Rule 1: The middle term must be distributed at least once.
Rule 2: No term undistributed in the premises may be distributed in the conclusion.
Rule 3: If both premises are negative then no conclusion is possible.
Rule 4: If one premise is negative then the conclusion must be negative.
Rule 5: If neither premise is negative then the conclusion must be affirmative.
Rule 6: If both premises are universal then the conclusion can not be particular.
| Syllogism | Rule 1 | Rule 2 | Rule 3 | Rule 4 | Rule 5 | Rule 6 | Validity |
| AAA-1 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| AII-1 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| EAE-1 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| EIO-1 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| AEE-2 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| AOO-2 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| EAE-2 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| EIO-2 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| AII-3 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| EIO-3 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| IAI-3 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| OAO-3 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| AEE-4 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| EIO-4 | PASS | PASS | PASS | PASS | PASS | PASS | True |
| IAI-4 | PASS | PASS | PASS | PASS | PASS | PASS | True |
(Query Optimised)
| syllogism | rule 5 | rule 6 | rule 2 | rule 4 | rule 1 | rule 3 |
| aaa 1 | pass | pass | pass | pass | pass | pass |
| aii 1 | pass | pass | pass | pass | pass | pass |
| eae 1 | pass | pass | pass | pass | pass | pass |
| eio 1 | pass | pass | pass | pass | pass | pass |
| aee 2 | pass | pass | pass | pass | pass | pass |
| aoo 2 | pass | pass | pass | pass | pass | pass |
| eae 2 | pass | pass | pass | pass | pass | pass |
| eio 2 | pass | pass | pass | pass | pass | pass |
| aii 3 | pass | pass | pass | pass | pass | pass |
| eio 3 | pass | pass | pass | pass | pass | pass |
| iai 3 | pass | pass | pass | pass | pass | pass |
| oao 3 | pass | pass | pass | pass | pass | pass |
| aee 4 | pass | pass | pass | pass | pass | pass |
| eio 4 | pass | pass | pass | pass | pass | pass |
| iai 4 | pass | pass | pass | pass | pass | pass |
| ooo 1 | pass | pass | pass | pass | pass | fail |
| eee 3 | pass | pass | pass | pass | pass | fail |
| eee 1 | pass | pass | pass | pass | pass | fail |
| eoe 3 | pass | pass | pass | pass | pass | fail |
| eoo 3 | pass | pass | pass | pass | pass | fail |
| eoo 1 | pass | pass | pass | pass | pass | fail |
| oee 1 | pass | pass | pass | pass | pass | fail |
| oee 3 | pass | pass | pass | pass | pass | fail |
| oeo 3 | pass | pass | pass | pass | pass | fail |
| eee 2 | pass | pass | pass | pass | pass | fail |
| eee 4 | pass | pass | pass | pass | pass | fail |
| oeo 1 | pass | pass | pass | pass | pass | fail |
| eoe 4 | pass | pass | pass | pass | pass | fail |
| eoo 4 | pass | pass | pass | pass | pass | fail |
| eoo 2 | pass | pass | pass | pass | pass | fail |
| iaa 1 | pass | pass | pass | pass | fail | pass |
| iai 1 | pass | pass | pass | pass | fail | pass |
| iii 3 | pass | pass | pass | pass | fail | pass |
| oio 1 | pass | pass | pass | pass | fail | pass |
| iii 1 | pass | pass | pass | pass | fail | pass |
| iaa 2 | pass | pass | pass | pass | fail | pass |
| oio 3 | pass | pass | pass | pass | fail | pass |
| iai 2 | pass | pass | pass | pass | fail | pass |
| aii 4 | pass | pass | pass | pass | fail | pass |
| aoe 4 | pass | pass | pass | pass | fail | pass |
| aoo 4 | pass | pass | pass | pass | fail | pass |
| iii 2 | pass | pass | pass | pass | fail | pass |
