The two-pion production reaction pp → ppπ+π− was measured with a polarized proton beam at Tp≈ 750 and 800MeV using the short version of the COSY-TOF spectrometer. The implementation of a delayed-pulse technique for Quirl and central calorimeter provided positive π+ identification in addition to the standard particle identification, energy determination as well as time-of-flight and angle measurements. Thus all four-momenta of the emerging particles could be determined with 1–4 overconstraints. Total and differential cross-sections as well as angular distributions of the vector analyzing power have been obtained. They are compared to previous data and theoretical calculations. In contrast to predictions we find significant analyzing-power values up to Ay= 0.3. The data taken in the energy region of the excitation of the Roper resonance confirm that its dominant ππ decay channel is N* → Nσ.