OPINION OF THE COURT
HARDIMAN, Circuit Judge.
Louis Sheddy and the Sheddy Family Trust (collectively, the Appellants) appeal the District Court’s summary judgment in favor of Piatt Township (Piatt or Township). We will affirm.
I.
Louis Sheddy is a trustee of the Sheddy Family Trust, which owns property at 500 Sams Road in Piatt Township, Pennsylvania.
In May 2002, Piatt served the Sheddys with an enforcement notice alleging that their use of the property — storing junk vehicles without a permit — violated a
Township ordinance. Approximately one month later, Piatt served the Sheddys with an enforcement notice ordering them to clean up the property and informing them that they had thirty days to appeal to the Township’s zoning hearing board. The Sheddys never appealed the enforcement notices.
Piatt initiated enforcement proceedings, and the local magistrate entered judgment against the Sheddys. They appealed the judgment and later filed (and amended) a complaint alleging that the relevant ordinance was unconstitutional on its face and as applied. Specifically, the Sheddys asserted an equal protection claim, charging that similarly situated individuals were not prosecuted. In 2003, the Lycoming County Court of Common Pleas held that the Sheddys could not raise a majority of their allegations because their failure to appeal the enforcement notices to the zoning hearing board constituted a waiver of any challenges to the merits of the ordinance or its application. With the Appellants’ constitutional claims dismissed, Piatt won the subsequent non-jury trial. The Commonwealth Court of Pennsylvania affirmed, and in August 2005, the Pennsylvania Supreme Court denied the Appellants’ petition for allowance of appeal.
In 2005, the Sheddys sought approval of the zoning hearing board to expand the junkyard, arguing that a special exemption to the ordinance existed for junkyards and auto salvage businesses. The board determined that the Sheddys did not meet the burden of establishing a preexisting nonconforming use. The Sheddys appealed to the Lycoming County Court of Common Pleas, which again entered judgment in favor of the Township. The Commonwealth Court affirmed, and the Appellants’ petition for allowance of appeal was again denied by the Pennsylvania Supreme Court.
In June 2008, the Sheddys filed a complaint against Piatt in the Middle District of Pennsylvania alleging that the 2002 enforcement notices violated their right to equal protection under the Fourteenth Amendment.
The District Court held that
res judicata
barred the Appellants’ claim because they had the opportunity to argue it in the state court litigation but failed to do so. Alternatively, the District Court found that the Sheddys failed to put forward evidence of any question of material fact warranting trial. This appeal followed.
II.
The Sheddys claim the District Court erred in applying
res judicata
and granting summary judgment in favor of Piatt Township.
A.
Under federal law, a state court decision is given the same
res judicata
effect in subsequent federal proceedings as it is given in the issuing state’s courts. 28 U.S.C. § 1738. To determine whether
res judicata
properly applies to a Pennsylvania state court decision, we look to Pennsylvania law.
McCarter v. Mitcham,
883 F.2d 196, 199 (3d Cir.1989).
This ease does not require us to analyze the elements of
res judicata,
however, because even if the Sheddys are correct that
res judicata
should not apply, summary judgment is nevertheless appropriate on the merits of their underlying equal protection claim.
B.
Summary judgment is appropriate when “the pleadings, the discovery and disclosure materials on file, and any affidavits show that there is no genuine issue as to any material fact.” Fed.R.Civ.P. 56(c)(2). A factual dispute is “genuine” and thus warrants trial “if the evidence is such that a reasonable jury could return a verdict for the nonmoving party.... The mere existence of a scintilla of evidence in support of the plaintiffs position will be insufficient; there must be [significantly probative] evidence on which the jury could reasonably find for the plaintiff.”
Anderson v. Liberty Lobby,
477 U.S. 242, 248-19, 252, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986). “Speculation and conclusory allegations do not satisfy this duty.... Ambiguous allegations and vague inferences ... cannot defeat summary judgment.”
Ridgewood Bd. of Educ. v. N.E. ex rel. M.E.,
172 F.3d 238, 252, 254 (3d Cir.1999) (citation omitted). Summary judgment must be entered against any party unable to present sufficient evidence in support of an essential element of a claim because “a complete failure of proof concerning an essential element of the nonmoving party’s case necessarily renders all other facts immaterial.”
