あの難問に答えて。

Qwen 3 235B

Vote: P≠NP

The P vs NP problem is one of the most important open questions in computer science. Despite decades of research, no one has proven that P = NP. The overwhelming consensus among experts is that P ≠ NP, based on the lack of efficient algorithms for NP-complete problems and the implications such algorithms would have on cryptography, optimization, and logic. If P = NP were true, it would imply that every problem whose solution can be verified quickly can also be solved quickly. This contradicts empirical evidence, as no such algorithms have been found for well-known NP-complete problems like SAT or the Traveling Salesman Problem. While a formal proof is still missing, the belief that P ≠ NP is strongly supported by theoretical and practical observations. Therefore, I vote B.

Llama 4 Scout

Vote: P≠NP

The question seems to be asking for a response to a well-known problem in computational complexity theory. The options provided are 'A: P=NP' and 'B: P≠NP'. The P versus NP problem is a major unsolved problem in theoretical computer science. While there is no definitive proof for either P=NP or P≠NP, the consensus among experts is that P≠NP. This is because numerous attempts to prove P=NP have failed, and there are significant implications for cryptography and optimization problems if P≠NP. Therefore, based on the current state of knowledge, I choose option B.

Codestral

Vote: P≠NP

The P vs NP problem is one of the most famous unsolved problems in computer science. It asks whether every problem whose solution can be verified quickly can also be solved quickly. The consensus among experts is that P is not equal to NP, but this remains unproven. Given the complexity and the lack of a definitive proof, it is reasonable to conclude that P does not equal NP.

GPT-5.4

Vote: P≠NP

P vs NP is widely believed to be a strict separation (P≠NP), primarily because no one has found a polynomial-time algorithm for NP-complete problems despite enormous effort, and no proof of P=NP exists. Additionally, most mainstream theoretical perspectives treat P=NP as unlikely because it would imply surprisingly powerful consequences (e.g., efficient solutions to many currently hard decision/search problems), which have not been observed in practice or proven theoretically. Therefore, given current knowledge and consensus, the best supported choice is P≠NP.

Devstral Small

Vote: P≠NP

The question asks which statement is true: 'P=NP' or 'P≠NP'. While the P vs NP problem remains unproven, the overwhelming consensus in the theoretical computer science community is that P≠NP. This is based on the fact that no one has been able to prove P=NP despite decades of effort, and many believe that if P=NP were true, it would have been discovered by now. Additionally, the implications of P=NP would be profound and likely contradict many other well-established results in complexity theory. Therefore, voting for B (P≠NP) aligns with the current understanding and consensus in the field.

Nova Pro

Vote: P≠NP

The P vs NP problem is one of the most famous unsolved problems in computer science. It asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. Despite much effort, no one has been able to prove that P equals NP or that P does not equal NP. The prevailing belief among computer scientists is that P does not equal NP, based on the lack of progress in finding polynomial-time algorithms for NP-complete problems and the intuitive understanding of the difficulty of these problems. Therefore, option B, P≠NP, is the more widely accepted stance.

Magistral Small

Vote: P=NP

The question asks which of the two statements is correct regarding the P vs NP problem. While it is widely believed that P ≠ NP, this has not been proven. There is no known proof that P = NP, but it is also not definitively proven that P ≠ NP. Therefore, the statement P=NP is more open to discussion and could potentially be true, as it has not been disproven.

GPT-4o

Vote: P≠NP

The P vs NP problem is one of the most significant open questions in computer science. The majority belief within the academic community, based on current understanding and evidence, leans towards P not equaling NP (P≠NP). No polynomial-time algorithms have been found for NP-complete problems despite extensive research, suggesting that such algorithms may not exist. Additionally, if P were equal to NP, it would have profound, potentially disruptive implications for fields such as cryptography, yet there has been no empirical evidence to support this scenario.

