MICHEL, Circuit Judge.
Defendants, Cat Contracting, Inc. (“CAT”), Michigan Sewer Construction (“MSC”), Kanal Sanierung Hans Mueller GmbH & Co. KG (“KM”), and Inliner U.S.A. (“Miner”) (collectively, “Defendants”) appeal the judgment of the United States District Court for the Southern District of Texas in Insituform, Technologies, Inc. v. Cat Contracting, Inc., CA No. H-90-1690 (Dec. 31, 1996) (hereinafter, “Insituform II ”), holding Inliner’s Processes 1 and 2 each infringes claim 1 of United States Patent No. 4,336,012 (the “’012 patent”) under the doctrine of equivalents and enjoining Defendants from practicing either Process 1 or 2. Because we hold that Miner’s Process 1 was shown to infringe the ’012 patent, but Inliner’s Process 2 was not shown to infringe, and because as to one defendant, KM, the finding of infringement was clearly erroneous as entirely unsupported, at least on the record on appeal, we affirm-in-part, reverse-in-part, va-eate-in-part and remand.
BACKGROUND
The ’012 patent is directed towards a process for lining pipelines and passageways, particularly sewers, which may suffer from leaks. Using the patented method, damaged underground pipelines and passageways can be repaired without removing them from the ground. Claim 1 covers a method for the impregnation of a flexible tube liner prior to installing the liner in a damaged pipeline. The liner has an outer layer of impermeable film and an inner, resin-absorbent, felt layer. The claimed method involves applying a vacuum to the inside of the liner by cutting a window in the outer impermeable film layer, applying a cup to the outside of the window, [690] and connecting the other end of the cup to a vacuum source using a flexible hose. As each section of the liner has its resin-absorbent material impregnated, the cup is moved downstream and the previous window is sealed. The process is repeated for respective lengths of liner until the entire liner has been impregnated. The resin-impregnated liner is then inserted into a damaged pipe. The method of installation in the pipe is not at issue here.
Inliner’s Process 1, the “multiple cup process,” uses four to six cups to draw a vacuum from a corresponding number of windows in the liner. When the cup closest to the advancing resin is removed and the window that was beneath it is sealed, the remaining downstream cups continue to draw a vacuum in the liner. See Insituform Gulf South, Inc. v. Cat Contracting, Inc., 99 F.3d 1098, 1104-05, 40 USPQ2d 1602, 1607 (Fed.Cir.1996) (hereafter, “Insituform I ”). Interruption of the vacuum during the impregnation process is thereby avoided or diminished by the use of the multiple cups. Inliner’s Process 2, the “multiple needle process,” replaces multiple cups with multiple metal tubes or needles. The needles are inserted through all of the layers of the liner rather than merely placed over holes in the outer layer, and they provide a continuous vacuum from inside the liner rather than through the felt. See id.1
In 1990, Insituform sued Defendants for infringement of the ’012 patent and of United States Patent No. 4,009,063 (the “ ’063 patent”),2 both claiming methods invented by Erie Wood and owned by Insituform Technologies, Inc. Liability and damages were bifurcated, and damages are not at issue here. In 1991, a jury returned a verdict that the ’012 patent was infringed by both Processes 1 and 2 and was not invalid. The district judge granted Inliner’s motion for JNOV with respect to literal infringement of both processes, and ordered a new trial with respect to infringement under the doctrine of equivalents. In 1995, at the retrial the court found equivalent infringement of claim 1 by both processes. On appeal, this court affirmed the order for JNOV with respect to literal infringement but vacated the district court’s determination of equivalent infringement as based on an erroneous claim construction and remanded the case for re-determination of equivalent infringement based on the correct claim construction. See Insituform I, 99 F.3d at 1109, 40 USPQ2d at 1610.
Method claim 1, the only claim at issue, is reproduced below.3 For background in the technology and in the patent in suit, the reader is directed to Insituform I, 99 F.3d [691]*6911098, 40 USPQ2d 1602. In Insituform I, this court interpreted certain limitations of claim 1. Specifically, we held that the literal scope of claim 1 is limited to “a process using only one vacuum cup which inherently creates a discontinuous vacuum.”
