diff --git a/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsSmokeTestGenerated.java b/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsSmokeTestGenerated.java
index ff572170599..0039fda0d40 100644
--- a/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsSmokeTestGenerated.java
+++ b/compiler/fir/resolve/tests/org/jetbrains/kotlin/fir/FirDiagnosticsSmokeTestGenerated.java
@@ -2393,6 +2393,11 @@ public class FirDiagnosticsSmokeTestGenerated extends AbstractFirDiagnosticsSmok
                 runTest("compiler/testData/diagnostics/tests/callableReference/resolve/overloadsMember.kt");
             }
 
+            @TestMetadata("resolveEqualsOperatorWithAnyExpectedType.kt")
+            public void testResolveEqualsOperatorWithAnyExpectedType() throws Exception {
+                runTest("compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.kt");
+            }
+
             @TestMetadata("valVsFun.kt")
             public void testValVsFun() throws Exception {
                 runTest("compiler/testData/diagnostics/tests/callableReference/resolve/valVsFun.kt");
diff --git a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/components/KotlinCallCompleter.kt b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/components/KotlinCallCompleter.kt
index 9c617f26115..6e64372e8a5 100644
--- a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/components/KotlinCallCompleter.kt
+++ b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/components/KotlinCallCompleter.kt
@@ -201,9 +201,8 @@ class KotlinCallCompleter(
         val variableWithConstraints = csBuilder.currentStorage().notFixedTypeVariables[constructor] ?: return false
         val constraints = variableWithConstraints.constraints
         return constraints.isNotEmpty() && constraints.all {
-            !trivialConstraintTypeInferenceOracle.isTrivialConstraint(it) &&
-                    with(context) { !it.type.typeConstructor().isIntegerLiteralTypeConstructor() } &&
-                    it.kind.isLower() && csBuilder.isProperType(it.type)
+                with(context) { !it.type.typeConstructor().isIntegerLiteralTypeConstructor() } &&
+                it.kind.isLower() && csBuilder.isProperType(it.type)
         }
 
     }
diff --git a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/ConstraintIncorporator.kt b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/ConstraintIncorporator.kt
index d0e786dd390..de3912a009e 100644
--- a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/ConstraintIncorporator.kt
+++ b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/ConstraintIncorporator.kt
@@ -156,13 +156,19 @@ class ConstraintIncorporator(
 
         if (baseConstraint.kind != ConstraintKind.UPPER) {
             val generatedConstraintType = approximateCapturedTypes(typeForApproximation, toSuper = false)
-            if (!trivialConstraintTypeInferenceOracle.isGeneratedConstraintTrivial(otherConstraint, generatedConstraintType)) {
+            if (!trivialConstraintTypeInferenceOracle.isGeneratedConstraintTrivial(
+                    otherConstraint, generatedConstraintType, isSubtype = true
+                )
+            ) {
                 addNewIncorporatedConstraint(generatedConstraintType, targetVariable.defaultType())
             }
         }
         if (baseConstraint.kind != ConstraintKind.LOWER) {
             val generatedConstraintType = approximateCapturedTypes(typeForApproximation, toSuper = true)
-            if (!trivialConstraintTypeInferenceOracle.isGeneratedConstraintTrivial(otherConstraint, generatedConstraintType)) {
+            if (!trivialConstraintTypeInferenceOracle.isGeneratedConstraintTrivial(
+                    otherConstraint, generatedConstraintType, isSubtype = false
+                )
+            ) {
                 addNewIncorporatedConstraint(targetVariable.defaultType(), generatedConstraintType)
             }
         }
diff --git a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/ConstraintInjector.kt b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/ConstraintInjector.kt
index aec7bbb85b9..219ac5631bd 100644
--- a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/ConstraintInjector.kt
+++ b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/ConstraintInjector.kt
@@ -101,7 +101,11 @@ class ConstraintInjector(val constraintIncorporator: ConstraintIncorporator, val
         }
 
