(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_fol_clause.ML

     Author:     Jia Meng, Cambridge University Computer Laboratory

 Storing/printing FOL clauses and arity clauses.  Typed equality is

 treated differently.

 FIXME: combine with res_hol_clause!

 *)

 signature SLEDGEHAMMER_FOL_CLAUSE =

 sig

   val schematic_var_prefix: string

   val fixed_var_prefix: string

   val tvar_prefix: string

   val tfree_prefix: string

   val clause_prefix: string

   val const_prefix: string

   val tconst_prefix: string

   val class_prefix: string

   val union_all: ''a list list -> ''a list

   val const_trans_table: string Symtab.table

   val type_const_trans_table: string Symtab.table

   val ascii_of: string -> string

   val undo_ascii_of: string -> string

   val paren_pack : string list -> string

   val make_schematic_var : string * int -> string

   val make_fixed_var : string -> string

   val make_schematic_type_var : string * int -> string

   val make_fixed_type_var : string -> string

   val make_fixed_const : bool -> string -> string

   val make_fixed_type_const : bool -> string -> string

   val make_type_class : string -> string

   datatype kind = Axiom | Conjecture

   type axiom_name = string

   datatype fol_type =

     TyVar of string |

     TyFree of string |

     TyConstr of string * fol_type list

   val string_of_fol_type : fol_type -> string

   datatype type_literal = LTVar of string * string | LTFree of string * string

   exception CLAUSE of string * term

   val add_typs : typ list -> type_literal list

   val get_tvar_strs: typ list -> string list

   datatype arLit =

       TConsLit of class * string * string list

     | TVarLit of class * string

   datatype arity_clause = ArityClause of

    {axiom_name: axiom_name, conclLit: arLit, premLits: arLit list}

   datatype classrel_clause = ClassrelClause of

    {axiom_name: axiom_name, subclass: class, superclass: class}

   val make_classrel_clauses: theory -> class list -> class list -> classrel_clause list

   val make_arity_clauses_dfg: bool -> theory -> string list -> class list -> class list * arity_clause list

   val make_arity_clauses: theory -> string list -> class list -> class list * arity_clause list

   val add_type_sort_preds: typ * int Symtab.table -> int Symtab.table

   val add_classrel_clause_preds : classrel_clause * int Symtab.table -> int Symtab.table

   val class_of_arityLit: arLit -> class

   val add_arity_clause_preds: arity_clause * int Symtab.table -> int Symtab.table

   val add_foltype_funcs: fol_type * int Symtab.table -> int Symtab.table

   val add_arity_clause_funcs: arity_clause * int Symtab.table -> int Symtab.table

   val init_functab: int Symtab.table

   val dfg_sign: bool -> string -> string

   val dfg_of_typeLit: bool -> type_literal -> string

   val gen_dfg_cls: int * string * kind * string list * string list * string list -> string

   val string_of_preds: (string * Int.int) list -> string

   val string_of_funcs: (string * int) list -> string

   val string_of_symbols: string -> string -> string

   val string_of_start: string -> string

   val string_of_descrip : string -> string

   val dfg_tfree_clause : string -> string

   val dfg_classrel_clause: classrel_clause -> string

   val dfg_arity_clause: arity_clause -> string

   val tptp_sign: bool -> string -> string

   val tptp_of_typeLit : bool -> type_literal -> string

   val gen_tptp_cls : int * string * kind * string list * string list -> string

   val tptp_tfree_clause : string -> string

   val tptp_arity_clause : arity_clause -> string

   val tptp_classrel_clause : classrel_clause -> string

 end

 structure Sledgehammer_FOL_Clause : SLEDGEHAMMER_FOL_CLAUSE =

 struct

 open Sledgehammer_Util

 val schematic_var_prefix = "V_";

 val fixed_var_prefix = "v_";

 val tvar_prefix = "T_";

 val tfree_prefix = "t_";

 val clause_prefix = "cls_";

 val arclause_prefix = "clsarity_"

 val clrelclause_prefix = "clsrel_";

 val const_prefix = "c_";

 val tconst_prefix = "tc_";

 val class_prefix = "class_";

 fun union_all xss = List.foldl (uncurry (union (op =))) [] xss;

