diff --git a/compiler/fir/analysis-tests/testData/resolve/samConversions/kotlinSam.fir.txt b/compiler/fir/analysis-tests/testData/resolve/samConversions/kotlinSam.fir.txt
index a7894e6c53f..7d55312bf1a 100644
--- a/compiler/fir/analysis-tests/testData/resolve/samConversions/kotlinSam.fir.txt
+++ b/compiler/fir/analysis-tests/testData/resolve/samConversions/kotlinSam.fir.txt
@@ -38,12 +38,12 @@ FILE: kotlinSam.kt
         }
         ))
         R|/foo1|(SAM(R|<local>/f|))
-        R|/foo2<Inapplicable(INAPPLICABLE): /foo2>#|(<L> = foo2@fun <anonymous>(x: R|kotlin/Nothing|): R|kotlin/Boolean| <inline=Unknown>  {
+        R|/foo2<Inapplicable(INAPPLICABLE): /foo2>#|(<L> = foo2@fun <anonymous>(x: <ERROR TYPE REF: Cannot infer type for parameter x>): <ERROR TYPE REF: Cannot infer type variable TypeVariable(_L)> <inline=Unknown>  {
             ^ CMP(>, R|<local>/x|.<Unresolved name: compareTo>#(Int(1)))
         }
         )
         R|/foo2<Inapplicable(INAPPLICABLE): /foo2>#|(R|<local>/f|)
-        R|/foo3<Inapplicable(INAPPLICABLE): /foo3>#|(<L> = foo3@fun <anonymous>(x: R|kotlin/Nothing|): R|kotlin/Boolean| <inline=Unknown>  {
+        R|/foo3<Inapplicable(INAPPLICABLE): /foo3>#|(<L> = foo3@fun <anonymous>(x: <ERROR TYPE REF: Cannot infer type for parameter x>): <ERROR TYPE REF: Cannot infer type variable TypeVariable(_L)> <inline=Unknown>  {
             ^ CMP(>, R|<local>/x|.<Unresolved name: compareTo>#(Int(1)))
         }
         )
diff --git a/compiler/fir/analysis-tests/testData/resolve/samConversions/kotlinSam.kt b/compiler/fir/analysis-tests/testData/resolve/samConversions/kotlinSam.kt
index 9b3f3f10ed7..083bc743415 100644
--- a/compiler/fir/analysis-tests/testData/resolve/samConversions/kotlinSam.kt
+++ b/compiler/fir/analysis-tests/testData/resolve/samConversions/kotlinSam.kt
@@ -29,10 +29,10 @@ fun main() {
     foo1 { x -> x > 1 }
     foo1(f)
 
-    foo2 <!ARGUMENT_TYPE_MISMATCH!>{ x -> x <!UNRESOLVED_REFERENCE!>><!> 1 }<!>
+    foo2 <!ARGUMENT_TYPE_MISMATCH!>{ <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> x <!UNRESOLVED_REFERENCE!>><!> 1 }<!>
     foo2(<!ARGUMENT_TYPE_MISMATCH!>f<!>)
 
-    foo3 <!ARGUMENT_TYPE_MISMATCH!>{ x -> x <!UNRESOLVED_REFERENCE!>><!> 1 }<!>
+    foo3 <!ARGUMENT_TYPE_MISMATCH!>{ <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> x <!UNRESOLVED_REFERENCE!>><!> 1 }<!>
     foo3(<!ARGUMENT_TYPE_MISMATCH!>f<!>)
 
