I really stuck on the following question (Assuming $ P\neq NP$ ):

$ $ L = \{a \mid a \in SAT \text{ and every clause consists of } \log_2|a| \text{ literals}\}$ $

I don’t understand how could $ L$ be in $ P$ while we know that the $ SAT \not\in P$ , how can one verify if $ a$ is satisfiable without using the Turing machine that verifies that $ a \in SAT$ .