diff --git a/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/DiagnosisCompilerFirTestdataTestGenerated.java b/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/DiagnosisCompilerFirTestdataTestGenerated.java
index d060b97196f..dda07b90f43 100644
--- a/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/DiagnosisCompilerFirTestdataTestGenerated.java
+++ b/analysis/low-level-api-fir/tests/org/jetbrains/kotlin/analysis/low/level/api/fir/diagnostic/compiler/based/DiagnosisCompilerFirTestdataTestGenerated.java
@@ -3551,6 +3551,18 @@ public class DiagnosisCompilerFirTestdataTestGenerated extends AbstractDiagnosis
                 runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastToTypeParameter.kt");
             }
 
+            @Test
+            @TestMetadata("smartcastsFromEquals_differentModule.kt")
+            public void testSmartcastsFromEquals_differentModule() throws Exception {
+                runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.kt");
+            }
+
+            @Test
+            @TestMetadata("smartcastsFromEquals_sameModule.kt")
+            public void testSmartcastsFromEquals_sameModule() throws Exception {
+                runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.kt");
+            }
+
             @Nested
             @TestMetadata("compiler/fir/analysis-tests/testData/resolve/smartcasts/booleans")
             @TestDataPath("$PROJECT_ROOT")
diff --git a/compiler/fir/analysis-tests/legacy-fir-tests/tests-gen/org/jetbrains/kotlin/fir/LazyBodyIsNotTouchedTilContractsPhaseTestGenerated.java b/compiler/fir/analysis-tests/legacy-fir-tests/tests-gen/org/jetbrains/kotlin/fir/LazyBodyIsNotTouchedTilContractsPhaseTestGenerated.java
index 4d07376ac64..a71c2e22c11 100644
--- a/compiler/fir/analysis-tests/legacy-fir-tests/tests-gen/org/jetbrains/kotlin/fir/LazyBodyIsNotTouchedTilContractsPhaseTestGenerated.java
+++ b/compiler/fir/analysis-tests/legacy-fir-tests/tests-gen/org/jetbrains/kotlin/fir/LazyBodyIsNotTouchedTilContractsPhaseTestGenerated.java
@@ -3139,6 +3139,16 @@ public class LazyBodyIsNotTouchedTilContractsPhaseTestGenerated extends Abstract
             runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastToTypeParameter.kt");
         }
 