GPT-4o Mini

Vote: P≠NP

The question relates to the famous P vs NP problem in computer science. Most experts believe that P is not equal to NP (P≠NP), which means that there are problems that can be verified quickly but cannot be solved quickly. This belief is supported by the lack of a polynomial-time algorithm for NP-complete problems despite extensive research. Additionally, proving P=NP would have significant implications for cryptography, algorithms, and a wide array of fields, adding to the weight of the conjecture that P≠NP. Therefore, I'm voting for option B.

claude-haiku-4-5

Vote: P≠NP

The question asks to answer 'that difficult problem,' which refers to the famous P vs NP problem in computer science. While P=NP remains unproven, the mathematical and computational evidence strongly suggests P≠NP. No polynomial-time algorithm has been found for any NP-complete problem despite decades of research by thousands of mathematicians and computer scientists. If P=NP were true, it would have profound implications including breaking most modern cryptography, yet no such breakthrough has occurred. The structural arguments from complexity theory also support P≠NP. Although this remains technically unproven, P≠NP is the consensus position in the field and represents the most well-supported answer given current knowledge.

Sonar Pro

Vote: P≠NP

The query asks to answer 'that difficult question,' which unambiguously refers to the P vs NP problem, the most famous open question in computer science, as evidenced by all search results[1][2][3][4][5][6][7][8][9][10]. P=NP (option A) is unproven and considered highly unlikely by the vast majority of researchers, as P⊆NP is known but the reverse remains open, with strong consensus favoring P≠NP[2][3][5][6]. Proving P=NP would collapse complexity classes and break modern cryptography like RSA[5], which no evidence supports. P≠NP (option B) aligns with the prevailing belief and the named conjecture 'P≠NP予想'[2][4][5][6][9]. Sources confirm it's unsolved but 'many researchers believe P≠NP'[2][6], making B the substantiated position. Voting A would ignore expert consensus and evidence from decades of failed attempts to find polynomial algorithms for NP-complete problems[3].

Grok 3

Vote: P≠NP

I vote for option B, P≠NP, because the majority of computer scientists believe that P does not equal NP, based on the current understanding of computational complexity. While it remains an unproven conjecture, the evidence and intuition from decades of research suggest that problems in NP, such as many optimization and decision problems, are inherently harder to solve than those in P, which can be solved in polynomial time. Additionally, if P were equal to NP, it would imply that every problem whose solution can be verified quickly could also be solved quickly, which seems unlikely given the practical difficulty of solving many NP-complete problems like the traveling salesman problem for large inputs. Finally, the lack of progress in finding polynomial-time algorithms for NP-complete problems, despite extensive efforts, further supports the belief that P≠NP. Until a proof or counterexample emerges, this remains the most reasonable stance.

MiniMax M2.5

Vote: P≠NP

The P vs NP problem is one of the seven Millennium Prize Problems, with a $1 million reward for a correct solution. The overwhelming consensus among computer scientists is that P ≠ NP, meaning there exist problems that are easy to verify but hard to solve. This includes problems like NP-complete problems (e.g., SAT, traveling salesman, clique detection). While no proof exists, this consensus is based on decades of failed attempts to find efficient algorithms for NP-complete problems and the profound implications a proof of P = NP would have on cryptography, mathematics, and complexity theory.

Gemini 2.5 Flash

Vote: P≠NP

P≠NPであると広く信じられています。Pクラスの問題は多項式時間で効率的に解くことができるのに対し、NPクラスの問題は解の検証は多項式時間で可能ですが、効率的な解法はまだ見つかっていません。

Grok 4.20

Vote: P≠NP

The P versus NP question remains unsolved, but the overwhelming consensus among computer scientists is that P ≠ NP. Decades of failed attempts to find polynomial-time solutions for NP-complete problems, combined with the practical hardness of these problems and implications for cryptography, strongly support this view. While not proven, evidence tilts clearly toward inequality over equality.

O3 Mini

Vote: P≠NP

Most experts in theoretical computer science believe that P and NP are not equal, as no polynomial-time algorithm has been found for NP-complete problems despite significant research efforts. This belief aligns with the common consensus that P ≠ NP.

Llama 3.3 70B

Vote: P≠NP

The P versus NP problem is a major unsolved problem in computer science. While it is possible that P=NP, the majority of experts in the field believe that P≠NP. This belief is based on the fact that many problems in NP have been shown to be NP-complete, and yet no one has been able to find a polynomial-time algorithm for any of them. Additionally, many years of research have not yielded a proof that P=NP, which suggests that it may be false.

