This appeal concerns United States patent no. 3,202,539 (“the Holt patent”), which was granted to Brown-Bridge Mills, Inc. on August 24, 1965 and is currently held by appellant, the Brown-Bridge division of Kimberly-Clark Corporation (“Brown-Bridge”).1 The Holt patent includes the disclosure of a dry gummed paper product with a water-insoluble binder.2 Brown-Bridge filed a complaint in May of 1975 alleging that appellee, Eastern Fine Paper (“Eastern”) had infringed the Holt patent by making, using, and selling gummed paper within the patent’s scope. Eastern counterclaimed that the patent was invalid and that it had been fraudulently obtained.
In December of 1977 Brown-Bridge, having concluded as the result of discovery that the binder formulation then used by Eastern did not infringe the Holt patent, moved to dismiss its own complaint and for partial summary judgment on Eastern’s counterclaims. In May of 1978 the district court dismissed the complaint with prejudice to any claim of past infringement by Eastern and with prejudice to any claim that the Holt patent is infringed by a product with solubility characteristics greater than those of a specified binder compound. It denied summary judgment on Eastern’s counterclaims.
Appellant filed a second complaint in April of 1979 alleging that appellee Eastern had recently changed its gummed paper products and was once again infringing the Holt patent. The complaint also alleged patent misuse, state and federal antitrust violations, and unfair trade practices. In a June 1979 pre-trial conference the district court ordered that action consolidated with the original action from which appellee’s counterclaims remained pending. In February of 1980 the court granted appellant’s motion for a separate trial of (1) the patent validity and infringement issues (including the counterclaim of fraudulent procurement) and (2) the patent misuse, unfair trade practice, and antitrust issues.
After trial of the patent validity and infringement issues in December of 1980, the court issued an opinion on September 14, 1981, holding that the patent was invalid and not infringed but that it was not procured by fraud. It also denied appellee’s motion for attorneys’ fees. On October 28, 1981 the court entered judgment with respect to the patent validity and infringement issues but declined to certify pursuant to Fed.R.Civ.P. 54(b) because of the remaining patent misuse, unfair trade practice, and antitrust claims. The parties having agreed to abandon their remaining claims and counterclaims with regard to those issues, final judgment was entered on July 8, 1982, and this appeal followed. We affirm the judgment of the district court.
I. Patent Validity
A patent is presumed to be valid, and the burden of establishing invalidity is on the party asserting it. 35 U.S.C. § 282. Acknowledging the statutory presumption, the district court held the Holt patent invalid and therefore unenforceable because of pri- or invention under 35 U.S.C. § 102(g)3 and because it failed to meet the definiteness requirements of 35 U.S.C. § 112.4 The *762court rejected various other grounds for invalidity advanced by appellee.
The court found that the subject matter of the Holt patent — a remoistenable gummed paper using a binder by itself insoluble — was invented and reduced to practice by Nashua Corporation (“Nashua”) before August 31, 1956, the earliest date that appellants claim reduction to practice. It therefore held the Holt patent invalid under § 102(g) because anticipated.
Appellant argued, as it does on appeal, that Nashua’s allegedly anticipatory invention — its “65-54” binder — is water-soluble within the meaning of the Holt patent and therefore did not anticipate it. In rejecting that argument the court relied on evidence showing that the 65-54 binder has 16.4 per cent water solubility. The court found that, “because of the position [appellant had] taken with respect to the solubility of 3RB-50 [the binder used by Eastern that appellant alleges infringes the Holt patent]”, appellant was “estopped from arguing that a material that is 16.4 per cent water soluble is not insoluble within the meaning of the Holt patent.”
“To anticipate under section 102, a prior art reference must disclose all the elements of the claimed invention or their equivalents functioning in essentially the same way.” Shanklin Corp. v. Springfield Photo Mount Co., 521 F.2d 609, 616 (1st Cir.1975), cert, denied, 429 U.S. 914, 96 S.Ct. 1112, 47 L.Ed.2d 318 (1976); accord Car ter-Wallace, Inc. v. Gillette, 675 F.2d 10, 15 (1st Cir. 1982). Appellant argues that the district court was clearly in error, see Fed.R.Civ.P. 52(a), when it found Nashua’s 65-54 binder sufficiently insoluble to be equivalent to the binder disclosed by the Holt patent. It points to evidence that, contrary to the court’s finding, the 65-54 binder, when measured by the same solubility test, is significantly more soluble than 3RB-50, a binder later used by Nashua and Eastern which appellant alleges is within the scope of the Holt patent.
and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor of carrying out his invention. The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.”
