(*  Title:      HOL/Tools/ATP/atp_proof.ML

    Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory

    Author:     Claire Quigley, Cambridge University Computer Laboratory

    Author:     Jasmin Blanchette, TU Muenchen

Abstract representation of ATP proofs and TSTP/SPASS syntax.

*)

signature ATP_PROOF =

sig

  type 'a atp_type = 'a ATP_Problem.atp_type

  type ('a, 'b) atp_term = ('a, 'b) ATP_Problem.atp_term

  type atp_formula_role = ATP_Problem.atp_formula_role

  type ('a, 'b, 'c, 'd) atp_formula = ('a, 'b, 'c, 'd) ATP_Problem.atp_formula

  type 'a atp_problem = 'a ATP_Problem.atp_problem

  exception UNRECOGNIZED_ATP_PROOF of unit

  datatype atp_failure =

    Unprovable |

    GaveUp |

    ProofMissing |

    ProofIncomplete |

    ProofUnparsable |

    UnsoundProof of bool * string list |

    CantConnect |

    TimedOut |

    Inappropriate |

    OutOfResources |

    NoPerl |

    NoLibwwwPerl |

    MalformedInput |

    MalformedOutput |

    Interrupted |

    Crashed |

    InternalError |

    UnknownError of string

  type atp_step_name = string * string list

  type ('a, 'b) atp_step =

    atp_step_name * atp_formula_role * 'a * 'b * atp_step_name list

  type 'a atp_proof = (('a, 'a, ('a, 'a atp_type) atp_term, 'a) atp_formula, string) atp_step list

  (* Named ATPs *)

  val agsyholN : string

  val alt_ergoN : string

  val dummy_thfN : string

  val dummy_thf_mlN : string

  val eN : string

  val e_malesN : string

  val e_parN : string

  val e_sineN : string

  val e_tofofN : string

  val iproverN : string

  val iprover_eqN : string

  val leo2N : string

  val satallaxN : string

  val snarkN : string

  val spassN : string

  val spass_pirateN : string

  val vampireN : string

  val waldmeisterN : string

  val waldmeister_newN : string

  val z3_tptpN : string

  val zipperpositionN : string

  val remote_prefix : string

  val agsyhol_core_rule : string

  val satallax_core_rule : string

  val spass_input_rule : string

  val spass_pre_skolemize_rule : string

  val spass_skolemize_rule : string

  val z3_tptp_core_rule : string

  val short_output : bool -> string -> string

  val string_of_atp_failure : atp_failure -> string

  val extract_important_message : string -> string

  val extract_known_atp_failure : (atp_failure * string) list -> string -> atp_failure option

  val extract_tstplike_proof_and_outcome :

    bool -> (string * string) list -> (atp_failure * string) list -> string

    -> string * atp_failure option

  val is_same_atp_step : atp_step_name -> atp_step_name -> bool

  val scan_general_id : string list -> string * string list

  val parse_formula : string list ->

    (string, string atp_type, (string, string atp_type) atp_term, string) atp_formula * string list

  val atp_proof_of_tstplike_proof : string -> string atp_problem -> string -> string atp_proof

  val clean_up_atp_proof_dependencies : string atp_proof -> string atp_proof

  val map_term_names_in_atp_proof : (string -> string) -> string atp_proof -> string atp_proof

  val nasty_atp_proof : string Symtab.table -> string atp_proof -> string atp_proof

end;

structure ATP_Proof : ATP_PROOF =

struct

open ATP_Util

open ATP_Problem

(* Named ATPs *)

val agsyholN = "agsyhol"

val alt_ergoN = "alt_ergo"

val dummy_thfN = "dummy_thf" (* for experiments *)

val dummy_thf_mlN = "dummy_thf_ml" (* for experiments *)

val eN = "e"

val e_malesN = "e_males"

val e_parN = "e_par"

val e_sineN = "e_sine"

val e_tofofN = "e_tofof"

val iproverN = "iprover"

val iprover_eqN = "iprover_eq"

val leo2N = "leo2"

val satallaxN = "satallax"

val snarkN = "snark"

val spassN = "spass"

val spass_pirateN = "spass_pirate"

val vampireN = "vampire"

val waldmeisterN = "waldmeister"

val waldmeister_newN = "waldmeister_new"