+        @TestMetadata("smartcastsFromEquals_differentModule.kt")
+        public void testSmartcastsFromEquals_differentModule() throws Exception {
+            runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.kt");
+        }
+
+        @TestMetadata("smartcastsFromEquals_sameModule.kt")
+        public void testSmartcastsFromEquals_sameModule() throws Exception {
+            runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.kt");
+        }
+
         @TestMetadata("compiler/fir/analysis-tests/testData/resolve/smartcasts/booleans")
         @TestDataPath("$PROJECT_ROOT")
         @RunWith(JUnit3RunnerWithInners.class)
diff --git a/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.fir.txt b/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.fir.txt
new file mode 100644
index 00000000000..6dcf1dd39b3
--- /dev/null
+++ b/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.fir.txt
@@ -0,0 +1,96 @@
+Module: lib
+FILE: module_lib_smartcastsFromEquals_differentModule.kt
+    public final class Final<T> : R|kotlin/Any| {
+        public constructor<T>(): R|Final<T>| {
+            super<R|kotlin/Any|>()
+        }
+
+    }
+    public open class Base<T> : R|kotlin/Any| {
+        public constructor<T>(): R|Base<T>| {
+            super<R|kotlin/Any|>()
+        }
+
+    }
+    public final class Derived<T> : R|Base<T>| {
+        public constructor<T>(): R|Derived<T>| {
+            super<R|Base<T>|>()
+        }
+
+    }
+    public final class FinalWithOverride<T> : R|kotlin/Any| {
+        public constructor<T>(): R|FinalWithOverride<T>| {
+            super<R|kotlin/Any|>()
+        }
+
+        public final override operator fun equals(other: R|kotlin/Any?|): R|kotlin/Boolean| {
+            ^equals ===(this@R|/FinalWithOverride|, R|<local>/other|)
+        }
+
+    }
+Module: main
+FILE: module_main_smartcastsFromEquals_differentModule.kt
+    public final fun testFinal(x: R|Final<*>|, y: R|Final<kotlin/Int>|): R|kotlin/Unit| {
+        when () {
+            ==(R|<local>/x|, R|<local>/y|) ->  {
+                <Inapplicable(INAPPLICABLE): /takeIntFinal>#(R|<local>/x|)
+            }
+        }
+
+        when () {
+            ===(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntFinal|(R|<local>/x|)
+            }
+        }
+
+    }
+    public final fun testBase(x: R|Base<*>|, y: R|Base<kotlin/Int>|): R|kotlin/Unit| {
+        when () {
+            ==(R|<local>/x|, R|<local>/y|) ->  {
+                <Inapplicable(INAPPLICABLE): /takeIntBase>#(R|<local>/x|)
+            }
+        }
+
+        when () {
+            ===(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntBase|(R|<local>/x|)
+            }
+        }
+
+    }
+    public final fun testDerived(x: R|Derived<*>|, y: R|Derived<kotlin/Int>|): R|kotlin/Unit| {
+        when () {
+            ==(R|<local>/x|, R|<local>/y|) ->  {
+                <Inapplicable(INAPPLICABLE): /takeIntDerived>#(R|<local>/x|)
+            }
+        }
+
+        when () {
+            ===(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntDerived|(R|<local>/x|)
+            }
+        }
+
+    }
+    public final fun testFinalWithOverride(x: R|FinalWithOverride<*>|, y: R|FinalWithOverride<kotlin/Int>|): R|kotlin/Unit| {
+        when () {
+            ==(R|<local>/x|, R|<local>/y|) ->  {
+                <Inapplicable(INAPPLICABLE): /takeIntFinalWithOverride>#(R|<local>/x|)
+            }
+        }
+
+        when () {
+            ===(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntFinalWithOverride|(R|<local>/x|)
+            }
+        }
+
+    }
+    public final fun takeIntFinal(x: R|Final<kotlin/Int>|): R|kotlin/Unit| {
+    }
+    public final fun takeIntBase(x: R|Base<kotlin/Int>|): R|kotlin/Unit| {
+    }
+    public final fun takeIntDerived(x: R|Derived<kotlin/Int>|): R|kotlin/Unit| {
+    }
+    public final fun takeIntFinalWithOverride(x: R|FinalWithOverride<kotlin/Int>|): R|kotlin/Unit| {
+    }
diff --git a/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.kt b/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.kt
new file mode 100644
index 00000000000..e6c3e3c79e5
--- /dev/null
+++ b/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.kt
@@ -0,0 +1,60 @@
+// SKIP_JAVAC
+// This directive is needed to skip this test in LazyBodyIsNotTouchedTilContractsPhaseTestGenerated,
+//  because it fails to parse module structure of multimodule test
+// ISSUE: KT-49127
+
+// MODULE: lib
+class Final<T>
+
+open class Base<T>
+
+class Derived<T> : Base<T>()
+
+class FinalWithOverride<T> {
+    override fun equals(other: Any?): Boolean {
+        // some custom implementation
+        return this === other
+    }
+}
+
+// MODULE: main(lib)
+fun testFinal(x: Final<*>, y: Final<Int>) {
+    if (x == y) {
+        takeIntFinal(<!ARGUMENT_TYPE_MISMATCH!>x<!>) // Error
+    }
+    if (x === y) {
+        takeIntFinal(x) // OK
+    }
+}
+
+fun testBase(x: Base<*>, y: Base<Int>) {
+    if (x == y) {
+        takeIntBase(<!ARGUMENT_TYPE_MISMATCH!>x<!>) // Error
+    }
+    if (x === y) {
+        takeIntBase(x) // OK
+    }
+}
+
+fun testDerived(x: Derived<*>, y: Derived<Int>) {
+    if (x == y) {
+        takeIntDerived(<!ARGUMENT_TYPE_MISMATCH!>x<!>) // Error
+    }
+    if (x === y) {
+        takeIntDerived(x) // OK
+    }
+}
+
+fun testFinalWithOverride(x: FinalWithOverride<*>, y: FinalWithOverride<Int>) {
+    if (x == y) {
+        takeIntFinalWithOverride(<!ARGUMENT_TYPE_MISMATCH!>x<!>) // Error
+    }