Insituform I, 99 F.3d at 1106, 40 USPQ2d at 1608. Under the correct claim construction, we affirmed the district court’s JNOV of no literal infringement because the accused Inliner methods use multiple cups or needles. See id. at 1107, 99 F.3d 1098, 40 USPQ2d at 1608. We also concluded that the doctrine of prosecution history estoppel did not preclude Insituform from asserting that its right to exclude extends broadly enough to cover either Process 1 or Process 2, but we did not affirm the district court’s finding of infringement under the doctrine of equivalents because it was based on an incorrect claim construction. See id. at 1109, 99 F.3d 1098, 40 USPQ2d at 1610. We therefore vacated the determination of infringement by Processes 1 and 2 under the doctrine of equivalents and remanded the case for the district court to re-determine equivalent infringement applying the correct claim construction. See id.
On remand the court determined that both Inliner’s Processes 1 and 2 infringed claim 1 of the ’012 patent under the doctrine of equivalents. Inliner timely appealed to this court, and the appeal was submitted for our decision following oral argument on July 8, 1998. We have jurisdiction over this appeal pursuant to 28 U.S.C. § 1295(a)(1) (1994).
DISCUSSION
I. Prosecution History Estoppel
Although we held in Insituform I that “the prosecution history does not estop Insi-tuform from asserting that the right to exclude extends broadly enough to cover either Process 1 or Process 2,” Insituform I, 99 F.3d at 1109, 40 USPQ2d at 1610, Defendants now argue that the district court erred in its determination on remand that “[tjhere is nothing in the file history of the ’012 patent or the prior art which prevents claim 1 from covering Defendants’ processes,” Insituform, slip op. at 20 (Dee. 31, 1996). According to Defendants, however, the Supreme Court’s Warner-Jenkinson decision, issued after our remand in Insituform I, further limited the doctrine of equivalents so that it cannot apply in this case. See Warner-Jenkinson Co. v. Hilton-Davis Chem. Co., 520 U.S. 17,-, 117 S.Ct. 1040, 1051, 137 L.Ed.2d 146, 41 USPQ2d 1865, 1873 (1997) (holding that where no explanation is given for an amendment made during prosecution of a patent, a presumption is to be applied against the patentee that the amendment was made for purposes of patentability). Inliner asserts that when Insituform amended claim 1 in response to a 35 U.S.C. § 103 rejection of application claims 1-6 based on United States Patent No. 4,182,262 to Everson (“Everson”), Insituform necessarily gave up coverage of any process in which the vacuum was created at multiple vacuum sources because it provided no explanation for such a narrowing amendment.
As we discussed in Insituform I, however, Everson discloses “both the use of a continuous vacuum and the creation of that vacuum from only a single vacuum source at the far end of the tube opposite the resin source.” Insituform I, 99 F.3d at 1108, 40 USPQ2d at 1609. Everson discloses nothing about multiple vacuum sources or their placement on the liner close to the resin front. In its response to the PTO rejection, Insituform canceled application claim 1 and filed a new, narrower claim in its place. The new claim, which became patent claim 1, incorporated each of canceled claims 1, 2, 3, and 4, but otherwise added no new limitations. In its remarks to the PTO, Insituform specifically noted that:
Everson’s method is ineffective when dealing with long lengths of tube because that method requires an exceedingly large suction compressor. Applicant’s method solves the problem of impregnating long lengths of tubing by forming a window in the tube’s impermeable skin, drawing the resin to the region of the window by a vacuum....
Response to First Office Action, March 30, 1982, p. 4. We held, therefore, in Insituform I:
[692] Insituform solved this [Everson] problem by placing the suction source closer to the resin front thus allowing the use of a smaller suction compressor. Thus, Insitu-form unequivocally gave up coverage to a process in which a single vacuum source is located at the far end of the tube.
Id. at 1108, 40 USPQ2d at 1610 (emphasis added). The stated reason, therefore, for Insituform’s amendment to overcome the Ev-erson reference was to avoid the need to use a large compressor when the vacuum is created a significant distance from the resin source. See id. The Wamer-Jenkinson presumption, therefore, which comes into play only when no explanation is given for a claim amendment, is not applicable to this ease because Insituform made clear that the reason for the amendment was to overcome the prior art teaching creation of a single source vacuum at the far end of the liner.
