Answer
$\bigwedge_{i=1}^{16} \wedge_{n=1}^{16} \vee_{j=1}^{16} p(i, j, n)$
$\bigwedge_{i=1}^{16} \wedge_{n=1}^{16} \vee_{j=1}^{16} p(i, j, n)$
$\bigwedge_{r=0}^{4} \wedge_{s=0}^{4} \wedge_{n=1}^{16} \mathrm{V}_{i=1}^{4} \mathrm{V}_{j=1}^{4} p(4 r+i, 4 s+j, n)$
$p(i, j, n) \rightarrow \neg p\left(i, j, n^{\prime}\right)$
Work Step by Step
Given:
$16$ x $16$ Sudoku puzzle (which contains every integer from $1$ to $16$ in each row, column, and $4$ x block).
Let $p (i, j, n)$ represent the cell in row $i$ and column $j$ and that has the value $n$ ($n$ is thus an integer between $1$ and $16$, inclusive).
Every row needs to contain every number between $1$ and $16$.There are $16$ rows and $16$ columns.
$\bigwedge_{i=1}^{16} \wedge_{n=1}^{16} \vee_{j=1}^{16} p(i, j, n)$
Every column needs to contain every number between $1$ and $16$.There are $16$ rows and $16$ columns.
$\bigwedge_{i=1}^{16} \wedge_{n=1}^{16} \vee_{j=1}^{16} p(i, j, n)$
Every $4 x 4$ block contains every number between $1 $and$ 4$.
$\bigwedge_{r=0}^{4} \wedge_{s=0}^{4} \wedge_{n=1}^{16} \mathrm{V}_{i=1}^{4} \mathrm{V}_{j=1}^{4} p(4 r+i, 4 s+j, n)$
Finally, no cells contain more than one number:
$p(i, j, n) \rightarrow \neg p\left(i, j, n^{\prime}\right)$