| aaa 2 | pass | pass | pass | pass | fail | pass |
| oae 1 | pass | pass | pass | pass | fail | pass |
| aii 2 | pass | pass | pass | pass | fail | pass |
| oao 1 | pass | pass | pass | pass | fail | pass |
| iii 4 | pass | pass | pass | pass | fail | pass |
| ooe 3 | pass | pass | pass | pass | fail | fail |
| ooo 3 | pass | pass | pass | pass | fail | fail |
| eaa 2 | pass | pass | pass | fail | pass | pass |
| iea 1 | pass | pass | pass | fail | pass | pass |
| iei 1 | pass | pass | pass | fail | pass | pass |
| eii 2 | pass | pass | pass | fail | pass | pass |
| iea 3 | pass | pass | pass | fail | pass | pass |
| iei 3 | pass | pass | pass | fail | pass | pass |
| eaa 1 | pass | pass | pass | fail | pass | pass |
| oai 3 | pass | pass | pass | fail | pass | pass |
| ioi 1 | pass | pass | pass | fail | pass | pass |
| aea 2 | pass | pass | pass | fail | pass | pass |
| aea 1 | pass | pass | pass | fail | pass | pass |
| iea 2 | pass | pass | pass | fail | pass | pass |
| iei 2 | pass | pass | pass | fail | pass | pass |
| aoi 1 | pass | pass | pass | fail | pass | pass |
| aea 4 | pass | pass | pass | fail | pass | pass |
| ioi 2 | pass | pass | pass | fail | pass | pass |
| oaa 2 | pass | pass | pass | fail | pass | pass |
| oai 2 | pass | pass | pass | fail | pass | pass |
| oii 2 | pass | pass | pass | fail | pass | pass |
| aea 3 | pass | pass | pass | fail | pass | pass |
| eii 4 | pass | pass | pass | fail | pass | pass |
| aoi 2 | pass | pass | pass | fail | pass | pass |
| aoa 3 | pass | pass | pass | fail | pass | pass |
| aoi 3 | pass | pass | pass | fail | pass | pass |
| eii 1 | pass | pass | pass | fail | pass | pass |
| iea 4 | pass | pass | pass | fail | pass | pass |
| iei 4 | pass | pass | pass | fail | pass | pass |
| eii 3 | pass | pass | pass | fail | pass | pass |
| oai 4 | pass | pass | pass | fail | pass | pass |
| oii 4 | pass | pass | pass | fail | pass | pass |
| eea 2 | pass | pass | pass | fail | pass | fail |
| ooi 2 | pass | pass | pass | fail | pass | fail |
| ooi 1 | pass | pass | pass | fail | pass | fail |
| eoi 1 | pass | pass | pass | fail | pass | fail |
| eea 4 | pass | pass | pass | fail | pass | fail |
| oei 1 | pass | pass | pass | fail | pass | fail |
| eoi 2 | pass | pass | pass | fail | pass | fail |
| eea 3 | pass | pass | pass | fail | pass | fail |
| eoa 4 | pass | pass | pass | fail | pass | fail |
| oea 3 | pass | pass | pass | fail | pass | fail |
| eoi 4 | pass | pass | pass | fail | pass | fail |
| eea 1 | pass | pass | pass | fail | pass | fail |
| oei 3 | pass | pass | pass | fail | pass | fail |
| oea 1 | pass | pass | pass | fail | pass | fail |
| oea 2 | pass | pass | pass | fail | pass | fail |
| eoa 3 | pass | pass | pass | fail | pass | fail |
| oei 2 | pass | pass | pass | fail | pass | fail |
| oea 4 | pass | pass | pass | fail | pass | fail |
| oei 4 | pass | pass | pass | fail | pass | fail |
| eoi 3 | pass | pass | pass | fail | pass | fail |
| ooa 4 | pass | pass | pass | fail | pass | fail |
| ooi 4 | pass | pass | pass | fail | pass | fail |
| oai 1 | pass | pass | pass | fail | fail | pass |
| oii 3 | pass | pass | pass | fail | fail | pass |
| ioa 4 | pass | pass | pass | fail | fail | pass |
| ioi 4 | pass | pass | pass | fail | fail | pass |
| aoa 4 | pass | pass | pass | fail | fail | pass |
| oaa 1 | pass | pass | pass | fail | fail | pass |
| aoi 4 | pass | pass | pass | fail | fail | pass |
| oii 1 | pass | pass | pass | fail | fail | pass |
| ioa 3 | pass | pass | pass | fail | fail | pass |
| ioi 3 | pass | pass | pass | fail | fail | pass |
| ooa 3 | pass | pass | pass | fail | fail | fail |
| ooi 3 | pass | pass | pass | fail | fail | fail |
