diff --git a/src/sat/Internal.ml b/src/sat/Internal.ml
index fd14ddf0..0db0df99 100644
--- a/src/sat/Internal.ml
+++ b/src/sat/Internal.ml
@@ -728,7 +728,6 @@ module Make (Th : Theory_intf.S) = struct
   end
 
   let[@inline] theory st = Lazy.force st.th
-
   let[@inline] nb_clauses st = Vec.size st.clauses
   let[@inline] decision_level st = Vec.size st.elt_levels
   let[@inline] base_level st = if decision_level st > 0 then 1 else 0 (* first level=assumptions *)
diff --git a/src/smt/Congruence_closure.ml b/src/smt/Congruence_closure.ml
index 4bcc4701..dab6b42a 100644
--- a/src/smt/Congruence_closure.ml
+++ b/src/smt/Congruence_closure.ml
@@ -72,8 +72,8 @@ let[@inline] on_backtrack cc f : unit =
 let[@inline] is_root_ (n:node) : bool = n.n_root == n
 
 let[@inline] size_ (r:repr) =
-  assert (is_root_ (r:>node));
-  Bag.size (r :> node).n_parents
+  assert (is_root_ r);
+  Bag.size r.n_parents
 
 (* check if [t] is in the congruence closure.
    Invariant: [in_cc t => in_cc u, forall u subterm t] *)
@@ -90,9 +90,9 @@ let rec find_rec cc (n:node) : repr =
     let old_root = n.n_root in
     let root = find_rec cc old_root in
     (* path compression *)
-    if (root :> node) != old_root then (
+    if root != old_root then (
       on_backtrack cc (fun () -> n.n_root <- old_root);
-      n.n_root <- (root :> node);
+      n.n_root <- root;
     );
     root
   )
@@ -154,8 +154,11 @@ let is_done (cc:t): bool =
   Vec.is_empty cc.combine
 
 let push_pending cc t : unit =
-  Log.debugf 5 (fun k->k "(@[<hv1>cc.push_pending@ %a@])" Equiv_class.pp t);
-  Vec.push cc.pending t
+  if not @@ Equiv_class.get_field Equiv_class.field_is_pending t then (
+    Log.debugf 5 (fun k->k "(@[<hv1>cc.push_pending@ %a@])" Equiv_class.pp t);
+    Equiv_class.set_field Equiv_class.field_is_pending true t;
+    Vec.push cc.pending t
+  )
 
 let push_combine cc t u e : unit =
   Log.debugf 5
@@ -322,11 +325,13 @@ let rec update_pending (cc:t): unit =
      might have changed *)
   while not (Vec.is_empty cc.pending) do
     let n = Vec.pop_last cc.pending in
+    Equiv_class.set_field Equiv_class.field_is_pending false n;
     (* check if some parent collided *)
     begin match find_by_signature cc n.n_term with
       | None ->
         (* add to the signature table [sig(n) --> n] *)
         add_signature cc n.n_term n
+      | Some u when n == u -> ()
       | Some u ->
         (* must combine [t] with [r] *)
         if not @@ same_class cc n u then (
@@ -337,8 +342,7 @@ let rec update_pending (cc:t): unit =
             | App_cst (f1, a1), App_cst (f2, a2) ->
               assert (Cst.equal f1 f2);
               assert (IArray.length a1 = IArray.length a2);
-              Explanation.mk_merges @@
-              IArray.map2 (fun u1 u2 -> add_ cc u1, add_ cc u2) a1 a2
+              Explanation.mk_merges @@ IArray.map2 (fun u1 u2 -> add_ cc u1, add_ cc u2) a1 a2
             | If _, _ | App_cst _, _ | Bool _, _
               -> assert false
           in
@@ -386,14 +390,12 @@ and update_combine cc =
       in
       (* remove [ra.parents] from signature, put them into [st.pending] *)
       begin
-        Bag.to_seq (r_from:>node).n_parents
+        Bag.to_seq r_from.n_parents
         |> Sequence.iter
           (fun parent -> push_pending cc parent)
       end;
       (* perform [union ra rb] *)
       begin
-        let r_from = (r_from :> node) in
-        let r_into = (r_into :> node) in
         let r_into_old_parents = r_into.n_parents in
         let r_into_old_tags = r_into.n_tags in
         on_backtrack cc
@@ -485,26 +487,26 @@ let add_seq cc seq =
 
