add tseitin-free example to the readme

README.md

@@ -53,11 +53,41 @@ as shown in the following code :
 ```ocaml
 (* Module initialization *)
 module Sat = Msat.Sat.Make()
-module F = Msat.Tseitin.Make(Msat.Sat.Expr)
+module E = Msat.Sat.Expr (* expressions *)
 
 (* We create here two distinct atoms *)
-let a = Msat.Sat.Expr.fresh ()    (* A 'new_atom' is always distinct from any other atom *)
-let b = Msat.Sat.Expr.make 1      (* Atoms can be created from integers *)
+let a = E.fresh ()    (* A 'new_atom' is always distinct from any other atom *)
+let b = E.make 1      (* Atoms can be created from integers *)
+
+(* We can try and check the satisfiability of some clauses --
+   here, the clause [a or b].
+   Sat.assume adds a list of clauses to the solver. *)
+let() = Sat.assume [[a; b]]
+let res = Sat.solve ()        (* Should return (Sat.Sat _) *)
+
+(* The Sat solver has an incremental mutable state, so we still have
+   the clause [a or b] in our assumptions.
+   We add [not a] and [not b] to the state. *)
+let () = Sat.assume [[E.neg a]; [E.neg b]]
+let res = Sat.solve ()        (* Should return (Sat.Unsat _) *)
+```
+
+
+#### Formulas API
+
+Writing clauses by hand can be tedious and error-prone.
+The functor `Msat.Tseitin.Make` proposes a formula AST (parametrized by
+atoms) and a function to convert these formulas into clauses:
+
+```ocaml
+(* Module initialization *)
+module Sat = Msat.Sat.Make()
+module E = Msat.Sat.Expr (* expressions *)
+module F = Msat.Tseitin.Make(E)
+
+(* We create here two distinct atoms *)
+let a = E.fresh ()    (* A 'new_atom' is always distinct from any other atom *)
+let b = E.make 1      (* Atoms can be created from integers *)
 
 (* Let's create some formulas *)
 let p = F.make_atom a
@@ -66,12 +96,12 @@ let r = F.make_and [p; q]
 let s = F.make_or [F.make_not p; F.make_not q]
 
 (* We can try and check the satisfiability of the given formulas *)
-Sat.assume (F.make_cnf r)
+let () = Sat.assume (F.make_cnf r)
 let _ = Sat.solve ()        (* Should return (Sat.Sat _) *)
 
 (* The Sat solver has an incremental mutable state, so we still have
  * the formula 'r' in our assumptions *)
-Sat.assume (F.make_cnf s)
+let () = Sat.assume (F.make_cnf s)
 let _ = Sat.solve ()        (* Should return (Sat.Unsat _) *)
 ```