Full opinion text
OPINION LATCHUM, Senior District Judge. 1. INTRODUCTION This patent infringement action is on remand from the Court Of Appeals for the Federal Circuit (the “Federal Circuit”) in accordance with its June 15, 1988 opinion, E.I. duPont de Nemours & Co. v. Phillips Petroleum Co., 849 F.2d 1430 (Fed.Cir.), cert. denied, — U.S. -, 109 S.Ct. 542, 102 L.Ed.2d 572 (1988). The Federal Circuit affirmed in part, reversed in part, and vacated in part this Court’s judgment after trial which held that Claims 1, 2, 5, 10, 12 and 14 of the patent in suit, U.S. Serial No. 4,076,698 (the “ ’698” patent), were not proved invalid and were infringed. The case has been remanded for reconsideration of the validity and infringement of Claims 1 and 12 of the ’698 patent. More particularly, this Court must now consider whether defendant (“Phillips”) has proved that Claims 1 and 12 as defined by the Federal Circuit are invalid, and if not whether plaintiff (“DuPont”) has proved infringement by Phillips of Claims 1 and 12 as defined on remand. II. THE FEDERAL CIRCUIT’S OPINION The ’698 patent relates, generally, to co-polymers of ethylene and higher alpha-ole-fins. This Court previously held that Phillips had not made out its defense of invalidity, and had infringed Claims 1, 2, 5, 10, 12 and 14 of the patent by making and selling approximately 80 copolymer resins or products made from the resins. See DuPont, 656 F.Supp. at 1392. On appeal the Federal Circuit held that it was legal error for this Court to have interpreted the claims of the patent to include two limitations which were disclosed in the specification but not expressly written into the claims. DuPont, 849 F.2d at 1434. The two improperly included limitations were “superior environmental stress crack resistance” and “superior impact strength.” Id. at 1433. Interpreting the claims without these limitations, the Federal Circuit held that Claims 2, 5, 10 and 14 were invalid as anticipated under 35 U.S.C. § 102(g) (“§ 102(g)”), because DuPont conceded at trial that certain copolymers made by Phillips in this country before the date of DuPont’s invention (the “Witt and Leatherman products”) satisfied the remaining limitations of those claims. Id. & n. 3. However, the Federal Circuit concluded that Claims 1 and 12 each had a limitation which DuPont did not concede was satisfied by the Witt and Leatherman products. Id. at 1434. Therefore, Claims 1 and 12 were remanded with instructions for this Court to address their validity and infringement without the improperly included limitations. Id. A. Validity of Claims 1 and 12 The Federal Circuit ruled that to find anticipation of Claims 1 and 12 under § 102(g), this Court must determine that Phillips has proved by clear and convincing evidence that the Witt and Leatherman products satisfied the express limitations of Claims 1 and 12 which were not conceded by DuPont. Id. at 1435. The express limitations which were not conceded are “an Elmendorf tear strength in the range of 150 to 400 grams per mil,” (“Elmendorf tear strength”) in Claim 1, and impact strength in terms of “hoop stress of 750 psi” at 60°C. for 3000 hours (“hoop stress resistance”) in Claim 12. Id. at 1434-35. The Federal Circuit also found that it was improper for this Court to have not considered certain notebook data presented at trial on the issue of anticipation under § 102(g). Id. Therefore, on remand Phillips is entitled to rely on the Witt and Leatherman U.S. and foreign patent applications, as well as the notebook data it presented at trial. Id. It need not prove that Witt and Leatherman were aware that their products possessed the properties embodied by the limitations of Claims 1 and 12. Id. The Federal Circuit also concluded that it was appropriate for this Court to reassess the nonobviousness of Claims 1 and 12 under 35 U.S.C. § 103 (“§ 103”) without the improperly included limitations, and provided guidance with respect to the “scope and content of prior art.” Id. The Federal Circuit held that the prior work of another under § 102(g), except as qualified by § 103 with respect to certain commonly owned subject matter, can be used as § 103 prior art so long as it has not been abandoned, suppressed, or concealed. Id. at 1436-37. However, the Federal Circuit apparently concluded that DuPont conceded that the Witt and Leatherman products were not abandoned, suppressed or concealed. Id. at 1436-37 n. 5. Therefore, the Witt and Leatherman products will be considered as § 103 prior art on remand. B. Infringement of Claims 1 and 12 The Federal Circuit has directed this Court to ascertain the meaning of a density of “0.95” and a crystallinity of “70%” as these terms are used in Claims 1 and 12, and if necessary then to reassess infringement of Claims 1 and 12. Id. at 1439. The Federal Circuit concluded that it appeared that this Court had disregarded statements made by DuPont during prosecution of the patent when interpreting the claims. Id. Therefore, the prosecution history of the patent, including arguments made during reissue/reexamination proceedings, are to be considered relevant in determining the meaning of the terms at issue on remand. Id. at 1438-39. Noted, particularly, were statements made by DuPont during prosecution of the '698 patent that certain densities and crystallinities were not within the claims. Id. If, in light of the prosecution history this Court decides to redefine density as 0.950 and crystallinity as 70% without variance, infringement must be reassessed under the doctrine of equivalents for the Phillips products having a density over 0.950 or a crystallinity over 70%. Id. at 1439. III. MOTION BY PHILLIPS ON REMAND After some maneuvering by the parties, this Court entered an order on November 7, 1988, concluding that the matters to be determined on remand could be performed properly from the present trial record taking into account all exhibits introduced and testimony presented at trial. (Docket Item [“D.I.”] 302.) Notwithstanding this order, on December 7, 1988, Phillips moved for summary judgment on the invalidity of Claims 1 and 12, or in the alternative, for this Court to reopen the record and take certain additional evidence directed to the invalidity of Claims 1 and 12. (D.I. 305.) The Court will address this motion before turning squarely to the matters remanded. A. Summary Judgment Phillips has moved for summary judgment under Rule 56, Fed.R.Civ.P., on the invalidity of Claims 1 and 12. (D.I. 305.) However, determination of whether Phillips has carried its burden of proving the invalidity of Claims 1 and 12 requires this Court to make further factual findings from the record. See DuPont, 849 F.2d at 1435, 1436. These findings will not be made on a motion for summary judgment. See DeLong Corp. v. Raymond Int'l, Inc., 622 F.2d 1135, 1138 n. 2 (3d Cir.1980); Florham Park Chevron, Inc. v. Chevron U.S.A., Inc., 680 F.Supp. 159, 161 (D.N.J.1988); see also Shipley v. First Federal Savings & Loan Ass’n, 703 F.Supp. 1122, 1125 (D.Del.1988). Therefore, Phillips’ motion for summary judgment will be denied. B. Reopen the Record As an alternative to summary judgment, Phillips has moved for this Court to reopen the record so that it may introduce additional evidence on the issue of whether the Witt and Leatherman products satisfied the limitations of Claims 1 and 12. (D.I. 305.) The evidence consists of three affidavits which Phillips asserts “report reproductions of the Witt and