diff --git a/src/base-term/Base_types.ml b/src/base-term/Base_types.ml
index ae67a54f..7d45cf3b 100644
--- a/src/base-term/Base_types.ml
+++ b/src/base-term/Base_types.ml
@@ -18,12 +18,6 @@ and 'a term_view =
   | Eq of 'a * 'a
   | Not of 'a
 
-(* boolean literal *)
-and lit = {
-  lit_term: term;
-  lit_sign: bool;
-}
-
 and fun_ = {
   fun_id: ID.t;
   fun_view: fun_view;
@@ -101,17 +95,8 @@ let[@inline] term_equal_ (a:term) b = a==b
 let[@inline] term_hash_ a = a.term_id
 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 term_cmp_ a.lit_term b.lit_term
-
 let fun_compare a b = ID.compare a.fun_id b.fun_id
 
-let hash_lit a =
-  let sign = a.lit_sign in
-  Hash.combine3 2 (Hash.bool sign) (term_hash_ a.lit_term)
-
 let pp_fun out a = ID.pp out a.fun_id
 let id_of_fun a = a.fun_id
 
@@ -167,10 +152,6 @@ let pp_term_top ~ids out t =
 let pp_term = pp_term_top ~ids:false
 let pp_term_view = pp_term_view_gen ~pp_id:ID.pp_name ~pp_t:pp_term
 
-let pp_lit out l =
-  if l.lit_sign then pp_term out l.lit_term
-  else Format.fprintf out "(@[@<1>¬@ %a@])" pp_term l.lit_term
-
 module Ty_card : sig
 type t = ty_card = Finite | Infinite
 
@@ -756,63 +737,6 @@ end = struct
     | Eq (a,b) -> eq tst (f a) (f b)
 end
 
-module Lit : sig
-  type t = lit = {
-    lit_term: term;
-    lit_sign : bool
-  }
-
-  val neg : t -> t
-  val abs : t -> t
-  val sign : t -> bool
-  val term : t -> term
-  val as_atom : t -> term * bool
-  val atom : Term.state -> ?sign:bool -> term -> t
-  val hash : t -> int
-  val compare : t -> t -> int
-  val equal : t -> t -> bool
-  val print : t Fmt.printer
-  val pp : t Fmt.printer
-  val apply_sign : t -> bool -> t
-  val norm_sign : t -> t * bool
-  val norm : t -> t * Msat.negated
-  module Set : CCSet.S with type elt = t
-  module Tbl : CCHashtbl.S with type key = t
-end = struct
-  type t = lit = {
-    lit_term: term;
-    lit_sign : bool
-  }
-
-  let[@inline] neg l = {l with lit_sign=not l.lit_sign}
-  let[@inline] sign t = t.lit_sign
-  let[@inline] term (t:t): term = t.lit_term
-
-  let[@inline] abs t: t = {t with lit_sign=true}
-
-  let make ~sign t = {lit_sign=sign; lit_term=t}
-
-  let atom tst ?(sign=true) (t:term) : t =
-    let t, sign' = Term.abs tst t in
-    let sign = if not sign' then not sign else sign in
-    make ~sign t
-
-  let[@inline] as_atom (lit:t) = lit.lit_term, lit.lit_sign
-
-  let hash = hash_lit
-  let compare = cmp_lit
-  let[@inline] equal a b = compare a b = 0
-  let pp = pp_lit
-  let print = pp
-
-  let apply_sign t s = if s then t else neg t
-  let norm_sign l = if l.lit_sign then l, true else neg l, false
-  let norm l = let l, sign = norm_sign l in l, if sign then Msat.Same_sign else Msat.Negated
-
-  module Set = CCSet.Make(struct type t = lit let compare=compare end)
-  module Tbl = CCHashtbl.Make(struct type t = lit let equal=equal let hash=hash end)
-end
-
 module Value : sig
   type t = value =
     | V_bool of bool
@@ -872,10 +796,3 @@ module Proof = struct
   type t = Default
   let default = Default
 end
-
-module type CC_ACTIONS = sig
-  val raise_conflict : Lit.t list -> Proof.t -> 'a
-  val propagate : Lit.t -> reason:(unit -> Lit.t list) -> Proof.t -> unit
-end
-
-type cc_actions = (module CC_ACTIONS)
diff --git a/src/base-term/Sidekick_base_term.ml b/src/base-term/Sidekick_base_term.ml
index 3bd3882f..535ce45e 100644
--- a/src/base-term/Sidekick_base_term.ml
+++ b/src/base-term/Sidekick_base_term.ml
@@ -8,17 +8,14 @@ module Term = Base_types.Term
 module Value = Base_types.Value
 module Term_cell = Base_types.Term_cell
 module Ty = Base_types.Ty
-module Lit = Base_types.Lit
 
