The proof of this is apparently in Particle accelerators. The half-life of a proton at "rest" is some very small part of a second. When it is accelerated up to some significant fraction of the speed of light, it sticks around for much longer.
I think you might mean neutron. (But they have half-lives around 12 minutes. They are also tough to accelerate without a charge.) Protons appear to be quite stable. There are some theories that predict an unstable proton, but so far I know of no experiment that has demonstrated such an effect. If the proton is unstable, it must have a very, very long half-life.
Another test is the muon--a more massive, unstable cousin of the electron. Muons have a half-life so short, that from where they are created in the upper atmosphere most would decay (even if they traveled at the speed-of-light) before reaching the surface of the Earth. The fact that many are found at the Earth's surface demonstrates the clock slowing effect of relativity.
Mmm. The unspoken assumption behind this is that there is an objective reality, "time". I seriously wonder if space and time "really" exist at all, or are just our way of dealing with the world. Things do get very weird at the extremes, don't they?