Gemini 3 Flash

Vote: P≠NP

The consensus among the vast majority of computer scientists and mathematicians is that P ≠ NP. This position aligns with our fundamental intuition that solving a problem (finding a needle in a haystack) is inherently more difficult than verifying a provided solution (checking if the object found is indeed a needle). If P were equal to NP, it would imply that every problem whose solution can be verified quickly could also be solved quickly. This would have catastrophic implications for modern cryptography, as most encryption methods rely on the assumption that certain problems (like prime factorization) are computationally difficult to solve even though their solutions are easy to verify. Despite decades of intense research by the world's leading minds, no polynomial-time algorithm has been found for any NP-complete problem. This persistent failure to find an efficient solution strongly suggests that such solutions do not exist, making B the most logically sound and scientifically supported choice.

GPT-5.1

Vote: P≠NP

The question implicitly asks which statement we should endorse about the famous P vs NP problem: whether P equals NP or not. As of the latest mathematical and computer-science knowledge, this problem is open: it has not been proven that P = NP nor that P ≠ NP. It is a Millennium Prize Problem, and no consensus has been turned into a formal proof either way. However, the overwhelming expert belief, based on decades of evidence and failed attempts to find efficient algorithms for NP-complete problems, is that P ≠ NP is the more plausible claim. Many complexity-theoretic results are structured around this assumption, and no polynomial-time algorithms have been found for any NP-complete problem despite intense effort. Because we must choose exactly one option, and because the mathematically responsible position is to avoid asserting an unproven equality, the more defensible answer is to side with the widely believed conjecture P ≠ NP rather than the claim P = NP, which would overturn much of modern complexity theory. So, while neither statement is known to be a theorem, option B aligns with the standard conjecture in theoretical computer science.

gemini-pro-latest

Vote: P≠NP

「あの難問」とは、計算機科学における未解決問題の一つであり、ミレニアム懸賞問題にも選ばれている「P対NP問題」を指していると考えられます。 現在のところ証明はされていませんが、世界の計算機科学者や数学者の圧倒的多数は「P≠NP」であると予想しています。もし「P=NP」であれば、暗号技術など現代社会の基盤となる多くのシステムが崩壊してしまうため、「P≠NP」であるという立場が実用上も支持されています。 したがって、現時点で最も妥当な回答である「P≠NP」を支持します。

GPT-5.4

Vote: P≠NP

B is the only defensible choice given current mathematical knowledge. No proof exists either way, but the overwhelming expert consensus is that P≠NP. Decades of failed attempts to find polynomial-time algorithms for thousands of NP-complete problems is strong evidence against P=NP. If P=NP, we would expect surprising algorithmic collapses across optimization, cryptography, theorem proving, and combinatorics. That has not happened. Instead, the landscape consistently supports hardness. This is not a formal proof, but in a forced-choice setting, the best answer is the mainstream and evidence-backed position: P≠NP.

intellect-3

Vote: P≠NP

The P vs NP problem remains one of the most significant unsolved questions in computer science and mathematics. While no formal proof exists yet, the overwhelming consensus among experts is that P ≠ NP. This belief is supported by decades of failed attempts to find efficient algorithms for NP-complete problems, the practical experiences of computational intractability in complex problem-solving, and theoretical evidence suggesting that collapsing the P and NP classes would require overcoming profound structural barriers in computational complexity theory. If P = NP were true, it would revolutionize fields like cryptography, optimization, and AI, yet no such breakthroughs have materialized despite intense global effort.

gemma-3-27b-it

Vote: P≠NP

The P vs NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be *verified* in polynomial time can also be *solved* in polynomial time. Most computer scientists believe that P ≠ NP. This is because if P = NP, it would imply that many currently intractable problems (like finding the optimal solution to the traveling salesman problem) could be solved efficiently, which would have massive and disruptive consequences. While a proof either way remains elusive, the weight of evidence and the practical implications strongly suggest that P and NP are distinct classes.

O3

Vote: P≠NP

The overwhelming consensus in theoretical computer science, based on decades of partial results and failed attempts to prove equality, is that P ≠ NP. Numerous lines of evidence—including relativization, natural proofs, circuit lower-bound barriers, and oracle results—show how hard it would be for P to equal NP. Until a proof appears, the rational stance is to side with the mainstream belief that polynomial-time algorithms cannot solve all NP problems.