Defendants argue, however, that other statements made in the remarks to the Patent Office warrant limitation of claim 1 by prosecution history estoppel to a single cup process. Again, we discussed such statements in Insituform I:
in explaining its amendments, Insituform discussed the use of a single vacuum source which was to be moved along the tube as the resin front advanced. This suggests that Insituform envisioned the use of discontinuous vacuum created sequentially by only one vacuum source. However, this statement alone is too equivocal to be read as a statement which would estop Insituform from equivalently covering a number of small compressors spread along the tube creating a continuous vacuum.
Id. at 1108, 40 USPQ2d at 1610 (emphasis added). Defendants urge that the above-emphasized statement in Insituform I proves that Insituform did not explain why claim 1 was limited, and “[i]n [these] circumstances, prosecution history estoppel [should] bar the application of a doctrine of equivalents as to that element,” Warner-Jenkinson, 117 S.Ct. at 1051, 41 USPQ2d at 1873.
In these remarks, however, Insituform was simply explaining the use of the claimed method and its statements did not negate the earlier-discussed, clear explanation of the reason for the amendment. Therefore, we hold that Insituform did explain the reason for its changes in claim 1, and those reasons do not prohibit application of the doctrine of equivalents completely, but only with respect to the subject matter surrender of a large, single vacuum source placed a significant distance from the resin front. See Insituform I, 99 F.3d at 1109, 40 USPQ2d at 1610. We conclude, as we did in Insituform I, that “prosecution history does not estop Insitu-form from asserting that the right to exclude extends broadly enough to cover either Process 1 or Process 2.” Id. Wamer-Jenkinson changed nothing applicable here. The district court’s determination on remand after Insitufomi I, therefore, is affirmed.
II. Infringement Under the Doctrine of Equivalents
Infringement, both literal and under the doctrine of equivalents, is a question of fact which we review for clear error when tried to the court. See SRI Int’l v. Matsushita Elec. Corp. of Am., 775 F.2d 1107, 1125, 227 USPQ 577, 589 (Fed.Cir.1985) (in banc); see also Hilton Davis Chem. Co. v. Warner-Jenkinson Co., Inc., 62 F.3d 1512, 1520, 35 USPQ2d 1641, 1657 (Fed.Cir.1995) (in banc), rev’d on other grounds, 520 U.S. 17, 117 S.Ct. 1040, 137 L.Ed.2d 146, 41 USPQ2d 1865 (1997). “In applying the doctrine of equivalents, it is often enough to assess whether the claimed and accused products or processes included substantially the same function, way, and result.” Hilton Davis, 62 F.3d at 1518, 35 USPQ2d at 1645.
A. Process 1
The district court held that Defendants’ Process 1, the multiple cup process, infringed claim 1 of the ’012 patent under the doctrine of equivalents. Defendants argue, however, that the district court’s determination was clearly erroneous because it ignores the substantial differences between the one-cup process of claim 1 and the accused multiple cup process.
Defendants specifically identify three “substantial differences”: “[m]ore cups, continuous vacuum, [and] ability to impregnate long[693] er, thicker liners faster, ... We address each of these differences in turn. First, although claim 1 only claims the method of using one cup to impregnate the tube with resin, the multiple cups used in the accused process each perform precisely the same steps and functions as the single cup of the claimed method. Every limitation in claim 1, therefore, is met by at least one cup in Defendants’ multiple cup process. That all the cups together may not meet every limitation does not necessarily avoid equivalent infringement.
Second, Defendants assert that their multiple cup process draws a vacuum continuously whereas claim 1 inherently draws a vacuum discontinuously. A discontinuous vacuum is not a limitation of claim 1, although it is inherent in the operation of a single cup. In Defendants’ accused method, the operation of each cup of the set draws a vacuum discontinuously, at least when it is moved from one location on the tube to another location further downstream of the resin front.
Moreover, the district court found that the use of multiple cups results “in a continuous vacuum which enhances the degree of vacuum achieved at the resin front,” but that “there is nonetheless an insubstantial difference between” claim 1 and the multiple-cup process. We discern no clear error in this finding. There was evidence that the degree to which the multiple-cup process enhances the vacuum at the resin front, as compared to the single-cup process, is insubstantial. In particular, there was evidence that, in the claimed single-cup process, the amount of time when no vacuum was applied at the resin front was minimal so there was no substantial effect on the vacuum at that location. Furthermore, there was evidence that, like the single-cup process, the shifting of cups in the multiple-cup process results in a lessening of the vacuum at the resin front.
