adjusted the polymorphism handling of Skolem constants so that proof reconstruction doesn't fail in "equality_inf"
(* Title: HOL/Tools/Sledgehammer/sledgehammer_hol_clause.ML
Author: Jia Meng, NICTA
Author: Jasmin Blanchette, TU Muenchen
FOL clauses translated from HOL formulae.
*)
signature SLEDGEHAMMER_HOL_CLAUSE =
sig
type name = Sledgehammer_FOL_Clause.name
type name_pool = Sledgehammer_FOL_Clause.name_pool
type kind = Sledgehammer_FOL_Clause.kind
type fol_type = Sledgehammer_FOL_Clause.fol_type
type classrel_clause = Sledgehammer_FOL_Clause.classrel_clause
type arity_clause = Sledgehammer_FOL_Clause.arity_clause
type axiom_name = string
type polarity = bool
type hol_clause_id = int
datatype combterm =
CombConst of name * fol_type * fol_type list (* Const and Free *) |
CombVar of name * fol_type |
CombApp of combterm * combterm
datatype literal = Literal of polarity * combterm
datatype hol_clause =
HOLClause of {clause_id: hol_clause_id, axiom_name: axiom_name, th: thm,
kind: kind, literals: literal list, ctypes_sorts: typ list}
val type_of_combterm : combterm -> fol_type
val strip_combterm_comb : combterm -> combterm * combterm list
val literals_of_term : theory -> term -> literal list * typ list
val conceal_skolem_somes :
int -> (string * term) list -> term -> (string * term) list * term
exception TRIVIAL
val make_conjecture_clauses : bool -> theory -> thm list -> hol_clause list
val make_axiom_clauses : bool -> theory ->
(thm * (axiom_name * hol_clause_id)) list -> (axiom_name * hol_clause) list
val type_wrapper_name : string
val get_helper_clauses :
bool -> theory -> bool -> hol_clause list
-> (thm * (axiom_name * hol_clause_id)) list -> hol_clause list
val write_tptp_file : bool -> bool -> bool -> Path.T ->
hol_clause list * hol_clause list * hol_clause list * hol_clause list *
classrel_clause list * arity_clause list -> name_pool option * int
val write_dfg_file : bool -> bool -> Path.T ->
hol_clause list * hol_clause list * hol_clause list * hol_clause list *
classrel_clause list * arity_clause list -> name_pool option * int
end
structure Sledgehammer_HOL_Clause : SLEDGEHAMMER_HOL_CLAUSE =
struct
open Sledgehammer_Util
open Sledgehammer_FOL_Clause
open Sledgehammer_Fact_Preprocessor
fun min_arity_of const_min_arity c = the_default 0 (Symtab.lookup const_min_arity c);
(*True if the constant ever appears outside of the top-level position in literals.
If false, the constant always receives all of its arguments and is used as a predicate.*)
fun needs_hBOOL explicit_apply const_needs_hBOOL c =
explicit_apply orelse
the_default false (Symtab.lookup const_needs_hBOOL c);
(******************************************************)
(* data types for typed combinator expressions *)
(******************************************************)
type axiom_name = string;
type polarity = bool;
type hol_clause_id = int;
datatype combterm =
CombConst of name * fol_type * fol_type list (* Const and Free *) |
CombVar of name * fol_type |
CombApp of combterm * combterm
datatype literal = Literal of polarity * combterm;
datatype hol_clause =
HOLClause of {clause_id: hol_clause_id, axiom_name: axiom_name, th: thm,
kind: kind, literals: literal list, ctypes_sorts: typ list};
(*********************************************************************)
(* convert a clause with type Term.term to a clause with type clause *)
(*********************************************************************)
fun isFalse (Literal (pol, CombConst ((c, _), _, _))) =
(pol andalso c = "c_False") orelse (not pol andalso c = "c_True")
| isFalse _ = false;
fun isTrue (Literal (pol, CombConst ((c, _), _, _))) =
(pol andalso c = "c_True") orelse
