diff --git a/src/HOL/Tools/Meson/meson_clausify.ML b/src/HOL/Tools/Meson/meson_clausify.ML
--- a/src/HOL/Tools/Meson/meson_clausify.ML
+++ b/src/HOL/Tools/Meson/meson_clausify.ML
@@ -1,385 +1,385 @@
 (*  Title:      HOL/Tools/Meson/meson_clausify.ML
     Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
     Author:     Jasmin Blanchette, TU Muenchen
 
 Transformation of HOL theorems into CNF forms.
 *)
 
 signature MESON_CLAUSIFY =
 sig
   val new_skolem_var_prefix : string
   val new_nonskolem_var_prefix : string
   val is_zapped_var_name : string -> bool
   val is_quasi_lambda_free : term -> bool
   val introduce_combinators_in_cterm : Proof.context -> cterm -> thm
   val introduce_combinators_in_theorem : Proof.context -> thm -> thm
   val cluster_of_zapped_var_name : string -> (int * (int * int)) * bool
   val ss_only : thm list -> Proof.context -> Proof.context
   val cnf_axiom : Meson.simp_options -> Proof.context -> bool -> bool -> int -> thm
     -> (thm * term) option * thm list
 end;
 
 structure Meson_Clausify : MESON_CLAUSIFY =
 struct
 
 (* the extra "Meson" helps prevent clashes (FIXME) *)
 val new_skolem_var_prefix = "MesonSK"
 val new_nonskolem_var_prefix = "MesonV"
 
 fun is_zapped_var_name s =
   exists (fn prefix => String.isPrefix prefix s)
          [new_skolem_var_prefix, new_nonskolem_var_prefix]
 
 (**** Transformation of Elimination Rules into First-Order Formulas****)
 
 val cfalse = Thm.cterm_of \<^theory_context>\<open>HOL\<close> \<^term>\<open>False\<close>;
 val ctp_false = Thm.cterm_of \<^theory_context>\<open>HOL\<close> (HOLogic.mk_Trueprop \<^term>\<open>False\<close>);
 
 (* Converts an elim-rule into an equivalent theorem that does not have the
    predicate variable. Leaves other theorems unchanged. We simply instantiate
    the conclusion variable to False. (Cf. "transform_elim_prop" in
    "Sledgehammer_Util".) *)
 fun transform_elim_theorem th =
   (case Thm.concl_of th of    (*conclusion variable*)
     \<^Const_>\<open>Trueprop for \<open>Var (v as (_, \<^Type>\<open>bool\<close>))\<close>\<close> =>
       Thm.instantiate (TVars.empty, Vars.make [(v, cfalse)]) th
   | Var (v as (_, \<^Type>\<open>prop\<close>)) =>
       Thm.instantiate (TVars.empty, Vars.make [(v, ctp_false)]) th
   | _ => th)
 
 
 (**** SKOLEMIZATION BY INFERENCE (lcp) ****)
 
 fun mk_old_skolem_term_wrapper t =
   let val T = fastype_of t
   in \<^Const>\<open>Meson.skolem T for t\<close> end
 
 fun beta_eta_in_abs_body (Abs (s, T, t')) = Abs (s, T, beta_eta_in_abs_body t')
   | beta_eta_in_abs_body t = Envir.beta_eta_contract t
 
 (*Traverse a theorem, accumulating Skolem function definitions.*)
 fun old_skolem_defs th =
   let
     fun dec_sko \<^Const_>\<open>Ex _ for \<open>body as Abs (_, T, p)\<close>\<close> rhss =
         (*Existential: declare a Skolem function, then insert into body and continue*)
         let
           val args = Misc_Legacy.term_frees body
           (* Forms a lambda-abstraction over the formal parameters *)
           val rhs =
             fold_rev (absfree o dest_Free) args
               (HOLogic.choice_const T $ beta_eta_in_abs_body body)
             |> mk_old_skolem_term_wrapper
           val comb = list_comb (rhs, args)
         in dec_sko (subst_bound (comb, p)) (rhs :: rhss) end
       | dec_sko \<^Const_>\<open>All _ for \<open>Abs abs\<close>\<close> rhss = dec_sko (#2 (Term.dest_abs abs)) rhss
       | dec_sko \<^Const_>\<open>conj for p q\<close> rhss = rhss |> dec_sko p |> dec_sko q
       | dec_sko \<^Const_>\<open>disj for p q\<close> rhss = rhss |> dec_sko p |> dec_sko q
       | dec_sko \<^Const_>\<open>Trueprop for p\<close> rhss = dec_sko p rhss
       | dec_sko _ rhss = rhss
   in  dec_sko (Thm.prop_of th) []  end;
 