 (* Provide readable names for the more common symbolic functions *)

 val const_trans_table =

   Symtab.make [(@{const_name "op ="}, "equal"),

                (@{const_name Orderings.less_eq}, "lessequals"),

                (@{const_name "op &"}, "and"),

                (@{const_name "op |"}, "or"),

                (@{const_name "op -->"}, "implies"),

                (@{const_name "op :"}, "in"),

                (@{const_name fequal}, "fequal"),

                (@{const_name COMBI}, "COMBI"),

                (@{const_name COMBK}, "COMBK"),

                (@{const_name COMBB}, "COMBB"),

                (@{const_name COMBC}, "COMBC"),

                (@{const_name COMBS}, "COMBS")];

 val type_const_trans_table =

   Symtab.make [("*", "prod"), ("+", "sum"), ("~=>", "map")];

 (*Escaping of special characters.

   Alphanumeric characters are left unchanged.

   The character _ goes to __

   Characters in the range ASCII space to / go to _A to _P, respectively.

   Other printing characters go to _nnn where nnn is the decimal ASCII code.*)

 val A_minus_space = Char.ord #"A" - Char.ord #" ";

 fun stringN_of_int 0 _ = ""

   | stringN_of_int k n = stringN_of_int (k-1) (n div 10) ^ Int.toString (n mod 10);

 fun ascii_of_c c =

   if Char.isAlphaNum c then String.str c

   else if c = #"_" then "__"

   else if #" " <= c andalso c <= #"/"

        then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space))

   else if Char.isPrint c

        then ("_" ^ stringN_of_int 3 (Char.ord c))  (*fixed width, in case more digits follow*)

   else ""

 val ascii_of = String.translate ascii_of_c;

 (** Remove ASCII armouring from names in proof files **)

 (*We don't raise error exceptions because this code can run inside the watcher.

   Also, the errors are "impossible" (hah!)*)

 fun undo_ascii_aux rcs [] = String.implode(rev rcs)

   | undo_ascii_aux rcs [#"_"] = undo_ascii_aux (#"_"::rcs) []  (*ERROR*)

       (*Three types of _ escapes: __, _A to _P, _nnn*)

   | undo_ascii_aux rcs (#"_" :: #"_" :: cs) = undo_ascii_aux (#"_"::rcs) cs

   | undo_ascii_aux rcs (#"_" :: c :: cs) =

       if #"A" <= c andalso c<= #"P"  (*translation of #" " to #"/"*)

       then undo_ascii_aux (Char.chr(Char.ord c - A_minus_space) :: rcs) cs

       else

         let val digits = List.take (c::cs, 3) handle Subscript => []

         in

             case Int.fromString (String.implode digits) of

                 NONE => undo_ascii_aux (c:: #"_"::rcs) cs  (*ERROR*)

               | SOME n => undo_ascii_aux (Char.chr n :: rcs) (List.drop (cs, 2))

         end

   | undo_ascii_aux rcs (c::cs) = undo_ascii_aux (c::rcs) cs;

 val undo_ascii_of = undo_ascii_aux [] o String.explode;

 (* convert a list of strings into one single string; surrounded by brackets *)

 fun paren_pack [] = ""   (*empty argument list*)

   | paren_pack strings = "(" ^ commas strings ^ ")";

 (*TSTP format uses (...) rather than the old [...]*)

 fun tptp_pack strings = "(" ^ space_implode " | " strings ^ ")";

 (*Remove the initial ' character from a type variable, if it is present*)

 fun trim_type_var s =

   if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)

   else error ("trim_type: Malformed type variable encountered: " ^ s);

 fun ascii_of_indexname (v,0) = ascii_of v

   | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ Int.toString i;

 fun make_schematic_var v = schematic_var_prefix ^ (ascii_of_indexname v);

 fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x);

 fun make_schematic_type_var (x,i) =

       tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i));

 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x));

 (* HACK because SPASS 3.0 truncates identifiers to 63 characters. (This is

    solved in 3.7 and perhaps in earlier versions too.) *)