Celotex Corp. v. Catrett,
477 U.S. 317, 322-23, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986). Finally, we assume also that the non-moving party’s allegations are true, and they “must receive the benefit of the doubt” when in conflict with the moving party’s claims.
Valhal Corp. v. Sullivan Assocs.,
44 F.3d 195, 200 (3d Cir.1995) (quoting
Goodman v. Mead Johnson & Co.,
534 F.2d 566, 573 (3d Cir.1976)).
In framing their equal protection claim, the Sheddys proceed on a “class of one” theory, which requires them to prove that they “ha[ve] been intentionally treated differently from others similarly situated and that there is no rational basis for the difference in treatment.”
Vill. of Willowbrook v. Olech,
528 U.S. 562, 564, 120 S.Ct. 1073, 145 L.Ed.2d 1060 (2000). One way to meet this standard is to show that the Township’s conduct was “irrational and wholly arbitrary.”
Id.
at 565, 120 S.Ct. 1073;
see also Eichenlaub v. Twp. of Indiana,
385 F.3d 274, 286 (3d Cir.2004).
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OPINION OF THE COURT
HARDIMAN, Circuit Judge.
Louis Sheddy and the Sheddy Family Trust (collectively, the Appellants) appeal the District Court’s summary judgment in favor of Piatt Township (Piatt or Township). We will affirm.
I.
Louis Sheddy is a trustee of the Sheddy Family Trust, which owns property at 500 Sams Road in Piatt Township, Pennsylvania.
In May 2002, Piatt served the Sheddys with an enforcement notice alleging that their use of the property — storing junk vehicles without a permit — violated a
Township ordinance. Approximately one month later, Piatt served the Sheddys with an enforcement notice ordering them to clean up the property and informing them that they had thirty days to appeal to the Township’s zoning hearing board. The Sheddys never appealed the enforcement notices.
Piatt initiated enforcement proceedings, and the local magistrate entered judgment against the Sheddys. They appealed the judgment and later filed (and amended) a complaint alleging that the relevant ordinance was unconstitutional on its face and as applied. Specifically, the Sheddys asserted an equal protection claim, charging that similarly situated individuals were not prosecuted. In 2003, the Lycoming County Court of Common Pleas held that the Sheddys could not raise a majority of their allegations because their failure to appeal the enforcement notices to the zoning hearing board constituted a waiver of any challenges to the merits of the ordinance or its application. With the Appellants’ constitutional claims dismissed, Piatt won the subsequent non-jury trial. The Commonwealth Court of Pennsylvania affirmed, and in August 2005, the Pennsylvania Supreme Court denied the Appellants’ petition for allowance of appeal.
In 2005, the Sheddys sought approval of the zoning hearing board to expand the junkyard, arguing that a special exemption to the ordinance existed for junkyards and auto salvage businesses. The board determined that the Sheddys did not meet the burden of establishing a preexisting nonconforming use. The Sheddys appealed to the Lycoming County Court of Common Pleas, which again entered judgment in favor of the Township. The Commonwealth Court affirmed, and the Appellants’ petition for allowance of appeal was again denied by the Pennsylvania Supreme Court.
In June 2008, the Sheddys filed a complaint against Piatt in the Middle District of Pennsylvania alleging that the 2002 enforcement notices violated their right to equal protection under the Fourteenth Amendment.
The District Court held that
res judicata
barred the Appellants’ claim because they had the opportunity to argue it in the state court litigation but failed to do so. Alternatively, the District Court found that the Sheddys failed to put forward evidence of any question of material fact warranting trial. This appeal followed.
II.
The Sheddys claim the District Court erred in applying
res judicata
and granting summary judgment in favor of Piatt Township.
A.
Under federal law, a state court decision is given the same
res judicata
effect in subsequent federal proceedings as it is given in the issuing state’s courts. 28 U.S.C. § 1738. To determine whether
res judicata
properly applies to a Pennsylvania state court decision, we look to Pennsylvania law.
McCarter v. Mitcham,
883 F.2d 196, 199 (3d Cir.1989).
This ease does not require us to analyze the elements of
res judicata,
however, because even if the Sheddys are correct that
res judicata
should not apply, summary judgment is nevertheless appropriate on the merits of their underlying equal protection claim.