| aoo 3 | pass | pass | fail | pass | pass | pass |
| eae 3 | pass | pass | fail | pass | pass | pass |
| ieo 2 | pass | pass | fail | pass | pass | pass |
| aaa 4 | pass | pass | fail | pass | pass | pass |
| iee 1 | pass | pass | fail | pass | pass | pass |
| eie 3 | pass | pass | fail | pass | pass | pass |
| ioe 2 | pass | pass | fail | pass | pass | pass |
| aia 1 | pass | pass | fail | pass | pass | pass |
| ioo 2 | pass | pass | fail | pass | pass | pass |
| eie 2 | pass | pass | fail | pass | pass | pass |
| oae 2 | pass | pass | fail | pass | pass | pass |
| eae 4 | pass | pass | fail | pass | pass | pass |
| ieo 1 | pass | pass | fail | pass | pass | pass |
| iaa 3 | pass | pass | fail | pass | pass | pass |
| eie 4 | pass | pass | fail | pass | pass | pass |
| oao 2 | pass | pass | fail | pass | pass | pass |
| aoo 1 | pass | pass | fail | pass | pass | pass |
| iee 3 | pass | pass | fail | pass | pass | pass |
| ioe 1 | pass | pass | fail | pass | pass | pass |
| ieo 3 | pass | pass | fail | pass | pass | pass |
| oie 2 | pass | pass | fail | pass | pass | pass |
| iaa 4 | pass | pass | fail | pass | pass | pass |
| aoe 2 | pass | pass | fail | pass | pass | pass |
| oio 2 | pass | pass | fail | pass | pass | pass |
| iee 4 | pass | pass | fail | pass | pass | pass |
| oae 3 | pass | pass | fail | pass | pass | pass |
| ieo 4 | pass | pass | fail | pass | pass | pass |
| eie 1 | pass | pass | fail | pass | pass | pass |
| aaa 3 | pass | pass | fail | pass | pass | pass |
| ioo 1 | pass | pass | fail | pass | pass | pass |
| oae 4 | pass | pass | fail | pass | pass | pass |
| aee 3 | pass | pass | fail | pass | pass | pass |
| oao 4 | pass | pass | fail | pass | pass | pass |
| aia 3 | pass | pass | fail | pass | pass | pass |
| aee 1 | pass | pass | fail | pass | pass | pass |
| oie 4 | pass | pass | fail | pass | pass | pass |
| iee 2 | pass | pass | fail | pass | pass | pass |
| oio 4 | pass | pass | fail | pass | pass | pass |
| aoe 3 | pass | pass | fail | pass | pass | pass |
| aoe 1 | pass | pass | fail | pass | pass | pass |
| eoe 1 | pass | pass | fail | pass | pass | fail |
| oee 4 | pass | pass | fail | pass | pass | fail |
| ooe 1 | pass | pass | fail | pass | pass | fail |
| oeo 4 | pass | pass | fail | pass | pass | fail |
| oee 2 | pass | pass | fail | pass | pass | fail |
| ooe 2 | pass | pass | fail | pass | pass | fail |
| eoe 2 | pass | pass | fail | pass | pass | fail |
| ooo 2 | pass | pass | fail | pass | pass | fail |
| ooe 4 | pass | pass | fail | pass | pass | fail |
| oeo 2 | pass | pass | fail | pass | pass | fail |
| ooo 4 | pass | pass | fail | pass | pass | fail |
| aia 4 | pass | pass | fail | pass | fail | pass |
| iia 3 | pass | pass | fail | pass | fail | pass |
| iia 2 | pass | pass | fail | pass | fail | pass |
| aia 2 | pass | pass | fail | pass | fail | pass |
| iia 4 | pass | pass | fail | pass | fail | pass |
| ioe 3 | pass | pass | fail | pass | fail | pass |
| iia 1 | pass | pass | fail | pass | fail | pass |
| ioe 4 | pass | pass | fail | pass | fail | pass |
| ioo 3 | pass | pass | fail | pass | fail | pass |
| ioo 4 | pass | pass | fail | pass | fail | pass |
| oie 3 | pass | pass | fail | pass | fail | pass |
| oie 1 | pass | pass | fail | pass | fail | pass |
| eaa 3 | pass | pass | fail | fail | pass | pass |
| eia 2 | pass | pass | fail | fail | pass | pass |
| aoa 2 | pass | pass | fail | fail | pass | pass |
| eia 4 | pass | pass | fail | fail | pass | pass |
| eia 1 | pass | pass | fail | fail | pass | pass |
| eia 3 | pass | pass | fail | fail | pass | pass |
| oia 4 | pass | pass | fail | fail | pass | pass |
| ioa 1 | pass | pass | fail | fail | pass | pass |
| oaa 3 | pass | pass | fail | fail | pass | pass |
