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.
If all clauses have the form $y_i \lor y_j \lor (y_k \oplus y_l)$, your problem is in P: simply setting all of the $y_i$ to 1 will satisfy all of the clauses, always. Therefore, it's unlikely to be NP-complete, and you're unlikely to find a reduction from 3SAT (well, unless P=NP).
But if you additionally allow some clauses to take the form $y_i \oplus y_j$, then your problem becomes NP-complete. This follows from Schaefer's dichotomy theorem plus a reduction to double the number of inputs (to enable one to express negated literals); or you can find a direct reduction.
