ring artifacts where applicable.

## Responsible AI Notes

The benchmark contains symbolic mathematical data, not human-subject, personal,
biometric, medical, or demographic records. The main risk is scientific
overclaiming: unknown frontier rows must remain unknown unless an explicit
certificate or obstruction is found.