
586 N.W.2d 452 (1998)
255 Neb. 572
Dennis R. BAUERS et al., appellants,
v.
CITY OF LINCOLN, a municipal corporation, appellee.
No. S-97-491.
Supreme Court of Nebraska.
November 20, 1998.
*456 K. Kristen Newcomb and Robert F. Bartle, of Healey & Wieland Law Firm, Lincoln, for appellants.
William F. Austin, Lincoln City Attorney, and James D. Faimon, Lincoln, for appellee.
HENDRY, C.J., and WRIGHT, CONNOLLY, GERRARD, STEPHAN, McCORMACK, and MILLER-LERMAN, JJ.
MILLER-LERMAN, Justice.
The plaintiffs, Dennis R. Bauers, Thomas L. Scharbach, Jerry Peterson, James E. Johnson, David C. Bowlin, and Roger L. Carmichael, commenced this action against the defendant, City of Lincoln (City), claiming variously that the City improperly offset payments from a disability pension plan by amounts paid as a result of workers' compensation awards, and seeking lump-sum returns of their pension contributions.
This is the second appearance of this case in this court. We examined the timeliness of the plaintiffs' filing of their claims against the City in Bauers v. City of Lincoln, 245 Neb. 632, 514 N.W.2d 625 (1994) (Bauers I). In Bauers I, we held that the plaintiffs were barred from asserting their claims for the return of their entire contributions under Neb.Rev.Stat. § 15-840 (Reissue 1991) but that certain claims under 42 U.S.C. § 1983 (1994) were viable. In Bauers I, we remanded the cause to the district court to allow the plaintiffs to present the trial court with evidence pertaining to the merits of their claims filed pursuant to 42 U.S.C. § 1983. After remand, the trial court found that the plaintiffs had failed to meet their burden of proof of alleged constitutional violations committed by the City, and the court dismissed the plaintiffs' claims. We affirm.

FACTS
A detailed statement of facts pertaining to each of the plaintiffs individually is set forth in Bauers I. Briefly summarized, the plaintiffs were employed as firefighters working for the City for some portion of the period 1966 through 1989. All were required during their employment to contribute approximately 7 percent of their gross pay from each pay period to a pension fund administered by the City. Each of the plaintiffs retired from his employment as a firefighter before the age of 55 because of injury or a physical disability which reasonably prevented continued performance as a firefighter. The plaintiffs were placed on the City's roll of firefighters receiving disability pensions. Johnson, Peterson, Bowlin, and Carmichael also received workers' compensation benefits for the injuries which led to their disability retirement. None of the plaintiffs was offered, in lieu of continuing disability pension payments, a lump-sum return of his wages contributed to the pension fund with accrued interest.
The plaintiffs filed administrative claims with the City on October 17, 1990. Bauers and Scharbach demanded the return of their wage contributions to the City's pension fund with accrued interest. Johnson, Peterson, Bowlin, and Carmichael likewise sought the return of their pension fund contributions with interest, and they also sought reimbursement for the amounts withheld or offset from their respective disability pension payments as a result of workers' compensation awards which each had received.
The City denied all of the relief requested in the plaintiffs' administrative claims. Thereafter, each of the plaintiffs filed an action in the district court, seeking the relief specified above on the basis of § 15-840 and *457 42 U.S.C. § 1983. Section 15-840 provides generally:
All liquidated and unliquidated claims and accounts payable against the city shall: (1) Be presented in writing; (2) state the name of the claimant and the amount of the claim; and (3) fully and accurately identify the items or services for which payment is claimed or the time, place, nature, and circumstances giving rise to the claim.... In order to maintain an action for a claim, other than a tort claim as defined in section 13-903, it shall be necessary, as a condition precedent, that the claimant file such claim within one year of the accrual thereof....
The trial court dismissed the plaintiffs' claims, holding that they were filed beyond the applicable statutes of limitation. On appeal, we found in Bauers I that although the plaintiffs' claims under § 15-840 for the return of their entire employee contributions were time barred, the plaintiffs' claims asserted under 42 U.S.C. § 1983 were not time barred, and we remanded the matter to the trial court for trial on these claims only.
