We developed the theory of superalgebraic spinors, which is based on the use of Grassmann densities and derivatives with respect to them in a pseudo-continuous space of momenta. The algebra that they form corresponds to the algebra of second quantization of fermions. We have constructed a vacuum state vector and have shown that it is symmetric with respect to P, CT and CPT transformations. Operators C and T transforms the vacuum into an alternative one. Therefore, time inversion T and charge conjugation C cannot be exact symmetries of the spinors.