(not pol andalso c = "c_False")
| isTrue _ = false;
fun isTaut (HOLClause {literals,...}) = exists isTrue literals;
fun type_of dfg (Type (a, Ts)) =
let val (folTypes,ts) = types_of dfg Ts in
(TyConstr (`(make_fixed_type_const dfg) a, folTypes), ts)
end
| type_of _ (tp as TFree (a, _)) = (TyFree (`make_fixed_type_var a), [tp])
| type_of _ (tp as TVar (x, _)) =
(TyVar (make_schematic_type_var x, string_of_indexname x), [tp])
and types_of dfg Ts =
let val (folTyps,ts) = ListPair.unzip (map (type_of dfg) Ts)
in (folTyps, union_all ts) end;
(* same as above, but no gathering of sort information *)
fun simp_type_of dfg (Type (a, Ts)) =
TyConstr (`(make_fixed_type_const dfg) a, map (simp_type_of dfg) Ts)
| simp_type_of _ (TFree (a, _)) = TyFree (`make_fixed_type_var a)
| simp_type_of _ (TVar (x, _)) =
TyVar (make_schematic_type_var x, string_of_indexname x);
(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
fun combterm_of dfg thy (Const (c, T)) =
let
val (tp, ts) = type_of dfg T
val tvar_list =
(if String.isPrefix skolem_theory_name c then
[] |> Term.add_tvarsT T |> map TVar
else
(c, T) |> Sign.const_typargs thy)
|> map (simp_type_of dfg)
val c' = CombConst (`(make_fixed_const dfg) c, tp, tvar_list)
in (c',ts) end
| combterm_of dfg _ (Free(v, T)) =
let val (tp,ts) = type_of dfg T
val v' = CombConst (`make_fixed_var v, tp, [])
in (v',ts) end
| combterm_of dfg _ (Var(v, T)) =
let val (tp,ts) = type_of dfg T
val v' = CombVar ((make_schematic_var v, string_of_indexname v), tp)
in (v',ts) end
| combterm_of dfg thy (P $ Q) =
let val (P',tsP) = combterm_of dfg thy P
val (Q',tsQ) = combterm_of dfg thy Q
in (CombApp(P',Q'), union (op =) tsP tsQ) end
| combterm_of _ _ (t as Abs _) = raise CLAUSE ("HOL clause", t);
fun predicate_of dfg thy ((@{const Not} $ P), polarity) = predicate_of dfg thy (P, not polarity)
| predicate_of dfg thy (t,polarity) = (combterm_of dfg thy (Envir.eta_contract t), polarity);
fun literals_of_term1 dfg thy args (@{const Trueprop} $ P) = literals_of_term1 dfg thy args P
| literals_of_term1 dfg thy args (@{const "op |"} $ P $ Q) =
literals_of_term1 dfg thy (literals_of_term1 dfg thy args P) Q
| literals_of_term1 dfg thy (lits,ts) P =
let val ((pred,ts'),pol) = predicate_of dfg thy (P,true)
in
(Literal(pol,pred)::lits, union (op =) ts ts')
end;
fun literals_of_term_dfg dfg thy P = literals_of_term1 dfg thy ([],[]) P;
val literals_of_term = literals_of_term_dfg false;
fun skolem_name i j num_T_args =
skolem_prefix ^ (space_implode "_" (map Int.toString [i, j, num_T_args])) ^
skolem_infix ^ "g"
fun conceal_skolem_somes i skolem_somes t =
if exists_Const (curry (op =) @{const_name skolem_id} o fst) t then
let
fun aux skolem_somes
(t as (Const (@{const_name skolem_id}, Type (_, [_, T])) $ _)) =
let
val (skolem_somes, s) =
if i = ~1 then
(skolem_somes, @{const_name undefined})
else case AList.find (op aconv) skolem_somes t of
s :: _ => (skolem_somes, s)
| _ =>
let
val s = skolem_theory_name ^ "." ^
skolem_name i (length skolem_somes)
(length (Term.add_tvarsT T []))
in ((s, t) :: skolem_somes, s) end
in (skolem_somes, Const (s, T)) end
| aux skolem_somes (t1 $ t2) =
let
val (skolem_somes, t1) = aux skolem_somes t1
val (skolem_somes, t2) = aux skolem_somes t2
in (skolem_somes, t1 $ t2) end
| aux skolem_somes (Abs (s, T, t')) =
let val (skolem_somes, t') = aux skolem_somes t' in
(skolem_somes, Abs (s, T, t'))
end
| aux skolem_somes t = (skolem_somes, t)
in aux skolem_somes t end
else
(skolem_somes, t)
(* Trivial problem, which resolution cannot handle (empty clause) *)
exception TRIVIAL;
(* making axiom and conjecture clauses *)
fun make_clause dfg thy (clause_id, axiom_name, kind, th) skolem_somes =
let