val z3_tptpN = "z3_tptp"

val zipperpositionN = "zipperposition"

val remote_prefix = "remote_"

val agsyhol_core_rule = "__agsyhol_core" (* arbitrary *)

val satallax_core_rule = "__satallax_core" (* arbitrary *)

val spass_input_rule = "Inp"

val spass_pre_skolemize_rule = "__Sko0" (* arbitrary *)

val spass_skolemize_rule = "__Sko" (* arbitrary *)

val z3_tptp_core_rule = "__z3_tptp_core" (* arbitrary *)

exception UNRECOGNIZED_ATP_PROOF of unit

datatype atp_failure =

  Unprovable |

  GaveUp |

  ProofMissing |

  ProofIncomplete |

  ProofUnparsable |

  UnsoundProof of bool * string list |

  CantConnect |

  TimedOut |

  Inappropriate |

  OutOfResources |

  NoPerl |

  NoLibwwwPerl |

  MalformedInput |

  MalformedOutput |

  Interrupted |

  Crashed |

  InternalError |

  UnknownError of string

fun short_output verbose output =

  if verbose then

    if output = "" then "No details available" else elide_string 1000 output

  else

    ""

val missing_message_tail =

  " appears to be missing. You will need to install it if you want to invoke \

  \remote provers."

fun from_lemmas [] = ""

  | from_lemmas ss = " from " ^ space_implode " " (Try.serial_commas "and" (map quote ss))

fun string_of_atp_failure Unprovable = "The generated problem is unprovable."

  | string_of_atp_failure GaveUp = "The prover gave up."

  | string_of_atp_failure ProofMissing =

    "The prover claims the conjecture is a theorem but did not provide a proof."

  | string_of_atp_failure ProofIncomplete =

    "The prover claims the conjecture is a theorem but provided an incomplete proof."

  | string_of_atp_failure ProofUnparsable =

    "The prover claims the conjecture is a theorem but provided an unparsable proof."

  | string_of_atp_failure (UnsoundProof (false, ss)) =

    "The prover derived \"False\"" ^ from_lemmas ss ^

    ". Specify a sound type encoding or omit the \"type_enc\" option."

  | string_of_atp_failure (UnsoundProof (true, ss)) =

    "The prover derived \"False\"" ^ from_lemmas ss ^

    ". This could be due to inconsistent axioms (including \"sorry\"s) or to \

    \a bug in Sledgehammer. If the problem persists, please contact the \

    \Isabelle developers."

  | string_of_atp_failure CantConnect = "Cannot connect to remote server."

  | string_of_atp_failure TimedOut = "Timed out."

  | string_of_atp_failure Inappropriate =

    "The generated problem lies outside the prover's scope."

  | string_of_atp_failure OutOfResources = "The prover ran out of resources."

  | string_of_atp_failure NoPerl = "Perl" ^ missing_message_tail

  | string_of_atp_failure NoLibwwwPerl =

    "The Perl module \"libwww-perl\"" ^ missing_message_tail

  | string_of_atp_failure MalformedInput =

    "The generated problem is malformed. Please report this to the Isabelle \

    \developers."

  | string_of_atp_failure MalformedOutput = "The prover output is malformed."

  | string_of_atp_failure Interrupted = "The prover was interrupted."

  | string_of_atp_failure Crashed = "The prover crashed."

  | string_of_atp_failure InternalError = "An internal prover error occurred."

  | string_of_atp_failure (UnknownError s) =

    "A prover error occurred" ^

    (if s = "" then ". (Pass the \"verbose\" option for details.)"

     else ":\n" ^ s)

fun extract_delimited (begin_delim, end_delim) output =

  (case first_field begin_delim output of

    SOME (_, tail) =>

    (case first_field "\n" tail of

      SOME (_, tail') =>

      if end_delim = "" then

        tail'

      else

        (case first_field end_delim tail' of

          SOME (body, _) => body

        | NONE => "")

    | NONE => "")

  | NONE => "")

val tstp_important_message_delims =

  ("% SZS start RequiredInformation", "% SZS end RequiredInformation")

fun extract_important_message output =

  (case extract_delimited tstp_important_message_delims output of

    "" => ""

  | s => s |> space_explode "\n" |> filter_out (curry (op =) "")

           |> map (perhaps (try (unprefix "%")))

           |> map (perhaps (try (unprefix " ")))

           |> space_implode "\n " |> quote)

