In neutrino oscillation with non-standard interactions (NSI) the system is enriched with CP violation caused by phases due to NSI in addition to the standard lepton Kobayashi-Maskawa phase delta. In this paper we show that it is possible to disentangle the two CP violating effects by measurement of muon neutrino appearance by a near-far two detector setting in neutrino factory experiments. Prior to the quantitative analysis we investigate in detail the various features of the neutrino oscillations with NSI, but under the assumption that only one of the NSI elements, epsilon_{e mu} or epsilon_{e tau}, is present. They include synergy between the near and the far detectors, the characteristic differences between the epsilon_{e mu} and epsilon_{etau} systems, and in particular, the parameter degeneracy. Finally, we use a concrete setting with the muon energy of 50 GeV and magnetized iron detectors at two baselines, one at L=3000 km and the other at L=7000 km, each having a fiducial mass of 50 kton to study the discovery potential of NSI and its CP violation effects. We demonstrate, by assuming 4 times 10^{21} useful muon decays for both polarities, that one can identify non-standard CP violation down to | epsilon_{e mu} | simeq text{a few} times 10^{-3}, and | epsilon_{e tau} | simeq 10^{-2} at 3sigma CL for theta_{13} down to sin^2 2theta_{13} = 10^{-4} in most of the region of delta. The impact of the existence of NSI on the measurement of delta and the mass hierarchy is also worked out.
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