The guardian ad litem, on behalf of the minor children, appeals the dismissal of the petition to terminate respondent’s parental rights. For the following reasons, we affirm the trial court’s order.
I. Background
Respondent and the mother1 are the parents of J.K.C. (“Jack”), born November 2002, and J.D.K. (“Jasmine”)2, born October 2004. The Guilford County Department of Social Services (“GCDSS”) has been involved with the family since May 2003 when GCDSS filed a juvenile petition alleging that Jack was a neglected and dependent child based upon drug abuse and domestic violence issues. The trial court adjudicated Jack a neglected juvenile and placed Jack in the legal and physical custody of GCDSS. About two years later, Jack was placed back in the custody of his mother who was living in New Hanover County
On 23 January 2006, the New Hanover County Department of Social Services took Jack, age 3, and Jasmine, age 1, into custody based upon the mother’s drug relapse and a domestic violence incident between respondent and the mother, which resulted in respondent’s arrest. Jack and Jasmine were adjudicated neglected on 16 March *252006. However, by 11 January 2007, the trial court returned custody to their mother based in part on her compliance with her substance abuse treatment.
On 20 February 2008, GCDSS filed a juvenile petition alleging Jack and Jasmine were neglected and dependent juveniles. The petition alleged that the mother was continuing to have substance abuse issues and that respondent was serving a nine-year prison sentence. The trial court adjudicated Jack and Jasmine neglected and dependent juveniles.
The trial court held a permanency planning review hearing in June 2008 and ordered a concurrent plan of adoption and reunification. At the September 2008 permanency planning hearing, the trial court suspended any visitation between respondent and the children because of his incarceration. After holding a permanency planning hearing on 15 January 2009, the trial court suspended the children’s visitation with the mother and ordered GCDSS to proceed with termination of parental rights within sixty days.
On 27 April 2009, GCDSS filed a Motion for Review “requestfing] the Court to reconsider Termination of Parental Rights in this matter.” By order filed 2 June 2009, the trial court relieved GCDSS of its duty to file the termination action and ordered the Guardian ad Litem program, who accepted responsibility for prosecuting the termination of parental rights, to proceed with filing the action.
On 13 August 2009, the guardian ad litem filed a petition to terminate the parental rights of the mother, respondent, and any unknown father. As to respondent, the petition alleged that grounds existed to terminate his parental rights under N.C. Gen. Stat. § 7B-llll(a)(l) (neglect); N.C. Gen. Stat. § 7B-llll(a)(2)(failure to make reasonable progress); N.C. Gen. Stat. § 7B-llll(a)(3)(failure to pay reasonable cost of care); N.C. Gen. Stat. § 7B-llll(a)(5)(failure to legitimate the juveniles); and N.C. Gen. Stat. § 7B-llll(a)(6) (incapable of providing care and supervision). The mother subsequently relinquished her parental rights to Jack and Jasmine. A hearing was held on the termination petition in November 2009. By order filed 22 March 2011, the trial court concluded that the guardian ad litem failed to show by clear, cogent, and convincing evidence that grounds existed to terminate the parental rights of respondent, and dismissed the petition. The guardian ad litem appeals.
*26II. Standard of Review
We have stated that “[t]he standard of review in termination of parental rights cases is whether the findings of fact are supported by clear, cogent and convincing evidence and whether these findings, in turn, support the conclusions of law.” In re Shepard, 162 N.C. App. 215, 221-22, 591 S.E.2d 1, 6 (citations and quotation marks omitted), disc. review denied sub nom. In re D.S., 358 N.C. 543, 599 S.E.2d 42 (2004). The burden is on the petitioner to prove the facts justifying termination by clear and convincing evidence. In re Nolen, 117 N.C. App. 693, 698, 453 S.E.2d 220, 223 (1995).
We first note that the guardian ad litem challenges only the trial court’s finding of fact 18 as not being supported by competent evidence. Respondent challenges finding of fact 17 based on N.C.R. App. P. 28(c). The trial court’s remaining unchallenged findings of fact are presumed to be supported by competent evidence and binding on appeal. Koufman v. Koufman, 330 N.C. 93, 97, 408 S.E.2d 729, 731 (1991). The trial court made the following unchallenged findings of fact in support of its conclusion that the guardian ad litem did not meet its burden as to respondent:
9. The minor children were adjudicated to be neglected on March 16, 2006. The Court order found that both parents have substantial problems of substance abuse and that the relationships of the parents “have been marred by domestic violence.”
