Eli Lilly and Company v. Teva Parenteral Medicines , 845 F.3d 1357 ( 2017 )


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  •   United States Court of Appeals
    for the Federal Circuit
    ______________________
    ELI LILLY AND COMPANY,
    Plaintiff-Appellee
    v.
    TEVA PARENTERAL MEDICINES, INC., APP
    PHARMACEUTICALS LLC, PLIVA HRVATSKA
    D.O.O., TEVA PHARMACEUTICALS USA, INC.,
    BARR LABORATORIES, INC.,
    Defendants-Appellants
    ______________________
    2015-2067
    ______________________
    Appeal from the United States District Court for the
    Southern District of Indiana in No. 1:10-cv-01376-TWP-
    DKL, Judge Tanya Walton Pratt.
    ______________________
    Decided: January 12, 2017
    ______________________
    ADAM LAWRENCE PERLMAN, Williams & Connolly LLP,
    Washington, DC, argued for plaintiff-appellee. Also repre-
    sented by DOV PHILIP GROSSMAN, BRUCE GENDERSON,
    DAVID M. KRINSKY, ALLISON JONES RUSHING, ELLEN E.
    OBERWETTER.
    WILLIAM M. JAY, Goodwin Procter LLP, Washington,
    DC, argued for defendants-appellants. Also represented
    by DARYL L. WIESEN, ELAINE BLAIS, EMILY L. RAPALINO,
    2       ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    HENRY C. DINGER, Boston, MA; BRIAN JOSEPH PREW,
    MICHAEL B. COTTLER, NATASHA ELISE DAUGHTREY, New
    York, NY.
    CHRISTINA JORDAN MCCULLOUGH, Perkins Coie, LLP,
    Seattle, WA, for amicus curiae Generic Pharmaceutical
    Association. Also represented by SHANNON BLOODWORTH,
    Washington, DC.
    KEVIN SCOTT PRUSSIA, Wilmer Cutler Pickering Hale
    and Dorr LLP, Boston, MA, for amicus curiae Pharmaceu-
    tical Research and Manufacturers of America. Also repre-
    sented by SAMEER AHMED; JAMIE WISZ, Washington, DC.
    DAVID S. FORMAN, Osha Liang LLP, Alexandria, VA,
    for amicus curiae Biotechnology Innovation Organization.
    Also represented by HANSJORG SAUER, Biotechnology
    Innovation Organization, Washington, DC.
    ______________________
    Before PROST, Chief Judge, NEWMAN and DYK, Circuit
    Judges.
    PROST, Chief Judge.
    Eli Lilly & Co. (“Eli Lilly”) is the owner of U.S. Patent
    No. 7,772,209 (“’209 patent”). It filed this consolidated
    Hatch-Waxman suit against Teva Parenteral Medicines,
    Inc.; APP Pharmaceuticals LLC; Pliva Hrvatska D.O.O.;
    Teva Pharmaceuticals USA, Inc.; and Barr Laboratories,
    Inc. (collectively, “Defendants”) to prevent Defendants
    from launching a generic version of a chemotherapy drug
    with accompanying product literature that would alleged-
    ly infringe methods of treatment claimed by the ’209
    patent. The United States District Court for the Southern
    District of Indiana held two bench trials, one on infringe-
    ment and one on invalidity. The district court found that
    no single actor performs all steps of the asserted claims
    because the actions of both physicians and patients are
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES       3
    required. Nonetheless, under Akamai Technologies, Inc.
    v. Limelight Networks, Inc. (Akamai V), 
    797 F.3d 1020
    ,
    1022 (Fed. Cir. 2015) (en banc) (per curiam), cert. denied,
    
    136 S. Ct. 1661
    (2016), the court found direct infringe-
    ment attributable to physicians and held Defendants
    liable for inducing that infringement. The court also
    determined that the asserted claims were not invalid for,
    inter alia, indefiniteness, obviousness, or obviousness-
    type double patenting.
    For the reasons below, we affirm.
    BACKGROUND
    The ’209 patent, which issued in 2010, relates to
    methods of administering the chemotherapy drug
    pemetrexed disodium (“pemetrexed”) after pretreatment
    with two common vitamins—folic acid and vitamin B12.
    Pemetrexed is an antifolate that kills cancer cells by
    inhibiting the function of folates, a class of nutrients
    necessary for cell reproduction. The purpose of the dual
    vitamin pretreatments is to reduce the toxicity of
    pemetrexed in patients. Eli Lilly markets pemetrexed
    under the brand name ALIMTA®, and the drug is used to
    treat certain types of lung cancer and mesothelioma.
    Around 2008–2009, Defendants notified Eli Lilly that
    they had submitted Abbreviated New Drug Applications
    (“ANDAs”) seeking approval by the Food and Drug Ad-
    ministration (“FDA”) to market generic versions of
    ALIMTA®. After the ’209 patent issued, Defendants sent
    Eli Lilly additional notices regarding their ANDAs, in-
    cluding notices that they had filed Paragraph IV certifica-
    tions under 21 U.S.C. § 355(j)(2)(A)(vii)(IV), declaring that
    the ’209 patent was invalid, unenforceable, or would not
    be infringed. Eli Lilly subsequently brought this consoli-
    dated action against Defendants for infringement under
    35 U.S.C. § 271(e)(2). Specifically, Eli Lilly alleged that
    Defendants’ generic drugs would be administered with
    folic acid and vitamin B12 pretreatments and, thus, result
    4      ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    in infringement of the ’209 patent. Defendants raised
    noninfringement and invalidity defenses.
    Eli Lilly asserted claims 9, 10, 12, 14, 15, 18, 19, and
    21 of the ’209 patent at trial. Importantly, all of the
    asserted claims require patient pretreatment by “admin-
    istering” or “administration of” folic acid. Claims 9 and 10
    depend from claim 1, which recites:
    1. A method of administering pemetrexed
    disodium to a patient in need thereof comprising
    administering an effective amount of folic acid and
    an effective amount of a methylmalonic acid low-
    ering agent followed by administering an effective
    amount of pemetrexed disodium, wherein
    the methylmalonic acid lowering agent is se-
    lected from the group consisting of vitamin B12,
    hydroxycobalamin,       cyano-10-chlorocobalamin,
    aquocobalamin perchlorate, aquo-10-cobalamin
    perchlorate, azidocobalamin, cobalamin, cyanoco-
    balamin, or chlorocobalamin.
    ’209 patent col. 10 ll. 55–65 (emphasis added). The addi-
    tional limitations of claims 9 and 10 restrict the dose of
    folic acid to particular ranges. 
    Id. at col.
    11 ll. 19–22.
    Asserted claim 12 is independent and recites:
    12. An improved method for administering
    pemetrexed disodium to a patient in need of
    chemotherapeutic treatment, wherein the im-
    provement comprises:
    a) administration of between about 350 μg
    and about 1000 μg of folic acid prior to the
    first administration of pemetrexed disodi-
    um;
    b) administration of about 500 μg to about
    1500 μg of vitamin B12, prior to the first
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES      5
    administration of pemetrexed disodium;
    and
    c) administration of pemetrexed disodium.
    
    Id. at col.