     foo4 { x -> x > 1 }
diff --git a/compiler/fir/analysis-tests/testData/resolve/samConversions/notSamBecauseOfSupertype.fir.txt b/compiler/fir/analysis-tests/testData/resolve/samConversions/notSamBecauseOfSupertype.fir.txt
index 34197c0b171..a8452efbadd 100644
--- a/compiler/fir/analysis-tests/testData/resolve/samConversions/notSamBecauseOfSupertype.fir.txt
+++ b/compiler/fir/analysis-tests/testData/resolve/samConversions/notSamBecauseOfSupertype.fir.txt
@@ -2,7 +2,7 @@ FILE: main.kt
     public final fun foo(m: R|MyRunnable|): R|kotlin/Unit| {
     }
     public final fun main(): R|kotlin/Unit| {
-        Q|JavaUsage|.R|/JavaUsage.foo*s<Inapplicable(INAPPLICABLE): /JavaUsage.foo>#|(<L> = foo@fun <anonymous>(x: R|kotlin/Nothing|): R|kotlin/Boolean| <inline=Unknown>  {
+        Q|JavaUsage|.R|/JavaUsage.foo*s<Inapplicable(INAPPLICABLE): /JavaUsage.foo>#|(<L> = foo@fun <anonymous>(x: <ERROR TYPE REF: Cannot infer type for parameter x>): <ERROR TYPE REF: Cannot infer type variable TypeVariable(_L)> <inline=Unknown>  {
             ^ CMP(>, R|<local>/x|.<Unresolved name: compareTo>#(Int(1)))
         }
         )
diff --git a/compiler/fir/analysis-tests/testData/resolve/samConversions/notSamBecauseOfSupertype.kt b/compiler/fir/analysis-tests/testData/resolve/samConversions/notSamBecauseOfSupertype.kt
index 2e8f15e87fa..d98e39988da 100644
--- a/compiler/fir/analysis-tests/testData/resolve/samConversions/notSamBecauseOfSupertype.kt
+++ b/compiler/fir/analysis-tests/testData/resolve/samConversions/notSamBecauseOfSupertype.kt
@@ -19,7 +19,7 @@ fun foo(m: MyRunnable) {}
 
 fun main() {
     JavaUsage.foo <!ARGUMENT_TYPE_MISMATCH!>{
-            x -> x <!UNRESOLVED_REFERENCE!>><!> 1
+            <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> x <!UNRESOLVED_REFERENCE!>><!> 1
     }<!>
 
     JavaUsage.foo(<!ARGUMENT_TYPE_MISMATCH!>{ <!UNRESOLVED_REFERENCE!>it<!> > 1 }<!>)
diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/ConeConstraintSystemUtilContext.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/ConeConstraintSystemUtilContext.kt
index 77acc18f4e4..0120ffe90e4 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/ConeConstraintSystemUtilContext.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/ConeConstraintSystemUtilContext.kt
@@ -108,8 +108,7 @@ object ConeConstraintSystemUtilContext : ConstraintSystemUtilContext {
         index: Int
     ): TypeVariableMarker {
         return ConeTypeVariableForLambdaParameterType(
-            PostponedArgumentInputTypesResolver.TYPE_VARIABLE_NAME_PREFIX_FOR_LAMBDA_PARAMETER_TYPE + index,
-            index
+            PostponedArgumentInputTypesResolver.TYPE_VARIABLE_NAME_PREFIX_FOR_LAMBDA_PARAMETER_TYPE + index
         )
     }
 
diff --git a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/PostponedArguments.kt b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/PostponedArguments.kt
index d924b1a3052..aa54ec8f9d7 100644
--- a/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/PostponedArguments.kt
+++ b/compiler/fir/resolve/src/org/jetbrains/kotlin/fir/resolve/inference/PostponedArguments.kt
@@ -23,6 +23,7 @@ import org.jetbrains.kotlin.resolve.calls.inference.ConstraintSystemBuilder
 import org.jetbrains.kotlin.resolve.calls.inference.addSubtypeConstraintIfCompatible
 import org.jetbrains.kotlin.resolve.calls.inference.model.ConstraintKind
 import org.jetbrains.kotlin.types.model.typeConstructor
+import org.jetbrains.kotlin.utils.addToStdlib.runIf
 
 fun Candidate.preprocessLambdaArgument(
     csBuilder: ConstraintSystemBuilder,
@@ -120,17 +121,18 @@ private fun extractLambdaInfo(
         argument.returnType
             ?: typeVariable.defaultType
 
-    val defaultType = when (candidate?.symbol?.origin) {
-        FirDeclarationOrigin.DynamicScope -> ConeDynamicType.create(session)
-        else -> session.builtinTypes.nothingType.type
+    val defaultType = runIf(candidate?.symbol?.origin == FirDeclarationOrigin.DynamicScope) { ConeDynamicType.create(session) }
+
+    val parameters = argument.valueParameters.mapIndexed { i, it ->
+        it.returnTypeRef.coneTypeSafe<ConeKotlinType>()
+            ?: defaultType
+            ?: ConeTypeVariableForLambdaParameterType("_P$i").apply { csBuilder.registerVariable(this) }.defaultType
     }
 