The case was tried to the district court on November 20, 1996. At trial, each of the plaintiffs testified that the City never gave him a written contract containing all of the terms of employment, including a description of pension options. The plaintiffs admitted that when they were placed on the roll of pensioned disabled firefighters, they belonged to a union of firefighter employees. On behalf of its members, the union's representatives bargained with the City to determine specific terms of the firefighters' employment contract. John Cripe, an employee of the City's personnel department who served as the City's pension administrator, testified that the only written contract relative to these proceedings is the one which the City negotiated with the firefighters' union. Cripe testified that the City did not execute employment contracts with individual firefighters. Cripe also testified that the pension options available to the plaintiffs and other firefighters which were defined by Nebraska statutes and Lincoln municipal ordinances were not expressly described in the contract between the City and the firefighters' union.
The trial evidence showed that disability pension benefits were paid to the plaintiffs by the City from accounts designated Fund 76 and Fund 77. These accounts were segregated from all of the City's other accounts. Funds 76 and 77 were composed of mandatory employee contributions; annual contributions by the City, the amount of which was determined by an independent actuary; and accrued interest, all of which was continuously invested and reinvested for further growth. Cripe testified that both disability pensions and regular retirement pensions are paid from these accounts.
Bauers and Scharbach did not receive workers' compensation benefits for the injuries or ailments which culminated in their early retirement. Johnson, Peterson, Bowlin, and Carmichael received workers' compensation payments pursuant to Neb.Rev.Stat. § 48-101 et seq. (Reissue 1988) in addition to the disability pension payments. An amount equivalent to some or all of the workers' compensation payments received by Johnson, Peterson, Bowlin, and Carmichael, respectively, was offset from the disability pension payments which each received.
Workers' compensation benefits were paid by the City to Johnson, Peterson, Bowlin, and Carmichael from Fund 88, a segregated, separately maintained account within the City's total operating budget set aside exclusively for such payments. The City was, for purposes of paying workers' compensation benefits, self-insured. Fund 88 comprised taxes and other monies derived from the City's general budget. Cripe testified at trial that funds from the pension and workers' compensation funds were not commingled.
At trial, the parties stipulated that Neb.Rev.Stat. § 15-1001 et seq. (Reissue 1983) governed the terms and conditions of the plaintiffs' pensions and provided terms and conditions for pensions and disability benefits for firefighters and police officers. Many of these statutes were repealed in 1987. The parties stipulated that amendments to the Lincoln Municipal Code effectively replaced those statutes governing pensions and disability benefits for Lincoln firefighters and *458 police officers and that these municipal ordinances took effect on May 11, 1987. The specific terms of the statutes and ordinances at issue and as relevant are set forth in our analysis of them.
The plaintiffs claimed at trial that the City's failure to offer each of them all of the pension options offered to retiring firefighters who were not disabled, including the option of receiving their contributions to the pension fund in a lump sum with accrued interest, violated the plaintiffs' constitutional rights to due process and equal protection. Johnson, Peterson, Bowlin, and Carmichael also claimed that the City effected an unconstitutional taking when the City offset their disability pension payments by amounts which the City had paid them as workers' compensation, as well as impairing their right to contract.
In a 14-page order filed March 3, 1997, in each of the plaintiffs' cases, the trial court denied the plaintiffs' claims generally on the basis of failure of proof. The plaintiffs appeal.

ASSIGNMENTS OF ERROR
Johnson, Peterson, Bowlin, and Carmichael assign as error the trial court's finding that they suffered no unconstitutional due process and contract violations in the City's offset of pension benefits by the amount of workers' compensation payments. The plaintiffs all claim that the trial court erred in failing to find unconstitutional due process and equal protection violations in the City's failure to offer the plaintiffs the opportunity to withdraw their pension fund contributions in a lump sum with accrued interest.

STANDARD OF REVIEW
In an appellate review of a bench trial in a law action, the trial court's factual findings have the effect of a jury verdict, and they will not be set aside on appeal unless they are clearly wrong. Blanchard v. City of Ralston, 251 Neb. 706, 559 N.W.2d 735 (1997).
Whether a statute is constitutional is a question of law on which the Nebraska Supreme Court is obligated to reach a conclusion independent of the decision of the trial court. Friehe v. Schaad, 249 Neb. 825, 545 N.W.2d 740 (1996). When passing upon the constitutionality of a statute, an appellate court begins with the presumption of validity, and the burden of demonstrating a constitutional defect rests with the challenger. Id.

