In literal frameworks, the rule of unity says that apparent contradictions should each be accepted as true, with the confidence that the contradiction will be resolved in a higher unity. 

Application of this rule gives us the Trinity in the face of the apparent contradiction that there is only one God, but the Father, Son and Holy Ghost are each God.

A corollary is that if a plausible answer exists that explains the apparent contradiction, it should be accepted as the 'higher unity'.

A higher unity is one where the mistakes which cause the apparent contradiction are resolved:

Reality - a mistaken concept of what is really real can produce contradictions. If eternity is timeless, and creation occurred in eternity, then there is no contradiction in the evidence of apparent long times required for light from distant stars to travel to earth, and the short time required for radiation halos in rock. 

Understanding - Words are reusable symbols for a plethora of ideas. Their use produces ambiguity of meaning. 

"The time" of Abiathar" is ambiguous. It does not state that Abiathar was high priest. Abiathar was the son of Ahimelech. The bread belonged to the priests and plausibly even belonged to Abiather. Certainly it was not unheard of for the high priest to have assistance in the performance of his duties, as Samuel was known to do for Eli.  

Therefore, the solution is that Abiathar was assisting in the tabernacle when David approached 
Ahimelech. Ahimelech was uncomfortable even with the presence of David, but Abiathar was disposed to help him and since it was his bread, prevailed upon Ahimelech to give it to David. Since we presume that not all conversations are recorded exhaustively, it is not difficult to imagine a brief conversation taking place concerning the disposition of bread belonging to the priest to whom it had been given. Could an adopted son of a priest eat the bread? Abiathar later joined David and was appointed high priest by him. 

The compromise was that they had been separate from women for three days. The grave of Christ separated him from the flesh for three days, after which, he was the High Priest. And through his adoption of us makes us a nation of priests.   David's and his men were made to be priest's figuratively, by being separate from the flesh for three days.

**Intentional 'mistake'**

The first case of a mistaken name of a high priest occurs when Uzziah is called Azariah. The king as a type of Christ "did everything according to his father", "offered himself in the tabernacle as the burnt offering/sweet savor of offering/incense", "bore our sin/made leprous", "cast out of the camp", and then "became the high priest/was called by the name of the high priest". 

Uzziah and Azariah represent Christ in the flesh and resurrection. Likewise Ahimelech and Abiathar represent Christ in the flesh and in resurrection.  Ahimelech was put to death, and Abiathar ruled in his place as appointed by David. 

Jesus used the same type of riddle that he found in scripture concerning Uzziah and Azariah (2 Kings 15:5-6). It was an intentional 'mistake' intended to point us to types of Christ buried in the riddles and apparent contradictions.

> Ps 78:2 I will open my mouth in a parable: I will utter dark sayings [riddles]
> of old:
> 
> Pr 1:6 To understand a proverb, and the interpretation; the words of
> the wise, and their dark sayings [riddles].