(* Splits by the first possible of a list of delimiters. *)

fun extract_tstplike_proof delims output =

  (case pairself (find_first (fn s => String.isSubstring s output)) (ListPair.unzip delims) of

    (SOME begin_delim, SOME end_delim) => extract_delimited (begin_delim, end_delim) output

  | _ => "")

fun extract_known_atp_failure known_failures output =

  known_failures

  |> find_first (fn (_, pattern) => String.isSubstring pattern output)

  |> Option.map fst

fun extract_tstplike_proof_and_outcome verbose proof_delims known_failures output =

  (case (extract_tstplike_proof proof_delims output,

      extract_known_atp_failure known_failures output) of

    (_, SOME ProofIncomplete) => ("", NONE)

  | (_, SOME ProofUnparsable) => ("", NONE)

  | ("", SOME ProofMissing) => ("", NONE)

  | ("", NONE) => ("", SOME (UnknownError (short_output verbose output)))

  | res as ("", _) => res

  | (tstplike_proof, _) => (tstplike_proof, NONE))

type atp_step_name = string * string list

fun is_same_atp_step (s1, _) (s2, _) = s1 = s2

val vampire_fact_prefix = "f"

fun vampire_step_name_ord p =

  let val q = pairself fst p in

    (* The "unprefix" part is to cope with Vampire's output. *)

    (case pairself (Int.fromString o perhaps (try (unprefix vampire_fact_prefix))) q of

      (SOME i, SOME j) => int_ord (i, j)

    | _ => raise Fail "not Vampire")

  end

type ('a, 'b) atp_step = atp_step_name * atp_formula_role * 'a * 'b * atp_step_name list

type 'a atp_proof = (('a, 'a, ('a, 'a atp_type) atp_term, 'a) atp_formula, string) atp_step list

(**** PARSING OF TSTP FORMAT ****)

(* Strings enclosed in single quotes (e.g., file names), identifiers possibly starting

   with "$" and possibly with "!" in them (for "z3_tptp"). *)

val scan_general_id =

  $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode

  || (Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig >> (op ^ o pairself implode))

    -- Scan.optional (Scan.repeat ($$ "!") -- Scan.many1 Symbol.is_letdig >> (op ^ o pairself implode)) ""

    >> op ^

val skip_term =

  let

    fun skip _ accum [] = (accum, [])

      | skip n accum (ss as s :: ss') =

        if s = "," andalso n = 0 then

          (accum, ss)

        else if member (op =) [")", "]"] s then

          if n = 0 then (accum, ss) else skip (n - 1) (s :: accum) ss'

        else if member (op =) ["(", "["] s then

          skip (n + 1) (s :: accum) ss'

        else

          skip n (s :: accum) ss'

  in

    skip 0 [] #>> (rev #> implode)

  end

datatype source =

  File_Source of string * string option |

  Inference_Source of string * string list

val dummy_phi = AAtom (ATerm (("", []), []))

val dummy_inference = Inference_Source ("", [])

val dummy_atype = AType(("", []), [])

(* "skip_term" is there to cope with Waldmeister nonsense such as "theory(equality)". *)

fun parse_dependency x =

  (parse_inference_source >> snd

   || scan_general_id --| skip_term >> single) x

and parse_dependencies x =

  (Scan.repeat (Scan.option ($$ ",") |-- parse_dependency)

   >> (flat #> filter_out (curry (op =) "theory"))) x

and parse_file_source x =

  (Scan.this_string "file" |-- $$ "(" |-- scan_general_id

   -- Scan.option ($$ "," |-- scan_general_id

     --| Scan.option ($$ "," |-- $$ "[" -- Scan.option scan_general_id --| $$ "]")) --| $$ ")") x

and parse_inference_source x =

  (Scan.this_string "inference" |-- $$ "(" |-- scan_general_id

   --| skip_term --| $$ "," --| skip_term --| $$ "," --| $$ "["