+    if (x === y) {
+        takeIntFinalWithOverride(x) // OK
+    }
+}
+
+fun takeIntFinal(x: Final<Int>) {}
+fun takeIntBase(x: Base<Int>) {}
+fun takeIntDerived(x: Derived<Int>) {}
+fun takeIntFinalWithOverride(x: FinalWithOverride<Int>) {}
diff --git a/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.fir.txt b/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.fir.txt
new file mode 100644
index 00000000000..c786a6ec95d
--- /dev/null
+++ b/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.fir.txt
@@ -0,0 +1,93 @@
+FILE: smartcastsFromEquals_sameModule.kt
+    public final class Final<T> : R|kotlin/Any| {
+        public constructor<T>(): R|Final<T>| {
+            super<R|kotlin/Any|>()
+        }
+
+    }
+    public open class Base<T> : R|kotlin/Any| {
+        public constructor<T>(): R|Base<T>| {
+            super<R|kotlin/Any|>()
+        }
+
+    }
+    public final class Derived<T> : R|Base<T>| {
+        public constructor<T>(): R|Derived<T>| {
+            super<R|Base<T>|>()
+        }
+
+    }
+    public final class FinalWithOverride<T> : R|kotlin/Any| {
+        public constructor<T>(): R|FinalWithOverride<T>| {
+            super<R|kotlin/Any|>()
+        }
+
+        public final override operator fun equals(other: R|kotlin/Any?|): R|kotlin/Boolean| {
+            ^equals ===(this@R|/FinalWithOverride|, R|<local>/other|)
+        }
+
+    }
+    public final fun testFinal(x: R|Final<*>|, y: R|Final<kotlin/Int>|): R|kotlin/Unit| {
+        when () {
+            ==(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntFinal|(R|<local>/x|)
+            }
+        }
+
+        when () {
+            ===(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntFinal|(R|<local>/x|)
+            }
+        }
+
+    }
+    public final fun testBase(x: R|Base<*>|, y: R|Base<kotlin/Int>|): R|kotlin/Unit| {
+        when () {
+            ==(R|<local>/x|, R|<local>/y|) ->  {
+                <Inapplicable(INAPPLICABLE): /takeIntBase>#(R|<local>/x|)
+            }
+        }
+
+        when () {
+            ===(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntBase|(R|<local>/x|)
+            }
+        }
+
+    }
+    public final fun testDerived(x: R|Derived<*>|, y: R|Derived<kotlin/Int>|): R|kotlin/Unit| {
+        when () {
+            ==(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntDerived|(R|<local>/x|)
+            }
+        }
+
+        when () {
+            ===(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntDerived|(R|<local>/x|)
+            }
+        }
+
+    }
+    public final fun testFinalWithOverride(x: R|FinalWithOverride<*>|, y: R|FinalWithOverride<kotlin/Int>|): R|kotlin/Unit| {
+        when () {
+            ==(R|<local>/x|, R|<local>/y|) ->  {
+                <Inapplicable(INAPPLICABLE): /takeIntFinalWithOverride>#(R|<local>/x|)
+            }
+        }
+
+        when () {
+            ===(R|<local>/x|, R|<local>/y|) ->  {
+                R|/takeIntFinalWithOverride|(R|<local>/x|)
+            }
+        }
+
+    }
+    public final fun takeIntFinal(x: R|Final<kotlin/Int>|): R|kotlin/Unit| {
+    }
+    public final fun takeIntBase(x: R|Base<kotlin/Int>|): R|kotlin/Unit| {
+    }
+    public final fun takeIntDerived(x: R|Derived<kotlin/Int>|): R|kotlin/Unit| {
+    }
+    public final fun takeIntFinalWithOverride(x: R|FinalWithOverride<kotlin/Int>|): R|kotlin/Unit| {
+    }
diff --git a/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.kt b/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.kt
new file mode 100644
index 00000000000..12bf5d7aeb5
--- /dev/null
+++ b/compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.kt
@@ -0,0 +1,55 @@
+// ISSUE: KT-49127
+
+class Final<T>
+
+open class Base<T>
+
+class Derived<T> : Base<T>()
+
+class FinalWithOverride<T> {
+    override fun equals(other: Any?): Boolean {
+        // some custom implementation
+        return this === other
+    }
+}
+
+fun testFinal(x: Final<*>, y: Final<Int>) {
+    if (x == y) {
+        takeIntFinal(x) // OK
+    }
+    if (x === y) {
+        takeIntFinal(x) // OK
+    }
+}
+
+fun testBase(x: Base<*>, y: Base<Int>) {
+    if (x == y) {
+        takeIntBase(<!ARGUMENT_TYPE_MISMATCH!>x<!>) // Error
+    }
+    if (x === y) {
+        takeIntBase(x) // OK
+    }
+}
+
+fun testDerived(x: Derived<*>, y: Derived<Int>) {
+    if (x == y) {
+        takeIntDerived(x) // OK
+    }
+    if (x === y) {
+        takeIntDerived(x) // OK
+    }
+}
+
+fun testFinalWithOverride(x: FinalWithOverride<*>, y: FinalWithOverride<Int>) {
+    if (x == y) {
+        takeIntFinalWithOverride(<!ARGUMENT_TYPE_MISMATCH!>x<!>) // Error
+    }
+    if (x === y) {
+        takeIntFinalWithOverride(x) // OK
+    }
+}
+
+fun takeIntFinal(x: Final<Int>) {}
+fun takeIntBase(x: Base<Int>) {}
+fun takeIntDerived(x: Derived<Int>) {}
+fun takeIntFinalWithOverride(x: FinalWithOverride<Int>) {}
diff --git a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirDiagnosticTestGenerated.java b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirDiagnosticTestGenerated.java
index 0fcb1434f6a..13e40e6c944 100644
--- a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirDiagnosticTestGenerated.java
+++ b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirDiagnosticTestGenerated.java
@@ -3551,6 +3551,18 @@ public class FirDiagnosticTestGenerated extends AbstractFirDiagnosticTest {
                 runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastToTypeParameter.kt");
             }
 