10. At the time the children' were taken into custody of [New Hanover Department of Social Services (“NHDSS”)], [respondent] was in jail in New Hanover County with charges of felony assault on [the mother]. It was ordered that [respondent] have supervised visitation upon his release from custody contingent upon clean drug screens and his being substance free. It was also concluded, but not ordered, that reunification efforts be discontinued with [respondent].
11. [Respondent] remained in the custody of the New Hanover County Sheriff until his conviction on Second Degree Kidnapping and Habitual Misdemeanor Assault on August 7, 2006. He .was and remains incarcerated in North Carolina Department of Corrections [sic] with a projected release date of January 4, 2013.
12. The minor children were returned to the legal and physical custody of their mother in January of 2007.
*2713. On February 20, 2008, the children were placed in the legal and physical custody of GCDSS pursuant to non secure custody order. On March 20, 2008, the minor children were adjudicated to be neglected and dependent pursuant to a stipulation by [the mother]. [Respondent] was not brought in from prison for the hearing.
14. [Respondent] was not provided a case plan but as noted in the September 11, 2008 [order] he had nine classes while incarcerated, was working to improve himself. He was also contacting the social worker. A case plan was mailed to [respondent] on August 22, 2008 and it was signed and returned in November of 2008. The components of the case plan and [respondent’s] compliance is as follows:
a. maintain contact with GCDSS: [Respondent] is in compliance and has regularly sent letters to social worker inquiring about the children, requesting pictures and provided updates regarding location and programs completed:
b. address substance abuse: attend Narcotics Anonymous and Alcohol Anonymous; attend classes as available: . [Respondent] is in compliance provided the following certificates: Inpatient Treatment for Chemical Dependency (DART): twelve session of DACPP Aftercare Program. [Respondent] is a Residential Chemical Dependency Program Treatment Assistant.
c. anger management: enroll in classes; [Respondent] is not able to be in compliance on this component as this type of class has not been offered in the prisons he has been placed;
d. parenting: participate in parenting classes if available: there is only [one] class offered by Department of Correction and [respondent] has completed this class;
e. update case plan upon his release from prison.
15. There are no classes available in the Department of Corrections [sic] to address domestic violence. [Respondent] did complete Basic Employability Skills Training, Thinking for Change, Masonry, Office Practice and Character Education Training.
16. [Respondent] is in substantial compliance with his case plan.
*2819. [Respondent] earns $1.00 a day in the Department of Corrections [sic]. He has family members and other friends who contribute to his account. His account in DOC currently totals $1,052.95. He has received over $5,000.00 since 2007.
20. The cost of foster care for [Jasmine] from February 2008 to October of 2009 is $9,397.10 and for [Jack] is $10,613.10. This does not include day care for [Jasmine].
21. [Respondent] has not paid anything toward the care of the children since his incarceration. However, he has written both Guilford County Child. Support Enforcement and the social worker inquiring about providing financial support and was informed that it could not be arranged at this time. Guilford County Child Support Enforcement Agency wrote [respondent] and stated that as he was earning less than minimum wage, the agency could not establish a child support case.
22. [Respondent] has not sent cards or letters to children since his incarceration. However, it also appears that at one time he was told not to contact the children and he did not think he was allowed to send anything directly to them. He has sent letters, cards and gifts to his mother so she could, when allowed, give these to the children.
23. He has sent one letter to [Jack], in care of the therapist, at her request, apologizing to [Jack] for his actions.
27. [Respondent] has not seen his children or had any contact with them since his incarceration on December 31, 2005 when [Jack] was three years of age and [Jasmine] was one year of age.
28. [Respondent’s] only relative to offer to provide a place for the minor children is his mother, but it has been judicially determined that his mother’s house is not appropriate.
Based on the evidence presented and the findings, the trial court determined that none of the grounds alleged by the guardian ad litem were established. We now address each ground in turn.
