DIANE P. WOOD, Circuit Judge.

In spite of the fact that courts sometimes talk about arbitral tribunals as nothing more than alternative fora in which to resolve disputes, parties often fight hard either to enforce or to defeat an alleged agreement to arbitrate. That is what is happening in this case: plaintiff R.J. Corman Derailment Services takes the position that a former agreement to arbitrate between Local 150 of the International Union of Operating Engineers and itself is no longer effective; the Union says that it is, and that a wage dispute must therefore be arbitrated. Proceedings in the district court came to an abrupt halt when the court, sua sponte, granted what it termed judgment on the pleadings under FED. R. CIV. P. 12(c) to the Union, thereby holding that the arbitration clause in the parties' expired collective bargaining agreement (CBA) covered the dispute. Apart from the fact that FED. R. CIV. P. 12(c) was not the proper vehicle to use, because the Union had not yet filed its answer to the complaint and the pleadings were thus not yet closed, we find that the court acted prematurely in its action. Judgment under FED. R. CIV. P. 12(b)(6) for the Union would also have been improper, given the allegations in Corman's pleadings, and summary judgment was equally unavailable without proper notice of conversion under FED. R. CIV. P. 12(b). We therefore reverse and remand for further proceedings.

I

Corman provides emergency railroad services across the country. Starting in January 1992, Local 150 represented Corman's Derailment Division employees at its Gary, Indiana, facility. The parties' CBA required Corman to pay bargaining unit members a regular wage rate of $12.35 per hour, a straight-time wreck rate of $16.25 per hour, and an overtime wreck rate of $22.65 per hour.

Article IX of the CBA outlines a four-step procedure for the resolution of grievances. Step one requires an aggrieved employee orally to notify her union steward and her supervisor of a grievance within ten working days of the grievance's occurrence. If after five additional working days the grievance is not resolved, step two requires the employee to submit a signed copy of her grievance in writing to the Union's Business Representative and to Corman or its representative. Corman then has five working days to respond in writing to the grievance. If this additional step fails to resolve the employee's grievance, step three provides for submission of the complaint to a grievance committee. If within ten additional working days the committee does not resolve the grievance, the aggrieved employee may proceed to step four and submit a written demand for arbitration. This written demand for arbitration must be made within forty-five days of the initial occurrence.

One month before the CBA's December 19, 1999, expiration date, Corman and the Union began to negotiate a new Agreement. These efforts ended when, in early June 2000, Corman took the position that Local 150 had lost the support of a majority of the employees in the Division and thus could no longer represent them. At the end of June, Corman closed its Gary facility, laying off all of those employees. One difficult question on which this case turns is whether the CBA continued to cover the parties' relationship during the six months between the formal expiration of the agreement and the closing of the facility, or if instead Corman was unilaterally abiding by the terms of the CBA after it expired in order to comply with its duty to bargain in good faith. Article XIII of the CBA sheds some light on this question, through its statement that "[t]his agreement shall be effective as of 12:01 A.M. on December 19, 1996 and continue in effect until midnight, December 19, 1999 and from year to year thereafter unless either party to this Agreement wishes to change or terminate the Agreement." If the CBA remained in effect, then it is at least possible that the parties were obliged to arbitrate their dispute.