val (skolem_somes, t) =
th |> prop_of |> conceal_skolem_somes clause_id skolem_somes
val (lits, ctypes_sorts) = literals_of_term_dfg dfg thy t
in
if forall isFalse lits then
raise TRIVIAL
else
(skolem_somes,
HOLClause {clause_id = clause_id, axiom_name = axiom_name, th = th,
kind = kind, literals = lits, ctypes_sorts = ctypes_sorts})
end
fun add_axiom_clause dfg thy (th, (name, id)) (skolem_somes, clss) =
let
val (skolem_somes, cls) =
make_clause dfg thy (id, name, Axiom, th) skolem_somes
in (skolem_somes, clss |> not (isTaut cls) ? cons (name, cls)) end
fun make_axiom_clauses dfg thy clauses =
([], []) |> fold (add_axiom_clause dfg thy) clauses |> snd
fun make_conjecture_clauses dfg thy =
let
fun aux _ _ [] = []
| aux n skolem_somes (th :: ths) =
let
val (skolem_somes, cls) =
make_clause dfg thy (n, "conjecture", Conjecture, th) skolem_somes
in cls :: aux (n + 1) skolem_somes ths end
in aux 0 [] end
(**********************************************************************)
(* convert clause into ATP specific formats: *)
(* TPTP used by Vampire and E *)
(* DFG used by SPASS *)
(**********************************************************************)
(*Result of a function type; no need to check that the argument type matches.*)
fun result_type (TyConstr (_, [_, tp2])) = tp2
| result_type _ = raise Fail "non-function type"
fun type_of_combterm (CombConst (_, tp, _)) = tp
| type_of_combterm (CombVar (_, tp)) = tp
| type_of_combterm (CombApp (t1, _)) = result_type (type_of_combterm t1);
(*gets the head of a combinator application, along with the list of arguments*)
fun strip_combterm_comb u =
let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
| stripc x = x
in stripc(u,[]) end;
val type_wrapper_name = "ti"
fun head_needs_hBOOL explicit_apply const_needs_hBOOL
(CombConst ((c, _), _, _)) =
needs_hBOOL explicit_apply const_needs_hBOOL c
| head_needs_hBOOL _ _ _ = true
fun wrap_type full_types (s, ty) pool =
if full_types then
let val (s', pool) = string_of_fol_type ty pool in
(type_wrapper_name ^ paren_pack [s, s'], pool)
end
else
(s, pool)
fun wrap_type_if full_types explicit_apply cnh (head, s, tp) =
if head_needs_hBOOL explicit_apply cnh head then
wrap_type full_types (s, tp)
else
pair s
fun apply ss = "hAPP" ^ paren_pack ss;
fun rev_apply (v, []) = v
| rev_apply (v, arg::args) = apply [rev_apply (v, args), arg];
fun string_apply (v, args) = rev_apply (v, rev args);
(* Apply an operator to the argument strings, using either the "apply" operator
or direct function application. *)
fun string_of_application full_types cma (CombConst ((s, s'), _, tvars), args)
pool =
let
val s = if s = "equal" then "c_fequal" else s
val nargs = min_arity_of cma s
val args1 = List.take (args, nargs)
handle Subscript =>
raise Fail (quote s ^ " has arity " ^ Int.toString nargs ^
" but is applied to " ^ commas (map quote args))
val args2 = List.drop (args, nargs)
val (targs, pool) = if full_types then ([], pool)
else pool_map string_of_fol_type tvars pool
val (s, pool) = nice_name (s, s') pool
in (string_apply (s ^ paren_pack (args1 @ targs), args2), pool) end
| string_of_application _ _ (CombVar (name, _), args) pool =
nice_name name pool |>> (fn s => string_apply (s, args))
fun string_of_combterm (params as (full_types, explicit_apply, cma, cnh)) t
pool =
let
val (head, args) = strip_combterm_comb t
val (ss, pool) = pool_map (string_of_combterm params) args pool
val (s, pool) = string_of_application full_types cma (head, ss) pool
in
wrap_type_if full_types explicit_apply cnh (head, s, type_of_combterm t)
pool
end
(*Boolean-valued terms are here converted to literals.*)
fun boolify params c =