III. Neglect.
[1] N.C. Gen. Stat. § 7B-101(15) (2009) defines a “Neglected juvenile” as “[a] juvenile who does not receive proper care, supervision, or discipline from the juvenile’s parent, guardian, custodian, or caretaker; *29or who has been abandoned[.]” Although a prior adjudication of neglect may be considered by the trial court in a termination hearing, a parent’s rights may not be terminated solely on the basis of past neglect where the conditions which led to the neglect no longer exist. In re Ballard, 311 N.C. 708, 713-14, 319 S.E.2d 227, 231-32 (1984). Where a child has been out of the custody of the parent for some time, “[t]he trial court must also consider any evidence of changed conditions in light of the evidence of prior neglect and the probability of a repetition of neglect.” Id. at 715, 319 S.E.2d at 232 (citation omitted). Determinative factors include “the fitness of the parent to care for the child at the time of the termination proceeding.” Id. (emphasis in original). Incarceration, by itself, is insufficient to establish neglect in a termination case, but it is relevant to whether a child is neglected. In re P.L.P., 173 N.C. App. 1, 10, 618 S.E.2d 241, 247 (2005), aff'd per curiam, 360 N.C. 360, 625 S.E.2d 779 (2006).
The guardian ad litem argues that the evidence was sufficient to show that respondent has neglected the minor children and that neglect would likely continue since his behavior has not changed since the children were born. To support her argument, the guardian ad litem attempts to distinguish In re Shermer, 156 N.C. App. 281, 576 S.E.2d 403 (2003), which was decided on similar facts. In Shermer, the respondent was incarcerated when the minor child was adjudicated neglected, the mother voluntarily relinquished her parental rights, and the respondent contacted social services from prison seeking involvement in the case and asking not to have his parental rights terminated. Id. at 282-83, 576 S.E.2d at 405. When the respond- ent contacted DSS after he was released from prison, he signed a case plan with social services, he was attempting to comply with the requirements of the case plan by the time of the termination hearing, he was in regular contact with his child, and he had had two visits with the child that went well. Id. at 283-84, 576 S.E.2d at 405-06. The trial court in Shermer found the child neglected and terminated the father’s rights on the grounds of neglect, willfully leaving the child in foster care without making reasonable progress, and willful abandonment. Id. at 285, 576 S.E.2d at 406. On appeal, this Court reversed the trial court’s decision after determining that the evidence was not clear and convincing that the respondent had neglected the minor child. Id. at 288, 576 S.E.2d at 408.
Here, the trial court determined that insufficient evidence was presented on the ground of neglect. In doing so, the trial court made findings of fact that the children were adjudicated neglected juve*30niles. The trial court then considered evidence of changed conditions, including respondent’s “substantial compliance with his case plan[,]” and did not find the probability of repetition of neglect. The guardian ad litem points out that respondent did not enroll in domestic violence counseling, is unable to demonstrate outside of prison his sobriety, and lacks a relationship with his children. However, the trial court found, based upon testimony from GCDSS social worker Suzanne Brogdon and respondent, that no anger management classes were offered in the prisons where respondent has been placed; that respondent was in compliance with his substance abuse component of his case plan; that respondent sent letters to the social worker inquiring about his children; and that respondent sent letters, cards, and gifts to the children via his mother.
Similar to Shermer, the circumstances in the instant case are sufficient to support the trial court’s determination that the guardian ad litem has not presented clear and convincing evidence of respondent’s neglect of the children. Therefore, we conclude that the trial court did not err in concluding based upon the findings of fact that respondent’s parental rights could not be terminated based on neglect.
IV. Willful failure to make reasonable progress
[2] Parental rights may be terminated when “[t]he parent has willfully left the juvenile in foster care or placement outside the home for more than 12 months without showing to the satisfaction of the court that reasonable progress under the circumstances has been made in correcting those conditions which led to the removal of the juvenile.” N.C. Gen. Stat. § 7B-llll(a)(2). Willfulness does not imply fault on the part of the parent, but may be “established when the respondent had the ability to show reasonable progress, but was unwilling to make the effort.” In re O.C. & O.B., 171 N.C. App. 457, 465, 615 S.E.2d 391, 396 (citation and quotation marks omitted), disc. review denied, 360 N.C. 64, 623 S.E.2d 587 (2005). “[incarceration, standing alone, neither precludes nor requires finding the respondent willfully left a child in foster care.” In re Harris, 87 N.C. App. 179, 184, 360 S.E.2d 485, 488 (1987) (citations omitted). The guardian ad litem argues that the evidence was sufficient to show that respondent’s parental rights should be terminated pursuant to N.C. Gen. Stat. § 7B-llll(a)(2).
