No, your answer is not correct, and for some reason you have four CNFs (I didn't understand why).
I'll give you some hints, how to reduce the Four Queens Problem to a CNF. I'll use notation, which is common for boolean variables and expressions. A boolean variable $x_{i,j}$, where $i,j \in [1,4]$, will be used to represent a queen in the cell $(i,j)$.
- You need to express the first requirement, that each row and each column contains at least one queen, as a boolean expression. This can be done with the aid of the logical OR operation ($\lor$). You need to logically OR all the $x_{i,j}$ variables separately for each row and each column. For example, this requirement for the first row can be expressed as:
$$x_{1,1} \lor x_{1,2} \lor x_{1,3} \lor x_{1,4}$$
- Also you need to express the second requirement, that all the queens don't pairwise attack each other. So, for each pair $((i,j),(k,l))$ of cells, such that a queen at the cell $(i,j)$ can attack the cell $(k,l)$, their corresponding variables $x_{i,j}$ and $x_{k,l}$ can't be both equal to $true$. The boolean expression $(\lnot x_{i,j} \lor \lnot x_{k,l})$ guarantees just that. For example, cells $(1,1)$ and $(3,3)$ are on the main diagonal, so the boolean expression below guarantees, that two queens can't be placed simultaneously at these two cells.
$$\lnot x_{1,1} \lor \lnot x_{3,3}$$
You can use these two types of clauses to create a CNF, which describes this problem as a CNF satisfiability problem - however, this CNF will be long (84 clauses). That's why (I think) you were asked to write a shorter CNF, which includes only clauses, where the variable $x_{1,1}$ is present.
