(*  Author: Jia Meng, Cambridge University Computer Laboratory

     ID: $Id$

     Copyright 2004 University of Cambridge

 ML data structure for storing/printing FOL clauses and arity clauses.

 Typed equality is treated differently.

 *)

 signature RES_CLAUSE =

   sig

     exception ARCLAUSE of string

     exception CLAUSE of string

     type arityClause 

     type classrelClause

     val classrelClauses_of :

        string * string list -> classrelClause list

     type clause

     val keep_types : bool ref

     val make_axiom_arity_clause :

        string * (string * string list list) -> arityClause

     val make_axiom_classrelClause :

        string * string option -> classrelClause

     val make_axiom_clause : Term.term -> string * int -> clause

     val make_axiom_clause_thm : Thm.thm -> string * int -> clause

     val make_conjecture_clause : Term.term -> clause

     val make_conjecture_clause_thm : Thm.thm -> clause

     val make_hypothesis_clause : Term.term -> clause

     val make_hypothesis_clause_thm : Thm.thm -> clause

     val special_equal : bool ref

     val tptp_arity_clause : arityClause -> string

     val tptp_classrelClause : classrelClause -> string

     val tptp_clause : clause -> string list

     val tptp_clauses2str : string list -> string

     val typed : unit -> unit

     val untyped : unit -> unit

     val clause2tptp : clause -> string * string list

     val tfree_clause : string -> string

   end;

 structure ResClause : RES_CLAUSE =

 struct

 (* Added for typed equality *)

 val special_equal = ref false; (* by default,equality does not carry type information *)

 val eq_typ_wrapper = "typeinfo"; (* default string *)

 val schematic_var_prefix = "V_";

 val fixed_var_prefix = "v_";

 val tvar_prefix = "Typ_";

 val tfree_prefix = "typ_";

 val clause_prefix = "cls_"; 

 val arclause_prefix = "arcls_" 

 val const_prefix = "const_";

 val tconst_prefix = "tconst_"; 

 val class_prefix = "clas_"; 

 (**** some useful functions ****)

 val const_trans_table =

       Symtab.make [("op =", "equal"),

 	  	   ("op <=", "lessequals"),

 		   ("op <", "less"),

 		   ("op &", "and"),

 		   ("op |", "or"),

 		   ("op -->", "implies"),

 		   ("op :", "in"),

 		   ("op Un", "union"),

 		   ("op Int", "inter")];

 (*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.*)

 local

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

 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 ("_" ^ Int.toString (Char.ord c))

   else ""

 in

 val ascii_of = String.translate ascii_of_c;

 end;

 (* another version of above functions that remove chars that may not be allowed by Vampire *)

 fun make_schematic_var v = schematic_var_prefix ^ (ascii_of v);

 fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x);

 fun make_schematic_type_var v = tvar_prefix ^ (ascii_of v);

 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of x);

 fun make_fixed_const c = const_prefix ^ (ascii_of c);

 fun make_fixed_type_const c = tconst_prefix ^ (ascii_of c);

 fun make_type_class clas = class_prefix ^ (ascii_of clas);

 fun lookup_const c =

     case Symtab.lookup (const_trans_table,c) of

         SOME c' => c'

       | NONE =>  make_fixed_const c;

 (***** definitions and functions for FOL clauses, prepared for conversion into TPTP format or SPASS format. *****)

 val keep_types = ref true; (* default is true *)

 fun untyped () = (keep_types := false);

 fun typed () = (keep_types := true);

 datatype kind = Axiom | Hypothesis | Conjecture;

 fun name_of_kind Axiom = "axiom"

   | name_of_kind Hypothesis = "hypothesis"

   | name_of_kind Conjecture = "conjecture";

 type clause_id = int;

 type axiom_name = string;

 type polarity = bool;

 type indexname = Term.indexname;

 (* "tag" is used for vampire specific syntax  *)

 type tag = bool; 

 fun string_of_indexname (name,index) = name ^ "_" ^ (string_of_int index);

 val id_ref = ref 0;

 fun generate_id () = 

      let val id = !id_ref

      in

 	 (id_ref:=id + 1; id)

      end;