We find that appellant’s contention is supported by the record. Both the 65-54 and 3RB-50 binders are copolymers of vinyl acetate (“PVA”) and vinyl pyrolidone (“PVP”). Appellant asserts and appellee does not contest that the water solubility of these binders depends directly upon the ratio of PVA to PVP, since PVA is water-insoluble by itself while PVP is water-soluble by itself. This analysis was apparently accepted by the district court when it granted appellant’s motion to dismiss its first infringement complaint.5 The court dismissed the complaint “with prejudice to any claim that [the Holt patent] is infringed by [Eastern’s] product or any other product having solubility characteristics above those of a compound having a PVArPVP ratio of 75:25, provided the PVArPVP reference material and the new material are tested for solubility by the same test.”
Appellant argues that the 65-54 binder, which has a PVArPVP ratio of 70:30 (and is therefore more water-soluble than a 75:25 compound), does not according to the “law of the case” infringe the Holt patent, and that it therefore also cannot be found to anticipate it. We do not agree that the order of another judge dismissing appellant’s prior complaint upon terms agreed to by the parties established a “law of the case” binding upon the court at a later trial of a separate complaint, or that the judge issuing that order so intended. We are persuaded, however, that the court below erroneously compared solubility on the basis of different solubility tests and thus erroneously concluded that appellant’s position with respect to the solubility of 3RB-50 estopped it from arguing that 65-54 was *763soluble within the meaning of the Holt patent. It is undisputed that 3RB-50 has a PVA:PVP ratio of 90:10. We find no evidence that, when measured by the same test, the 65-54 binder is less soluble than the 3RB-50 binder or than a binder with a 75:25 ratio.
The district court also held that the Holt patent was invalid under 35 U.S.C. § 112 because it failed to provide a single test for measuring solubility.6 Appellant argues that this is not a serious defect since any valid test for solubility will suffice to apprise one skilled in the art of the scope of the invention, so long as the same test is used to determine the solubility of the examples claimed in the Holt patent and to determine the solubility of any possibly infringing product. But even accepting that argument, we find that appellant has failed to demonstrate that water-insolubility is a sufficiently critical limitation to satisfy the requirements of § 112.
Water solubility is an enunciated limitation of the Holt patent; indeed, it is the all important limitation at issue in appellant’s infringement action against appellee. Appellant contends that the 65-54 binder, with a 70:30 PVA:PVP ratio, is water soluble and therefore did not anticipate (or infringe) the Holt patent. It also contends, however, that any PVA:PVP binder with a ratio higher than 75:25 is insoluble and therefore infringes the Holt patent.
A patent applicant who discloses in a claim that a limitation is critical has the further burden, in order to satisfy the specificity requirement of § 112, of showing that the limitation is critical in fact. California Research Corp. v. Ladd, 356 F.2d 813, 819 (D.C.Cir.1966). To be critical, a limitation in a product claim must show an advance over prior products; “[a] mere location of optimum conditions and characteristics, however useful, is said not to warrant a patent monopoly.” Id., at 820.
Appellant has nowhere demonstrated, either in the patent application process or in the long course of this litigation, that insolubility is a significant operative characteristic of a gummed paper binder resin or, even assuming the significance of insolubility, that the Holt patent has critically defined the limits of that characteristic.
“A patentee may not arbitrarily select a point in a progressive change and maintain a patent monopoly for all operations in that progressive change falling on one side of that arbitrarily selected point. It is only where the selected point corresponds with the physical phenomenon and the patentee has discovered the point at which that physical phenomenon occurs that the maintenance of a patent monopoly is admissible.” Helene Curtis Industries v. Sales Affiliates, 233 F.2d 148, 153 (2d Cir.1956) (quoting Kwik Set, Inc. v. Welch Grape Juice Co., 86 F.2d 945, 947 (2d Cir.1936)).
Because the Holt patent fails to demonstrate the criticality of an essential limitation, we uphold the district court’s determination that the patent is invalid under 35 U.S.C. § 112. We need not, therefore, address other grounds advanced by appellee for the invalidity of the patent.7 Because we have found the patent invalid, it follows without more that the patent has not been *764infringed by appellee’s gummed paper products.
