How are proofs formatted when the answer is a counterexample?
Solution 1:
I would say something along the lines of:
The proposed result is false. Here is a counterexample...
Solution 2:
In these cases on my homework when I type it up, I just change the statement of the theorem to match what is true. Given that problem on my homework I would write
$\textbf{Theorem:}$ It is not necessarily the case that the sum of two integers is odd.
$\textbf{Proof:}$ Observe that $1+1=2$. Since $1$ is an integer and $2$ is not odd, we have proved the result.$\blacksquare$