  Let $V$ be a cubic surface defined by the equation $T_0^3+T_1^3+T_2^3+\theta
T_3^3=0$ over a quadratic extension of 3-adic numbers $k=\mathbb{Q}_3(\theta)$,
where $\theta^3=1$. We show that a relation on a set of geometric k-points on
$V$ modulo $(1-\theta)^3$ (in a ring of integers of $k$) defines an admissible
relation and a commutative Moufang loop associated with classes of this
admissible equivalence is non-associative. This answers a problem that was
formulated by Yu. I. Manin more than 50 years ago about existence of a cubic
surface with a non-associative Moufang loop of point classes.