II. Fraud in Procurement of the Holt Patent
Appellee asserted by way of counterclaim below that appellant had procured the Holt patent by fraud. It appeals from the district court’s denial of that counterclaim. We have already sustained the district court’s holding that the patent is invalid. On that basis, appellee has in hand the full measure of equitable relief that it could obtain from succeeding on its counterclaim. What damages if any resulted to appellee from appellant’s procurement of the Holt patent, if the procurement were in fact fraudulent, is unclear. A finding of fraud would, however, as noted within, add substantial support to appellee’s motion for attorneys’ fees. We therefore consider appellee’s allegations of error in the court’s failure to find fraud.
The burden on appellee is a heavy one. “The question of fraud is one of fact, to which the ‘clearly erroneous’ standard of Fed.R.Civ.P. 52(a) applies. An allegation of fraud must be proved by clear, unequivocal and convincing evidence and not by a mere preponderance of the evidence which leaves the issue in doubt.” Norton Co. v. Carborundum Co., 530 F.2d 435, 444 (1st Cir.1976) (citations omitted). Appellee makes two primary allegations of fraud: (1) the Holt patent applicants fraudulently withheld material documents from the Board of Patent Interference; (2) the Holt applicants falsely claimed to be inventors of three binders listed as examples in their patent application.
A. The Interference Proceedings. The Holt patent application, filed on December 17, 1957, disclosed the production of dry gummed paper by an electrostatic method. It claimed that the electrostatic process could be used effectively with either water-soluble or water-insoluble binders but indicated “wider applicability” when “the binder material is effectively insoluble.” It gave five examples of water-insoluble binders and three examples of water-soluble binders that could be used with the electrostatic process.
On February 28,1958 Nashua filed a patent application which disclosed and claimed the use of water-insoluble PVA:PVP copolymers as binders in the manufacture of dry gummed paper. An interference search in connection with that application turned up the Holt application and three other patent applications claiming substantially the same subject matter. Proceedings before the Board of Patent Interference were instituted to determine which of the patent applicants had first reduced to practice non-curling gummed paper with a water-insoluble binder resin possessing certain properties.8 In October of 1963 the Board of Patent Interference issued a decision awarding priority to the Holt patent on the basis of evidence that the Holt inventors had produced gummed labels conforming to the limitations of the interference count by August 31, 1956.9
The Holt applicants offered, in the interference proceedings, testimony, physical exhibits, and research memoranda (from August 31, 1956 and prior dates) to show that the use of a particular binder resin — “60:30:10” 10 — had produced a non-curling gummed paper which satisfied the *765limitations of the interference count and had essential properties comparable to or better than competitive products. Appellee claims that the applicants committed fraud on the Patent and Trademark Office (“the PTO”) by not disclosing research memoranda from a period after August 31, 1956, which would have shown that 60:30:10 was in fact a failed and discarded experiment and thus not reduced to practice by the claimed date. Appellant points to research memoranda indicating problems with the tack and brittleness of the 60:30:10 binder and, in particular, to a March 1957 memorandum indicating that the 60:30:10 binder “does not appear to be of further interest.”
A patent applicant’s duty of disclosure to the PTO has been codified in 37 C.F.R. § 1.56. That regulation places on patent applicants a duty to disclose to the PTO “information they are aware of which is material to the examination of the application. Such information is material where there is a substantial likelihood that a reasonable examiner would consider it important in deciding whether to allow the application to issue as a patent.” We have applied a somewhat higher standard of materiality, however, for a showing of fraud on the PTO. “To establish fraud, ... the non-disclosed information must be such as to have a likely effect on the scope of allowable claims or the issuance of the patent. It is not enough that the information be simply ‘relevant’ in some general sense to the subject matter of the claimed invention, or even to the invention’s patentability.” Digital Equipment Corp. v. Diamond, 653 F.2d 701, 716 (1st Cir.1981). In addition, such nondisclosure must result from “culpable behavior”; though “an intentional scheme of deception is not necessary to a showing of ‘fraud on the Patent Office,’ ” there must be “a not insubstantial degree of ‘wrongfulness.’ ” Id. at 715.