+            @Test
+            @TestMetadata("smartcastsFromEquals_differentModule.kt")
+            public void testSmartcastsFromEquals_differentModule() throws Exception {
+                runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.kt");
+            }
+
+            @Test
+            @TestMetadata("smartcastsFromEquals_sameModule.kt")
+            public void testSmartcastsFromEquals_sameModule() throws Exception {
+                runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.kt");
+            }
+
             @Nested
             @TestMetadata("compiler/fir/analysis-tests/testData/resolve/smartcasts/booleans")
             @TestDataPath("$PROJECT_ROOT")
diff --git a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirDiagnosticsWithLightTreeTestGenerated.java b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirDiagnosticsWithLightTreeTestGenerated.java
index d0a7bf1ce69..8f3be700607 100644
--- a/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirDiagnosticsWithLightTreeTestGenerated.java
+++ b/compiler/fir/analysis-tests/tests-gen/org/jetbrains/kotlin/test/runners/FirDiagnosticsWithLightTreeTestGenerated.java
@@ -3551,6 +3551,18 @@ public class FirDiagnosticsWithLightTreeTestGenerated extends AbstractFirDiagnos
                 runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastToTypeParameter.kt");
             }
 
+            @Test
+            @TestMetadata("smartcastsFromEquals_differentModule.kt")
+            public void testSmartcastsFromEquals_differentModule() throws Exception {
+                runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_differentModule.kt");
+            }
+
+            @Test
+            @TestMetadata("smartcastsFromEquals_sameModule.kt")
+            public void testSmartcastsFromEquals_sameModule() throws Exception {
+                runTest("compiler/fir/analysis-tests/testData/resolve/smartcasts/smartcastsFromEquals_sameModule.kt");
+            }
+
             @Nested
             @TestMetadata("compiler/fir/analysis-tests/testData/resolve/smartcasts/booleans")
             @TestDataPath("$PROJECT_ROOT")
diff --git a/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/checkers/declaration/FirMethodOfAnyImplementedInInterfaceChecker.kt b/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/checkers/declaration/FirMethodOfAnyImplementedInInterfaceChecker.kt
index f1d8349ec3c..c72501ec5b0 100644
--- a/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/checkers/declaration/FirMethodOfAnyImplementedInInterfaceChecker.kt
+++ b/compiler/fir/checkers/src/org/jetbrains/kotlin/fir/analysis/checkers/declaration/FirMethodOfAnyImplementedInInterfaceChecker.kt
@@ -6,19 +6,19 @@
 package org.jetbrains.kotlin.fir.analysis.checkers.declaration
 
 import org.jetbrains.kotlin.builtins.StandardNames.HASHCODE_NAME
+import org.jetbrains.kotlin.diagnostics.DiagnosticReporter
+import org.jetbrains.kotlin.diagnostics.reportOn
 import org.jetbrains.kotlin.fir.analysis.checkers.FirDeclarationPresenter
 import org.jetbrains.kotlin.fir.analysis.checkers.context.CheckerContext
-import org.jetbrains.kotlin.diagnostics.DiagnosticReporter
 import org.jetbrains.kotlin.fir.analysis.diagnostics.FirErrors
-import org.jetbrains.kotlin.diagnostics.reportOn
 import org.jetbrains.kotlin.fir.analysis.diagnostics.withSuppressedDiagnostics
-import org.jetbrains.kotlin.fir.declarations.*
+import org.jetbrains.kotlin.fir.declarations.FirRegularClass
+import org.jetbrains.kotlin.fir.declarations.FirSimpleFunction
 import org.jetbrains.kotlin.fir.declarations.utils.hasBody
 import org.jetbrains.kotlin.fir.declarations.utils.isInterface
 import org.jetbrains.kotlin.fir.declarations.utils.isOverride
-import org.jetbrains.kotlin.fir.types.isNullableAny
+import org.jetbrains.kotlin.fir.resolve.isEquals
 import org.jetbrains.kotlin.name.CallableId
-import org.jetbrains.kotlin.util.OperatorNameConventions.EQUALS
 import org.jetbrains.kotlin.util.OperatorNameConventions.TO_STRING
 