-    val parameters = argument.valueParameters.map {
-        it.returnTypeRef.coneTypeSafe<ConeKotlinType>() ?: defaultType
-    }
-
-    val contextReceivers = argument.contextReceivers.map {
-        it.typeRef.coneTypeSafe<ConeKotlinType>() ?: defaultType
+    val contextReceivers = argument.contextReceivers.mapIndexed { i, it ->
+        it.typeRef.coneTypeSafe<ConeKotlinType>()
+            ?: defaultType
+            ?: ConeTypeVariableForLambdaParameterType("_C$i").apply { csBuilder.registerVariable(this) }.defaultType
     }
 
     val newTypeVariableUsed = returnType == typeVariable.defaultType
diff --git a/compiler/fir/semantics/src/org/jetbrains/kotlin/fir/resolve/inference/ConeTypeVariables.kt b/compiler/fir/semantics/src/org/jetbrains/kotlin/fir/resolve/inference/ConeTypeVariables.kt
index 34fcf130317..5c770488347 100644
--- a/compiler/fir/semantics/src/org/jetbrains/kotlin/fir/resolve/inference/ConeTypeVariables.kt
+++ b/compiler/fir/semantics/src/org/jetbrains/kotlin/fir/resolve/inference/ConeTypeVariables.kt
@@ -11,7 +11,7 @@ import org.jetbrains.kotlin.fir.types.ConeTypeVariable
 import org.jetbrains.kotlin.name.SpecialNames
 
 class ConeTypeVariableForPostponedAtom(name: String) : ConeTypeVariable(name)
-class ConeTypeVariableForLambdaParameterType(name: String, val index: Int) : ConeTypeVariable(name)
+class ConeTypeVariableForLambdaParameterType(name: String) : ConeTypeVariable(name)
 class ConeTypeVariableForLambdaReturnType(val argument: FirAnonymousFunction, name: String) : ConeTypeVariable(name)
 
 class ConeTypeParameterBasedTypeVariable(
diff --git a/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveFunctionLiteralsNoUse.fir.kt b/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveFunctionLiteralsNoUse.fir.kt
deleted file mode 100644
index c90d9f55e36..00000000000
--- a/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveFunctionLiteralsNoUse.fir.kt
+++ /dev/null
@@ -1,6 +0,0 @@
-package f
-
-fun <R> h(i: Int, a: Any, r: R, f: (Boolean) -> Int) = 1
-fun <R> h(a: Any, i: Int, r: R, f: (Boolean) -> Int) = 1
-
-fun test() = <!OVERLOAD_RESOLUTION_AMBIGUITY!>h<!>(1, 1, 1, { b -> 42 })
diff --git a/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveFunctionLiteralsNoUse.kt b/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveFunctionLiteralsNoUse.kt
index 8978c920a84..72eee805f8c 100644
--- a/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveFunctionLiteralsNoUse.kt
+++ b/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveFunctionLiteralsNoUse.kt
@@ -1,3 +1,4 @@
+// FIR_IDENTICAL
 package f
 
 fun <R> h(i: Int, a: Any, r: R, f: (Boolean) -> Int) = 1
diff --git a/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveWithFunctionLiterals.fir.kt b/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveWithFunctionLiterals.fir.kt
deleted file mode 100644
index 4f7d4791c23..00000000000
--- a/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveWithFunctionLiterals.fir.kt
+++ /dev/null
@@ -1,9 +0,0 @@
-// !DIAGNOSTICS: -CONFLICTING_JVM_DECLARATIONS
-package f
-
-fun <R> h(f: (Boolean) -> R) = 1
-fun <R> h(f: (String) -> R) = 2
-
-fun test() = <!OVERLOAD_RESOLUTION_AMBIGUITY!>h<!>{ i -> getAnswer() }
-
-fun getAnswer() = 42
diff --git a/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveWithFunctionLiterals.kt b/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveWithFunctionLiterals.kt
index c630f37b25b..4e88bd4e9b7 100644
--- a/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveWithFunctionLiterals.kt
+++ b/compiler/testData/diagnostics/tests/inference/cannotCompleteResolveWithFunctionLiterals.kt
@@ -1,3 +1,4 @@
+// FIR_IDENTICAL
 // !DIAGNOSTICS: -CONFLICTING_JVM_DECLARATIONS
 package f
 