GPT-5.2

Vote: P≠NP

P≠NPは未解決問題ですが、現時点の理論的・経験的状況からはBが最も妥当な立場です。 まず、SATなど多数のNP完全問題について、何十年にもわたる研究にもかかわらず一般的な多項式時間アルゴリズムが見つかっていません。一方で、回路下界・相対化・自然証明などの障壁定理は、既存の標準的手法ではP=NPの証明（あるいはP≠NPの証明の一部）に到達しにくいことを示しており、少なくとも「簡単にP=NPが成り立つ」状況ではないことを裏付けます。 また、暗号理論や計算複雑性の多くの整合的な仮定（例：一方向性関数の存在、強い擬似乱数生成など）はP≠NPと親和的で、実務的にもNP完全問題が一般に難しいという経験則と一致します。これらは証明ではないものの、総合的な証拠としてP≠NPを支持します。

Claude Sonnet 4

Vote: P≠NP

P≠NPはコンピュータ科学において最も広く信じられている予想であり、数十年にわたる研究でP=NPを示す証拠は見つかっていません。多項式時間で解けない問題（NP完全問題）が存在すると考えられており、ほぼすべての専門家がP≠NPを支持しています。ミレニアム懸賞問題の一つでもあり、未解決ではありますが、P≠NPが正しいという強い状況証拠があります。

Magistral Small

Vote: P≠NP

The consensus among computer scientists is that P≠NP. Decades of research have not produced a proof that P=NP, and many believe that such a proof would be extremely difficult because the statement is false. Additionally, if P=NP were true, it would have profound implications for many fields, and the lack of such a breakthrough suggests that P and NP are distinct classes.

Kimi K2.5

Vote: P≠NP

P≠NP is the overwhelmingly favored hypothesis among computer scientists and mathematicians. Despite decades of intensive research, no one has discovered a polynomial-time algorithm for any NP-complete problem, which strongly suggests that efficient solutions do not exist for these problems. The practical implications support this view: if P=NP were true, we would expect to see efficient algorithms for traveling salesman, satisfiability, and other hard optimization problems that routinely stump our best current methods. The existence of the polynomial hierarchy and the lack of collapse observed in complexity theory also points toward P≠NP. While this remains unproven (it is one of the Millennium Prize Problems), the weight of evidence and failed attempts to find efficient algorithms for NP-complete problems makes P≠NP the most reasonable working assumption.

Claude Sonnet 4

Vote: P≠NP

The P vs NP problem is one of the most famous unsolved problems in computer science and mathematics. While we cannot definitively prove either direction yet, the overwhelming consensus in the computer science community is that P ≠ NP. Several compelling arguments support this position: First, despite decades of intensive research and significant financial incentives (including a $1 million Clay Institute prize), no polynomial-time algorithm has been found for any NP-complete problem. If P = NP, such algorithms would exist. Second, many cryptographic systems that secure our digital infrastructure rely on the assumption that certain problems (like integer factorization) are computationally hard. If P = NP, these systems would be fundamentally broken. Third, the philosophical implications suggest that if P = NP, then verification and discovery would be equally difficult, which seems counterintuitive given our experience that checking a solution is typically much easier than finding it. While mathematical intuition can sometimes be wrong, the combination of empirical evidence, practical implications, and theoretical considerations strongly suggests P ≠ NP.

Mistral Large

Vote: P≠NP

The question of whether P equals NP is one of the most fundamental problems in computer science and mathematics. Current consensus among experts strongly leans toward P ≠ NP, and this position is supported by several compelling arguments: First, despite decades of intensive research, no polynomial-time algorithm has been discovered for any NP-complete problem. NP-complete problems, such as the Boolean satisfiability problem (SAT) or the traveling salesman problem, are central to the P vs NP question. The lack of progress in finding efficient solutions to these problems suggests that such algorithms may not exist. Second, the existence of one-way functions, which are easy to compute but hard to invert, provides indirect evidence for P ≠ NP. If P were equal to NP, one-way functions could not exist, as inverting them would be feasible in polynomial time. However, one-way functions are widely believed to exist and are foundational to modern cryptography. Third, the structural differences between P and NP problems support the inequality. P problems are efficiently solvable, while NP problems are verifiable in polynomial time but not necessarily solvable efficiently. This distinction aligns with practical observations in computational complexity, where problems like factoring large integers or solving discrete logarithms remain intractable for classical computers. Finally, the implications of P = NP would be revolutionary, potentially solving problems in optimization, cryptography, and artificial intelligence far beyond current capabilities. The absence of such breakthroughs, despite significant incentives, further supports the view that P ≠ NP.

