code: def _attempt_proof(self, agenda, accessible_vars, atoms, debug):
      (current, context), category = agenda.pop_first()
  
      # if there's nothing left in the agenda, and we haven't closed the path
      if not current:
          debug.line("AGENDA EMPTY")
          return False
  
      proof_method = {
          Categories.ATOM: self._attempt_proof_atom,
          Categories.PROP: self._attempt_proof_prop,
          Categories.N_ATOM: self._attempt_proof_n_atom,
          Categories.N_PROP: self._attempt_proof_n_prop,
          Categories.APP: self._attempt_proof_app,
          Categories.N_APP: self._attempt_proof_n_app,
          Categories.N_EQ: self._attempt_proof_n_eq,
          Categories.D_NEG: self._attempt_proof_d_neg,
          Categories.N_ALL: self._attempt_proof_n_all,
          Categories.N_EXISTS: self._attempt_proof_n_some,
          Categories.AND: self._attempt_proof_and,
          Categories.N_OR: self._attempt_proof_n_or,
          Categories.N_IMP: self._attempt_proof_n_imp,
          Categories.OR: self._attempt_proof_or,
          Categories.IMP: self._attempt_proof_imp,
          Categories.N_AND: self._attempt_proof_n_and,
          Categories.IFF: self._attempt_proof_iff,
          Categories.N_IFF: self._attempt_proof_n_iff,
          Categories.EQ: self._attempt_proof_eq,
          Categories.EXISTS: self._attempt_proof_some,
          Categories.ALL: self._attempt_proof_all,
      }[category]
  
      debug.line((current, context))
      return proof_method(
          current, context, agenda, accessible_vars, atoms, debug
      )
  
imports: from nltk.inference.api import BaseProverCommand, Prover
  from nltk.internals import Counter
  from nltk.sem.logic import AbstractVariableExpression, AllExpression, AndExpression, ApplicationExpression, EqualityExpression, ExistsExpression, Expression, FunctionVariableExpression, IffExpression, ImpExpression, LambdaExpression, NegatedExpression, OrExpression, Variable, VariableExpression, unique_variable
label_desc: Use image node_id 2 for calling the TableauProver obj's underlying member method code with example usage: obj._attempt_proof(agenda, accessible_vars, atoms, debug) and returns: proof_method, False