         if (constraintType.isSimpleType()) {
-            if (constraint.kind == UPPER && constraintType.isNullableAny()) return true // T <: Any?
+            if (constraint.position.from is DeclaredUpperBoundConstraintPosition &&
+                constraint.kind == UPPER && constraintType.isNullableAny()
+            ) {
+                return true // T <: Any?
+            }
         }
 
         return false
diff --git a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/TrivialConstraintTypeInferenceOracle.kt b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/TrivialConstraintTypeInferenceOracle.kt
index 853a8aaedd5..024bb92c860 100644
--- a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/TrivialConstraintTypeInferenceOracle.kt
+++ b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/TrivialConstraintTypeInferenceOracle.kt
@@ -7,19 +7,19 @@ package org.jetbrains.kotlin.resolve.calls.inference.components
 
 import org.jetbrains.kotlin.resolve.calls.inference.model.Constraint
 import org.jetbrains.kotlin.resolve.calls.inference.model.ConstraintKind
+import org.jetbrains.kotlin.resolve.calls.inference.model.NewTypeVariable
+import org.jetbrains.kotlin.types.UnwrappedType
 import org.jetbrains.kotlin.types.model.KotlinTypeMarker
-import org.jetbrains.kotlin.types.model.TypeSystemInferenceExtensionContext
-import org.jetbrains.kotlin.types.model.TypeSystemInferenceExtensionContextDelegate
+import org.jetbrains.kotlin.types.typeUtil.contains
+import org.jetbrains.kotlin.types.typeUtil.isNothing
+import org.jetbrains.kotlin.types.typeUtil.isNullableNothing
 
 class TrivialConstraintTypeInferenceOracle(context: TypeSystemInferenceExtensionContextDelegate) :
     TypeSystemInferenceExtensionContext by context {
     // The idea is to add knowledge that constraint `Nothing(?) <: T` is quite useless and
     // it's totally fine to go and resolve postponed argument without fixation T to Nothing(?).
     // In other words, constraint `Nothing(?) <: T` is *not* proper
-    fun isTrivialConstraint(
-        constraint: Constraint
-    ): Boolean {
-        // TODO: probably we also can take into account `T <: Any(?)` constraints
+    fun isNotInterestingConstraint(constraint: Constraint): Boolean {
         return constraint.kind == ConstraintKind.LOWER && constraint.type.typeConstructor().isNothingConstructor()
     }
 
@@ -39,9 +39,11 @@ class TrivialConstraintTypeInferenceOracle(context: TypeSystemInferenceExtension
     // Therefore, here we avoid adding such trivial constraints to have stable constraint system
     fun isGeneratedConstraintTrivial(
         otherConstraint: Constraint,
-        generatedConstraintType: KotlinTypeMarker
+        generatedConstraintType: KotlinTypeMarker,
+        isSubtype: Boolean
     ): Boolean {
-        if (generatedConstraintType.isNothing()) return true
+        if (isSubtype && generatedConstraintType.isNothing()) return true
+        if (!isSubtype && generatedConstraintType.isNullableAny()) return true
 
         // If type that will be used to generate new constraint already contains `Nothing(?)`,
         // then we can't decide that resulting constraint will be useless
diff --git a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/VariableFixationFinder.kt b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/VariableFixationFinder.kt
index f37cdfa03b3..49c08abd48f 100644
--- a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/VariableFixationFinder.kt
+++ b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/components/VariableFixationFinder.kt
@@ -107,7 +107,7 @@ class VariableFixationFinder(
     private fun Context.variableHasTrivialOrNonProperConstraints(variable: TypeConstructorMarker): Boolean {
         return notFixedTypeVariables[variable]?.constraints?.all { constraint ->
             val isProperConstraint = isProperArgumentConstraint(constraint)
-            isProperConstraint && trivialConstraintTypeInferenceOracle.isTrivialConstraint(constraint) || !isProperConstraint
+            isProperConstraint && trivialConstraintTypeInferenceOracle.isNotInterestingConstraint(constraint) || !isProperConstraint
         } ?: false
     }
 