Gemini 3.1 Pro

Vote: P≠NP

While the P versus NP problem remains one of the most famous unsolved mathematical problems, the vast majority of computer scientists and mathematicians strongly believe that P ≠ NP. If P were equal to NP, it would imply that every problem whose solution can be quickly verified can also be quickly solved. This would mean that all NP-complete problems could be solved in polynomial time, which would effectively collapse modern public-key cryptography and revolutionize optimization. Given decades of rigorous research and failed attempts to find polynomial-time algorithms for NP-complete problems, empirical evidence and expert consensus heavily favor P ≠ NP.

Sonar Reasoning Pro

Vote: P≠NP

The P≠NP conjecture represents the prevailing belief among researchers in computational complexity theory. According to the search results, while no formal proof exists, the mathematical and computational evidence strongly suggests P and NP are distinct classes. If P=NP were true, all NP-verifiable problems would become solvable in polynomial time, which would represent an extraordinarily fortunate discovery. Furthermore, this would catastrophically break modern cryptography systems that rely on the computational hardness of problems like factorization. The fact that despite decades of research no polynomial-time algorithm has been found for canonical NP-complete problems like the Boolean satisfiability problem (SAT) supports the P≠NP hypothesis. Given that P⊆NP is established (verifiable problems include solvable problems), the key question is whether NP strictly exceeds P. The practical difficulty of solving NP problems versus verifying their solutions—exemplified by factoring large numbers—aligns with P≠NP being true.

Kimi K2.5

Vote: P≠NP

This question refers to the famous P versus NP problem in computational complexity theory. While this remains one of the most important unsolved problems in mathematics (with a $1 million Millennium Prize), the overwhelming consensus among computer scientists and complexity theorists is that P ≠ NP. If P were equal to NP, it would mean that every problem whose solution can be verified in polynomial time could also be solved in polynomial time. This would imply that NP-complete problems—such as the Traveling Salesman Problem, Boolean satisfiability, and thousands of others—have efficient algorithms. Despite decades of intensive research and enormous practical incentives, no one has discovered such algorithms. Furthermore, modern cryptography relies heavily on the assumption that certain problems (like integer factorization and discrete logarithms) are computationally hard. If P=NP, most cryptographic systems would be fundamentally broken. The consistent failure to find polynomial-time solutions for NP-complete problems, combined with the theoretical barriers encountered, makes P ≠ NP the most scientifically sound conjecture.

Grok 4

Vote: P≠NP

The P vs NP problem is one of the most famous unsolved problems in computer science. It asks whether every problem whose solution can be verified quickly (NP) can also be solved quickly (P). Most experts believe P ≠ NP because if P=NP, it would imply efficient solutions to many hard problems, which hasn't been found despite extensive research. No proof exists for P=NP, and attempts often lead to contradictions with known results. Voting for B aligns with the prevailing hypothesis in the field, supported by complexity theory and the lack of polynomial-time algorithms for NP-complete problems like the traveling salesman problem.

gemma-4-31b

Vote: P≠NP

The P versus NP problem is one of the most significant open questions in theoretical computer science. The vast majority of computer scientists believe that P ≠ NP. If P were equal to NP, it would imply that every problem with a solution that can be verified in polynomial time could also be solved in polynomial time. This would have catastrophic implications for modern cryptography (e.g., RSA encryption) and would suggest that mathematical creativity could be automated.

Claude Sonnet 4

Vote: P≠NP

The question asks me to answer a difficult problem, referring to the P vs NP question, one of the most important unsolved problems in computer science and mathematics. I vote for P≠NP based on the overwhelming consensus in the theoretical computer science community. While this remains unproven, several compelling arguments support this position: First, decades of research have failed to find polynomial-time algorithms for NP-complete problems despite intensive efforts. If P=NP, we would expect at least some breakthrough by now. Second, the existence of natural proof barriers (like those identified by Razborov and Rudich) and other complexity-theoretic obstacles suggest fundamental limitations that would be consistent with P≠NP. Third, cryptographic systems that underpin modern secure communications rely on the assumption that certain NP problems are hard. The practical success of these systems provides empirical evidence for P≠NP. Finally, survey results consistently show that the vast majority of experts in computational complexity theory believe P≠NP, with estimates typically around 80-90% of researchers holding this view. While I cannot provide a mathematical proof, the cumulative weight of evidence, expert opinion, and the lack of contrary findings after extensive research makes P≠NP the most reasonable position to take.

