The phrase "will prove impossible" is correct and usable in written English.
It can be used to indicate that something is expected to be unachievable or infeasible in the future.
Example: "Despite our best efforts, it seems that completing the project on time will prove impossible."
Alternatives: "will turn out to be impossible" or "is likely to be unfeasible."
A deficit deal will prove impossible.
While these disorders can be managed, some toxic leaders will prove impossible to change.
Both are now focusing on other things – aware, perhaps, that these eight episodes will prove impossible to top.
Her suggestion of how to solve the Page 3 conundrum - no spoilers here - is a little piece of common sense genius that will prove impossible to forget.
But when Franki (Marc Senter), one of Erica's former one-night stands, reappears bearing terrible news, a chain of events is unfurled that will prove impossible to break.
What is more, he thinks that the elaborate vacuum chambers and expensive equipment used by the Augsburg researchers will prove impossible to scale up into a commercial plant.
Politics is cruel, and if the impression develops that Boris is terminally accident prone it will soon prove impossible to eradicate.
And though it will certainly prove impossible to quash private traders completely, their distribution channels at present the only reasonably efficient way for many farmers to get their produce to market will suffer greatly.
Even if Harkin's bill can pass the Senate, the bills are so far apart that reconciling them in conference will likely prove impossible.
Similarly, it has been, and will continue to prove, impossible to convince the fossil fuel-reliant economies like Russia and the oil producing nations of the Middle East to sacrifice supposed national economic self-interest in favour of the future wellbeing of human and other species.
Filling all those spaces will prove nearly impossible.
