For a problem A $,$ we denote by $\backslash (($I$,$ S$)\backslash )$ a pair such that $\backslash ($ I $\backslash )$ is an input of $\backslash ($ A $\backslash ),$ and $\backslash ($ S $\backslash )$ is a candidate solution for the corresponding input $\backslash ($ I $\backslash ).$ You are told there exists a polynomial time algorithm that takes a pair $\backslash (($I$,$ S$)\backslash )$ and returns True if $\backslash ($ S $\backslash )$ is a solution of problem $\backslash ($ A $\backslash )$ for input $\backslash ($ I $\backslash ),$ and returns False otherwise.

Which of the following must be true?

Problem A is NP$-$hard.

Problem A can be reduced to the Clique problem in polynomial time.

There is a polynomial time solution that solves problem $\backslash ($ A $\backslash ).$

If there is a reduction from problem $\backslash ($ A $\backslash )$ to $\backslash ($ S A T $\backslash ),$ then $\backslash ($ P$=$N P $\backslash ).$