Here, as noted above, the trial court made detailed findings regarding respondent’s case plan and his compliance with that plan. Finding of fact 14 states that respondent was not provided with a case plan until August of 2008, which he signed and returned in November *31of 2008. Finding of fact 14 further notes that pursuant to the case plan, respondent had maintained contact with GCDSS, attended ongoing substance abuse treatment, completed the only parenting class offered by the Department of Correction, but had not attended anger management because this type of class was not offered at the prisons in which he had been placed. Finding of fact 15 further states that although there were “no classes available in the Department of Correction to address domestic violence[,]” respondent had completed “Basic Employability Skills Training, Thinking for a Change, Masonry, Office Practice and Character Education Training.” Further, finding of fact 16 finds that respondent “is in substantial compliance with his case plan.” We conclude that the unchallenged findings of fact 14, 15, and 16 support the trial court’s conclusion that the evidence does not clearly and convincingly show that respondent willfully left the children in foster care without making reasonable progress to correct the conditions which led to the removal of the children from their mother’s home.
Y. Failure to pay cost of care
[3] In order to support termination of parental rights on the ground of willful failure to pay a reasonable cost of care of the child, the petitioner has the burden of presenting evidence of the parent’s ability to pay. N.C. Gen. Stat. § 7B-llll(a)(3); In re Ballard, 311 N.C. at 716-17, 319 S.E.2d at 233. In the context of N.C. Gen. Stat. § 7B-1111(a)(3), this Court has stated that the word “willful” “imports knowledge and a stubborn resistance . . . one does not willfully fail to do something which it is not in his power to do.” In re Matherly, 149 N.C. App. 452, 455, 562 S.E.2d 15, 18 (2002) (citation and quotation marks omitted).
We note that the trial court does not specifically reference section “7B-llll(a)(3)” in its conclusion of law which states that the guardian ad litem did not prove grounds existed to terminate respondent’s parental rights. It is clear, however, that the trial court dismissed the entire termination petition, which included the ground of failure to pay cost of care under section 7B-llll(a)(3).
The guardian ad litem asserts that the evidence showed that the father had the ability to pay an amount greater than zero despite his incarceration and, therefore, the trial court should have terminated respondent’s rights on the ground of failure to pay.
Even though the trial court’s finding of fact 21 states that respondent had “not paid anything toward the care of the children since his *32incarceration[,]” it further states that respondent had written to GCDSS about providing support but “was informed that it could not be arranged at this time” as “he was earning less than minimum wage, [and] the agency could not establish a child support case.” Therefore, respondent’s failure to pay was not based on “stubborn resistance[,]” see Matherly, 149 N.C. App. at 455, 562 S.E.2d at 18, but on GCDSS’ inability to receive any support from him at that time. Accordingly, the trial court correctly did not terminate respondent’s parental rights pursuant to N.C. Gen. Stat. § 7B-llll(a)(3).
VI. Paternity
[4] Next, the guardian ad litem challenges the trial court’s conclusion that sufficient evidence was not presented to terminate respondent’s parental rights based on his failure to legitimate the children. N.C. Gen. Stat. § 7B-llll(a)(5) provides that atrial court may terminate parental rights when the “father of a juvenile bom out of wedlock has not, prior to the filing of a petition or motion to terminate parental rights:
a. Established paternity judicially or by affidavit which has been filed in a central registry maintained by the Department of Health and Human Services; provided, the court shall inquire of the Department of Health and Human Services as to whether such an affidavit has been so filed and shall incorporate into the case record the Department’s certified reply; or
b. Legitimated the juvenile pursuant to provisions of G.S. 49-10 or filed a petition for this specific purpose; or
c. Legitimated the juvenile by marriage to the mother of the juvenile; or
d. Provided substantial financial support or consistent care with respect to the juvenile and mother.
N.C. Gen. Stat. § 7B-llll(a)(5). When basing the termination of parental rights on this statutory provision, the court must make specific findings of fact as to all four subsections and the petitioner bears the burden of proving the father has failed to take any of the four actions. In re Harris, 87 N.C. App. at 188, 360 S.E.2d at 490. The guardian ad litem argues that the trial court erred in failing to terminate the parental rights of respondent pursuant to N.C. Gen. Stat. § 7B-llll(a)(5) as to both Jack and Jasmine.
