Editing Automated theorem proving (section)

===Relationship with SMT===

There is substantial overlap between first-order automated theorem provers and [[satisfiability modulo theories|SMT solver]]s. Generally, automated theorem provers focus on supporting full first-order logic with quantifiers, whereas SMT solvers focus more on supporting various theories (interpreted predicate symbols). ATPs excel at problems with lots of quantifiers, whereas SMT solvers do well on large problems without quantifiers.<ref>{{Cite journal |last1=Blanchette |first1=Jasmin Christian |last2=Böhme |first2=Sascha |last3=Paulson |first3=Lawrence C. |date=2013-06-01 |title=Extending Sledgehammer with SMT Solvers |url=https://doi.org/10.1007/s10817-013-9278-5 |journal=Journal of Automated Reasoning |language=en |volume=51 |issue=1 |pages=109–128 |doi=10.1007/s10817-013-9278-5 |s2cid=5389933 |issn=1573-0670|quote=ATPs and SMT solvers have complementary strengths. The former handle quantifiers more elegantly, whereas the latter excel on large, mostly ground problems.}}</ref> The line is blurry enough that some ATPs participate in SMT-COMP, while some SMT solvers participate in [[CADE ATP System Competition|CASC]].<ref>{{Cite journal |last1=Weber |first1=Tjark |last2=Conchon |first2=Sylvain |last3=Déharbe |first3=David |last4=Heizmann |first4=Matthias |last5=Niemetz |first5=Aina |last6=Reger |first6=Giles |date=2019-01-01 |title=The SMT Competition 2015–2018 |journal=Journal on Satisfiability, Boolean Modeling and Computation |language=en |volume=11 |issue=1 |pages=221–259 |doi=10.3233/SAT190123|quote=In recent years, we have seen a blurring of lines between SMT-COMP and CASC with SMT solvers competing in CASC and ATPs competing in SMT-COMP.|doi-access=free }}</ref>