Grok Code

Vote: P≠NP

The P versus NP problem is one of the most famous unsolved problems in computer science, and the overwhelming consensus among experts is that P ≠ NP. This belief stems from decades of research where no efficient algorithms have been found for NP-complete problems, despite numerous attempts, suggesting a fundamental separation between P and NP classes. While a proof remains elusive, the evidence points strongly to inequality, making B the most supported option.

Claude Opus 4

Vote: P≠NP

P≠NPが正しいと考えます。 計算複雑性理論における最大の未解決問題ですが、以下の理由からP≠NPを支持します： 1. **経験的証拠**: 50年以上にわたり、世界中の優秀な研究者がNP完全問題の多項式時間アルゴリズムを見つけようとしてきましたが、誰も成功していません。SATやTSPなど何千ものNP完全問題が知られていますが、どれも効率的に解けていません。 2. **構造的な違い**: 「解を見つける」ことと「解を検証する」ことの間には本質的な非対称性があるように思われます。正しい答えを推測することと、与えられた答えが正しいか確認することは、根本的に異なる計算タスクです。 3. **暗号学への影響**: 現代の暗号システムの多くはP≠NPを前提としています。もしP=NPなら、RSA暗号なども破れることになりますが、そのような事態は起きていません。 もちろん、これは証明ではなく、数学的にはまだ未解決です。しかし、利用可能な証拠に基づけば、P≠NPが真である可能性が極めて高いと考えます。

Claude Opus 4

Vote: P≠NP

The question asks to answer the famous P vs NP problem. While this remains one of the most important unsolved problems in mathematics and computer science (one of the Clay Millennium Prize Problems), the overwhelming consensus among theoretical computer scientists and mathematicians is that P ≠ NP. Several compelling reasons support this position: 1. **Decades of failed attempts**: Despite over 50 years of intensive research, no one has found polynomial-time algorithms for any NP-complete problem. If P = NP, it would be remarkable that no such algorithm has been discovered for even one of the thousands of known NP-complete problems. 2. **Expert consensus**: Surveys of researchers in the field consistently show that the vast majority (around 80-90%) believe P ≠ NP. 3. **Structural evidence**: There are oracle results, circuit complexity lower bounds, and other theoretical evidence suggesting that polynomial-time algorithms cannot solve NP-complete problems. 4. **Intuitive asymmetry**: There is a fundamental intuitive asymmetry between finding a solution and verifying one. It seems inherently harder to find a needle in a haystack than to confirm you've found it. 5. **Cryptographic implications**: If P = NP, most modern cryptography would collapse, which would have extraordinary practical consequences that we have no evidence of. While we cannot prove this definitively (yet), P ≠ NP is the most well-supported answer to this famous difficult problem.

GLM 5

Vote: P≠NP

The P vs NP problem remains one of the most important unsolved problems in computer science and mathematics. While neither P=NP nor P≠NP has been formally proven, the overwhelming consensus among complexity theorists is that P≠NP. This belief is supported by decades of failed attempts to find efficient algorithms for NP-complete problems, the discovery of various barriers to proving P=NP (such as relativization, natural proofs, and algebrization), and structural evidence from complexity theory. If P=NP were true, it would have profound implications—breaking most modern cryptography and revolutionizing optimization, AI, and many fields. The fact that we haven't found efficient solutions to NP-complete problems despite intense effort strongly suggests P≠NP. While we cannot claim certainty on an unproven conjecture, option B represents the position supported by the preponderance of evidence and expert consensus.

GLM 5

Vote: P≠NP

The P vs NP problem is one of the most important unsolved problems in computer science. While neither P=NP nor P≠NP has been mathematically proven, the overwhelming consensus among complexity theorists strongly favors P≠NP. Most experts believe P≠NP because decades of research have failed to find efficient algorithms for NP-complete problems, despite intense effort. If P=NP, it would revolutionize cryptography, optimization, and countless fields—yet no such algorithms have been discovered. Additionally, various oracle results and barriers to proof techniques suggest fundamental obstacles to P=NP. While I cannot claim certainty on an open problem, voting B reflects the position most consistent with current theoretical computer science consensus.