 object FirMethodOfAnyImplementedInInterfaceChecker : FirRegularClassChecker(), FirDeclarationPresenter {
@@ -44,11 +44,8 @@ object FirMethodOfAnyImplementedInInterfaceChecker : FirRegularClassChecker(), F
                 (function.name == HASHCODE_NAME || function.name == TO_STRING)
             ) {
                 methodOfAny = true
-            } else {
-                val singleParameter = function.valueParameters.singleOrNull() ?: continue
-                if (singleParameter.returnTypeRef.isNullableAny && function.name == EQUALS) {
-                    methodOfAny = true
-                }
+            } else if (function.isEquals()) {
+                methodOfAny = true
             }
 
             if (methodOfAny) {
diff --git a/compiler/fir/providers/src/org/jetbrains/kotlin/fir/resolve/SupertypeUtils.kt b/compiler/fir/providers/src/org/jetbrains/kotlin/fir/resolve/SupertypeUtils.kt
index 6cebf2cf6fe..3e2faeb81a0 100644
--- a/compiler/fir/providers/src/org/jetbrains/kotlin/fir/resolve/SupertypeUtils.kt
+++ b/compiler/fir/providers/src/org/jetbrains/kotlin/fir/resolve/SupertypeUtils.kt
@@ -17,12 +17,14 @@ import org.jetbrains.kotlin.fir.resolve.substitution.ConeSubstitutor
 import org.jetbrains.kotlin.fir.resolve.substitution.ConeSubstitutorByMap
 import org.jetbrains.kotlin.fir.scopes.FirScope
 import org.jetbrains.kotlin.fir.scopes.FirTypeScope
+import org.jetbrains.kotlin.fir.symbols.ConeClassLikeLookupTag
 import org.jetbrains.kotlin.fir.symbols.ensureResolved
 import org.jetbrains.kotlin.fir.symbols.impl.*
 import org.jetbrains.kotlin.fir.types.*
 import org.jetbrains.kotlin.types.model.CaptureStatus
 import org.jetbrains.kotlin.utils.SmartList
 import org.jetbrains.kotlin.utils.SmartSet
+import org.jetbrains.kotlin.utils.addIfNotNull
 
 abstract class SupertypeSupplier {
     abstract fun forClass(firClass: FirClass, useSiteSession: FirSession): List<ConeClassLikeType>
@@ -44,6 +46,48 @@ abstract class SupertypeSupplier {
     }
 }
 
+fun collectSymbolsForType(type: ConeKotlinType, useSiteSession: FirSession): List<FirClassSymbol<*>> {
+    val lookupTags = mutableListOf<ConeClassLikeLookupTag>()
+
+    fun ConeKotlinType.collectClassIds() {
+        when (val unwrappedType = lowerBoundIfFlexible().fullyExpandedType(useSiteSession)) {
+            is ConeClassLikeType -> lookupTags.addIfNotNull(unwrappedType.lookupTag)
+            is ConeIntersectionType -> unwrappedType.intersectedTypes.forEach { it.collectClassIds() }
+            else -> {}
+        }
+    }
+
+    type.collectClassIds()
+    return lookupTags.mapNotNull { it.toSymbol(useSiteSession) as? FirClassSymbol<*> }
+}
+
+fun lookupSuperTypes(
+    type: ConeKotlinType,
+    lookupInterfaces: Boolean,
+    deep: Boolean,
+    useSiteSession: FirSession,
+    substituteTypes: Boolean,
+    supertypeSupplier: SupertypeSupplier = SupertypeSupplier.Default,
+): List<ConeClassLikeType> {
+    return lookupSuperTypes(collectSymbolsForType(type, useSiteSession), lookupInterfaces, deep, useSiteSession, substituteTypes, supertypeSupplier)
+}
+
+fun lookupSuperTypes(
+    symbols: List<FirClassifierSymbol<*>>,
+    lookupInterfaces: Boolean,
+    deep: Boolean,
+    useSiteSession: FirSession,
+    substituteTypes: Boolean,
+    supertypeSupplier: SupertypeSupplier = SupertypeSupplier.Default,
+): List<ConeClassLikeType> {
+    return SmartList<ConeClassLikeType>().also {
+        val visitedSymbols = SmartSet.create<FirClassifierSymbol<*>>()
+        for (symbol in symbols) {
+            symbol.collectSuperTypes(it, visitedSymbols, deep, lookupInterfaces, substituteTypes, useSiteSession, supertypeSupplier)
+        }
+    }
+}
+
 fun lookupSuperTypes(
     klass: FirClass,
     lookupInterfaces: Boolean,
diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/ResolveUtils.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/ResolveUtils.kt
index 42d884fc6bd..4fd22705353 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/ResolveUtils.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/ResolveUtils.kt
@@ -34,6 +34,7 @@ import org.jetbrains.kotlin.fir.resolve.dfa.FirDataFlowAnalyzer
 import org.jetbrains.kotlin.fir.resolve.dfa.PropertyStability
 import org.jetbrains.kotlin.fir.resolve.diagnostics.ConeUnresolvedNameError
 import org.jetbrains.kotlin.fir.resolve.providers.symbolProvider
+import org.jetbrains.kotlin.fir.resolve.transformers.ReturnTypeCalculator
 import org.jetbrains.kotlin.fir.resolve.transformers.body.resolve.resultType
 import org.jetbrains.kotlin.fir.scopes.impl.delegatedWrapperData
 import org.jetbrains.kotlin.fir.scopes.impl.importedFromObjectData
@@ -49,6 +50,7 @@ import org.jetbrains.kotlin.name.Name
 import org.jetbrains.kotlin.name.StandardClassIds
 import org.jetbrains.kotlin.resolve.ForbiddenNamedArgumentsTarget
 import org.jetbrains.kotlin.types.SmartcastStability
+import org.jetbrains.kotlin.util.OperatorNameConventions
 import org.jetbrains.kotlin.utils.addToStdlib.safeAs
 
