  The two-pion production reaction $\vec{p}p\to pp\pi^+\pi^-$ was measured with
a polarized proton beam at $T_p \approx$ 750 and 800 MeV using the short
version of the COSY-TOF spectrometer. The implementation of a delayed pulse
technique for Quirl and central calorimeter provided positive $\pi^+$
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 $A_y$ = 0.3.