The district court heard conflicting expert testimony on the significance of the withheld information. A former patent commissioner, testifying for appellee, when asked, “Can you point to me any case you can think of ... which contains more egregious instances of fraud in the patent process?” replied: “I cannot.” But another former patent commissioner, testifying for appellant, concluded: “In my opinion there has not been any fraud committed in this case, either in the ex parte prosecution or in the inter parties proceedings.”
The court credited testimony from the Holt applicants that the “of no further interest” comment resulted from problems in the manufacturing process rather than in the formulation itself — that the binder was of no further interest only for present experimental purposes. The full comment in the March 1957 research memorandum reads:
“Adhesives containing the rosin-Carbowax [60:30:10] binder were not combined with other binders as planned this month because the rosin separated in the coating unit and the deposition of the coating could not be controlled reproducibly. In view of this result and the fact that the inert rosin binder produces low tack, this coating does not appear to be of further interest.”
We cannot say that the court’s conclusions with respect to the memorandum were clearly erroneous.
The court also reasoned that “[f]raud cannot be predicated on nondisclosure of the post-August 1956 statements in question since they have no bearing on whether 60:30:10 had been reduced to practice as of August 1956.” Similarly, relying on Schnick v. Fenn, 277 F.2d 935, 941 (C.C.P.A. 1960), the court discounted the significance of any continuing experimentation beyond the alleged date of reduction to practice. The Court of Customs and Patent Appeals said in Schnick: “With respect to the issue of the device being an abandoned experiment, once reduction to practice has been found that question no longer exists... . Therefore evidence of subsequent experimenting and testing is without probative value.” Id. at 941.
We think this reasoning somewhat begs the question. We are not so sure that subsequent experimentation and observation might not be relevant to the often *766murky question of whether an invention was indeed reduced to practice on a prior date. Though it is not necessary for reduction to practice that a product be at a commercially satisfactory stage of development, Randolph v. Shoberg, 590 F.2d 923, 926 (C.C.P.A.1979), “an invention is not reduced to practice until its practice or utility is demonstrated pursuant to its intended use.” Wiesner v. Weigert, 666 F.2d 582,588 (C.C.P.A.1981); cf. Gross v. General Motors Gorp., 521 F.2d 45, 49 (1st Cir.1975) (“utility” standard of patentability requires tests showing invention will work as intended in its contemplated use). Tests on a claimed invention, though conducted subsequent to a claimed reduction to practice, might either confirm or call into question the reliability of earlier tests of utility and thus be highly relevant in determining the actual date of reduction to practice.
We cannot say here, however, that the district court was clearly erroneous in concluding that the non-disclosed research memoranda would have been unlikely to effect the outcome of the patent interference proceedings. The Holt applicants presented contemporaneous accounts of the alleged reduction to practice indicating their product conformed to the limitations of the interference count. They also presented physical evidence of the product itself. Nor are we sure that anything in the subsequent research reports demonstrates that the 60:30:10 product does not conform to the interference count.
One additional factor, not considered by the district court, weighs against a finding of fraud on the part of the Holt applicants in the interference proceeding. None of the authorities cited to us with regard to the patent applicant’s duty of disclosure have applied that duty to presentation of evidence in an interference proceeding. Unlike a single party patent application in which the PTO. must rely heavily on the representations of the applicant, an interference proceeding is an adversary proceeding over priority of invention in which the contending parties have full rights of discovery in accord with the Federal Rules of Civil Procedure. See, e.g., In re Natta, 388 F.2d 215, 217 (3d Cir.1968); Gladrow v. Weisz, 354 F.2d 464, 468 (5th Cir.1965); Vogel v. Jones, 350 F.Supp. 1297, 1299 (D.N.J.1972), affirmed, Vogel v. Jones, 464 F.2d 573 (3d Cir.1972).11
B. Examples I-III in the Holt Patent Application. Appellee also contends that the Holt applicants fraudulently represented that they were the original inventors of three binders containing PVA which were claimed as examples I-III in the Holt patent application. Appellee claims that Nashua was the true inventor of those binders. But the only evidence that appellee relies on is a June 1957 memorandum from one Brown-Bridge researcher to another indicating that a third researcher had heard that Nashua was using PVA in some of its binders. The same memorandum indicates that “we did some work with this sort of material at one time” and evinces an intention to “take another look at it.” There is no evidence in the record that the actual composition of the three PVA binders in the Holt application, each of which include PVA as one of three binder resin materials, was previously produced by Nashua or anyone else. We cannot say the district court, which credited testimony supporting its conclusions, was clearly erroneous in finding that appellee had not sustained its burden of showing fraudulent representation on the part of the Holt applicants in purporting to be the inventors of the three PVA binders.
