The 19/20-parameter p(henomenological)MSSM with either a neutralino or gravitino LSP offers a flexible framework for the study of a wide variety of R-parity conserving MSSM SUSY phenomena at the 7, 8 and 14 TeV LHC. Here we present the results of a study of SUSY signatures at these facilities obtained via a fast Monte Carlo replication of the ATLAS SUSY analysis suite. In particular, we show the ranges of the sparticle masses that are either disfavored or remain viable after all of the various searches at the 7 and 8 TeV runs are combined. We then extrapolate to 14 TeV with both 300 fb^-1 and 3 ab^-1 of integrated luminosity and determine the sensitivity of a jets + MET search to the pMSSM parameter space. We find that the high-luminosity LHC performs extremely well in probing natural SUSY models.
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