   -- parse_dependencies --| $$ "]" --| $$ ")") x

and skip_introduced x =

  (Scan.this_string "introduced" |-- $$ "(" |-- skip_term

   -- Scan.repeat ($$ "," |-- skip_term) --| $$ ")") x

and parse_source x =

  (parse_file_source >> File_Source

   || parse_inference_source >> Inference_Source

   || skip_introduced >> K dummy_inference (* for Vampire *)

   || scan_general_id >> (fn s => Inference_Source ("", [s])) (* for E *)

   || skip_term >> K dummy_inference) x

fun list_app (f, args) = fold (fn arg => fn f => ATerm ((tptp_app, []), [f, arg])) args f

fun parse_class x = scan_general_id x

and parse_classes x = (parse_class ::: Scan.repeat ($$ "&" |-- parse_class)) x

fun parse_type x =

  (scan_general_id -- Scan.optional ($$ "{" |-- parse_classes --| $$ "}") []

    -- Scan.optional ($$ "(" |-- parse_types --| $$ ")") []

   >> AType) x

and parse_types x = (parse_type ::: Scan.repeat ($$ "," |-- parse_type)) x

(* We currently ignore TFF and THF types. *)

fun parse_type_signature x = Scan.repeat (($$ tptp_has_type || $$ tptp_fun_type) |-- parse_arg) x

and parse_arg x =

  ($$ "(" |-- parse_term --| $$ ")" --| parse_type_signature

   || scan_general_id --| parse_type_signature

       -- Scan.optional ($$ "<" |-- parse_types --| $$ ">") []

       -- Scan.optional ($$ "(" |-- parse_terms --| $$ ")") []

     >> ATerm) x

and parse_term x =

  (parse_arg -- Scan.repeat ($$ tptp_app |-- parse_arg)

   --| Scan.option parse_type_signature >> list_app) x

and parse_terms x = (parse_term ::: Scan.repeat ($$ "," |-- parse_term)) x

fun parse_atom x =

  (parse_term -- Scan.option (Scan.option ($$ tptp_not_infix) --| $$ tptp_equal -- parse_term)

   >> (fn (u1, NONE) => AAtom u1

        | (u1, SOME (neg, u2)) =>

          AAtom (ATerm (("equal", []), [u1, u2])) |> is_some neg ? mk_anot)) x

(* TPTP formulas are fully parenthesized, so we don't need to worry about operator precedence. *)

fun parse_literal x =

  ((Scan.repeat ($$ tptp_not) >> length)

      -- ($$ "(" |-- parse_formula --| $$ ")"

          || parse_quantified_formula

          || parse_atom)

      >> (fn (n, phi) => phi |> n mod 2 = 1 ? mk_anot)) x

and parse_formula x =

  (parse_literal

   -- Scan.option ((Scan.this_string tptp_implies

                    || Scan.this_string tptp_iff

                    || Scan.this_string tptp_not_iff

                    || Scan.this_string tptp_if

                    || $$ tptp_or

                    || $$ tptp_and) -- parse_formula)

   >> (fn (phi1, NONE) => phi1

        | (phi1, SOME (c, phi2)) =>

          if c = tptp_implies then mk_aconn AImplies phi1 phi2

          else if c = tptp_iff then mk_aconn AIff phi1 phi2

          else if c = tptp_not_iff then mk_anot (mk_aconn AIff phi1 phi2)

          else if c = tptp_if then mk_aconn AImplies phi2 phi1

          else if c = tptp_or then mk_aconn AOr phi1 phi2

          else if c = tptp_and then mk_aconn AAnd phi1 phi2

          else raise Fail ("impossible connective " ^ quote c))) x

and parse_quantified_formula x =

  (($$ tptp_forall >> K AForall || $$ tptp_exists >> K AExists)

   --| $$ "[" -- parse_terms --| $$ "]" --| $$ ":" -- parse_literal

   >> (fn ((q, ts), phi) => AQuant (q, map (fn ATerm ((s, []), _) => (s, NONE)) ts, phi))) x

val parse_tstp_extra_arguments =

  Scan.optional ($$ "," |-- parse_source --| Scan.option ($$ "," |-- skip_term)) dummy_inference

val waldmeister_conjecture_name = "conjecture_1"

val tofof_fact_prefix = "fof_"

fun is_same_term subst tm1 tm2 =

  let

    fun do_term_pair (AAbs (((var1, typ1), body1), args1)) (AAbs (((var2, typ2), body2), args2))