 (* to do after backtracking: reset task lists *)
 let reset_tasks cc : unit =
+  Vec.iter (Equiv_class.set_field Equiv_class.field_is_pending false) cc.pending;
   Vec.clear cc.pending;
   Vec.clear cc.combine;
   ()
 
 (* assert that this boolean literal holds *)
-let assert_lit cc lit : unit = match Lit.view lit with
-  | Lit_fresh _ -> ()
-  | Lit_atom t ->
-    assert (Ty.is_prop t.term_ty);
-    Log.debugf 5 (fun k->k "(@[cc.assert_lit@ %a@])" Lit.pp lit);
-    let sign = Lit.sign lit in
-    (* equate t and true/false *)
-    let rhs = if sign then true_ cc else false_ cc in
-    let n = add cc t in
-    (* TODO: ensure that this is O(1).
-       basically, just have [n] point to true/false and thus acquire
-       the corresponding value, so its superterms (like [ite]) can evaluate
-       properly *)
-    push_combine cc n rhs (E_lit lit);
-    ()
+let assert_lit cc lit : unit =
+  let t = Lit.view lit in
+  assert (Ty.is_prop t.term_ty);
+  Log.debugf 5 (fun k->k "(@[cc.assert_lit@ %a@])" Lit.pp lit);
+  let sign = Lit.sign lit in
+  (* equate t and true/false *)
+  let rhs = if sign then true_ cc else false_ cc in
+  let n = add cc t in
+  (* TODO: ensure that this is O(1).
+     basically, just have [n] point to true/false and thus acquire
+     the corresponding value, so its superterms (like [ite]) can evaluate
+     properly *)
+  push_combine cc n rhs (E_lit lit);
+  ()
 
 let assert_eq cc (t:term) (u:term) expl : unit =
   let n1 = add cc t in
diff --git a/src/smt/Equiv_class.ml b/src/smt/Equiv_class.ml
index 1f8d3c4e..13f73a3d 100644
--- a/src/smt/Equiv_class.ml
+++ b/src/smt/Equiv_class.ml
@@ -5,6 +5,7 @@ type t = cc_node
 type payload = cc_node_payload = ..
 
 let field_is_active = Node_bits.mk_field()
+let field_is_pending = Node_bits.mk_field()
 let () = Node_bits.freeze()
 
 let[@inline] equal (n1:t) n2 = n1==n2
@@ -59,6 +60,9 @@ let payload_pred ~f:p n =
     | l -> List.exists p l
   end
 
+let[@inline] get_field f t = Node_bits.get f t.n_bits
+let[@inline] set_field f b t = t.n_bits <- Node_bits.set f b t.n_bits
+
 module Tbl = CCHashtbl.Make(struct
     type t = cc_node
     let equal = equal
diff --git a/src/smt/Equiv_class.mli b/src/smt/Equiv_class.mli
index 3f46b88b..9885094f 100644
--- a/src/smt/Equiv_class.mli
+++ b/src/smt/Equiv_class.mli
@@ -27,6 +27,9 @@ val field_is_active : Node_bits.field
 (** The term is needed for evaluation. We must try to evaluate it
     or to find a value for it using the theory *)
 
+val field_is_pending : Node_bits.field
+(** true iff the node is in the [cc.pending] queue *)
+
 (** {2 basics} *)
 
 val term : t -> term
@@ -49,6 +52,9 @@ val set_payload : ?can_erase:(payload -> bool) -> t -> payload -> unit
     @param can_erase if provided, checks whether an existing value
       is to be replaced instead of adding a new entry *)
 
+val get_field : Node_bits.field -> t -> bool
+val set_field : Node_bits.field -> bool -> t -> unit
+
 module Tbl : CCHashtbl.S with type key = t
 
 (**/**)
diff --git a/src/smt/Lit.ml b/src/smt/Lit.ml
index 11719c27..c2cae168 100644
--- a/src/smt/Lit.ml
+++ b/src/smt/Lit.ml
@@ -2,48 +2,31 @@
 open Solver_types
 
 type t = lit = {
-  lit_view : lit_view;
+  lit_term: term;
   lit_sign : bool
 }
 
-and view = lit_view =
-  | Lit_fresh of ID.t
-  | Lit_atom of term
-
 let neg l = {l with lit_sign=not l.lit_sign}
 