diff --git a/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/basic.fir.kt b/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/basic.fir.kt
index c292016c533..3046989943a 100644
--- a/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/basic.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/basic.fir.kt
@@ -184,7 +184,7 @@ fun main() {
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function1<kotlin.Number, java.io.Serializable>")!>select(A3(), { <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Number")!>it<!> }, { a -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Number")!>a<!> })<!>
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction<kotlin.Any>")!>select(A3(), <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>)<!>
     // Should be error as `A3::foo1` is `KFunction2`, but the remaining arguments are `KFuncion1` or `Function1`
-    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(A3(), <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>, { a -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>a<!> }, { it -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>it<!> })<!>
+    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(A3(), <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>, { <!CANNOT_INFER_PARAMETER_TYPE!>a<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter a")!>a<!> }, { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter it")!>it<!> })<!>
     // It's OK because `A3::foo2` is from companion of `A3`
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function1<kotlin.Int, kotlin.Any>")!>select(A3(), <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction1<kotlin.Int, kotlin.Unit>")!>A3::foo2<!>, { a -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Int")!>a<!> }, { it -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Int")!>it<!> })<!>
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function1<kotlin.Int, kotlin.Comparable<*> & java.io.Serializable>")!>select(A4(), { x: Number -> "" })<!>
@@ -192,10 +192,10 @@ fun main() {
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function3<kotlin.Int, kotlin.String, kotlin.Float, kotlin.Float>")!>select(A2(), id { a, b, c -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Int")!>a<!>; <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.String")!>b<!>; <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Float")!>c<!> })<!>
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function1<kotlin.Number, java.io.Serializable>")!>select(id(A3()), { <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Number")!>it<!> }, { a -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Number")!>a<!> })<!>
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction<kotlin.Any>")!>select(A3(), id(<!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>))<!>
-    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(A3(), <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>, id { a -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>a<!> }, { it -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>it<!> })<!>
-    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(A3(), <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>, { a -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>a<!> }, id { it -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>it<!> })<!>
-    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(id(A3()), id(<!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>), { a -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>a<!> }, { it -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>it<!> })<!>
-    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(id(A3()), id(<!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>), { a -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>a<!> }, id { it -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Nothing")!>it<!> })<!>
+    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(A3(), <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>, id { <!CANNOT_INFER_PARAMETER_TYPE!>a<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter a")!>a<!> }, { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter it")!>it<!> })<!>
+    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(A3(), <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>, { <!CANNOT_INFER_PARAMETER_TYPE!>a<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter a")!>a<!> }, id { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter it")!>it<!> })<!>
+    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(id(A3()), id(<!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>), { <!CANNOT_INFER_PARAMETER_TYPE!>a<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter a")!>a<!> }, { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter it")!>it<!> })<!>
+    <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(id(A3()), id(<!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>), { <!CANNOT_INFER_PARAMETER_TYPE!>a<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter a")!>a<!> }, id { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> <!DEBUG_INFO_EXPRESSION_TYPE("ERROR CLASS: Cannot infer type for parameter it")!>it<!> })<!>
     // If lambdas' parameters are specified explicitly, we don't report an error, because there is proper CST – Function<Unit>
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(id(A3()), id(<!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>), { a: Number -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Number")!>a<!> })<!>
     <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Function<kotlin.Any>")!>select(id(A3()), id(<!DEBUG_INFO_EXPRESSION_TYPE("kotlin.reflect.KFunction2<A3, kotlin.Int, kotlin.Unit>")!>A3::foo1<!>), id { a: Number -> <!DEBUG_INFO_EXPRESSION_TYPE("kotlin.Number")!>a<!> })<!>
diff --git a/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.fir.kt b/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.fir.kt
index 34db412d752..a05294b978d 100644
--- a/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/completion/postponedArgumentsAnalysis/notInferableParameterOfAnonymousFunction.fir.kt
@@ -5,14 +5,14 @@ fun <T> select(vararg x: T) = x[0]
 fun <K> id(x: K) = x
 