 module Arg
-  : Sidekick_core.TERM_LIT
+  : Sidekick_core.TERM
     with type Term.t = Term.t
-     and type Lit.t = Lit.t
      and type Fun.t = Fun.t
      and type Ty.t = Ty.t
 = struct
   module Term = Term
-  module Lit = Lit
   module Fun = Fun
   module Ty = Ty
 end
diff --git a/src/cc/Sidekick_cc.ml b/src/cc/Sidekick_cc.ml
index f66d5c94..2c5b5027 100644
--- a/src/cc/Sidekick_cc.ml
+++ b/src/cc/Sidekick_cc.ml
@@ -17,14 +17,14 @@ module Make(CC_A: ARG) = struct
   module A = CC_A.A
   type term = A.Term.t
   type term_state = A.Term.state
-  type lit = A.Lit.t
+  type lit = CC_A.Lit.t
   type fun_ = A.Fun.t
   type proof = A.Proof.t
   type actions = CC_A.Actions.t
 
   module T = A.Term
   module Fun = A.Fun
-  module Lit = A.Lit
+  module Lit = CC_A.Lit
 
   module Bits = CCBitField.Make()
   (* TODO: give theories the possibility to allocate new bits in nodes *)
diff --git a/src/core/Sidekick_core.ml b/src/core/Sidekick_core.ml
index 044b03eb..03867f7a 100644
--- a/src/core/Sidekick_core.ml
+++ b/src/core/Sidekick_core.ml
@@ -78,6 +78,8 @@ module type TERM = sig
     val bool : state -> bool -> t (* build true/false *)
     val as_bool : t -> bool option
 
+    val abs : state -> t -> t * bool
+
     val map_shallow : state -> (t -> t) -> t -> t
     (** Map function on immediate subterms *)
 
@@ -87,56 +89,37 @@ module type TERM = sig
   end
 end
 
-module type TERM_LIT = sig
+module type TERM_PROOF = sig
   include TERM
 
-  module Lit : sig
-    type t
-    val neg : t -> t
-    val equal : t -> t -> bool
-    val compare : t -> t -> int
-    val hash : t -> int
-    val pp : t Fmt.printer
-
-    val term : t -> Term.t
-    val sign : t -> bool
-    val abs : t -> t
-    val apply_sign : t -> bool -> t
-    val norm_sign : t -> t * bool
-    (** Invariant: if [u, sign = norm_sign t] then [apply_sign u sign = t] *)
-
-
-    val atom : Term.state -> ?sign:bool -> Term.t -> t
-  end
-end
-
-module type TERM_LIT_PROOF = sig
-  include TERM_LIT
-
   module Proof : sig
     type t
     val pp : t Fmt.printer
 
     val default : t
-    (* TODO: to give more details? or make this extensible?
-       or have a generative function for new proof cstors?
-    val cc_lemma : unit -> t
-       *)
   end
 end
 
 module type CC_ARG = sig
-  module A : TERM_LIT_PROOF
+  module A : TERM_PROOF
 
   val cc_view : A.Term.t -> (A.Fun.t, A.Term.t, A.Term.t Iter.t) CC_view.t
   (** View the term through the lens of the congruence closure *)
 
