You say that nothing can travel at a speed greater than the speed of light, but there is evidence that tachyons travel faster than light.
Tachyons, if they were to exist, would by definition always travel faster than the speed of light. But there's no observational evidence that tachyons exist. The only reason why some people have proposed that such a particle might exist is because "faster-than-light" particles would satisfy all the relativity equations.
I may be using the word "satisfy" a bit loosely however. Tachyons would have to either have a mass or an energy which is an imaginary number. One could argue that this is a pretty nonphysical idea. They'd also have the bizarre property that if you give a tachyon more energy, it would slow down (but never move as "slow" as the speed of light).
Tachyons do serve one useful purpose though. They're frequently invoked in discussions of time travel in science fiction. :)
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