ORDER
After a scuffle with prison guards on June 1, 2003, Sherrell Towns, an Illinois prisoner, was cited for misconduct on June 3 and later disciplined for assaulting a staff member. But in this suit under 42 U.S.C. § 1983, he alleges that the guards attacked him without provocation and falsified the disciplinary report. He also says that he was denied medical care for his injuries. The district court conducted an evidentiary hearing to resolve whether Towns had exhausted his administrative *98remedies, concluded that he did not, and dismissed the lawsuit. Towns appeals.
Towns attached to his complaint copies of two prison grievances, one dated June 1 and the other, June 8, 2003. The first concerns the alleged assault, and the second asserts that the misconduct charge was bogus. The defendants concede that Towns’s prison counselor processed the June 1 grievance as an “informal” grievance and rejected it as unsubstantiated on July 24. Towns says he forwarded this rejection to the prison grievance officer and, after two months passed without a response, sent a copy to the Administrative Review Board, the final level of review. Towns also says that no one answered his June 3 grievance, which he filed directly with the grievance officer (since prison counselors do not deal with disputes about discipline), and so he mailed a copy to the Board on October 2. The Board did not respond to either grievance.
At summary judgment the defendants said nothing about the June 1 grievance. They acknowledged that the June 3 grievance was received but contended that the warden had denied it and that Towns never appealed. The defendants attached a copy of the denial (which conveys, strangely, that the warden — the deciding official— received the June 3 grievance in October 2003 though the grievance officer — the initial reviewer — did not evaluate it until January 2004) and submitted an affidavit from a Department of Corrections employee who attests that she searched the Administrative Review Board’s files and located appeals from Towns before and after 2003 but found no record of “a timely grievance to this office for an issue allegedly occurring in 2003.” It followed, according to the defendants, that Towns did not exhaust his administrative remedies.
After Towns responded with an affidavit tracking the allegations in his complaint, the district court acknowledged the exhaustion dispute and conducted a hearing to resolve it. See Pavey v. Conley, 544 F.3d 739 (7th Cir.2008). At that hearing the defendants asserted, without referring to evidence in the record, that the June 3 grievance was the only one Towns had filed at the institutional level. The defendants then relied solely on the affidavit from the DOC employee who wasn’t able to find a “timely grievance” relating to events in 2003 in the files of the Administrative Review Board. Towns, who participated by telephone, detailed his travails with the June 1 grievance and emphasized that he mailed a copy to the Board after months had passed with no answer. In response, defense counsel fell back on the “no record” affidavit from the DOC employee and insisted that the Board does not ignore grievances. At the same time, though, counsel conceded that a claim by Towns “that at the institutional level he had problems dealing with the grievance would be more credible.”
In ruling for the defendants, the district judge did not say whether he thought Towns was telling the truth that he submitted his grievances then mailed copies to the Administrative Review Board after not receiving a response. Instead, the district court rested its ruling on the affidavit from the DOC employee. The court reasoned that other appeals filed by Towns had made their way to the Board, and so the absence of appeals in this instance must be the fault of Towns. The court thus concluded that Towns had not exhausted his grievances and dismissed the lawsuit.
The Prison Litigation Reform Act, see 42 U.S.C. § 1997e(a), mandates that inmates exhaust administrative remedies “as are available” before suing about prison conditions. Woodford v. Ngo, 548 U.S. 81, 84, 126 S.Ct. 2378, 165 L.Ed.2d 368 (2006); Macias v. Zenk, 495 F.3d 37, 40-41 (2d *99Cir.2007); Dale v. Lappin, 376 F.3d 652, 655-56 (7th Cir.2004). The Illinois Administrative Code defines the three-step grievance process for state inmates, beginning with an attempt at an informal resolution though a prison counselor, then proceeding to institutional-level review, and culminating in an appeal to the Illinois Department of Corrections. 20 Ill. Admin. Code §§ 504.810(a), 504.850(a). (An inmate may begin directly at the institutional level, however, if grieving a disciplinary report. Id. § 504.810(a).) It was the defendants’ burden to raise failure to exhaust as an affirmative defense and prove that there were remedies available to Towns that he did not use. See Jones v. Bock, 549 U.S. 199, 216, 127 S.Ct. 910, 166 L.Ed.2d 798 (2007); Turner v. Burnside, 541 F.3d 1077, 1082-83 (11th Cir.2008); Kaba v. Stepp, 458 F.3d 678, 686 (7th Cir.2006). We review the court’s factual findings for clear error, see Fed.R.Civ.P. 52(a)(6); Bryant v. Rich, 530 F.3d 1368, 1379 (11th Cir.2008), and legal conclusions de novo, Dole v. Chandler, 438 F.3d 804, 809 (7th Cir.2006).