 (* 32-bit hash, so we expect no collisions. *)

 fun controlled_length dfg s =

   if dfg andalso size s > 60 then Word.toString (hashw_string (s, 0w0)) else s;

 fun lookup_const dfg c =

     case Symtab.lookup const_trans_table c of

         SOME c' => c'

       | NONE => controlled_length dfg (ascii_of c);

 fun lookup_type_const dfg c =

     case Symtab.lookup type_const_trans_table c of

         SOME c' => c'

       | NONE => controlled_length dfg (ascii_of c);

 (* "op =" MUST BE "equal" because it's built into ATPs. *)

 fun make_fixed_const _ (@{const_name "op ="}) = "equal"

   | make_fixed_const dfg c = const_prefix ^ lookup_const dfg c;

 fun make_fixed_type_const dfg c = tconst_prefix ^ lookup_type_const dfg c;

 fun make_type_class clas = class_prefix ^ ascii_of clas;

 (***** definitions and functions for FOL clauses, for conversion to TPTP or DFG format. *****)

 datatype kind = Axiom | Conjecture;

 type axiom_name = string;

 (**** Isabelle FOL clauses ****)

 datatype fol_type =

   TyVar of string |

   TyFree of string |

   TyConstr of string * fol_type list

 fun string_of_fol_type (TyVar s) = s

   | string_of_fol_type (TyFree s) = s

   | string_of_fol_type (TyConstr (tcon, tps)) =

       tcon ^ (paren_pack (map string_of_fol_type tps));

 (*First string is the type class; the second is a TVar or TFfree*)

 datatype type_literal = LTVar of string * string | LTFree of string * string;

 exception CLAUSE of string * term;

 fun atomic_type (TFree (a,_)) = TyFree(make_fixed_type_var a)

   | atomic_type (TVar (v,_))  = TyVar(make_schematic_type_var v);

 (*Flatten a type to a fol_type while accumulating sort constraints on the TFrees and

   TVars it contains.*)

 fun type_of dfg (Type (a, Ts)) =

       let val (folTyps, ts) = types_of dfg Ts

           val t = make_fixed_type_const dfg a

       in (TyConstr (t, folTyps), ts) end

   | type_of dfg T = (atomic_type T, [T])

 and types_of dfg Ts =

       let val (folTyps,ts) = ListPair.unzip (map (type_of dfg) Ts)

       in (folTyps, union_all ts) end;

 (*Make literals for sorted type variables*)

 fun sorts_on_typs_aux (_, [])   = []

   | sorts_on_typs_aux ((x,i),  s::ss) =

       let val sorts = sorts_on_typs_aux ((x,i), ss)

       in

           if s = "HOL.type" then sorts

           else if i = ~1 then LTFree(make_type_class s, make_fixed_type_var x) :: sorts

           else LTVar(make_type_class s, make_schematic_type_var (x,i)) :: sorts

       end;

 fun sorts_on_typs (TFree (a,s)) = sorts_on_typs_aux ((a,~1),s)

   | sorts_on_typs (TVar (v,s))  = sorts_on_typs_aux (v,s);

 fun pred_of_sort (LTVar (s,ty)) = (s,1)

   | pred_of_sort (LTFree (s,ty)) = (s,1)

 (*Given a list of sorted type variables, return a list of type literals.*)

 fun add_typs Ts = List.foldl (uncurry (union (op =))) [] (map sorts_on_typs Ts);

 (*The correct treatment of TFrees like 'a in lemmas (axiom clauses) is not clear.

   * Ignoring them leads to unsound proofs, since we do nothing to ensure that 'a

     in a lemma has the same sort as 'a in the conjecture.

   * Deleting such clauses will lead to problems with locales in other use of local results

     where 'a is fixed. Probably we should delete clauses unless the sorts agree.

   * Currently we include a class constraint in the clause, exactly as with TVars.

