Reasoning Models Re-derive What They Are Told Is Valid

When a reasoner has already derived the consequences of a knowledge base and one premise changes, an exact incremental procedure revisits only the part of the derivation that the change can reach. We test whether reasoning models do this when the reuse is handed to them. In synthetic Horn-rule worlds, three open-weight reasoning models (Gemma 4 31B, Muse Glimmer 30B, Qwen3.8-27B) receive the current world, a one-element edit, an exact record of the previously derived closure and, in the key condition, the list of properties whose status the edit can change; they must output the complete revised closure. A preregistered decision table, 5,236 model calls and a blinded, independently double-annotated validation of a measure of which rules a visible reasoning trace evaluates decide what can be claimed. The re-derivation claim holds in all three models, for Muse at the boundary of one criterion, which a post hoc full-trace audit leaves unchanged. In single-component worlds, where only 40.1% of the rules conclude a property whose status can change and an exact incremental update needs 7.8% of the from-scratch operations, the models' visible reasoning re-evaluates 67–99% of the remaining rules, and they spend 0.90–1.23 times the thinking tokens of solving from scratch. A post hoc decomposition shows near-exhaustive visible coverage in two of the models: they re-evaluate even non-firing rules whose conclusions already hold through other rules about as often as when solving from scratch, a profile compatible with re-solving or with extensive verification, neither of which the task requires outside the cone. In secondary conditions these two keep re-deriving when told the exact change or instructed to work locally. In worlds eight times larger this re-evaluation falls by 0.52–0.67, and telling the models which properties can change raises exact whole-state accuracy over the record alone by 44 and 25 points in two of them. Three preregistered claims are not supported: selective maintenance at small size; localization with size, met by one model; and steering of targeted answers by the record's values, where accuracy is near ceiling and the difference-in-differences estimates lie between -0.03 and 0.00.