Halperin's conjecture on totally non-cohomologous to zero fibrations

Let $F$ be an elliptic space with minimal model $\Lambda V$, and let $F\to X\to B$ be a fibration. The condition that $\dim V^{\mathrm{odd}}=\dim V^{\mathrm{even}}$ is imposed on the minimal model of $F$. Halperin's conjecture. Every such fibration is totally non-cohomologous to zero (TNCZ). This conjecture concerns the behavior of the cohomology of elliptic fibers in fibrations. Although affirmative cases of Halperin's conjecture have been studied, the conjecture remains open.