-let sign t = t.lit_sign
-let view (t:t): lit_view = t.lit_view
+let[@inline] sign t = t.lit_sign
+let[@inline] view (t:t): term = t.lit_term
 
-let abs t: t = {t with lit_sign=true}
+let[@inline] abs t: t = {t with lit_sign=true}
 
-let make ~sign v = {lit_sign=sign; lit_view=v}
+let make ~sign t = {lit_sign=sign; lit_term=t}
 
-(* assume the ID is fresh *)
-let fresh_with id = make ~sign:true (Lit_fresh id)
-
-(* fresh boolean literal *)
-let fresh: unit -> t =
-  let n = ref 0 in
-  fun () ->
-    let id = ID.makef "#fresh_%d" !n in
-    incr n;
-    make ~sign:true (Lit_fresh id)
-
-let dummy = fresh()
+let dummy = make ~sign:true Term.dummy
 
 let atom ?(sign=true) (t:term) : t =
   let t, sign' = Term.abs t in
   let sign = if not sign' then not sign else sign in
-  make ~sign (Lit_atom t)
+  make ~sign t
 
-let as_atom (lit:t) : (term * bool) option = match lit.lit_view with
-  | Lit_atom t -> Some (t, lit.lit_sign)
-  | _ -> None
+let[@inline] as_atom (lit:t) = lit.lit_term, lit.lit_sign
 
 let hash = hash_lit
 let compare = cmp_lit
-let equal a b = compare a b = 0
+let[@inline] equal a b = compare a b = 0
 let pp = pp_lit
 let print = pp
 
diff --git a/src/smt/Lit.mli b/src/smt/Lit.mli
index 6aac0a76..055fa373 100644
--- a/src/smt/Lit.mli
+++ b/src/smt/Lit.mli
@@ -3,21 +3,15 @@
 open Solver_types
 
 type t = lit = {
-  lit_view : lit_view;
+  lit_term: term;
   lit_sign : bool
 }
 
-and view = lit_view =
-  | Lit_fresh of ID.t
-  | Lit_atom of term
-
 val neg : t -> t
 val abs : t -> t
 val sign : t -> bool
-val view : t -> lit_view
-val as_atom : t -> (term * bool) option
-val fresh_with : ID.t -> t
-val fresh : unit -> t
+val view : t -> term
+val as_atom : t -> term * bool
 val dummy : t
 val atom : ?sign:bool -> term -> t
 val hash : t -> int
diff --git a/src/smt/Solver_types.ml b/src/smt/Solver_types.ml
index 0f7ce5f1..ec311bdb 100644
--- a/src/smt/Solver_types.ml
+++ b/src/smt/Solver_types.ml
@@ -55,14 +55,10 @@ and explanation =
 
 (* boolean literal *)
 and lit = {
-  lit_view: lit_view;
+  lit_term: term;
   lit_sign: bool;
 }
 
-and lit_view =
-  | Lit_fresh of ID.t (* fresh literals *)
-  | Lit_atom of term
-
 and cst = {
   cst_id: ID.t;
   cst_view: cst_view;
@@ -143,25 +139,13 @@ let[@inline] term_cmp_ a b = CCInt.compare a.term_id b.term_id
 let cmp_lit a b =
   let c = CCBool.compare a.lit_sign b.lit_sign in
   if c<>0 then c
-  else (
-    let int_of_cell_ = function
-      | Lit_fresh _ -> 0
-      | Lit_atom _ -> 1
-    in
-    match a.lit_view, b.lit_view with
-      | Lit_fresh i1, Lit_fresh i2 -> ID.compare i1 i2
-      | Lit_atom t1, Lit_atom t2 -> term_cmp_ t1 t2
-      | Lit_fresh _, _ | Lit_atom _, _
-        -> CCInt.compare (int_of_cell_ a.lit_view) (int_of_cell_ b.lit_view)
-  )
+  else term_cmp_ a.lit_term b.lit_term
 
 let cst_compare a b = ID.compare a.cst_id b.cst_id
 
 let hash_lit a =
   let sign = a.lit_sign in
-  match a.lit_view with
-    | Lit_fresh i -> Hash.combine3 1 (Hash.bool sign) (ID.hash i)
-    | Lit_atom t -> Hash.combine3 2 (Hash.bool sign) (term_hash_ t)
+  Hash.combine3 2 (Hash.bool sign) (term_hash_ a.lit_term)
 