+  module Lit : sig
+    type t
+    val term : t -> A.Term.t
+    val sign : t -> bool
+    val neg : t -> t
+    val pp : t Fmt.printer
+  end
+
   module Actions : sig
     type t
 
-    val raise_conflict : t -> A.Lit.t list -> A.Proof.t -> 'a
+    val raise_conflict : t -> Lit.t list -> A.Proof.t -> 'a
 
-    val propagate : t -> A.Lit.t -> reason:(unit -> A.Lit.t list) -> A.Proof.t -> unit
+    val propagate : t -> Lit.t -> reason:(unit -> Lit.t list) -> A.Proof.t -> unit
   end
 end
 
@@ -146,7 +129,7 @@ module type CC_S = sig
   type term_state = A.Term.state
   type term = A.Term.t
   type fun_ = A.Fun.t
-  type lit = A.Lit.t
+  type lit = CC_A.Lit.t
   type proof = A.Proof.t
   type actions = CC_A.Actions.t
 
@@ -302,12 +285,11 @@ end
 
 (** A view of the solver from a theory's point of view *)
 module type SOLVER_INTERNAL = sig
-  module A : TERM_LIT_PROOF 
+  module A : TERM_PROOF 
   module CC_A : CC_ARG with module A = A
   module CC : CC_S with module CC_A = CC_A
 
   type ty = A.Ty.t
-  type lit = A.Lit.t
   type term = A.Term.t
   type term_state = A.Term.state
   type proof = A.Proof.t
@@ -324,6 +306,23 @@ module type SOLVER_INTERNAL = sig
   val cc : t -> CC.t
   (** Congruence closure for this solver *)
 
+  (** {3 Literals}
+
+      A literal is a (preprocessed) term along with its sign.
+      It is directly manipulated by the SAT solver.
+  *)
+  module Lit : sig
+    type t
+    val term : t -> term
+    val sign : t -> bool
+    val neg : t -> t
+
+    val equal : t -> t -> bool
+    val hash : t -> int
+    val pp : t Fmt.printer
+  end
+  type lit = Lit.t
+
   (** {3 Simplifiers} *)
 
   module Simplify : sig
@@ -440,7 +439,11 @@ module type SOLVER_INTERNAL = sig
       literals suitable for reasoning.
       Typically some clauses are also added to the solver. *)
 
-  type preprocess_hook = t -> add_clause:(lit list -> unit) -> term -> term option
+  type preprocess_hook =
+    t ->
+    mk_lit:(term -> lit) ->
+    add_clause:(lit list -> unit) ->
+    term -> term option
   (** Given a term, try to preprocess it. Return [None] if it didn't change.
       Can also add clauses to define new terms. *)
 
@@ -449,16 +452,18 @@ end
 
 (** Public view of the solver *)
 module type SOLVER = sig
-  module A : TERM_LIT_PROOF
+  module A : TERM_PROOF
   module CC_A : CC_ARG with module A = A
   module Solver_internal : SOLVER_INTERNAL with module A = A and module CC_A = CC_A
   (** Internal solver, available to theories.  *)
 
+  module Lit = Solver_internal.Lit
+
   type t
   type solver = t
   type term = A.Term.t
   type ty = A.Ty.t
-  type lit = A.Lit.t
+  type lit = Solver_internal.Lit.t
   type lemma = A.Proof.t
 
   (** {3 A theory}
@@ -583,10 +588,6 @@ module type SOLVER = sig
 
   val mk_atom_t : t -> ?sign:bool -> term -> Atom.t
 
-  val add_clause_lits : t -> lit IArray.t -> unit
-
-  val add_clause_lits_l : t -> lit list -> unit
-
   val add_clause : t -> Atom.t IArray.t -> unit
 
   val add_clause_l : t -> Atom.t list -> unit
diff --git a/src/msat-solver/Sidekick_msat_solver.ml b/src/msat-solver/Sidekick_msat_solver.ml
index 1f85faac..a29916f3 100644
--- a/src/msat-solver/Sidekick_msat_solver.ml
+++ b/src/msat-solver/Sidekick_msat_solver.ml
@@ -5,30 +5,71 @@ module Log = Msat.Log
 module IM = Util.Int_map
 