*33As to Jack, the guardian ad litem first argues that the trial court’s finding of fact 18 is not supported by competent evidence. Finding of fact 18 states:
18. [Respondent] had [at] some point, in some legal proceeding, submitted to a blood test and was found to be the biological father of [Jack], [Jack’s] birth certificate was amended to include [respondent’s] name. No court order was introduced as evidence which included a judicial finding of paternity but the parties agree that this did occur at some point in some case.
As to Jasmine, finding of fact 17 states:
17. [Respondent] has not legitimated [Jasmine] either judicially or by affidavit; has not filed a petition to legitimate [Jasmine] and has not legitimated the child by marriage to the mother.
Although these findings are quite different from one another, the same legal principles apply to both children, so we will address these principles first. Also, respondent was identified as the father of both children on their respective birth certificates, both of which are marked as “amended” certificates.
We first note that N.C. Gen. Stat. § 7B-llll(a)(5) places an unusual burden upon the petitioner, as it requires the petitioner for termination of parental rights to prove a negative: that the respondent has not taken any of the actions listed. A party who must prove a negative “faces a greater burden . . . .” State v. Ipock, 129 N.C. App. 530, 533, 500 S.E.2d 449, 451 (1998). In addition, petitioner has the burden to prove this negative by “clear, cogent and convincing” evidence. See Shepard, 162 N.C. App. at 221-22, 591 S.E.2d at 6. But the guardian ad litem’s argument entirely ignores the fact that respondent was listed as the father of both children on their birth certificates. In fact, copies of the birth certificates were attached to the petition for termination of parental rights, which was filed by the guardian ad litem. As the birth certificate is a document which is issued by the State Registrar pursuant to statutory requirements as to its contents, we do not believe that the birth certificate can be ignored. We will therefore consider the legal sufficiency of the birth certificate as a means of proving that paternity has been established judicially, pursuant to N.C. Gen. Stat. § 7B-llll(a)(5)(a).
In this case, the mother and respondent were never married to one another and there is no evidence that the mother was married to anyone else at any relevant time. Issuance of a birth certificate at *34birth would therefore have been governed by N.C. Gen. Stat. § 130A-101(f) (2009), which provides:
(f) If the mother was unmarried at all times from date of conception through date of birth, the name of the father shall not be entered on the certificate unless the child’s mother and father complete an affidavit acknowledging paternity which contains the following:
(1) A sworn statement by the mother consenting to the assertion of paternity by the father and declaring that the father is the child’s natural father and that the mother was unmarried at all times from the date of conception through the date of birth;
(2) A sworn statement by the father declaring that he believes he is the natural father of the child;
(3) Information explaining in plain language the effect of signing the affidavit, including a statement of parental rights and responsibilities and an acknowledgment of the receipt of this information; and
(4) The social security numbers of both parents.
The State Registrar, in consultation with the Child Support Enforcement Section of the Division of Social Services, shall develop and disseminate a form affidavit for use in compliance with this section, together with an information sheet that contains all the information required to be disclosed by subdivision (3) of this subsection.
Upon the execution of the affidavit, the declaring father shall be listed as the father on the birth certificate, subject to the declaring father’s right to rescind under G.S. 110-132. The executed affidavit shall be filed with the registrar along with the birth certificate. In the event paternity-is properly placed at issue, a certified copy of the affidavit shall be admissible in any action to establish paternity. . . .
Thus, respondent’s name could not have been placed on the birth certificate when it was originally issued unless both parents completed “an affidavit acknowledging paternity” in a format and containing the information as required by N.C. Gen. Stat. § 130A-101(f).
The birth certificates both indicate that they were “amended,” although the certificates do not state what the particular amendments were. Based upon the evidence presented, it would appear that the *35amendments were made to add respondent’s name as the father of the children. The guardian ad litem volunteer testified that a 2003 guardian ad litem report showed that respondent took a paternity test and respondent could not be excluded as the father of Jack. Additionally, the 2 October 2003 GCDSS court summary noted that paternity had been established for Jack. We further note that finding of fact 18 also states that “[n]o court order was introduced as evidence which included a judicial finding of paternity [as to Jack] but the parties agree that this did occur at some point in some case.” Regarding Jasmine, in court summaries from GCDSS, dated 22 March 2008, 9 April 2009, and 1 October 2009, respondent is named as the “Biological[,]” rather than the putative, father of Jasmine, and the summaries state that paternity had been established. Additionally, GCDSS court summaries dated 12 June 2008, 11 September 2008, and 15 January 2009 specifically state that Jasmine’s biological father is respondent and that paternity had been established “by Civil Adjudication^]” Thus, the evidence as to both Jack and Jasmine indicates that there was a judicial determination of paternity, which resulted in the amendments to their birth certificates.