 let cmp_cc_node a b = term_cmp_ a.n_term b.n_term
 
@@ -236,12 +220,8 @@ let pp_term = pp_term_top ~ids:false
 let pp_term_view = pp_term_view ~pp_id:ID.pp_name ~pp_t:pp_term
 
 let pp_lit out l =
-  let pp_lit_view out = function
-    | Lit_fresh i -> Format.fprintf out "#%a" ID.pp i
-    | Lit_atom t -> pp_term out t
-  in
-  if l.lit_sign then pp_lit_view out l.lit_view
-  else Format.fprintf out "(@[@<1>¬@ %a@])" pp_lit_view l.lit_view
+  if l.lit_sign then pp_term out l.lit_term
+  else Format.fprintf out "(@[@<1>¬@ %a@])" pp_term l.lit_term
 
 let pp_cc_node out n = pp_term out n.n_term
 
diff --git a/src/smt/Theory_combine.ml b/src/smt/Theory_combine.ml
index 83076f71..54b18f5d 100644
--- a/src/smt/Theory_combine.ml
+++ b/src/smt/Theory_combine.ml
@@ -48,10 +48,9 @@ let assume_lit (self:t) (lit:Lit.t) : unit =
     (fun k->k "(@[<1>@{<green>th_combine.assume_lit@}@ @[%a@]@])" Lit.pp lit);
   (* check consistency first *)
   begin match Lit.view lit with
-    | Lit_fresh _ -> ()
-    | Lit_atom {term_view=Bool true; _} -> ()
-    | Lit_atom {term_view=Bool false; _} -> ()
-    | Lit_atom _ ->
+    | {term_view=Bool true; _} -> ()
+    | {term_view=Bool false; _} -> ()
+    | _ ->
       (* transmit to theories. *)
       C_clos.assert_lit (cc self) lit;
       theories self (fun (module Th) -> Th.on_assert Th.state lit);
@@ -98,11 +97,9 @@ let assume_real (self:t) (slice:Lit.t Sat_solver.slice_actions) =
     )
 
 let add_formula (self:t) (lit:Lit.t) =
-  match Lit.view lit with
-  | Lit_atom t ->
-    let lazy cc = self.cc in
-    ignore (C_clos.add cc t : cc_node)
-  | Lit_fresh _ -> ()
+  let t = Lit.view lit in
+  let lazy cc = self.cc in
+  ignore (C_clos.add cc t : cc_node)
 
 (* propagation from the bool solver *)
 let assume (self:t) (slice:_ Sat_solver.slice_actions) =
diff --git a/src/smt/th_bool/Sidekick_th_bool.ml b/src/smt/th_bool/Sidekick_th_bool.ml
index b7d255b7..268baf0f 100644
--- a/src/smt/th_bool/Sidekick_th_bool.ml
+++ b/src/smt/th_bool/Sidekick_th_bool.ml
@@ -236,13 +236,11 @@ let tseitin (self:t) (lit:Lit.t) (lit_t:term) (v:term view) : unit =
     )
 
 let on_assert (self:t) (lit:Lit.t) =
-  match Lit.view lit with
-  | Lit.Lit_atom t ->
-    begin match view t with
-      | B_atom _ -> ()
-      | v -> tseitin self lit t v
-    end
-  | _ -> ()
+  let t = Lit.view lit in
+  begin match view t with
+    | B_atom _ -> ()
+    | v -> tseitin self lit t v
+  end
 
 let final_check _ _ : unit = ()
 
diff --git a/src/smtlib/Process.ml b/src/smtlib/Process.ml
index 170c7904..384f7442 100644
--- a/src/smtlib/Process.ml
+++ b/src/smtlib/Process.ml
@@ -228,10 +228,8 @@ let check_smt_model (solver:Solver.Sat_solver.t) (hyps:_ Vec.t) (m:Model.t) : un
     let is_true = S.Atom.is_true a in
     let is_false = S.Atom.is_true (S.Atom.neg a) in
     let sat_value = if is_true then Some true else if is_false then Some false else None in
-    begin match Lit.as_atom lit with
-    | None -> assert false
-    | Some (t, sign) ->
-      match Model.eval m t with
+    let t, sign = Lit.as_atom lit in
+    begin match Model.eval m t with
       | Some (V_bool b) ->
         let b = if sign then b else not b in
         if (is_true || is_false) && ((b && is_false) || (not b && is_true)) then (