ANALYSIS
Nebraska law recognizes that pensions received by government employees are a form of deferred compensation. Halpin v. Nebraska State Patrolmen's Retirement System, 211 Neb. 892, 320 N.W.2d 910 (1982). "`For the civil service employees, the price of the pension plan, whether specifically discussed or not, is part of the total wage package negotiated when salary raises are determined. Pensions are bargained as an integral part of the wage-and-fringe benefit calculus.'" Id. at 898, 320 N.W.2d at 914, citing with approval Kleinfeldt v. New York City Emp. Ret. Sys., 73 Misc.2d 310, 341 N.Y.S.2d 784 (1973). The trial court was a proper forum for the plaintiffs to present their constitutional claims regarding their pensions, pursuant to 42 U.S.C. § 1983, for the states have concurrent jurisdiction with the federal courts to entertain such actions. Whitehead Oil Co. v. City of Lincoln, 245 Neb. 680, 515 N.W.2d 401 (1994).
At trial, the parties stipulated to the introduction of photocopies of §§ 15-1006, 15-1007.03 through 15-1009, and 15-1013.02. These statutes were part of a collection of Nebraska statutes pertaining to pensions for firefighters and police officers, many of which were in effect from at least 1975 until 1987, when they were repealed. The source notation included at the end of the text of each of these statutes suggests that many of these statutes were amended at least once between 1975 and 1987. However, the parties submitted no evidence of versions of these statutes which predated that set forth in the copies accepted into evidence at trial.
Section 15-1006, a copy of which was in evidence, generally provided that in case of total and permanent disability, a firefighter's regular salary was discontinued and the firefighter was instead paid a pension which was computed using a base benefit rate determined *459 as a percentage ranging from 15 to 50 percent of the firefighter's salary prior to his or her disability.
Section 15-1008, a copy of which was in evidence, stated that benefits which a disabled firefighter was entitled to receive according to Nebraska's then Workmen's Compensation Act, § 48-101 et seq., would be paid in full to him or her, "but all amounts paid by the city or its insurer under said act... shall be considered as payments on account of such salary or pension and shall be credited thereon." § 15-1008.
With respect to firefighters who retired voluntarily or involuntarily for reasons other than death or disability, § 15-1013.02, which was also in evidence, provided the schedule of pension benefit options as follows: (1) A firefighter with less than 10 years of service would receive the lump-sum return of his or her accumulated contributions with regular interest to the date of termination. (2) If the firefighter had 10 years or more of service but had not yet reached the age of 50, he or she could opt to take (a) a deferred annuity to commence at age 55 on a regular basis or at age 50 on an actuarially equivalent basis or (b) a lump-sum return of contributions and accrued interest, plus a reduced paid-up deferred annuity equal to the amount of the deferred annuity which would otherwise commence at age 55. The reduced annuity received by the firefighter with this option would be reduced by an amount equivalent to the lump-sum return of employee contributions and accrued interest. (3) If a firefighter had 10 years or more of service and was at least 50 years old, he or she could opt to receive a deferred annuity to commence at age 55 on a regular basis. If a firefighter selected this option, he or she was not eligible to receive a return of employee contributions and interest in a lump sum separately from the annuity.
At trial, the parties also stipulated to the introduction of selected portions of the Lincoln Municipal Code, including Lincoln Mun.Code §§ 2.64.010 through 2.64.013 and 2.64.018 through 2.64.026. These ordinances became effective on May 11, 1987. There is no dispute that the statutes and ordinances relative to the issues in this case are substantially alike.
Statutes which are in effect at the time a contract is made are as much a part of the contract as if they were set forth therein. In re Estate of Peterson, 221 Neb. 792, 381 N.W.2d 109 (1986); Haakinson & Beaty Co. v. Inland Ins. Co., 216 Neb. 426, 344 N.W.2d 454 (1984). In Bauers I, the firefighters agreed, and this court found, that the Lincoln ordinances in evidence were substantially the same as the state statutes and that any difference between the statutes and the ordinances was immaterial to the resolution of this case. That finding governs this appeal, for it is now the law of the case, which will not be considered again unless it is shown that the facts presented at the second trial are materially and substantially different from the facts presented in the first instance, a showing which has not been made in the case sub judice. See State v. Jacob, 253 Neb. 950, 574 N.W.2d 117 (1998).
Workers' Compensation Offset: Interference With Contractual Rights Claim.
