So the application is done and can be used by following this link. The GitRepo can be found here.
The application can for example be run on the proposition ~(p /\ q) <-> (~p \/ ~q) which is a tautology and hence valid.
For now I have made some limits to how long an expression can be, and how many variables it can contain. This is done so to ease the load on this server. There are algorithms that can be used to compute whether a proposition is valid, in linear time. When I find time I might implement one of those.
If you are more of a terminal person, you can type the following in terminus
prop2table "~(p /\ q) <-> (~p \/ ~q)"