The posted input files are now all mechanically generated from a master list of theorems.
The times shown in the following table are not the times required to find the proof, but rather
the maximum time allocated to Otter to find the proof. The time is shown only when it had to be longer than
the default, which was often 20 seconds when hints were used and 120 seconds when hints were not used.
For more information about our methodology see the top page of this project.
| Input File |
Proof |
Length |
Strategy |
Seconds |
Commentary |
| Satz3.1 | Satz3.1.prf | 2 | | | $ T(a,b,b) $ | | Satz3.2 | Satz3.2.prf | 4 | | | $ T(a,b,c) \rightarrow T(c,b,a) $ | | Satz3.3 | Satz3.3.prf | 1 | | | $ T(a,a,b) $ | | Satz3.4 | Satz3.4.prf | 9 | | | $ T(a,b,c) \land T(b,a,c) \rightarrow a=b $ | | Satz3.5a | Satz3.5a.prf | 4 | | | $ T(a,b,d) \land T(b,c,d) \rightarrow T(a,b,c) $ | | Satz3.6a | Satz3.6a.prf | 4 | | | $ T(a,b,c) \land T(a,c,d) \rightarrow T(b,c,d) $ | | Satz3.7a | Satz3.7a.prf | 8 | | | $T(a,b,c) \land T(b,c,d) \land b\neq c\rightarrow T(a,c,d) $ | | Satz3.5b | Satz3.5b.prf | 5 | | | $ T(a,b,d) \land T(b,c,d) \rightarrow T(a,c,d) $ | | Satz3.6b | Satz3.6b.prf | 4 | | | $T(a,b,c) \land T(a,c,d) \rightarrow T(a,d,b) $ | | Satz3.7b | Satz3.7b.prf | 2 | | | $ T(a,b,c) \land T(b,c,d) \land b\neq c\rightarrow T(a,b,d) $ | | Satz3.13a | Satz3.13a.prf | 1 | | | $\alpha \neq \beta $ | | Satz3.13b | Satz3.13b.prf | 1 | | | $ \beta \neq \gamma $ | | Satz3.13c | Satz3.13c.prf | 1 | | | $\alpha \neq \gamma $ | | Satz3.14a | Satz3.14a.prf | 0 | | | $ T(a,b,ext(a,b,\alpha,\gamma) $ | | Satz3.14b | Satz3.14b.prf | 3 | | | $ b\neq ext(a,b,\alpha,\gamma) $ | | Satz3.17 | Satz3.17.prf | 8 | diagram | | $ T(a,b,c) \land T(a_1,b_1,c) \land T(a,p,a_1) \rightarrow
\exists q(T(p,q,c) \land T(b,q,b_1) $ |
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