 
 (**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
 
 fun is_quasi_lambda_free \<^Const_>\<open>Meson.skolem _ for _\<close> = true
   | is_quasi_lambda_free (t1 $ t2) =
     is_quasi_lambda_free t1 andalso is_quasi_lambda_free t2
   | is_quasi_lambda_free (Abs _) = false
   | is_quasi_lambda_free _ = true
 
 fun abstract ctxt ct =
   let
       val Abs (_, _, body) = Thm.term_of ct
       val (x, cbody) = Thm.dest_abs ct
       val (A, cbodyT) = Thm.dest_funT (Thm.ctyp_of_cterm ct)
       fun makeK () = Thm.instantiate' [SOME A, SOME cbodyT] [SOME cbody] @{thm abs_K}
   in
       case body of
           Const _ => makeK()
         | Free _ => makeK()
         | Var _ => makeK()  (*though Var isn't expected*)
         | Bound 0 => Thm.instantiate' [SOME A] [] @{thm abs_I} (*identity: I*)
         | rator$rand =>
             if Term.is_dependent rator then (*C or S*)
                if Term.is_dependent rand then (*S*)
                  let val crator = Thm.lambda x (Thm.dest_fun cbody)
                      val crand = Thm.lambda x (Thm.dest_arg cbody)
                      val (C, B) = Thm.dest_funT (Thm.dest_ctyp1 (Thm.ctyp_of_cterm crator))
                      val abs_S' = @{thm abs_S}
                        |> instantiate'_normalize [SOME A, SOME B, SOME C] [SOME crator, SOME crand]
                      val (_,rhs) = Thm.dest_equals (Thm.cprop_of abs_S')
                  in
                    Thm.transitive abs_S' (Conv.binop_conv (abstract ctxt) rhs)
                  end
                else (*C*)
                  let val crator = Thm.lambda x (Thm.dest_fun cbody)
                      val crand = Thm.dest_arg cbody
                      val (C, B) = Thm.dest_funT (Thm.dest_ctyp1 (Thm.ctyp_of_cterm crator))
                      val abs_C' = @{thm abs_C}
                        |> instantiate'_normalize [SOME A, SOME B, SOME C] [SOME crator, SOME crand]
                      val (_,rhs) = Thm.dest_equals (Thm.cprop_of abs_C')
                  in
                    Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv (abstract ctxt)) rhs)
                  end
             else if Term.is_dependent rand then (*B or eta*)
                if rand = Bound 0 then Thm.eta_conversion ct
                else (*B*)
                  let val crator = Thm.dest_fun cbody
                      val crand = Thm.lambda x (Thm.dest_arg cbody)
                      val (C, B) = Thm.dest_funT (Thm.ctyp_of_cterm crator)
                      val abs_B' = @{thm abs_B}
                       |> instantiate'_normalize [SOME A, SOME B, SOME C] [SOME crator, SOME crand]
                      val (_,rhs) = Thm.dest_equals (Thm.cprop_of abs_B')
                  in Thm.transitive abs_B' (Conv.arg_conv (abstract ctxt) rhs) end
             else makeK ()
         | _ => raise Fail "abstract: Bad term"
   end;
 
