Very nice Saint Swithin. Paph laevigatum was discarded as a name over 25 years ago, it was reduced to a synonym of philippinense. The name laevigatum only survives in horticultural circles these days, partly because there are a few awarded or named plants that were originally assigned this name, and in order to not loose the fact that a plant is a division of one of these old collected clones, the name keeps getting revived. One such example is Paph laevigatum 'Frank', a vigorous growing philippinense collected and imported back in the 1960's. Many divisions of 'Frank' were made over time and was rather widely distributed. (I still have a division myself).
Another reason the name is still around is some people read the old literature and just assume the old names are still good.
Third there are those hobbyists that want a species level name for every perceivable difference between two plants, with no regard to the consensus that taxonomists have developed that these minor differences aren't enough to define a new species. What ever the reason, laevigatum = philippinense and that makes your plant a perfectly good Saint Swithin.
If you enter laevigatum into the grex name search on the RHS website, it will return that it is a synonym of philippinense.