    11 l. 25–col. 12 l. 4 (emphasis added). Asserted
    claims 14, 15, 18, 19, and 21 depend from claim 12 and
    further limit the dose, schedule, or route of folic acid or
    vitamin B12 administration. 
    Id. at col.
    12 ll. 7–11, col. 12
    ll. 16–20, col. 12 ll. 24–27.
    The parties agree for purposes of this appeal that no
    single actor performs all steps of the asserted claims;
    rather, the steps are divided between physicians and
    patients. Though physicians administer vitamin B12 and
    pemetrexed, patients self-administer folic acid with
    guidance from physicians. Eli Lilly’s theory of infringe-
    ment therefore requires establishing liability for divided
    infringement—an area of law that this court was actively
    reconsidering during the pendency of this case.
    In June 2013, Defendants conditionally conceded in-
    duced infringement under then-current law set forth in
    Akamai Technologies, Inc. v. Limelight Networks, Inc.
    (Akamai II), 
    692 F.3d 1301
    (Fed. Cir. 2012) (en banc) (per
    curiam), rev’d, 
    134 S. Ct. 2111
    (2014). 1 At the time, the
    Akamai II decision was the subject of a petition to the
    Supreme Court for a writ of certiorari. The parties’
    stipulation included a provision reserving Defendants’
    right to litigate infringement if the Supreme Court re-
    versed or vacated Akamai II.
    Eli Lilly and Defendants proceeded with a bench trial
    on invalidity, after which the district court held that the
    asserted claims were not invalid for, inter alia, obvious-
    1    Akamai II held that “induced infringement can be
    found even if there is no single party who would be liable
    for direct 
    infringement.” 692 F.3d at 1317
    –18.
    6       ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    ness or obviousness-type double patenting. The court had
    also previously rejected Defendants’ contention that the
    asserted claims were invalid for indefiniteness of the term
    “vitamin B12.” Defendants filed an appeal on invalidity,
    which was docketed in this court as Case No. 14-1455.
    While that appeal was pending, the Supreme Court
    reversed Akamai II, holding that liability for inducement
    cannot be found without direct infringement, and remand-
    ing for this court to possibly reconsider the standards for
    direct infringement. Limelight Networks, Inc. v. Akamai
    Techs., Inc. (Akamai III), 
    134 S. Ct. 2111
    (2014). In view
    of that development, the parties in this case filed a joint
    motion to remand the matter to the district court for the
    limited purpose of litigating infringement. We granted
    the motion.
    The district court held a second bench trial in May
    2015 and concluded in a decision issued on August 25,
    2015 that Defendants would induce infringement of the
    ’209 patent. As explained in further detail below, the
    court applied our intervening Akamai V decision, which
    had broadened the circumstances in which others’ acts
    may be attributed to a single actor to support direct-
    infringement liability in cases of divided infringement. 2
    See Akamai 
    V, 797 F.3d at 1022
    . The court accordingly
    entered final judgment against Defendants, barring them
    2   Following remand from the Supreme Court, a
    panel of this court initially found that the accused in-
    fringer in Akamai was not liable for direct infringement,
    Akamai Techs., Inc. v. Limelight Networks, Inc. (Akamai
    IV), 
    786 F.3d 899
    (Fed. Cir. 2015), as had the first panel
    in the case, Akamai Techs., Inc. v. Limelight Networks,
    Inc. (Akamai I), 
    629 F.3d 1311
    (Fed. Cir. 2010). We later
    vacated Akamai IV and took the case en banc, which
    resulted in the Akamai V decision.
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES     7
    from launching their generic products before the expira-
    tion of the ’209 patent.
    Defendants timely appealed.       We have jurisdiction
    under 28 U.S.C. § 1295(a)(1).
    DISCUSSION
    Defendants appeal the district court’s finding of in-
    duced infringement, as well as the court’s decision that
    the asserted claims are not invalid for indefiniteness,
    obviousness, or obviousness-type double patenting. We
    will address each of these issues in turn.
    I
    Pursuant to 35 U.S.C. § 271(b), “[w]hoever actively
    induces infringement of a patent shall be liable as an
    infringer.” 3 Importantly, liability for induced infringe-
    ment under § 271(b) “must be predicated on direct in-
    fringement.” Akamai 
    III, 134 S. Ct. at 2117
    . The
    patentee must also show that the alleged infringer pos-
    sessed the requisite intent to induce infringement, which
    we have held requires that the alleged infringer “knew or
    should have known his actions would induce actual in-
    fringements.” DSU Med. Corp. v. JMS Co., 
    471 F.3d 1293
    , 1304 (Fed. Cir. 2006) (en banc in relevant part)
    (internal quotation marks omitted). A patentee seeking
    relief under § 271(e)(2) bears the burden of proving in-
    fringement by a preponderance of the evidence. Warner-
    Lambert Co. v. Apotex Corp., 
    316 F.3d 1348
    , 1366 (Fed.
    Cir. 2003).
    “Infringement is a question of fact that, after a bench
    trial, we review for clear error.” Alza Corp. v. Mylan
    Labs, Inc., 
    464 F.3d 1286
    , 1289 (Fed. Cir. 2006). Reversal
    3    Section 271 was not amended by the Leahy-Smith
    America Invents Act (“AIA”), Pub. L. No. 112–29, 125
    Stat. 284 (2011).
    8      ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    for clear error is appropriate “only when this court is left
    with a definite and firm conviction that the district court
    was in error.” 
    Id. The district
    court relied in part on Defendants’ pro-
    posed product labeling as evidence of infringement. For
    purposes of this case, the parties have agreed that De-
    fendants’ product labeling would be materially the same
    as the ALIMTA® product labeling, which consists of two
    documents: the Physician Prescribing Information and
    the Patient Information. Both documents include instruc-
    tions regarding the administration of folic acid—the step
    that the district court found would be performed by pa-
    tients but attributable to physicians. For example, the
    Physician Prescribing Information provides, among other
    things:
    “Instruct patients to initiate folic acid 400 [μg] to 1000
    [μg] orally once daily beginning 7 days before the first
    dose of [pemetrexed] . . . .” J.A. 11256.
    “Instruct patients on the need for folic acid and vita-
    min B12 supplementation to reduce treatment-related
    hematologic and gastrointestinal toxicity . . . .” J.A.
    11278.
    The Patient Information includes similar information:
    “To lower your chances of side effects of [pemetrexed],
    you must also take folic acid . . . prior to and during
    your treatment with [pemetrexed].” J.A. 11253 (em-
    phasis omitted).
    “It is very important to take folic acid and vitamin B12
    during your treatment with [pemetrexed] to lower
    your chances of harmful side effects. You must start
    taking 400–1000 micrograms of folic acid every day
    for at least 5 days out of the 7 days before your first
    dose of [pemetrexed]. . . .” 
    Id. (emphasis omitted).
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES        9
    A
    Where, as here, no single actor performs all steps of a
    method claim, direct infringement only occurs if “the acts
    of one are attributable to the other such that a single
    entity is responsible for the infringement.” Akamai 
    V, 797 F.3d at 1022
    . The performance of method steps is
    attributable to a single entity in two types of circum-
    stances: when that entity “directs or controls” others’
    performance, or when the actors “form a joint enterprise.”