-(* Traverse a theorem, remplacing lambda-abstractions with combinators. *)
+(* Traverse a theorem, replacing lambda-abstractions with combinators. *)
 fun introduce_combinators_in_cterm ctxt ct =
   if is_quasi_lambda_free (Thm.term_of ct) then
     Thm.reflexive ct
   else case Thm.term_of ct of
     Abs _ =>
     let
       val (cv, cta) = Thm.dest_abs ct
       val (v, _) = dest_Free (Thm.term_of cv)
       val u_th = introduce_combinators_in_cterm ctxt cta
       val cu = Thm.rhs_of u_th
       val comb_eq = abstract ctxt (Thm.lambda cv cu)
     in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end
   | _ $ _ =>
     let val (ct1, ct2) = Thm.dest_comb ct in
         Thm.combination (introduce_combinators_in_cterm ctxt ct1)
                         (introduce_combinators_in_cterm ctxt ct2)
     end
 
 fun introduce_combinators_in_theorem ctxt th =
   if is_quasi_lambda_free (Thm.prop_of th) then
     th
   else
     let
       val th = Drule.eta_contraction_rule th
       val eqth = introduce_combinators_in_cterm ctxt (Thm.cprop_of th)
     in Thm.equal_elim eqth th end
     handle THM (msg, _, _) =>
            (warning ("Error in the combinator translation of " ^ Thm.string_of_thm ctxt th ^
               "\nException message: " ^ msg);
             (* A type variable of sort "{}" will make "abstraction" fail. *)
             TrueI)
 
 (*cterms are used throughout for efficiency*)
 val cTrueprop = Thm.cterm_of \<^theory_context>\<open>HOL\<close> HOLogic.Trueprop;
 
 (*Given an abstraction over n variables, replace the bound variables by free
   ones. Return the body, along with the list of free variables.*)
 fun c_variant_abs_multi (ct0, vars) =
       let val (cv,ct) = Thm.dest_abs ct0
       in  c_variant_abs_multi (ct, cv::vars)  end
       handle CTERM _ => (ct0, rev vars);
 
 (* Given the definition of a Skolem function, return a theorem to replace
    an existential formula by a use of that function.
    Example: "\<exists>x. x \<in> A \<and> x \<notin> B \<Longrightarrow> sko A B \<in> A \<and> sko A B \<notin> B" *)
 fun old_skolem_theorem_of_def ctxt rhs0 =
   let
     val rhs = rhs0 |> Type.legacy_freeze_thaw |> #1 |> Thm.cterm_of ctxt
     val rhs' = rhs |> Thm.dest_comb |> snd
     val (ch, frees) = c_variant_abs_multi (rhs', [])
     val (hilbert, cabs) = ch |> Thm.dest_comb |>> Thm.term_of
     val T =
       case hilbert of
         Const (_, Type (\<^type_name>\<open>fun\<close>, [_, T])) => T
       | _ => raise TERM ("old_skolem_theorem_of_def: expected \"Eps\"", [hilbert])
     val cex = Thm.cterm_of ctxt (HOLogic.exists_const T)
     val ex_tm = Thm.apply cTrueprop (Thm.apply cex cabs)
     val conc =
       Drule.list_comb (rhs, frees)
       |> Drule.beta_conv cabs |> Thm.apply cTrueprop
     fun tacf [prem] =
       rewrite_goals_tac ctxt @{thms skolem_def [abs_def]}
       THEN resolve_tac ctxt
         [(prem |> rewrite_rule ctxt @{thms skolem_def [abs_def]})
           RS Global_Theory.get_thm (Proof_Context.theory_of ctxt) "Hilbert_Choice.someI_ex"] 1
   in
     Goal.prove_internal ctxt [ex_tm] conc tacf
     |> forall_intr_list frees
     |> Thm.forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
     |> Thm.varifyT_global
   end
 
 fun to_definitional_cnf_with_quantifiers ctxt th =
   let
     val eqth = CNF.make_cnfx_thm ctxt (HOLogic.dest_Trueprop (Thm.prop_of th))
     val eqth = eqth RS @{thm eq_reflection}
     val eqth = eqth RS @{thm TruepropI}
   in Thm.equal_elim eqth th end
 
 fun zapped_var_name ((ax_no, cluster_no), skolem) index_no s =
   (if skolem then new_skolem_var_prefix else new_nonskolem_var_prefix) ^
   "_" ^ string_of_int ax_no ^ "_" ^ string_of_int cluster_no ^ "_" ^
   string_of_int index_no ^ "_" ^ Name.desymbolize (SOME false) s
 
