This refers to a Circle Trip Minimum Fare Check (CTMFC). This is getting into the wonderful world of fares and where it starts to get just a little more complicated. It is similar-ish to a HIP Check (Higher Intermediate Point).

I am trying to remember the exact wording, but it's something like 'the minimum fare cannot undercut the fare between any two ticketed stopover (not transfer!) points.'

The LHR-CAI-LCA routing is a nice example. The overall fare for LHR-LCA cannot undercut the LHR-CAI fare so, if LHR-LCA is £500 and LHR-CAI is £700, this would mean that there would be a 'plus up' of £200 as not to undercut the LHR-CAI fare. The fare on your ticket would show the normal levels LHR-LCA fare levels, until just before they are added up at the very end when the plus up appears as 'P LONCAI200.00' and the overall fare total appears.

These can get a little more complicated when some wiseguy decides he wants to travel on some daft routing such as LHR-FRA-HKG-MNL-DXB-MXP-LHR as on this type of routing there are several CTMFC's that you have to work out. Logic would dictate that LHR-MNL, being longest routing, would have the higher fare but reality will usually prove something else. Usually, selling systems will work out simple ones such as these, but there are a few occasions when you have to get out your pen, paper and calculator.

The Mileage Surcharge is completely unrelated, and I wouldn't be surprised if all the LHR-LCA routings you mentioned (via BEY, DAM, TLV and CAI) had a surcharge. This is just shown beside the fare component in the construction as a 5M or 10M etc (depending upon by how much you exceed the Maximum Permitted Mileage), so someone knows when they look at the figure that it has already been 'surcharged.'

It probably all comes across a bit arse over elbow when written down, but is quite straightforward when you see the actual figures.