    
    Id. Eli Lilly
    did not pursue a joint enterprise theory, so
    the question of direct infringement before us is whether
    physicians direct or control their patients’ administration
    of folic acid. 4
    In Akamai V, we held that directing or controlling
    others’ performance includes circumstances in which an
    actor: (1) “conditions participation in an activity or receipt
    of a benefit” upon others’ performance of one or more
    steps of a patented method, and (2) “establishes the man-
    ner or timing of that performance.” 
    Id. at 1023
    (emphases
    added). In addition to this two-prong test, we observed
    that, “[i]n the future, other factual scenarios may arise
    which warrant attributing others’ performance of method
    steps to a single actor. Going forward, principles of at-
    tribution are to be considered in the context of the partic-
    ular facts presented.” 
    Id. 4 Before
    the district court, Eli Lilly also asserted
    theories of direct infringement that did not rely on show-
    ing physicians’ direction or control of patient action,
    arguing that: (1) as a matter of claim construction, physi-
    cians “administer” folic acid; and (2) under the doctrine of
    equivalents, physicians’ actions are equivalent to putting
    folic acid into patients’ bodies. The district court did not
    reach those issues. Although Eli Lilly asks us to reach
    them in the alternative, we need not do so in light of our
    decision to affirm the district court under Akamai V.
    10     ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    Here, the district court decided that “the factual cir-
    cumstances [we]re sufficiently analogous to those in
    Akamai [V] to support a finding of direct infringement by
    physicians.” Eli Lilly & Co. v. Teva Parenteral Meds., Inc.
    (Eli Lilly III), 
    126 F. Supp. 3d 1037
    , 1041 (S.D. Ind. 2015).
    The court observed initially that taking folic acid in the
    manner recited by the asserted claims is a “critical” and
    “necessary” step to “reduc[e] . . . potentially life-
    threatening toxicities caused by pemetrexed,” i.e., to
    “receive the benefit of the patented method.” 
    Id. at 1042.
    Regarding the first Akamai V prong, the court found,
    based on the product labeling, that “taking folic acid in
    the manner specified is a condition of the patient’s partic-
    ipation in pemetrexed treatment.” 
    Id. Regarding the
    second prong, the court found that physicians would
    “prescrib[e] an exact dose of folic acid and direct[] that it
    be ingested daily.” 
    Id. at 1043.
    The court therefore held
    that, under Akamai V, the performance of all steps of the
    asserted claims would be attributable to physicians.
    1
    With respect to the first prong—conditioning partici-
    pation in an activity or receipt of a benefit upon perfor-
    mance of one or more method steps—Defendants argue at
    the outset that the district court did not make a relevant
    finding because it misidentified the benefit that would be
    conditioned as the “benefit of the patented method, i.e., a
    reduction of potentially life-threatening toxicities caused
    by pemetrexed.” Appellants’ Opening Br. 21–22. We
    agree that a reduction in toxicities is not a benefit that
    physicians can condition (as it follows from folic acid
    pretreatment) and that the relevant benefit that may be
    conditioned on folic acid administration is pemetrexed
    treatment.     But the court’s discussion of reducing
    pemetrexed toxicities in relation to its direction-or-control
    analysis was not erroneous. A reduction in pemetrexed
    toxicities is relevant only if pemetrexed treatment is
    administered, and it provides a reason why physicians
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES     11
    would condition the receipt of pemetrexed treatment on
    folic acid administration. The court recognized this
    relationship and correctly identified pemetrexed treat-
    ment as the benefit to be conditioned: “What is relevant is
    whether the physician sufficiently directs or controls the
    acts of the patients in such a manner as to condition
    participation in an activity or receipt of a benefit—in this
    case, treatment with pemetrexed in the manner that
    reduces toxicities—upon the performance of a step of the
    patented method and establishes the manner and timing
    of the performance.” Eli Lilly 
    III, 126 F. Supp. 3d at 1042
    (emphasis added); see also 
    id. (“[T]aking folic
    acid in the
    manner specified is a condition of the patient’s participa-
    tion in pemetrexed treatment.” (emphasis added)).
    The district court’s finding that physicians “condition”
    pemetrexed treatment on the administration of folic acid
    is supported by the record evidence. The Physician Pre-
    scribing Information, which is “directed to the physician,”
    J.A. 2181, explains that folic acid is a “[r]equirement for
    [p]remedication” in order “to reduce the severity of hema-
    tologic and gastrointestinal toxicity of [pemetrexed].” J.A.
    11258. Consistent with the importance of folic acid pre-
    treatment, the product labeling repeatedly states that
    physicians should “[i]nstruct patients” to take folic acid
    and includes information about folic acid dosage ranges
    and schedules. J.A. 11256; see also J.A. 11255, 11278.
    The Patient Information also informs patients that physi-
    cians may withhold pemetrexed treatment: “You will have
    regular blood tests before and during your treatment with
    [pemetrexed]. Your doctor may adjust your dose of
    [pemetrexed] or delay treatment based on the results of
    your blood test and on your general condition.” J.A.
    11253 (emphasis added).
    Furthermore, Eli Lilly’s expert, Dr. Chabner, testified
    that it is “the physician’s responsibility to initiate the
    supplementation” of folic acid. J.A. 2181. He explained
    that the product labeling shows that taking folic acid is
    12     ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    “an absolute requirement” before pemetrexed treatment
    because “it wouldn’t be safe to take the drug without the
    vitamin supplementation. . . . [I]t must be done this way.”
    J.A. 2192; see also J.A. 2195 (“[I]t’s an absolute require-
    ment.”), 2246 (“I think it’s that important.”). He further
    testified that if a physician realizes that a patient did not
    follow his or her instructions to take folic acid, then the
    “doctor will not give the pemetrexed.” J.A. 2218. Even
    Defendants’ expert, Dr. Schulz, acknowledged that it is
    “standard practice”—both his personally and physicians’
    generally—that a patient “must have taken their required
    folic acid in order to have the pemetrexed administered.”
    J.A. 2329–40; see also J.A. 2304 (“I would withhold the
    pemetrexed therapy until [the patient] had initiated or
    resumed their folic acid treatment . . . [s]o as to avoid the
    toxicities associated with pemetrexed without vitamin
    replacement.”). Dr. Schulz agreed that he was “not aware
    of any reputable institution or doctor . . . who, when they
    think the patient hasn’t taken the required folic acid”
    would go ahead and administer pemetrexed. J.A. 2330–
    31.
    The record is thus replete with evidence that physi-
    cians delineate the step of folic acid administration that
    patients must perform if they wish to receive pemetrexed
    treatment.
    Defendants argue that mere guidance or instruction is
    insufficient to show “conditioning” under Akamai V. But
    the evidence regarding the critical nature of folic acid
    pretreatment and physicians’ practices support a finding
    that physicians cross the line from merely guiding or
    instructing patients to take folic acid to conditioning
    pemetrexed treatment on their administration of folic
    acid. If a patient does not take folic acid as instructed, a
    physician, in his or her discretion, need not provide
    pemetrexed treatment based on the patient’s failure to
    perform the step of folic acid administration. Defendants
    also complain that there is no evidence that physicians go
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES       13
    further to “verify compliance” with their instructions or to
    “threaten” denial of pemetrexed treatment. Appellants’
    Opening Br. 22. Conditioning, however, does not neces-
    sarily require double-checking another’s performance or
    making threats.
