<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019fde40-c20a-7ada-b255-e9218b0b9275,g:4d181f64-0736-4235-a40a-ae50171c152c-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://infinitynaturalresources.com/role/Cover" xlink:type="simple" xlink:href="inr-20260805.xsd#Cover"/>
  <link:presentationLink xlink:role="http://infinitynaturalresources.com/role/Cover" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_019fde40-c20a-77b5-90ad-50fa5b707114" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_DocumentType_019fde40-c20a-77b5-90ad-50fa5b707114" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_019fde40-c20a-7d47-acfd-d6a4a03426f7" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_DocumentPeriodEndDate_019fde40-c20a-7d47-acfd-d6a4a03426f7" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_019fde40-c20a-734d-837f-e3257bd0f961" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityRegistrantName_019fde40-c20a-734d-837f-e3257bd0f961" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_019fde40-c20a-7710-9531-42125e91f6dc" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityIncorporationStateCountryCode_019fde40-c20a-7710-9531-42125e91f6dc" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_019fde40-c20a-7529-abf3-2128b97f3ab8" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityFileNumber_019fde40-c20a-7529-abf3-2128b97f3ab8" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_019fde40-c20a-77a5-ac86-d08e9c0649c1" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityTaxIdentificationNumber_019fde40-c20a-77a5-ac86-d08e9c0649c1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_019fde40-c20a-7d28-8f13-ab85cc95cc0e" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityAddressAddressLine1_019fde40-c20a-7d28-8f13-ab85cc95cc0e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_019fde40-c20a-72ba-a218-94e02088fd20" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityAddressCityOrTown_019fde40-c20a-72ba-a218-94e02088fd20" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince_019fde40-c20a-7ac2-904f-d799bcef6faf" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityAddressStateOrProvince_019fde40-c20a-7ac2-904f-d799bcef6faf" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_019fde40-c20a-730b-b791-27ce60e802db" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityAddressPostalZipCode_019fde40-c20a-730b-b791-27ce60e802db" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_019fde40-c20a-777d-b154-8d011c86d316" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_CityAreaCode_019fde40-c20a-777d-b154-8d011c86d316" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_019fde40-c20a-7efc-a6f5-1ba93ae7a9de" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_LocalPhoneNumber_019fde40-c20a-7efc-a6f5-1ba93ae7a9de" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_019fde40-c20a-7864-acb1-06c3d4dbb04c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_WrittenCommunications_019fde40-c20a-7864-acb1-06c3d4dbb04c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_019fde40-c20a-75e3-83a5-2843b59fccac" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_SolicitingMaterial_019fde40-c20a-75e3-83a5-2843b59fccac" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_019fde40-c20a-7a52-b13e-276d2e456b2d" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_PreCommencementTenderOffer_019fde40-c20a-7a52-b13e-276d2e456b2d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_019fde40-c20a-741d-862f-21e186bc7f43" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_019fde40-c20a-741d-862f-21e186bc7f43" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_019fde40-c20a-726c-9f69-9d9e6ab858de" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_Security12bTitle_019fde40-c20a-726c-9f69-9d9e6ab858de" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_019fde40-c20a-7d03-b029-6c35193baf15" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_TradingSymbol_019fde40-c20a-7d03-b029-6c35193baf15" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_019fde40-c20a-7d57-b0d1-72ab27a4b2ca" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_SecurityExchangeName_019fde40-c20a-7d57-b0d1-72ab27a4b2ca" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_019fde40-c20a-7a57-b820-ef6fe5c11d66" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityEmergingGrowthCompany_019fde40-c20a-7a57-b820-ef6fe5c11d66" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod_019fde40-c20a-7c72-8003-86ddf4bf067f" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityExTransitionPeriod"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityExTransitionPeriod_019fde40-c20a-7c72-8003-86ddf4bf067f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_019fde40-c20a-7ab5-9758-4eb85a44cf1a" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_AmendmentFlag_019fde40-c20a-7ab5-9758-4eb85a44cf1a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_019fde40-c20a-7680-bdc5-cbc00923d15f" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="23" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019fde40-c20a-7626-a732-ae9e1ae8f58f" xlink:to="loc_dei_EntityCentralIndexKey_019fde40-c20a-7680-bdc5-cbc00923d15f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