Leatherman ethylene-hexene copolymers” and evaluations of the reproductions. (D.I. 306 at 2.) Phillips argues that admission of this evidence is required by the Federal Circuit’s mandate in this case, and by the controlling authorities. (D.I. 306 at 8.) This Court reads neither the Federal Circuit’s mandate nor controlling authority as requiring the record to be reopened in this case. While the Federal Circuit did rule that Phillips can rely on the notebook data presented at trial, DuPont, 849 F.2d at 1436, it did not direct this Court to take additional evidence. The Federal Circuit’s failure to specifically direct the taking of additional evidence can, “at most,” be construed as leaving the matter to the sound discretion of this Court. Skehan v. Board of Trustees of Bloomsburg State College, 590 F.2d 470, 478 (3d Cir.1978), cert. denied, 444 U.S. 832, 100 S.Ct. 61, 62 L.Ed.2d 41 (1979); accord Hartford Accident and Indemnity Co. v. Gulf Ins. Co., 837 F.2d 767, 773 (7th Cir.1988); see also Adelson v. United States, 782 F.2d 1010, 1012 (Fed.Cir.1986); Noble v. National Mines Corp., 774 F.2d 144, 149 (6th Cir.1985); Air Et Chaleur, S.A. v. Janeway, 757 F.2d 489, 495 (2d Cir.1985); Spring Mills, Inc. v. Ultracashmere House, Ltd., 724 F.2d 352, 355 (2d Cir.1983); Pittsburgh Press Club v. United States, 579 F.2d 751, 755 (3d Cir.1978); Rochez Bros., Inc. v. Rhoades, 527 F.2d 891, 894 n. 6 (3d Cir.1975), cert. denied, 425 U.S. 993, 96 S.Ct. 2205, 48 L.Ed.2d 817 (1976). Cf. Littlejohn v. BIC Corp., 851 F.2d 673, 686 (3d Cir.1988) (whether to reopen discovery on remand is within trial court’s discretion). The Third Circuit has enumerated three factors which should concern this Court in the exercise of its discretion: the burden that would be placed on the parties and witnesses by additional proceedings; whether “undue prejudice” may result by not taking additional evidence; and, whether taking additional evidence would unnecessarily drain judicial time and resources. Pittsburgh Press Club, 579 F.2d at 755; see also Skehan, 590 F.2d at 478; Rochez Bros., Inc., 527 F.2d at 894 n. 6. 1. The Burden On The Parties And Witnesses Phillips argues that the burden on the parties and their witnesses would be “small” because the evidence is limited and can be considered on a motion for summary judgment or “in a very short evidentiary hearing;” and because Phillips is going to present this same evidence to the Patent Office during reexamination of the ’698 patent. (D.I. 306 at 11.) The Court cannot concur with Phillips’ view. However accurate Phillips’ estimate may be with regard to the presentation of its own evidence, it hardly accounts for what DuPont may be required to do to address this evidence. Phillips’ evidence includes facts and opinions which would inject a myriad of new issues of both substance and credibility into the case, which DuPont would be entitled to address. Moreover, since the evidence involves reproductions rather than the Witt and Leatherman products themselves, the comparability of the reproductions would also be an issue. The Court assumes DuPont would be required to address each of these issues with discovery, preparation and marshalling experts of its own. Calling on its experience in these matters, the Court concludes that allowing the additional evidence would place a great burden on DuPont and its witnesses, after having once tried the case. 2. Undue Prejudice Phillips argues that because it had the burden of proving the invalidity of Claims 1 and 12 at trial it “might be prejudiced if it is denied the right to introduce new evidence” now. (D.I. 306 at 11.) Phillips contends that because of certain statements made by DuPont’s counsel during trial, “the only issue of fact on the validity side of the case” at trial was whether Witt and Leatherman recognized the superior properties of their products. (Id. at 11-12.) As support for its argument, Phillips cites two excerpts from the trial transcript. The first excerpt prefaced DuPont’s “judicially binding admission” that Witt and Leatherman made certain copo-lymers satisfying the limitations of Claims 2, 5, 10 and 14 in this country before the date of DuPont’s invention. (Transcript [“Tr.”] at 1279); see also DuPont, 849 F.2d at 1434 & n. 3. DuPont’s counsel stated: “I do this (i.e. make the “judicially binding admission”] to focus the case and to shorten it by making presentation of less pertinent evidence unnecessary.” (Tr. at 1279.) The second excerpt was not part of the “admission.” There, DuPont’s counsel stated that: [prior invention under 35 U.S.C. § 102(g) ] would invalidate ... [the ’698] patent if Witt and Leatherman made the discovery that the higher alpha olefins had superior stress crack and impact resistance to the butene copolymers or to free radical polyethylene. And they made the discovery before DuPont did. And, further, that they didn’t — and this is in the words of the statute — they didn’t abandon, suppress or conceal it. (Id. at 1282.) Phillips’ argument is not convincing as a matter of law or fact. It is precisely because Phillips had the burden to prove invalidity at trial that its argument that it will be unduly prejudiced fails here. As a matter of law, neither of the excerpted statements made recognition by Witt and Leatherman the only issue of fact necessary for Phillips to prove the invalidity of Claims 1 and 12 at trial. Each claim of the ’698 patent was presumed valid. 35 U.S.C. § 282. By asserting invalidity as a defense to infringement Phillips had to prove by clear and convincing evidence that each of the claims asserted against it, including Claims 1 and 12, was invalid. See American Hoist & Derrick Co. v. Sowa & Sons, Inc., 725 F.2d 1350, 1360 (Fed.Cir.), cert. denied, 469 U.S. 821, 105 S.Ct. 95, 83 L.Ed.2d 41 (1984); DuPont, 656 F.Supp. at 1354. Since DuPont did not concede the invalidity of Claims 1 and 12, see DuPont, 849 F.2d at 1434, Phillips had to adduce sufficient facts to establish their invalidity. See ACS Hospital Systems, Inc. v. Montefiore Hospital, 732 F.2d 1572,1574-75 (Fed.Cir.1984). DuPont’s position that Witt and Leatherman had to recognize the superior properties of their products to invalidate the ’698 patent under § 102(g) did not obviate the need for Phillips to prove that the Witt and Leatherman products were identical to the claimed interpolymers. DuPont neither admitted that the Witt and Leather-man products were identical to the invention nor dictated the law of the case by stating its position at trial. See Monroe v. United Air Lines, Inc., 736 F.2d 394, 408 (7th Cir.1984), cert. denied, 470 U.S. 1004, 105 S.Ct. 1356, 84 L.Ed.2d 378 (1985); Glick v. White Motor Co., 458 F.2d 1287, 1291 (3d Cir.1972); New Amsterdam Cas. Co. v. Waller, 323 F.2d 20, 24 (4th Cir.1963), cert. denied, 376 U.S. 963, 84 S.Ct. 1124, 11 L.Ed.2d 981 (1964); Childs v. Franco, 563 F.Supp. 290, 292 (E.D.Pa.1983). Cf. Jurinko v. Edwin L. Wiegand Co., 477 F.2d 1038, 1045 (3d Cir.), vacated, 414 U.S. 970, 94 S.Ct. 293, 38 L.Ed.2d 214 (1973). Phillips’ argument is also factually flawed. It is apparently Phillips’ position now that DuPont framed the issue of validity during trial such that Phillips was prevented from, or justifiably forewent, introducing evidence on the issue now before the Court. But Phillips’ position now is inconsistent with its actions taken after the allegedly “issue” framing activity of DuPont. It is clear that it was Phillips’ position, both at trial and