    We also reject Defendants’ argument that an actor
    can only condition the performance of a step “by imposing
    a legal obligation to do so, by interposing that step as an
    unavoidable technological prerequisite to participation,
    or, as in [Akamai V], both.” 
    Id. In Akamai
    V, we found
    “conditioning” based on evidence that the defendant
    required all of its customers to sign a standard contract
    delineating the steps that customers had to perform to
    use the defendant’s 
    service. 797 F.3d at 1024
    . But we did
    not limit “conditioning” to legal obligations or technologi-
    cal prerequisites. 5 We cautioned that “principles of
    attribution are to be considered in the context of the
    particular facts presented” and even expressly held that
    § 271(a) infringement “is not limited solely to principal-
    agent relationships, contractual arrangements, and joint
    enterprise.” 
    Id. at 1023
    .
    The product labeling, combined with the testimony
    discussed above, provide sufficient evidence that physi-
    cians condition pemetrexed treatment on folic acid pre-
    treatment.
    5   As Eli Lilly points out, nor did we rely on legal ob-
    ligations or technological prerequisites to reach our deci-
    sion in Akamai V. The standard contract in that case was
    not significant for imposing potential civil liability but for
    “delineat[ing] the steps” that customers would have to
    perform “if [they] wish[ed] to use [defendant’s] product.”
    Akamai 
    V, 797 F.3d at 1024
    . And we did not focus on
    whether a customer’s failure to perform certain steps
    might have made it technologically impossible for other
    steps to occur. 
    Id. 14 ELI
    LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    2
    With respect to the second prong—establishing the
    manner or timing of performance—Defendants argue that
    the product labeling “gives patients wide berth to select
    the dose . . . , the dosage form . . . , and the timing . . . of
    folic acid self-administration.” Appellants’ Opening Br.
    23. Eli Lilly submits that expert testimony and product
    labeling demonstrate that “physicians prescribe or specify
    a dose of folic acid, specify that patients must ingest the
    folic acid daily during a particular span of days, and
    withhold pemetrexed if patients do not follow orders.”
    Appellee’s Br. 25. We agree with Eli Lilly.
    The product labeling is again informative. For in-
    stance, the Physician Prescription Information instructs
    physicians not only to tell patients to take folic acid
    orally, but also to take “400 [μg] to 1000 [μg] [of folic acid]
    once daily beginning 7 days before the first dose of
    [pemetrexed],” accompanied with warnings about the
    consequences of non-compliance. J.A. 11256. That
    dosage range and schedule overlaps with all of the assert-
    ed claims’ dosage ranges and schedules. 6 In addition, Dr.
    Chabner testified that “it’s the doctor” who “decides how
    much [folic acid] the patient will take and when the
    patient takes it.” J.A. 2197. In view of the record evi-
    6   Asserted claims 9, 12, 14, and 15 recite adminis-
    tering “about 350 μg to about 1000 μg” of folic acid. ’209
    patent col. 11 ll. 19–20, col. 11 l. 25–col. 12 l. 4, col. 12
    ll. 7–11. Asserted claims 10, 18, and 19 recite administer-
    ing “350 μg to 600 μg” of folic acid. 
    Id. at col.
    11 ll. 21–23,
    col. 12 ll. 16–20. Asserted claim 21 recites either of those
    folic acid dosage ranges. 
    Id. at col.
    12 ll. 24–27. Asserted
    claim 19 further recites a schedule for folic acid admin-
    istration “wherein folic acid is administered 1 to 3 weeks
    prior to the first administration of the pemetrexed.” 
    Id. at col.
    12 ll. 18–20.
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES     15
    dence, the court’s finding that physicians establish the
    manner and timing of patients’ folic acid intake is not
    clearly erroneous. Even if, as Defendants argue, patients
    are able to seek additional outside assistance regarding
    folic acid administration, such guidance is beyond what is
    required here to establish the manner or timing of per-
    formance and is therefore immaterial.
    We therefore see no reversible error in the district
    court’s finding that physicians condition patient partici-
    pation in an activity or receipt of a benefit (pemetrexed
    treatment) on folic acid administration and also establish
    the manner or timing of performance. Our holding today
    does not assume that patient action is attributable to a
    prescribing physician solely because they have a physi-
    cian-patient relationship. We leave to another day what
    other scenarios also satisfy the “direction or control”
    requirement. The two-prong test that we set forth in
    Akamai V is applicable to the facts of this case and re-
    solves the existence of underlying direct infringement.
    B
    Although we conclude that the two-prong Akamai V
    test is met here, this does not end our inquiry. “The mere
    existence of direct infringement by physicians, while
    necessary to find liability for induced infringement, is not
    sufficient for inducement.” Takeda Pharm. USA, Inc. v.
    West-Ward Pharm. Corp., 
    785 F.3d 625
    , 631 (Fed. Cir.
    2015). To show inducement, Eli Lilly carries the burden
    of further proving “specific intent and action to induce
    infringement.”      
    Takeda, 785 F.3d at 631
    .           Mere
    “knowledge of the acts alleged to constitute infringement”
    is not sufficient. DSU 
    Med., 471 F.3d at 1305
    .
    As noted before, the district court found that the ad-
    ministration of folic acid before pemetrexed administra-
    tion was “not merely a suggestion or recommendation, but
    a critical step.” Eli Lilly 
    III, 126 F. Supp. 3d at 1042
    . It
    further held that Defendants induce physicians’ infringe-
    16     ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    ment because physicians act “in accordance with Defend-
    ants’ proposed labeling.” 
    Id. Accordingly, the
    district
    court concluded that Defendants would induce infringe-
    ment of the ’209 patent.
    Defendants submit that, even if there is direct in-
    fringement, their product labeling does not induce such
    infringement. They argue that Eli Lilly has not offered
    any evidence of what physicians do “in general,” offering
    instead only “speculation about how physicians may act.”
    Appellants’ Opening Br. 24 (second emphasis added).
    Furthermore, they submit that physicians “who merely
    follow the product label” are not induced to infringe
    because physicians must go beyond the labeling instruc-
    tions—such as by prescribing specific doses of folic acid or
    requiring patients to keep “pill counts” or “pill diaries”—
    to infringe. 
    Id. at 23,
    26. We agree with Eli Lilly that
    Defendants’ arguments are unavailing.
    We make two observations at the outset. First, to be
    clear, the intent for inducement must be with respect to
    the actions of the underlying direct infringer, here physi-
    cians. Second, we have not required evidence regarding
    the general prevalence of the induced activity. When the
    alleged inducement relies on a drug label’s instructions,
    “[t]he question is not just whether [those] instructions
    describ[e] the infringing mode, . . . but whether the in-
    structions teach an infringing use such that we are willing
    to infer from those instructions an affirmative intent to
    infringe the patent.” 
    Takeda, 785 F.3d at 631
    (internal
    quotation marks omitted). “The label must encourage,
    recommend, or promote infringement.” 