On appeal, Johnson, Peterson, Bowlin, and Carmichael claim that their constitutionally protected contractual rights have been abridged because the City offset their disability pension benefit payments by the amount of some or all of the workers' compensation benefits which each received. A public employee's constitutionally protected right to his or her pension as an incident of employment vests upon the employee's acceptance and commencement of employment, subject to reasonable or equitable unilateral changes by the Legislature. Calabro v. City of Omaha, 247 Neb. 955, 531 N.W.2d 541 (1995). "` "Vesting in a legal sense ... refers to a contractual right to and interest in a pension that may be upheld at law."'" Id. at 967, 531 N.W.2d at 550. U.S. Const. art. I, § 10, provides, inter alia, that the state may not pass laws impairing the obligation of contracts. Nebraska public employees have reasonable expectations with regard to their pension rights which are protected by the law of contracts, since public pensions are considered as deferred compensation. *460 Hoiengs v. County of Adams, 245 Neb. 877, 516 N.W.2d 223 (1994).
Our analysis of this contract-impairment and offset claim necessitates a three-pronged inquiry: first, whether there has, in fact, been an impairment of the plaintiffs' contracts; second, if an impairment does exist, whether the City's actions substantially impaired the contractual relationship; and third, if so, whether the impairment caused by the City is nonetheless a permissible, legitimate exercise of the City's sovereign powers. See Calabro v. City of Omaha, supra. See, also, Halpin v. Nebraska State Patrolmen's Retirement System, 211 Neb. 892, 320 N.W.2d 910 (1982). As discussed below, we agree with the trial court that there was no impairment of the plaintiffs' contracts regarding the offset of pension payments by workers' compensation benefits.
In Halpin, a retired member of the Nebraska State Patrol challenged a revised calculation formula used to determine pension income, claiming that the new formula wrongfully impaired and decreased his vested contractual pension rights. This court found that the calculation formula used when Halpin's pension rights vested was the subject of express oral promises to Halpin and other employees and that the formula had been used by the Nebraska State Patrol on a longstanding basis. On the facts in Halpin, we found that the revised calculation formula which decreased the employees' pension benefits substantially impaired their contractual rights and that the new calculation was therefore inapplicable to them. See, also, Omer v. Tagg, 235 Neb. 527, 455 N.W.2d 815 (1990).
Essential elements common to Halpin and Omer are evidence supporting the employees' claims that a valuable benefit was promised to them by their employer, the employees' reliance on that promise, that the benefit was subsequently taken from the employees as a result of a unilateral employer decision, and that the employees were afforded no other benefit to replace that which was taken from them. Without such proof, it is doubtful that a claim of unconstitutional contract impairment could succeed. A contractual right cannot be founded solely on an employee's hope or expectation, as opposed to consideration which truly exists and which has been offered by the employer to the employee. "[W]hat is protected is the settled or reasonable expectation of the employee, not the contract as might be written by the courts." Miller v. City of Omaha, 253 Neb. 798, 808, 573 N.W.2d 121, 128 (1998).
Miller was decided after the case at bar was tried and decided in the district court. Factually, Miller addressed contract claims much like those raised by Johnson, Peterson, Bowlin, and Carmichael in the case at bar. Gary E. Miller, a former city government employee, sought declaratory judgment to determine to what extent, if any, disability pension benefits paid to him could be offset by workers' compensation benefits and Social Security he received which were related to the same injury which resulted in his disability. In Miller, there was evidence that city ordinances pertaining to pension benefits changed after Miller's contractual pension rights vested in 1964. This court held that the mere occurrence of change did not determine whether Miller's constitutional contractual rights were impaired, for
[t]he Contract Clause of the federal Constitution does not prohibit changes in the contract.... Rather, the issue is whether Miller has been made worse off by the 1972 ordinance, and it is Miller's burden to prove that his situation is worse than that which existed when his rights were created.
(Emphasis supplied.) 253 Neb. at 807, 573 N.W.2d at 128, relying on Caruso v. City of Omaha, 222 Neb. 257, 383 N.W.2d 41 (1986). See Calabro v. City of Omaha, 247 Neb. 955, 531 N.W.2d 541 (1995).
