al Derivation(RND): For any derivation D in natural deduction, D is acceptable only if D is (in principle) convertible into a normal derivation. Furthermore, while he compares his natural deduction system for naive set-theory and Fitch's, Prawitz (1965, p. 95) introduces a similar requirement with RND by saying, 'the set-theoretical paradoxes ruled out by the requirement that the [derivations] shall be normal.' Prawitz (1965, p. 96) also claims that his requirement is less ad hoc than Fitch's simple/special restrictions introduced by Fitch (1952, Sec. 18 and 20). Even though both Prawitz and Tennant did not explicitly claim that RND (or a similar requirement) could be a solution to the paradoxes, it is possible from their views that they would have in mind that RND could be the solution. Hence, our question is whether RND can really be a solution to the paradoxes. In order for RND to be the proof-theoretic solution, three things must be answered: (i) which paradox is a genuine paradox and which formalization is legitimate for the genuine paradox, (ii) why the only normalizable derivations are acceptable, and (iii) why the only propositional constant ⊥ for absurdity is an unacceptable conclusion. This chapter aims to discuss that there are some obstacles to claim that RND is the proof-theoretic solution to the paradoxes. For the first question (i), since RND is proposed on the perspectives on TCP, the following conjecture for genuine paradoxes should be true. Tennant's Conjecture for Genuine Paradoxes: For any derivation D in natural deduction, D formalizes a genuine paradox iff D is a T-paradox with respect to TCP. As we have noted, TCP itself assumes the conjecture for genuine paradoxes. However, since the notion of a 'genuine paradox' is informal, it is unclear what kinds of paradoxes are 134 genuine paradoxes. Tennant has claimed that Russell's paradox is not a genuine paradox, whereas the Liar paradox is a genuine one. In Section 4.1, we shall introduce his argument on why Russell's paradox is not a genuine