after, that DuPont’s position was wrong as a matter of law, that Phillips did not have to show that Witt and Leatherman recognized the superior properties in order to invalidate the claims under § 102(g). (Tr. at 1285; D.I. 259 at 35.) In fact, Phillips apparently concedes that it has continued to maintain that DuPont’s position was wrong. (D.I. 310 at 3.) Furthermore, Phillips squarely addressed the issue in its post-trial brief, arguing that Claims 1 and 12, including the Elmendorf tear strength and hoop stress limitations at issue here, were fully met under § 102(g) by the Witt and Leatherman products. (D.I. 259 at 43-47.) Therefore, Phillips’ argument that it will be unduly prejudiced fails as well. 3. Drain On Judicial Resources Phillips argues that there will be minimal use of judicial resources in taking the additional evidence because the amount of time necessary to consider it would be “quite short — on the order of two days;” and because if not considered here, it will “no doubt be considered in other forums” such as the Patent Office. (D.I. 806 at 14.) Phillips’ argument here is similar to that advanced with respect to the “burden on the parties and their witnesses.” See Section III.B.l. supra. The Court finds this argument equally unconvincing. The Court is not convinced that Phillips’ estimate of 2 days is an accurate one for Phillips to present the additional evidence and for DuPont to address it. Also, Phillips naively suggests that “taking” the evidence ends the drain on judicial resources. In fact, after “taking” the evidence the Court would have to consider it in view of the entire record, including the testimony given at the original trial. However, the Court would not have the benefit of having the additional evidence integrated into the original trial so it could be tested by the entire proceeding. Contrary to Phillips’ suggestion, this would be a substantial drain on the resources of the Court. All of this would be unnecessary because, for the reasons stated in Section III.B.2. supra, Phillips had a full opportunity to present this evidence at trial. Therefore, the Court concludes that reopening the record would substantially and unnecessarily drain the resources of this Court. In the Court’s view Phillips has asked for the record to be reopened so that it can introduce additional evidence on an issue squarely before the Court at trial and addressed by Phillips without restraint by the Court or DuPont. Phillips was required to be reasonably alert at trial in the protection of its own interests. Moylan v. Sicilano, 292 F.2d 704, 705 (9th Cir.1961). It had a full and unrestrained opportunity to present evidence on whether Claims 1 and 12 were fully met by the Witt and Leather-man products. If this presentation was inadequate, it was the fault of Phillips, not DuPont. Cf. Skehan, 590 F.2d at 478-79. Accordingly, after considering the foregoing, Phillips’ motion to reopen the record will be denied. IV. CONSIDERATION OF THE MATTERS REMANDED The Court will now address the matters remanded by the Federal Circuit, specifically the validity and infringement of Claims, 1 and 12 of the ’698 patent. After carefully considering the sufficiency, weight and credibility of the evidence proffered by the parties at trial and their arguments, the Court enters the following findings of fact and conclusions of law which are embodied in this opinion as permitted by Rule 52(a), Fed.R.Civ.P. A. Validity of Claims 1 and 12 Claims 1 and 12 are presumed valid, 35 U.S.C. § 282, and Phillips must prove facts to establish their invalidity by clear and convincing evidence. Ethicon, Inc. v. Quigg, 849 F.2d 1422, 1427 (Fed.Cir.1988); see also American Hoist & Derrick, 725 F.2d at 1360. 1. Anticipation By The Witt And Leath-erman Products Under § 102(g) To find anticipation this Court must determine that Phillips has proved by clear and convincing evidence that the Witt and Leatherman products had the Elmendorf tear strength and hoop stress resistance of Claims 1 and 12. DuPont, 849 F.2d at 1435. Anticipation is a factual determination. Lindemann Maschinenfabrik v. American Hoist & Derrick Co., 730 F.2d 1452, 1458 (Fed.Cir.1984). a. Elmendorf Tear Strength of Claim 1 On the issue of whether the Witt and Leatherman products had the Elmendorf tear strength of Claim 1, Phillips proffers the laboratory notebook (DX 206) and testimony (Tr. 2732-33) of John N. Scott, a Phillips chemist, and certain testimony of Dr. John Knox Beasley, an expert called by DuPont (Tr. at 627). Phillips argues that Dr. Beasley “admitted” that the Witt and Leatherman products would satisfy the limitations of the claims if the products were made “properly,” and that the environmental stress crack resistance data contained in the Scott notebook show that they were. (D.I. 306 at 18.) The proferred testimony of Dr. Beasley was related to neither the Witt and Leath-erman products nor prior invention under § 102(g). Rather his testimony related to whether a higher alpha-olefin copolymer known to have a density within the claims would infringe. Phillips has not established the relevance of the proffered testimony to the issue of whether the Witt and Leatherman products had the Elmendorf tear strength of Claim l, or to its defense of prior invention under § 102(g). Next, Phillips relies on certain proofs of infringement adduced by DuPont at trial. (D.I. 306 at 19.) Phillips proffers the facts that eight Phillips commercial resins were found to be within the scope of Claim 1, and that one had a melt index of 0.33 and a density of 0.940 and was measured to have an Elmendorf tear strength of 181 grams per mil. (D.I. 306 at 19.) Phillips also proffers the fact that a Witt and Leather-man ethylene-hexene copolymer had a density of 0.940 and a melt index of 0.27. (Id. citing DX 786E.) Phillips argues that because of the similarity between the melt index and density of the infringing resin and those of the Witt and Leatherman co-polymer, the latter “necessarily” met the Elmendorf tear strength limitation of Claim 1. (D.I. 306 at 19.) The Court does not find Phillips’ argument convincing. Phillips asks the Court to infer that the Witt and Leatherman products met the Elmendorf tear strength of Claim 1 because another copolymer having the same density and melt index did. However, Phillips proffers no persuasive evidence of the likelihood that copolymers having the same density and melt index will have the same Elmendorf tear strength. Dr. Beasley testified that while it was important for any comparison to be of copolymers having the same density and melt index (Tr. at 594), this did not mean that two copolymers were the same: “As I said before, in polymers there are many different properties. They are complex materials. You don’t have the same polymer just because you have the same density, melt index and so on.” (Tr. at 105.) Furthermore, at least one of the two properties asserted as a basis for the eom-parison, the melt index, is not the same, and no persuasive evidence is proffered that the commercial resin would also satisfy the claim if it had a .27 melt index. As noted above, according to the testimony of Dr. Beasley it is important when comparing copolymers to at least have the same melt index and density. (Tr. at 594.) Moreover, DuPont proffers evidence that the infringing products were made with a different catalyst than the Witt and Leatherman products, and that this would result in the infringing products