string_of_combterm params c #>> prefix "hBOOL" o paren_pack o single
fun string_of_predicate (params as (_, explicit_apply, _, cnh)) t =
case t of
(CombApp (CombApp (CombConst (("equal", _), _, _), t1), t2)) =>
(* DFG only: new TPTP prefers infix equality *)
pool_map (string_of_combterm params) [t1, t2]
#>> prefix "equal" o paren_pack
| _ =>
case #1 (strip_combterm_comb t) of
CombConst ((s, _), _, _) =>
(if needs_hBOOL explicit_apply cnh s then boolify else string_of_combterm)
params t
| _ => boolify params t
(*** TPTP format ***)
fun tptp_of_equality params pos (t1, t2) =
pool_map (string_of_combterm params) [t1, t2]
#>> space_implode (if pos then " = " else " != ")
fun tptp_literal params
(Literal (pos, CombApp (CombApp (CombConst (("equal", _), _, _), t1),
t2))) =
tptp_of_equality params pos (t1, t2)
| tptp_literal params (Literal (pos, pred)) =
string_of_predicate params pred #>> tptp_sign pos
(* Given a clause, returns its literals paired with a list of literals
concerning TFrees; the latter should only occur in conjecture clauses. *)
fun tptp_type_literals params pos (HOLClause {literals, ctypes_sorts, ...})
pool =
let
val (lits, pool) = pool_map (tptp_literal params) literals pool
val (tylits, pool) = pool_map (tptp_of_type_literal pos)
(type_literals_for_types ctypes_sorts) pool
in ((lits, tylits), pool) end
fun tptp_clause params (cls as HOLClause {axiom_name, clause_id, kind, ...})
pool =
let
val ((lits, tylits), pool) =
tptp_type_literals params (kind = Conjecture) cls pool
in
((gen_tptp_cls (clause_id, axiom_name, kind, lits, tylits), tylits), pool)
end
(*** DFG format ***)
fun dfg_literal params (Literal (pos, pred)) =
string_of_predicate params pred #>> dfg_sign pos
fun dfg_type_literals params pos (HOLClause {literals, ctypes_sorts, ...}) =
pool_map (dfg_literal params) literals
#>> rpair (map (dfg_of_type_literal pos)
(type_literals_for_types ctypes_sorts))
fun get_uvars (CombConst _) vars pool = (vars, pool)
| get_uvars (CombVar (name, _)) vars pool =
nice_name name pool |>> (fn var => var :: vars)
| get_uvars (CombApp (P, Q)) vars pool =
let val (vars, pool) = get_uvars P vars pool in get_uvars Q vars pool end
fun get_uvars_l (Literal (_, c)) = get_uvars c [];
fun dfg_vars (HOLClause {literals, ...}) =
pool_map get_uvars_l literals #>> union_all
fun dfg_clause params (cls as HOLClause {axiom_name, clause_id, kind,
ctypes_sorts, ...}) pool =
let
val ((lits, tylits), pool) =
dfg_type_literals params (kind = Conjecture) cls pool
val (vars, pool) = dfg_vars cls pool
val tvars = get_tvar_strs ctypes_sorts
in
((gen_dfg_cls (clause_id, axiom_name, kind, lits, tylits, tvars @ vars),
tylits), pool)
end
(** For DFG format: accumulate function and predicate declarations **)
fun add_types tvars = fold add_fol_type_funcs tvars
fun add_decls (full_types, explicit_apply, cma, cnh)
(CombConst ((c, _), ctp, tvars)) (funcs, preds) =
(if c = "equal" then
(add_types tvars funcs, preds)
else
let val arity = min_arity_of cma c
val ntys = if not full_types then length tvars else 0
val addit = Symtab.update(c, arity + ntys)
in
if needs_hBOOL explicit_apply cnh c then
(add_types tvars (addit funcs), preds)
else
(add_types tvars funcs, addit preds)
end) |>> full_types ? add_fol_type_funcs ctp
| add_decls _ (CombVar (_, ctp)) (funcs, preds) =
(add_fol_type_funcs ctp funcs, preds)
| add_decls params (CombApp (P, Q)) decls =
decls |> add_decls params P |> add_decls params Q
fun add_literal_decls params (Literal (_, c)) = add_decls params c
fun add_clause_decls params (HOLClause {literals, ...}) decls =
fold (add_literal_decls params) literals decls
handle Symtab.DUP a => error ("function " ^ a ^ " has multiple arities")
