How did the inequality of matter and antimatter become known?

About dull belief in the symmetry of interactions

Almost immediately after the discovery of the left-right (mirror) symmetry breaking in the weak interactions, it has been also experimentally proven the violation of the charge symmetry, i.e., non-invariance under replacement of particles by antiparticles. Then L. Landau has introduced the concept of combined symmetry — invariance w.r.t. the mirror reflection plus charge conjugation. His assumption of conservation of the combined symmetry restored equality between the right and the left, provided the conversion of a particle into corresponding antiparticle. Thus, the symmetry between matter and antimatter was restored at a new level. The faith in the combined symmetry of nature was so strong that some even considered its experimental verification as being unnecessary. In physics laboratories of Russia, there were technical capabilities for the respective measurements, but influential theorists were not in favor of them. Meanwhile, in 1964, US experimenters Cronin and Fitch have proved the combined symmetry violation in decays of neutral kaons, and then this has been verified in other processes. In 1967, A. Sakharov has noticed that the violation of the combined symmetry is just necessary to explain the baryon asymmetry of the universe.

Matter begins to annihilate with antimatter

And we still have to check the symmetry with respect to time reversal.

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