Third, Defendants argue that their method is more efficient because it can impregnate “longer, thicker liners faster.” While Defendants’ claim may be true, it is irrelevant because every one of claim l’s limitations is still met, at least equivalently. Hence, it does not matter that Defendants’ Process 1 may be better or more efficient. See Amstar Corp. v. Envirotech Corp., 730 F.2d 1476, 1482, 221 USPQ 649, 653 (Fed.Cir.1984) (quoting McCullough Tool Co. v. Well Surveys, Inc., 343 F.2d 381, 402, 145 USPQ 6, 22 (10th Cir.1965) (“infringement cannot be avoided by the mere fact that the accused device is more or less efficient or performs additional functions”)).
Defendants, therefore, have not identified to us any substantial differences between the accused method and the limitations of the method of claim 1. The district court’s determination of infringement of claim 1 by Process 1 under the doctrine of equivalents is therefore affirmed.
B. Process 2
The district court held that there were no substantial differences between Defendants’ accused Process 2, the multiple needle process, and the method of claim 1. Insituforrn, slip op. at 18-19. The district court found:
Both the cup and the tube [needle] are, as claim 1 states, “connected by a flexible hose to a vacuum source”, both are the means provided for the application of vacuum, they both do the same thing (suck a vacuum) by the same means (being connected to a vacuum source) to achieve the same result (produce a satisfactory vacuum at the resin front).
Id. at 19. From this analysis it appears that the district court determined the “function” of the cup to be to “suck a vacuum,” the “way” to be by “being connected to a vacuum source,” and the “result” to be to “produce a satisfactory vacuum at the resin front.” Defendants assert on appeal that the court’s function-way-result analysis is fatally flawed because it describes Everson. Although not clear to us that the district court’s function-way-result analysis for the cup limitation would encompass the Everson patent, we nevertheless hold that the district court’s function-way-result analysis involves too much overlapping and is overly broad. Specifically, the district court’s identification of the limitation’s “function” merges with the “way” and the “result”: to provide a vacuum, to be connected to a vacuum source, and to [694] produce a satisfactory vacuum at the resin front all define basically the same thing.
Under the proper “way” part of the function-way-result analysis, the “way” the cup provides a vacuum is by being disposed over a “window” cut in the outer, plastic liner of the tube and pressed on top of the exposed felt layer and being connected at the other end to a vacuum source. By contrast, the “way” Process 2 needles provide a vacuum is by being inserted through multiple punctures into the center of the tube (through the felt layer) and being connected at their other ends to a vacuum source. The question then becomes: are these two “ways” equivalent, or did the district court clearly err in holding that Defendant’s Process 2 infringed claim 1 under the doctrine of equivalents? Defendants assert that the distinction between the cup and the needle is substantial, and the fact that the district court dismissed this distinction as “irrelevant” under the equivalents analysis is fatal.
Another factor that affects our equivalent infringement analysis is that the inventor of the ’012 patent attempted to use a needle instead of a cup prior to filing his application. For a reason that is disputed by the parties, he changed to a cup, and when his patent application was filed, no mention of the possible use of a needle was made. Insituform argues that the inventor’s early use of needles shows that needles are old in the art and are known substitutions for cups. Defendants argue, however, that the inventor’s “failure” with needles is evidence of a substantial difference between needles and cups. It is not apparent from the district court’s opinion that it considered this prior attempt with needles. The evidence that the inventor first tried to use needles and then changed to cups without disclosing to the public that needles were, indeed, an option, supports an inference that the inventor was unable satisfactorily to practice his claimed method using a needle instead of a cup.
We therefore hold that, based on the evidence of substantial differences between the claimed single cup process and the accused multiple needle process, and the district court’s legal errors in defining incorrectly the “way” in its function-way-result analysis and dismissing structural differences as irrelevant, the district court reversibly erred in finding that Defendants’ multiple needle process infringed Insituform’s claim 1 under the doctrine of equivalents. Once the “way” is correctly defined and the structural differences are properly considered, no reasonable trier of fact could have found the claimed single cup process and the accused multiple needle process to be equivalent.