diff --git a/compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.kt b/compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.kt
new file mode 100644
index 00000000000..5a9c7237ffb
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.kt
@@ -0,0 +1,11 @@
+// !LANGUAGE: +NewInference
+
+interface Base
+
+fun <K> materialize(): K = TODO()
+
+fun <T : Base> Base.transform(): T = materialize()
+
+fun test(child: Base) {
+    child == child.transform()
+}
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.txt b/compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.txt
new file mode 100644
index 00000000000..f45cacf7c43
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.txt
@@ -0,0 +1,11 @@
+package
+
+public fun </*0*/ K> materialize(): K
+public fun test(/*0*/ child: Base): kotlin.Unit
+public fun </*0*/ T : Base> Base.transform(): T
+
+public interface Base {
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
diff --git a/compiler/testData/diagnostics/tests/dataFlowInfoTraversal/BinaryExpression.kt b/compiler/testData/diagnostics/tests/dataFlowInfoTraversal/BinaryExpression.kt
index 46ae3651bf0..48408d23083 100644
--- a/compiler/testData/diagnostics/tests/dataFlowInfoTraversal/BinaryExpression.kt
+++ b/compiler/testData/diagnostics/tests/dataFlowInfoTraversal/BinaryExpression.kt
@@ -6,6 +6,6 @@ fun foo() {
     val x: Int? = null
 
     bar(1 + (if (x == null) 0 else x))
-    bar(<!NI;TYPE_MISMATCH!>if (x == null) <!DEBUG_INFO_CONSTANT, NI;TYPE_MISMATCH, NI;TYPE_MISMATCH, OI;TYPE_MISMATCH!>x<!> else x<!>)
+    bar(<!NI;TYPE_MISMATCH!>if (x == null) <!DEBUG_INFO_CONSTANT, OI;TYPE_MISMATCH!>x<!> else x<!>)
     if (x != null) bar(x + x/(x-x*x))
 }
diff --git a/compiler/testData/diagnostics/tests/dataFlowInfoTraversal/ExclExcl.kt b/compiler/testData/diagnostics/tests/dataFlowInfoTraversal/ExclExcl.kt
index 4499a4f5fe8..317f7af809c 100644
--- a/compiler/testData/diagnostics/tests/dataFlowInfoTraversal/ExclExcl.kt
+++ b/compiler/testData/diagnostics/tests/dataFlowInfoTraversal/ExclExcl.kt
@@ -4,7 +4,7 @@ fun bar(x: Int) = x + 1
 fun f1(x: Int?) {
     bar(<!TYPE_MISMATCH!>x<!>)
     if (x != null) bar(x<!UNNECESSARY_NOT_NULL_ASSERTION!>!!<!>)
-    if (x == null) <!OI;UNREACHABLE_CODE!>bar(<!><!ALWAYS_NULL!>x<!>!!<!OI;UNREACHABLE_CODE!>)<!>
+    if (x == null) <!UNREACHABLE_CODE!>bar(<!><!ALWAYS_NULL!>x<!>!!<!UNREACHABLE_CODE!>)<!>
 }
 
 fun f2(x: Int?) {    
diff --git a/compiler/testData/diagnostics/tests/delegatedProperty/inference/differentDelegatedExpressions.kt b/compiler/testData/diagnostics/tests/delegatedProperty/inference/differentDelegatedExpressions.kt
index ddf52904c36..3b587e9a4c0 100644
--- a/compiler/testData/diagnostics/tests/delegatedProperty/inference/differentDelegatedExpressions.kt
+++ b/compiler/testData/diagnostics/tests/delegatedProperty/inference/differentDelegatedExpressions.kt
@@ -13,7 +13,7 @@ class A(outer: Outer) {
     var b: String by  foo(<!OI;TYPE_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>getMyProperty<!>())
     var r: String by  foo(outer.getContainer().<!OI;TYPE_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>getMyProperty<!>())
     var e: String by  <!NI;DELEGATE_SPECIAL_FUNCTION_NONE_APPLICABLE, NI;TYPE_MISMATCH!><!OI;DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>+<!> <!OI;TYPE_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>foo<!>(<!OI;TYPE_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>getMyProperty<!>())<!>
-    var f: String by  <!NI;TYPE_MISMATCH!><!OI;TYPE_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>foo<!>(<!OI;TYPE_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>getMyProperty<!>()) <!OI;DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>-<!> 1<!>
+    var f: String by  <!NI;DELEGATE_SPECIAL_FUNCTION_NONE_APPLICABLE, NI;TYPE_MISMATCH!><!OI;TYPE_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>foo<!>(<!OI;TYPE_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>getMyProperty<!>()) <!OI;DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>-<!> 1<!>
 }
 
