TINDER, Circuit Judge.

28 U.S.C. § 2241 and 28 U.S.C. § 2255 provide federal prisoners with distinct forms of collateral relief. Section 2255 applies to challenges to the validity of convictions and sentences, whereas § 2241 applies to challenges to the fact or duration of confinement. See Walker v. O'Brien, 216 F.3d 626, 629 (7th Cir.2000). A federal prisoner may use a § 2241 petition for a writ of habeas corpus to attack his conviction or sentence only if § 2255 is "inadequate or ineffective." 28 U.S.C. § 2255(e).

Michael Hill appeals the district court's judgment denying his § 2241 petition, in which he claims that his sentence was erroneously enhanced under the Armed Career Criminal Act ("ACCA"), 18 U.S.C. § 924(e), based on a battery conviction. Because Hill has not shown that the remedy under § 2255 is inadequate or ineffective, we affirm.

In 1999, Hill was convicted in the United States District Court for the Northern District of Illinois of possession with intent to distribute cocaine base, 21 U.S.C. § 841(a)(1); use of a firearm during and in relation to a drug trafficking crime, 18 U.S.C. § 924(c); and possession of a firearm by a convicted felon, id. § 922(g)(1). The district court found that each of Hill's prior state convictions — one for attempted murder; two for aggravated battery — qualified as a career-offender "crime of violence," see U.S.S.G. § 4B1.2(a)(1), and a "violent felony" under the Armed Career Criminal Act (ACCA), see 18 U.S.C. § 924(e)(2)(B)(i). Only the second aggravated battery conviction is at issue here. In 1992 Hill was in a county courthouse and struck his criminal defense lawyer in the back of the head with his hand in violation of the Illinois Revised Statutes, Chapter 38, Section 12-3. The crime of simple battery was elevated to aggravated battery because it occurred on public property, id. 12-4(b)(8). Hill was convicted in 1993 and sentenced to a four years' imprisonment.

Based on the prior convictions, the district court sentenced Hill as a career offender on the drug offense to 216 months' imprisonment and sentenced him as an armed career criminal on the felon-in-possession offense to 216 months' imprisonment, to run concurrently with each other and consecutively to a 60-month sentence on the use of a firearm "during and in relation to" offense, for a total of 276 months. Hill's plea agreement contained a waiver of his right to appeal any sentence within the statutory maximum or to collaterally attack his sentence or the manner in which it was determined, including a § 2255 petition.

The procedural history of Hill's case gets a little convoluted after sentencing, so we will spell out the various steps along the way to this appeal. In 2000, Hill petitioned the district court in the Northern District of Illinois to vacate his federal sentence under § 2255, alleging that his indictment was defective and his trial counsel was ineffective. The petition was summarily denied. Hill later filed two motions to modify his sentence pursuant to 18 U.S.C. § 3582, which were also denied.

In 2010, Hill filed a pro se petition for a writ of habeas corpus under 28 U.S.C. § 2241 in the Western District of Wisconsin. He claimed that his classification as a career offender and armed career criminal was erroneous and that he was "innocent" of the sentence enhancements imposed under the ACCA and Career Offender Guideline, U.S.S.G. § 4B1.1. Specifically, he challenged whether his aggravated battery convictions constituted "violent felonies" or "crimes of violence" under the ACCA and guidelines. The district court denied the petition, finding that Hill failed to show that the remedy under § 2255 was foreclosed to him. Hill appealed and we vacated the district court's judgment based on the determination that he had not filed a § 2255 motion in the district of conviction. (As it turns out, we were wrong about that; he had filed a § 2255 petition in 2000.) On remand, the district court in the Western District of Wisconsin transferred the 2010 petition to the Northern District of Illinois.

Hill then filed an application in this court, seeking authorization to file a second or successive § 2255 motion. He argued, inter alia, that his 1993 aggravated battery conviction was not a violent felony and should not have been used to sentence him as an armed career criminal and career offender. We denied authorization to file a successive collateral attack under § 2255.

Meanwhile, Hill moved for reconsideration of the transfer order, which was granted. The Western District of Wisconsin district court proceeded to consider his § 2241 petition. The court determined that Hill's two aggravated battery convictions were under subsection (1) of 720 ILCS 5/12-3, not subsection (2), and concluded that the convictions constituted "violent felonies." Thus, the court decided that Hill's aggravated battery convictions were properly used to enhance his sentence under the ACCA and denied his § 2241 petition. The court noted Hill's challenge to his career offender guideline enhancement, but concluded that his claim "rises and falls with his career criminal enhancement" and focused exclusively on that enhancement. Hill moved for reconsideration, the court denied it, and he appealed.

