diff --git a/src/arith/lra/Sidekick_arith_lra.ml b/src/arith/lra/Sidekick_arith_lra.ml
index 98d69326..85946fb4 100644
--- a/src/arith/lra/Sidekick_arith_lra.ml
+++ b/src/arith/lra/Sidekick_arith_lra.ml
@@ -82,7 +82,7 @@ module Make(A : ARG) : S with module A = A = struct
     neq_encoded: unit T.Tbl.t;
     (* if [a != b] asserted and not in this table, add clause [a = b \/ a<b \/ a>b] *)
     mutable t_defs: (T.t * LE.t) list; (* term definitions *)
-    pred_defs: (pred * LE.t * LE.t) T.Tbl.t; (* predicate definitions *)
+    pred_defs: (pred * LE.t * LE.t * T.t * T.t) T.Tbl.t; (* predicate definitions *)
   }
 
   let create tst : state =
@@ -178,7 +178,7 @@ module Make(A : ARG) : S with module A = A = struct
       let l1 = as_linexp ~f:recurse t1 in
       let l2 = as_linexp ~f:recurse t2 in
       let proxy = fresh_term self ~pre:"_pred_lra_" Ty.bool in
-      T.Tbl.add self.pred_defs proxy (pred, l1, l2);
+      T.Tbl.add self.pred_defs proxy (pred, l1, l2, t1, t2);
       Log.debugf 5 (fun k->k"@[<hv2>lra.preprocess.step %a@ :into %a@ :def %a@]"
                        T.pp t T.pp proxy pp_pred_def (pred,l1,l2));
       Some proxy
@@ -191,41 +191,59 @@ module Make(A : ARG) : S with module A = A = struct
       Some proxy
     | LRA_const _ | LRA_other _ -> None
 
-  (* partial check: just ensure [a != b] triggers the clause
+  (* ensure that [a != b] triggers the clause
      [a=b \/ a<b \/ a>b] *)
-  let partial_check_ (self:state) si (acts:SI.actions) (trail:_ Iter.t) : unit =
+  let encode_neq self si acts trail : unit =
     let tst = self.tst in
     begin
       trail
-      |> Iter.filter (fun lit -> not (Lit.sign lit))
       |> Iter.filter_map
         (fun lit ->
            let t = Lit.term lit in
-           match A.view_as_lra t with
-           | LRA_pred (Eq, a, b) when not (T.Tbl.mem self.neq_encoded t) ->
-             Some (lit, a,b)
-           | _ -> None)
+           Log.debugf 50 (fun k->k "@[lra: check lit %a@ :t %a@ :sign %B@]"
+                             Lit.pp lit T.pp t (Lit.sign lit));
+           begin match T.Tbl.find self.pred_defs t with
+             | (pred, _, _, ta, tb) ->
+               let pred = if Lit.sign lit then pred else FM.Pred.neg pred in
+               Log.debugf 50 (fun k->k "pred = `%s`" (FM.Pred.to_string pred));
+               if pred = Neq && not (T.Tbl.mem self.neq_encoded t) then (
+                 Some (lit, ta, tb)
+               ) else None
+             | exception Not_found ->
+               begin match A.view_as_lra t with
+                 | LRA_pred (Neq, a, b) when not (T.Tbl.mem self.neq_encoded t) ->
+                   Some (lit, a, b)
+                 | _ -> None
+               end
+           end)
       |> Iter.iter
         (fun (lit,a,b) ->
+           Log.debugf 50 (fun k->k "encode neq in %a" Lit.pp lit);
            let c = [
-             Lit.abs lit;
+             Lit.neg lit;
              SI.mk_lit si acts (A.mk_lra tst (LRA_pred (Lt, a, b)));
              SI.mk_lit si acts (A.mk_lra tst (LRA_pred (Lt, b, a)));
            ] in
            SI.add_clause_permanent si acts c;
-           T.Tbl.add self.neq_encoded (Lit.term lit) ();
+           T.Tbl.add self.neq_encoded (Lit.term (Lit.abs lit)) ();
         )
     end
 
+  let dedup_lits lits : _ list =
+    let module LTbl = CCHashtbl.Make(Lit) in
+    let tbl = LTbl.create 16 in
+    List.iter (fun l -> LTbl.replace tbl l ()) lits;
+    LTbl.keys_list tbl
+
   let final_check_ (self:state) si (acts:SI.actions) (trail:_ Iter.t) : unit =
     Log.debug 5 "(th-lra.final-check)";
+    encode_neq self si acts trail;
     let fm = FM_A.create() in
     (* first, add definitions *)
     begin
       List.iter
         (fun (t,le) ->
            let open LE.Infix in
-           let le = le - LE.var t in
            let c = FM_A.Constr.mk ?tag:None Eq (LE.var t) le in
            FM_A.assert_c fm c)
         self.t_defs
@@ -239,7 +257,7 @@ module Make(A : ARG) : S with module A = A = struct
            let t = Lit.term lit in
            begin match T.Tbl.find self.pred_defs t with
              | exception Not_found -> ()
-             | (pred, a, b) ->
+             | (pred, a, b, _, _) ->
                let pred = if sign then pred else FM.Pred.neg pred in
                if pred = Neq then (
                  Log.debugf 50 (fun k->k "skip neq in %a" T.pp t);
@@ -259,7 +277,9 @@ module Make(A : ARG) : S with module A = A = struct
            unsat core translates directly into a conflict clause *)
         Log.debugf 5 (fun k->k"lra: solver returns UNSAT@ with cert %a"
                          (Fmt.Dump.list Lit.pp) lits);
-        let confl = List.rev_map Lit.neg lits in
+        let confl =
+          List.rev_map Lit.neg lits |> dedup_lits
+        in
         (* TODO: produce and store a proper LRA resolution proof *)
         SI.raise_conflict si acts confl SI.P.default
     end;
@@ -270,7 +290,6 @@ module Make(A : ARG) : S with module A = A = struct
     let st = create (SI.tst si) in
     (* TODO    SI.add_simplifier si (simplify st); *)
     SI.add_preprocess si (preproc_lra st);
-    SI.on_partial_check si (partial_check_ st);
     SI.on_final_check si (final_check_ st);
     (*     SI.add_preprocess si (cnf st); *)
     (* TODO: theory combination *)