 fun main() {
-    val x1 = select<Any?>(id { x, y -> }, { x: Int, y -> })
+    val x1 = select<Any?>(id { x, <!CANNOT_INFER_PARAMETER_TYPE!>y<!> -> }, { x: Int, <!CANNOT_INFER_PARAMETER_TYPE!>y<!> -> })
     val x2 = <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>select<!>(<!CANNOT_INFER_PARAMETER_TYPE{LT}!><!CANNOT_INFER_PARAMETER_TYPE{PSI}!><!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>id<!> { x, <!CANNOT_INFER_PARAMETER_TYPE!>y<!> -> }<!>, { x: Int, <!CANNOT_INFER_PARAMETER_TYPE!>y<!> -> }<!>)
 
     val x3 = <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>select<!>(<!CANNOT_INFER_PARAMETER_TYPE{LT}!><!CANNOT_INFER_PARAMETER_TYPE{PSI}!><!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>id<!>(fun (x, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {})<!>, fun (x: Int, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {}<!>)
 
-    val x4 = select<Any?>((fun (x, y) {}), fun (x: Int, y) {})
-    val x5 = select<Any?>(id(fun (<!CANNOT_INFER_PARAMETER_TYPE!>x<!>, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {}), fun (x: Int, y) {})
-    val x6 = id<Any?>(fun (x) {})
+    val x4 = select<Any?>((fun (<!CANNOT_INFER_PARAMETER_TYPE!>x<!>, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {}), fun (x: Int, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {})
+    val x5 = select<Any?>(id(fun (<!CANNOT_INFER_PARAMETER_TYPE!>x<!>, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {}), fun (x: Int, <!CANNOT_INFER_PARAMETER_TYPE!>y<!>) {})
+    val x6 = id<Any?>(fun (<!CANNOT_INFER_PARAMETER_TYPE!>x<!>) {})
 
-    select<Any?>(fun (x) {}, fun (x) {})
+    select<Any?>(fun (<!CANNOT_INFER_PARAMETER_TYPE!>x<!>) {}, fun (<!CANNOT_INFER_PARAMETER_TYPE!>x<!>) {})
 }
diff --git a/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt b/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
index 4a0a1e59823..ec045700126 100644
--- a/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/nonFunctionalExpectedTypeForLambdaArgument.fir.kt
@@ -4,17 +4,17 @@ fun callAny(arg: Any?) {}
 fun <T> callParam(arg: T) {}
 
 fun testAny() {
-    callAny { error -> error }
-    callAny l@{ error -> error }
-    callAny({error -> error})
-    callAny(({error -> error}))
-    callAny(l@{error -> error})
-    callAny((l@{error -> error}))
+    callAny { <!CANNOT_INFER_PARAMETER_TYPE!>error<!> -> error }
+    callAny l@{ <!CANNOT_INFER_PARAMETER_TYPE!>error<!> -> error }
+    callAny({<!CANNOT_INFER_PARAMETER_TYPE!>error<!> -> error})
+    callAny(({<!CANNOT_INFER_PARAMETER_TYPE!>error<!> -> error}))
+    callAny(l@{<!CANNOT_INFER_PARAMETER_TYPE!>error<!> -> error})
+    callAny((l@{<!CANNOT_INFER_PARAMETER_TYPE!>error<!> -> error}))
 }
 
 fun testAnyCall() {
     callAny {
-        error -> <!UNRESOLVED_REFERENCE!>error<!>()
+        <!CANNOT_INFER_PARAMETER_TYPE!>error<!> -> <!UNRESOLVED_REFERENCE!>error<!>()
     }
 }
 
