Which experiment proves existence of time (apart from some physical process), especially its slowdown and acceleration, like in famous theoretical example with

Which experiment proves existence of time (apart from some physical process), especially its slowdown and acceleration, like in famous theoretical example with accelerated clocks? As far as I remember, in the philosophy of science a single contradiction is enough to refute a hypothesis and is the reason to check one's premises.. Some himera made out of math and popular but unproven theories is a himera nevertheless.