    Id. For purposes
    of inducement, “it is irrelevant that some users may
    ignore the warnings in the proposed label.” AstraZeneca
    LP v. Apotex, Inc., 
    633 F.3d 1042
    , 1060 (Fed. Cir. 2010).
    Depending on the clarity of the instructions, the deci-
    sion to continue seeking FDA approval of those instruc-
    tions may be sufficient evidence of specific intent to
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES     17
    induce infringement. 
    Id. at 1059.
    With respect to those
    instructions, we held in AstraZeneca that a label that
    instructed users to follow the instructions in an infringing
    manner was sufficient even though some users would not
    follow the instructions. 
    Id. at 1059–60.
    This was true
    even though the product in question had substantial
    noninfringing uses. 
    Id. Conversely, “vague”
    instructions that require one to
    “look outside the label to understand the alleged implicit
    encouragement” do not, without more, induce infringe-
    ment. 
    Takeda, 785 F.3d at 632
    , 634. Defendants try to
    analogize the product labeling here to the labeling in
    Takeda that we held did not provide clear enough instruc-
    tions for the infringing use to show inducement. Takeda,
    however, is distinguishable. The generic manufacturer in
    that case sought FDA approval for a generic drug to be
    used as a prophylaxis for gout flares—a use not covered
    by the patents that had been asserted. 
    Id. at 628.
    The
    only link between the proposed use described on the
    labeling and the patented use was an instruction stating,
    “[i]f you have a gout flare while taking [the drug], tell
    your healthcare provider.” 
    Id. at 632
    (first alteration in
    original) (internal quotation marks omitted). The patent
    owner argued that physicians who are accordingly con-
    sulted might prescribe the drug for the infringing, off-
    label use and that the accused infringer was willfully
    blind to this possibility. 
    Id. We rejected
    the patent
    owner’s reliance on such “vague label language” and
    “speculation about how physicians may act.” 
    Id. The product
    labeling here is not so tenuously related to the
    use covered by the asserted claims, and Eli Lilly does not
    need to rely on speculation about physician behavior.
    Again, the product labeling includes repeated instruc-
    tions and warnings regarding the importance of and
    reasons for folic acid treatment, and there is testimony
    that the Physician Prescribing Information, as the name
    indicates, is directed at physicians. See J.A. 2181, 11253,
    18       ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    11255, 11256, 11258, 11278. The instructions are unam-
    biguous on their face and encourage or recommend in-
    fringement.
    Defendants rely heavily on evidence that physicians
    as a matter of practice take steps beyond the instructions
    in the product labeling, such as asking patients to keep
    pill diaries or pill counts, or confirming compliance with
    folic acid administration. For example, they point to Dr.
    Chabner’s testimony that he gives patients instructions
    “beyond what the instruction is in th[e] patient infor-
    mation.” J.A. 2235–36. But the asserted claims do not
    recite additional steps such as pill diaries, pill counts, and
    compliance measures. Where the product labeling al-
    ready encourages infringement of the asserted claims, as
    it does here, a physician’s decision to give patients even
    more specific guidance is irrelevant to the question of
    inducement. 7
    In sum, evidence that the product labeling that De-
    fendants seek would inevitably lead some physicians to
    infringe establishes the requisite intent for inducement.
    The district court did not clearly err in concluding that
    Defendants would induce infringement of the asserted
    claims of the ’209 patent.
    II
    We turn next to the district court’s holding that the
    limitation “vitamin B12” was not indefinite. Pursuant to
    35 U.S.C. § 112, ¶ 2, a patent specification must “conclude
    with one or more claims particularly pointing out and
    distinctly claiming the subject matter which the applicant
    7  As Dr. Chabner testified, such additional instruc-
    tions are rightfully “left to the medical judgment of [the]
    doctor,” depending on the circumstances. J.A. 2231.
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES      19
    regards as his invention.” 8 The district court considered
    the indefiniteness of the asserted claims before the Su-
    preme Court changed the relevant standard in Nautilus,
    Inc. v. Biosig Instruments, Inc., 
    134 S. Ct. 2120
    (2014),
    and held that “vitamin B12” was not indefinite. 9 Eli Lilly
    & Co. v. Teva Parenteral Meds., Inc. (Eli Lilly I), No. 1:10-
    cv-1376-TWP-DKL, 
    2012 WL 2358102
    , at *11–12 (S.D.
    Ind. June 20, 2012). The district court further construed
    “vitamin B12” to mean “cyanocobalamin,” a particular
    vitamin supplement. 
    Id. at *12.
        In Nautilus, the Supreme Court rejected our “not
    amenable to construction or insolubly ambiguous” stand-
    ard for indefiniteness and articulated, instead, that “a
    patent is invalid for indefiniteness if its claims, read in
    light of the specification delineating the patent, and the
    prosecution history, fail to inform, with reasonable cer-
    tainty, those skilled in the art about the scope of the
    
    invention.” 134 S. Ct. at 2124
    . Indefiniteness is a ques-
    tion of law that we review de novo. Teva Pharm. USA,
    Inc. v. Sandoz, Inc., 
    789 F.3d 1335
    , 1341 (Fed. Cir. 2015).
    We have reiterated post-Nautilus that “general principles
    of claim construction apply” to the question of indefinite-
    8   Paragraph 2 of 35 U.S.C. § 112 was replaced with
    § 112(b) by § 4(c) of the AIA, and § 4(e) makes that change
    applicable “to any patent application that is filed on or
    after” September 16, 2012. Pub. L. No. 112–29, § 4, 125
    Stat. at 296–97. Because the application resulting in the
    ’209 patent was filed before that date, we refer to the pre-
    AIA version of § 112.
    9   Under the prevailing standard at the time, a term
    was indefinite only if it was “not amenable to construc-
    tion” or was “insolubly ambiguous.” Datamize, LLC v.
    Plumtree Software, Inc., 
    417 F.3d 1342
    , 1347 (Fed. Cir.
    2005) (internal quotation marks omitted), overruled by
    
    Nautilus, 134 S. Ct. at 2124
    .
    20        ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    ness. Biosig Instruments, Inc. v. Nautilus, Inc., 
    783 F.3d 1374
    , 1377 (Fed. Cir. 2015) (internal quotation marks
    omitted).    Accordingly, we review subsidiary factual
    determinations made by the district court based on ex-
    trinsic evidence for clear error. Id.; see also 
    Teva, 789 F.3d at 1341
    –42 (reviewing subsidiary factual findings in
    the indefiniteness context for clear error).
    The parties do not dispute that, depending on the con-
    text, “vitamin B12” can be used in the art to refer either
    to cyanocobalamin specifically or, more broadly, to a class
    of compounds including pharmaceutical derivatives of
    cyanocobalamin. The parties do not dispute that the
    written description of the ’209 patent uses the term both
    ways. 10 Defendants argue that, because “vitamin B12” is
    used in two different ways in the intrinsic record, “it is
    impossible to determine” which meaning applies to the
    claims “with any reasonable certainty,” as required by
    Nautilus. Appellants’ Opening Br. 31. Eli Lilly counters
    that the claims of the ’209 patent “involve administering a
    vitamin B12 supplement to a patient,” and in that context,
    “the one and only meaning” of vitamin B12 to a person of
    ordinary skill is cyanocobalamin. Appellee’s Br. 35.
