Jose Acacio de Barros discusses as follows [{Jose Acacio de Barros, Int. J. Theor. Phys. {\bf 50}, 1828 (2011)}]. Nagata claims to derive inconsistencies from quantum mechanics [{K. Nagata, Int. J. Theor. Phys. {\bf 48}, 3532 (2009)}]. Jose Acacio de Barros considers that the inconsistencies do not come from quantum mechanics, but from extra assumptions about the reality of observables. Here we discuss the fact that there is a contradiction within the quantum theory. We discuss the fact that only one expected value in a spin-1/2 pure state $\langle\sigma_x\rangle$ rules out the reality of the observable. We do not accept extra assumptions about the reality of observables. We use the actually measured results of quantum measurements (raw data). We use a single Pauli observable. We stress that we can use the quantum theory even if we give up the axiomatic system for the quantum theory.