In Miller, supra, we held that amendments to city ordinances passed after Miller's pension rights vested effected a change in Miller's pension benefits, but that the change did not impair Miller's rights. We nevertheless reversed the trial court's summary judgment order favoring the employer in order to allow Miller to prove his claim of reliance upon his employer's promises and practices, including the effect, if any, of the employer's commingling of workers' compensation and *461 pension benefit funds, a practice which was disapproved of in Novotny v. City of Omaha, 207 Neb. 535, 299 N.W.2d 757 (1980) (holding that funds for payment of pension and workers' compensation benefits should not be commingled and that no employee contribution may be used to fund workers' compensation benefits). In Miller, we emphasized that the holding in Novotny was limited to determining that workers could not be compelled to pay for their own workers' compensation benefits, nor could other benefits be considered in paying workers' compensation benefits.
With the principles of Novotny, Caruso, Calabro, and Miller in mind, we turn to the impairment-of-contract and offset claim asserted by Johnson, Peterson, Bowlin, and Carmichael in the case at bar. Each received workers' compensation benefits for the job-related injuries which ultimately rendered him permanently disabled, and amounts were set off from his disability pension payments in an amount equivalent to some or all of the workers' compensation payments which he received. For the sake of completeness, we note that it is uncontroverted that Fund 88, the account maintained by the City from which workers' compensation payments were made to Johnson, Peterson, Bowlin, and Carmichael contained no contributions by the plaintiffs or City employees, consistent with Novotny, supra.
The record shows that Johnson commenced employment with the City in 1975, Peterson in 1977, Carmichael in 1978, and Bowlin in 1981. The pension rights of Johnson, Peterson, Bowlin, and Carmichael became vested on the day upon which each accepted his employment with the City and commenced work. See Calabro, supra. The dimensions of the rights vested in each of the plaintiffs were determined by the pension plan as it existed at the time each accepted and commenced his employment. See Miller v. City of Omaha, 253 Neb. 798, 573 N.W.2d 121 (1998).
As noted above, at trial the parties stipulated to the introduction into evidence of §§ 15-1006, 15-1007.03 through 15-1009, and 15-1013.02, all of which were later repealed, and portions of the Lincoln Municipal Code which replaced these state statutes for purposes of the issues in the instant case. The statutes and code were received in evidence.
Section 15-1008 specifically stated that disability pension payments received by a firefighter may be reduced by an amount representing a credit for workers' compensation payments received by the firefighter. Indeed, according to § 15-1008:
Notwithstanding any prior provisions of this act, no firefighter or police officer shall be entitled during any period of disability to receive in full both his or her pension or salary, as herein provided, and in addition benefits under the Workmen's Compensation Act. All Workmen's Compensation Act benefits shall be payable in full to such firefighter or police officer or his or her dependents as provided in said act, but all amounts paid by the city or its insurer under said act to any disabled firefighter or police officer entitled to receive a salary or pension during such disability ... shall be considered as payments on account of such salary or pension and shall be credited thereon. The remaining balance of such pension or salary, if any, shall be payable as otherwise provided by this act.
(Emphasis supplied.) Lincoln Mun.Code § 2.64.018, which became effective May 11, 1987, contains equivalent provisions.
It has been observed: "[N]ot every change constitutes an impairment under the federal Constitution. The change must take something away and not work to the parties' benefit.... Absent such a showing, there is no proof of any `impairment.'" (Emphasis in original.) Caruso v. City of Omaha, 222 Neb. 257, 260, 383 N.W.2d 41, 44 (1986). At trial and on appeal, the plaintiffs did not claim that they received less than the full measure of workers' compensation benefits awarded to them. Johnson, Peterson, Bowlin, and Carmichael offered no policy, ordinance, statute, or other evidence which contradicted the terms of § 15-1008. Although the terms of § 15-1008 were in place at the time of initial employment, each testified that he was generally unaware of the setoff provisions in § 15-1008 and Lincoln Mun.Code § 2.64.018 until the credits *462 were actually applied against his disability pension payments. The plaintiffs introduced neither evidence that applicable laws or City policies were amended nor evidence that such were amended to the plaintiffs' detriment after each of the plaintiffs' contractual rights had vested.
