213 F.3d 404 (7th Cir. 2000)
Consolidation Coal Company,    Plaintiff-Appellee, Defendant-Appellee,v.United Mine Workers of America, District 12,  Local Union 1545,    Defendant-Appellant, Plaintiff-Appellant.
Nos. 99-1640 and 99-1641
In the  United States Court of Appeals  For the Seventh Circuit
Argued January 13, 2000
Decided May 17, 2000

Appeals from the United States District Court  for the Southern District of Illinois, Benton Division.  Nos. 98 C 4176 & 96 C 4267--James L. Foreman, Judge.
Before Posner, Chief Judge, and Bauer and Rovner,  Circuit Judges.
Posner, Chief Judge.


1
The parties to these  consolidated appeals, an employer and a union,  have a collective bargaining agreement that  provides for arbitration of disputes arising  under it. The employer changed certain of its  staffing practices in an effort to avoid paying  overtime wages. The change precipitated a slew of  grievances by the union, of which seven resulted  in arbitration proceedings (all before different  arbitrators) that are relevant to the appeal. The  issue in all the arbitrations was the same:  whether the change in staffing practices violated  the collective bargaining agreement. The employer  won all but the fourth of the arbitrations. The  fourth differs from the other six in not  involving claims for compensation for individual  workers adversely affected by the challenged  staffing practice. The award in the fourth is a  general declaration that the staffing practice  violates the collective bargaining agreement. The  other six sought compensation for individual  workers. The union sought enforcement of the  award in its favor in a federal district court  under the Taft-Hartley Act, which in section 301  (29 U.S.C. sec. 185) makes collective bargaining  agreements enforceable. The court enforced the  award, and the employer did not appeal.


2
The company had won the first three arbitrations  after the hearing before the fourth arbitrator  but before he rendered his award in favor of the  union. But neither party told the fourth  arbitrator about the outcome of those  arbitrations. In the case under review--the  second round in the district court, the first  having ended with the court's confirmation of the  fourth award, the one in favor of the union--the  district court confirmed the six arbitration  awards that the company had won, all of which  were rendered before the district court confirmed  the fourth award. The union appeals.


3
The upshot of the two district court decisions,  one enforcing the award in favor of the union and  the other enforcing the awards in favor of the  company, is not a happy one, since the decisions  are inconsistent, with six of them rejecting the  premise of the seventh (that is, of number 4).  Yet it is not quite the recipe for anarchy that  it may appear to be. The first district court  decision, in confirming the fourth arbitrator's  award, did not order the employer to rescind the  change in its staffing practices (courts are  reluctant to issue labor injunctions, though they  will enforce an arbitrator's injunction, e.g.,  Local 1545 v. Inland Steel Coal Co., 876 F.2d  1288, 1292-96 (7th Cir. 1989); United Electrical,  Radio & Machine Workers v. Honeywell Inc., 522  F.2d 1221, 1225-28 (7th Cir. 1975); Derwin v.  General Dynamics Corp., 719 F.2d 484, 491 (1st  Cir. 1983), which however the fourth arbitrator's  award was not), while the second decision,  confirming a bunch of awards in favor of the  employer, authorizes the employer to continue in  its changed course with respect to the workers  involved in those arbitrations but does not  rescind the order of the fourth arbitrator, which  would be flatly contrary to the district court's  first decision. (Hence the district court was  correct to reject the union's argument that by  continuing to arbitrate the issue resolved in the  union's favor by the fourth arbitrator, the  company was in contempt of the district court's  order confirming the fourth arbitrator's award.)  Any subsequent disputes are likely to be resolved  in the company's favor as well, as we shall see;  and the company points out that in any event,  since judicial review of an arbitration award is  so limited as to be little better than a rubber  stamp, arbitral awards based on diametrically  opposed interpretations of the identical contract  can all withstand judicial review. E.g., American  Nat'l Can Co. v. United Steelworkers of America,  120 F.3d 886, 891-93 (8th Cir. 1997); Connecticut  Light & Power Co. v. Local 420, 718 F.2d 14, 20-  21 (2d Cir. 1983); Westinghouse Elevators of  Puerto Rico, Inc. v. S.I.U. de Puerto Rico, 583  F.2d 1184 (1st Cir. 1978). This is provided that  the inconsistent interpretations do not result in  the kind of impasse that would be presented if  the employer were simultaneously enjoined by a  court from continuing, and authorized by the  court to continue, the identical practice. But,  as we have seen, that is not a problem here.


