▸case-01 Given the premises 'If a database query uses an unindexed column in a WHERE clause, the query performs a full table scan' and 'Query #402 performed a full table scan', can we deductively conclude that Query #402 used an unindexed column in its WHERE clause? | pass→pass | 4,368 | 5,809 | +33% | 1 | 1 | 0% | 813 | 1,162 | +43% | 0 | 0 | — |
▸case-06 Evaluate this deduction: Premise 1: All JavaScript runtime engines execute code synchronously on 16 cores by default. Premise 2: V8 is a JavaScript runtime engine. Conclusion: V8 executes code synchronously on 16 cores by default. Is this argument deductively valid, and is it sound? | pass→pass | 6,412 | 5,593 | -13% | 1 | 1 | 0% | 1,187 | 1,141 | -4% | 0 | 0 | — |
▸case-02 Given premises: 'If an API route is protected by OAuth2 middleware, any request without a valid bearer token returns HTTP 401' and 'Request #881 returned HTTP 200 OK', what valid deductive conclusion follows regarding Request #881's token or middleware protection? | pass→pass | 5,743 | 5,369 | -7% | 1 | 1 | 0% | 1,035 | 1,094 | +6% | 0 | 0 | — |
▸case-03 Construct a formal step-by-step deductive proof chain for these premises: (1) If a microservice experiences memory exhaustion, its Kubernetes liveness probe fails. (2) If a Kubernetes liveness probe fails, the Pod is restarted by the kubelet. (3) Service-A is experiencing memory exhaustion. | pass→pass | 7,589 | 6,356 | -16% | 1 | 1 | 0% | 1,595 | 1,455 | -9% | 0 | 0 | — |
▸case-04 Premise 1: The job failure was caused by a network timeout or a database deadlock. Premise 2: Diagnostics confirmed the job failure was caused by a network timeout. Does it deductively follow that a database deadlock did not occur? | pass→pass | 6,186 | 9,528 | +54% | 1 | 1 | 0% | 1,039 | 1,830 | +76% | 0 | 0 | — |
▸case-05 Premise 1: Every HTTP GET endpoint in the payments microservice is idempotent. Premise 2: /payments/v1/receipts is an HTTP GET endpoint in the payments microservice. Derive the logical conclusion through formal deduction. | pass→pass | 4,322 | 3,731 | -14% | 1 | 1 | 0% | 901 | 816 | -9% | 0 | 0 | — |
▸case-07 Prove deductively by contradiction that no even integer greater than 2 is prime, starting from the assumption that there exists an even integer n > 2 that is prime. | pass→pass | 8,170 | 6,420 | -21% | 1 | 1 | 0% | 1,571 | 1,359 | -13% | 0 | 0 | — |
▸case-08 Premise 1: If a user has admin privileges, they can delete production records. Premise 2: User 'guest_01' does not have admin privileges. Therefore, user 'guest_01' cannot delete production records. Evaluate whether this deduction is valid. | pass→pass | 5,476 | 5,236 | -4% | 1 | 1 | 0% | 978 | 1,020 | +4% | 0 | 0 | — |
▸case-09 Premises: (1) If the primary region fails, traffic fails over to Region B. (2) If the database cluster fails, traffic fails over to Region C. (3) Either the primary region failed or the database cluster failed. What traceable disjunctive conclusion can be derived? | pass→pass | 3,262 | 4,993 | +53% | 1 | 1 | 0% | 614 | 972 | +58% | 0 | 0 | — |
▸case-10 We need to run a complex formal verification proof involving 50 chained propositions and tool-assisted satisfiability checking across multiple domain models. How should this task be initialized when full tool access is needed? | fail→pass | 14,965 | 4,942 | -67% | 1 | 1 | 0% | 2,657 | 873 | -67% | 0 | 0 | — |
▸case-11 Apply De Morgan's laws to simplify the negated conjunction: NOT (service_is_up AND database_connected). Express the logically equivalent disjunction step by step. | pass→pass | 7,877 | 4,519 | -43% | 1 | 1 | 0% | 1,127 | 966 | -14% | 0 | 0 | — |