To prevail, the defendants had to establish that Towns bypassed a remedy that was “available” to him. See Pavey, 544 F.3d at 742; Dale, 376 F.3d at 655-56. But the defendants did not establish that Towns ever had an opportunity to appeal these to grievances to the Administrative Review Board, and therefore the district court’s conclusion that he did not appeal to the Board — whether or not that conclusion is sound — is irrelevant.
The DOC employee explains in her affidavit that an inmate may appeal a warden’s adverse ruling “after receiving” the decision. The sensible inference — uncontradicted by the defendants — is that an inmate must have the institutional decision before appealing. But as far as this record shows, Towns never received a ruling from the warden on either grievance. As to the June 3 grievance, the defendants point to the denial that they submitted at summary judgment, but they offer no proof that Towns actually received it. Unlike the form used to convey disciplinary rulings, which bears the date served and the signature of the employee who served it, rulings on grievances do not evidence delivery to the inmate, and the defendants introduced no evidence of actual receipt by Towns or information about how rulings typically are delivered to inmates. All the denial establishes is that the warden eventually made a decision, either in October 2003 or January 2004. Whichever month it was, Towns had not received a decision within the two-month response time required “where reasonably feasible under the circumstances,” 20 III. Admin. Code § 504.830, or even after four months when, by his account, he mailed a copy of the unanswered grievance to the Board.
As to the June 1 grievance, Towns maintains in his affidavit that he mailed it to the grievance officer after his counselor’s rejection, and he spoke at length about this process during the evidentiary hearing. Counsel for the defendants represented that Towns had submitted only the June 3 grievance, but a lawyer’s statement is not evidence. The defendants made no effort to contradict Towns’s affidavit, not even with evidence that a records custodian had conducted a diligent search for the June 1 grievance but found nothing. If anything, counsel undermined the defendants’ exhaustion defense by conceding that Towns might well have encountered problems with the grievance process at the institutional level. And just as the defendants did not dispute that Towns had submitted the June 1 grievance, they did not dispute his affidavit or representations at the hearing that he never got a ruling.
As the record stands, it is undisputed that Towns submitted two grievances *100about his claims, the first dated June 1, 2003, and the other dated two days later. It is also undisputed that he received no reply from prison officials to either grievance. The defendants proved nothing, then, by producing evidence that a DOC employee found no record of an appeal. Towns has never contended that he filed “appeals” with the Administrative Review Board; what he has said all along is that he sent copies of the two grievances to the Board because those grievances had gone unanswered. It comes as no surprise that the DOC employee located no record of an appeal or of “a timely grievance” filed with the Board about the events of June 2003; grievances are sent to the prison’s grievance officer, not the Board, and an appeal cannot be taken without a decision by the warden. The DOC employee’s carefully worded affidavit omits whether she looked for correspondence from Towns other than a “timely grievance.”
At the evidentiary hearing, of course, the district court was not compelled to accept Towns’s word that he submitted his grievances and received no response. But the court did not make a credibility finding; rather, it simply accepted the defendants’ misguided premise that Towns did not exhaust because he did not appeal rulings that he never received. The court offered no other basis for its decision, and though we give great deference to credibility findings based on demeanor, see, e.g., Pinkston v. Madry, 440 F.3d 879, 891 (7th Cir.2006), that same level of deference is not due when a district court relies instead on faulty logic, see Carradine v. Barnhart, 360 F.3d 751, 754 (7th Cir.2004). The exhaustion requirement of § 1997e(a) does not require that inmates appeal from unresolved grievances. Walker v. Sheahan, 526 F.3d 973, 979 (7th Cir.2008). It is enough that an inmate exhaust “available” remedies, and a prison system that fails to respond to an inmate’s grievance has made its grievance process “unavailable.” Lewis v. Washington, 300 F.3d 829, 833 (7th Cir.2002).
Accordingly, we VACATE the dismissal and REMAND for further proceedings. Towns’s pending motion for appointment of appellate counsel is DENIED as unnecessary.