src/HOL/simpdata.ML
author wenzelm
Thu Mar 11 13:20:35 1999 +0100 (1999-03-11)
changeset 6349 f7750d816c21
parent 6301 08245f5a436d
child 6394 3d9fd50fcc43
permissions -rw-r--r--
removed foo_build_completed -- now handled by session management (via usedir);
     1 (*  Title:      HOL/simpdata.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   1991  University of Cambridge
     5 
     6 Instantiation of the generic simplifier for HOL.
     7 *)
     8 
     9 section "Simplifier";
    10 
    11 (*** Addition of rules to simpsets and clasets simultaneously ***)
    12 
    13 infix 4 addIffs delIffs;
    14 
    15 (*Takes UNCONDITIONAL theorems of the form A<->B to 
    16         the Safe Intr     rule B==>A and 
    17         the Safe Destruct rule A==>B.
    18   Also ~A goes to the Safe Elim rule A ==> ?R
    19   Failing other cases, A is added as a Safe Intr rule*)
    20 local
    21   val iff_const = HOLogic.eq_const HOLogic.boolT;
    22 
    23   fun addIff ((cla, simp), th) = 
    24       (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
    25                 (Const("Not", _) $ A) =>
    26                     cla addSEs [zero_var_indexes (th RS notE)]
    27               | (con $ _ $ _) =>
    28                     if con = iff_const
    29                     then cla addSIs [zero_var_indexes (th RS iffD2)]  
    30                               addSDs [zero_var_indexes (th RS iffD1)]
    31                     else  cla addSIs [th]
    32               | _ => cla addSIs [th],
    33        simp addsimps [th])
    34       handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 
    35                          string_of_thm th);
    36 
    37   fun delIff ((cla, simp), th) = 
    38       (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
    39                 (Const ("Not", _) $ A) =>
    40                     cla delrules [zero_var_indexes (th RS notE)]
    41               | (con $ _ $ _) =>
    42                     if con = iff_const
    43                     then cla delrules [zero_var_indexes (th RS iffD2),
    44                                        make_elim (zero_var_indexes (th RS iffD1))]
    45                     else cla delrules [th]
    46               | _ => cla delrules [th],
    47        simp delsimps [th])
    48       handle _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
    49                           string_of_thm th); (cla, simp));
    50 
    51   fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp)
    52 in
    53 val op addIffs = foldl addIff;
    54 val op delIffs = foldl delIff;
    55 fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms);
    56 fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms);
    57 end;
    58 
    59 
    60 qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y"
    61   (fn [prem] => [rewtac prem, rtac refl 1]);
    62 
    63 local
    64 
    65   fun prover s = prove_goal HOL.thy s (K [Blast_tac 1]);
    66 
    67 in
    68 
    69 (*Make meta-equalities.  The operator below is Trueprop*)
    70 
    71 fun mk_meta_eq r = r RS eq_reflection;
    72 
    73 val Eq_TrueI  = mk_meta_eq(prover  "P --> (P = True)"  RS mp);
    74 val Eq_FalseI = mk_meta_eq(prover "~P --> (P = False)" RS mp);
    75 
    76 fun mk_eq th = case concl_of th of
    77         Const("==",_)$_$_       => th
    78     |   _$(Const("op =",_)$_$_) => mk_meta_eq th
    79     |   _$(Const("Not",_)$_)    => th RS Eq_FalseI
    80     |   _                       => th RS Eq_TrueI;
    81 (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
    82 
    83 fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI);
    84 
    85 fun mk_meta_cong rl =
    86   standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
    87   handle THM _ =>
    88   error("Premises and conclusion of congruence rules must be =-equalities");
    89 
    90 val not_not = prover "(~ ~ P) = P";
    91 
    92 val simp_thms = [not_not] @ map prover
    93  [ "(x=x) = True",
    94    "(~True) = False", "(~False) = True",
    95    "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
    96    "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
    97    "(True --> P) = P", "(False --> P) = True", 
    98    "(P --> True) = True", "(P --> P) = True",
    99    "(P --> False) = (~P)", "(P --> ~P) = (~P)",
   100    "(P & True) = P", "(True & P) = P", 
   101    "(P & False) = False", "(False & P) = False",
   102    "(P & P) = P", "(P & (P & Q)) = (P & Q)",
   103    "(P & ~P) = False",    "(~P & P) = False",
   104    "(P | True) = True", "(True | P) = True", 
   105    "(P | False) = P", "(False | P) = P",
   106    "(P | P) = P", "(P | (P | Q)) = (P | Q)",
   107    "(P | ~P) = True",    "(~P | P) = True",
   108    "((~P) = (~Q)) = (P=Q)",
   109    "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
   110 (*two needed for the one-point-rule quantifier simplification procs*)
   111    "(? x. x=t & P(x)) = P(t)",		(*essential for termination!!*)
   112    "(! x. t=x --> P(x)) = P(t)" ];      (*covers a stray case*)
