Medium Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Clearance
Flight Crew Took Evasive Action
Human Factors
We called for taxi clearance at the top of the box and were directed to taxi Runway XL via C5 Bravo. The aircraft behind us in the box; Aircraft Z; then called for taxi and was given 6R via C5 Bravo Lima North Route. As we turned onto C5; Aircraft Y; at the top of C6 alley; called for taxi; and was assigned Runway XR via Bravo Lima North Route; give way to the Aircraft Z; (presumably the aircraft behind us). Aircraft Y read back the clearance. As we entered the intersection of Bravo and C6 at around 10 knots; I saw Aircraft Y off my right; and expected that it was going to stop to give way to the aircraft behind us. Instead; Aircraft Y sped up in front of us; cut the corner of C6/Bravo; and went straight onto Bravo in front of us. I immediately slammed on the brakes to prevent a collision; missing Aircraft Y's left wing by about 20-30 feet. Aircraft Y continued down Bravo at a very high speed. Due to the business of the frequency at the time; we were not able to get a word in to query with ground. We resumed taxi and rest of flight was normal.The other aircraft did not follow its taxi clearance and nearly caused a collision with us. ATC can give instructions; but ultimately it's up to us to remain vigilant at all times and verify that other aircraft are doing what they are supposed to do.
Air carrier Captain reported a ground conflict event with another air carrier during taxi out.