Because each of these accelerators, accelerates literally trillions of particles per second to speeds approaching that of light. The interactions that occur are carefully measured to determine the particle types, charges, spins, momenta and so on. Any interactions that lead to byproducts whose properties do not make sense based on relativity, or on the expected particle types automatically trigger the electronics to 'store' the information so that physicists can carefully replay literally one interaction out of trillions each year. If any gross errors in special relativity were present, it would have been detected, especially at the electron accelerators where electrons are boosted to speeds approaching 99.999 percent the speed of light.