          (SOME subst) =

        if typ1 <> typ2 andalso length args1 = length args2 then NONE

        else

          let val ls = length subst in

            SOME ((var1, var2) :: subst)

            |> do_term_pair body1 body2

            |> (fn SOME subst => SOME (nth_drop (length subst - ls - 1) subst)

                 | NONE => NONE)

            |> (if length args1 = length args2

              then fold2 do_term_pair args1 args2

              else K NONE)

          end

      | do_term_pair (ATerm ((s1, _), args1)) (ATerm ((s2, _), args2)) (SOME subst) =

        (case pairself is_tptp_variable (s1, s2) of

          (true, true) =>

          (case AList.lookup (op =) subst s1 of

            SOME s2' => if s2' = s2 then SOME subst else NONE

          | NONE =>

            if null (AList.find (op =) subst s2) then SOME ((s1, s2) :: subst)

            else NONE)

        | (false, false) =>

          if s1 = s2 then

            SOME subst

          else

            NONE

        | _ => NONE) |> (if length args1 = length args2

                       then fold2 do_term_pair args1 args2

                       else K NONE)

      | do_term_pair _ _ _ = NONE

  in

    SOME subst |> do_term_pair tm1 tm2 |> is_some

  end

fun is_same_formula comm subst (AQuant (q1, xs1, phi1)) (AQuant (q2, xs2, phi2)) =

    q1 = q2 andalso length xs1 = length xs2 andalso

    is_same_formula comm ((map fst xs1 ~~ map fst xs2) @ subst) phi1 phi2

  | is_same_formula comm subst (AConn (c1, phis1)) (AConn (c2, phis2)) =

    c1 = c2 andalso length phis1 = length phis2 andalso

    forall (uncurry (is_same_formula comm subst)) (phis1 ~~ phis2)

  | is_same_formula comm subst (AAtom (tm1 as ATerm (("equal", tys), [tm11, tm12]))) (AAtom tm2) =

    is_same_term subst tm1 tm2 orelse

    (comm andalso is_same_term subst (ATerm (("equal", tys), [tm12, tm11])) tm2)

  | is_same_formula _ subst (AAtom tm1) (AAtom tm2) = is_same_term subst tm1 tm2

  | is_same_formula _ _ _ _ = false

fun matching_formula_line_identifier phi (Formula ((ident, _), _, phi', _, _)) =

    if is_same_formula true [] phi phi' then SOME (ident, phi') else NONE

  | matching_formula_line_identifier _ _ = NONE

fun find_formula_in_problem phi =

  maps snd

  #> map_filter (matching_formula_line_identifier phi)

  #> try (single o hd)

  #> the_default []

fun commute_eq (AAtom (ATerm ((s, tys), tms))) = AAtom (ATerm ((s, tys), rev tms))

  | commute_eq _ = raise Fail "expected equation"

fun role_of_tptp_string "axiom" = Axiom

  | role_of_tptp_string "definition" = Definition

  | role_of_tptp_string "lemma" = Lemma

  | role_of_tptp_string "hypothesis" = Hypothesis

  | role_of_tptp_string "conjecture" = Conjecture

  | role_of_tptp_string "negated_conjecture" = Negated_Conjecture

  | role_of_tptp_string "plain" = Plain

  | role_of_tptp_string "type" = Type_Role

  | role_of_tptp_string _ = Unknown

val tptp_binary_op_list = [tptp_and, tptp_not_and, tptp_or, tptp_not_or, tptp_implies, tptp_if,

                             tptp_iff, tptp_not_iff, tptp_equal, tptp_app]

fun parse_binary_op x =

  (foldl1 (op ||) (map Scan.this_string tptp_binary_op_list)

    >> (fn c => if c = tptp_equal then "equal" else c)) x

fun parse_thf0_type x =

  (($$ "(" |-- parse_thf0_type --| $$ ")" || scan_general_id >> (fn t => AType ((t, []), [])))

     -- Scan.option ($$ tptp_fun_type |-- parse_thf0_type)

