diff --git a/src/th-distinct/Sidekick_th_distinct.ml b/src/th-distinct/Sidekick_th_distinct.ml
new file mode 100644
index 00000000..91858e47
--- /dev/null
+++ b/src/th-distinct/Sidekick_th_distinct.ml
@@ -0,0 +1,206 @@
+
+module Term = Sidekick_smt.Term
+module Theory = Sidekick_smt.Theory
+
+module type ARG = sig
+  module T : sig
+    type t
+    type state
+    val pp : t Fmt.printer
+    val equal : t -> t -> bool
+    val hash : t -> int
+    val as_distinct : t -> t Sequence.t option
+    val mk_eq : state -> t -> t -> t
+  end
+  module Lit : sig
+    type t
+    val term : t -> T.t
+    val neg : t -> t
+    val sign : t -> bool
+    val compare : t -> t -> int
+    val atom : T.t -> t
+    val pp : t Fmt.printer
+  end
+end
+  
+module type S = sig
+  type term
+  type term_state
+  type lit
+
+  type data
+  val key : (term, lit, data) Sidekick_cc.Key.t
+  val th : Sidekick_smt.Theory.t
+end
+
+module Make(A : ARG with type Lit.t = Sidekick_smt.Lit.t
+                     and type T.t = Sidekick_smt.Term.t
+                     and type T.state = Sidekick_smt.Term.state) = struct
+  module T = A.T
+  module Lit = A.Lit
+  module IM = CCMap.Make(Lit)
+
+  type term = T.t
+  type lit = A.Lit.t
+  type data = term IM.t (* "distinct" lit -> term appearing under it*)
+
+  let key : (term,lit,data) Sidekick_cc.Key.t =
+    let merge m1 m2 =
+      IM.merge_safe m1 m2
+        ~f:(fun _ pair -> match pair with
+            | `Left x | `Right x -> Some x
+            | `Both (x,_) -> Some x)
+    and eq = IM.equal T.equal
+    and pp out m =
+      Fmt.fprintf out
+        "{@[%a@]}" Fmt.(seq ~sep:(return ",@ ") @@ pair Lit.pp T.pp) (IM.to_seq m)
+    in
+    Sidekick_cc.Key.create
+      ~pp
+      ~name:"distinct"
+      ~merge ~eq ()
+
+  (* micro theory *)
+  module Micro(CC : Sidekick_cc.Congruence_closure.S
+               with type term = T.t
+                and type lit = Lit.t
+                and module Key = Sidekick_cc.Key) = struct
+    exception E_exit
+
+    let on_merge cc n1 m1 n2 m2 expl12 =
+      try
+        let _i =
+          IM.merge
+            (fun lit o1 o2 ->
+               match o1, o2 with
+               | Some t1, Some t2 ->
+                 (* conflict! two terms under the same "distinct" [lit]
+                    are merged, where [lit = distinct(t1,t2,…)].
+                    The conflict is:
+                    [lit, t1=n1, t2=n2, expl-merge(n1,n2) ==> false]
+                 *)
+                 assert (not @@ T.equal t1 t2);
+                 let expl = CC.Expl.mk_list
+                     [expl12;
+                      CC.Expl.mk_lit lit;
+                      CC.Expl.mk_merge n1 (CC.Theory.add_term cc t1);
+                      CC.Expl.mk_merge n2 (CC.Theory.add_term cc t2);
+                     ] in
+                 CC.Theory.raise_conflict cc expl;
+                 raise_notrace E_exit
+               | _ -> None)
+            m1 m2
+        in
+        ()
+      with E_exit -> ()
+
+    let on_new_term _ _ = None
+
+    let m_th =
+      CC.Theory.make ~key ~on_merge ~on_new_term ()
+  end
+
+  module T_tbl = CCHashtbl.Make(T)
+  type st = {
+    tst: T.state;
+    expanded: unit T_tbl.t; (* negative "distinct" that have been case-split on *)
+  }
+
+  let create tst : st = { expanded=T_tbl.create 12; tst; }
+
+  let pp_c out c = Fmt.fprintf out "(@[<hv>%a@])" (Util.pp_list Lit.pp) c
+
+  module CC = Sidekick_smt.CC
+
+  let process_lit (st:st) (acts:Theory.actions) (lit:Lit.t) (lit_t:term) (subs:term Sequence.t) : unit =
+    let (module A) = acts in
+    Log.debugf 5 (fun k->k "(@[th_distinct.process@ %a@])" Lit.pp lit);
+    let add_axiom c = A.add_persistent_axiom c in
+    let cc = A.cc in
+    if Lit.sign lit then (
+      (* assert [distinct subs], so we update the node of each [t in subs]
+         with [lit] *)
+      (* FIXME: detect if some subs are already equal *)
+      subs
+        (fun sub ->
+          let n = CC.Theory.add_term cc sub in
