diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/calls/ConeInferenceContext.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/calls/ConeInferenceContext.kt
index 8855c11fecf..6790fd4748f 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/calls/ConeInferenceContext.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/calls/ConeInferenceContext.kt
@@ -40,10 +40,6 @@ interface ConeInferenceContext : TypeSystemInferenceExtensionContext,
         return StandardClassIds.Nothing(symbolProvider).constructType(emptyArray(), false)
     }
 
-    override fun anyType(): SimpleTypeMarker {
-        return StandardClassIds.Any(symbolProvider).constructType(emptyArray(), false)
-    }
-
     override fun createFlexibleType(lowerBound: SimpleTypeMarker, upperBound: SimpleTypeMarker): KotlinTypeMarker {
         require(lowerBound is ConeKotlinType)
         require(upperBound is ConeKotlinType)
diff --git a/compiler/frontend/src/org/jetbrains/kotlin/resolve/calls/DiagnosticReporterByTrackingStrategy.kt b/compiler/frontend/src/org/jetbrains/kotlin/resolve/calls/DiagnosticReporterByTrackingStrategy.kt
index 2d6a3880fce..a630395347a 100644
--- a/compiler/frontend/src/org/jetbrains/kotlin/resolve/calls/DiagnosticReporterByTrackingStrategy.kt
+++ b/compiler/frontend/src/org/jetbrains/kotlin/resolve/calls/DiagnosticReporterByTrackingStrategy.kt
@@ -135,7 +135,7 @@ class DiagnosticReporterByTrackingStrategy(
                 require(diagnostic is ArgumentTypeMismatchDiagnostic)
                 reportIfNonNull(callArgument.safeAs<PSIKotlinCallArgument>()?.valueArgument?.getArgumentExpression()) {
                     if (it.isNull()) {
-                        trace.reportDiagnosticOnce(NULL_FOR_NONNULL_TYPE.on(it, diagnostic.expectedType))
+                        trace.report(NULL_FOR_NONNULL_TYPE.on(it, diagnostic.expectedType))
                     } else {
                         trace.report(TYPE_MISMATCH.on(it, diagnostic.expectedType, diagnostic.actualType))
                     }
diff --git a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/components/SimpleArgumentsChecks.kt b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/components/SimpleArgumentsChecks.kt
index b2801012180..6b7f00d384a 100644
--- a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/components/SimpleArgumentsChecks.kt
+++ b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/components/SimpleArgumentsChecks.kt
@@ -25,7 +25,6 @@ import org.jetbrains.kotlin.resolve.calls.inference.model.ArgumentConstraintPosi
 import org.jetbrains.kotlin.resolve.calls.inference.model.ConstraintPosition
 import org.jetbrains.kotlin.resolve.calls.inference.model.ReceiverConstraintPosition
 import org.jetbrains.kotlin.resolve.calls.model.*
-import org.jetbrains.kotlin.types.NotNullTypeVariable
 import org.jetbrains.kotlin.types.UnwrappedType
 import org.jetbrains.kotlin.types.checker.captureFromExpression
 import org.jetbrains.kotlin.types.checker.hasSupertypeWithGivenTypeConstructor
@@ -82,20 +81,6 @@ private fun checkExpressionArgument(
 
     val expectedNullableType = expectedType.makeNullableAsSpecified(true)
     val position = if (isReceiver) ReceiverConstraintPosition(expressionArgument) else ArgumentConstraintPosition(expressionArgument)
-
-    // Used only for arguments with @NotNull annotation
-    if (expectedType is NotNullTypeVariable) {
-        var expectedTypeIsNull: Boolean = false
-        csBuilder.runTransaction {
-            addNotNullUpperConstraint(argumentType, position)
-            expectedTypeIsNull = hasContradiction
-            false
-        }
-        if (expectedTypeIsNull) {
-            diagnosticsHolder.addDiagnostic(ArgumentTypeMismatchDiagnostic(expectedType, argumentType, expressionArgument))
-        }
-    }
-
     if (expressionArgument.isSafeCall) {
         if (!csBuilder.addSubtypeConstraintIfCompatible(argumentType, expectedNullableType, position)) {
             diagnosticsHolder.addDiagnosticIfNotNull(
diff --git a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/ConstraintSystemBuilder.kt b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/ConstraintSystemBuilder.kt
index 6657838e332..71cf58dd8d5 100644
--- a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/ConstraintSystemBuilder.kt
+++ b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/ConstraintSystemBuilder.kt
@@ -40,8 +40,6 @@ interface ConstraintSystemOperation {
     fun isPostponedTypeVariable(typeVariable: TypeVariableMarker): Boolean
 
     fun getProperSuperTypeConstructors(type: KotlinTypeMarker): List<TypeConstructorMarker>
-
-    fun addNotNullUpperConstraint(type: KotlinTypeMarker, position: ConstraintPosition)
 }
 