  >> (fn (a, NONE) => a

       | (a, SOME b) => AFun (a, b))) x

fun mk_ho_of_fo_quant q =

  if q = tptp_forall then tptp_ho_forall

  else if q = tptp_exists then tptp_ho_exists

  else raise Fail ("unrecognized quantification: " ^ q)

fun remove_thf_app (ATerm ((x, ty), arg)) =

  if x = tptp_app then

    (case arg of

      ATerm ((x, ty), arg) :: t => remove_thf_app (ATerm ((x, ty), map remove_thf_app arg @ t))

    | [AAbs ((var, tvar), phi), t] =>

      remove_thf_app (AAbs ((var, tvar), map remove_thf_app phi @ [t])))

  else ATerm ((x, ty), map remove_thf_app arg)

  | remove_thf_app (AAbs (((x, ty), arg), t)) = AAbs (((x, ty), remove_thf_app arg), t)

fun parse_thf0_typed_var x =

  (Scan.repeat (scan_general_id -- Scan.option ($$ ":" |-- parse_thf0_type)

     --| Scan.option (Scan.this_string ","))

   || $$ "(" |-- parse_thf0_typed_var --| $$ ")") x

fun parse_simple_thf0_term x =

  ((Scan.this_string tptp_forall || Scan.this_string tptp_exists || Scan.this_string tptp_lambda)

        -- ($$ "[" |-- parse_thf0_typed_var --| $$ "]" --| $$ ":") -- parse_thf0_term

      >> (fn ((q, ys), t) =>

          fold_rev

            (fn (var, ty) => fn r =>

                AAbs (((var, the_default dummy_atype ty), r), [])

                |> (if tptp_lambda <> q then

                      mk_app (q |> mk_ho_of_fo_quant

                                |> mk_simple_aterm)

                    else I))

            ys t)

  || Scan.this_string tptp_not |-- parse_thf0_term >> mk_app (mk_simple_aterm tptp_not)

  || scan_general_id --| $$ ":" -- parse_thf0_type >> (fn (var, typ) => ATerm ((var, [typ]), []))

  || (Scan.this_string tptp_ho_forall || Scan.this_string tptp_ho_exists) >> mk_simple_aterm

  || $$ "(" |-- parse_thf0_term --| $$ ")"

  || scan_general_id >> mk_simple_aterm) x

and parse_thf0_term x =

  (parse_simple_thf0_term

      -- Scan.option (parse_binary_op

      -- parse_thf0_term)

    >> (fn (t1, SOME (c, t2)) =>

           if c = tptp_app then mk_app t1 t2 else mk_apps (mk_simple_aterm c) [t1, t2]

         | (t, NONE) => t)) x

fun parse_thf0_formula x = (parse_thf0_term #>> remove_thf_app #>> AAtom) x

fun parse_tstp_thf0_line problem =

  ((Scan.this_string tptp_cnf || Scan.this_string tptp_fof

    || Scan.this_string tptp_tff || Scan.this_string tptp_thf)

  -- $$ "(") |-- scan_general_id --| $$ "," -- Symbol.scan_ascii_id --| $$ ","

  -- parse_thf0_formula -- parse_tstp_extra_arguments --| $$ ")" --| $$ "."

  >> (fn (((num, role), phi), deps) =>

      let

        val role' = role_of_tptp_string role

        val ((name, phi), rule, deps) =

          (case deps of

            File_Source (_, SOME s) =>

            if role' = Definition then

              (((num, map fst (find_formula_in_problem phi problem)), phi), "", [])

            else

              (((num, [s |> perhaps (try (unprefix tofof_fact_prefix))]), phi), "", [])

          | Inference_Source (rule, deps) => (((num, []), phi), rule, deps))

      in

        [(name, role', phi, rule, map (rpair []) deps)]

      end)

(* Syntax: (cnf|fof|tff|thf)\(<num>, <formula_role>, <formula> <extra_arguments>\).

   The <num> could be an identifier, but we assume integers. *)

fun parse_tstp_line problem =

  ((Scan.this_string tptp_cnf || Scan.this_string tptp_fof

    || Scan.this_string tptp_tff || Scan.this_string tptp_thf) -- $$ "(")

    |-- scan_general_id --| $$ "," -- Symbol.scan_ascii_id --| $$ ","

    -- (parse_formula || skip_term >> K dummy_phi) -- parse_tstp_extra_arguments

    --| $$ ")" --| $$ "."