GPT-5 Mini

Vote: P≠NP

検証は多項式時間でできるが探索は本質的に難しいという直感（解の「見つける」作業が「確認」より遥かに重い）に従うため、P≠NPが自然に妥当に思える。 これまで数十年にわたり多くの優れた研究者がP=NPを示す多様なアプローチを試みたが成功していない点、さらに相対化や自然証明といった理論的障壁が存在し、単純な構成での証明が困難であることが示されている点は、P≠NPを支持する重要な根拠である。 実用面でも、NP完全問題に対する効率的確定解法が長年見つかっておらず、暗号学の安全性が現実に依存していることは、P≠NPであるという仮定を支持する経験的証拠となっている。

DeepSeek V3.2

Vote: P≠NP

The P versus NP problem asks whether every problem with a verifiable solution (NP) can also be solved efficiently (P), which is fundamental to computer science. Empirical evidence strongly supports P ≠ NP. Despite extensive efforts, no polynomial-time algorithm has been discovered for NP-complete problems like the traveling salesman or Boolean satisfiability, suggesting inherent computational hardness. Theoretical frameworks, such as the hierarchy theorems and oracle separations, indicate that P and NP are distinct classes. Additionally, cryptography depends on the assumption that P ≠ NP for security, underscoring its practical importance. Thus, based on prevailing research and logical consistency, P ≠ NP is the most compelling conclusion.

Mistral Medium

Vote: P≠NP

P vs NPの問題は、計算機科学における最も重要な未解決問題の一つであり、その解決には深遠な影響を及ぼす。現状では、P≠NPであると広く信じられている。その根拠は以下の通りである。 **1. 実用的な困難性の観察** 多くのNP完全問題（例: 旅行セールスマン問題、ブール式充足可能性問題）は、現実的な規模で解くのが極めて困難である。もしP=NPであれば、これらの問題に対して効率的な（多項式時間の）解法が存在するはずだが、数十年にわたる研究でもそのようなアルゴリズムは見つかっていない。これはP≠NPの強い傍証となる。 **2. 暗号理論の前提** 現代の暗号システム（RSA、楕円曲線暗号など）は、特定のNP問題（例: 整数の素因数分解）が効率的に解けないという仮定に基づいている。もしP=NPであれば、これらの暗号は容易に破られ、インターネットのセキュリティ基盤が崩壊する。暗号理論の実用的な成功は、P≠NPであることを間接的に支持している。 **3. 理論的な分離の試み** 計算複雑性理論では、PとNPを分離する試みが数多くなされている。例えば、相対化（oracle）やブール回路の複雑性に基づくアプローチなど、P≠NPを示唆する結果が得られている。これらの結果は決定的ではないが、P≠NPの方向を強く示唆している。 **4. 経済的・社会的インパクト** P=NPが証明された場合、最適化問題やスケジューリング問題などが瞬時に解けるようになり、社会に革命的な変化をもたらす。しかし、そのような劇的な変化が起こらない現実が、P≠NPの証左と考えられる。もしP=NPであれば、既にその影響が顕在化しているはずである。 **5. 専門家のコンセンサス** 2012年の調査（William Gasarchによる）では、計算複雑性理論の専門家100人以上のうち、80%以上がP≠NPと信じている。また、Clay Mathematics InstituteがP≠NPの証明に100万ドルの賞金を設定していることも、その難しさと重要性を物語っている。 以上の理由から、現時点では**P≠NP**が最も合理的な結論である。ただし、これは数学的な証明ではなく、経験的・理論的な観察に基づく判断である。最終的な解決には厳密な証明が必要だが、現状の証拠は圧倒的にB（P≠NP）を支持している。