fun decls_of_clauses params clauses arity_clauses =
let val functab =
init_functab |> fold Symtab.update [(type_wrapper_name, 2), ("hAPP", 2),
("tc_bool", 0)]
val predtab = Symtab.empty |> Symtab.update ("hBOOL", 1)
val (functab, predtab) =
(functab, predtab) |> fold (add_clause_decls params) clauses
|>> fold add_arity_clause_funcs arity_clauses
in (Symtab.dest functab, Symtab.dest predtab) end
fun add_clause_preds (HOLClause {ctypes_sorts, ...}) preds =
fold add_type_sort_preds ctypes_sorts preds
handle Symtab.DUP a => error ("predicate " ^ a ^ " has multiple arities")
(*Higher-order clauses have only the predicates hBOOL and type classes.*)
fun preds_of_clauses clauses clsrel_clauses arity_clauses =
Symtab.empty
|> fold add_clause_preds clauses
|> fold add_arity_clause_preds arity_clauses
|> fold add_classrel_clause_preds clsrel_clauses
|> Symtab.dest
(**********************************************************************)
(* write clauses to files *)
(**********************************************************************)
val init_counters =
Symtab.make [("c_COMBI", 0), ("c_COMBK", 0), ("c_COMBB", 0), ("c_COMBC", 0),
("c_COMBS", 0)];
fun count_combterm (CombConst ((c, _), _, _)) =
Symtab.map_entry c (Integer.add 1)
| count_combterm (CombVar _) = I
| count_combterm (CombApp (t1, t2)) = count_combterm t1 #> count_combterm t2
fun count_literal (Literal (_, t)) = count_combterm t
fun count_clause (HOLClause {literals, ...}) = fold count_literal literals
fun cnf_helper_thms thy = cnf_rules_pairs thy o map (`Thm.get_name_hint)
fun get_helper_clauses dfg thy isFO conjectures axcls =
if isFO then
[]
else
let
val axclauses = map snd (make_axiom_clauses dfg thy axcls)
val ct = init_counters
|> fold (fold count_clause) [conjectures, axclauses]
fun needed c = the (Symtab.lookup ct c) > 0
val IK = if needed "c_COMBI" orelse needed "c_COMBK"
then cnf_helper_thms thy [@{thm COMBI_def}, @{thm COMBK_def}]
else []
val BC = if needed "c_COMBB" orelse needed "c_COMBC"
then cnf_helper_thms thy [@{thm COMBB_def}, @{thm COMBC_def}]
else []
val S = if needed "c_COMBS" then cnf_helper_thms thy [@{thm COMBS_def}]
else []
val other = cnf_helper_thms thy [@{thm fequal_imp_equal},
@{thm equal_imp_fequal}]
in map snd (make_axiom_clauses dfg thy (other @ IK @ BC @ S)) end
(*Find the minimal arity of each function mentioned in the term. Also, note which uses
are not at top level, to see if hBOOL is needed.*)
fun count_constants_term toplev t (const_min_arity, const_needs_hBOOL) =
let val (head, args) = strip_combterm_comb t
val n = length args
val (const_min_arity, const_needs_hBOOL) =
(const_min_arity, const_needs_hBOOL)
|> fold (count_constants_term false) args
in
case head of
CombConst ((a, _),_,_) => (*predicate or function version of "equal"?*)
let val a = if a="equal" andalso not toplev then "c_fequal" else a
in
(const_min_arity |> Symtab.map_default (a, n) (Integer.min n),
const_needs_hBOOL |> not toplev ? Symtab.update (a, true))
end
| _ => (const_min_arity, const_needs_hBOOL)
end;
(*A literal is a top-level term*)
fun count_constants_lit (Literal (_,t)) (const_min_arity, const_needs_hBOOL) =
count_constants_term true t (const_min_arity, const_needs_hBOOL);
fun count_constants_clause (HOLClause {literals, ...})
(const_min_arity, const_needs_hBOOL) =
fold count_constants_lit literals (const_min_arity, const_needs_hBOOL);
fun display_arity explicit_apply const_needs_hBOOL (c,n) =
trace_msg (fn () => "Constant: " ^ c ^
" arity:\t" ^ Int.toString n ^
(if needs_hBOOL explicit_apply const_needs_hBOOL c then
" needs hBOOL"
else
""))
fun count_constants explicit_apply
(conjectures, _, extra_clauses, helper_clauses, _, _) =
if not explicit_apply then