 interface ConstraintSystemBuilder : ConstraintSystemOperation {
diff --git a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/model/NewConstraintSystemImpl.kt b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/model/NewConstraintSystemImpl.kt
index f0063d8e613..379b4084f64 100644
--- a/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/model/NewConstraintSystemImpl.kt
+++ b/compiler/resolution/src/org/jetbrains/kotlin/resolve/calls/inference/model/NewConstraintSystemImpl.kt
@@ -302,8 +302,4 @@ class NewConstraintSystemImpl(
 
         return constraints.any { (it.kind == ConstraintKind.UPPER || it.kind == ConstraintKind.EQUALITY) && it.type.isUnit() }
     }
-
-    override fun addNotNullUpperConstraint(type: KotlinTypeMarker, position: ConstraintPosition) {
-        addSubtypeConstraint(type, anyType(), position)
-    }
 }
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/generics/projectionsScope/starNullabilityRecursive.kt b/compiler/testData/diagnostics/tests/generics/projectionsScope/starNullabilityRecursive.kt
index 7a5f0dc7fdd..7cc339fe377 100644
--- a/compiler/testData/diagnostics/tests/generics/projectionsScope/starNullabilityRecursive.kt
+++ b/compiler/testData/diagnostics/tests/generics/projectionsScope/starNullabilityRecursive.kt
@@ -5,5 +5,6 @@ interface A<T : A<T?>?> {
     fun foo(): T?
 }
 fun testA(a: A<*>) {
-    a.foo() checkType { _<A<*>?>() }
+    // in new inference here we have A<A<A<*>>>
+    a.foo() checkType { <!NI;DEBUG_INFO_UNRESOLVED_WITH_TARGET, NI;UNRESOLVED_REFERENCE_WRONG_RECEIVER!>_<!><A<*>?>() }
 }
diff --git a/compiler/testData/diagnostics/tests/j+k/sam/enhancedSamConstructor.kt b/compiler/testData/diagnostics/tests/j+k/sam/enhancedSamConstructor.kt
index b08bed6f734..940d1900a42 100644
--- a/compiler/testData/diagnostics/tests/j+k/sam/enhancedSamConstructor.kt
+++ b/compiler/testData/diagnostics/tests/j+k/sam/enhancedSamConstructor.kt
@@ -18,11 +18,11 @@ public interface J2 extends J {
 fun main() {
     J <!NI;TYPE_MISMATCH!>{ <!EXPECTED_PARAMETER_TYPE_MISMATCH!>s: String<!> -> s}<!> // should be prohibited, because SAM value parameter has nullable type
     J { "" + it<!UNSAFE_CALL!>.<!>length }
-    J { <!NULL_FOR_NONNULL_TYPE!>null<!> }
+    J { <!NI;NULL_FOR_NONNULL_TYPE, NULL_FOR_NONNULL_TYPE!>null<!> }
     J { <!NI;TYPE_MISMATCH, TYPE_MISMATCH!>it?.length?.toString()<!> }
 
     J2 <!NI;TYPE_MISMATCH!>{ <!EXPECTED_PARAMETER_TYPE_MISMATCH!>s: String<!> -> s}<!>
     J2 { "" + it<!UNSAFE_CALL!>.<!>length }
-    J2 { <!NULL_FOR_NONNULL_TYPE!>null<!> }
+    J2 { <!NI;NULL_FOR_NONNULL_TYPE, NULL_FOR_NONNULL_TYPE!>null<!> }
     J2 { <!NI;TYPE_MISMATCH, TYPE_MISMATCH!>it?.length?.toString()<!> }
 }
diff --git a/compiler/testData/diagnostics/tests/platformTypes/notNullTypeParameter/methodTypeParameter.kt b/compiler/testData/diagnostics/tests/platformTypes/notNullTypeParameter/methodTypeParameter.kt
index b3cfaecde22..e1baf17bc99 100644
--- a/compiler/testData/diagnostics/tests/platformTypes/notNullTypeParameter/methodTypeParameter.kt
+++ b/compiler/testData/diagnostics/tests/platformTypes/notNullTypeParameter/methodTypeParameter.kt
@@ -11,15 +11,13 @@ public class A {
 // FILE: k.kt
 
 fun test() {
-    A.<!OI;TYPE_INFERENCE_INCORPORATION_ERROR!>bar<!>(<!NULL_FOR_NONNULL_TYPE!>null<!>, "")
+    A.<!OI;TYPE_INFERENCE_INCORPORATION_ERROR!>bar<!>(<!OI;NULL_FOR_NONNULL_TYPE!>null<!>, "")
 