 fun List<FirQualifierPart>.toTypeProjections(): Array<ConeTypeProjection> =
diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/dfa/FirDataFlowAnalyzer.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/dfa/FirDataFlowAnalyzer.kt
index 6e9a4d4c5a0..9a104625a92 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/dfa/FirDataFlowAnalyzer.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/dfa/FirDataFlowAnalyzer.kt
@@ -6,6 +6,7 @@
 package org.jetbrains.kotlin.fir.resolve.dfa
 
 import org.jetbrains.kotlin.config.LanguageFeature
+import org.jetbrains.kotlin.descriptors.Modality
 import org.jetbrains.kotlin.fir.*
 import org.jetbrains.kotlin.fir.contracts.FirResolvedContractDescription
 import org.jetbrains.kotlin.fir.contracts.description.ConeBooleanConstantReference
@@ -18,24 +19,23 @@ import org.jetbrains.kotlin.fir.declarations.utils.isLocal
 import org.jetbrains.kotlin.fir.expressions.*
 import org.jetbrains.kotlin.fir.references.FirControlFlowGraphReference
 import org.jetbrains.kotlin.fir.references.FirResolvedNamedReference
-import org.jetbrains.kotlin.fir.resolve.PersistentImplicitReceiverStack
-import org.jetbrains.kotlin.fir.resolve.ResolutionMode
+import org.jetbrains.kotlin.fir.resolve.*
 import org.jetbrains.kotlin.fir.resolve.dfa.cfg.*
 import org.jetbrains.kotlin.fir.resolve.dfa.contracts.buildContractFir
 import org.jetbrains.kotlin.fir.resolve.dfa.contracts.createArgumentsMapping
-import org.jetbrains.kotlin.fir.resolve.fullyExpandedType
 import org.jetbrains.kotlin.fir.resolve.substitution.ConeSubstitutor
 import org.jetbrains.kotlin.fir.resolve.substitution.ConeSubstitutorByMap
-import org.jetbrains.kotlin.fir.resolve.toSymbol
 import org.jetbrains.kotlin.fir.resolve.transformers.body.resolve.FirAbstractBodyResolveTransformer
 import org.jetbrains.kotlin.fir.resolve.transformers.body.resolve.resultType
+import org.jetbrains.kotlin.fir.scopes.getFunctions
+import org.jetbrains.kotlin.fir.scopes.impl.declaredMemberScope
 import org.jetbrains.kotlin.fir.symbols.FirBasedSymbol
-import org.jetbrains.kotlin.fir.symbols.impl.FirTypeParameterSymbol
-import org.jetbrains.kotlin.fir.symbols.impl.FirVariableSymbol
+import org.jetbrains.kotlin.fir.symbols.impl.*
 import org.jetbrains.kotlin.fir.types.*
 import org.jetbrains.kotlin.fir.visitors.transformSingle
 import org.jetbrains.kotlin.name.StandardClassIds
 import org.jetbrains.kotlin.types.ConstantValueKind
+import org.jetbrains.kotlin.util.OperatorNameConventions
 import org.jetbrains.kotlin.utils.addIfNotNull
 import org.jetbrains.kotlin.utils.addToStdlib.firstIsInstanceOrNull
 
@@ -570,9 +570,7 @@ abstract class FirDataFlowAnalyzer<FLOW : Flow>(
             rightIsNullable -> processEqNull(node, rightOperand, operation.invert(), ::shouldAddImplicationForStatement)
         }
 