having different or even better properties than the Witt and Leatherman products. (D.I. 309 at 26 citing Tr. at 2308.) Therefore, the Court finds that Phillips has failed to carry its burden of proving by clear and convincing evidence that the Witt and Leatherman products satisfied the El-mendorf tear strength limitation of Claim 1. b. Hoop Stress of Claim 12 Phillips proffers the same evidence in the Scott notebook and testimony (DX 206; Tr. at 2732-33), and Beasley testimony (Tr. at 627) to establish that the Witt and Leather-man products had the hoop stress resistance of Claim 12. (D.I. 306 at 20.) The Court finds, similarly, that the evidence fails to establish anticipation of Claim 12. As the Court found in Section IV.A.l.a. of this opinion, Phillips has not established the relevance of the proffered Beasley testimony to anticipation of DuPont’s inven- tion under § 102(g). As with Elmendorf tear strength, Phillips has failed to establish the relevance of the Beasley testimony to the issue of whether the Witt and Leath-erman products had the hoop stress resistance of Claim 12. Next Phillips proffers the Scott notebook data on the stress crack resistance of the Witt and Leatherman products, certain findings of infringement by this Court, and other stress crack resistance data for one of the infringing products (PX 378). (D.I. 306 at 20-21.) Phillips argues that because the Court found that the infringing product, commercial resin HHM 5502, met the hoop stress resistance limitation of Claim 12, and that this product showed 50% failures in 45 hours in the same test for environmental stress crack resistance in which the Witt and Leatherman products showed no failures after 360, 456 and 504 hours, it follows that the Witt and Leatherman products must have met the hoop stress resistance limitation of Claim 12. (Id. at 20-21.) The Court finds that Phillips has not carried its burden on anticipation of Claim 12 with this evidence either. Phillips’ argument depends on the inference that a copolymer having a higher environmental stress crack resistance than another copo-lymer will also have a higher hoop stress resistance. In support of the inference, Phillips asserts that environmental stress crack resistance and hoop stress resistance are measurements of the same aspect of a copolymer. (D.I. 306 at 20 citing DuPont, 656 F.Supp. at 1351; Tr. at 90-93.) However, the Court does not find any support in the evidence for Phillips’ assertion. While environmental stress crack resistance and hoop stress resistance may both measure the endurance over time of a copo-lymer under stress, see DuPont, 656 F.Supp. at 1351 citing Tr. at 92-92, Phillips offers nothing to convince the Court that environmental stress crack resistance and hoop stress resistance are covariant. Furthermore, the Court seriously questions whether, without more, a valid comparison can be made of the Witt and Leath-erman products and the infringing resin, or of their environmental stress crack resistance data. Phillips concedes that new catalysts developed in the early 1970’s, well after the work of Witt and Leatherman, “resulted in polymers with improved physical properties that had not been obtained previously,” and which allowed Phillips “to produce pipe having better properties than had been previously achieved.” (D.I. 259 at 25.) With regard to the stress data, while Phillips cites evidence supporting failures of the infringing resin after 45 hours (PX 378), DuPont cites other evidence that the same resin would withstand 1000 hours (PX 640), well in excess of the time reported for the Witt and Leatherman products. Therefore, the Court finds that Phillips has not proved anticipation of Claim 12 by clear and convincing evidence. 2. Nonobviousness Of Claims 1 And 12 The Court must now reassess the nonobviousness of Claims 1 and 12 without the “stress crack resistance” and “impact strength” limitations. DuPont, 849 F.2d at 1436. More particularly, the Court must determine whether Phillips has shown, by clear and convincing evidence, that the differences between the subject matter of Claims 1 and 12 and the prior art are such that the claimed subject matter as a whole would have been obvious at the time the invention was made to a person having ordinary skill in the pertinent art. See 35 U.S.C. § 103. This requires consideration of (1) the scope and content of the prior art, (2) the differences between the prior art and Claims 1 and 12, (3) the level of ordinary skill in the pertinent art, and (4) objective evidence of secondary considerations. Graham v. John Deere Co., 383 U.S. 1, 17-18, 86 S.Ct. 684, 693-94, 15 L.Ed.2d 545 (1966); see also DuPont, 656 F.Supp. at 1363. a. The Invention of Claims 1 and 12 Claims 1 and 12 claim interpolymers, or copolymers, of ethylene and higher alpha-olefins having a melt index in the ranges of 0.3 to 20, a density within a specified range, and an Elmendorf tear strength (Claim 1) or a hoop stress resistance (Claim 12). Construed in light of the specification, see United States v. Adams, 383 U.S. 39, 49, 86 S.Ct. 708, 713, 16 L.Ed.2d 572 (1966), the Court concludes that the invention claimed is branched copolymers having an advantageous combination of properties obtained by copolymerizing higher alpha-olefins with ethylene. (PX 1, col. 3, 11, 15-18.) More particularly, the invention is a copolymer of ethylene and higher alpha-olefins having an improved property (viz: Elmendorf tear strength or hoop stress resistance) desirable in the ultimate service or performance of an article fabricated from it, and at the same time retaining other properties (e.g. melt index) which are amenable to conventional fabricating techniques. (See, e.g., PX 1, col. 3-4.) To carry its burden of proof, Phillips must prove by clear and convincing evidence that it was obvious to the artisan at the time of DuPont’s invention in view of the prior art to obtain copolymers of ethylene and higher alpha-olefins having the combination of properties claimed, b. Scope and Content of the Prior Art The Court will readdress the scope and content of the prior art relied on by Phillips at trial, focusing now on the invention of Claims 1 and 12 as defined by the Federal Circuit. The following findings of fact supplement rather than supplant the findings contained in the Court’s earlier opinion. See DuPont, 656 F.Supp. at 1364-72. i. The Witt and Leatherman Products DuPont admitted that the Witt and Leatherman products included an ethylene/1-pentene and ethylene/1-hexene co-polymer with a comonomer-type, density, melt index, percent crystallinity and weight percent comonomer content falling within the ranges of the claims of the ’698 patent. (Tr. at 1279; see also DuPont, 849 F.2d at 1434 & n. 3.) However, Phillips has not proved that the Witt and Leatherman products had these properties in combination with the improved Elmendorf tear strength or hoop stress resistance set forth in Claims 1 and 12. See Section IV.A., supra. Thus, in considering the Witt and Leatherman products as § 103 prior art, the Court will not assume the products had these properties. Nor has Phillips shown by clear and convincing evidence that the combination of properties obtained with higher alpha-ole-fins in accordance with DuPont’s invention would have been obvious to the artisan at the time of the invention, in view of the Witt and Leatherman products. The Court found that in the mid 1950’s, one would have been taught to decrease branch