4
Yet when multiple suits as closely related as  are these seven arbitrations are filed in court,  they invariably are consolidated. However, the  consolidation of arbitrations, as distinct from  the consolidation of court suits, is a creature  of contract, Connecticut Gen'l Life Ins. Co. v.  Sun Life Assurance Co., No. 99-4085, 2000 210 F.3d 771, 773 (7th Cir. April 27, 2000), and the  collective bargaining agreement in this case  permits consolidation of grievances (the filing  of a grievance being the first stage in the  dispute resolution process that includes, as its  final stage before judicial review, the  proceeding before the arbitrator) only if both  union and employer agree to consolidate them, and  they did not do so here. Nevertheless, when,  before the fourth arbitrator ruled, the first  three arbitrations came out in favor of the  employer, one might have expected the employer to  so advise the fourth arbitrator, and this it  failed to do. It argues that it could not do so  because the collective bargaining agreement  forbids reopening the record after the hearing  before the arbitrator. The argument is unsound.  The decisions of the other three arbitrators were  not evidence--the sort of thing a prohibition  against reopening the record would cover. They  were the arbitral equivalents of judicial  decisions, of which, of course, a court can take  judicial notice; and in just the same way an  arbitrator can take "arbitral notice" of a  previous decision by another arbitrator dealing  with the same or a related issue--especially  since, as we are about to see, the collective  bargaining agreement requires arbitrators to give  prior arbitral decisions preclusive effect, which  they cannot do if no one informs them of those  decisions.


5
That effect, like most features of arbitration,  is indeed a matter of contract rather than a  matter of law. E.g., Pierce v. Commonwealth  Edison Co., 112 F.3d 893, 895-96 (7th Cir. 1997);  Brotherhood of Maintenance of Way Employees v.  Burlington Northern R.R., 24 F.3d 937, 940 (7th  Cir. 1994); American Nat'l Can Co. v. United  Steelworkers of America, supra, 120 F.3d at 891-  92; Hotel Ass'n of Washington, D.C., Inc. v.  Hotel & Restaurant Employees Union, 963 F.2d 388  (D.C. Cir. 1992); District 37 v. Lockheed  Engineering & Mgmt. Services Co., 897 F.2d 768,  773 (5th Cir. 1990); G. Richard Shell, "Res  Judicata and Collateral Estoppel Effects of  Commercial Arbitration," 35 UCLA L. Rev. 623,  660-63 (1988). If the parties to the collective  bargaining agreement want the first arbitrator's  interpretation of a provision of the agreement or  resolution of a dispute arising under the  agreement to have preclusive effect, they can so  provide; and whether they do so or not, the  question of the preclusive force of the first  arbitration is, like any other defense, itself an  issue for a subsequent arbitrator to decide.  E.g., Independent Lift Truck Builders Union v.  NACCO Materials Handling Group, Inc., 202 F.3d  965, 968 (7th Cir. 2000); Brotherhood of  Maintenance of Way Employees v. Burlington  Northern R.R., supra, 24 F.3d at 940; Chiron  Corp. v. Ortho Diagnostic Systems, Inc., 207 F.3d  1126, 1132-33 (9th Cir. 2000); John Hancock  Mutual Life Ins. Co. v. Olick, 151 F.3d 132, 139-  40 (3d Cir. 1998); National Union Fire Ins. Co.  v. Belco Petroleum Corp., 88 F.3d 129, 135-36 (2d  Cir. 1996). Most arbitrators, applying the  arbitral equivalent of common law, would indeed  give preclusive effect to the first arbitration,  even in the absence of contractual guidance,  provided that the usual conditions of res  judicata were fulfilled. See Fairweather's  Practice & Procedure in Labor Arbitration 525-33  (4th ed., Ray J. Schoonhoven ed. 1999); Timothy  J. Heinsz, "Grieve It Again: Of Stare Decisis,  Res Judicata and Collateral Estoppel in Labor  Arbitration," 38 B.C. L. Rev. 275, 286-93 (1997);  Shell, supra, 35 UCLA L. Rev. at 663-64. Anyway,  here the contract did make clear that res  judicata is a defense in a subsequent  arbitration. See Heinsz, supra, 38 B.C. L. Rev.  at 286-87, describing the contract. So by failing  to argue preclusion to the fourth arbitrator, the  employer forfeited a good defense that would have  headed off the confusion that ensued.


