Datasets:
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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.
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