The ATP Process

• Convert the problem from it's domain language to (first-order) logic
  • Axioms
  • Conjecture

• Create a file of the the axioms and conjecture, in a machine readable syntax (using the TPTP syntax).

• Check the syntax of the (machine readable) formulae
  • OK - goto "Check consistency of axioms"
  • Error - goto "Convert to logic"

• Check the consistency of the axioms
  • Try to establish that the axioms are satisfiable
    • Yes - goto "Establish logical consequence"
    • No - examine model/saturation, goto "Convert to logic"
    • Unknown - goto "Try to establish axioms are unsatisfiable"
  • Try to establish that the axioms are unsatisfiable
    • Yes - examine refutation, goto "Convert to logic"
    • No - goto "Establish logical consequence"
    • Unknown - goto "Establish logical consequence" (and worry)

• Establish logical consequence
  • Try to prove logical consequence
    • Yes - goto "Process proof"
    • No - goto "Convert to logic"
    • Unknown - goto "Try to prove non-logical consequence"
  • Try to prove non-logical consequence
    • Yes - goto "Convert to logic"
    • No - goto "Process proof"
    • Unknown - goto "Advanced trickery"

• Process proof
  • Recall if axioms are known to be consistent
    • Yes - done
    • No - goto "Check if conjecture is used in proof"
  • Check if conjecture is used in proof
    • Yes - done (and worry a bit)
    • No - examine refutation, goto "Convert to logic"

Exam Style Questions