  Weyl semimetals typically appear in systems in which either time-reversal (T)
or inversion (P}) symmetry are broken. Here we show that in the presence of
gauge potentials these topological states of matter can also arise in fermionic
lattices preserving both T and P. We analyze in detail the case of a cubic
lattice model with $\pi$-fluxes, discussing the role of gauge symmetries in the
formation of Weyl points and the difference between the physical and the
canonical T and P symmetries. Motivated by advances in ultracold atom
experiments and by the possibility of using synthetic magnetic fields, we
examine the robustness of the Weyl semimetal phase in the presence of trapping
potentials and random perturbations of the magnetic fluxes, which can be
compared to a local disorder in realistic scenarios.