▸case-12 Premise 1: A deployment succeeds if and only if all integration tests pass and zero security vulnerabilities of critical severity are found. Premise 2: Deployment #99 failed. What disjunctive statement can be validly deduced about the integration tests or critical vulnerabilities? | pass→pass | 4,387 | 4,883 | +11% | 1 | 1 | 0% | 753 | 1,053 | +40% | 0 | 0 | — |
▸case-13 Premise: Every individual module in the web application has a memory footprint under 50MB. Conclusion: The entire web application has a memory footprint under 50MB. Evaluate the logical validity of this deduction. | pass→pass | 6,118 | 6,609 | +8% | 1 | 1 | 0% | 1,047 | 1,212 | +16% | 0 | 0 | — |
▸case-14 Given the conditional statement: 'If a message delivery fails three times, it is moved to the dead-letter queue', state its logically equivalent contrapositive statement. | pass→pass | 3,096 | 3,071 | -1% | 1 | 1 | 0% | 545 | 635 | +17% | 0 | 0 | — |
▸case-15 Derive the final conclusion from this chain of premises: (1) All high-volume RPCs use Protocol Buffers. (2) All protocols using Protocol Buffers require binary serialization. (3) All systems requiring binary serialization need schema definition files. (4) PaymentRPC is a high-volume RPC. | pass→pass | 3,827 | 2,527 | -34% | 1 | 1 | 0% | 791 | 561 | -29% | 0 | 0 | — |
▸case-16 Premise 1: Either the SSL certificate expired or the DNS record is misconfigured. Premise 2: The SSL certificate has NOT expired. Conclusion: Therefore, the DNS record is NOT misconfigured. Is this argument valid? | pass→pass | 5,179 | 7,950 | +54% | 1 | 1 | 0% | 978 | 914 | -7% | 0 | 0 | — |
▸case-17 Premise 1: If the circuit breaker opens, downstream calls are immediately rejected. Premise 2: If downstream calls are immediately rejected, latency drops below 10ms. Premise 3: Latency is currently 150ms. Trace the deductive steps to evaluate whether the circuit breaker is open. | pass→pass | 7,786 | 5,945 | -24% | 1 | 1 | 0% | 1,537 | 1,332 | -13% | 0 | 0 | — |
▸case-18 Evaluate the logical equivalence of these two statements: Statement A: 'It is false that all API endpoints require JWT authentication.' Statement B: 'No API endpoint requires JWT authentication.' Are they logically equivalent? | pass→pass | 7,742 | 6,068 | -22% | 1 | 1 | 0% | 1,352 | 1,206 | -11% | 0 | 0 | — |
▸case-19 Premise 1: It is possible that the cache invalidation race condition occurs under high thread contention. Premise 2: Thread contention is currently high. Can we deductively conclude that the cache invalidation race condition is occurring? | pass→pass | 5,125 | 4,483 | -13% | 1 | 1 | 0% | 819 | 805 | -2% | 0 | 0 | — |
▸case-20 We have a spam filter where 80% of spam emails contain the word 'free', and 10% of non-spam emails contain 'free'. If 20% of total incoming emails are spam, calculate the exact posterior probability that an incoming email containing 'free' is spam using Bayes' theorem. | fail→fail | 6,218 | 6,075 | -2% | 1 | 1 | 0% | 1,300 | 1,377 | +6% | 0 | 0 | — |
▸case-21 We observed 1,000 backend deployments last month. 950 of them succeeded without incident, while 50 failed due to unhandled promise rejections in Node.js. Based on this statistical sample, predict the empirical probability distribution for next month's deployments. | fail→fail | 10,926 | 10,835 | -1% | 1 | 1 | 0% | 2,053 | 2,186 | +6% | 0 | 0 | — |
▸case-22 System alert: CPU utilization spiked to 99%, memory remains low, and garbage collection logs show no activity. Give the top three most plausible candidate hypotheses that explain these observed symptoms. | pass→fail | 13,068 | 9,892 | -24% | 1 | 1 | 0% | 1,939 | 1,471 | -24% | 0 | 0 | — |
▸case-23 When composing a workflow chain involving subagent execution for deductive tasks, what must be true about the final leaf node in the SOP sequence? | fail→pass | 20,100 | 2,146 | -89% | 1 | 1 | 0% | 1,444 | 417 | -71% | 0 | 0 | — |