    The district court expressly “accept[ed]” the testimony
    of Eli Lilly’s expert, Dr. O’Dwyer, who concluded that a
    person of ordinary skill would understand “vitamin B12”
    to mean cyanocobalamin in the context of the patent
    claims. Eli Lilly I, 
    2012 WL 2358102
    , at *11. We do not
    10 The specification provides that “[t]he term ‘vita-
    min B12’ refers to vitamin B12 and its pharmaceutical
    derivatives,” and that “[p]referably the term refers to
    vitamin B12, cobalamin, and chlorocobalamin.” ’209
    patent col. 5 ll. 5–10. The district court held, and Defend-
    ants do not dispute on appeal, that this language did not
    signify that the patentee was redefining the term “vita-
    min B12.” Eli Lilly I, 
    2012 WL 2358102
    , at *10–11.
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES      21
    defer to Dr. O’Dwyer’s “ultimate conclusion about claim
    meaning in the context of th[e] patent,” as that is a legal
    question. 
    Teva, 789 F.3d at 1342
    . But the district court’s
    underlying determination, based on extrinsic evidence, of
    what a person of ordinary skill would understand “vita-
    min B12” to mean in different contexts is a question of
    fact. See 
    id. (“Understandings that
    lie outside the patent
    documents about the meaning of terms to one of skill in
    the art or the science or state of the knowledge of one of
    skill in the art are factual issues.”). Dr. O’Dwyer testified
    that, although “vitamin B12” can refer to a class of com-
    pounds in other contexts, it refers specifically to cyanoco-
    balamin when “vitamin B12” is prescribed in the medical
    field. See, e.g., J.A. 3571 (“‘Vitamin B12’ is used by medi-
    cal oncologists to mean a particular vitamin supplement,
    and medical oncologists refer to ‘vitamin B12,’ and pre-
    scribe ‘vitamin B12,’ without further explanation or
    definition.”). We see no clear error in the district court’s
    acceptance of the understanding that “vitamin B12,”
    when used to refer to vitamin B12 supplementation in a
    medical context, refers to cyanocobalamin. 11 In view of
    this understanding, and because the specification uses
    “vitamin B12” primarily in two ways, we do not face the
    problem that we did in Teva, in which the disputed term
    did “not have a plain meaning to one of skill in the art”
    that could be determined from 
    context. 789 F.3d at 1345
    .
    The claim language here would inform a person of or-
    dinary skill that the term “vitamin B12,” as used in the
    ’209 patent claims, refers to “cyanocobalamin.” First, the
    claims, on their face, are directed to administering vita-
    11  Indeed, Defendants’ expert, Dr. Green, agreed
    that “in the strict biochemical nomenclature, the term
    ‘vitamin B12’ is restricted to cyanocobalamin,” J.A. 3767,
    and that it can refer specifically to cyanocobalamin in the
    context of vitamin B12 injections, J.A. 3748–49.
    22    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    min supplements, including vitamin B12, followed by
    chemotherapy treatment. This context informs persons of
    ordinary skill that “vitamin B12” is being used to refer to
    the supplementation form of vitamin B12, cyanocobala-
    min. Second, the structure of the claims also supports
    such an understanding. Claim 1 requires administering a
    “methylmalonic acid lowering agent . . . selected from the
    group consisting of,” inter alia, vitamin B12 and cyanoco-
    balamin. ’209 patent col. 10 ll. 61–65. Claim 2, which
    depends from claim 1, further requires that “the
    methylmalonic acid lowering agent is vitamin B12.” 
    Id. at col.
    10 ll. 66–67. Eli Lilly asserts, and Defendants do not
    dispute, that if “vitamin B12” were to refer to a class of
    compounds, then claim 2 would be the same scope as
    claim 1, as claim 2 “would encompass the same
    methylmalonic acid lowering agents set forth in claim 1.”
    Appellee’s Br. 36. The doctrine of claim differentiation,
    however, presumes that dependent claims are “of narrow-
    er scope than the independent claims from which they
    depend.” AK Steel Corp. v. Sollac & Ugine, 
    344 F.3d 1234
    , 1242 (Fed. Cir. 2003). Reading the claims to re-
    quire “vitamin B12” to be a specific compound in the class
    of “methylmalonic acid lowering agents” would avoid this
    problem, as it would render claim 2, and all of the claims
    that depend from it, narrower than claim 1.
    Defendants submit that, if “vitamin B12” means “cya-
    nocobalamin,” then claim 1 recites a Markush group of
    “methylmalonic acid lowering agents” that lists the same
    compound twice. Although we have in some instances
    interpreted claim terms to avoid redundancy, “the rule is
    not inflexible.” Power Mosfet Techs., LLC v. Siemens AG,
    
    378 F.3d 1396
    , 1409–10 (Fed. Cir. 2004); see also Multi-
    layer Stretch Cling Film Holdings, Inc. v. Berry Plastics
    Corp., 
    831 F.3d 1350
    , 1363–64 (Fed. Cir. 2016); Manual of
    Patent Examining Procedure § 2173.05(h)(I) (“The mere
    fact that a compound may be embraced by more than one
    member of a Markush group recited in the claim does not
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES     23
    necessarily render the scope of the claim unclear.”). Here,
    the redundancy is supported by the prosecution history,
    during which the examiner stated that vitamin B12 and
    cyanocobalamin “are the same” agents. J.A. 4239. There-
    fore, faced with an interpretation that would read redun-
    dancy into claim 1 and another that would violate the
    doctrine of claim differentiation, we hold that the claims
    here support the former result over the latter.
    We are not persuaded by Defendants’ contention that
    the prosecution history fails to “provide reasonable confi-
    dence in any particular meaning of the term ‘vitamin
    B12.’” Appellants’ Opening Br. 30. In response to the
    examiner’s statement that “vitamin B12” and “cyanoco-
    balamin” are synonymous, the patentee initially removed
    the term “cyanocobalamin” from the proposed claims. See
    J.A. 4825–27, 4832–33. Later during prosecution, the
    patentee added “cyanocobalamin” back into the claim that
    eventually issued as claim 1. J.A. 4836. Defendants do
    not point to any reason, though, that a person of ordinary
    skill would understand the patentee’s decision to ulti-
    mately include “cyanocobalamin” in the claim language to
    be a departure from the understanding expressed by the
    examiner that “vitamin B12” and “cyanocobalamin” refer
    to the same compound. The prosecution history here does
    not detract from, and is consistent with, the other intrin-
    sic evidence that would inform a skilled artisan regarding
    the scope of the claim term “vitamin B12.”
    We therefore hold that a person of ordinary skill in
    the art would understand the scope of the claim term
    “vitamin B12” with reasonable certainty. Applying Nauti-
    lus in this case does not lead us to a different result from
    the district court’s conclusion on the question of indefi-
    niteness.