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

 (* by default it is false *)

 val tagged = ref false;

 type pred_name = string;

 type sort = Term.sort;

 type fol_type = string;

 datatype type_literal = LTVar of string | LTFree of string;

 datatype folTerm = UVar of string * fol_type| Fun of string * fol_type * folTerm list;

 datatype predicate = Predicate of pred_name * fol_type * folTerm list;

 datatype literal = Literal of polarity * predicate * tag;

 datatype typ_var = FOLTVar of indexname | FOLTFree of string;

 (* ML datatype used to repsent one single clause: disjunction of literals. *)

 datatype clause = 

 	 Clause of {clause_id: clause_id,

 		    axiom_name: axiom_name,

 		    kind: kind,

 		    literals: literal list,

 		    types_sorts: (typ_var * sort) list, 

                     tvar_type_literals: type_literal list, 

                     tfree_type_literals: type_literal list };

 exception CLAUSE of string;

 (*** make clauses ***)

 fun make_clause (clause_id,axiom_name,kind,literals,types_sorts,tvar_type_literals,tfree_type_literals) =

      Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind, literals = literals, types_sorts = types_sorts,tvar_type_literals = tvar_type_literals,tfree_type_literals = tfree_type_literals};

 fun type_of (Type (a, [])) = (make_fixed_type_const a,[]) 

   | type_of (Type (a, Ts)) = 

     let val foltyps_ts = map type_of Ts

         val (folTyps,ts) = ResLib.unzip foltyps_ts

         val ts' = ResLib.flat_noDup ts

     in    

         (((make_fixed_type_const a) ^ (ResLib.list_to_string folTyps)),ts') 

     end

   | type_of (TFree (a, s)) = (make_fixed_type_var a, [((FOLTFree a),s)])

   | type_of (TVar (v, s))  = (make_schematic_type_var (string_of_indexname v), [((FOLTVar v),s)]);

 (* added: checkMeta: string -> bool *)

 (* Any meta vars like ?x should be treated as universal vars,although it is represented as "Free(...)" by Isabelle *)

 fun checkMeta s =

     let val chars = explode s

     in

 	["M", "E", "T", "A", "H", "Y", "P", "1"] prefix chars

     end;

 fun pred_name_type (Const(c,T)) = (lookup_const c,type_of T)

   | pred_name_type (Free(x,T))  = 

     let val is_meta = checkMeta x

     in

 	if is_meta then (raise CLAUSE("Predicate Not First Order")) else

 	(make_fixed_var x,type_of T)

     end

   | pred_name_type (Var(_,_))   = raise CLAUSE("Predicate Not First Order")

   | pred_name_type _          = raise CLAUSE("Predicate input unexpected");

 (* For type equality *)

 (* here "arg_typ" is the type of "="'s argument's type, not the type of the equality *)

 (* Find type of equality arg *)

 fun eq_arg_type (Type("fun",[T,_])) = 

     let val (folT,_) = type_of T;

     in

 	folT

     end;

 fun fun_name_type (Const(c,T)) = (lookup_const c,type_of T)

   | fun_name_type (Free(x,T)) = (make_fixed_var x,type_of T)

   | fun_name_type _ = raise CLAUSE("Function Not First Order");

 fun term_of (Var(ind_nm,T)) = 

     let val (folType,ts) = type_of T

     in

 	(UVar(make_schematic_var(string_of_indexname ind_nm),folType),ts)

     end

   | term_of (Free(x,T)) = 

     let val is_meta = checkMeta x

 	val (folType,ts) = type_of T

     in

 	if is_meta then (UVar(make_schematic_var x,folType),ts)

 	else

             (Fun(make_fixed_var x,folType,[]),ts)

     end

   | term_of (Const(c,T)) =  (* impossible to be equality *)

     let val (folType,ts) = type_of T

      in

         (Fun(lookup_const c,folType,[]),ts)

     end    

   | term_of (app as (t $ a)) = 

     let val (f,args) = strip_comb app

         fun term_of_aux () = 

             let val (funName,(funType,ts1)) = fun_name_type f

                  val (args',ts2) = ResLib.unzip (map term_of args)

                  val ts3 = ResLib.flat_noDup (ts1::ts2)

             in

 		(Fun(funName,funType,args'),ts3)

             end

 	fun term_of_eq ((Const ("op =", typ)),args) =

 	    let val arg_typ = eq_arg_type typ

 		val (args',ts) = ResLib.unzip (map term_of args)

