A system for additively manufacturing a composite part is disclosed. The system comprises a delivery guide, movable relative to a surface. The delivery guide is configured to deposit at least a segment of a continuous flexible line along a print path. The print path is stationary relative to the surface. The continuous flexible line comprises a non-resin component and a thermosetting-epoxy-resin component that is partially cured. The system also comprises a feed mechanism, configured to push the continuous flexible line through the delivery guide. The system further comprises a cooling system, configured to maintain the thermosetting-epoxy-resin component of the continuous flexible line below a threshold temperature prior to depositing the segment of the continuous flexible along the print path via the delivery guide.