= Solution
A safe one-rule <Datalog with negation> example with no <stable model> is
$$
\boxed{\operatorname{not}P(a)\to P(a).}
$$
There are no variables, so no safety condition is violated. If $P(a)$ is absent from a proposed <stable model>, its reduct contains the fact $P(a)$, whose <least Herbrand model> contains $P(a)$. If $P(a)$ is present, the rule is deleted, and the reduct has empty <least Herbrand model>. Either choice disagrees with its reduct's <least Herbrand model>. Additional unsupported atoms cannot repair the disagreement. Hence there is no <stable model>.
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