Run Detail
completedgrok-4.6Recorded for these videos
Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
19.9s
Total Tokens
1,316
Input Tokens
276
Output Tokens
1,040
Reasoning Tokens
893
Reasoning Effort
default
Cached Input Tokens
128
Est. Cost
$0.0066
Started
8/13/2026, 12:11:40 AM
OR Provider
xAI
Finish Reason
stop
Generation ID
gen-1786579901-pZevyWHmx631gY0SEEeU
Turns (1)
Turn #1
276 in1,040 out893 reasoning128 cached1,316 total19.9s
user
Evaluate whether the following conclusion is valid given the premises:
- All mammals are warm-blooded.
- All whales are mammals.
- Some sea creatures are whales.
- All warm-blooded animals need oxygen.
Conclusion: Some sea creatures need oxygen.
Provide a step-by-step logical derivation. Identify any hidden assumptions.
assistant
The given premises entail the conclusion via the following chain of categorical inferences (universal instantiation + modus ponens, followed by existential generalization):
- From (2) and (1): every whale is warm-blooded.
- From the preceding line together with the background fact that whales (being mammals) are animals, every whale is a warm-blooded animal.
- From that line and (4): every whale needs oxygen.
- From the preceding line and (3): at least one sea creature needs oxygen.
The only extra-logical assumption required is that mammals are animals (so that the predicate “warm-blooded animal” in (4) applies to them). With that commonplace biological classification granted, the argument is valid.