# Questions tagged [theorem-provers]

Automatic proof checkers verify the validity of formal proofs, while proof assistants aid in the construction of formal proofs. Some popular systems: Mizar, Coq, Isabelle. For automated theorem provers use the (automated-theorem-proving) tag

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### Isabelle/HOL sequents: meaning of types o, seq', meaning of nonterminals seq, seqobj, seqcont

I am trying to understand https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/Sequents/Sequents/Sequents.html and https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/Sequents/Sequents/...
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### Interactive proof assistants (IPA) and automated theorem provers (ATP) for analysis and variational calculus?

Is it possible to use (and how) interactive proof assistants (like Isabelle/HOL, Coq) and automated theorem provers (like E) for proving theorems in analysis and variational calculus and solving ...
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### First Order Logic Inference , Proof of sentence

I need to find a proof for my goal , given some assumptions. The assumptions and the goal were translated from english sentences. My assumptions(KB) John ,Mary,Helen,George are the only members of ...
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### Peano/Presburger axioms - “find” numbers lower or equal than another number

[EDIT/CONCLUSION] It turns out it was actually working.. I was just like too stupid to let the prover run for more time and assumed it would take a lot / not be able to prove with what I've provided ...
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### Is there any mathematical work on formalizing problems and their solutions as mathematical objects?

Problems (tasks?) are an important part of life, science, math, basically everything. Do people study them as mathematical objects? Theorem proving seems close, however, I'm interested more in the ...
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### Help with Prover9 for weak propositional systems

I am trying to get Prover9 to work, but apparently am not using exactly the correct commands. Can someone give me a hint, please? This is just a test case, but ...
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### An endless loop in a program that search for mathematical theorems and proofs − a milestone? [closed]

I don't know if there exist computer programs working on its own, trying to find and prove theorems, delivering proofs and go on searching for new theorems. But if (when) there are such programs, ...
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### How does one prove that a computational theorem prover is correct?

There are many computational theorem provers, such as Z3 (http://z3.codeplex.com/). Such provers employ many thousands of lines of code. How can one prove that the results are correct and can be ...
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### Status of declarative proof languages in proof assistants

I'm interested in formalising mathematics and logics in a proof assistant, both to get to know a proof assistant and to make an archive of proofs for myself (nothing too fancy, mainly first order ...
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### Why is automated proof checking so hard?

(Warn: this is not about automated proving which is impossible. It is about the automatized proof checking). For example, there is no automated test developed for Wiles Theorem (aka Fermat last ...
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### Proving that e.g. 421 is prime in a formal system

I'm working in the formal system Metamath, and in the course of learning about number theory I've become acquainted with theorems, such as Bertrand's postulate, that require hand-calculation that a ...
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### Automatic theorem prover for proving simple theorems?

Is there a simple software that I could use to practice proving theorems in my course of mathematical logic? Basically what I need is ability to 1) define what axioms and laws I am allowed to use in ...
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### Why this first-order logic formula is not correct?

I'm studing computer science at university, in specific Artificial Intelligence. We are using Otter as Theorem prover. I'm having some problems formalizing this: "John, Mary and Derek are three ...
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### natural language proof assistant

I was wondering whether there has been any attempt to create a proof assistant that you write in it, in english, I mean you write your proof the usual way in TeX(maybe use a 'simpler english') then ...
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### Is it possible to prove everything in mathematics by theorem provers such as Coq?

Coq has been used to provide formal proofs to the Four Colour theorem, the Feit–Thompson theorem, and I'm sure many more. I was wondering - is there anything that can't be proved in theorem provers ...
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### Why do we need tactics, reflection and other techniques when we have Curry-Howard for theorem proving?

First of all, I apologize if this question is slightly misplaced, but this seemed the best place to ask it given the mathematical/theoretical nature of the discussion. Given that the Curry-Howard ...
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### Are coinductive proofs necessary?

I've been exploring corecursion in Coq (specifically, infinite streams of natural numbers) lately and so far any coinductive predicate I've constructed and its coinductive proof can be transformed ...