 Solution

A corrected STRIPS model can fix object roles in the action names, leaving only room parameters to instantiate. Use the same $a,w,g,r$ and introduce static $\mathrm{pitfree}(z)$ and $\mathrm{exit}(z)$ facts, plus a planning fluent $\mathrm{clear}(z)$ meaning “no live monster occupies $z$”. Unlike the supplied adjacency relation, let $\mathrm{adj}$ describe all geometrically adjacent rooms; safety is then explicit rather than hidden by missing edges.

Initially the agent, monster and gold have their specified locations, $\mathrm{have}(a,r)$, $\mathrm{alive}(w)$ and $\mathrm{active}$ hold, $\mathrm{exit}(s_{11})$ holds, $\mathrm{pitfree}$ holds at every room except $s_{12}$, and $\mathrm{clear}$ holds at every room except $s_{23}$. All unlisted facts are false by the closed-world assumption. The following positive preconditions, add lists and delete lists are a complete action specification:Require $\mathrm{exited}$ as the goal. If reaching the exit suffices, omit $\mathrm{Leave}$ and use the original two goal facts. Instantiating these schemata over the finite room set gives ordinary ground STRIPS actions.

Only $a$ moves, only $g$ is collectible and only $r$ can be fired at $w$. No action changes the monster’s location; its corpse can stay there, while $\mathrm{clear}$ records that it is harmless. The gold stays at its original room until collection. The arrow is consumed by its only use. By mathematical induction on plan length, every applicable action preserves the planning state invariant that the active agent occupies one pit-free room without a live monster. Consequently every solution is a safe execution. The plan in part a, followed by $\mathrm{Leave}(s_{11})$, is one such execution.