diff --git a/compiler/testData/diagnostics/tests/inference/nothingType/kt34335.fir.kt b/compiler/testData/diagnostics/tests/inference/nothingType/kt34335.fir.kt
deleted file mode 100644
index 0feb52c1e13..00000000000
--- a/compiler/testData/diagnostics/tests/inference/nothingType/kt34335.fir.kt
+++ /dev/null
@@ -1,17 +0,0 @@
-// !DIAGNOSTICS: -UNUSED_PARAMETER
-
-fun call(vararg x: Any?) {}
-fun <R> Any.call(vararg args: Any?): R = TODO()
-fun println(message: Any?) {}
-
-fun foo(action: (Int) -> Unit) {
-    action(10)
-}
-
-fun test1() {
-    call({ x -> println(x::class) }) // x inside the lambda is inferred to `Nothing`, the lambda is `(Nothing) -> Unit`.
-}
-
-fun test2() {
-    ::foo.<!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>call<!>({ x -> println(x::class) })
-}
diff --git a/compiler/testData/diagnostics/tests/inference/nothingType/kt34335.kt b/compiler/testData/diagnostics/tests/inference/nothingType/kt34335.kt
index 6b215a320fc..fa041e833c6 100644
--- a/compiler/testData/diagnostics/tests/inference/nothingType/kt34335.kt
+++ b/compiler/testData/diagnostics/tests/inference/nothingType/kt34335.kt
@@ -1,4 +1,5 @@
-// !DIAGNOSTICS: -UNUSED_PARAMETER
+// !DIAGNOSTICS: -UNUSED_PARAMETER, -DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE
+// FIR_IDENTICAL
 
 fun call(vararg x: Any?) {}
 fun <R> Any.call(vararg args: Any?): R = TODO()
@@ -9,9 +10,9 @@ fun foo(action: (Int) -> Unit) {
 }
 
 fun test1() {
-    call({ <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> println(<!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>x<!>::class) }) // x inside the lambda is inferred to `Nothing`, the lambda is `(Nothing) -> Unit`.
+    call({ <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> println(x::class) }) // x inside the lambda is inferred to `Nothing`, the lambda is `(Nothing) -> Unit`.
 }
 
 fun test2() {
-    ::foo.<!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>call<!>({ <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> println(<!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>x<!>::class) })
+    ::foo.<!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>call<!>({ <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> println(x::class) })
 }
diff --git a/compiler/testData/diagnostics/tests/inference/reportingImprovements/FunctionPlaceholder.fir.kt b/compiler/testData/diagnostics/tests/inference/reportingImprovements/FunctionPlaceholder.fir.kt
index 82e60c60f65..a914effeb9d 100644
--- a/compiler/testData/diagnostics/tests/inference/reportingImprovements/FunctionPlaceholder.fir.kt
+++ b/compiler/testData/diagnostics/tests/inference/reportingImprovements/FunctionPlaceholder.fir.kt
@@ -7,7 +7,7 @@ fun <T, R> bar(f: (T) -> R) = f
 
 fun test() {
     foo <!ARGUMENT_TYPE_MISMATCH!>{ <!UNRESOLVED_REFERENCE!>it<!> }<!>
-    foo <!ARGUMENT_TYPE_MISMATCH!>{ x -> x}<!>
+    foo <!ARGUMENT_TYPE_MISMATCH!>{ <!CANNOT_INFER_PARAMETER_TYPE!>x<!> -> x}<!>
     foo <!ARGUMENT_TYPE_MISMATCH!>{ x: Int -> x}<!>
 
     <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>bar<!> <!CANNOT_INFER_PARAMETER_TYPE!>{ it + 1 }<!>
diff --git a/compiler/testData/diagnostics/tests/inference/resolveWithUnknownLambdaParameterType.fir.kt b/compiler/testData/diagnostics/tests/inference/resolveWithUnknownLambdaParameterType.fir.kt
deleted file mode 100644
index 0ca80a96baf..00000000000
--- a/compiler/testData/diagnostics/tests/inference/resolveWithUnknownLambdaParameterType.fir.kt
+++ /dev/null
@@ -1,11 +0,0 @@
-// !DIAGNOSTICS: -UNUSED_PARAMETER -UNUSED_ANONYMOUS_PARAMETER
-
-fun baz(f: (Int) -> String) {}
-
-object Foo {
-    fun baz(vararg anys: Any?) {}
-
-    fun testResolvedToMember() {
-        baz({ x -> "" }) // should be an error
-    }
-}
diff --git a/compiler/testData/diagnostics/tests/inference/resolveWithUnknownLambdaParameterType.kt b/compiler/testData/diagnostics/tests/inference/resolveWithUnknownLambdaParameterType.kt
index aa0d8da79fc..3392520ade3 100644
--- a/compiler/testData/diagnostics/tests/inference/resolveWithUnknownLambdaParameterType.kt
+++ b/compiler/testData/diagnostics/tests/inference/resolveWithUnknownLambdaParameterType.kt
@@ -1,3 +1,4 @@
+// FIR_IDENTICAL
 // !DIAGNOSTICS: -UNUSED_PARAMETER -UNUSED_ANONYMOUS_PARAMETER
 