 *)

 (** make axiom and conjecture clauses. **)

 fun get_tvar_strs [] = []

   | get_tvar_strs ((TVar (indx,s))::Ts) =

       insert (op =) (make_schematic_type_var indx) (get_tvar_strs Ts)

   | get_tvar_strs((TFree _)::Ts) = get_tvar_strs Ts

 (**** Isabelle arities ****)

 exception ARCLAUSE of string;

 datatype arLit = TConsLit of class * string * string list

                | TVarLit of class * string;

 datatype arity_clause =

          ArityClause of {axiom_name: axiom_name,

                          conclLit: arLit,

                          premLits: arLit list};

 fun gen_TVars 0 = []

   | gen_TVars n = ("T_" ^ Int.toString n) :: gen_TVars (n-1);

 fun pack_sort(_,[])  = []

   | pack_sort(tvar, "HOL.type"::srt) = pack_sort(tvar, srt)   (*IGNORE sort "type"*)

   | pack_sort(tvar, cls::srt) =  (cls, tvar) :: pack_sort(tvar, srt);

 (*Arity of type constructor tcon :: (arg1,...,argN)res*)

 fun make_axiom_arity_clause dfg (tcons, axiom_name, (cls,args)) =

    let val tvars = gen_TVars (length args)

        val tvars_srts = ListPair.zip (tvars,args)

    in

       ArityClause {axiom_name = axiom_name, 

                    conclLit = TConsLit (cls, make_fixed_type_const dfg tcons, tvars),

                    premLits = map TVarLit (union_all(map pack_sort tvars_srts))}

    end;

 (**** Isabelle class relations ****)

 datatype classrel_clause =

          ClassrelClause of {axiom_name: axiom_name,

                             subclass: class,

                             superclass: class};

 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)

 fun class_pairs thy [] supers = []

   | class_pairs thy subs supers =

       let val class_less = Sorts.class_less(Sign.classes_of thy)

           fun add_super sub (super,pairs) =

                 if class_less (sub,super) then (sub,super)::pairs else pairs

           fun add_supers (sub,pairs) = List.foldl (add_super sub) pairs supers

       in  List.foldl add_supers [] subs  end;

 fun make_classrel_clause (sub,super) =

   ClassrelClause {axiom_name = clrelclause_prefix ^ ascii_of sub ^ "_" ^ ascii_of super,

                   subclass = make_type_class sub,

                   superclass = make_type_class super};

 fun make_classrel_clauses thy subs supers =

   map make_classrel_clause (class_pairs thy subs supers);

 (** Isabelle arities **)

 fun arity_clause dfg _ _ (tcons, []) = []

   | arity_clause dfg seen n (tcons, ("HOL.type",_)::ars) =  (*ignore*)

       arity_clause dfg seen n (tcons,ars)

   | arity_clause dfg seen n (tcons, (ar as (class,_)) :: ars) =

       if class mem_string seen then (*multiple arities for the same tycon, class pair*)

           make_axiom_arity_clause dfg (tcons, lookup_type_const dfg tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) ::

           arity_clause dfg seen (n+1) (tcons,ars)

       else

           make_axiom_arity_clause dfg (tcons, lookup_type_const dfg tcons ^ "_" ^ class, ar) ::

           arity_clause dfg (class::seen) n (tcons,ars)

 fun multi_arity_clause dfg [] = []

   | multi_arity_clause dfg ((tcons,ars) :: tc_arlists) =

       arity_clause dfg [] 1 (tcons, ars)  @  multi_arity_clause dfg tc_arlists

 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy

   provided its arguments have the corresponding sorts.*)

 fun type_class_pairs thy tycons classes =

   let val alg = Sign.classes_of thy

       fun domain_sorts (tycon,class) = Sorts.mg_domain alg tycon [class]

       fun add_class tycon (class,pairs) =

             (class, domain_sorts(tycon,class))::pairs

             handle Sorts.CLASS_ERROR _ => pairs

       fun try_classes tycon = (tycon, List.foldl (add_class tycon) [] classes)

   in  map try_classes tycons  end;

 (*Proving one (tycon, class) membership may require proving others, so iterate.*)

 fun iter_type_class_pairs thy tycons [] = ([], [])

   | iter_type_class_pairs thy tycons classes =

       let val cpairs = type_class_pairs thy tycons classes

           val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))

             |> subtract (op =) classes |> subtract (op =) HOLogic.typeS

           val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses

       in (union (op =) classes' classes, union (op =) cpairs' cpairs) end;

 fun make_arity_clauses_dfg dfg thy tycons classes =

   let val (classes', cpairs) = iter_type_class_pairs thy tycons classes

   in  (classes', multi_arity_clause dfg cpairs)  end;

 val make_arity_clauses = make_arity_clauses_dfg false;

