Sentence improvement (existence expression): choose the best substitute for the underlined part in the sentence below. This telephone number is not existing.

Introduction / Context:
This question examines your ability to choose a natural English expression to talk about existence or non existence. When a phone number is invalid or not in service, native speakers use a very simple structure. Overcomplicated or literal translations into English often sound wrong, and exams test whether you can avoid such unnatural phrases.

Given Data / Assumptions:

• Original sentence: This telephone number is not existing.
• The focus is on describing that the number does not exist in the system.
• Options: does not exist, has not been existing, has had no existence, No improvement.
• The sentence is about the current status of the number, not a long history.

Concept / Approach:
The verb \"exist\" is generally used in simple tenses to describe whether something is present or real. For something that is simply not there, the standard sentence is \"It does not exist.\" Progressive forms like \"is existing\" or \"has been existing\" are not used in ordinary English for this meaning. Therefore, the best correction is \"This telephone number does not exist.\"

Step-by-Step Solution:
Step 1: Identify the key message: the telephone number is invalid or not present in the database. Step 2: Replace the awkward \"is not existing\" with a more natural expression. Step 3: Use the present simple negative: \"does not exist\" for a general statement about existence. Step 4: Form the corrected sentence: \"This telephone number does not exist.\" Step 5: Check that this structure matches standard English usage in service messages and everyday speech.

Verification / Alternative check:
Think of common phrases: \"Unicorns do not exist\", \"That record does not exist any more\", \"Such a rule does not exist\". You almost never hear \"is not existing\" for this idea. Automated messages from phone networks typically say \"The number you have dialled does not exist\". This confirms that \"does not exist\" is the correct expression.

Why Other Options Are Wrong:
Option \"has not been existing\": This is an unnatural progressive perfect form. English does not normally say something \"has been existing\" in this context. Option \"has had no existence\": This is grammatically possible but too heavy and unnatural for a simple statement about a phone number. Option \"No improvement\": This would keep \"is not existing\", which is incorrect in standard English.

Common Pitfalls:
A frequent error is to overuse the continuous or progressive aspect with verbs that already describe states, such as \"exist\", \"know\", or \"believe\". These verbs usually prefer simple forms rather than continuous ones when talking about general truths or permanent states.

Final Answer:
The improved sentence is: This telephone number does not exist. Therefore, the correct option is does not exist.