     A.bar<String>(<!NULL_FOR_NONNULL_TYPE!>null<!>, "")
-    A.bar<String?>(<!NULL_FOR_NONNULL_TYPE!>null<!>, "")
-    A.bar<String?>("", "")
-
-    A.<!OI;TYPE_INFERENCE_INCORPORATION_ERROR!>bar<!>(<!NULL_FOR_NONNULL_TYPE!>null<!>, A.platformString())
+    A.bar<String?>(<!OI;NULL_FOR_NONNULL_TYPE!>null<!>, "")
+    A.<!OI;TYPE_INFERENCE_INCORPORATION_ERROR!>bar<!>(<!OI;NULL_FOR_NONNULL_TYPE!>null<!>, A.platformString())
 
     val x: String? = null
-    A.<!OI;TYPE_INFERENCE_INCORPORATION_ERROR!>bar<!>(<!TYPE_MISMATCH!>x<!>, "")
-    A.<!OI;TYPE_INFERENCE_INCORPORATION_ERROR!>bar<!>(<!NULL_FOR_NONNULL_TYPE!>null<!>, "")
+    A.<!OI;TYPE_INFERENCE_INCORPORATION_ERROR!>bar<!>(<!OI;TYPE_MISMATCH!>x<!>, "")
+    A.<!OI;TYPE_INFERENCE_INCORPORATION_ERROR!>bar<!>(<!OI;NULL_FOR_NONNULL_TYPE!>null<!>, "")
 }
diff --git a/core/descriptors.jvm/src/org/jetbrains/kotlin/load/java/typeEnhancement/typeEnhancement.kt b/core/descriptors.jvm/src/org/jetbrains/kotlin/load/java/typeEnhancement/typeEnhancement.kt
index f73f8c9de52..197f2461af3 100644
--- a/core/descriptors.jvm/src/org/jetbrains/kotlin/load/java/typeEnhancement/typeEnhancement.kt
+++ b/core/descriptors.jvm/src/org/jetbrains/kotlin/load/java/typeEnhancement/typeEnhancement.kt
@@ -215,7 +215,7 @@ private object EnhancedTypeAnnotationDescriptor : AnnotationDescriptor {
     override fun toString() = "[EnhancedType]"
 }
 
-internal class NotNullTypeParameter(override val delegate: SimpleType) : NotNullTypeVariable, DelegatingSimpleType() {
+internal class NotNullTypeParameter(override val delegate: SimpleType) : CustomTypeVariable, DelegatingSimpleType() {
 
     override val isTypeVariable: Boolean
         get() = true
diff --git a/core/descriptors/src/org/jetbrains/kotlin/types/TypeCapabilities.kt b/core/descriptors/src/org/jetbrains/kotlin/types/TypeCapabilities.kt
index 428df8a0d3f..33924046ca8 100644
--- a/core/descriptors/src/org/jetbrains/kotlin/types/TypeCapabilities.kt
+++ b/core/descriptors/src/org/jetbrains/kotlin/types/TypeCapabilities.kt
@@ -27,10 +27,6 @@ interface CustomTypeVariable {
     fun substitutionResult(replacement: KotlinType): KotlinType
 }
 
-// That interface is needed to provide information about definitely not null
-//   type parameters (e.g. from @NotNull annotation) to type system
-interface NotNullTypeVariable : CustomTypeVariable
-
 fun KotlinType.isCustomTypeVariable(): Boolean = (unwrap() as? CustomTypeVariable)?.isTypeVariable ?: false
 fun KotlinType.getCustomTypeVariable(): CustomTypeVariable? =
         (unwrap() as? CustomTypeVariable)?.let {
diff --git a/core/descriptors/src/org/jetbrains/kotlin/types/checker/ClassicTypeSystemContext.kt b/core/descriptors/src/org/jetbrains/kotlin/types/checker/ClassicTypeSystemContext.kt
index c1f1411db37..570f1215948 100644
--- a/core/descriptors/src/org/jetbrains/kotlin/types/checker/ClassicTypeSystemContext.kt
+++ b/core/descriptors/src/org/jetbrains/kotlin/types/checker/ClassicTypeSystemContext.kt
@@ -333,10 +333,6 @@ interface ClassicTypeSystemContext : TypeSystemInferenceExtensionContext {
         return builtIns.nothingType
     }
 
-    override fun anyType(): SimpleTypeMarker {
-        return builtIns.anyType
-    }
-
     val builtIns: KotlinBuiltIns get() = throw UnsupportedOperationException("Not supported")
 
     override fun KotlinTypeMarker.makeDefinitelyNotNullOrNotNull(): KotlinTypeMarker {
diff --git a/core/type-system/src/org/jetbrains/kotlin/types/model/TypeSystemContext.kt b/core/type-system/src/org/jetbrains/kotlin/types/model/TypeSystemContext.kt
index 39ff35c9caf..062d58c8a36 100644
--- a/core/type-system/src/org/jetbrains/kotlin/types/model/TypeSystemContext.kt
+++ b/core/type-system/src/org/jetbrains/kotlin/types/model/TypeSystemContext.kt
@@ -49,7 +49,6 @@ interface TypeSystemBuiltInsContext {
     fun nullableNothingType(): SimpleTypeMarker
     fun nullableAnyType(): SimpleTypeMarker
     fun nothingType(): SimpleTypeMarker
-    fun anyType(): SimpleTypeMarker
 }
 
 interface TypeSystemTypeFactoryContext {