We study the ion acoustic solitary waves in the four component plasma consisting of clod inertial ions, hot positrons, cold electrons and hot electrons, where the two-temperature electrons follow the Carins-Tsallis distribution. Base on the hydrodynamic equations of the plasma and the Sagdeev pseudo-potential theory, we derive the condition for the solitary waves to exist and the related quantities such as the Sagdeev pseudo-potential, the normalized electrostatic potential, the allowable lower and upper limits of Mach number, and the condition for the solitary waves to be compressive or rarefactive. Properties of the quantities are numerically analyzed for the nonextensive parameters q and nonthermal parameter alpha in the Carins-Tsallis distribution. We show that the parameters q and alpha have significant effects on the above quantities and so the properties of solitary waves in the plasma are generally different from those in the same plasma with a Maxwellian distribution.