   113 
   114 (* Add congruence rules for = (instead of ==) *)
   115 
   116 (* ###FIXME: Move to simplifier, 
   117    taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *)
   118 infix 4 addcongs delcongs;
   119 fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs);
   120 fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs);
   121 fun Addcongs congs = (simpset_ref() := simpset() addcongs congs);
   122 fun Delcongs congs = (simpset_ref() := simpset() delcongs congs);
   123 
   124 
   125 val imp_cong = impI RSN
   126     (2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
   127         (fn _=> [Blast_tac 1]) RS mp RS mp);
   128 
   129 (*Miniscoping: pushing in existential quantifiers*)
   130 val ex_simps = map prover 
   131                 ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
   132                  "(EX x. P & Q x)   = (P & (EX x. Q x))",
   133                  "(EX x. P x | Q)   = ((EX x. P x) | Q)",
   134                  "(EX x. P | Q x)   = (P | (EX x. Q x))",
   135                  "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
   136                  "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
   137 
   138 (*Miniscoping: pushing in universal quantifiers*)
   139 val all_simps = map prover
   140                 ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
   141                  "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
   142                  "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
   143                  "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
   144                  "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
   145                  "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
   146 
   147 
   148 (* elimination of existential quantifiers in assumptions *)
   149 
   150 val ex_all_equiv =
   151   let val lemma1 = prove_goal HOL.thy
   152         "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
   153         (fn prems => [resolve_tac prems 1, etac exI 1]);
   154       val lemma2 = prove_goalw HOL.thy [Ex_def]
   155         "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
   156         (fn prems => [REPEAT(resolve_tac prems 1)])
   157   in equal_intr lemma1 lemma2 end;
   158 
   159 end;
   160 
   161 (* Elimination of True from asumptions: *)
   162 
   163 val True_implies_equals = prove_goal HOL.thy
   164  "(True ==> PROP P) == PROP P"
   165 (K [rtac equal_intr_rule 1, atac 2,
   166           METAHYPS (fn prems => resolve_tac prems 1) 1,
   167           rtac TrueI 1]);
   168 
   169 fun prove nm thm  = qed_goal nm HOL.thy thm (K [Blast_tac 1]);
   170 
   171 prove "conj_commute" "(P&Q) = (Q&P)";
   172 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   173 val conj_comms = [conj_commute, conj_left_commute];
   174 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   175 
   176 prove "disj_commute" "(P|Q) = (Q|P)";
   177 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   178 val disj_comms = [disj_commute, disj_left_commute];
   179 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   180 
   181 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   182 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   183 
   184 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   185 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   186 
   187 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   188 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   189 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   190 
   191 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   192 prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
   193 prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
   194 
   195 prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
   196 prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
   197 
   198 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   199 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   200 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   201 prove "not_iff" "(P~=Q) = (P = (~Q))";
   202 prove "disj_not1" "(~P | Q) = (P --> Q)";
   203 prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
   204 prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
   205 
   206 prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
   207 
   208 
   209 (*Avoids duplication of subgoals after split_if, when the true and false 
   210   cases boil down to the same thing.*) 
   211 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   212 
   213 prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   214 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   215 prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   216 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   217 
   218 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   219 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   220 
   221 (* '&' congruence rule: not included by default!
