It can theoretically be proven, but not with current technology.
If you take a brute force approach, there is some difficulty due to the number of positions.
In analysis of the Shannon Number, it is suggested that the game tree complexity is at least 10^123 for games of max length 80 moves. Let's assume that it is 10^123 for the purposes of this discussion.
10 ^ 81 = Estimated number of atoms in the universe
10 ^ 12 = Operations per second of a terahertz processor core (your
processor probably runs at about 1/300th of this speed.)
10 ^ 7 = Rounded-off seconds per year
10 ^ 12 = 1 trillion years
Let's also assume that our processors can evaluate a chess position in only 1 processor cycle.
So, let's make every atom in the universe operate as a terahertz processor core for 1 trillion years.
Can we evaluate each position for 80-max length games?
10^81 x 10^12 x 10^7 x 10^12 = 10^112
We fall short to the tune of being only 0.0000000001% complete with the calculation.
With advanced pruning (throwing out bad lines and their descendants), better technology, and some crafty programming... maybe we'll see 40-max games solved in our lifetime! We can also prune out positions that we've seen before (we can arrive there via transposition), but keep in mind it will take at least a CPU cycle to determine that we've evaluated the position before!
However, this should help you see why it's so far out of reach at the moment.