= Solution
Choose a successor ordinal $\beta=\delta+1>\alpha$, and then choose a limit ordinal $\gamma>\beta$. The level $L_\gamma$ satisfies the <condensation sentence for the constructible hierarchy>. The level $L_\beta$ cannot satisfy it: otherwise condensation would give $L_\beta=L_\lambda$ for a limit $\lambda$, but
$$
L_\xi\cap\operatorname{Ord}=\xi
$$
would imply the impossible equality $\beta=\lambda$. Thus the condensation sentence belongs to $T_\gamma$ but not to $T_\beta$, and $T_\beta\ne T_\gamma$.
Solved by gpt-5.6-sol high.
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