A birth certificate can be amended as provided by N.C. Gen. Stat. § 130A-118 (2009), which provides in pertinent part as follows:
(a) After acceptance for registration by the State Registrar, no record made in accordance with this Article shall be altered or changed, except by a request for amendment. The State Registrar may adopt rules governing the form of these requests and the type and amount of proof required.
(b) A new certificate of birth shall be made by the State Registrar when:
2) Notification is received by the State Registrar from the clerk of a court of competent jurisdiction of a judgment, order or decree disclosing different or additional information relating to the parentage of a person;
(3) Satisfactory proof is submitted to the State Registrar that there has been entered in a court of competent jurisdiction a judgment, order of decree disclosing different or additional information relating to the parentage of aperson[. . . .]
Thus, respondent could not have been listed as the “father” of either child unless his name was placed on the certificates in accordance *36with either N.C. Gen. Stat. § 130A-101(f) (by affidavit of paternity) or N.C. Gen. Stat. § 130A-118(b) (by amendment based upon a judicial determination of parentage.)3
We also recognize that a birth certificate may be amended to remove a father who was originally identified on the certificate in some circumstances, although none of those situations are present in this case, as neither respondent, nor the mother, nor any other putative father has challenged respondent’s status as biological father of either child. See, e.g., N.C. Gen. Stat. § 110-132 (2009).
In the context of a proceeding for termination of parental rights, where the petitioner has the burden of proving by clear, cogent, and convincing evidence that a respondent has not established paternity of a child, the practical effect of a birth certificate bearing the respondent’s name as father of the child is the creation of a rebuttable presumption that the respondent has in fact established paternity of the child either judicially or by affidavit as required by N.C. Gen. Stat. § 7B-llll(a)(5)(a). Although our Courts have not previously identified this as a rebuttable presumption, N.C. Gen. Stat. §§ 130A-101, 130A-118, and 130A-1194, taken together, create a rebuttable presumption that the respondent has taken the legal steps necessary to establish paternity; otherwise, his name logically could not appear on the birth certificate. McCormick on Evidence states that *37Kenneth S. Broun et al., 2 McCormick on Evidence § 343, at 500-01 (6th ed. 2006) (footnote omitted). In this instance, there is no other logical explanation for fact B — that respondent is listed on the birth certificates as father — than the existence of Fact A — that respondent judicially established paternity. We believe this presumption is also consistent with the long-recognized presumption of legitimacy of “[a] child born in wedlock.” Wright v. Wright, 281 N.C. 159, 172, 188 S.E.2d 317, 325 (1972) (citation omitted). If a child born to a marriage is presumed to be legitimate, we see no reason why a similar presumption should not arise where a child’s birth certificate identifies its father, as our statutory scheme requires a determination of paternity by affidavit or judicially before the father’s name can be shown on the birth certificate. Of course, this presumption can be rebutted, but in this case, there is no evidence to rebut the presumption raised by the birth certificates. To the contrary, our record does not reveal any significant question or doubt that respondent had established paternity of both children. As noted above, evidence included in the record showed that respondent took a paternity test which showed that he was the father of Jack. Also, respondent is consistently identified as Jasmine’s “father” on numerous documents in the record, from 23 January 2006 until 29 October 2009, including juvenile petitions, orders from the court, permanency planning orders, guardian ad litem reports, and DSS reports to the court. As also noted above, several court summaries from GCDSS identify respondent as the “Biological],]” rather than the putative, father of Jasmine, and the summaries state that paternity had been established “by Civil Adjudication].]” The trial court, by written orders dated 24 June 2008, and 8 October 2008, accepted and “incorporated by reference” these GCDSS summaries in its findings of fact. Additionally, Martha Harris, the guardian ad litem, testified that at a 20 March 2008 adjudication and disposition hearing that the mother testified that respondent was the biological father of Jasmine and “there were no other possible fathers of [Jasmine].” Respondent is referred to as the “putative father” only twice in the record, once in a 20 February 2008 juvenile petition and again in the guardian ad litem’s petition to terminate parental rights, in which the guardian sought to use the failure to establish paternity as a ground for termination.