    III
    Next, we address Defendants’ arguments that the as-
    serted claims were obvious over several references that
    24     ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    are not disputed to be prior art as of the critical date in
    June 1999. To prevail on obviousness, an alleged infring-
    er must prove by clear and convincing evidence “that a
    skilled artisan would have been motivated to combine the
    teachings of the prior art references to achieve the
    claimed invention, and that the skilled artisan would
    have had a reasonable expectation of success in doing so.”
    Procter & Gamble Co. v. Teva Pharm. USA, Inc., 
    566 F.3d 989
    , 994 (Fed. Cir. 2009) (internal quotation marks omit-
    ted). Obviousness is a question of law based on underly-
    ing facts, and “[o]n appeal from a bench trial, this court
    reviews the district court’s conclusions of law de novo and
    findings of fact for clear error.” Prometheus Labs., Inc. v.
    Roxane Labs., Inc., 
    805 F.3d 1092
    , 1097 (Fed. Cir. 2015)
    (internal quotation marks omitted).
    In a thorough opinion, the district court found, inter
    alia, that a skilled artisan would not have been motivated
    to: (1) use folic acid pretreatment with pemetrexed; (2)
    use vitamin B12 pretreatment with pemetrexed; or (3) use
    the claimed doses and schedules of folic acid and vitamin
    B12 pretreatments with pemetrexed. The court also
    found that Eli Lilly had established several secondary
    considerations in favor of nonobviousness. On appeal,
    Defendants contend that all of those findings were erro-
    neous. Eli Lilly submits that Defendants’ arguments
    “amount to nothing more than an effort to reargue the
    facts.” Appellee’s Br. 46.
    We agree with Eli Lilly that Defendants’ arguments
    fail to raise reversible error with respect to at least the
    findings that a skilled artisan would not have been moti-
    vated to use vitamin B12 pretreatment with pemetrexed,
    let alone the appropriate doses and schedules of such
    vitamin B12 pretreatment.
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES       25
    A
    The district court found, based upon two abstracts
    published in 1998 by Dr. Niyikiza (“the Niyikiza ab-
    stracts”), 12 that a skilled artisan “would have concluded
    that vitamin B12 deficiency was not the problem in
    pemetrexed toxicity.” Eli Lilly & Co. v. Teva Parenteral
    Meds., Inc. (Eli Lilly II), No. 1:10-cv-01376-TWP-DWL,
    
    2014 WL 1350129
    , at *10 (S.D. Ind. Mar. 31, 2014). It
    further found that a skilled artisan would not have used
    vitamin B12 supplementation to address antifolate toxici-
    ties because of “concern[] about . . . a reduction of efficacy
    of the antifolate” treatment. 
    Id. at *11.
          Dr. Niyikiza was an Eli Lilly scientist at the time and
    is the named inventor on the ’209 patent. In 1997, he
    performed statistical analyses to try to determine which
    clinical trial patients were likely to develop toxicities from
    pemetrexed treatment. J.A. 1045, 1071–72. He published
    the results in the Niyikiza abstracts and reported a
    correlation between increased pemetrexed toxicities and
    elevated homocysteine levels. J.A. 7948, 7950–51. Ele-
    vated homocysteine levels serve as an indicator of either a
    folic acid or vitamin B12 deficiency, but they do not indi-
    cate which of those two vitamins is specifically lacking.
    J.A. 622, 719, 7910. Levels of another marker, methylma-
    lonic acid (“MMA”), serve more specifically as an indicator
    of vitamin B12 deficiency. J.A. 720. But the Niyikiza
    abstracts reported that “no correlation between toxicity
    . . . and [MMA levels] was seen.” J.A. 7948.
    12  C. Niyikiza et al., LY231514 (MTA): Relationship
    of Vitamin Metabolite Profile to Toxicity, 17 PROC. OF AM.
    SOCIETY OF CLINICAL ONCOLOGY 558a, Abstract 2139
    (1998); C. Niyikiza et al., MTA (LY231514): Relationship
    of Vitamin Metabolite Profile, Drug Exposure, and Other
    Patient Characteristics to Toxicity, 9 ANNALS OF
    ONCOLOGY 126, Abstract 609P (4th Supp. 1998).
    26     ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    Given the toxicity correlations that Dr. Niyikiza ob-
    served with homocysteine levels but not with MMA levels,
    Eli Lilly’s experts testified that the Niyikiza abstracts
    “present[ed] no evidence for a relationship of vitamin B12
    and pemetrexed toxicity” and would not have motivated a
    skilled artisan to administer vitamin B12 to patients to
    address pemetrexed toxicity. J.A. 1466–67; see also J.A.
    1475, 1942. Defendants’ expert, Dr. Ratain, confirmed
    that if a patient exhibits elevated homocysteine but
    normal MMA levels, a skilled artisan “would conclude
    that that patient was folate deficient” but “not [vitamin]
    B12 deficient.” J.A. 622–23.
    To try to overcome this missing link between vitamin
    B12 deficiency and pemetrexed toxicity, Defendants turn
    to other prior art references. They argue that, based on
    those references and perhaps preexisting knowledge, a
    person of ordinary skill would have known that folate
    deficiency is correlated with pemetrexed toxicity and that
    vitamin B12 “directly affect[s] the amount of folate avail-
    able to healthy cells.” Appellants’ Opening Br. 45 (citing
    J.A. 2482, 7894, 7910–11, 8086). As a result, they argue,
    skilled artisans would have been motivated to use vitamin
    B12, along with folic acid, to address pemetrexed toxici-
    ties. 
    Id. Put another
    way, if we assume that the prior art
    would have motivated skilled artisans to use folic acid
    pretreatment to counter pemetrexed toxicity (an issue we
    do not reach), Defendants submit that those skilled arti-
    sans would have also used vitamin B12 as part of the
    pretreatment because the biochemical pathways for
    vitamin B12 and folic acid are related. Defendants fur-
    ther submit that other prior art “expressly teaches that
    folic acid supplementation improves the therapeutic index
    of pemetrexed,” so a skilled artisan would not have been
    concerned about using vitamin B12 supplementation to
    reduce pemetrexed toxicities. 
    Id. at 46.
        But the parties’ experts agreed that nothing in the lit-
    erature as of the critical date described “cancer patients
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES      27
    being provided with vitamin B12 supplementation prior to
    receiving any antifolate,” with or without folic acid. J.A.
    597–98; see also J.A. 1957. Defendants fail to point to
    evidence that, even if folic acid supplementation were
    known to improve effects of pemetrexed treatment, a
    skilled artisan would have thought the same of vitamin
    B12. Indeed, Eli Lilly offered expert testimony that a
    skilled artisan would have viewed the use of vitamin B12
    with antifolates as “a problem” based on “having to in-
    crease the [antifolate] dose to get the same activity” of
    cancer treatment. J.A. 1453–54.
    We are therefore not convinced that the district court
    committed clear error in concluding that Defendants
    failed to carry their burden of proving that it would have
    been obvious to a person of ordinary skill to use vitamin
    B12 pretreatment to reduce pemetrexed toxicities.
    B
    Regarding the dose and schedule of vitamin B12, the
    district court reiterated that “there are no prior art refer-
    ences where any amount of vitamin B12 pretreatment had
    been used with an antifolate in the treatment of cancer.”
    Eli Lilly II, 
    2014 WL 1350129
    , at *13 (emphasis added).
