I have the following problem, and I want to show that it is NP-hard (or NP-complete).
Consider a clause which can have OR and XOR relationship between literals, e.g. $c_1=y_1 \lor y_2 \lor (y_3\oplus y_4)$. Will the assignment of literals such that the equation given by the conjunction of such clauses, e.g. $c_1\wedge c_2 \wedge c_3 \ldots$ is satisfiable or not a problem in NPC or P?
I suspect that the CIRCUIT SAT can be reduced to it, but I am unable to reach there.