The gravamen of the impairment-of-contract and offset claim asserted by Johnson, Peterson, Bowlin, and Carmichael is that they were simply unaware that when each firefighter's contractual pension rights vested, Nebraska statutes defining and governing those rights provided that "no firefighter or police officer shall be entitled during any period of disability to receive in full both his or her pension or salary, as herein provided, and in addition benefits under the Workmen's Compensation Act." § 15-1008. Everyone is presumed to know the law. Bakody Homes & Dev. v. City of Omaha, 246 Neb. 1, 516 N.W.2d 244 (1994); Haman v. Marsh, 237 Neb. 699, 467 N.W.2d 836 (1991). We cannot agree with the plaintiffs that their lack of knowledge of these state statutes and the comparable city ordinances which replaced them amounted to an impairment by the City of the plaintiffs' contractual rights.
We observe that at the time that Johnson, Peterson, Bowlin, and Carmichael applied for their respective disability pensions and workers' compensation benefits, each was a member of the firefighters union which negotiated with the City on behalf of the firefighters regarding the terms, conditions, and benefits of the firefighters' employment. Johnson, Peterson, and Carmichael were also individually represented by counsel. Further, in the execution of documents pursuant to his workers' compensation award, Carmichael expressly acknowledged that he knew that his pension benefits could be subject to a setoff for the workers' compensation benefits which he received.
Johnson, Peterson, Bowlin, and Carmichael failed to present the trial court with evidence that the City unconstitutionally impaired their vested pension rights by crediting the amounts of the workers' compensation benefits against the disability pension benefits received by each of the plaintiffs. No change occurred in city or state policies, practices, or laws which diminished the contractual pension benefits of Johnson, Peterson, Bowlin, and Carmichael.
The plaintiffs failed to meet their evidentiary burden to prove that the City unconstitutionally impaired their rights to contract. See Caruso, supra. Therefore, we affirm the trial court's order dismissing the constitutional impairment-of-contract and offset claim asserted by Johnson, Peterson, Bowlin, and Carmichael.
Lump-Sum Return of Contributions: Due Process Claims.
The plaintiffs allege that the City wrongly denied them due process rights to which they were entitled by virtue of the 14th Amendment to the U.S. Constitution and Neb. Const. art. I, § 3. The firefighters claim that the City, by failing to offer disabled firefighters the option of receiving their employee contributions in a lump sum with accrued interest and reduced annuity pension benefits unconstitutionally deprived the plaintiffs of rights to which they were entitled.
On appeal, the plaintiffs do not distinguish whether the due process rights which they claim were denied to them are procedural or substantive in nature. Substantive due process requires a determination whether a right in which the plaintiff has a legitimate property interest is at issue and, if it is, whether that right was unconstitutionally taken from the plaintiff. See, e.g., Caruso v. City of Omaha, 222 Neb. 257, 383 N.W.2d 41 (1986). Procedural due process limits the ability of the government to deprive persons of interests which constitute "liberty" or "property" interests within the meaning of the Due Process Clause and requires that parties deprived of such interests be provided adequate notice and an opportunity to be heard. Friehe v. Schaad, 249 Neb. 825, 545 N.W.2d 740 (1996), citing with approval Mathews v. Eldridge, 424 U.S. 319, 96 S.Ct. 893, 47 L.Ed.2d 18 (1976). See, also, McAllister v. Nebraska Dept. of Corr. Servs., 253 Neb. 910, 573 N.W.2d 143 (1998).
The trial court's order dismissing the plaintiffs' due process claims analyzed them as a substantive due process complaint, a *463 characterization with which we agree. It is beyond dispute that the plaintiffs possessed a vested property interest in receiving pension funds from the City. See, Miller v. City of Omaha, 253 Neb. 798, 573 N.W.2d 121 (1998); Calabro v. City of Omaha, 247 Neb. 955, 531 N.W.2d 541 (1995). The issue in the trial court, and on appeal, is whether the plaintiffs proved that the City unconstitutionally deprived them of those vested rights, thereby denying them the beneficial ownership and exercise of those rights. Like the constitutional impairment-of-contract claim analyzed above, claims of unconstitutional due process deprivation cannot succeed in the absence of trial evidence showing that the City improperly took the plaintiffs' vested rights away from them. See Caruso, supra.
Sections 15-1006, 15-1007.03 through 15-1009, and 15-1013.02 and the Lincoln municipal ordinances which replaced them clearly and consistently provided that firefighters receiving disability pensions were not within the category of firefighters eligible to receive lump-sum returns of their employee contributions to the pension fund. Simply, the plaintiffs, while recipients of disability pensions, never possessed the right of a lumpsum return of contributions made to the pension fund. It was therefore impossible for the City to take away a right which the plaintiffs did not possess. This fact alone defeats the plaintiffs' due process claims. See Caruso, supra.