points to improve properties such as stress crack resistance and impact strength, and that the artisan would have been taught that lower alpha-olefins were preferred for this. DuPont, 656 F.Supp. 1351. In fact, the Court found that the environmental stress crack resistance data for the Witt and Leatherman products showed no difference between higher and lower alpha-olefin co-polymers, see Section IV.A.1, supra; see also DuPont, 656 F.Supp. at 1354-56, and that the “Izod impact strength” data supports a preference for lower alpha-olefins. Id. at 1354 (citing PX 88, Table VI; Tr. 168-73; Tr. at 2059; Tr. at 1472.) Therefore, if the Witt and Leatherman products taught anything with regard to the combination of properties of Claims 1 and 12 it was that the combination was less likely with copolymers of ethylene and higher alpha-olefins. ii. Richards, Roedel, Franta, and Buckley and Ray Richards (DX 151) taught that flexibility and toughness could be improved by lowering the crystallinity (or density). (Id. at 372). The Court found that Richards taught nothing about the effect of the length of the branches or side chains, or improved impact strength or stress crack resistance. DuPont, 656 F.Supp. at 1364. The Court finds further that Richards taught nothing about improved Elmendorf tear strength or hoop stress resistance. Furthermore, it would not have been obvious to the artisan in view of Richards that longer branches would be better than shorter branches in producing an ethylene copolymer with superior Elmendorf tear strength or hoop stress resistance. Therefore, nothing in Richards suggested that higher alpha-olefins could be polymerized with ethylene to effect this end. The Roedel article (DX 152) proposed mechanisms to account for the occurrence of long and short chain branching in free-radical polyethylene. DuPont, 656 F.Supp. at 1364. Roedel suggested that by controlling the average molecular weight and degree of long and short chain branching, properties of polyethylene polymers could be varied. (Tr. at 6112.) However, there was no suggestion that Elmendorf tear strength or hoop stress resistance could be improved by addition of higher alpha-ole-fins to ethylene polymers. In fact, Roedel taught that long chain branching would not effect solid state properties such as Elmen-dorf tear strength or hoop stress resistance. (Tr. at 1717-18). The Franta patent (DX 38) disclosed free radical ethylene homopolymers having a high density and stiffness, but having a melt viscosity suitable for molding operations. (Id. at col. 3.) Franta taught that this “anomalistic result” was obtained by carrying out the polymerization of ethylene at a known pressure and temperature with an accepted catalyst and in the presence of a prescribed quantitative amount of cyclo-hexane. (Id. at col. 2-3.) Franta taught that the cyclohexane controlled chain growth during polymerization and the amount present was crucial to obtaining a polymer with the desired combination of properties. (Id. at col. 3.) Franta did not, however, suggest that these polymers had superior properties such as Elmendorf tear strength or hoop stress resistance, nor that the combination of properties which was claimed by it could be obtained with higher alpha-olefin copolymers. The focus of the Franta reference was the addition, and thus the presence, of cyclohexane to effect the properties. The Buckley and Ray article (DX 121) disclosed materials made from the decomposition mixtures of diazomethane and 1-diazohexane. While the article suggested that the crystallinity of a copolymer made by decomposition of diazo compounds could be decreased by either increasing the number of branches or using longer branches (id. at 3702); see also DuPont, 656 F.Supp. at 1366, it did not suggest a scheme to obtain the combination of properties in Claims 1 and 12. The bare suggestion that the physical properties of the materials depended on both the number and length of branches provided no guidance toward the invention of Claim 1 or 12, where particular properties are achieved in a particular way, viz: the addition of higher alpha-olefins to ethylene polymers. iii.Anderson ’645, Hagemeyer ’413, and Belgian ’782 The Court’s prior findings with respect to the remaining prior art references relied on by Phillips — the Anderson ’645 patent (DX 6), the Hagemeyer ’413 patent (DX 41), and the Belgian ’782 patent (DX 106A)— are unchanged with respect to Claims 1 and 12 as defined by the Federal Circuit. Furthermore, nothing in those references taught or suggested that the claimed combinations of properties could be obtained with copolymers of ethylene and higher alpha-olefins. iv.DuPont Ethylene-Butene Copolymers Phillips now relies on certain DuPont ethylene-butene copolymers (D.I. 306 at 25), although it did not rely on these in its post-trial argument with respect to the scope and content of § 103 prior art. However, assuming that the DuPont ethylene-butene copolymers are available as § 103 prior art against Claims 1 and 12, they did not render the claims obvious to the artisan. Ethylene-butene copolymers are lower alpha-olefin copolymers. (Tr. at 87-88, 108.) Phillips argues that because they had Elmendorf tear strengths or hoop stress resistances within the claims, they rendered the higher alpha-olefin copolym-ers of the invention obvious. (D.I. 306 at 25.) However, the DuPont lower alpha-olefin copolymers did not suggest anything to the artisan with respect to higher alpha-olefin copolymers; and as found above, the art, including work by Phillips, suggested that higher alpha-olefin copolymers would not perform as well as lower alpha-olefin copolymers such as ethylene-butene. DuPont found that the opposite was true. Therefore, the Court is not convinced by this “eleventh hour” argument made by Phillips. c. Differences Between Claims 1 and 12 and the Prior Art The crucial difference between the prior art and Claims 1 and 12 is that there was nothing in the prior art that disclosed or suggested to the contemporary artisan that a material having the claimed combination of properties could be obtained by a copo-lymer of ethylene and higher alpha-olefins. In fact, rather than clearly and convincingly establishing that the copolymers of Claims 1 and 12 were obvious to the artisan, the evidence tends to support the non-obviousness of them. The evidence shows that at the time of DuPont’s invention the teachings with regard to free radical ethylene polymers were that the physical properties such as impact resistance, stress crack resistances, Elmendorf tear strength and hoop stress resistance varied inversely with respect to other properties such as melt index and density. That is, in order to obtain a polymer with an advantageous Elmendorf tear strength or hoop stress resistance, an advantageous melt index had to be sacrificed. (Tr. at 101-109; DX 38 col. 1-3.) Moreover, according to these teachings the introduction of higher alpha-olefins into ethylene polymers would have been disadvantageous with respect to properties such as Elmendorf tear strength and hoop stress resistance. (Tr. at 101-103, 109.) Phillips argues that Claims 1 and 12 were obvious because the prior art taught that in order to improve the claimed strength properties, such as Elmendorf tear strength and hoop stress resistance, the artisan would have lowered the density and melt index rather than have employed higher alpha-olefins; and that the Witt and Leatherman products