On appeal, Hill no longer challenges the first aggravated battery conviction. He contests only whether his 1993 aggravated battery conviction for committing simple battery in a public place constitutes a violent felony under the ACCA. We review the denial of a § 2241 petition de novo. See Flowers v. Anderson, 661 F.3d 977, 980 (8th Cir.2011); Barnard v. Henman, 89 F.3d 373, 376 (7th Cir.1996).

Under the ACCA, an offender who is convicted under 18 U.S.C. § 922(g) as a felon in possession of a firearm and has three prior convictions for a violent felony or serious drug offense receives a mandatory minimum 15-year prison sentence. 18 U.S.C. § 924(e)(1). The ACCA defines "violent felony" as any crime punishable by a year or more in prison that

Id. § 924(e)(2)(B). Thus, for a prior conviction to be considered a "violent felony" for purposes of the ACCA sentencing enhancement, it must be a crime that "has as an element the use, attempted use, or threatened use of physical force" against another, belongs to the list of enumerated offenses, or otherwise involves conduct presenting "a serious potential risk of physical injury." See 18 U.S.C. § 924(e)(2)(B)(i) and (ii). In Johnson v. United States, ___ U.S. ___, 130 S.Ct. 1265, 176 L.Ed.2d 1 (2010), the Supreme Court interpreted "physical force" as used in the ACCA definition of "violent felony" to mean "violent force — that is, force capable of causing physical pain or injury to another person." Id. at 1271.

Hill claims that his 1993 conviction for aggravated battery causing bodily harm does not have as an element violent force and therefore does not count as "violent felony" under the ACCA. Respondent argues that Hill waived any right to collaterally attack his sentence. That may be. But respondent, by failing to raise the defense of waiver in the district court, has forfeited it. See, e.g., Canaan v. McBride, 395 F.3d 376, 382 (7th Cir.2005). Although we could address the forfeited argument, see Wood v. Milyard, ___ U.S. ___, 132 S.Ct. 1826, 1834, 182 L.Ed.2d 733 (2012) (noting appellate court's authority to address sua sponte a forfeited timeliness-of-a-habeas-petition defense), respondent has presented nothing to show that this is an "exceptional case" in which we should base our decision on a forfeited ground, see id. And, as we shall see, Hill's petition fails on another ground anyway.

In general, "§ 2255 is the exclusive means for a federal prisoner to attack his conviction" or sentence. See Kramer v. Olson, 347 F.3d 214, 217 (7th Cir.2003) (per curiam). However, in a narrow class of cases, under § 2255's "savings clause," a federal prisoner may bring a § 2241 petition if he can show that the § 2255 remedy "is inadequate or ineffective to test the legality of his detention." Unthank v. Jett, 549 F.3d 534, 535 (7th Cir.2008) (quoting § 2255(e)). "Inadequate or ineffective" means that "a legal theory that could not have been presented under § 2255 establishes the petitioner's actual innocence." Taylor v. Gilkey, 314 F.3d 832, 835 (7th Cir.2002); see also In re Davenport, 147 F.3d 605, 608 (7th Cir.1998).

We considered the meaning of "inadequacy" in Davenport and said that "[a] procedure for postconviction relief can fairly be termed inadequate when it is so configured as to deny a convicted defendant any opportunity for judicial rectification of so fundamental a defect in his conviction as having been imprisoned for a nonexistent offense." 147 F.3d at 611. One of the petitioners, Nichols, sought relief from his conviction for using a firearm in the commission of a drug offense, see 18 U.S.C. § 924(c)(1). When Nichols was convicted and brought his first § 2255 motion, the settled law of the circuit was that mere possession of a firearm was sufficient to constitute "use" under the statute. After his direct appeal and denial of his initial § 2255 motion, the Supreme Court decided Bailey v. United States, 516 U.S. 137, 143, 116 S.Ct. 501, 133 L.Ed.2d 472 (1995), holding that "use" in § 924(c)(1) "does not include mere possession." Nichols filed another motion for postconviction relief. Davenport, 147 F.3d at 607. He had a claim that he was imprisoned "for a nonexistent crime," id. at 610, but he could not have presented the claim in his direct appeal, first § 2255 motion, or a successive § 2255 petition. Id. at 610-11. (A successive § 2255 motion is allowed if a petitioner offers newly discovered evidence that would establish that he is not guilty, or a new rule of constitutional law made retroactive to cases on collateral review by the Supreme Court. See id. at 607.)

We held that § 2255 was inadequate to test the legality of his detention and he could seek relief under § 2241. Id. at 610-11. In doing so, we explained that "[a] federal prisoner should be permitted to seek habeas corpus only if he had no reasonable opportunity to obtain earlier judicial correction of a fundamental defect in his conviction or sentence because the law changed after his first 2255 motion." Id. at 611. The rule has three qualifications. First, the "the change of law has to have been made retroactive by the Supreme Court." Id. Second, "it must be a change that eludes the permission in section 2255 for successive motions." Id. Third, "`change in law' is not to be equated to a difference between the law in the circuit in which the prisoner was sentenced and the law in the circuit in which he is incarcerated." Id. at 612.

