Do Gospels Contradict? Who Carried Jesus’ Cross/Stake?

The gospels seem to contradict about who carried Jesus’ cross/stake, , which critics seize upon.
Seeming contradiction:
“Did Jesus bear his own cross?
(a) Yes (John 19:17)
(b) No (Matthew 27:31-32)”
THE PROBLEM
Who carried the crossbeam or pole? Let’s look at the four gospels, and see who each gospel names as the one who carried Jesus’ execution stake to Golgotha:
· Matthew 27:32 – Simon
Mark 15:21 – Simon
· Luke 23:26 – Simon
· John 19:17 – Jesus