Theorem Proving via General Matings
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Journal of Automated Reasoning
The Complexity of Resource-Bounded First-Order Classical Logic
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Model elimination and connection tableau procedures
Handbook of automated reasoning
Encoding First Order Proofs in SAT
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
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We present a method for encoding first order proofs in SMT. Our implementation, called ChewTPTP-SMT, transforms a set of first order clauses into a propositional encoding (modulo theories) of the existence of a rigid first order connection tableau and the satisfiability of unification constraints, which is then fed to Yices. For the unification constraints, terms are represented as recursive datatypes, and unification constraints are equations on terms. The finiteness of the tableau is encoded by linear real arithmetic inequalities. We compare our implementation with our previous implementation ChewTPTP-SAT, encoding rigid connection tableau in SAT, and show that for Horn clauses many fewer propositional clauses are generated by ChewTPTP-SMT, and ChewTPTP-SMT is much faster than ChewTPTP-SAT. This is not the case for our non-Horn clause encoding. We explain this, and we conjecture a rule of thumb on when to use theories in encoding a problem.