*36the most important consideration in the creation of presumptions is probability. Most presumptions have come into existence primarily because the judges have believed that proof of fact B renders the inference of the existence of fact A so probable that it is sensible and timesaving to assume the truth of fact A until the adversary disproves it.
*37 [5] With this rebuttable presumption in mind, we will now address the trial court’s findings as to each child. The guardian ad litem argues that as to Jack, there is no documentation in the record to support the finding that respondent was the biological father of Jack. Respondent testified that around 2004 he took a DNA test, he was *38found to be the father of Jack, and Guilford County entered a child support order for Jack. The guardian ad litem argues that “there is no documentation of [a DNA test]... and more importantly [respondent] took none of the steps listed in N.C.G.S. § 7B-llll(a)(5) to legitimate [Jack.]” However, the birth certificate itself belies the guardian ad litem’s argument. The trial court’s finding 18, regarding Jack, is clearly supported by competent record evidence and that finding supports the conclusion that the paternity of Jack had been judicially established prior to the filing of the petition for termination of parental rights. See N.C. Gen. Stat. § 7B-1111(a)(5)(a). The guardian ad litem makes no further challenges based on N.C. Gen. Stat. § 7B-llll(a)(5) as to Jack. Accordingly, the trial court properly concluded that the guardian ad litem had not met its burden and respondent’s parental rights as to Jack could not be terminated based on N.C. Gen. Stat. § 7B-1111(a)(5).
[6] The finding as to Jasmine is more problematic, as it finds that “[respondent] has not legitimated [Jasmine] either judicially or by affidavit; has not filed a petition to legitimate [Jasmine] and has not legitimated the child by marriage to the mother.” The guardian ad litem argues that the trial court’s findings do not support its conclusion that it failed to show by clear and convincing evidence that grounds existed to terminated respondent’s parental rights as to Jasmine, pursuant to N.C. Gen. Stat. § 7B-llll(a)(5). As noted above, the trial court is required to make specific findings of fact as to all four subsections of N.C. Gen. Stat. § 7B-1111(a)(5). See Harris, 87 N.C. App. at 188, 360 S.E.2d at 490.
The guardian ad litem does not challenge finding No. 17 but argues that this finding tends to support a conclusion that respondent’s parental rights should be terminated pursuant to N.C. Gen. Stat. § 7B-llll(a)(5). However, we note that although the findings address the first three subsections of N.C. Gen. Stat. § 7B-llll(a)(5), the trial court failed to address subsection (d), whether respondent “[provided substantial financial support or consistent care with respect to the juvenile and mother.” See id.; In re Harris, 87 N.C. App. at 188, 360 S.E.2d at 490. Therefore, this incomplete finding of fact could not support the trial court’s conclusion.
Respondent raises an alternative basis for the trial court’s conclusion5, arguing that finding of fact 17 is not supported by com*39petent evidence, as the evidence in the record shows that he has established paternity of Jasmine judicially, pursuant to N.C. Gen. Stat. § 7B-llll(a)(5)(a). Based upon our determination as discussed above that Jasmine’s birth certificate raised a rebuttable presumption that respondent had established paternity judicially, we agree with respondent. This presumption was not rebutted. In addition to the evidence as discussed above, there is also no suggestion in any of the documentation included in the record on appeal that respondent was required to establish paternity of Jasmine as part of a case plan or requiring respondent to take a paternity test to establish paternity for Jasmine. Therefore, the trial court’s finding that respondent had “not legitimated [Jasmine] judicially” is not supported by the clear, cogent, and convincing evidence required for termination of parental rights. See Shepard, 162 N.C. App. at 221-22, 591 S.E.2d at 6.6
We note that the trial court made no findings regarding the above evidence that respondent had established paternity of Jasmine pursuant to N.C. Gen. Stat. § 7B-1111(a)(5)(a) to support its conclusion of law that parental rights should not be terminated. However, we have stated that “when a court fails to make appropriate findings or conclusions, this Court is not required to remand the matter if the facts are not in dispute and only one inference can be drawn from them.” Green Tree Financial Servicing Corp. v. Young, 133 N.C. App. 339, 341, 515 S.E.2d 223, 224 (1999). The guardian ad litem does not challenge this evidence and only one inference can be drawn from it. See id. In addition, the birth certificate identifying respondent as Jasmine’s father established a rebuttable presumption, which has not been rebutted by any of the evidence. Accordingly, we need not remand this case for additional findings, and we hold that the trial court did not err in dismissing the petition to terminate respondent’s parental rights pursuant to N.C. Gen. Stat. § 7B-llll(a)(5), as the guardian ad litem did not meet its burden to show by “clear, cogent and convincing evidence[,]” see Shepard, 162 N.C. App. at 221-22, 591 S.E.2d at 6, that respondent had not established paternity judicially.
