TLA$^{+}$-Bench: An Execution-Grounded Benchmark and Dataset for Natural-Language to TLA+ Specification Generation

Large language models increasingly write TLA^{+} formal specifications from natural-language descriptions, but progress is hard to measure: existing resources grade by resemblance to a reference or by whether the output parses, neither of which shows correctness. We present TLA^{+}-Bench, a dataset and benchmark that grades by execution. Every gold specification ships a configuration the TLA^{+} model checker runs over the full reachable state space, deciding exactly whether the specification holds the properties that configuration names. The dataset holds 403 model-checked gold and 897 parse-only silver specifications from 13 public repositories, subsumes prior TLA^{+} generation data, and carries four model-written descriptions in two styles from two providers, with difficulty and category labels. Our main finding is about measurement itself: an exact oracle gives not one correctness number but a range. Varying only the grading choices earlier benchmarks leave unstated, on one fixed set of model outputs, the correct rate moves sixfold, from 10.0% to 1.7%; adding the interface-supply choice, where the model is told the configuration's names, widens the range to elevenfold, from 18.7% to 1.7%. We call this range the correctness envelope and measure each of its bounds. The findings inside it are stable. Every model writes valid TLA^{+} far more often than correct TLA^{+}: the strongest is correct 16% of the time by default and 26% when given the interface names, open models at most 1%, and correctness falls sharply with difficulty.