   >> (fn (((num, role), phi), deps) =>

          let

            val ((name, phi), rule, deps) =

              (* Waldmeister isn't exactly helping. *)

              (case deps of

                File_Source (_, SOME s) =>

                (if s = waldmeister_conjecture_name then

                   (case find_formula_in_problem (mk_anot phi) problem of

                     (* Waldmeister hack: Get the original orientation of the equation to avoid

                        confusing Isar. *)

                     [(s, phi')] =>

                     ((num, [s]),

                      phi |> not (is_same_formula false [] (mk_anot phi) phi') ? commute_eq)

                   | _ => ((num, []), phi))

                 else

                   ((num, [s |> perhaps (try (unprefix tofof_fact_prefix))]),

                    phi),

                 "", [])

              | File_Source _ =>

                (((num, map fst (find_formula_in_problem phi problem)), phi), "", [])

              | Inference_Source (rule, deps) => (((num, []), phi), rule, deps))

            fun mk_step () = (name, role_of_tptp_string role, phi, rule, map (rpair []) deps)

          in

            [(case role_of_tptp_string role of

               Definition =>

               (case phi of

                 AAtom (ATerm (("equal", _), _)) =>

                  (* Vampire's equality proxy axiom *)

                  (name, Definition, phi, rule, map (rpair []) deps)

               | _ => mk_step ())

             | _ => mk_step ())]

          end)

(**** PARSING OF SPASS OUTPUT ****)

(* SPASS returns clause references of the form "x.y". We ignore "y", whose role

   is not clear anyway. *)

val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id

val parse_spass_annotations =

  Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name --| Scan.option ($$ ","))) []

(* It is not clear why some literals are followed by sequences of stars and/or

   pluses. We ignore them. *)

fun parse_decorated_atom x =

  (parse_atom --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")) x

fun mk_horn ([], []) = AAtom (ATerm (("c_False", []), []))

  | mk_horn ([], pos_lits) = foldr1 (uncurry (mk_aconn AOr)) pos_lits

  | mk_horn (neg_lits, []) = mk_anot (foldr1 (uncurry (mk_aconn AAnd)) neg_lits)

  | mk_horn (neg_lits, pos_lits) =

    mk_aconn AImplies (foldr1 (uncurry (mk_aconn AAnd)) neg_lits)

                      (foldr1 (uncurry (mk_aconn AOr)) pos_lits)

fun parse_horn_clause x =

  (Scan.repeat parse_decorated_atom --| $$ "|" --| $$ "|"

     -- Scan.repeat parse_decorated_atom --| $$ "-" --| $$ ">"

     -- Scan.repeat parse_decorated_atom

   >> (mk_horn o apfst (op @))) x

val parse_spass_debug =

  Scan.option ($$ "(" |-- Scan.repeat (scan_general_id --| Scan.option ($$ ",")) --| $$ ")")

(* Syntax: <num>[0:<inference><annotations>] <atoms> || <atoms> -> <atoms> .

           derived from formulae <ident>* *)

fun parse_spass_line x =

  (parse_spass_debug |-- scan_general_id --| $$ "[" --| Scan.many1 Symbol.is_digit --| $$ ":"

     -- Symbol.scan_ascii_id -- parse_spass_annotations --| $$ "]" -- parse_horn_clause --| $$ "."

     -- Scan.option (Scan.this_string "derived from formulae "

                     |-- Scan.repeat (scan_general_id --| Scan.option ($$ " ")))

   >> (fn ((((num, rule), deps), u), names) =>

          [((num, these names), Unknown, u, rule, map (rpair []) deps)])) x

fun parse_spass_pirate_dependency x = (Scan.option ($$ "-") |-- scan_general_id) x

fun parse_spass_pirate_dependencies x =

  Scan.repeat (parse_spass_pirate_dependency --| Scan.option ($$ "," || $$ " ")) x

fun parse_spass_pirate_file_source x =

  ((Scan.this_string "Input" || Scan.this_string "Conj") |-- $$ "(" |-- scan_general_id

     --| $$ ")") x

fun parse_spass_pirate_inference_source x =

  (scan_general_id -- ($$ "(" |-- parse_spass_pirate_dependencies --| $$ ")")) x

fun parse_spass_pirate_source x =

  (parse_spass_pirate_file_source >> (fn s => File_Source ("", SOME s))

   || parse_spass_pirate_inference_source >> Inference_Source) x

(* Syntax: <num> <stuff> || <atoms> -> <atoms> . origin\(<origin>\) *)

fun parse_spass_pirate_line x =

  (scan_general_id --| Scan.repeat (~$$ "|") -- parse_horn_clause --| $$ "."

