diff --git a/src/sat/expr_sat.ml b/src/sat/expr_sat.ml
new file mode 100644
index 00000000..23c0498d
--- /dev/null
+++ b/src/sat/expr_sat.ml
@@ -0,0 +1,64 @@
+(*
+MSAT is free software, using the Apache license, see file LICENSE
+Copyright 2016 Guillaume Bury
+Copyright 2016 Simon Cruanes
+*)
+
+exception Bad_atom
+
+type t = int
+type proof = unit
+
+let max_lit = max_int
+let max_fresh = ref (-1)
+let max_index = ref 0
+
+let _make i =
+  if i <> 0 && (abs i) < max_lit then begin
+    max_index := max !max_index (abs i);
+    i
+  end else
+    raise Bad_atom
+
+let dummy = 0
+
+let neg a = - a
+
+let norm a =
+  abs a, if a < 0 then
+    Formula_intf.Negated
+  else
+    Formula_intf.Same_sign
+
+let abs = abs
+
+let sign i = i > 0
+
+let apply_sign b i = if b then i else neg i
+
+let set_sign b i = if b then abs i else neg (abs i)
+
+let hash (a:int) = a land max_int
+let equal (a:int) b = a=b
+let compare (a:int) b = Pervasives.compare a b
+
+let make i = _make (2 * i)
+
+let fresh, iter =
+  let create () =
+    incr max_fresh;
+    _make (2 * !max_fresh + 1)
+  in
+  let iter: (t -> unit) -> unit = fun f ->
+    for j = 1 to !max_index do
+      f j
+    done
+  in
+  create, iter
+
+let print fmt a =
+  Format.fprintf fmt "%s%s%d"
+    (if a < 0 then "~" else "")
+    (if a mod 2 = 0 then "v" else "f")
+    ((abs a) / 2)
+
diff --git a/src/sat/expr_sat.mli b/src/sat/expr_sat.mli
new file mode 100644
index 00000000..f4b72e48
--- /dev/null
+++ b/src/sat/expr_sat.mli
@@ -0,0 +1,8 @@
+(*
+MSAT is free software, using the Apache license, see file LICENSE
+Copyright 2016 Guillaume Bury
+Copyright 2016 Simon Cruanes
+*)
+
+include Formula_intf.S
+
diff --git a/src/sat/sat.ml b/src/sat/sat.ml
index 2c91c65f..9e0442f3 100644
--- a/src/sat/sat.ml
+++ b/src/sat/sat.ml
@@ -5,5 +5,5 @@ Copyright 2014 Simon Cruanes
 *)
 
 module Make(Dummy : sig end) =
-  Solver.Make(Expr.Atom)(Solver.DummyTheory(Expr.Atom))(struct end)
+  Solver.Make(Expr_sat)(Solver.DummyTheory(Expr_sat))(struct end)
 
diff --git a/src/sat/sat.mli b/src/sat/sat.mli
index 79c9b6b0..dc20113a 100644
--- a/src/sat/sat.mli
+++ b/src/sat/sat.mli
@@ -4,6 +4,6 @@ Copyright 2014 Guillaume Bury
 Copyright 2014 Simon Cruanes
 *)
 
-module Make(Dummy : sig end) : Solver.S with type St.formula = Expr.Atom.t
+module Make(Dummy : sig end) : Solver.S with type St.formula = Expr_sat.t