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# Questions tagged [automated-theorem-proving]

Machine-checked, machine-generated or machine-verified proofs

10 questions with no upvoted or accepted answers
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39 views

### Modern presentation of Ackermann's “Solvable Cases?”

Ackermann's book "Solvable Cases of the Decision Problem" discusses decidable instances of first order logic, particularly monadic logic, and so called "equality formulas". However, the book is from ...
32 views

### Is there a correspondence of steps between DPLL and sequent-calculus?

Is there a correspondence between the steps in using DPLL to find out that a formula in propositional logic is unsatisfiable and using sequent calculus to prove that its negation is valid? And given ...
40 views

### Sorts and constructors for modelling classes in a theorem prover

I have been working in the Welder theorem prover for some time now. But I'm confused in the way they handle data-types. I'm not familiar with the terminology of sorts and constructors. Here is how one ...
28 views

### Superposition calculus: greater vs greater-or-equal

Bachmair and Ganzinger 1991, 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', specifies the criterion for using an equation as, by some appropriate ordering, ...
41 views

### Unification algorithm that directly finds multiple substitutions?

Systems of formal logic generally have inference rules that require certain expressions to be syntactically the same in multiple steps. Typically two steps are involved, as for modus ponens, where ...
19 views

### Why aren’t (type theory based) automated theorem provers efficient?

Note: my main experience with theorem provers is with Type theory based proof-assistant, rather than an actual automated theorem prover. It is obvious why naive automated theorem proving is ...
52 views

### Are there any interesting terms in pure LF or $\lambda\Pi$?

In my searching, I've seen that if Church numerals are encoded in a dependently typed Lambda calculus, that we can't derive induction or that $0 \neq 1$. I know that LF and the dependently typed ...
59 views

### Type theory based automated theorem prover?

I know that there exist type theory based proof-checker, and I know that there are logic/sequent-calculus based automated theorem provers. But I haven’t heard of a type-theory based automated theorem ...
I have a formula in FOL: $\forall x \exists y: B(x) \implies C(y)$ and in SPASS: forall([X], exists[Y], implies(B(X),C(Y))) I want to check the formula: \$\exists x:...