code: def _attempt_proof_prop(
      self, current, context, agenda, accessible_vars, atoms, debug
  ):
      # Check if the branch is closed.  Return 'True' if it is
      if (current, True) in atoms:
          debug.line("CLOSED", 1)
          return True
  
      # mark all AllExpressions as 'not exhausted' into the agenda since we are (potentially) adding new accessible vars
      agenda.mark_alls_fresh()
      return self._attempt_proof(
          agenda, accessible_vars, atoms | {(current, False)}, debug + 1
      )
  
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 5 for calling the TableauProver obj's underlying member method code with example usage: obj._attempt_proof_prop(current, context, agenda, accessible_vars, atoms, debug) and returns: self, True