A Weyl semimetallic state with pairs of nondegenerate Dirac cones in three dimensions was recently predicted to occur in the antiferromagnetic state of the pyrochlore iridates. Here, we show that the THz optical conductivity and temperature dependence of the free carrier response in pyrochlore Eu2Ir2O7{\mathrm{Eu}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7} match the predictions for a Weyl semimetal and suggest novel Dirac liquid behavior. The interband optical conductivity vanishes continuously at low freq