 fun cluster_of_zapped_var_name s =
   let val get_int = the o Int.fromString o nth (space_explode "_" s) in
     ((get_int 1, (get_int 2, get_int 3)),
      String.isPrefix new_skolem_var_prefix s)
   end
 
 fun rename_bound_vars_to_be_zapped ax_no =
   let
     fun aux (cluster as (cluster_no, cluster_skolem)) index_no pos t =
       case t of
         (t1 as Const (s, _)) $ Abs (s', T, t') =>
         if s = \<^const_name>\<open>Pure.all\<close> orelse s = \<^const_name>\<open>All\<close> orelse
            s = \<^const_name>\<open>Ex\<close> then
           let
             val skolem = (pos = (s = \<^const_name>\<open>Ex\<close>))
             val (cluster, index_no) =
               if skolem = cluster_skolem then (cluster, index_no)
               else ((cluster_no ||> cluster_skolem ? Integer.add 1, skolem), 0)
             val s' = zapped_var_name cluster index_no s'
           in t1 $ Abs (s', T, aux cluster (index_no + 1) pos t') end
         else
           t
       | (t1 as Const (s, _)) $ t2 $ t3 =>
         if s = \<^const_name>\<open>Pure.imp\<close> orelse s = \<^const_name>\<open>HOL.implies\<close> then
           t1 $ aux cluster index_no (not pos) t2 $ aux cluster index_no pos t3
         else if s = \<^const_name>\<open>HOL.conj\<close> orelse
                 s = \<^const_name>\<open>HOL.disj\<close> then
           t1 $ aux cluster index_no pos t2 $ aux cluster index_no pos t3
         else
           t
       | (t1 as Const (s, _)) $ t2 =>
         if s = \<^const_name>\<open>Trueprop\<close> then
           t1 $ aux cluster index_no pos t2
         else if s = \<^const_name>\<open>Not\<close> then
           t1 $ aux cluster index_no (not pos) t2
         else
           t
       | _ => t
   in aux ((ax_no, 0), true) 0 true end
 
 fun zap pos ct =
   ct
   |> (case Thm.term_of ct of
         Const (s, _) $ Abs (s', _, _) =>
         if s = \<^const_name>\<open>Pure.all\<close> orelse s = \<^const_name>\<open>All\<close> orelse
            s = \<^const_name>\<open>Ex\<close> then
           Thm.dest_comb #> snd #> Thm.dest_abs_name s' #> snd #> zap pos
         else
           Conv.all_conv
       | Const (s, _) $ _ $ _ =>
         if s = \<^const_name>\<open>Pure.imp\<close> orelse s = \<^const_name>\<open>implies\<close> then
           Conv.combination_conv (Conv.arg_conv (zap (not pos))) (zap pos)
         else if s = \<^const_name>\<open>conj\<close> orelse s = \<^const_name>\<open>disj\<close> then
           Conv.combination_conv (Conv.arg_conv (zap pos)) (zap pos)
         else
           Conv.all_conv
       | Const (s, _) $ _ =>
         if s = \<^const_name>\<open>Trueprop\<close> then Conv.arg_conv (zap pos)
         else if s = \<^const_name>\<open>Not\<close> then Conv.arg_conv (zap (not pos))
         else Conv.all_conv
       | _ => Conv.all_conv)
 
 fun ss_only ths ctxt = clear_simpset (put_simpset HOL_basic_ss ctxt) addsimps ths
 
 val cheat_choice =
   \<^prop>\<open>\<forall>x. \<exists>y. Q x y \<Longrightarrow> \<exists>f. \<forall>x. Q x (f x)\<close>
   |> Logic.varify_global
   |> Skip_Proof.make_thm \<^theory>
 
