//Opgave 5.1
//Declare an F# function isConsistent that checks the consistency of a set of literals.
//Set version, men mit dilemma er at jeg ikke formår at matche x mod sin modsætning, e.g. x er endten Neg(Prop) eller A(c)
let rec isConsistentset :Set<Prop> -> bool = function
    |latSet ->  let comparisonSet = Set.foldBack(fun x set -> if(x = Neg of Prop)if Set.contains x (Set.remove x latSet) then Set.add x Set.empty else set) latSet Set.empty
                if Set.intersect latSet comparisonSet <> Set.empty then false else true


//List version af isConsistent
let rec isConsistent :Prop list*Prop list -> bool = function
    |[],auxlist              -> true //Base case
    |Neg(A(p))::pp,auxlist   -> if List.exists(fun y -> y = A(p)) auxlist then
                                                                            false
                                                                          else
                                                                            isConsistent(pp,A(p)::auxlist)
    |A(p)::pp,auxlist        -> if List.exists(fun y -> y = A(p)) auxlist then
                                                                            false
                                                                          else
                                                                            isConsistent(pp,A(p)::auxlist)