human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "on the complexity of finding falsifying assignments for herbrand disjunctions"
  Abstract: Suppose that $\Phi$ is a consistent sentence. Then there is no Herbrand proof of $\neg \Phi$, which means that any Herbrand disjunction made from the prenex form of $\neg \Phi$ is falsifiable. We show that the problem of finding such a falsifying assignment is hard in the following sense. For every total polynomial search problem $R$, there exists a consistent $\Phi$ such that finding solutions to $R$ can be reduced to finding a falsifying assignment to an Herbrand disjunction made from $\neg \Phi$. It has been conjectured that there are no complete total polynomial search problems. If this conjecture is true, then for every consistent sentence $\Phi$, there exists a consistence sentence $\Psi$, such that the search problem associated with $\Psi$ cannot be reduced to the search problem associated with $\Phi$.

Connected through hyperedge HE-1 (induced by source paper "the classes ppa k existence from arguments modulo k"):
  with members:
    - "the hairy ball problem is ppad complete"
    - "the complexity of splitting necklaces and bisecting ham sandwiches"
    - "ppp completeness with connections to cryptography"
    - "unique end of potential line"
    - "consensus halving is ppa complete"
    - "integer factoring and modular square roots"
    - "the complexity of non monotone markets"
    - "settling the complexity of arrow debreu equilibria in markets with additively separable utilities"

Connected through hyperedge HE-2 (induced by source paper "consensus halving is ppa complete"):
  with members:
    - "on the polynomial parity argument complexity of the combinatorial nullstellensatz"
    - "computational social choice and computational complexity bffs"
    - "integer factoring and modular square roots"
    - "hardness results for consensus halving"
    - "settling the complexity of computing approximate two player nash equilibria"
    - "on the complexity of nash equilibria in anonymous games"
    - "inapproximability of nash equilibrium"
    - "constant rank bimatrix games are ppad hard"

Question: Please tell me which class the center node belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.LO(Logic in Computer Science)