   222    May slow rewrite proofs down by as much as 50% *)
   223 
   224 let val th = prove_goal HOL.thy 
   225                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   226                 (fn _=> [Blast_tac 1])
   227 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   228 
   229 let val th = prove_goal HOL.thy 
   230                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   231                 (fn _=> [Blast_tac 1])
   232 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   233 
   234 (* '|' congruence rule: not included by default! *)
   235 
   236 let val th = prove_goal HOL.thy 
   237                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   238                 (fn _=> [Blast_tac 1])
   239 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   240 
   241 prove "eq_sym_conv" "(x=y) = (y=x)";
   242 
   243 
   244 (** if-then-else rules **)
   245 
   246 qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x"
   247  (K [Blast_tac 1]);
   248 
   249 qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y"
   250  (K [Blast_tac 1]);
   251 
   252 qed_goalw "if_P" HOL.thy [if_def] "!!P. P ==> (if P then x else y) = x"
   253  (K [Blast_tac 1]);
   254 
   255 qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y"
   256  (K [Blast_tac 1]);
   257 
   258 qed_goal "split_if" HOL.thy
   259     "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))" (K [
   260 	res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1,
   261          stac if_P 2,
   262          stac if_not_P 1,
   263          ALLGOALS (Blast_tac)]);
   264 (* for backwards compatibility: *)
   265 val expand_if = split_if;
   266 
   267 qed_goal "split_if_asm" HOL.thy
   268     "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))"
   269     (K [stac split_if 1,
   270 	Blast_tac 1]);
   271 
   272 qed_goal "if_cancel" HOL.thy "(if c then x else x) = x"
   273   (K [stac split_if 1, Blast_tac 1]);
   274 
   275 qed_goal "if_eq_cancel" HOL.thy "(if x = y then y else x) = x"
   276   (K [stac split_if 1, Blast_tac 1]);
   277 
   278 (*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
   279 qed_goal "if_bool_eq_conj" HOL.thy
   280     "(if P then Q else R) = ((P-->Q) & (~P-->R))"
   281     (K [rtac split_if 1]);
   282 
   283 (*And this form is useful for expanding IFs on the LEFT*)
   284 qed_goal "if_bool_eq_disj" HOL.thy
   285     "(if P then Q else R) = ((P&Q) | (~P&R))"
   286     (K [stac split_if 1,
   287 	Blast_tac 1]);
   288 
   289 
   290 (*** make simplification procedures for quantifier elimination ***)
   291 
   292 structure Quantifier1 = Quantifier1Fun(
   293 struct
   294   (*abstract syntax*)
   295   fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
   296     | dest_eq _ = None;
   297   fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
   298     | dest_conj _ = None;
   299   val conj = HOLogic.conj
   300   val imp  = HOLogic.imp
   301   (*rules*)
   302   val iff_reflection = eq_reflection
   303   val iffI = iffI
   304   val sym  = sym
   305   val conjI= conjI
   306   val conjE= conjE
   307   val impI = impI
   308   val impE = impE
   309   val mp   = mp
   310   val exI  = exI
   311   val exE  = exE
   312   val allI = allI
   313   val allE = allE
   314 end);
   315 
   316 local
   317 val ex_pattern =
   318   read_cterm (sign_of HOL.thy) ("EX x. P(x) & Q(x)",HOLogic.boolT)
   319 
   320 val all_pattern =
   321   read_cterm (sign_of HOL.thy) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
   322 
   323 in
   324 val defEX_regroup =
   325   mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
   326 val defALL_regroup =
   327   mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
   328 end;
   329 
   330 
   331 (*** Case splitting ***)
   332 
   333 structure SplitterData =
   334   struct
   335   structure Simplifier = Simplifier
   336   val mk_eq          = mk_eq
   337   val meta_eq_to_iff = meta_eq_to_obj_eq
   338   val iffD           = iffD2
   339   val disjE          = disjE
   340   val conjE          = conjE
   341   val exE            = exE
   342   val contrapos      = contrapos
   343   val contrapos2     = contrapos2
   344   val notnotD        = notnotD
   345   end;
   346 
   347 structure Splitter = SplitterFun(SplitterData);
   348 
   349 val split_tac        = Splitter.split_tac;
   350 val split_inside_tac = Splitter.split_inside_tac;
   351 val split_asm_tac    = Splitter.split_asm_tac;
   352 val op addsplits     = Splitter.addsplits;
   353 val op delsplits     = Splitter.delsplits;
   354 val Addsplits        = Splitter.Addsplits;
   355 val Delsplits        = Splitter.Delsplits;
   356 
   357 (** 'if' congruence rules: neither included by default! *)
   358 
   359 (*In general it seems wrong to add distributive laws by default: they
   360   might cause exponential blow-up.  But imp_disjL has been in for a while
   361   and cannot be removed without affecting existing proofs.  Moreover, 
   362   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   363   grounds that it allows simplification of R in the two cases.*)
   364 
   365 fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
   366 
   367 val mksimps_pairs =
   368   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   369    ("All", [spec]), ("True", []), ("False", []),