     --| Scan.this_string "origin" --| $$ "(" -- parse_spass_pirate_source --| $$ ")"

   >> (fn ((((num, u), source))) =>

     let

       val (names, rule, deps) =

         (case source of

           File_Source (_, SOME s) => ([s], spass_input_rule, [])

         | Inference_Source (rule, deps) => ([], rule, deps))

     in

       [((num, names), Unknown, u, rule, map (rpair []) deps)]

     end)) x

fun core_inference inf fact = ((fact, [fact]), Unknown, dummy_phi, inf, [])

(* Syntax: <name> *)

fun parse_satallax_core_line x =

  (scan_general_id --| Scan.option ($$ " ") >> (single o core_inference satallax_core_rule)) x

(* Syntax: SZS core <name> ... <name> *)

fun parse_z3_tptp_core_line x =

  (Scan.this_string "SZS core" |-- Scan.repeat ($$ " " |-- scan_general_id)

   >> map (core_inference z3_tptp_core_rule)) x

fun parse_line local_name problem =

  if local_name = leo2N then parse_tstp_thf0_line problem

  else if local_name = satallaxN then parse_satallax_core_line

  else if local_name = spassN then parse_spass_line

  else if local_name = spass_pirateN then parse_spass_pirate_line

  else if local_name = z3_tptpN then parse_z3_tptp_core_line

  else parse_tstp_line problem

fun parse_proof local_name problem =

  strip_spaces_except_between_idents

  #> raw_explode

  #> Scan.error (!! (fn _ => raise UNRECOGNIZED_ATP_PROOF ())

       (Scan.finite Symbol.stopper (Scan.repeat1 (parse_line local_name problem) >> flat)))

  #> fst

fun core_of_agsyhol_proof s =

  (case split_lines s of

    "The transformed problem consists of the following conjectures:" :: conj ::

    _ :: proof_term :: _ => SOME (unprefix " " conj :: find_enclosed "<<" ">>" proof_term)

  | _ => NONE)

fun atp_proof_of_tstplike_proof _ _ "" = []

  | atp_proof_of_tstplike_proof local_prover problem tstp =

    (case core_of_agsyhol_proof tstp of

      SOME facts => facts |> map (core_inference agsyhol_core_rule)

    | NONE =>

      tstp ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)

      |> parse_proof local_prover problem

      |> local_prover = vampireN ? perhaps (try (sort (vampire_step_name_ord o pairself #1)))

      |> local_prover = zipperpositionN ? rev)

fun clean_up_dependencies _ [] = []

  | clean_up_dependencies seen ((name, role, u, rule, deps) :: steps) =

    (name, role, u, rule, map_filter (fn dep => find_first (is_same_atp_step dep) seen) deps) ::

    clean_up_dependencies (name :: seen) steps

fun clean_up_atp_proof_dependencies proof = clean_up_dependencies [] proof

fun map_term_names_in_atp_proof f =

  let

    fun map_type (AType ((s, clss), tys)) = AType ((f s, map f clss), map map_type tys)

      | map_type (AFun (ty, ty')) = AFun (map_type ty, map_type ty')

      | map_type (APi (ss, ty)) = APi (map f ss, map_type ty)

    fun map_term (ATerm ((s, tys), ts)) = ATerm ((f s, map map_type tys), map map_term ts)

      | map_term (AAbs (((s, ty), tm), args)) =

        AAbs (((f s, map_type ty), map_term tm), map map_term args)

    fun map_formula (AQuant (q, xs, phi)) = AQuant (q, map (apfst f) xs, map_formula phi)

      | map_formula (AConn (c, phis)) = AConn (c, map map_formula phis)

      | map_formula (AAtom t) = AAtom (map_term t)

    fun map_step (name, role, phi, rule, deps) = (name, role, map_formula phi, rule, deps)

  in

    map map_step

  end

fun nasty_name pool s = Symtab.lookup pool s |> the_default s

fun nasty_atp_proof pool =

  not (Symtab.is_empty pool) ? map_term_names_in_atp_proof (nasty_name pool)

end;