 fun <A, B> foo(<!UNUSED_PARAMETER!>a<!>: Any?) = MyProperty<A, B>()
diff --git a/compiler/testData/diagnostics/tests/nullabilityAndSmartCasts/kt2164.kt b/compiler/testData/diagnostics/tests/nullabilityAndSmartCasts/kt2164.kt
index 0b4f9a7dc02..50032992b3a 100644
--- a/compiler/testData/diagnostics/tests/nullabilityAndSmartCasts/kt2164.kt
+++ b/compiler/testData/diagnostics/tests/nullabilityAndSmartCasts/kt2164.kt
@@ -23,8 +23,8 @@ fun main() {
         foo(<!DEBUG_INFO_SMARTCAST!>x<!>)
     } else {
         foo(<!DEBUG_INFO_CONSTANT, TYPE_MISMATCH!>x<!>)
-        <!OI;UNREACHABLE_CODE!>foo(<!><!ALWAYS_NULL!>x<!>!!<!OI;UNREACHABLE_CODE!>)<!>
-        <!OI;UNREACHABLE_CODE!>foo(<!DEBUG_INFO_SMARTCAST!>x<!>)<!>
+        <!UNREACHABLE_CODE!>foo(<!><!ALWAYS_NULL!>x<!>!!<!UNREACHABLE_CODE!>)<!>
+        <!UNREACHABLE_CODE!>foo(<!DEBUG_INFO_SMARTCAST!>x<!>)<!>
     }
 
     foo(<!DEBUG_INFO_SMARTCAST!>x<!>)
diff --git a/compiler/testData/diagnostics/tests/overload/defaultParameters.kt b/compiler/testData/diagnostics/tests/overload/defaultParameters.kt
index a3ef5a4614c..abc3d7231bc 100644
--- a/compiler/testData/diagnostics/tests/overload/defaultParameters.kt
+++ b/compiler/testData/diagnostics/tests/overload/defaultParameters.kt
@@ -55,5 +55,5 @@ fun test() {
 
     withGenericDefaults("")
 
-    <!OI;UNREACHABLE_CODE!><!OVERLOAD_RESOLUTION_AMBIGUITY!>wrong<!>(<!>null!!<!OI;UNREACHABLE_CODE!>)<!>
+    <!UNREACHABLE_CODE!><!OVERLOAD_RESOLUTION_AMBIGUITY!>wrong<!>(<!>null!!<!UNREACHABLE_CODE!>)<!>
 }
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/resolve/specialConstructions/reportTypeMismatchDeeplyOnBranches.kt b/compiler/testData/diagnostics/tests/resolve/specialConstructions/reportTypeMismatchDeeplyOnBranches.kt
index cce34aa4cca..dc507807c72 100644
--- a/compiler/testData/diagnostics/tests/resolve/specialConstructions/reportTypeMismatchDeeplyOnBranches.kt
+++ b/compiler/testData/diagnostics/tests/resolve/specialConstructions/reportTypeMismatchDeeplyOnBranches.kt
@@ -8,15 +8,15 @@ fun test(a: Int?, b: Int?) {
 }
 
 fun test(a: Int?, b: Int?, c: Int?) {
-    bar(<!NI;TYPE_MISMATCH, NI;TYPE_MISMATCH!>if (a == null) return else if (b == null) return else <!OI;TYPE_MISMATCH!>c<!><!>)
+    bar(<!NI;TYPE_MISMATCH!>if (a == null) return else if (b == null) return else <!OI;TYPE_MISMATCH!>c<!><!>)
 }
 