III. District Court’s Refusal to Consider New Evidence
Prior to remand, this case had been tried twice on the issue of equivalent infringement, once to a jury and a second time to the court. Defendants now argue that the district court erred reversibly in refusing on remand to consider them new evidence of lack of equivalent infringement. We review the district court’s refusal to allow Defendants to supplement the record on remand for abuse of discretion. See Westvaco Corp. v. International Paper Co., 991 F.2d 735, 745, 26 USPQ2d 1353, 1362 (Fed.Cir.1993) (applying regional circuit law); Rollins v. Fort Bend Indep. School Dist., 89 F.3d 1205, 1220 (5th Cir.1996) (abuse of discretion standard).
Defendants assert that this “new” evidence showed, inter alia, the substantiality of the differences between the accused processes and method claim 1, and that Insituform witnesses had “not been truthful during testimony taken at the 1995 trial.” Further, asserts Defendants, this court on remand gave the district court a “directive” to make new findings in accordance with the corrected claim construction, presumably necessitating at least the submission of further evidence.
We are unpersuaded, however, that the reasons cited by Defendants for the district court to accept supplemental evidence “mandate” its acceptance. First, our reversal today of the district court’s finding of equivalent infringement of the multiple needle process shows that sufficient evidence was already present in the record based upon which the district court could have correctly decided the issue without submission of new evidence. Nor have Defendants shown that [695] the evidence could not have been found and submitted at the first trial. Second, a review of the relevant language in Insituform I does not reveal a “mandate” for further, broader fact-finding by the district court. We therefore conclude that the district court did not abuse its discretion on remand in refusing to admit Defendants’ supplemental evidence.
IV. Liability of KM
Defendants assert that the district court committed reversible error in holding that KM induced infringement of the ’012 patent. This issue was decided by the district court in 1995 and appealed to this court. Insitu-form argues that we considered this issue already in Insituform I, and that, therefore, it is the law of the case. We disagree. In Insituform I, we did not reach this issue because we vacated the district court’s finding of direct infringement. See Met-Coil Sys. Corp. v. Korners Unlimited, Inc., 803 F.2d 684, 687 (Fed.Cir.1986) (Liability for inducement under § 271(b) is dependent on showing that the conduct being induced constitutes direct infringement.).
Defendants argue, inter alia, that the evidence fails to show that KM induced infringement of the ’012 patent because the district court found, and Insituform does not dispute, that KM did not know of the existence of the ’012 patent until after Insituform filed its complaint on February 2, 1990. Thus, Defendants assert, KM’s acts cannot establish liability for inducing infringement of the ’012 patent, because all accused acts by KM occurred before KM knew of the patent. A crucial element of induced infringement is that the inducer must have actual or constructive knowledge of the patent. A separate corporation related to KM licensed the infringing technology to Inliner after KM received notice of the ’012 patent. The separate corporation is not a party to this case, and there were no findings that this affiliate was KM’s alter ego. We agree that Defendants have shown clear error on the district court’s finding that KM induced infringement. As the trial court made no finding on the alter ego issue, instead of reversing, we vacate the district court’s holding and remand as to that issue.
V. Liability of MSC
Defendants assert that the district court committed reversible error in holding MSC fully liable as the other defendants. Defendants argue that MSC’s sole contribution to the joint venture was to provide financing, if necessary, and bonding. Defendants argue that “[djuring trial in 1995, Inliner moved for JMOL on this issue,” and the district court denied the motion. Defendants, however, did not raise this issue in Insituform I; and therefore, it is not properly before the court today. Because Defendants did not properly appeal this issue after the 1995 decision, it has been waived. Moreover, as Insituform asserts in response, the bifurcated damages trial will determine for what amount MSC is actually responsible, which may be less than for other defendants.
CONCLUSION
Because Defendants did not demonstrate clear error by the district court in its finding that Process 1 equivalently infringed claim 1 of the ’012 patent, we affirm with respect to Process 1. With respect to Process 2, however, we hold that the district court did clearly err in finding that Defendants infringed and legally erred in its methodology; and therefore, we reverse. We further hold that the district court clearly erred in finding that KM induced infringement, and we vacate its holding and remand as to this issue. We do not review the district court’s determinations of liability for MSC as that issue is not properly before us. The decision, therefore, is
AFFIRMED-IN PART, REVERSED-IN-PART, VACATED-IN-PART and REMANDED.
COSTS
Each party shall bear its own costs.