-        if (operation == FirOperation.IDENTITY || operation == FirOperation.NOT_IDENTITY) {
-            processIdentity(node, leftOperand, rightOperand, operation)
-        }
+        processPossibleIdentity(node, leftOperand, rightOperand, operation)
     }
 
     /*
@@ -639,8 +637,11 @@ abstract class FirDataFlowAnalyzer<FLOW : Flow>(
         node.flow = flow
     }
 
-    private fun processIdentity(
-        node: EqualityOperatorCallNode, leftOperand: FirExpression, rightOperand: FirExpression, operation: FirOperation
+    private fun processPossibleIdentity(
+        node: EqualityOperatorCallNode,
+        leftOperand: FirExpression,
+        rightOperand: FirExpression,
+        operation: FirOperation,
     ) {
         val flow = node.flow
         val expressionVariable = variableStorage.getOrCreateVariable(node.previousFlow, node.fir)
@@ -648,6 +649,13 @@ abstract class FirDataFlowAnalyzer<FLOW : Flow>(
         val rightOperandVariable = variableStorage.getOrCreateVariable(node.previousFlow, rightOperand)
         val leftOperandType = leftOperand.coneType
         val rightOperandType = rightOperand.coneType
+
+        if (!leftOperandVariable.isReal() && !rightOperandVariable.isReal()) return
+
+        if (operation == FirOperation.EQ || operation == FirOperation.NOT_EQ) {
+            if (hasOverriddenEquals(leftOperandType)) return
+        }
+
         val isEq = operation.isEq()
 
         if (leftOperandVariable.isReal()) {
@@ -663,6 +671,40 @@ abstract class FirDataFlowAnalyzer<FLOW : Flow>(
         node.flow = flow
     }
 
+    private fun hasOverriddenEquals(type: ConeKotlinType): Boolean {
+        val session = components.session
+        val symbolsForType = collectSymbolsForType(type, session)
+        if (symbolsForType.any { it.hasEqualsOverride(session, checkModality = true) }) return true
+
+        val superTypes = lookupSuperTypes(
+            symbolsForType,
+            lookupInterfaces = false,
+            deep = true,
+            session,
+            substituteTypes = false
+        )
+        val superClassSymbols = superTypes.mapNotNull {
+            it.fullyExpandedType(session).toSymbol(session) as? FirRegularClassSymbol
+        }
+
+        return superClassSymbols.any { it.hasEqualsOverride(session, checkModality = false) }
+    }
+
+    private fun FirClassSymbol<*>.hasEqualsOverride(session: FirSession, checkModality: Boolean): Boolean {
+        val status = resolvedStatus
+        if (checkModality && status.modality != Modality.FINAL) return true
+        if (status.isExpect) return true
+        when (classId) {
+            StandardClassIds.Any, StandardClassIds.String -> return false
+        }
+        if (moduleData != session.moduleData) {
+            return true
+        }
+        return session.declaredMemberScope(this)
+            .getFunctions(OperatorNameConventions.EQUALS)
+            .any { it.fir.isEquals() }
+    }
+
     // ----------------------------------- Jump -----------------------------------
 
     fun exitJump(jump: FirJump<*>) {
diff --git a/compiler/fir/semantics/src/org/jetbrains/kotlin/fir/resolve/DeclarationUtils.kt b/compiler/fir/semantics/src/org/jetbrains/kotlin/fir/resolve/DeclarationUtils.kt
index 8f6043f25db..248bdda85e1 100644
--- a/compiler/fir/semantics/src/org/jetbrains/kotlin/fir/resolve/DeclarationUtils.kt
+++ b/compiler/fir/semantics/src/org/jetbrains/kotlin/fir/resolve/DeclarationUtils.kt
@@ -15,6 +15,7 @@ import org.jetbrains.kotlin.fir.symbols.impl.FirTypeParameterSymbol
 import org.jetbrains.kotlin.fir.symbols.impl.LookupTagInternals
 import org.jetbrains.kotlin.fir.types.*
 import org.jetbrains.kotlin.name.ClassId
+import org.jetbrains.kotlin.util.OperatorNameConventions
 
 fun FirClassLikeDeclaration.getContainingDeclaration(session: FirSession): FirClassLikeDeclaration? {
     if (isLocal) {
@@ -86,3 +87,10 @@ var FirConstructor.originalConstructorIfTypeAlias: FirConstructor? by FirDeclara
 