*40VII. Dependency
[7] The guardian ad litem also argues that it was error for the trial court to not terminate respondent’s parental rights based on dependency pursuant to N.C. Gen. Stat. § 7B-llll(a)(6). As for the ground of dependency, the trial court may terminate parental rights based on a finding “[t]hat the parent is incapable of providing for the proper care and supervision of the juvenile, such that the juvenile is a dependent juvenile within the meaning of G.S. 7B-101, and that there is a reasonable probability that such incapability will continue for the foreseeable future. . . .” N.C. Gen. Stat. § 7B-llll(a)(6). N.C. Gen. Stat. § 7B-101(9) (2009) defines a dependent juvenile as “[a] juvenile in need of assistance or placement because . . . [the juvenile’s] parent, guardian, or custodian is unable to provide for the care or supervision and lacks an appropriate alternative child care arrangement.” Under this definition, the trial court’s findings “must address both (1) the parent’s ability to provide care or supervision, and (2) the availability to the parent of alternative child care arrangements.” In re P.M., 169 N.C. App. 423, 427, 610 S.E.2d 403, 406 (2005).
The guardian ad litem argues the trial court’s findings support a conclusion that Jack and Jasmine are dependent juveniles. The guardian ad litem seeks to distinguish In re Clark, 151 N.C. App. 286, 565 S.E.2d 245, disc. review denied, 356 N.C. 302, 570 S.E.2d 501 (2002) to support her argument. In Clark, the father had been incarcerated for most of the child’s life and the mother, who had a substance abuse problem, could not care for the child. Id. at 286-87, 565 S.E.2d at 246. The trial court concluded that the father had failed to pay a reasonable portion of the cost of care for the child although physically and financially able to do so, and was incapable of providing for the proper care and supervision of the child and that such inability would continue for the foreseeable future. Id. at 287, 565 S.E.2d at 246. On appeal, this Court reversed the trial court’s decision, holding that there was insufficient evidence to support the trial court’s conclusion. Id. at 289-90, 565 S.E.2d at 248. This Court specifically determined that there also was no evidence at trial to suggest that the father suffered from any physical or mental illness, disability, or “similar cause or condition” that would prevent him from providing proper care and supervision for the child. Id. at 289, 565 S.E.2d at 247-48.
The guardian ad litem argues that Clark is inapplicable because: (1) respondent’s projected release date is not for another four years, whereas the father in Clark was due for release in seventeen months; *41and (2) respondent’s alternative care arrangement was determined to be inappropriate, whereas the father in Clark provided names of relatives to DSS, but DSS did not contact the relatives. See id. at 287, 565 S.E.2d at 246.
Here, the trial court found that respondent would be incarcerated until 2013 and that respondent’s only relative who had offered to provide for Jack and Jasmine was respondent’s mother who was determined to be inappropriate. Although the trial court found that respondent lacked an alternative child care arrangement, the trial court did not find respondent was incapable of providing care and supervision. Similar to the facts in Clark, the guardian ad litem here did not present any evidence that respondent’s incapability of providing care and supervision was due to one of the specified conditions or any other similar cause or condition. See id. Without such a determination, we conclude the trial court did not err in dismissing the termination petition based on N.C. Gen. Stat. § 7B-llll(a)(6).
VIII. Abandonment
[8] We note that the trial court erroneously dismissed the petition with respect to N.C. Gen. Stat. § 7B-llll(a)(7). The termination petition alleged the ground of abandonment only as to “any unknown putative father” and not to respondent. Thus, dismissing the petition on this ground was unnecessary and also did not prejudice any party.
IX. Conclusion
For the foregoing reasons, we affirm the trial court’s dismissal of the petition to terminate respondent’s parental rights.
AFFIRMED.
Judges STEPHENS and BEASLEY concur.