 		val equal_name = lookup_const ("op =")

 	    in

 		(Fun(equal_name,arg_typ,args'),ResLib.flat_noDup ts)

 	    end

     in

         case f of Const ("op =", typ) => term_of_eq (f,args)

 	        | Const(_,_) => term_of_aux ()

                 | Free(s,_)  => if (checkMeta s) then (raise CLAUSE("Function Not First Order")) else term_of_aux ()

                 | _          => raise CLAUSE("Function Not First Order")

     end

   | term_of _ = raise CLAUSE("Function Not First Order"); 

 fun pred_of_eq ((Const ("op =", typ)),args) =

     let val arg_typ = eq_arg_type typ 

 	val (args',ts) = ResLib.unzip (map term_of args)

 	val equal_name = lookup_const "op ="

     in

 	(Predicate(equal_name,arg_typ,args'),ResLib.flat_noDup ts)

     end;

 (* changed for non-equality predicate *)

 (* The input "pred" cannot be an equality *)

 fun pred_of_nonEq (pred,args) = 

     let val (predName,(predType,ts1)) = pred_name_type pred

 	val (args',ts2) = ResLib.unzip (map term_of args)

 	val ts3 = ResLib.flat_noDup (ts1::ts2)

     in

 	(Predicate(predName,predType,args'),ts3)

     end;

 (* Changed for typed equality *)

 (* First check if the predicate is an equality or not, then call different functions for equality and non-equalities *)

 fun predicate_of term =

     let val (pred,args) = strip_comb term

     in

 	case pred of (Const ("op =", _)) => pred_of_eq (pred,args)

 		   | _ => pred_of_nonEq (pred,args)

     end;

 fun literals_of_term ((Const("Trueprop",_) $ P),lits_ts) = literals_of_term(P,lits_ts)

   | literals_of_term ((Const("op |",_) $ P $ Q),(lits,ts)) = 

     let val (lits',ts') = literals_of_term(P,(lits,ts))

     in

         literals_of_term(Q,(lits',ts'))

     end

   | literals_of_term ((Const("Not",_) $ P),(lits,ts)) = 

     let val (pred,ts') = predicate_of P

         val lits' = Literal(false,pred,false) :: lits

         val ts'' = ResLib.no_rep_app ts ts'

     in

         (lits',ts'')

     end

   | literals_of_term (P,(lits,ts)) = 

     let val (pred,ts') = predicate_of P

         val lits' = Literal(true,pred,false) :: lits

         val ts'' = ResLib.no_rep_app ts ts' 

     in

         (lits',ts'')

     end

   | literals_of_term _ = raise CLAUSE("Unexpected clause format");

 fun literals_of_thm thm = 

     let val term_of_thm = prop_of thm

     in

 	literals_of_term (term_of_thm,([],[]))

     end;

 fun sorts_on_typs (_, []) = []

   | sorts_on_typs ((FOLTVar(indx)), [s]) = [LTVar((make_type_class s) ^ "(" ^ (make_schematic_type_var(string_of_indexname indx)) ^ ")")]

   | sorts_on_typs ((FOLTVar(indx)), (s::ss))=  LTVar((make_type_class s) ^ "(" ^ (make_schematic_type_var(string_of_indexname indx)) ^ ")") :: (sorts_on_typs ((FOLTVar(indx)), ss))

   | sorts_on_typs ((FOLTFree(x)), [s]) = [LTFree((make_type_class s) ^ "(" ^ (make_fixed_type_var(x)) ^ ")")]

   | sorts_on_typs ((FOLTFree(x)), (s::ss)) = LTFree((make_type_class s) ^ "(" ^ (make_fixed_type_var(x)) ^ ")") :: (sorts_on_typs ((FOLTFree(x)), ss));

 fun add_typs_aux [] = ([],[])

   | add_typs_aux ((FOLTVar(indx),s)::tss) = 

     let val vs = sorts_on_typs (FOLTVar(indx),s)

         val (vss,fss) = add_typs_aux tss

     in

         (ResLib.no_rep_app vs vss,fss)

     end

   | add_typs_aux ((FOLTFree(x),s)::tss) =

     let val fs = sorts_on_typs (FOLTFree(x),s)

         val (vss,fss) = add_typs_aux tss

     in

         (vss,ResLib.no_rep_app fs fss)

     end;

 fun add_typs (Clause cls) = 

     let val ts = #types_sorts cls

     in

 	add_typs_aux ts

     end;    