    The court also discounted Defendants’ citations to litera-
    ture outside the field of oncology. 
    Id. at *13–14.
        Defendants argue that, “[o]nce a [skilled artisan] is
    motivated to use vitamin B12 pretreatment,” selecting a
    dose and schedule for vitamin B12 “would have been
    routine.” Appellants’ Opening Br. 47. Setting aside
    motivation to use vitamin B12 pretreatment in the first
    instance, Defendants only cite evidence of vitamin B12
    doses and schedules that are “routine” in other medical
    contexts. See, e.g., J.A. 8150, 8169, 756–57. There is no
    evidence that, considering the context of pemetrexed
    treatment and associated toxicity problems, a person of
    ordinary skill would have applied such doses and sched-
    ules wholesale.
    28     ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    We therefore also see no clear error in the court’s find-
    ing that Defendants failed to carry their burden of prov-
    ing that the prior art disclosed the claimed doses and
    schedules of vitamin B12 for purposes of pemetrexed
    pretreatment.
    C
    Defendants make two additional, overarching argu-
    ments that we also find unavailing.
    First, Defendants cite PharmaStem Therapeutics, Inc.
    v. ViaCell, Inc., 
    491 F.3d 1342
    (Fed. Cir. 2007), to argue
    that the district court erred by accepting expert testimony
    that was inconsistent with the express disclosures of the
    prior art. But PharmaStem is distinguishable. In that
    case, we discounted testimony regarding prior art refer-
    ences that “[could not] be reconciled with statements
    made by the inventors in the joint specification [of the
    asserted patents] and with the prior art references them-
    selves.” 
    Id. at 1361.
    Here, despite Defendants’ aver-
    ments, we do not perceive any irreconcilable differences
    between the prior art disclosures on their face and the
    testimony regarding whether a person of ordinary skill
    would have been motivated to use vitamin B12 pretreat-
    ment in the claimed doses and schedules with pemetrexed
    treatment.
    Second, Defendants argue that the district court
    committed legal error by requiring an express prior art
    disclosure of the claimed combination because KSR Inter-
    national Co. v. Teleflex Inc., 
    550 U.S. 398
    (2007), rejected
    such a “rigid” formula in favor of a more flexible inquiry.
    
    Id. at 402–03.
    While KSR did make the obviousness
    inquiry more flexible, it does not advance Defendants’
    position here. Defendants cite to two prior art references
    that would purportedly “motivate a [skilled artisan] to
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES      29
    review literature regarding known doses and schedules
    for vitamin B12 supplementation.” Appellants’ Opening
    Br. 51. But those references merely note in passing that
    vitamin B12 can be related to homocysteine levels and
    folate biochemical pathways. See J.A. 7894, 7910. De-
    fendants do not cite to any testimony to support their
    contention that those references would motivate a skilled
    artisan to arrive at the claimed use of vitamin B12 as a
    pretreatment for pemetrexed, especially in view of the
    evidence of gaps and concerns regarding the prior art
    discussed above.
    The district court did not commit reversible error in
    finding that the prior art fails to render obvious use of
    vitamin B12 pretreatment with pemetrexed, or use of the
    doses and schedules of vitamin B12 that are recited in the
    asserted claims. We therefore affirm the determination of
    nonobviousness. We need not reach the other grounds put
    forth for obviousness.
    IV
    Finally, we address Defendants’ argument that the
    district court erred in holding that the asserted claims are
    not invalid for obviousness-type double patenting over
    U.S. Patent No. 5,217,974 (“’974 patent”), an earlier
    patent also owned by Eli Lilly.
    The judicially-created “doctrine of obviousness-type
    double patenting is intended to ‘prevent the extension of
    the term of a patent . . . by prohibiting the issuance of the
    claims in a second patent not patentably distinct from the
    claims of the first patent.’” Eli Lilly & Co. v. Teva Paren-
    teral Meds., Inc., 
    689 F.3d 1368
    , 1376 (Fed. Cir. 2012)
    (alteration in original) (quoting In re Longi, 
    759 F.2d 887
    ,
    892 (Fed. Cir. 1985)). After determining the differences in
    the claims of the earlier and later patents, the court must
    determine if the alleged infringer has proven by clear and
    convincing evidence that the claims are not patentably
    30     ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES
    distinct. Eli Lilly & Co. v. Barr Labs., Inc., 
    251 F.3d 955
    ,
    962, 968 (Fed. Cir. 2001). “A later patent claim is not
    patentably distinct from an earlier claim if the later claim
    is obvious over, or anticipated by, the earlier claim.” 
    Id. Even where
    a patent is found invalid for obviousness-type
    double patenting, though, a patentee may file a terminal
    disclaimer. Boehringer Ingelheim Int’l GmbH v. Barr
    Labs., Inc., 
    592 F.3d 1340
    , 1347 (Fed. Cir. 2010); see also
    Perricone v. Medicis Pharm. Corp., 
    432 F.3d 1368
    , 1375
    (Fed. Cir. 2005) (noting that there is no “prohibition on
    post-issuance terminal disclaimers” and that “[a] terminal
    disclaimer can indeed supplant a finding of invalidity for
    double patenting”). Obviousness-type double patenting is
    a question of law based on underlying facts, so “[o]n
    appeal from a bench trial, this court reviews the district
    court’s conclusions of law de novo and findings of fact for
    clear error.” 
    Prometheus, 805 F.3d at 1097
    (internal
    quotation marks omitted).
    Defendants argued to the district court that the as-
    serted claims of the ’209 patent are obvious variants of
    claim 20 of the ’974 patent. The court found that the
    asserted claims differ from claim 20 of the ’974 patent “in
    that the Asserted Claims limit the drug to pemetrexed
    and the administration to a patient, use a dose range for
    folic acid of 350–1000 μg or 350–600 μg and add[] vitamin
    B12, whereas claim 20 of the ’974 Patent discloses the use
    of a much greater amount of folic acid—500–30,000 μg—
    with an antifolate . . . administered to a mammal.” Eli
    Lilly II, 
    2014 WL 1350129
    , at *17. In particular, the ’974
    patent lacks any recitation of vitamin B12 pretreatment,
    let alone dosage ranges or schedules of such pretreatment.
    For many of the same reasons it articulated in its ob-
    viousness analysis and with additional explanation, the
    district court found that the use of pemetrexed, use of
    vitamin B12, and doses and schedules of the asserted
    claims were patentably distinct from claim 20 of the ’974
    patent. 
    Id. at *17–18.
    In relevant part, the district court
    ELI LILLY AND COMPANY   v. TEVA PARENTERAL MEDICINES    31
    held that, “as previously discussed, there would have been
    no reason for a [skilled artisan] to add vitamin B12 to the
    folic acid pretreatment.” 
    Id. at *17.
    For the same reasons
    that we discussed with respect to nonobviousness, the
    court did not err in finding that those limitations regard-
    ing vitamin B12 would not have been obvious to a person
    of ordinary skill.
    Therefore, we affirm the district court’s conclusion
    that the asserted claims are not invalid for obviousness-
    type double patenting.
    CONCLUSION
    For the foregoing reasons, we affirm the district
    court’s judgment.
    AFFIRMED