Hill can satisfy the second requirement: His claim is not based on newly discovered evidence or on a new rule of constitutional law; it is based on the Supreme Court's interpretation of "violent felony" in Johnson. But he cannot show that a § 2255 remedy is inadequate or ineffective. He has failed to show that his claim could not have been presented in his direct appeal or § 2255 motion.

In Morales v. Bezy, 499 F.3d 668 (7th Cir.2007), we determined that the petitioner could not show that his § 2255 remedy was inadequate or ineffective because his claim was not foreclosed by binding precedent. Id. at 672. We concluded that "the fact that a position is novel does not allow a prisoner to bypass section 2255.... Only if the position is foreclosed (as distinct from not being supported by — from being, in other words, novel) by precedent" is a § 2255 remedy inadequate. See id.; see also Davenport, 147 F.3d at 610 (concluding that petitioner had no reasonable opportunity on direct appeal or in his first 2255 petition to challenge the legality of his conviction where "[t]he law of the circuit was so firmly against him that we have held that in that period defendants in this circuit did not have to raise [the] issue in order to preserve it as a basis for collateral attack later on").

Hill has not argued that binding precedent foreclosed his claim that his 1993 aggravated battery conviction did not constitute a violent felony under the ACCA because physical force is not an element of battery causing bodily harm under Illinois law. Instead, he asserts that before Johnson, the law was unclear regarding what amount of force was necessary to constitute a "violent felony" under the ACCA. Any lack of clarity in the law before Johnson did not prevent Hill from bringing his claim either in a direct appeal or in his § 2255 motion. Furthermore, Johnson did not change the law so as to interpret "physical force" in the ACCA's definition of "violent felony" in a way that Hill would have a claim that his sentence was enhanced based on nonexistent violent felony. Accordingly, he cannot prevail on his § 2241 petition.1

And if we were to reach the merits, we would affirm. The first prong of the Illinois battery statute under which Hill was convicted reads: "A person commits battery if he intentionally or knowingly without legal justification and by any means, (1) causes bodily harm to an individual...." Ill.Rev.Stat., ch. 38, ¶ 12-3(a)(1) (now codified as 720 ILCS 5/12-3(a)(1)).2 Simple battery is treated as a felony aggravated battery if one of several aggravating factors is present. See id. 5/12-4. Hill was convicted of simple battery which was elevated to felony aggravated battery because the person battered was on public property. See id. 5/12-4(b)(8). In Johnson, the Supreme Court held that as long as a felony conviction has as an element the use, attempted use, or threatened use of "force capable of causing physical pain or injury to another person," the conviction constitutes a "violent felony" under the ACCA. 130 S.Ct. at 1271. The second amended information charged that in 1992 "Hill committed the offense of AGGRAVATED BATTERY in that [he]... in committing a battery, ..., without legal justification and w[h]ile Janet Glick was at the Winnebago County Courthouse, a public property, caused bodily harm to Janet Glick in that he struck Janet Glick in the back of her head with his hand...." Thus, the information tracked the language of the first prong of the battery statute, 720 ILCS 5/12-3(a)(1). Consistent with the charge, the jury instruction on the elements of the offense stated that the State had to prove, inter alia, that Hill "intentionally caused bodily harm," also tracking the language of the first prong. Therefore, it is clear that Hill was charged and convicted under the first prong of the battery statute.

We have previously decided that a conviction under the first prong of the Illinois battery statute, 720 ILCS 5/12-3, which requires that the person "causes bodily harm," has as an element "the use, attempted use, or threatened use of physical force." See United States v. Rodriguez-Gomez, 608 F.3d 969, 973-74 (7th Cir.2010) (holding that prior conviction for aggravated battery based on simple battery causing bodily harm under first prong of the statute is a "crime of violence" warranting a sentencing enhancement under U.S.S.G. § 2L1.2(b)(1)(A)(ii)); United States v. Aviles-Solarzano, 623 F.3d 470, 474 (7th Cir.2010) (same); De Leon Castellanos v. Holder, 652 F.3d 762, 764-67 (7th Cir. 2011) (holding conviction for domestic battery causing bodily harm in violation of 720 ILCS 5/12-3.2(a)(1) qualifies as a "crime of violence" under 18 U.S.C. § 16(a)).3 Accordingly, Hill's 1993 conviction for aggravated battery qualifies as a "violent felony" under the ACCA.

All that said, the petition fails on a preliminary ground: Hill cannot show that the § 2255 remedy is inadequate or ineffective to test the legality of his detention.

The district court's judgment denying habeas relief is AFFIRMED.