could have been modified in this way. (D.I. 306 at 24-25, 27-28.) This argument is fundamentally flawed for several reasons. First, copo-lymers of ethylene and higher alpha-ole-fins, i.e., 5-10 carbon chains, are what is claimed, in addition to the density, melt index and Elmendorf tear strength or hoop stress resistance. The coincidence of the claimed elements is the invention. The Court has found that Phillips has not shown that it would have been obvious that the invention “as a whole” could be obtained by copolymers of ethylene and higher alpha-olefins. Second, Phillips has not shown that varying the properties of the Witt and Leather-man products in the way it now suggests would have resulted in a copolymer within the claims at issue here. In fact, as DuPont argues, based on the available data, the properties of the Witt and Leatherman products would not have been within the claims if varied in the way suggested by Phillips. (D.I. 309 at 39.) Accordingly, Phillips has not established a prima facie case of the obviousness of Claim 1 or 12. Therefore, in view of the Court’s finding in Section IY.A.l. of this opinion, supra, Phillips has not carried its burden of showing that Claim 1 or 12 are invalid. Thus, the claims are presumed valid. 35 U.S.C. § 282. B. Infringement of Claims 1 and 12 Having concluded in Section IV.A., supra, that Phillips has not proved that Claim 1 or 12 are invalid, the Court turns to the Federal Circuit's remand instructions regarding infringement. The Federal Circuit vacated this Court’s judgment of infringement for Claims 1 and 12, and instructed this Court to reconsider the “0.95” density and “70%” crystallinity parameters “appearing in claims 1 and 12.” DuPont, 849 F.2d at 1437-38. However, Claim 1 does not contain the parameters referred to by the Federal Circuit. Therefore, the Court reiterates here its pri- or findings of infringement with respect to Claim 1, see DuPont, 656 F.Supp. at 1390-91, and finds that eight copolymers infringe Claim 1: HHM TR-130, HHM TR-230, HHM TR-232 Black, HHM TR-232 Yellow, HHM TR-418 Black, HHM TR-418 Orange, 728 Fluff, and 728-01. Claim 12 does, however, contain the “0.95” density and “70%” crystallinity limitations. This Court’s prior findings of infringement of Claim 12 were that Phillips directly infringed by making and selling nine pipe products, and actively induced infringement by making and selling four resins for use in pipe products. See DuPont, 656 F.Supp. at 1391-92. Eight resins were in one or both categories of infringement: HHM TR-401, HHM TR-418 Black, HHM TR-418 Orange, HHM TR-480 Black, HHM TR-130, HHM TR-140, HHM 5202, and HHM 5502. The only resins at issue on remand are those having a density above 0.950 or a crystallinity above 70%. See DuPont, 849 F.2d at 1439. Therefore, of the eight resins found to have infringed claim 12, five are at issue here: HHM 5202, HHM 5502, HHM TR-401, HHM TR-480 Black, and HHM TR-140. Their densities and crys-tallinities are tabulated below. RESIN DENSITY o co HHM 5502 0.9516 or 0.956 —3| JO; to! HHM 5202 0.9504 or 0.952 —3 co HHM TR-140 0.9444 —3 |>o in HHM TR-401 0.9428 —3 j — i HHM TR-480 Black 0.9555 -3 The data reflected in this table were taken from Appendix A of this Court’s earlier opinion. See DuPont, 656 F.Supp. at 1396 et seq. In accordance with the Federal Circuit’s instructions the Court must readdress its interpretation of the “0.95” density and “70%” crystallinity limitations in Claim 12, and then, readdress infringement by the five resins at issue with respect to these limitations. 1. The Meaning Of The “0.95” and “70%” Limitations The Federal Circuit ruled that the prosecution history of the ’698 patent is relevant to the meaning of the “0.95” density and “70%” crystallinity limitations, and specifically noted instances in the prosecution history where DuPont stated that certain densities and crystallinities were not within the claims. DuPont, 849 F.2d at 1438-39. Thus, the Court must ascertain the meaning” of these limitations by resort to the specification and claims as well as the prosecution history. Id. at 1439. a. The “0.95” Density Limitation The Federal Circuit has pointed to several statements made by DuPont to the Patent Office during the prosecution of the ’698 patent with regard to the “0.95” density limitation. The statements were that 0.954 and 0.9547 fell outside the scope of the claims, that 0.9557 was “far above” the invention, and that 0.9585 was “a quite high density.” See id. at 1438. DuPont argues that density can be accurately reported to four significant figures, that “0.95” is set forth to only two, and therefore it includes “the values between 0.9451 and 0.9550.” (D.I. 304 at 12.) Phillips argues, of course, that “0.95” means “0.950.” (D.I. 307 at 4, 7.) DuPont’s argument apparently is that if it had meant to be more precise in specifying the upper density limit it would have done so by tacking one or more zero’s onto 0.95, i.e. 0.950 or 0.9500; and that since it did not, it intended 0.95 to be read to two significant figures. This argument finds some support in the claims and specification. DuPont reported density data to 3 and 4 figures, and in several instances employed a zero as the last figure {see, e.g., PX 1, Tables II, V). DuPont also set forth densities and ranges of densities throughout the specification to 1, 2 and 3 figures, and in several instances used a zero as the last figure {see, e.g., PX 1, col. 8,11. 33-51; col. 13, 11. 9-12). In the claims, densities were set forth to 1, 2 and 3 figures and again in several instances a zero was used as a last figure {see, e.g., PX 1, col. 13,1. 4, col. 14, 11. 10, 27). Thus, since DuPont used 1, 2, 3 and 4 figures to refer to densities and a zero as the last figure in several instances, the Court could infer that DuPont deliberately claimed the upper density limit to two figures, i.e., “0.95,” rather than to more. As found in this Court’s earlier opinion, scientifically, “0.95” is less precise than 0.950 or 0.9500. See DuPont, 656 F:Supp. at 1385 {see also PX 3 at 000419). However, in view of the statements made by DuPont during the prosecution of the ’698 patent, the Court is unable to accept DuPont’s position now that “0.95” includes all densities above 0.9500 but below 0.9550. In response to a reference cited by the examiner, DuPont stated: [W]herever given in Field and Feller, the densities of the “normally solid hydrocarbon material” polymerization product, where some olefinic material, other than propylene, was included in the reaction mixture with ethylene, were in the range of linear polyethylene homopolymers (0.954-0.97) rather than in the range (0.9 to 0.95) of the novel branched polyethyl-enes (ethylene 1-olefin copolymers) claimed by applicants. While density alone is not enough to define precisely the structures of an olefin polymer, such differences are sufficient to show that the polymers are quite different and distinct, both in structure and in physical properties dependent on density and crystallinity. (PX 3 at 000404.) DuPont also stated that 0.9547, the density of a certain solid hydrocarbon resin product, was “well above densities of applicants’ branched polyethyl-enes.” (Id. at 000405.) These statements simply do not square with the interpretation DuPont advances now. If the Court interpreted 0.95 the way DuPont urges, both 0.954 and 0.9547 would be included within the range. Furthermore, no non-arbitrary limit between 0.950 and 0.954 is advanced by DuPont, and the Court can find support for none. Therefore, the Court concludes that the “0.95” density upper limit means 0.950. However, the Court finds that 0.95 does not mean 0.9500 or anything more precise. While density may be accurately ascertained to four significant figures, (Tr. at 359), and, in fact, DuPont reported density data to four significant figures in the specification, no density limitation in any claim of the ’698 patent is so precise. Nor is any range of densities for the invention described in the specification with such precise limits. DuPont’s statements that 0.9547, 0.9557, and 0.9585 were not within the claims do not persuade the Court to interpret the 0.95 density limit to mean 0.9500. b. The “70%” Crystallinity Limitation In its prior opinion this Court found that the “70%” upper crystallinity limit of Claim 12 meant 70%. See DuPont, 656 F.Supp. at 1387. To the extent that this Court’s earlier opinion can be construed as interpreting the 70% limit to mean something higher (or lower), the Court now makes clear that the 70% upper limit means 70%. 