 fun test(a: Any?, b: Any?, c: Int?) {
-    bar(<!NI;TYPE_MISMATCH, NI;TYPE_MISMATCH!>if (a == null) if (b == null) <!OI;TYPE_MISMATCH!>c<!> else return else return<!>)
+    bar(<!NI;TYPE_MISMATCH!>if (a == null) if (b == null) <!OI;TYPE_MISMATCH!>c<!> else return else return<!>)
 }
 
 fun test(a: Int?, b: Any?, c: Int?) {
-    bar(<!NI;TYPE_MISMATCH, NI;TYPE_MISMATCH!>if (a == null) {
+    bar(<!NI;TYPE_MISMATCH!>if (a == null) {
         return
     } else {
         if (b == null) {
diff --git a/compiler/testData/diagnostics/tests/when/kt9972.kt b/compiler/testData/diagnostics/tests/when/kt9972.kt
index c2a485d038c..814813cabeb 100644
--- a/compiler/testData/diagnostics/tests/when/kt9972.kt
+++ b/compiler/testData/diagnostics/tests/when/kt9972.kt
@@ -1,6 +1,6 @@
 // !WITH_NEW_INFERENCE
 fun test1(): Int {
-    val x: String = <!NI;TYPE_MISMATCH, NI;TYPE_MISMATCH, NI;TYPE_MISMATCH, NI;TYPE_MISMATCH!>if (true) {
+    val x: String = <!NI;TYPE_MISMATCH!>if (true) {
         when {
             true -> <!OI;TYPE_MISMATCH!>Any()<!>
             else -> <!OI;NULL_FOR_NONNULL_TYPE!>null<!>
@@ -10,7 +10,7 @@ fun test1(): Int {
 }
 
 fun test2(): Int {
-    val x: String = <!NI;TYPE_MISMATCH, NI;TYPE_MISMATCH!>when {
+    val x: String = <!NI;TYPE_MISMATCH!>when {
                         true -> <!OI;TYPE_MISMATCH!>Any()<!>
                         else -> null
                     } ?: return 0<!>
diff --git a/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java b/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
index 2d4eb02f5e0..5a4a4fcafa6 100644
--- a/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
+++ b/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
@@ -2400,6 +2400,11 @@ public class DiagnosticsTestGenerated extends AbstractDiagnosticsTest {
                     runTest("compiler/testData/diagnostics/tests/callableReference/resolve/overloadsMember.kt");
                 }
 
+                @TestMetadata("resolveEqualsOperatorWithAnyExpectedType.kt")
+                public void testResolveEqualsOperatorWithAnyExpectedType() throws Exception {
+                    runTest("compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.kt");
+                }
+
                 @TestMetadata("valVsFun.kt")
                 public void testValVsFun() throws Exception {
                     runTest("compiler/testData/diagnostics/tests/callableReference/resolve/valVsFun.kt");
diff --git a/compiler/tests/org/jetbrains/kotlin/checkers/javac/DiagnosticsUsingJavacTestGenerated.java b/compiler/tests/org/jetbrains/kotlin/checkers/javac/DiagnosticsUsingJavacTestGenerated.java
index 17d5a3063cd..0e96e8e1284 100644
--- a/compiler/tests/org/jetbrains/kotlin/checkers/javac/DiagnosticsUsingJavacTestGenerated.java
+++ b/compiler/tests/org/jetbrains/kotlin/checkers/javac/DiagnosticsUsingJavacTestGenerated.java
@@ -2395,6 +2395,11 @@ public class DiagnosticsUsingJavacTestGenerated extends AbstractDiagnosticsUsing
                     runTest("compiler/testData/diagnostics/tests/callableReference/resolve/overloadsMember.kt");
                 }
 
+                @TestMetadata("resolveEqualsOperatorWithAnyExpectedType.kt")
+                public void testResolveEqualsOperatorWithAnyExpectedType() throws Exception {
+                    runTest("compiler/testData/diagnostics/tests/callableReference/resolve/resolveEqualsOperatorWithAnyExpectedType.kt");
+                }
+
                 @TestMetadata("valVsFun.kt")
                 public void testValVsFun() throws Exception {
                     runTest("compiler/testData/diagnostics/tests/callableReference/resolve/valVsFun.kt");