 (* Converts an Isabelle theorem into NNF. *)
 fun nnf_axiom simp_options choice_ths new_skolem ax_no th ctxt =
   let
     val thy = Proof_Context.theory_of ctxt
     val th =
       th |> transform_elim_theorem
          |> zero_var_indexes
          |> new_skolem ? Thm.forall_intr_vars
     val (th, ctxt) = Variable.import true [th] ctxt |>> snd |>> the_single
     val th = th |> Conv.fconv_rule (Object_Logic.atomize ctxt)
                 |> Meson.cong_extensionalize_thm ctxt
                 |> Meson.abs_extensionalize_thm ctxt
                 |> Meson.make_nnf simp_options ctxt
   in
     if new_skolem then
       let
         fun skolemize choice_ths =
           Meson.skolemize_with_choice_theorems simp_options ctxt choice_ths
           #> simplify (ss_only @{thms all_simps[symmetric]} ctxt)
         val no_choice = null choice_ths
         val pull_out =
           if no_choice then
             simplify (ss_only @{thms all_simps[symmetric] ex_simps[symmetric]} ctxt)
           else
             skolemize choice_ths
         val discharger_th = th |> pull_out
         val discharger_th =
           discharger_th |> Meson.has_too_many_clauses ctxt (Thm.concl_of discharger_th)
                            ? (to_definitional_cnf_with_quantifiers ctxt
                               #> pull_out)
         val zapped_th =
           discharger_th |> Thm.prop_of |> rename_bound_vars_to_be_zapped ax_no
           |> (if no_choice then
                 Skip_Proof.make_thm thy #> skolemize [cheat_choice] #> Thm.cprop_of
               else
                 Thm.cterm_of ctxt)
           |> zap true
         val fixes =
           [] |> Term.add_free_names (Thm.prop_of zapped_th)
              |> filter is_zapped_var_name
         val ctxt' = ctxt |> Variable.add_fixes_direct fixes
         val fully_skolemized_t =
           zapped_th |> singleton (Variable.export ctxt' ctxt)
                     |> Thm.cprop_of |> Thm.dest_equals |> snd |> Thm.term_of
       in
         if exists_subterm (fn Var ((s, _), _) =>
                               String.isPrefix new_skolem_var_prefix s
                             | _ => false) fully_skolemized_t then
           let
             val (fully_skolemized_ct, ctxt) =
               yield_singleton (Variable.import_terms true) fully_skolemized_t ctxt
               |>> Thm.cterm_of ctxt
           in
             (SOME (discharger_th, fully_skolemized_ct),
              (Thm.assume fully_skolemized_ct, ctxt))
           end
        else
          (NONE, (th, ctxt))
       end
     else
       (NONE, (th |> Meson.has_too_many_clauses ctxt (Thm.concl_of th)
                     ? to_definitional_cnf_with_quantifiers ctxt, ctxt))
   end
 
 (* Convert a theorem to CNF, with additional premises due to skolemization. *)
 fun cnf_axiom simp_options ctxt0 new_skolem combinators ax_no th =
   let
     val choice_ths = Meson.choice_theorems (Proof_Context.theory_of ctxt0)
     val (opt, (nnf_th, ctxt1)) =
       nnf_axiom simp_options choice_ths new_skolem ax_no th ctxt0
     fun clausify th =
       Meson.make_cnf
        (if new_skolem orelse null choice_ths then []
         else map (old_skolem_theorem_of_def ctxt1) (old_skolem_defs th))
        th ctxt1
     val (cnf_ths, ctxt2) = clausify nnf_th
     fun intr_imp ct th =
       Thm.instantiate
         (TVars.empty, Vars.make [(\<^var>\<open>?i::nat\<close>, Thm.cterm_of ctxt2 (HOLogic.mk_nat ax_no))])
         (zero_var_indexes @{thm skolem_COMBK_D})
       RS Thm.implies_intr ct th
   in
     (opt |> Option.map (I #>> singleton (Variable.export ctxt2 ctxt0)
                         ##> (Thm.term_of #> HOLogic.dest_Trueprop
                              #> singleton (Variable.export_terms ctxt2 ctxt0))),
      cnf_ths |> map (combinators ? introduce_combinators_in_theorem ctxt2
                      #> (case opt of SOME (_, ct) => intr_imp ct | NONE => I))
              |> Variable.export ctxt2 ctxt0
              |> Meson.finish_cnf
              |> map (Thm.close_derivation \<^here>))
   end
   handle THM _ => (NONE, [])
 
 end;