   370    ("If", [if_bool_eq_conj RS iffD1])];
   371 
   372 (* ###FIXME: move to Provers/simplifier.ML
   373 val mk_atomize:      (string * thm list) list -> thm -> thm list
   374 *)
   375 (* ###FIXME: move to Provers/simplifier.ML *)
   376 fun mk_atomize pairs =
   377   let fun atoms th =
   378         (case concl_of th of
   379            Const("Trueprop",_) $ p =>
   380              (case head_of p of
   381                 Const(a,_) =>
   382                   (case assoc(pairs,a) of
   383                      Some(rls) => flat (map atoms ([th] RL rls))
   384                    | None => [th])
   385               | _ => [th])
   386          | _ => [th])
   387   in atoms end;
   388 
   389 fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
   390 
   391 fun unsafe_solver prems = FIRST'[resolve_tac (reflexive_thm::TrueI::refl::prems),
   392 				 atac, etac FalseE];
   393 (*No premature instantiation of variables during simplification*)
   394 fun   safe_solver prems = FIRST'[match_tac (reflexive_thm::TrueI::prems),
   395 				 eq_assume_tac, ematch_tac [FalseE]];
   396 
   397 val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
   398 			    setSSolver   safe_solver
   399 			    setSolver  unsafe_solver
   400 			    setmksimps (mksimps mksimps_pairs)
   401 			    setmkeqTrue mk_eq_True;
   402 
   403 val HOL_ss = 
   404     HOL_basic_ss addsimps 
   405      ([triv_forall_equality, (* prunes params *)
   406        True_implies_equals, (* prune asms `True' *)
   407        if_True, if_False, if_cancel, if_eq_cancel,
   408        imp_disjL, conj_assoc, disj_assoc,
   409        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
   410        disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq]
   411      @ ex_simps @ all_simps @ simp_thms)
   412      addsimprocs [defALL_regroup,defEX_regroup]
   413      addcongs [imp_cong]
   414      addsplits [split_if];
   415 
   416 (*Simplifies x assuming c and y assuming ~c*)
   417 val prems = Goalw [if_def]
   418   "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
   419 \  (if b then x else y) = (if c then u else v)";
   420 by (asm_simp_tac (HOL_ss addsimps prems) 1);
   421 qed "if_cong";
   422 
   423 (*Prevents simplification of x and y: much faster*)
   424 qed_goal "if_weak_cong" HOL.thy
   425   "b=c ==> (if b then x else y) = (if c then x else y)"
   426   (fn [prem] => [rtac (prem RS arg_cong) 1]);
   427 
   428 (*Prevents simplification of t: much faster*)
   429 qed_goal "let_weak_cong" HOL.thy
   430   "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"
   431   (fn [prem] => [rtac (prem RS arg_cong) 1]);
   432 
   433 qed_goal "if_distrib" HOL.thy
   434   "f(if c then x else y) = (if c then f x else f y)" 
   435   (K [simp_tac (HOL_ss setloop (split_tac [split_if])) 1]);
   436 
   437 
   438 (*For expand_case_tac*)
   439 val prems = goal HOL.thy "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   440 by (case_tac "P" 1);
   441 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   442 val expand_case = result();
   443 
   444 (*Used in Auth proofs.  Typically P contains Vars that become instantiated
   445   during unification.*)
   446 fun expand_case_tac P i =
   447     res_inst_tac [("P",P)] expand_case i THEN
   448     Simp_tac (i+1) THEN 
   449     Simp_tac i;
   450 
   451 
   452 (* install implicit simpset *)
   453 
   454 simpset_ref() := HOL_ss;
   455 
   456 
   457 
   458 (*** integration of simplifier with classical reasoner ***)
   459 
   460 structure Clasimp = ClasimpFun
   461  (structure Simplifier = Simplifier 
   462         and Classical  = Classical 
   463         and Blast      = Blast);
   464 open Clasimp;
   465 
   466 val HOL_css = (HOL_cs, HOL_ss);
   467 
   468 
   469 (*** A general refutation procedure ***)
   470  
   471 (* Parameters:
   472 
   473    test: term -> bool
   474    tests if a term is at all relevant to the refutation proof;
   475    if not, then it can be discarded. Can improve performance,
   476    esp. if disjunctions can be discarded (no case distinction needed!).
   477 
   478    prep_tac: int -> tactic
   479    A preparation tactic to be applied to the goal once all relevant premises
   480    have been moved to the conclusion.
   481 
   482    ref_tac: int -> tactic
   483    the actual refutation tactic. Should be able to deal with goals
   484    [| A1; ...; An |] ==> False
   485    where the Ai are atomic, i.e. no top-level &, | or ?
   486 *)
   487 
   488 fun refute_tac test prep_tac ref_tac =
   489   let val nnf_simps =
   490         [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
   491          not_all,not_ex,not_not];
   492       val nnf_simpset =
   493         empty_ss setmkeqTrue mk_eq_True
   494                  setmksimps (mksimps mksimps_pairs)
   495                  addsimps nnf_simps;
   496       val prem_nnf_tac = full_simp_tac nnf_simpset;
   497 
   498       val refute_prems_tac =
   499         REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
   500                filter_prems_tac test 1 ORELSE
   501                etac disjE 1) THEN
   502         ref_tac 1;
   503   in EVERY'[TRY o filter_prems_tac test,
   504             DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
   505             SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
   506   end;