The dispute that the Union would like to put before the arbitrators came to light in an unusual way. In July 2000, the Trustees of the Midwest Operating Engineers Pension and Benefits Funds (the Funds) filed an ERISA lawsuit in the Northern District of Illinois under 29 U.S.C. §§ 1132, 1145, to compel an audit of Corman's fund contributions and to collect any under-payments revealed by that audit. (The appeal from this lawsuit is presently before this court in the case of Dugan v. R.J. Corman Derailment Services, LLC, No. 03-1011 (7th Cir. argued June 2, 2003). The parties failed to notify the court that this related case was pending when it came to their attention, which would have been far better practice. Had it not been for our independent discovery of the relation between the two cases, the parties' failure to call this later case to our attention would have made it difficult for this court to ensure consistency in its decisions.) One year later, in July 2001, the Funds' auditors issued their report. Following the issuance of this report, Local 150 contacted Corman in an attempt to "schedule a meeting in accordance with Article 9, Section A, Step 2" to resolve what it claimed was a wage dispute under the CBA. The Union insists that the underlying discrepancy about which it complained ($11,013.92 in claimed underpaid wages) was discovered as a result of the Funds' ERISA audit. Local 150's wage discrepancy claim covered wages that were paid before the CBA expired in December, 1999, in addition to post-expiration wages that were paid up until the Gary facility closed six months later. Although the Union's complaint was brought to Corman's attention shortly after the Pension Funds' audit was completed, this was long after the expiration of the forty-five day period set forth in Article IX of the CBA for bringing the wage discrepancy claim. In fact, as Corman points out in its brief to this court, the Union's wage discrepancy claim did not comply with any of the steps that the parties agreed had to precede arbitration of a dispute.

Following a flurry of correspondence between the Union and Corman and their lawyers, Local 150 threatened to invoke Article IX's arbitration procedures to resolve the wage dispute. Rather than waiting to see if the Union would make good on its threat to arbitrate, Corman filed a two-count complaint in the District Court. Count I of the complaint sought a declaratory judgment that the parties' dispute was not subject to the CBA's arbitration provision. Count II sought a permanent injunction preventing Local 150 from submitting or threatening to submit its wage discrepancy claim to arbitration. Nearly one month after Corman filed its complaint, and before Local 150 filed its answer, Corman filed a motion for a preliminary injunction that tracked Count II of its complaint. In a footnote in its Reply Memorandum in Support of Plaintiff's Motion for Preliminary Injunction, Corman asked the district court, in the alternative, to treat its motion as a motion for summary judgment on both counts of the complaint. Rather than granting Corman the relief that it sought, the district court denied the motion for a preliminary injunction. The court also denied Corman's alternative request for summary judgment. Instead of granting Corman the injunctive relief that it sought, the district court sua sponte entered declaratory judgment on the pleadings, citing FED. R. CIV. P. 12(c), finding that the Union's wage dispute was subject to arbitration. Corman now appeals that ruling.

II

As a general matter, our court reviews a decision to grant judgment on the pleadings using the same standard that applies to dismissals under FED. R. CIV. P. 12(b)(6) for failure to state a claim on which relief can be granted. See Gustafson v. Jones, 117 F.3d 1015, 1017 (7th Cir. 1997). In such cases, judgment may not be granted against the non-moving party "unless it appears beyond a doubt that the [non-moving party] cannot prove any facts that would support his claim for relief." Id. (internal quotation marks omitted). We take the facts alleged in the complaint in the light most favorable to the non-moving party, and we review the district court's decision de novo. Id. Both FED. R. CIV. P. 12(b)(6) and FED. R. CIV. P. 12(c) also provide that if, on a motion under the rule, matters outside the pleadings are presented to and not excluded by the court, then the motion must be converted to one for summary judgment under FED. R. CIV. P. 56, and "all parties shall be given reasonable opportunity to present all material made pertinent to such a motion by Rule 56." FED. R. CIV. P. 12(b), (c). See also Church v. General Motors Corp., 74 F.3d 795, 798 (7th Cir. 1996).

This case is somewhat unusual, both because no answer was ever filed, and because it was Corman, not the Union, which asked for its preliminary injunction motion to be treated in the alternative as a motion for summary judgment. By granting summary judgment for the Union, the court in effect created an implied cross-motion for summary judgment "filed" on behalf of the Union. The existence of cross-motions for summary judgment does not, however, imply that there are no genuine issues of material fact. See generally 10A CHARLES A. WRIGHT, ARTHUR R. MILLER MARY KAY KANE, FEDERAL PRACTICE PROCEDURE § 2720 at 327-28 (3d ed. 1998). Parties have different burdens of proof with respect to particular facts; different legal theories will have an effect on which facts are material; and the process of taking the facts in the light most favorable to the non-movant, first for one side and then for the other, may highlight the point that neither side has enough to prevail without a trial. Here, the district court did rely on materials outside of the pleadings, because it took into account Corman's motion for a preliminary injunction, Local 150's response to that motion, and the materials that the Union submitted along with its response. Because it relied on FED. R. CIV. P. 12(c) as the basis for its action, however, it never formally converted the proceeding into a summary judgment motion "filed" on behalf of the Union. This truncated procedure created a number of problems, which we now address.