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

 local 

     fun replace_dot "." = "_"

       | replace_dot c = c;

 in

 fun proper_ax_name ax_name = 

     let val chars = explode ax_name

     in

 	implode (map replace_dot chars)

     end;

 end;

 fun make_axiom_clause_thm thm (name,number)=

     let val (lits,types_sorts) = literals_of_thm thm

 	val cls_id = number

 	val (tvar_lits,tfree_lits) = add_typs_aux types_sorts

 	val ax_name = proper_ax_name name

     in 

 	make_clause(cls_id,ax_name,Axiom,lits,types_sorts,tvar_lits,tfree_lits)

     end;

 fun make_hypothesis_clause_thm thm =

     let val (lits,types_sorts) = literals_of_thm thm

 	val cls_id = generate_id()

 	val (tvar_lits,tfree_lits) = add_typs_aux types_sorts

     in

 	make_clause(cls_id,"",Hypothesis,lits,types_sorts,tvar_lits,tfree_lits)

     end;

 fun make_conjecture_clause_thm thm =

     let val (lits,types_sorts) = literals_of_thm thm

 	val cls_id = generate_id()

 	val (tvar_lits,tfree_lits) = add_typs_aux types_sorts

     in

 	make_clause(cls_id,"",Conjecture,lits,types_sorts,tvar_lits,tfree_lits)

     end;

 fun make_axiom_clause term (name,number)=

     let val (lits,types_sorts) = literals_of_term (term,([],[]))

 	val cls_id = number

 	val (tvar_lits,tfree_lits) = add_typs_aux types_sorts

 	val ax_name = proper_ax_name name

     in 

 	make_clause(cls_id,ax_name,Axiom,lits,types_sorts,tvar_lits,tfree_lits)

     end;

 fun make_hypothesis_clause term =

     let val (lits,types_sorts) = literals_of_term (term,([],[]))

 	val cls_id = generate_id()

 	val (tvar_lits,tfree_lits) = add_typs_aux types_sorts

     in

 	make_clause(cls_id,"",Hypothesis,lits,types_sorts,tvar_lits,tfree_lits)

     end;

 fun make_conjecture_clause term =

     let val (lits,types_sorts) = literals_of_term (term,([],[]))

 	val cls_id = generate_id()

 	val (tvar_lits,tfree_lits) = add_typs_aux types_sorts

     in

 	make_clause(cls_id,"",Conjecture,lits,types_sorts,tvar_lits,tfree_lits)

     end;

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

 exception ARCLAUSE of string;

 type class = string; 

 type tcons = string; 

 datatype arLit = TConsLit of bool * (class * tcons * string list) | TVarLit of bool * (class * string);

 datatype arityClause =  

 	 ArityClause of {clause_id: clause_id,

 			 kind: kind,

 			 conclLit: arLit,

 			 premLits: arLit list};

 fun get_TVars 0 = []

   | get_TVars n = ("T_" ^ (string_of_int n)) :: get_TVars (n-1);

 fun pack_sort(_,[])  = raise ARCLAUSE("Empty Sort Found") 

   | pack_sort(tvar, [cls]) = [(make_type_class cls, tvar)] 

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

 fun make_TVarLit (b,(cls,str)) = TVarLit(b,(cls,str));

 fun make_TConsLit (b,(cls,tcons,tvars)) = TConsLit(b,(make_type_class cls,make_fixed_type_const tcons,tvars));

 fun make_arity_clause (clause_id,kind,conclLit,premLits) =

     ArityClause {clause_id = clause_id, kind = kind, conclLit = conclLit, premLits = premLits};

 fun make_axiom_arity_clause (tcons,(res,args)) =

      let val cls_id = generate_id()

 	 val nargs = length args

 	 val tvars = get_TVars nargs

 	 val conclLit = make_TConsLit(true,(res,tcons,tvars))

          val tvars_srts = ResLib.zip tvars args

 	 val tvars_srts' = ResLib.flat_noDup(map pack_sort tvars_srts)

          val false_tvars_srts' = ResLib.pair_ins false tvars_srts'

 	 val premLits = map make_TVarLit false_tvars_srts'

      in

 	 make_arity_clause (cls_id,Axiom,conclLit,premLits)

      end;