We further observe that the trial court correctly noted that without exception, the plaintiffs received disability pension benefits from the City which far exceeded each of their contributions to the pension fund plus accrued interest on those contributions. The trial court found that Bauers contributed $38,782.13 in employee contributions and accrued interest; by the time of trial, he had received disability pension benefits of approximately $129,752.25. Scharbach's total pension contribution plus accrued interest totaled $45,014.93 at the time he was retired on disability status in 1988. He died prior to trial, and his widow continued to collect his pension benefits which, at the time of trial, cumulatively totaled approximately $95,218.02. Peterson contributed $10,855.17 in wage deductions and accrued interest, and he had received $124,775 in disability benefits by the time of trial. Johnson's wage contributions totaled $31,366.86, and he had received $115,496.40 in benefits before the trial. Bowlin worked for the City for 13 months before he was placed on permanent disability status, and he had contributed $5,678.49 to the pension fund. He had received monthly disability benefits which, at the time of trial, amounted to roughly $127,046.04 and which continued to be paid to him monthly. Carmichael contributed $12,761 in wage deductions to the City employee pension before he was placed on disability status. By the time of trial, he had received $125,092.13. We also note that the record shows that each of the plaintiffs obtained other employment soon after he was declared permanently disabled from firefighting and that all were continuously engaged in full-time employment after they ceased employment as firefighters for the City.
Cripe, the City's pension plan administrator, testified that disabled firefighters received their disability pensions every month from the date of the declaration of disability until the pensioner's death, regardless of the amount of the firefighter's contribution to the pension fund during his or her active employment. According to Cripe, if a disabled firefighter died before he or she had received disability pension benefits in an amount at least equal to the firefighter's wage contributions plus accrued interest, the City would return to the firefighter's estate all unpaid employee contributions, plus accrued interest, in a lump-sum payment. Cripe also testified that surviving spouses of deceased disabled firefighters receive the firefighter's disability pension benefits until the spouse dies and that dependent children are entitled to receive their deceased parent's disability pension benefits until they reach the age of 19.
We are unpersuaded by the plaintiffs' claims that notwithstanding the statutes and ordinances which they admit defined their disability pension benefits, they were nonetheless unconstitutionally deprived of a property right by being unable to exercise *464 the option to receive their employee contributions in a lump sum with accrued interest and a reduced pension benefit. None of the plaintiffs testified that he would have exercised this option had it been offered to him or that it would have yielded him greater or more meaningful pension benefits. We agree with the trial court that the plaintiffs in the instant case produced no evidence which showed that the City unconstitutionally deprived them of any vested right. Constitutional deprivations are not founded upon speculation, or mere possibilities. Walker v. Nelson, 863 F.Supp. 1059 (D.Neb.1994), aff'd 70 F.3d 1276 (8th Cir.1995). As we stated in Caruso v. City of Omaha, 222 Neb. 257, 261, 383 N.W.2d 41, 44 (1986):
While Halpin [v. Nebraska State Patrolmen's Retirement System, 211 Neb. 892, 320 N.W.2d 910 (1982)] stands for the proposition that pensions are not gratuities and are matters of contract, it does not stand for the proposition that a public employee is entitled to the best pension the public employee might desire.
We affirm the trial court's order dismissing the plaintiffs' due process claims.
Lump-Sum Return of Contributions: Equal Protection Claims.
The plaintiffs' final claim on appeal is that the City wrongfully denied them equal protection of laws in violation of U.S. Const. amend. XIV by the City's failure to offer the plaintiffs the option to receive a lump-sum return of their wage contributions to the pension fund, plus accrued interest. The plaintiffs do not allege a violation of Neb.Const. art. III, § 18. See, e.g., Haman v. Marsh, 237 Neb. 699, 467 N.W.2d 836 (1991); Jaksha v. State, 241 Neb. 106, 486 N.W.2d 858 (1992). Thus, we limit ourselves to the plaintiffs' federal equal protection claim.
The initial inquiry in an equal protection analysis focuses on whether the plaintiff has demonstrated that he or she was treated differently than others similarly situated. If that showing is not made, there is no viable equal protection claim. State v. Atkins, 250 Neb. 315, 549 N.W.2d 159 (1996).