We consider first whether, taking the allegations of Corman's complaint in the appropriate light, the Union was entitled to judgment as a matter of law under what should have been FED. R. CIV. P. 12(b)(6). The answer is an unequivocal no. Corman alleged in ¶ 6 of the complaint that the CBA expired on December 19, 1999; later, in ¶ 15, it refers to the September 12, 2001, letter as having been "presented more than 20 months after the 1997 Bargaining Agreement expired. . . ." The complaint also alleges that the first Corman knew of the wage dispute was when it read the letter from the Local 150 representative dated September 12, 2001. ¶ 14. The complaint itself says nothing about the way in which Local 150 learned about any alleged wage dispute; nowhere does it refer to the Funds or their audit. It merely takes the position that the wage dispute was not presented to it in a proper or timely fashion, and thus that it is not subject to arbitration. Taking these facts in the light most favorable to Corman, we would have to conclude that the agreement expired according to its own terms, that any wage dispute was not properly presented, and thus that arbitration was not available.

The district court, however, found that the parties had agreed to extend their CBA. In reaching this conclusion, it relied on Article XIII of the CBA, which says that the CBA remains in effect until "December 19, 1999 and from year to year thereafter unless either party to this Agreement wishes to change or terminate the Agreement." The CBA does not appear to have been appended to the complaint, although if it had been, it would have been proper for the court to take its provisions into account. Accepting for the moment that there was some justification for reviewing it anyway, we find Article XIII less than conclusive. By its own language, it says that the CBA will remain in effect unless either party wishes to change or terminate it. We know from the complaint, ¶ 7, that the parties were negotiating over a new CBA, which (in the light most favorable to Corman) indicates that one or both of them wanted to change the agreement. A trier of fact could find, therefore, that Article XIII did not of its own force continue the agreement. Furthermore, the bare complaint and CBA do not reveal whether Corman was continuing to abide by at least the wage terms of the expired CBA because (a) it believed that there was a new agreement between the parties, (b) it believed that the old agreement had been extended, or (c) because as a unilateral matter it was simply abiding by the old terms in good faith while attempting to negotiate a new agreement. Last, we know nothing about whether Corman was also abiding by other terms of the expired CBA, such as the obligation to make pension contributions at issue in the related Dugan litigation.

These are significant disputed facts. The fact that Corman had asked that its own motion for a preliminary injunction be considered in the alternative as a motion for summary judgment does not mean that it was on notice of the fact that a motion the Union never filed might also be treated as a motion for summary judgment. This lack of notice means that Corman never had the opportunity to present facts and argument to the district court in support of its position. The issue of when the CBA expired is, after all, a central one: if the CBA remained in effect after December 19, 1999, then Local 150 might have had a longer period of time in which to assert its wage discrepancy claim (though the forty-five day period still might cause trouble for it).

The district court also found as an undisputed fact that Local 150's auditors sought Corman's business and payroll records for the purpose of conducting a wage audit before the Union brought its grievance. Certainly from the point of view of the pleadings alone, and in our view more generally, the record is devoid of evidence that would permit a conclusion that the audit was undertaken by Local 150 or on its behalf. It is at least equally plausible that the Funds had their own interests in mind when they instituted the audit for purposes of ensuring that Corman was not skimping on its contributions; indeed, the existence of the Dugan litigation conclusively shows that the Funds have their own ax to grind here. The record does not establish that the audit's focus was on wage under-payments, rather than pension and other fringe benefits. The district court relied heavily on this factual conclusion in finding that Local 150's initiation of grievance and arbitration proceedings was timely as a matter of law. But if Local 150 is simply piggy-backing on the Funds' independent and unrelated audit (which may have generated information about wages as a step along the way to ascertaining whether contribution levels were correct), the court's conclusion that the grievance was timely is unsupported. Once again, had Corman known that it was facing a de facto summary judgment motion from the Union, it would have had the opportunity to contest this fact. It now insists that if it had known that the district court was considering this type of resolution of the case, it would have introduced evidence tending to show that Local 150 was not entitled to rely on the Funds' independent audit as a basis for the delay in seeking to arbitrate its wage dispute.