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

 datatype classrelClause = 

 	 ClassrelClause of {clause_id: clause_id,

 			    subclass: class,

 			    superclass: class option};

 fun make_classrelClause (clause_id,subclass,superclass) =

     ClassrelClause {clause_id = clause_id,subclass = subclass, superclass = superclass};

 fun make_axiom_classrelClause (subclass,superclass) =

     let val cls_id = generate_id()

 	val sub = make_type_class subclass

 	val sup = case superclass of NONE => NONE 

 				   | SOME s => SOME (make_type_class s)

     in

 	make_classrelClause(cls_id,sub,sup)

     end;

 fun classrelClauses_of_aux (sub,[]) = []

   | classrelClauses_of_aux (sub,(sup::sups)) = make_axiom_classrelClause(sub,SOME sup) :: (classrelClauses_of_aux (sub,sups));

 fun classrelClauses_of (sub,sups) = 

     case sups of [] => [make_axiom_classrelClause (sub,NONE)]

 	       | _ => classrelClauses_of_aux (sub, sups);

 (***** convert clauses to tptp format *****)

 fun string_of_clauseID (Clause cls) = clause_prefix ^ (string_of_int (#clause_id cls));

 fun string_of_kind (Clause cls) = name_of_kind (#kind cls);

 fun string_of_axiomName (Clause cls) = #axiom_name cls;

 (****!!!! Changed for typed equality !!!!****)

 fun wrap_eq_type typ t = eq_typ_wrapper ^"(" ^ t ^ "," ^ typ ^ ")";

 (****!!!! Changed for typed equality !!!!****)

 (* Only need to wrap equality's arguments with "typeinfo" if the output clauses are typed && if we specifically ask for types to be included.   *)

 fun string_of_equality (typ,terms) =

     let val [tstr1,tstr2] = map string_of_term terms

     in

 	if ((!keep_types) andalso (!special_equal)) then 

 	    "equal(" ^ (wrap_eq_type typ tstr1) ^ "," ^ (wrap_eq_type typ tstr2) ^ ")"

 	else

 	    "equal(" ^ tstr1 ^ "," ^ tstr2 ^ ")"

     end

 and

     string_of_term (UVar(x,_)) = x

   | string_of_term (Fun("equal",typ,terms)) = string_of_equality(typ,terms)

   | string_of_term (Fun (name,typ,[])) = name

   | string_of_term (Fun (name,typ,terms)) = 

     let val terms' = map string_of_term terms

     in

         if (!keep_types) then name ^ (ResLib.list_to_string (typ :: terms'))

         else name ^ (ResLib.list_to_string terms')

     end;

 (* Changed for typed equality *)

 (* before output the string of the predicate, check if the predicate corresponds to an equality or not. *)

 fun string_of_predicate (Predicate("equal",typ,terms)) = string_of_equality(typ,terms)

   | string_of_predicate (Predicate(name,_,[])) = name 

   | string_of_predicate (Predicate(name,typ,terms)) = 

     let val terms_as_strings = map string_of_term terms

     in

         if (!keep_types) then name ^ (ResLib.list_to_string  (typ :: terms_as_strings))

         else name ^ (ResLib.list_to_string terms_as_strings) 

     end;

 fun tptp_literal (Literal(pol,pred,tag)) =

     let val pred_string = string_of_predicate pred

 	val tagged_pol = if (tag andalso !tagged) then (if pol then "+++" else "---")

                          else (if pol then "++" else "--")

      in

 	tagged_pol ^ pred_string

     end;

 fun tptp_of_typeLit (LTVar x) = "--" ^ x

   | tptp_of_typeLit (LTFree x) = "++" ^ x;

 fun gen_tptp_cls (cls_id,ax_name,knd,lits) = 

     let val ax_str = (if ax_name = "" then "" else ("_" ^ ax_name))

     in

 	"input_clause(" ^ cls_id ^ ax_str ^ "," ^ knd ^ "," ^ lits ^ ")."