III. Attorneys’ fees
Appellee alleges finally that the district court erred in denying its motion for attorneys’ fees. “The court in exceptional cases may award reasonable attorney fees to the prevailing party [in a patent *767action].” 35 U.S.C. § 285. Though “conduct short of ‘fraud’ can make a case exceptional within the meaning of § 285 ... this is a matter which is committed to the sound discretion of the district court and which an appellate court will not disturb absent a showing of abuse of discretion.” Norton Co., supra, 530 F.2d at 445 (citations omitted); see also Kahn v. Dynamics Corp. of America, 508 F.2d 939, 945 (2d Cir.1974) (excess of simple negligence coupled with bad faith may constitute “exceptional” case); True Temper Corp. v. GF & I Steel Corp., 601 F.2d 495, 508 (10th Cir.1979). In a carefully supported supplemental opinion, the district court found no exceptional circumstances warranting the award of attorneys’ fees. We find no abuse of discretion.
The judgment of the district court is affirmed.
. Brown-Bridge Mills, Inc. was merged into Kimberly-Clark Corporation December 31, 1977. It is undisputed that since that date Kimberly-Clark Corporation has been the owner of all rights, title, and interest in the Holt patent.
. “Dry” or “non-curling” gummed paper is used for products such as printed labels and stamps which have on one side a dry adhesive coating capable of becoming sticky when moistened with water so that they can be affixed to another surface.
. Section 102(g) provides:
“A person shall be entitled to a patent unless before the applicant’s invention thereof the invention was made in this country by another who had not abandoned, suppressed, or concealed it. In determining priority of invention there shall be considered not only the respective dates of conception and reduction to practice of the invention, but also the reasonable diligence of one who was first to conceive and last to reduce to practice, from a time prior to conception by the other.”
. Section 112 provides in relevant part:
“The specification shall contain a written description of the invention, and of the manner
. The judge granting the motion to dismiss appellant’s first complaint is not the same judge whose decision we review here.
. The court reasoned: “In view of the multitude of tests by which solubility may be measured, the court is unable to conclude that the Holt patent reasonably apprises persons skilled in the art of the scope of the claimed invention.”
. We note, however, that interrelated with criticality is the requirement of 35 U.S.C. § 103 that a patentable invention be nonobvious in light of the prior art. See California Research Corp., supra, 356 F.2d at 820; Helene Curtis Industries, supra, 233 F.2d at 152. We find it somewhat anomalous that the district court, having determined that the Holt patent was anticipated by a prior invention and therefore invalid under § 102, went on to hold that the patent was not invalid for obviousness. “The defense of obviousness is less strict than that of anticipation .... Prior art which is insufficiently similar to support anticipation ... may still render the claimed patent obvious in combining various elements.” Shanklin Corp., supra, 521 F.2d at 617; see also Kamei-Autokomofort v. Eurasian Automotive Products, 553 F.2d 603, 607 (1977), cert, denied, 434 U.S. 860, 98 S.Ct. 186, 54 L.Ed.2d 133 (1977).
. The Count in the interference read in full: “A non-curling gummed paper comprising a paper base having adherent thereto a dry non-tacky water-activatable adhesive coating, said coating comprising as a dispersed phase discrete solid particles of water-activatable adhesive which are dispersed in an exterior phase which binds the particles to one another and to the paper, which exterior phase comprises an essentially continuous film of a resinous material in itself insoluble in water, but which taken separately as a dry film has plastic extensibility and low elastic recovery and is capable of adsorbing [sic] at least about five per cent of water.”
. It is the claim to such a product that is the basis of appellant’s infringement action, not the electrostatic process that was also disclosed by the Holt patent.
. The “60:30:10” binder was comprised of 60 parts animal glue, 30 parts Water White rosin, and 10 parts Carbowax 6000.
. Appellees point to two letters in the record from interference adversaries to appellant asking for more evidence of reduction to practice. We find no evidence, however, that those parties made formal discovery requests for documents subsequent to the alleged date of reduction to practice.