 val FirConstructorSymbol.isTypeAliasedConstructor: Boolean
     get() = fir.originalConstructorIfTypeAlias != null
+
+fun FirSimpleFunction.isEquals(): Boolean {
+    if (name != OperatorNameConventions.EQUALS) return false
+    if (valueParameters.size != 1) return false
+    val parameter = valueParameters.first()
+    return parameter.returnTypeRef.isNullableAny
+}
diff --git a/compiler/testData/diagnostics/tests/smartCasts/fakeSmartCastOnEquality.fir.kt b/compiler/testData/diagnostics/tests/smartCasts/fakeSmartCastOnEquality.fir.kt
index 278a5576dbc..aa3f520c669 100644
--- a/compiler/testData/diagnostics/tests/smartCasts/fakeSmartCastOnEquality.fir.kt
+++ b/compiler/testData/diagnostics/tests/smartCasts/fakeSmartCastOnEquality.fir.kt
@@ -34,11 +34,11 @@ fun foo(x: FinalClass?, y: Any) {
         // OK
         x.hashCode()
         // OK
-        y.<!UNRESOLVED_REFERENCE!>use<!>()
+        y.use()
     }
     when (x) {
         // OK (equals from FinalClass)
-        y -> y.<!UNRESOLVED_REFERENCE!>use<!>()
+        y -> y.use()
     }
     when (y) {
         // ERROR (equals from Any)
@@ -92,4 +92,4 @@ sealed class Sealed {
             <!UNRESOLVED_REFERENCE!>gav<!>()
         }
     }
-}
\ No newline at end of file
+}
diff --git a/compiler/tests-spec/testData/diagnostics/notLinked/dfa/neg/1.fir.kt b/compiler/tests-spec/testData/diagnostics/notLinked/dfa/neg/1.fir.kt
index 1bb1e638156..4d3815eb1cd 100644
--- a/compiler/tests-spec/testData/diagnostics/notLinked/dfa/neg/1.fir.kt
+++ b/compiler/tests-spec/testData/diagnostics/notLinked/dfa/neg/1.fir.kt
@@ -181,11 +181,11 @@ fun case_12(x: TypealiasNullableStringIndirect, y: TypealiasNullableStringIndire
 
 // TESTCASE NUMBER: 13
 fun case_13(x: <!UNRESOLVED_REFERENCE!>otherpackage.Case13<!>?) =
-    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>if ((x == null !is Boolean) !== true) {
+    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Boolean")!>if ((x == null !is Boolean) !== true) {
         throw Exception()
     } else {
-        <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Symbol not found for otherpackage.Case13?")!>x<!>
-        <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Symbol not found for otherpackage.Case13?")!>x<!>.<!OVERLOAD_RESOLUTION_AMBIGUITY!>equals<!>(x)
+        <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Symbol not found for otherpackage.Case13? & kotlin.Boolean & ERROR CLASS: Symbol not found for otherpackage.Case13?")!>x<!>
+        <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Symbol not found for otherpackage.Case13? & kotlin.Boolean & ERROR CLASS: Symbol not found for otherpackage.Case13?")!>x<!>.equals(x)
     }<!>
 
 // TESTCASE NUMBER: 14
diff --git a/compiler/tests-spec/testData/diagnostics/notLinked/dfa/pos/6.fir.kt b/compiler/tests-spec/testData/diagnostics/notLinked/dfa/pos/6.fir.kt
index dbaa694dcef..af94732476e 100644
--- a/compiler/tests-spec/testData/diagnostics/notLinked/dfa/pos/6.fir.kt
+++ b/compiler/tests-spec/testData/diagnostics/notLinked/dfa/pos/6.fir.kt
@@ -203,7 +203,7 @@ fun case_11(x: TypealiasNullableString<!REDUNDANT_NULLABLE!>?<!>, y: TypealiasNu
     } else {
         if (y != z) {
             if (nullableStringProperty == z) {
-                if (u != z || u != v) {
+                if (u != z || <!SENSELESS_COMPARISON!>u != v<!>) {
                     <!DEBUG_INFO_EXPRESSION_TYPE("TypealiasNullableString?")!>x<!>
                     <!DEBUG_INFO_EXPRESSION_TYPE("TypealiasNullableString?")!>x<!>.equals(null)
                     <!DEBUG_INFO_EXPRESSION_TYPE("TypealiasNullableString?")!>x<!>.propT
@@ -790,7 +790,7 @@ fun case_42() {
 fun case_43(x: TypealiasNullableString) {
     val z = null
 
-    if (x == z && <!DEBUG_INFO_EXPRESSION_TYPE("TypealiasNullableString")!>x<!> == z) {
+    if (x == z && <!SENSELESS_COMPARISON!><!DEBUG_INFO_EXPRESSION_TYPE("TypealiasNullableString & kotlin.Nothing?")!>x<!> == z<!>) {
         <!DEBUG_INFO_EXPRESSION_TYPE("TypealiasNullableString")!>x<!>
         <!DEBUG_INFO_EXPRESSION_TYPE("TypealiasNullableString")!>x<!>.hashCode()
     }