 module type ARG = sig
-  include Sidekick_core.TERM_LIT_PROOF
+  include Sidekick_core.TERM_PROOF
   val cc_view : Term.t -> (Fun.t, Term.t, Term.t Iter.t) Sidekick_core.CC_view.t
 end
 
 module type S = Sidekick_core.SOLVER
 
 module Make(A : ARG)
-  : S with module A = A
+(*   : S with module A = A *)
 = struct
   module A = A
   module T = A.Term
-  module Lit = A.Lit
   module Ty = A.Ty
-  type lit = Lit.t
   type term = T.t
   type ty = Ty.t
   type lemma = A.Proof.t
 
+  module Lit = struct
+    type t = {
+      lit_term: term;
+      lit_sign : bool
+    }
+
+    let[@inline] neg l = {l with lit_sign=not l.lit_sign}
+    let[@inline] sign t = t.lit_sign
+    let[@inline] term (t:t): term = t.lit_term
+
+    let[@inline] abs t: t = {t with lit_sign=true}
+
+    let make ~sign t = {lit_sign=sign; lit_term=t}
+
+    let atom tst ?(sign=true) (t:term) : t =
+      let t, sign' = T.abs tst t in
+      let sign = if not sign' then not sign else sign in
+      make ~sign t
+
+    let[@inline] as_atom (lit:t) = lit.lit_term, lit.lit_sign
+
+    let equal a b =
+      a.lit_sign = b.lit_sign &&
+      T.equal a.lit_term b.lit_term
+
+    let hash a =
+      let sign = a.lit_sign in
+      CCHash.combine3 2 (CCHash.bool sign) (T.hash a.lit_term)
+
+    let pp out l =
+      if l.lit_sign then T.pp out l.lit_term
+      else Format.fprintf out "(@[@<1>¬@ %a@])" T.pp l.lit_term
+
+    let print = pp
+
+    let apply_sign t s = if s then t else neg t
+    let norm_sign l = if l.lit_sign then l, true else neg l, false
+    let norm l = let l, sign = norm_sign l in l, if sign then Msat.Same_sign else Msat.Negated
+  end
+
+  type lit = Lit.t
+
   (* actions from msat *)
   type msat_acts = (Msat.void, Lit.t, Msat.void, A.Proof.t) Msat.acts
 
   (* the full argument to the congruence closure *)
   module CC_A = struct
     module A = A
+    module Lit = Lit
     let cc_view = A.cc_view
 
     module Actions = struct
@@ -49,6 +90,7 @@ module Make(A : ARG)
   module Solver_internal = struct
     module A = A
     module CC_A = CC_A
+    module Lit = Lit
     module CC = CC
     module N = CC.N
     type term = T.t
@@ -119,7 +161,12 @@ module Make(A : ARG)
       mutable on_partial_check: (t -> actions -> lit Iter.t -> unit) list;
       mutable on_final_check: (t -> actions -> lit Iter.t -> unit) list;
     }
-    and preprocess_hook = t -> add_clause:(lit list -> unit) -> term -> term option
+
+    and preprocess_hook =
+      t ->
+      mk_lit:(term -> lit) ->
+      add_clause:(lit list -> unit) ->
+      term -> term option
 
     type solver = t
 
@@ -159,6 +206,7 @@ module Make(A : ARG)
       acts.Msat.acts_add_clause ~keep lits A.Proof.default
 
     let preprocess_lit_ (self:t) ~add_clause (lit:lit) : lit =
+      let mk_lit t = Lit.atom self.tst t in
       (* compute and cache normal form of [t] *)
       let rec aux t =
         match T.Tbl.find self.preprocess_cache t with
@@ -174,7 +222,7 @@ module Make(A : ARG)
       and aux_rec t hooks = match hooks with
         | [] -> t
         | h :: hooks_tl ->
-          match h self ~add_clause t with
+          match h self ~mk_lit ~add_clause t with
           | None -> aux_rec t hooks_tl
           | Some u ->
             Log.debugf 30 
@@ -188,7 +236,7 @@ module Make(A : ARG)
         (fun k->k "(@[msat-solver.preprocess@ :lit %a@ :into %a@])" Lit.pp lit Lit.pp lit');
       lit'
 