All of this is by way of prelude to our consideration of the district court's finding that the Union was entitled as a matter of law to have the wage dispute submitted to arbitration. We have already indicated that this conclusion cannot be drawn from the face of the pleadings, or the pleadings supplemented by the CBA. The district court should not have converted Corman's alternative motion for summary judgment into a motion brought by the Union without notice to the parties. Furthermore, this error was not harmless. Corman points out that the court relied on factual conclusions — that the parties agreed to extend the CBA and that Local 150 undertook a wage audit — that were unsupported by the scant record that the parties developed, that neither side advanced, and that Corman lacked an opportunity to refute. We agree that these points were subject to dispute, and more fundamentally that Corman never had the opportunity to which it is entitled to present opposing evidence to the court. We are also troubled by the district court's legal conclusions, which were based on those questionable fact findings. Specifically, the district court found the parties' dispute subject to arbitration in this case because it believed that the twenty-one month delay between the termination of the CBA and the time Local 150 first notified Corman of the wage dispute was reasonable in light of the fact that the Union did not know the basis for its wage claim until its audit was completed. Since we do not know whether Local 150 actually undertook a wage audit, this conclusion was premature. For that reason, we do not offer an opinion on the ultimate question of arbitrability.

On remand, there will be a number of new problems. Most importantly, the district court must consider whether Corman has any entitlement to either declaratory or injunctive relief in light of the prohibitions of the Norris-LaGuardia Act, 29 U.S.C. §§ 101- 15, and this court's holding in AT T Broadband LLC v. International Brotherhood of Electrical Workers, 317 F.3d 758 (7th Cir. 2003), which held that a district court may not enjoin the arbitration of a labor dispute. Id. at 763. Although AT T may seem dispositive here, in the interest of fairness to the parties (who did not have an opportunity to brief the issue), we leave that question to the district court in the first instance.

If there is any life remaining in this case, the parties will also need on remand to confront another aspect of the timeliness of Local 150's grievance. The district court's analysis did not take into account the common sense argument that Corman presses on appeal — that the wage dispute was discoverable as soon as wages were paid and therefore regardless of the audit, Local 150's grievance was not timely filed. Local 150 makes a weak waiver argument in response, but a party cannot waive something that it does not know is at issue. In our view, Corman's failure to argue this point below corroborates its claim of surprise. Once again, the fact that Corman itself sought summary judgment for different reasons does not mean that it was fairly apprised of the ultimate basis for the district court's reasoning. This is the precise reason why our court has repeatedly explained that it is appropriate to grant summary judgment sua sponte only when it is clear that neither side will be disadvantaged or unfairly surprised by the move. See, e.g., Jones v. Union Pacific R.R. Co., 302 F.3d 735, 740 (7th Cir. 2002) (holding sua sponte summary judgment proper "as long as the losing party is given notice and an opportunity to come forward with its evidence"); Goldstein v. Fidelity Guar. Ins. Underwriters, Inc., 86 F.3d 749, 751 (7th Cir. 1996) (affirming sua sponte summary judgment because losing party had adequate notice and no genuine issue of material fact established). We recently expressed our disfavor of this procedure, noting that sua sponte awards of summary judgment "tend to defeat the very purpose they are designed to serve — judicial efficiency." Southern Illinois Riverboat Casino Cruises, Inc. v. Triangle Insulation Sheet Metal Co., 302 F.3d 667, 668 (7th Cir. 2002).

