Nonbirationality conjecture for Type i KSS pairs

Let $(A_i,B_i)$, for $i=1,\ldots,12$, be one of the twelve Type $i$ KSS pairs of smooth elliptic Calabi--Yau $3$-folds over $\mathbb{P}^2$. The pair is called nonbirational when no birational map exists between $A_i$ and $B_i$. Nonbirationality conjecture. Each Type $i$ KSS pair $(A_i,B_i)$ is nonbirational. The abstract states that, except for one self-dual pair, the pairs are nonbirational derived-equivalent; because the statement includes the self-dual pair, the conjecture as written is refuted by the isomorphic Type $11$ pair.