diff --git a/src/backend/coq.ml b/src/backend/coq.ml
index 360f15fd..51bd105c 100644
--- a/src/backend/coq.ml
+++ b/src/backend/coq.ml
@@ -81,14 +81,43 @@ module Make(S : Res.S)(A : Arg with type hyp := S.clause
     (** Prove the goal: intro the axioms, then perform resolution *)
     if Array.length goal.S.St.atoms = 0 then begin
       let m = M.empty in
-      Format.fprintf fmt "exact @[<hov 1>(%a)@].@\n" (resolution_aux m a h1 h2) ()
+      Format.fprintf fmt "exact @[<hov 1>(%a)@].@\n" (resolution_aux m a h1 h2) ();
+      false
     end else begin
       let m = clause_map goal in
       Format.fprintf fmt "pose proof @[<hov>(fun %a=>@ %a)@ as %s.@]@\n"
-        (clause_iter m "%s@ ") goal (resolution_aux m a h1 h2) () (name goal)
+        (clause_iter m "%s@ ") goal (resolution_aux m a h1 h2) () (name goal);
+      true
     end
 
 
+  (* Count uses of hypotheses *)
+  let incr_use h c =
+    let i = try S.H.find h c with Not_found -> 0 in
+    S.H.add h c (i + 1)
+
+  let decr_use h c =
+    let i = S.H.find h c - 1 in
+    assert (i >= 0);
+    let () = S.H.add h c i in
+    i <= 0
+
+  let clear fmt c =
+    Format.fprintf fmt "clear %s." (name c)
+
+  let rec clean_aux fmt = function
+    | [] -> ()
+    | [x] ->
+      Format.fprintf fmt "%a@\n" clear x
+    | x :: ((_ :: _) as r) ->
+      Format.fprintf fmt "%a@ %a" clear x clean_aux r
+
+  let clean h fmt l =
+    match List.filter (decr_use h) l with
+    | [] -> ()
+    | l' ->
+      Format.fprintf fmt "(* Clearing unused clauses *)@\n%a" clean_aux l'
+
   let prove_node t fmt node =
     let clause = node.S.conclusion in
     match node.S.step with
@@ -99,17 +128,29 @@ module Make(S : Res.S)(A : Arg with type hyp := S.clause
     | S.Lemma _ ->
       A.prove_lemma fmt (name clause) clause
     | S.Duplicate (p, l) ->
-      let c = (S.expand p).S.conclusion in
-      elim_duplicate fmt clause c l
+      let p' = S.expand p in
+      let c = p'.S.conclusion in
+      let () = elim_duplicate fmt clause c l in
+      clean t fmt [c]
     | S.Resolution (p1, p2, a) ->
       let c1 = (S.expand p1).S.conclusion in
       let c2 = (S.expand p2).S.conclusion in
-      resolution fmt clause c1 c2 a
+      if resolution fmt clause c1 c2 a then clean t fmt [c1; c2]
+
+  let count_uses p =
+    let h = S.H.create 4013 in
+    let aux () node =
+      List.iter (fun p' ->
+          incr_use h S.((expand p').conclusion))
+        (S.parents node.S.step)
+    in
+    let () = S.fold aux () p in
+    h
 
   (* Here the main idea is to always try and have exactly
      one goal to prove, i.e False. So each  *)
   let print fmt p =
-    let h = S.H.create 4013 in
+    let h = count_uses p in
     let aux () node =
       Format.fprintf fmt "%a" (prove_node h) node
     in
diff --git a/src/core/res_intf.ml b/src/core/res_intf.ml
index 72eb12fe..20b689f1 100644
--- a/src/core/res_intf.ml
+++ b/src/core/res_intf.ml
@@ -117,7 +117,7 @@ module type S = sig
   (** {3 Unsafe} *)
 
   module H : Hashtbl.S with type key = clause
-  (** Hashtable over clauses. Uses the details of the internal representation
+  (** Hashtable over proofs. Uses the details of the internal representation
       to achieve the best performances, however hashtables from this module
       become invalid when solving is restarted, so they should only be live
       during inspection of a single proof. *)