= Solution
The complete numbered axioms in the rule fragment <RL description logic> are $\boxed{(1),(3),(4)}$. Their translations to <Datalog> with constraints are
$$
\boxed{\begin{aligned}
R(x,y)&\to C(y),\\
R(x,y)\land R(y,z)\land A(z)\land R(x,w)&\to A(w),\\
R(x,y)\land R(y,z)\land B(z)\land R(x,w)&\to A(w),\\
A(x)\land B(x)&\to\bot.
\end{aligned}}
$$
The first rule is (1). For (3), its existential antecedent needs a two-edge $R$ path ending at an $A$ or $B$ element. Split that disjunction into two <Datalog> rules, and use a separate variable $w$ for an arbitrary immediate $R$-successor of $x$. The conclusion applies to every such successor, not merely the path witness $y$.
The last rule is a constraint: a ground instance with both premises true makes the <knowledge base> inconsistent. If an implementation permits only positive <Datalog> heads, replace $\bot$ by a fresh nullary predicate $\mathit{Bad}$ and separately check that it is never derived. Merely deriving $\mathit{Bad}$ without that check would not express disjointness.
Axiom (2) requires an existential witness in its head and is outside <RL description logic>. Axiom (5), considered as the whole equivalence, is outside for the same reason in the direction $C\sqsubseteq\exists P.\top$. If definitions are split before selecting eligible <general concept inclusions>, its reverse direction is eligible and adds $\boxed{P(x,y)\to C(x)}$. Keep the difference between selecting the complete equivalence and retaining its rule-expressible half explicit. The permitted positions of existential and universal restrictions are specified in the <OWL 2 Web Ontology Language Profiles (Second Edition)>[Section 4.2.3: subclass and superclass expressions; Section 4.2.5: class axioms]{ref}.
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