2. Literal Infringement The Court’s inquiry with respect to literal infringement is whether the density and crystallinity limitations of Claim 12, as interpreted above, read on those of the five resins at issue. See Loctite Corp. v. Ultraseal Ltd., 781 F.2d 861, 866 (Fed.Cir.1985). a. Literal Infringement of the 0.95” Density Limitation The densities of HHM TR-140 and HHM TR-401 are below 0.950 and thus are not at issue here. See DuPont, 849 F.2d at 1429. 0.950 does not read on 0.9516, the density of HHM 5502 posited by DuPont, or on 0.9550 the density of HHM TR-480 Black. Therefore, neither HHM 5502 nor HHM TR-480 Black literally infringes Claim 12. 0.950 reads on 0.9504, the density of HHM 5202 posited by DuPont, although not on 0.952, the density posited by Phillips. The different densities result from different methods of determination, the “DuPont 1955 method,” and the “ASTM D 1928 method.” The density posited by DuPont was determined by the “DuPont 1955 method.” As the Court found in its prior opinion, the evidence at trial established the competence of the density values determined by the “DuPont 1955 method.” See DuPont, 656 F.Supp. at 1386-87. Therefore, the Court finds that DuPont has shown by a preponderance of the evidence that HHM 5202 had a density of .9504 and thus literally infringes “0.95” as interpreted above. b. Literal Infringement Of The 70% Crystallinity Limitation The crystallinity of HHM TR-480 Black, 67%, is literally within the 40-70% range claimed. Therefore, DuPont has proved by a preponderance of the evidence that HHM TR-480 Black literally infringes the claimed crystallinity of Claim 12. In its prior opinion the Court found that the other four resins at issue here, which have measured crystallinities above 70.0%, infringed the 40-70% range claimed. The Court found that the evidence at trial established that measurements of the crystal-linity of a given resin could vary from 10-20%. See DuPont, 656 F.Supp. at 1387. Therefore, although a resin actually had a crystallinity within the claimed range its crystallinity could be measured to be up to 20% outside of the range. (Tr. at 620.) The Court did not specifically address whether DuPont had proved literal infringement by these resins, since the Court found that the resins infringed under the doctrine of equivalents. See id. at 1387-88. After considering the evidence, the Court finds that DuPont has not proved by a preponderance of the evidence that resins HHM 5202, HHM 5502, HHM TR-140 and HHM TR-401 having crystallinities of 79.2%, 74.3%, 72.5%, and 71.4%, respectively, literally infringe Claim 12. 3. Infringement Under Doctrine Of Equivalents DuPont has not proved that any of the five resins at issue literally infringed Claim 12, because their density or crystallinity is outside of the literal range. However, infringement may nonetheless be found under the doctrine of equivalents if the accused resins and the claimed interpolymer perform substantially the same function in substantially the same way to yield substantially the same result. Atlas Powder Co. v. E.I. DuPont de Nemours & Co., 750 F.2d 1569, 1579 (Fed.Cir.1984) citing Graver Tank & Mfg. Co. v. Linde Air Products Co., 339 U.S. 605, 608-09, 70 S.Ct. 854, 856-57, 94 L.Ed. 1097 (1950); see also ZMI Corp. v. Cardiac Resuscitator Corp., 844 F.2d 1576, 1581 (Eed.Cir.1988). The doctrine exists for “the equitable purpose of ‘prevent[ingj an infringer from stealing the benefit of an invention.’ ” Texas Instruments, Inc. v. ITC, 805 F.2d 1558, 1572 (Fed.Cir.1986) citing Graver Tank, 339 U.S. at 608, 70 S.Ct. at 856. To find infringement under the doctrine the Court must find that the five resins at issue possessed, equivalently, the limitations of Claim 12 not possessed literally. See ZMI Corp., 844 F.2d at 1582. The Court will, therefore, determine whether the densities and crystallinities of the resins at issue which are outside the literal ranges claimed are substantially equivalent to those literally claimed. To be a substantial equivalent the difference between the claimed density or crystallinity and that of the resin at issue must not be such that would substantially change the way in which the claimed interpolymer performs. see Perkin-Elmer Corp. v. Westinghouse Electric Corp., 822 F.2d 1528, 1533 (Fed.Cir.1987). a. Equivalents of the Claimed Density The Court must determine whether the densities of HHM TR-480 Black, 0.9555, and HHM 5502, 0.9516, are the substantial equivalents of that claimed, i.e. “0.9 to 0.95.” The purpose of the density limitation is to distinguish the interpolymers of the invention from homopolymers. (Tr. at 888-89.) During the prosecution of the patent DuPont stated that the range of densities for linear polyethylene homopolymers was “0.954-0.97.” (PX 3 at 000403.) The density of HHM TR-480 Black, 0.9555, is within this range. Therefore, the Court finds that it is not the substantial equivalent of the range of densities claimed. The density of HHM 5502, 0.9516, is not within the range posited by DuPont for linear homopolymers. Dr. Beasley testified that with respect to DuPont’s invention a density of .9525 was equivalent to 0.95 (Tr. at 538-39), and that the density ranges of .954 to .957 and .953 to .956 were “[ejssentially equivalent” (Tr. 523). Phillips’ own expert, Dr. Levett, testified that Phillips “traditionally” allowed the density in most of its products to cover four in the third decimal place spread [i.e.] .953, .954, .955, .956” (Tr. at 3157), and that the range of densities sold as HHM 5502 was .953 to .956 (Tr. at 3197-99). Dr. Levett also testified that purchasers of Phillips products could expect “a tolerance of plus or minus .002.” (Tr. at 3158.) Therefore, the Court finds that the density of HHM 5502, .9516, is substantially equivalent to the 0.9-0.95 range of densities claimed. b. Equivalents of the Claimed Crystallinity The crystallinities of HHM 5502, HHM 5202, HHM TR-140, and HHM TR-401 are literally above the 40-70% range of crystal-linities claimed. The Court must determine whether each is substantially equivalent to those claimed. Dr. Beasley testified that crystallinity values reported above 90% would be outside the range of the invention (Tr. at 619-20), but that values up to 90% would be “close enough.” (Tr. at 621.) The Court finds that Dr. Beasley’s testimony was that the higher alpha-olefin copolymers of the invention, including Claim 12, could have crystallinity values of up to 90% and still be equivalent to those literally claimed, that is they could still capture the advantages of the invention, viz: melt processability and improved hoop stress resistance. Each of the crystallinity values at issue here is well below the 90% limit, and their hoop stress resistances and melt indices are within the claims. Furthermore, Dr. Beasley testified specifically that the crystallinity values for each of the resins at issue was equivalent to that claimed. (Tr. at 407 [HHM 5502, 79.2%]; Tr. at 402, 491 [HHM 5202, 74.3%]; Tr. at 429 [HHM TR-140, 72.5%]; Tr. at 469 [HHM TR-401, 71.4%].) Additionally, the patent teaches a relationship between the density and crystallinity of the claimed copolymers. (PX 1, col. 8, 11. 