TAOCP 7.2.2.2 Exercise 157
Take the formula F=\{ab,\ \bar a\bar b\}.
Section 7.2.2.2: Satisfiability
Exercise 157. [10] [10] Give an example of an autarky that is not a pure literal.
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Take the formula
$$ F={ab,\ \bar a\bar b}. $$
The set of literals $L={a,\bar b}$ is an autarky, because the clause $ab$ contains $a$, which is true under $L$, and the clause $\bar a\bar b$ contains $\bar b$, which is true under $L$. Hence every clause touched by $L$ is satisfied by the literals in $L$.
Neither $a$ nor $\bar b$ is a pure literal, since $a$ occurs in both $ab$ and $\bar a\bar b$, and $b$ occurs in both polarities as well. Therefore $L$ is an autarky that is not a pure literal. $\boxed{L={a,\bar b}}$