Membranes composed of Polymers of Intrinsic Microporosity (PIMs) have the potential for energy efficient industrial gas separations. Here we report the synthesis and gas permeability data of a series of ultrapermeable PIMs, of two-dimensional chain conformation and based on benzotriptycene structural units, that demonstrate remarkable ideal selectivity for most gas pairs of importance. In particular, the CO2 ultrapermeability and high selectivity for CO2 over CH4, of key importance for the upgrading of natural gas and biogas, and for CO2 over N2, of importance for cost-effective carbon capture from power plants, exceed the performance of the current state-of-the-art polymers. All of the gas permeability data from this series of benzotriptycene-based PIMs are placed well above the current 2008 Robeson upper bounds for CO2/CH4 and CO2/N2. Indeed, the data for some of these polymers fall into a linear correlations on the benchmark Robeson plots [i.e. log(PCO2/PCH4) versus logPCO2 and log(PCO2/PN2) versus logPCO2], which are parallel to, but significantly above, that of the 2008 CO2/CH4 and CO2/N2 upper bounds, allowing their revision. The redefinition of these upper bounds sets new aspirational targets for polymer chemists to aim for and will result in more attractive parametric estimates of energy and cost efficiencies for carbon capture and natural/bio gas upgrading using state-of-the-art CO2 separation membranes.