Answer
If a computer program is of reasonable correctness, then the program has an absence of error messages during translation. But there exists a program that has an absence of error messages during translation and that program does not have reasonable correctness.
Work Step by Step
Recall the definition of sufficient:
"$\forall x$, r(x) is a sufficient condition for s(x)" means "$\forall x$, if r(x) then s(x)."
Recall the definition of necessary:
"$\forall x$, r(x) is a necessary condition for s(x)" means "$\forall x$, if ~r(x) then ~s(x)" or equivalently "$\forall x$, if s(x) then r(x)."
In this case r(x) is: a computer program has an absence of error messages during translation.
s(x) is: the program is of reasonable correctness.
So the rewriting of the necessary statement without the use of necessary is: if s(x) then r(x), which is, "if a computer program is of reasonable correctness, then the program has an absence of error messages during translation."
Recall the form of the negation of a universal conditional statement:
$~(\forall x, P(x) \rightarrow Q(x)) \equiv \exists x$ such that $(P(x) \land $ ~$Q(x))$
So the negation of the sufficient statement is r(x) and ~s(x) which is, "there exists a program that has an absence of error messages during translation and that program does not have reasonable correctness."