 (**** Find occurrences of predicates in clauses ****)

 (*FIXME: multiple-arity checking doesn't work, as update_new is the wrong

   function (it flags repeated declarations of a function, even with the same arity)*)

 fun update_many (tab, keypairs) = List.foldl (uncurry Symtab.update) tab keypairs;

 fun add_type_sort_preds (T, preds) =

       update_many (preds, map pred_of_sort (sorts_on_typs T));

 fun add_classrel_clause_preds (ClassrelClause {subclass,superclass,...}, preds) =

   Symtab.update (subclass,1) (Symtab.update (superclass,1) preds);

 fun class_of_arityLit (TConsLit (tclass, _, _)) = tclass

   | class_of_arityLit (TVarLit (tclass, _)) = tclass;

 fun add_arity_clause_preds (ArityClause {conclLit,premLits,...}, preds) =

   let val classes = map (make_type_class o class_of_arityLit) (conclLit::premLits)

       fun upd (class,preds) = Symtab.update (class,1) preds

   in  List.foldl upd preds classes  end;

 (*** Find occurrences of functions in clauses ***)

 fun add_foltype_funcs (TyVar _, funcs) = funcs

   | add_foltype_funcs (TyFree a, funcs) = Symtab.update (a,0) funcs

   | add_foltype_funcs (TyConstr (a, tys), funcs) =

       List.foldl add_foltype_funcs (Symtab.update (a, length tys) funcs) tys;

 (*TFrees are recorded as constants*)

 fun add_type_sort_funcs (TVar _, funcs) = funcs

   | add_type_sort_funcs (TFree (a, _), funcs) =

       Symtab.update (make_fixed_type_var a, 0) funcs

 fun add_arity_clause_funcs (ArityClause {conclLit,...}, funcs) =

   let val TConsLit (_, tcons, tvars) = conclLit

   in  Symtab.update (tcons, length tvars) funcs  end;

 (*This type can be overlooked because it is built-in...*)

 val init_functab = Symtab.update ("tc_itself", 1) Symtab.empty;

 (**** String-oriented operations ****)

 fun string_of_clausename (cls_id,ax_name) =

     clause_prefix ^ ascii_of ax_name ^ "_" ^ Int.toString cls_id;

 fun string_of_type_clsname (cls_id,ax_name,idx) =

     string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);

 (**** Producing DFG files ****)

 (*Attach sign in DFG syntax: false means negate.*)

 fun dfg_sign true s = s

   | dfg_sign false s = "not(" ^ s ^ ")"

 fun dfg_of_typeLit pos (LTVar (s,ty))  = dfg_sign pos (s ^ "(" ^ ty ^ ")")

   | dfg_of_typeLit pos (LTFree (s,ty)) = dfg_sign pos (s ^ "(" ^ ty ^ ")");

 (*Enclose the clause body by quantifiers, if necessary*)

 fun dfg_forall [] body = body

   | dfg_forall vars body = "forall([" ^ commas vars ^ "],\n" ^ body ^ ")"

 fun gen_dfg_cls (cls_id, ax_name, Axiom, lits, tylits, vars) =

       "clause( %(axiom)\n" ^

       dfg_forall vars ("or(" ^ commas (tylits@lits) ^ ")") ^ ",\n" ^

       string_of_clausename (cls_id,ax_name) ^  ").\n\n"

   | gen_dfg_cls (cls_id, ax_name, Conjecture, lits, _, vars) =

       "clause( %(negated_conjecture)\n" ^

       dfg_forall vars ("or(" ^ commas lits ^ ")") ^ ",\n" ^

       string_of_clausename (cls_id,ax_name) ^  ").\n\n";

 fun string_of_arity (name, num) =  "(" ^ name ^ "," ^ Int.toString num ^ ")"

 fun string_of_preds [] = ""