6
It might seem that once the fourth arbitrator's  decision came down, res judicata clicked in and  entitled the union to block any subsequent  inconsistent arbitration awards unless and until  that decision was vacated by a reviewing court.  Not so. It was up to the subsequent arbitrators,  5 through 7, to decide what significance to  attach to the employer's having booted its res  judicata defense before the fourth arbitrator;  and they decided to give it no weight. They  forgave the employer's waiver, and like other  procedural questions in arbitration not regulated  by law their determination as to whether to  forgive the waiver cannot be second-guessed by a  court. Connecticut Gen'l Life Ins. Co. v. Sun  Life Assurance Co., supra, at 773; Baravati v.  Josephthal, Lyon & Ross, Inc., 28 F.3d 704, 709  (7th Cir. 1994); UHC Management Co. v. Computer  Sciences Corp., 148 F.3d 992, 997 (8th Cir.  1998). They did it, oddly, out of a commitment to  res judicata so profound as not to brook a  forfeiture: they held that they were bound by the  decisions made by the first three arbitrators.


7
It doesn't follow that it was right for the  district court in the second go round to enforce  the other arbitration awards (that is, 1 through  3 and 5 through 7). We must consider the possible  res judicata effect of the first district court  decision, a distinct issue from the res judicata  effect of the arbitral awards. The union argues  that the district court's judgment in the first  round, when the issue before the court was  whether to enforce the fourth arbitrator's award,  which was in favor of the union, was res  judicata. The other six awards, the ones in favor  of the employer, all were rendered before the  district court confirmed the fourth award. The  employer's claim for judicial confirmation of  those awards was, the union argues, a compulsory  counterclaim to the union's claim for enforcement  of the fourth arbitrator's award, because both  claims arose out of the same transaction or  occurrence, Fed. R. Civ. P. 13(a), and failure to  plead a compulsory counterclaim bars as a matter  of res judicata its being presented in a  subsequent suit. Baker v. Gold Seal Liquors,  Inc., 417 U.S. 467, 469 n. 1 (1974); Publicis  Communication v. True North Communications Inc.,  132 F.3d 363, 365 (7th Cir. 1997); Olympia Hotels  Corp. v. Johnson Wax Development Corp., 908 F.2d  1363, 1367 (7th Cir. 1990); Driver Music Co. v.  Commercial Union Ins. Cos., 94 F.3d 1428, 1435  (10th Cir. 1996); 6 Charles Alan Wright, Arthur  R. Miller & Mary Kay Kane, Federal Practice &  Procedure sec. 1417, p. 129 (2d ed. 1990).


8
But while the seven arbitrations all arose out  of the same transaction or occurrence, namely the  staffing dispute, the two district court  proceedings did not. They arose out of the  arbitrations, which we deem to have been separate  transactions or occurrences. We make this  classification not under the compulsion of the  words of Rule 13(a), but because of the need to  respect the right of the arbitrators to resolve  disputes within the scope of the authority  granted them by the collective bargaining  agreement. The arbitrators who administer this  agreement have, we noted, a fierce commitment to  res judicata. Paradoxically, it would be  nullified were we to display an equal zeal for  the principle of res judicata embedded in Rule  13(a)--if, that is to say, we agreed with the  union that the district court was precluded from  confirming the arbitral awards that were based on  the arbitrators' commitment to arbitral res  judicata. And, precisely because of their  commitment, we needn't worry overmuch that the  district court will be asked to confirm  inconsistent awards from now until every single  worker at Consolidation Coal Company's plant has  gone through arbitration. Given the rule of res  judicata applied by the arbitrators under this  collective bargaining agreement, it is reasonably  certain that all subsequent arbitrations will be  decided in favor of the company and will be  confirmed by the district court if the union  refuses to bow to them. The essential point,  however, is that the res judicata effect of a  judicial decision merely confirming an arbitral  award is extremely limited. All it amounts to is  a determination that there is no basis for  upending that award; the effect on subsequent  awards must be left to the arbitrators who make  them.


9
The union has no colorable defense to the  confirmation of the awards in favor of the  company other than res judicata, and so the  district court's judgment is    Affirmed.