Finally, it is important to clarify an additional point. Although the district court ultimately found the parties' dispute subject to arbitration as a matter of law, its opinion contains language that suggests that whether this particular wage dispute is subject to arbitration is a procedural question for the arbitrator and not the court to decide. In reaching this conclusion the judge relied on a decision of this court that holds that procedural questions concerning the arbitration process itself are to be decided by the arbitrator. In Beer, Soft Drink, Water, Fruit Juice, Local Union 744 v. Metropolitan Distributors, Inc., 763 F.2d 300 (7th Cir. 1985), we held that after a court ascertains that the subject matter of a particular dispute is covered by the parties' arbitration agreement, any procedural questions — such as whether the arbitration procedures were properly followed — are reserved for the arbitrator. Id. at 302-03. The district court read Metropolitan Distributors to mean that whether the parties in this case must arbitrate the recently-complained-of wage discrepancy is for the arbitrator to decide. But the question in this case does not concern the scope of an arbitration agreement that everyone agrees governs a general relationship. It is instead the question whether there is an agreement to arbitrate this subject matter at all. The Supreme Court has held that it is the court and not an arbitrator that must decide the question of arbitrability, unless the parties have explicitly provided otherwise in their agreement. See First Options of Chicago, Inc. v. Kaplan, 514 U.S. 938, 943-44, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995); Litton Fin. Printing Div. v. Nat'l Labor Relations Bd., 501 U.S. 190, 208, 111 S.Ct. 2215, 115 L.Ed.2d 177 (1991). See also Nissan North Am., Inc. v. Jim M'Lady Oldsmobile, Inc., 307 F.3d 601, 604 (7th Cir. 2002); Air Line Pilots Ass'n Int'l v. Midwest Express Airlines, Inc., 279 F.3d 553, 555 (7th Cir. 2002). This is especially true where, as here, grievance procedures are invoked well after the parties' collective bargaining agreement has expired. In Nissan North America, Inc. v. Jim M'Lady Oldsmobile, Inc., we explained that "courts handling [cases involving expired fixed-term contracts] must determine not only whether the parties entered an agreement to arbitrate some issues, but also whether the particular dispute in question falls within the scope of the arbitration agreement." 307 F.3d at 604 (emphasis in original). In other words, the fact that some post-expiration grievances remain subject to arbitration does not mean that all such grievances are arbitrable. Jim M'Lady Oldsmobile made clear that this latter question must be decided by the courts before a contested issue may be submitted to arbitration. Id. Cf. Local 703, Int'l Bhd. of Teamsters v. Kennicott Bros. Co., 771 F.2d 300, 303-04 (7th Cir. 1985) (affirming district court's refusal to order arbitration of post-expiration grievance that occurred six months after parties' agreement expired).

Whether Local 150's wage dispute is subject to arbitration is a question that the district court must decide. We are not persuaded that the Ninth Circuit's decision in Goss Golden West Sheet Metal, Inc. v. Sheet Metal Workers International Union, Local 104, 933 F.2d 759 (9th Cir. 1991), would support a different result. As the facts in Goss suggest, that case involved a grievance that arose during the life of the parties' agreement that was probably only discoverable post-expiration because of the employer's successful cover-up efforts. 933 F.2d at 763 n. 2. As we have already noted, our case presents a very different set of facts. On this record, we have no reason to believe that Local 150 could not have grieved the under-payment of its members' wages as they occurred. In deciding Goss, the Ninth Circuit did not focus on the question whether a grievance that arises pre-expiration and that could have been raised during the life of the parties' agreement, may nonetheless be raised for the first time after the agreement has expired.

Finally, we briefly turn to the district court's decision to deny Corman's motion for a preliminary injunction. Corman's briefs on appeal do not directly question the district court's analysis of its preliminary injunction motion. Because no argument was raised on this issue, we find it waived and summarily affirm the denial of a preliminary injunction. Williams v. REP Corp., 302 F.3d 660, 666 (7th Cir. 2002).

III

Because we agree with Corman that the district court did not follow the proper procedures here, and thus did not give Corman the chance to contest the facts on which it based its de facto summary judgment in the Union's favor, we REVERSE and REMAND for further proceedings consistent with this opinion.