The plaintiffs claim in essence that they were unequally treated because certain retiring nondisabled firefighters could receive a lump-sum return of contributions, whereas the plaintiffs, who are disabled firefighters, could not. A review of the statutes and ordinances shows that as to disabled firefighters, none could receive a lump-sum payout, and as to nondisabled retiring firefighters, certain categories of nondisabled retiring firefighters could receive a lump-sum payment while other nondisabled retiring firefighters could not receive a lump-sum payment. See §§ 15-1006 and 15-1013.02. In essence, the plaintiffs, who are disabled firefighters, claim they were similarly situated but treated differently than certain nondisabled firefighters who were eligible to receive a lump-sum payment. The trial court found it "questionable" whether the plaintiffs were similarly situated to other firefighters generally, and to the category of nondisabled firefighters who were eligible to receive a lump-sum payment in particular. We agree with the trial court's observation that disabled and nondisabled firefighters are not similarly situated. See Atkins, supra.
To the extent that the plaintiffs could be said arguendo to be similarly situated to nondisabled retiring firefighters, there is a rational reason demonstrated by the record in this case for treating disabled and nondisabled firefighters differently, and, therefore, the failure to offer disabled firefighters a lump-sum payout does not offend the equal protection clause.
It is well settled that when a fundamental right or suspect classification is not implicated in an equal protection challenge, a legislative act is viewed as a valid exercise of state power if the act is rationally related to a legitimate governmental purpose. State ex rel. Dept. of Health v. Jeffrey, 247 Neb. 100, 525 N.W.2d 193 (1994). See, also, Caruso v. City of Omaha, 222 Neb. 257, 383 N.W.2d 41 (1986), citing Vance v. Bradley, 440 U.S. 93, 99 S.Ct. 939, 59 L.Ed.2d 171 (1979). The rational relationship standard is the most relaxed and tolerant form of judicial scrutiny under the Equal Protection Clause, and it "`is offended only if the classification rests on grounds wholly irrelevant to the achievement of the [government's] objective.'" Atkins, 250 Neb. at 321, 549 N.W.2d *465 at 163, quoting McGowan v. Maryland, 366 U.S. 420, 81 S.Ct. 1101, 6 L.Ed.2d 393 (1961).
A review of the record, including but not limited to Cripe's testimony, shows that the pension contributions from the disabled and nondisabled firefighters were in effect treated separately for accounting purposes because the risk to the City of long-term pension payments to a disabled firefighter was greater than the risk of long-term payments to a nondisabled firefighter. The evidence shows that there is a higher risk to the City of performing the obligation to make pension payments which will exceed employee contributions as to the pool of disabled firefighters than there is as to the pool of nondisabled retiring firefighters. There is a rational basis to allow the option for a lump-sum return of the contributions of a retiring nondisabled firefighter exiting the pension system and to not allow an option for lump-sum return of employee contributions to a firefighter who is retiring due to disability and who will typically be receiving pension payments for a length of time exceeding the term of active employment and in an amount exceeding the amount of his or her contributions to the pension fund. The trial evidence proved that there was a rational relationship that supported the City's differing treatment of the categories of disabled and nondisabled pensioned firefighters, and the plaintiffs' evidence did not overcome the presumption of the validity of the statutes and ordinances in question. See Friehe v. Schaad, 249 Neb. 825, 545 N.W.2d 740 (1996).
We also agree with the trial court's finding that no equal protection claim is implied or proved by the fact that since 1992, the City now has the technological and actuarial means to provide a retiring firefighter with an analysis projecting the total amount of benefits which he or she may receive from the City depending on the pension options available to the firefighter. Relying on Walker v. Nelson, 863 F.Supp. 1059 (D.Neb.1994), and Caruso v. City of Omaha, 222 Neb. 257, 383 N.W.2d 41 (1986), the trial court found this claim meritless, for "[t]o hold otherwise would require the Court to find an equal protection violation every time an advancement in technology is adopted which improves the situation of current employees over that which past employees enjoyed." The availability of the more sophisticated reports does not alter the underlying entitlement to the vested rights reflected in the reports. This claim was without merit, and the trial court properly so found. We affirm the trial court's order dismissing the plaintiffs' equal protection claims.

CONCLUSION
The trial court's order dismissing the plaintiffs' constitutional claims against the City for impairment-of-contract, due process, and equal protection violations is affirmed in all respects.
AFFIRMED.