 fun baz(f: (Int) -> String) {}
diff --git a/compiler/testData/diagnostics/tests/resolve/newLineLambda.fir.kt b/compiler/testData/diagnostics/tests/resolve/newLineLambda.fir.kt
index 86b296be1dd..516a18f144d 100644
--- a/compiler/testData/diagnostics/tests/resolve/newLineLambda.fir.kt
+++ b/compiler/testData/diagnostics/tests/resolve/newLineLambda.fir.kt
@@ -112,6 +112,6 @@ fun testTwoLambdas() {
 fun f1(): (() -> Unit) -> (() -> Unit) -> Unit {
     return <!RETURN_TYPE_MISMATCH!>{ l1 ->
         l1()
-        <!TOO_MANY_ARGUMENTS!>{ l2 -> <!UNRESOLVED_REFERENCE!>l2<!>() }<!>
+        <!TOO_MANY_ARGUMENTS!>{ <!CANNOT_INFER_PARAMETER_TYPE!>l2<!> -> <!UNRESOLVED_REFERENCE!>l2<!>() }<!>
     }<!>
 }
diff --git a/compiler/testData/diagnostics/tests/resolve/overloadConflicts/allLambdas.fir.kt b/compiler/testData/diagnostics/tests/resolve/overloadConflicts/allLambdas.fir.kt
deleted file mode 100644
index 326b937ef3c..00000000000
--- a/compiler/testData/diagnostics/tests/resolve/overloadConflicts/allLambdas.fir.kt
+++ /dev/null
@@ -1,9 +0,0 @@
-// !DIAGNOSTICS: -UNUSED_PARAMETER
-
-object X1
-object X2
-
-fun <T1> foo(x: T1, f: (T1) -> T1) = X1
-fun <T2> foo(xf: () -> T2, f: (T2) -> T2) = X2
-
-val test: X2 = <!OVERLOAD_RESOLUTION_AMBIGUITY!>foo<!>({ 0 }, { it -> it + 1 })
diff --git a/compiler/testData/diagnostics/tests/resolve/overloadConflicts/allLambdas.kt b/compiler/testData/diagnostics/tests/resolve/overloadConflicts/allLambdas.kt
index fc64260ac88..0b1a1e57f82 100644
--- a/compiler/testData/diagnostics/tests/resolve/overloadConflicts/allLambdas.kt
+++ b/compiler/testData/diagnostics/tests/resolve/overloadConflicts/allLambdas.kt
@@ -1,4 +1,5 @@
-// !DIAGNOSTICS: -UNUSED_PARAMETER
+// !DIAGNOSTICS: -UNUSED_PARAMETER, -DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE, -DEBUG_INFO_MISSING_UNRESOLVED
+// FIR_IDENTICAL
 
 object X1
 object X2
@@ -6,4 +7,4 @@ object X2
 fun <T1> foo(x: T1, f: (T1) -> T1) = X1
 fun <T2> foo(xf: () -> T2, f: (T2) -> T2) = X2
 
-val test: X2 = <!OVERLOAD_RESOLUTION_AMBIGUITY!>foo<!>({ 0 }, { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>it<!> <!DEBUG_INFO_MISSING_UNRESOLVED!>+<!> 1 })
+val test: X2 = <!OVERLOAD_RESOLUTION_AMBIGUITY!>foo<!>({ 0 }, { <!CANNOT_INFER_PARAMETER_TYPE!>it<!> -> it + 1 })