+          CC.Theory.add_data cc n key (IM.singleton lit sub));
+    ) else if not @@ T_tbl.mem st.expanded lit_t then (
+      (* add clause [distinct t1…tn ∨ ∨_{i,j>i} t_i=j] *)
+      T_tbl.add st.expanded lit_t ();
+      let l = Sequence.to_list subs in
+      let c =
+        Sequence.diagonal_l l
+        |> Sequence.map (fun (t,u) -> Lit.atom @@ T.mk_eq st.tst t u)
+        |> Sequence.to_rev_list
+      in
+      let c = Lit.neg lit :: c in
+      Log.debugf 5 (fun k->k "(@[tseitin.distinct.case-split@ %a@])" pp_c c);
+      add_axiom c
+    )
+
+  let partial_check st (acts:Theory.actions) lits : unit =
+    lits
+      (fun lit ->
+         let t = Lit.term lit in
+         match T.as_distinct t with
+         | None -> ()
+         | Some subs -> process_lit st acts lit t subs)
+
+  let th =
+    Sidekick_smt.Theory.make
+      ~name:"distinct"
+      ~partial_check
+      ~final_check:(fun _ _ _ -> ())
+      ~create ()
+end
+
+module T = struct
+  open Sidekick_smt
+  open Sidekick_smt.Solver_types
+  module T = Term
+
+  type t = Term.t
+  type terms = t IArray.t
+  let compare = Term.compare
+  let to_seq = IArray.to_seq
+
+  let id_distinct = ID.make "distinct"
+
+  let relevant _id _ _ = true
+  let get_ty _ _ = Ty.prop
+  let abs ~self _a = self, true
+
+  let as_distinct t : _ option =
+    match T.view t with
+    | T.App_cst ({cst_id;_}, args) when ID.equal cst_id id_distinct ->
+      Some (IArray.to_seq args)
+    | _ -> None
+
+  let eval args =
+    let module Value = Sidekick_smt.Value in
+    if
+      Sequence.diagonal (IArray.to_seq args)
+      |> Sequence.for_all (fun (x,y) -> not @@ Value.equal x y)
+    then Value.true_
+    else Value.false_
+
+  let c_distinct =
+    {cst_id=id_distinct;
+     cst_view=Cst_def {
+         pp=None; abs; ty=get_ty; relevant; do_cc=true; eval; }; }
+
+  let distinct st a =
+    if IArray.length a <= 1
+    then T.true_ st
+    else T.app_cst st c_distinct a
+
+  let distinct_l st = function
+    | [] | [_] -> T.true_ st
+    | xs -> distinct st (IArray.of_list xs)
+end
+
+let distinct = T.distinct
+let distinct_l = T.distinct_l
+
+include Make(T)
diff --git a/src/th-distinct/Sidekick_th_distinct.mli b/src/th-distinct/Sidekick_th_distinct.mli
new file mode 100644
index 00000000..4ce5b68a
--- /dev/null
+++ b/src/th-distinct/Sidekick_th_distinct.mli
@@ -0,0 +1,53 @@
+
+(** {1 Theory of "distinct"}
+
+    This is an extension of the congruence closure that handles
+    "distinct" efficiently.
+  *)
+
+module Term = Sidekick_smt.Term
+
+module type ARG = sig
+  module T : sig
+    type t
+    type state
+    val pp : t Fmt.printer
+    val equal : t -> t -> bool
+    val hash : t -> int
+    val as_distinct : t -> t Sequence.t option
+    val mk_eq : state -> t -> t -> t
+  end
+  module Lit : sig
+    type t
+    val term : t -> T.t
+    val neg : t -> t
+    val sign : t -> bool
+    val compare : t -> t -> int
+    val atom : T.t -> t
+    val pp : t Fmt.printer
+  end
+end
+  
+module type S = sig
+  type term
+  type term_state
+  type lit
+
+  type data
+  val key : (term, lit, data) Sidekick_cc.Key.t
+  val th : Sidekick_smt.Theory.t
+end
+
+(* TODO: generalize theories *)
+module Make(A : ARG with type T.t = Sidekick_smt.Term.t
+              and type T.state = Sidekick_smt.Term.state
+              and type Lit.t = Sidekick_smt.Lit.t) :
+  S with type term = A.T.t
+     and type lit = A.Lit.t
+     and type term_state = A.T.state
+
+val distinct : Term.state -> Term.t IArray.t -> Term.t
+val distinct_l : Term.state -> Term.t list -> Term.t
+
+(** Default instance *)
+include S with type term = Term.t and type lit = Sidekick_smt.Lit.t
diff --git a/src/th-distinct/dune b/src/th-distinct/dune
new file mode 100644
index 00000000..57fcb854
--- /dev/null
+++ b/src/th-distinct/dune
@@ -0,0 +1,7 @@
+
+(library
+  (name Sidekick_th_distinct)
+  (public_name sidekick.smt.th-distinct)
+  (libraries containers sidekick.smt)
+  (flags :standard -open Sidekick_util))
+