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The given language is not a context-sensitive language (CSL). In order for a language to be a CSL, it must satisfy the condition that for any string in the language, the length of the string must be at least as large as the length of the shortest context-free grammar (CFG) that can generate the string. However, the language L contains strings of the form a^n b^n c^n d^n, which can be generated by a CFG with just four production rules:

S -> aSbScSd
S -> ε

The length of this CFG is just four, which is much shorter than the length of any string in L. 

In order for a language to be a context-sensitive language (CSL), it must satisfy the condition that for any string in the language, the length of the string must be at least as large as the length of the shortest context-free grammar (CFG) that can generate the string. This means that if we have a CFG with a small number of production rules, it cannot generate strings in a CSL unless those strings are also relatively short.

The length of this CFG is just four, which is much smaller than the length of any string in L. For example, the string a^5 b^5 c^5 d^5 has a length of 20, which is much larger than the length of the CFG that can generate it. Therefore, L is not a CSL and the given statement is false.

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