   | string_of_preds preds = "predicates[" ^ commas(map string_of_arity preds) ^ "].\n";

 fun string_of_funcs [] = ""

   | string_of_funcs funcs = "functions[" ^ commas(map string_of_arity funcs) ^ "].\n" ;

 fun string_of_symbols predstr funcstr =

   "list_of_symbols.\n" ^ predstr  ^ funcstr  ^ "end_of_list.\n\n";

 fun string_of_start name = "begin_problem(" ^ name ^ ").\n\n";

 fun string_of_descrip name =

   "list_of_descriptions.\nname({*" ^ name ^

   "*}).\nauthor({*Isabelle*}).\nstatus(unknown).\ndescription({*auto-generated*}).\nend_of_list.\n\n"

 fun dfg_tfree_clause tfree_lit =

   "clause( %(negated_conjecture)\n" ^ "or( " ^ tfree_lit ^ "),\n" ^ "tfree_tcs" ^ ").\n\n"

 fun dfg_of_arLit (TConsLit (c,t,args)) =

       dfg_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")")

   | dfg_of_arLit (TVarLit (c,str)) =

       dfg_sign false (make_type_class c ^ "(" ^ str ^ ")")

 fun dfg_classrelLits sub sup =  "not(" ^ sub ^ "(T)), " ^ sup ^ "(T)";

 fun dfg_classrel_clause (ClassrelClause {axiom_name,subclass,superclass,...}) =

   "clause(forall([T],\nor( " ^ dfg_classrelLits subclass superclass ^ ")),\n" ^

   axiom_name ^ ").\n\n";

 fun string_of_ar axiom_name = arclause_prefix ^ ascii_of axiom_name;

 fun dfg_arity_clause (ArityClause{axiom_name,conclLit,premLits,...}) =

   let val TConsLit (_,_,tvars) = conclLit

       val lits = map dfg_of_arLit (conclLit :: premLits)

   in

       "clause( %(axiom)\n" ^

       dfg_forall tvars ("or( " ^ commas lits ^ ")") ^ ",\n" ^

       string_of_ar axiom_name ^ ").\n\n"

   end;

 (**** Produce TPTP files ****)

 fun tptp_sign true s = s

   | tptp_sign false s = "~ " ^ s

 fun tptp_of_typeLit pos (LTVar (s, ty))  = tptp_sign pos (s ^ "(" ^ ty ^ ")")

   | tptp_of_typeLit pos (LTFree (s, ty)) = tptp_sign pos (s ^ "(" ^ ty ^ ")")

 fun tptp_cnf name kind formula =

   "cnf(" ^ name ^ ", " ^ kind ^ ",\n    " ^ formula ^ ").\n"

 fun gen_tptp_cls (cls_id, ax_name, Axiom, lits, tylits) =

       tptp_cnf (string_of_clausename (cls_id, ax_name)) "axiom"

                (tptp_pack (tylits @ lits))

   | gen_tptp_cls (cls_id, ax_name, Conjecture, lits, _) =

       tptp_cnf (string_of_clausename (cls_id, ax_name)) "negated_conjecture"

                (tptp_pack lits)

 fun tptp_tfree_clause tfree_lit =

     tptp_cnf "tfree_tcs" "negated_conjecture" (tptp_pack [tfree_lit])

 fun tptp_of_arLit (TConsLit (c,t,args)) =

       tptp_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")")

   | tptp_of_arLit (TVarLit (c,str)) =

       tptp_sign false (make_type_class c ^ "(" ^ str ^ ")")

 fun tptp_arity_clause (ArityClause{axiom_name,conclLit,premLits,...}) =

   tptp_cnf (string_of_ar axiom_name) "axiom"

            (tptp_pack (map tptp_of_arLit (conclLit :: premLits)))

 fun tptp_classrelLits sub sup =

   let val tvar = "(T)"

   in  tptp_pack [tptp_sign false (sub^tvar), tptp_sign true (sup^tvar)]  end;

 fun tptp_classrel_clause (ClassrelClause {axiom_name,subclass,superclass,...}) =

   tptp_cnf axiom_name "axiom" (tptp_classrelLits subclass superclass)

 end;