# Counterexample in Sistla and Clarke's paper

I'm reading Sistla and Clarke's paper "The Complexity of Propositional Linear Temporal Logics". In section 4 they start with the following set up:

Let $$S=(s, \xi), T=(t, \pi)$$ be structures such that, for some $$m \geq 0$$, the following conditions are satisfied: $$\forall i, 0 \leq i \leq m, t_{i}=s_{i} ; \quad \forall i, i>m+1, t_{i}=s_{i-1} \text {, }$$ and $$\pi$$ is an extension of $$\xi$$, that is $$\pi(t_r) = \begin{cases} \xi(s_r) & 0 \le r \le m \\ \xi(s_{r-1}) & m < r \end{cases}$$ such that $$\pi\left(t_{m+1}\right)=\pi\left(t_{m}\right)$$ that is, $$T$$ is obtained by duplicating the $$m$$-th state in $$S$$ successively once. The following lemma is easily proved by induction on the formula $$f$$.

Lemma:

For any $$f \in L(\mathbf{U})$$,

$$T, t_{m} \vDash f$$ iff $$T, t_{m+1} \vDash f$$ and for any $$\delta$$ in $$s$$, $$S, \delta \vDash f$$ iff $$T, \delta \vDash f$$.

Note that I added what they mean by extension myself.

After the lemma, which I proved, they say:

Note that the lemma is not true for $$\mathbf{L}(\mathbf{U}, \mathbf{X})$$.

I've been playing around with formulas in $$\mathbf{L}(\mathbf{U}, \mathbf{X})$$, however, I could not find the counterexample. Is this counterexample standard?