The anti-conjecture to unknotting additivity

Let $K$ and $K^\prime$ be knots, let $u(K)$ denote unknotting number, and call $K$ and $K^\prime$ symbionts when

$$u(K\#K^\prime)<u(K)+u(K^\prime).$$

Anti-conjecture to the Unknotting Additivity Conjecture. For every non-trivial knot $K$, there is a symbiont knot $K^\prime$ for which

$$u(K\#K^\prime)<u(K)+u(K^\prime).$$

That is, every non-trivial knot $K$ has a connected sum for which the Unknotting Additivity Conjecture is false. This proposal is motivated by examples of knots with symbionts and by the suggestion that, asymptotically, most knots may contain $3_1$ or $4_1$ in a minimal unknotting sequence. No resolution is supplied in the source.