| aoa 1 | pass | pass | fail | fail | pass | pass |
| oia 2 | pass | pass | fail | fail | pass | pass |
| ioa 2 | pass | pass | fail | fail | pass | pass |
| oaa 4 | pass | pass | fail | fail | pass | pass |
| eaa 4 | pass | pass | fail | fail | pass | pass |
| eoa 1 | pass | pass | fail | fail | pass | fail |
| ooa 1 | pass | pass | fail | fail | pass | fail |
| eoa 2 | pass | pass | fail | fail | pass | fail |
| ooa 2 | pass | pass | fail | fail | pass | fail |
| oia 1 | pass | pass | fail | fail | fail | pass |
| oia 3 | pass | pass | fail | fail | fail | pass |
| aeo 2 | pass | fail | pass | pass | pass | pass |
| eao 1 | pass | fail | pass | pass | pass | pass |
| aai 4 | pass | fail | pass | pass | pass | pass |
| aai 1 | pass | fail | pass | pass | pass | pass |
| aai 3 | pass | fail | pass | pass | pass | pass |
| aeo 4 | pass | fail | pass | pass | pass | pass |
| eao 4 | pass | fail | pass | pass | pass | pass |
| eao 3 | pass | fail | pass | pass | pass | pass |
| eao 2 | pass | fail | pass | pass | pass | pass |
| eeo 1 | pass | fail | pass | pass | pass | fail |
| eeo 3 | pass | fail | pass | pass | pass | fail |
| eeo 2 | pass | fail | pass | pass | pass | fail |
| eeo 4 | pass | fail | pass | pass | pass | fail |
| aai 2 | pass | fail | pass | pass | fail | pass |
| aei 2 | pass | fail | pass | fail | pass | pass |
| eai 3 | pass | fail | pass | fail | pass | pass |
| eai 2 | pass | fail | pass | fail | pass | pass |
| aei 3 | pass | fail | pass | fail | pass | pass |
| aei 4 | pass | fail | pass | fail | pass | pass |
| aei 1 | pass | fail | pass | fail | pass | pass |
| eai 1 | pass | fail | pass | fail | pass | pass |
| eai 4 | pass | fail | pass | fail | pass | pass |
| eei 3 | pass | fail | pass | fail | pass | fail |
| eei 1 | pass | fail | pass | fail | pass | fail |
| eei 4 | pass | fail | pass | fail | pass | fail |
| eei 2 | pass | fail | pass | fail | pass | fail |
| aeo 1 | pass | fail | fail | pass | pass | pass |
| aeo 3 | pass | fail | fail | pass | pass | pass |
| aae 2 | fail | pass | pass | pass | fail | pass |
| aio 2 | fail | pass | pass | pass | fail | pass |
| aio 4 | fail | pass | pass | pass | fail | pass |
| aae 3 | fail | pass | fail | pass | pass | pass |
| aae 4 | fail | pass | fail | pass | pass | pass |
| aio 1 | fail | pass | fail | pass | pass | pass |
| aie 1 | fail | pass | fail | pass | pass | pass |
| iae 4 | fail | pass | fail | pass | pass | pass |
| iae 3 | fail | pass | fail | pass | pass | pass |
| iao 4 | fail | pass | fail | pass | pass | pass |
| aie 3 | fail | pass | fail | pass | pass | pass |
| iao 3 | fail | pass | fail | pass | pass | pass |
| aae 1 | fail | pass | fail | pass | pass | pass |
| aio 3 | fail | pass | fail | pass | pass | pass |
| iie 3 | fail | pass | fail | pass | fail | pass |
| iie 2 | fail | pass | fail | pass | fail | pass |
| iio 3 | fail | pass | fail | pass | fail | pass |
| iio 1 | fail | pass | fail | pass | fail | pass |
| iio 2 | fail | pass | fail | pass | fail | pass |
| iie 4 | fail | pass | fail | pass | fail | pass |
| iao 2 | fail | pass | fail | pass | fail | pass |
| iio 4 | fail | pass | fail | pass | fail | pass |
| aie 2 | fail | pass | fail | pass | fail | pass |
| iae 1 | fail | pass | fail | pass | fail | pass |
| iie 1 | fail | pass | fail | pass | fail | pass |
| aie 4 | fail | pass | fail | pass | fail | pass |
| iao 1 | fail | pass | fail | pass | fail | pass |
| iae 2 | fail | pass | fail | pass | fail | pass |
| aao 4 | fail | fail | pass | pass | pass | pass |
| aao 2 | fail | fail | pass | pass | fail | pass |
| aao 1 | fail | fail | fail | pass | pass | pass |
| aao 3 | fail | fail | fail | pass | pass | pass |