-    let[@inline] mk_lit self acts ?sign t =
+    let mk_lit self acts ?sign t =
       let add_clause lits =
         Stat.incr self.count_preprocess_clause;
         add_sat_clause_ self acts ~keep:true lits
@@ -423,16 +471,18 @@ module Make(A : ARG)
          ignore (mk_atom_t_ self sub : Sat_solver.atom))
 
   let rec mk_atom_lit self lit : Atom.t =
-    let lit =
+    let lit = preprocess_lit_ self lit in
+    add_bool_subterms_ self (Lit.term lit);
+    Sat_solver.make_atom self.solver lit
+
+  and preprocess_lit_ self lit : Lit.t =
       Solver_internal.preprocess_lit_
         ~add_clause:(fun lits ->
             (* recursively add these sub-literals, so they're also properly processed *)
             Stat.incr self.si.count_preprocess_clause;
             let atoms = List.map (mk_atom_lit self) lits in
             Sat_solver.add_clause self.solver atoms A.Proof.default)
-        self.si lit in
-    add_bool_subterms_ self (Lit.term lit);
-    Sat_solver.make_atom self.solver lit
+        self.si lit
 
   let[@inline] mk_atom_t self ?sign t : Atom.t =
     let lit = Lit.atom (tst self) ?sign t in
@@ -500,13 +550,6 @@ module Make(A : ARG)
 
   let add_clause_l self c = add_clause self (IArray.of_list c)
 
-  let add_clause_lits (self:t) (c:Lit.t IArray.t) : unit =
-    let c = IArray.map (mk_atom_lit self) c in
-    add_clause self c
-
-  let add_clause_lits_l (self:t) (c:Lit.t list) : unit =
-    add_clause self (IArray.of_list_map (mk_atom_lit self) c)
-
   (* TODO: remove? use a special constant + micro theory instead?
   let[@inline] assume_distinct self l ~neq lit : unit =
     CC.assert_distinct (cc self) l lit ~neq
diff --git a/src/smtlib/Process.ml b/src/smtlib/Process.ml
index 71f30ca8..1287d5a0 100644
--- a/src/smtlib/Process.ml
+++ b/src/smtlib/Process.ml
@@ -406,6 +406,7 @@ end
 module Solver = Sidekick_msat_solver.Make(Solver_arg)
 
 module Check_cc = struct
+  module Lit = Solver.Lit
   module SI = Solver.Solver_internal
   module CC = Solver.Solver_internal.CC
   module MCC = Sidekick_mini_cc.Make(Solver_arg)
@@ -604,9 +605,9 @@ let process_stmt
       if pp_cnf then (
         Format.printf "(@[<hv1>assert@ %a@])@." Term.pp t
       );
-      let atom = Lit.atom tst t in
+      let atom = Solver.mk_atom_t solver t in
       CCOpt.iter (fun h -> Vec.push h [atom]) hyps;
-      Solver.add_clause_lits solver (IArray.singleton atom);
+      Solver.add_clause solver (IArray.singleton atom);
       E.return()
     | A.Goal (_, _) ->
       Error.errorf "cannot deal with goals yet"
diff --git a/src/smtlib/Process.mli b/src/smtlib/Process.mli
index 6d845728..9eb818f3 100644
--- a/src/smtlib/Process.mli
+++ b/src/smtlib/Process.mli
@@ -5,7 +5,6 @@ open Sidekick_base_term
 module Solver
   : Sidekick_msat_solver.S with type A.Term.t = Term.t
                             and type A.Term.state = Term.state
-                            and type A.Lit.t = Lit.t
                             and type A.Ty.t = Ty.t
 