let val (const_min_arity, const_needs_hBOOL) =
fold count_constants_clause conjectures (Symtab.empty, Symtab.empty)
|> fold count_constants_clause extra_clauses
|> fold count_constants_clause helper_clauses
val _ = app (display_arity explicit_apply const_needs_hBOOL)
(Symtab.dest (const_min_arity))
in (const_min_arity, const_needs_hBOOL) end
else (Symtab.empty, Symtab.empty);
fun header () =
"% This file was generated by Isabelle (most likely Sledgehammer)\n" ^
"% " ^ timestamp () ^ "\n"
(* TPTP format *)
fun write_tptp_file readable_names full_types explicit_apply file clauses =
let
fun section _ [] = []
| section name ss =
"\n% " ^ name ^ plural_s (length ss) ^ " (" ^ Int.toString (length ss) ^
")\n" :: ss
val pool = empty_name_pool readable_names
val (conjectures, axclauses, _, helper_clauses,
classrel_clauses, arity_clauses) = clauses
val (cma, cnh) = count_constants explicit_apply clauses
val params = (full_types, explicit_apply, cma, cnh)
val ((conjecture_clss, tfree_litss), pool) =
pool_map (tptp_clause params) conjectures pool |>> ListPair.unzip
val tfree_clss = map tptp_tfree_clause (fold (union (op =)) tfree_litss [])
val (ax_clss, pool) = pool_map (apfst fst oo tptp_clause params) axclauses
pool
val classrel_clss = map tptp_classrel_clause classrel_clauses
val arity_clss = map tptp_arity_clause arity_clauses
val (helper_clss, pool) = pool_map (apfst fst oo tptp_clause params)
helper_clauses pool
val conjecture_offset =
length ax_clss + length classrel_clss + length arity_clss
+ length helper_clss
val _ =
File.write_list file
(header () ::
section "Relevant fact" ax_clss @
section "Class relationship" classrel_clss @
section "Arity declaration" arity_clss @
section "Helper fact" helper_clss @
section "Conjecture" conjecture_clss @
section "Type variable" tfree_clss)
in (pool, conjecture_offset) end
(* DFG format *)
fun dfg_tfree_predicate s = (first_field "(" s |> the |> fst, 1)
fun write_dfg_file full_types explicit_apply file clauses =
let
(* Some of the helper functions below are not name-pool-aware. However,
there's no point in adding name pool support if the DFG format is on its
way out anyway. *)
val pool = NONE
val (conjectures, axclauses, _, helper_clauses,
classrel_clauses, arity_clauses) = clauses
val (cma, cnh) = count_constants explicit_apply clauses
val params = (full_types, explicit_apply, cma, cnh)
val ((conjecture_clss, tfree_litss), pool) =
pool_map (dfg_clause params) conjectures pool |>> ListPair.unzip
val tfree_lits = union_all tfree_litss
val problem_name = Path.implode (Path.base file)
val (axstrs, pool) = pool_map (apfst fst oo dfg_clause params) axclauses pool
val tfree_clss = map dfg_tfree_clause tfree_lits
val tfree_preds = map dfg_tfree_predicate tfree_lits
val (helper_clauses_strs, pool) =
pool_map (apfst fst oo dfg_clause params) helper_clauses pool
val (funcs, cl_preds) = decls_of_clauses params (helper_clauses @ conjectures @ axclauses) arity_clauses
val ty_preds = preds_of_clauses axclauses classrel_clauses arity_clauses
val preds = tfree_preds @ cl_preds @ ty_preds
val conjecture_offset =
length axclauses + length classrel_clauses + length arity_clauses
+ length helper_clauses
val _ =
File.write_list file
(header () ::
string_of_start problem_name ::
string_of_descrip problem_name ::
string_of_symbols (string_of_funcs funcs)
(string_of_preds preds) ::
"list_of_clauses(axioms, cnf).\n" ::
axstrs @
map dfg_classrel_clause classrel_clauses @
map dfg_arity_clause arity_clauses @
helper_clauses_strs @
["end_of_list.\n\nlist_of_clauses(conjectures, cnf).\n"] @
conjecture_clss @
tfree_clss @
["end_of_list.\n\n",
"end_problem.\n"])
in (pool, conjecture_offset) end
end;