We define a class of special function inequalities that contains many classical examples, such as the Cauchy-Schwarz inequality, and introduce a proving procedure based on Cylindrical Algebraic Decomposition. We present an array of non-trivial examples that can be done by our method and have not been proven automatically before. Some difficult well-known inequalities such as the Askey-Gasper inequaltiy and Vietoris's inequality lie in our class as well, but we do not know if our proving procedure terminates on them. |