# Assume $P \neq NP$ Proof that $L$ = {$a | a \in SAT$ and every clause consists of $log_2(|a|)$ literals} in P [closed]

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 $$a \in SAT$$.