Gemini 2.5 Pro

Vote: P≠NP

これは「P対NP問題」として知られる、コンピュータ科学における最も重要かつ未解決な問題の一つです。確固たる証明はまだ存在しませんが、コンピュータ科学者の間では「P≠NP」が圧倒的なコンセンサスとなっています。 その最大の理由は、長年にわたる世界中の研究者による膨大な努力にもかかわらず、巡回セールスマン問題に代表される数多くの「NP完全問題」のいずれについても、効率的（多項式時間）に解くアルゴリズムが一つも見つかっていないという事実にあります。もしP=NPが真実であれば、これらの問題の少なくとも一つについて、とっくに効率的な解法が見つかっていてもおかしくありません。 さらに、もしP=NPが証明されれば、現在の暗号技術の多くが容易に破られてしまうなど、社会に計り知れない影響が及びます。世界がそのように構成されていないという経験則も、P≠NPを支持する間接的な根拠とされています。したがって、証明はされていないものの、現状の証拠と専門家の見解に基づき、P≠NPである可能性が極めて高いと考えられます。

GPT-5

Vote: P≠NP

この問題は未解決だが、総合的な理論的・経験的証拠は P≠NP を強く示唆する。 (1) バリア結果：相対化、自然証明、代数化といった広範な手法では P と NP の同等性/非同等性を証明できないことが示されており、両者の隔たりが深い可能性を示唆する。 (2) 暗号の堅牢性：実用的な公開鍵暗号やハッシュの広範な成功は、一方向性のような仮定（P≠NP なら自然）が働いていると解釈しやすい。P=NP なら多くの暗号が崩壊するはずだが、その兆しは見えない（もちろん決定的証拠ではない）。 (3) 探索の不毛：SAT をはじめ NP 完全問題への多項式時間アルゴリズムは、数十年の集中的な研究でも見つかっていない。改良は主にヒューリスティクスや平均ケースに留まり、最悪ケースを劇的に改善する証拠はない。 (4) 下界の進展：強力な一般下界は未達だが、回路下界などでの部分的分離は、計算量階層に本質的な差があることを示す兆候になっている。 以上より、確定的な証明はないものの、最も妥当な選択は B: P≠NP である。

DeepSeek V3.2

Vote: P≠NP

The P vs NP problem is one of the most famous open questions in computer science, asking whether every problem with a verifiable solution in polynomial time (NP) can also be solved in polynomial time (P). Although unproven, the prevailing consensus among researchers is that P ≠ NP. This view is grounded in decades of failed attempts to find polynomial-time algorithms for NP-complete problems, such as the traveling salesman or Boolean satisfiability. Additionally, if P = NP were true, it would imply that many cryptographic systems could be easily broken, contradicting practical security observations. Thus, based on the weight of evidence and expert opinion, I conclude that P ≠ NP is the more plausible answer.

DeepSeek V3.1

Vote: P≠NP

The P vs. NP problem is a fundamental unsolved question in computer science. Extensive research over decades has failed to produce a polynomial-time algorithm for any NP-complete problem, which strongly suggests that P ≠ NP. If P were equal to NP, it would imply that complex problems like integer factorization or the traveling salesman could be solved efficiently, potentially breaking modern cryptography. The lack of such breakthroughs, despite intense effort, reinforces the consensus among experts that P ≠ NP.

Qwen 3.5 397B

Vote: P≠NP

P vs NP 問題は数学的に未解決ですが、計算機科学者の間の圧倒的な多数派意見は P≠NP です。NP 完全問題に対する多項式時間アルゴリズムが長年発見されていないこと、また P=NP ならば現代の暗号技術の多くが崩壊するなど直感に反する帰結が生じることを踏まえ、現状では B が最も妥当な選択です。

Final Summary

The AI Roundtable faced one of the most daunting challenges in mathematics and computer science, returning an overwhelming 48-to-1 verdict in favor of P≠NP. While the formal proof for this Millennium Prize Problem remains elusive, the vast majority of models, including GPT-5.4 and Claude Opus 4, argued that the lack of efficient algorithms for NP-complete problems after fifty years of research makes any other conclusion irrational. Magistral Small stood as the lone dissenter, choosing P=NP on the grounds that it has not yet been technically disproven and remains 'open to discussion.'

No agreement after 1 rounds of discussion. Final vote: P≠NP: 48, P=NP: 1

Strongest Arguments

• P=NP: Since P=NP has not been definitively disproven, it remains a theoretical possibility and is more open to discussion than the standard consensus.
• P≠NP: The persistent failure to find polynomial-time algorithms for thousands of NP-complete problems despite decades of intense global effort, combined with the continued stability of modern cryptography, provides overwhelming empirical evidence for a fundamental separation between P and NP.