33-62.) Dr. Price also testified to such a relationship (Tr. at 1318, 1334,1357; see also Tr. at 1334-34a), and that “density is a very accurate measurement.” (Tr. at 1352.) Dr. Beasley testified that crystallinity measurements, on the other hand, should not, by themselves, be relied on to any great extent in characterizing copolym-ers. (Tr. at 619.) Dr. Wilson, an expert with nearly 30 years’ experience with X-ray diffraction which is used to measure crys-tallinity, testified that because of the subjective judgment involved in crystallinity measurements they can vary 10-20% from one lab to the next, and that there was no “standard correction formula” to account for this variance. (Tr. at 1041.) Therefore, that the densities of the four resins at issue are literally within Claim 12, or in one case is equivalent, and the hoop stress resistances and melt indices meet the claim, further supports the equivalence of the claimed crystallinities and the reported crystallinity values of the four resins at issue. That DuPont stated during the prosecution of the patent that crystallinities of 32% and 38% were outside of the 40-70% range claimed (DX 724 at 39), does not persuade the Court that the crystallinities at issue here are not substantially equivalent to those claimed. These statements themselves do not control the breadth of equivalents available. Texas Instruments, Inc., 805 F.2d at 1572; Hughes Aircraft Co., 717 F.2d at 1363. Moreover, the lower limit of the claimed range of crystallinities, 40%, serves a different purpose than the 70% limit at issue. The lower limit serves to distinguish the copolymers of the invention from “rubber-like” linear copolymers (Tr. at 859-60), while the upper limit serves to distinguish the copolymers of the invention from ethylene homopolymers. (Tr. at 132.) The Court has not been persuaded that there is any mathematical symmetry between the respective distinctions that the upper and lower limits of the claimed range serve to make. To require mathematical symmetry, for its own sake, between the ranges of equivalents at opposite ends of the claimed range would be to impose an artificial limitation on the breadth of available equivalents. Inventions are appropriated not the several words, or numbers, that describe them. See Laitram, 863 F.2d at 857. The Court finds that each of the crystal-linity values for HHM 5502, HHM 5202, HHM TR-140, and HHM TR-401 is substantially equivalent to those of Claim 12. c. Invention of Claim 12 As a Whole Each of the resins HHM 5502, HHM 5202, HHM TR-140 and HHM TR-401 possesses every limitation, or its substantial equivalent, of Claim 12. Furthermore, viewing the invention of Claim 12 as “a whole,” see Hughes Aircraft Co., 717 F.2d at 1364; see also Perkin-Elmer Corp., 822 F.2d at 1532-33; Martin v. Barber, 755 F.2d 1564, 1568 (Fed.Cir.1985); Carman Indus., Inc. v. Wahl, 724 F.2d 932, 942 (Fed.Cir.1983); Medtronic, Inc. v. Cardiac Pacemakers, Inc., 721 F.2d 1563, 1567 (Fed.Cir.1983), the Court finds that the resins, and a priori pipe products made from the resins, appropriated the invention. The four resins perform substantially the same function in substantially the same way to yield substantially the same result as the claimed copolymers. They achieved melt processable copolymers with the claimed hoop stress resistance, and the same or a substantially equivalent density and crys-tallinity, by the addition of higher alpha-olefins to ethylene polymers. To find that Phillips has avoided infringement with resins because the densities or crystallinities varied from the literal description in Claim 12 to the extent at issue here while capturing the advantages of DuPont’s discovery would trouble the conscience of this Court. Accordingly, the Court finds that DuPont has shown by a preponderance of the evidence that HHM TR-130, HHM TR-230, HHM TR-232 Black, HHM TR-232 Yellow, HHM TR-418 Black, HHM TR-418 Orange, 729 Fluff, and 728-01 each infringe Claim 1 of the ’698 patent. With respect to Claim 12, DuPont has shown that HHM 5502, HHM 5202, HHM TR-140, and HHM TR-401 each infringe under the doctrine of equivalents. However, DuPont has not shown that HHM TR-480 Black infringes literally or under the doctrine of equivalents. Therefore, Phillips directly infringed Claim 12 by making and selling Driscopipe 1000, Driscopipe 6300, Driscopipe 6400, Driscopipe 6500, Driscopipe 3300, Driscopipe 3400, Drisco-pipe 3700, Driscopipe 3800, and Driscopipe 3900 where these products employed one or more of the foregoing infringing resins. Phillips actively induced infringement by making and selling HHM TR-401, HHM TR-418 Black, and HHM TR-418 Orange. V. PERMANENT INJUNCTION This Court previously entered an injunction in this case after trial which permanently enjoined Phillips from continued infringement of the ’698 patent. (D.I. 265.) This Court also denied Phillips’ motion to stay the injunction pending appeal. See E.I. DuPont de Nemours & Co. v. Phillips Petroleum Co., 659 F.Supp. 92 (D.Del.1987). This Court’s decision notwithstanding, the Federal Circuit granted Phillips’ motion to stay “[i]n view of the substantial legal issues presented on appeal, the harm to Phillips, the harm to the public, and the comparative lack of harm to DuPont.” E.I. DuPont de Nemours & Co. v. Phillips Petroleum Co., 835 F.2d 277 (Fed.Cir.1987). DuPont has again asked the Court to enjoin Phillips from continued infringement of Claims 1 and 12 of the ’698 patent. (D.I. 304 at 22.) Therefore, having found infringement of Claims 1 and 12, see Section IV.B. supra, the Court will consider the propriety of an injunction. Whether to enter an injunction against future infringement under 35 U.S.C. § 283 is left to the sound discretion of this Court. Roche Products, Inc. v. Bolar Pharmaceutical Co., 733 F.2d 858, 865 (Fed.Cir.), cert. denied, 469 U.S. 856, 105 S.Ct. 183, 83 L.Ed.2d 117 (1984). The Court must consider the facts of this case in view of historical equitable principles applicable to injunctions. See id. at 865, 867. Thus, the Court must consider the adequacy of DuPont’s legal remedy without the issuance of an injunction, irreparable harm, the relative hardships which would befall the parties, and the public interest. See id. The ’698 patent issued on February 28, 1978 (PX 1), and, thus, will not expire until 1995. See 35 U.S.C. § 154. DuPont will be entitled to bring suit to obtain damages for any infringement that may occur in the future. 35 U.S.C. § 284. But the Court cannot now conclude that this remedy would be adequate in view of the multiplicity of suits that might be necessary over the remaining life of the pat