 val th_bool : Solver.theory
@@ -24,7 +23,7 @@ module Check_cc : sig
 end
 
 val process_stmt :
-  ?hyps:Lit.t list Vec.t ->
+  ?hyps:Solver.Atom.t list Vec.t ->
   ?gc:bool ->
   ?restarts:bool ->
   ?pp_cnf:bool ->
diff --git a/src/th-bool-static/Sidekick_th_bool_static.ml b/src/th-bool-static/Sidekick_th_bool_static.ml
index 602ac914..e5ce0711 100644
--- a/src/th-bool-static/Sidekick_th_bool_static.ml
+++ b/src/th-bool-static/Sidekick_th_bool_static.ml
@@ -54,7 +54,7 @@ module Make(A : ARG) : S with module A = A = struct
   module A = A
   module Ty = A.S.A.Ty
   module T = A.S.A.Term
-  module Lit = A.S.A.Lit
+  module Lit = A.S.Lit
   module SI = A.S.Solver_internal
 
   type state = {
@@ -122,28 +122,28 @@ module Make(A : ARG) : S with module A = A = struct
     | B_atom _ -> None
 
   let fresh_term self ~pre ty = A.Gensym.fresh_term self.gensym ~pre ty
-  let fresh_lit (self:state) ~pre : Lit.t =
+  let fresh_lit (self:state) ~mk_lit ~pre : Lit.t =
     let t = fresh_term ~pre self Ty.bool in
-    Lit.atom self.tst t
+    mk_lit t
 
   (* TODO: polarity? *)
-  let cnf (self:state) (_solver:SI.t) ~add_clause (t:T.t) : T.t option =
+  let cnf (self:state) (_si:SI.t) ~mk_lit ~add_clause (t:T.t) : T.t option =
     let rec get_lit (t:T.t) : Lit.t =
       match A.view_as_bool t with
-      | B_bool b -> Lit.atom self.tst ~sign:b (T.bool self.tst true)
+      | B_bool b -> mk_lit (T.bool self.tst b)
       | B_not u ->
         let lit = get_lit u in
         Lit.neg lit
       | B_and l ->
         let subs = IArray.to_list_map get_lit l in
-        let proxy = fresh_lit ~pre:"and_" self in
+        let proxy = fresh_lit ~mk_lit ~pre:"and_" self in
         (* add clauses *)
         List.iter (fun u -> add_clause [Lit.neg proxy; u]) subs;
         add_clause (proxy :: List.map Lit.neg subs);
         proxy
       | B_or l ->
         let subs = IArray.to_list_map get_lit l in
-        let proxy = fresh_lit ~pre:"or_" self in
+        let proxy = fresh_lit ~mk_lit ~pre:"or_" self in
         (* add clauses *)
         List.iter (fun u -> add_clause [Lit.neg u; proxy]) subs;
         add_clause (Lit.neg proxy :: subs);
@@ -154,11 +154,11 @@ module Make(A : ARG) : S with module A = A = struct
           IArray.append (IArray.map (not_ self.tst) args) (IArray.singleton u) in
         get_lit t'
       | B_ite _ | B_eq _ ->
-        Lit.atom self.tst t
+        mk_lit t
       | B_equiv (a,b) ->
         let a = get_lit a in
         let b = get_lit b in
-        let proxy = fresh_lit ~pre:"equiv_" self in
+        let proxy = fresh_lit ~mk_lit ~pre:"equiv_" self in
         (* proxy => a<=> b,
            ¬proxy => a xor b *)
         add_clause [Lit.neg proxy; Lit.neg a; b];
@@ -166,7 +166,7 @@ module Make(A : ARG) : S with module A = A = struct
         add_clause [proxy; a; b];
         add_clause [proxy; Lit.neg a; Lit.neg b];
         proxy
-      | B_atom u -> Lit.atom self.tst u
+      | B_atom u -> mk_lit u
     in
     let lit = get_lit t in
     let u = Lit.term lit in