     end;

 fun gen_tptp_type_cls (cls_id,knd,tfree_lit,idx) = "input_clause(" ^ cls_id ^ "_tcs" ^ (string_of_int idx) ^ "," ^ knd ^ ",[" ^ tfree_lit ^ "]).";

 fun tptp_clause_aux (Clause cls) = 

     let val lits = map tptp_literal (#literals cls)

 	val tvar_lits_strs = if (!keep_types) then (map tptp_of_typeLit (#tvar_type_literals cls)) else []

 	val tfree_lits = if (!keep_types) then (map tptp_of_typeLit (#tfree_type_literals cls)) else []

     in

 	(tvar_lits_strs @ lits,tfree_lits)

     end; 

 fun tptp_clause cls =

     let val (lits,tfree_lits) = tptp_clause_aux cls (*"lits" includes the typing assumptions (TVars)*)

 	val cls_id = string_of_clauseID cls

 	val ax_name = string_of_axiomName cls

 	val knd = string_of_kind cls

 	val lits_str = ResLib.list_to_string' lits

 	val cls_str = gen_tptp_cls(cls_id,ax_name,knd,lits_str) 			fun typ_clss k [] = []

           | typ_clss k (tfree :: tfrees) = 

             (gen_tptp_type_cls(cls_id,knd,tfree,k)) ::  (typ_clss (k+1) tfrees)

     in 

 	cls_str :: (typ_clss 0 tfree_lits)

     end;

 fun clause2tptp cls =

     let val (lits,tfree_lits) = tptp_clause_aux cls (*"lits" includes the typing assumptions (TVars)*)

 	val cls_id = string_of_clauseID cls

 	val ax_name = string_of_axiomName cls

 	val knd = string_of_kind cls

 	val lits_str = ResLib.list_to_string' lits

 	val cls_str = gen_tptp_cls(cls_id,ax_name,knd,lits_str) 

     in

 	(cls_str,tfree_lits) 

     end;

 fun tfree_clause tfree_lit = "input_clause(" ^ "tfree_tcs," ^ "conjecture" ^ ",[" ^ tfree_lit ^ "]).";

 val delim = "\n";

 val tptp_clauses2str = ResLib.list2str_sep delim; 

 fun string_of_arClauseID (ArityClause arcls) = arclause_prefix ^ string_of_int(#clause_id arcls);

 fun string_of_arLit (TConsLit(b,(c,t,args))) =

     let val pol = if b then "++" else "--"

 	val  arg_strs = (case args of [] => "" | _ => ResLib.list_to_string args)

     in 

 	pol ^ c ^ "(" ^ t ^ arg_strs ^ ")"

     end

   | string_of_arLit (TVarLit(b,(c,str))) =

     let val pol = if b then "++" else "--"

     in

 	pol ^ c ^ "(" ^ str ^ ")"

     end;

 fun string_of_conclLit (ArityClause arcls) = string_of_arLit (#conclLit arcls);

 fun strings_of_premLits (ArityClause arcls) = map string_of_arLit (#premLits arcls);

 fun string_of_arKind (ArityClause arcls) = name_of_kind(#kind arcls);

 fun tptp_arity_clause arcls = 

     let val arcls_id = string_of_arClauseID arcls

 	val concl_lit = string_of_conclLit arcls

 	val prems_lits = strings_of_premLits arcls

 	val knd = string_of_arKind arcls

 	val all_lits = concl_lit :: prems_lits

     in

 	"input_clause(" ^ arcls_id ^ "," ^ knd ^ "," ^ (ResLib.list_to_string' all_lits) ^ ")."

     end;

 val clrelclause_prefix = "relcls_";

 fun tptp_classrelLits sub sup = 

     let val tvar = "(T)"

     in 

 	case sup of NONE => "[++" ^ sub ^ tvar ^ "]"

 		  | (SOME supcls) =>  "[--" ^ sub ^ tvar ^ ",++" ^ supcls ^ tvar ^ "]"

     end;

 fun tptp_classrelClause (ClassrelClause cls) =

     let val relcls_id = clrelclause_prefix ^ string_of_int(#clause_id cls)

 	val sub = #subclass cls

 	val sup = #superclass cls

 	val lits = tptp_classrelLits sub sup

     in

 	"input_clause(" ^ relcls_id ^ ",axiom," ^ lits ^ ")."

     end; 

 end;