B.
Summary judgment is appropriate when “the pleadings, the discovery and disclosure materials on file, and any affidavits show that there is no genuine issue as to any material fact.” Fed.R.Civ.P. 56(c)(2). A factual dispute is “genuine” and thus warrants trial “if the evidence is such that a reasonable jury could return a verdict for the nonmoving party.... The mere existence of a scintilla of evidence in support of the plaintiffs position will be insufficient; there must be [significantly probative] evidence on which the jury could reasonably find for the plaintiff.”
Anderson v. Liberty Lobby,
477 U.S. 242, 248-19, 252, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986). “Speculation and conclusory allegations do not satisfy this duty.... Ambiguous allegations and vague inferences ... cannot defeat summary judgment.”
Ridgewood Bd. of Educ. v. N.E. ex rel. M.E.,
172 F.3d 238, 252, 254 (3d Cir.1999) (citation omitted). Summary judgment must be entered against any party unable to present sufficient evidence in support of an essential element of a claim because “a complete failure of proof concerning an essential element of the nonmoving party’s case necessarily renders all other facts immaterial.”
Celotex Corp. v. Catrett,
477 U.S. 317, 322-23, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986). Finally, we assume also that the non-moving party’s allegations are true, and they “must receive the benefit of the doubt” when in conflict with the moving party’s claims.
Valhal Corp. v. Sullivan Assocs.,
44 F.3d 195, 200 (3d Cir.1995) (quoting
Goodman v. Mead Johnson & Co.,
534 F.2d 566, 573 (3d Cir.1976)).
In framing their equal protection claim, the Sheddys proceed on a “class of one” theory, which requires them to prove that they “ha[ve] been intentionally treated differently from others similarly situated and that there is no rational basis for the difference in treatment.”
Vill. of Willowbrook v. Olech,
528 U.S. 562, 564, 120 S.Ct. 1073, 145 L.Ed.2d 1060 (2000). One way to meet this standard is to show that the Township’s conduct was “irrational and wholly arbitrary.”
Id.
at 565, 120 S.Ct. 1073;
see also Eichenlaub v. Twp. of Indiana,
385 F.3d 274, 286 (3d Cir.2004).
Considering the record in the light most favorable to the Sheddys, there is insufficient evidence to allow any reasonable jury to reach a verdict in their favor. The record evidence contains nothing more than vague and conclusory allegations about other Piatt residents and their uses of land in the Township, and as the Dis
trict Court rightly found, none of the Appellants’ comparisons are apt. Contrary to the Appellants’ bald assertions, there is no evidence that Robert Aikey ever violated any Township ordinance.
The Sheddys admit in them concise statement of material facts filed in opposition to Piatt’s motion for summary judgment that Mr. Rice — whose first name is omitted throughout the record — was never the subject of any complaint to the Township, so the Township was never prompted to initiate enforcement proceedings against him. Buster Barlock’s property was in an area zoned commercial, whereas the Appellants’ property was located in an agricultural zone. Finally, C. Edward Sheddy operated a junkyard on the same 500 Sams Road property at issue in this case, but he supposedly did so from 1960 to 1964, approximately forty years before Piatt enforced its ordinance against the Sheddys.
The Sheddys fail to provide any evidence explaining how these distinctions do not amount to a “rational basis for the difference in treatment” with their purported comparators.
The Sheddys contend that these comparators were “individuals whom the Defendant identifies as not being ‘similar’, but the fact remains they were not prosecuted and Plaintiff Louis Sheddy was not utilizing ‘similar’ as the term of art Defendant wants to depict it as.” Appellants’ Br. at 18. In light of the fact that them “class of one” equal protection claim hinges entirely on the Appellants’ showing that they were “intentionally treated differently from others
similarly
situated”
Olech,
528 U.S. at 564, 120 S.Ct. 1073 (emphasis added), their insistence on not using “similar” as a term of art is tantamount to a concession that they cannot establish an element of the claim, thus rendering any lingering questions of fact immaterial. Moreover, based on the record, we can find nothing that would allow a factfinder to infer that the Township behaved irrationally, arbitrarily, or discriminatorily.
III.
For the foregoing reasons, we will affirm the District Court’s summary judgment in favor of Piatt Township.