Certified Equational Reasoning via Ordered Completion

This website summarizes the experiments conducted for the paper Certified Equational Reasoning via Ordered Completion by Christian Sternagel and Sarah Winkler.

Below you can find three kinds of experiments:

In all three cases we use the certifier CeTA 2.36 to validate the generated certificates.

Infeasibility Problems for CTRS Confluence

The results of CTRS experiments are available in the table below. In the table, Cops numbers are hyperlinked to the corresponding input and answers to proofs (pretty printed CPF certificates in case of "-cert" columns and plain text files, otherwise). The two new problems mentioned in our paper are 340 and 361.

Furthermore, we provide a ZIP archive with all required (Linux) binaries and scripts to reproduce our experiments. (See also the corresponding README.)

Cops1.7-cert1.8-cert1.71.8
262NONONONO
263MAYBEMAYBEMAYBEMAYBE
264YESYESYESYES
266YESYESYESYES
267YESYESYESYES
268YESYESYESYES
271NONONONO
272YESYESYESYES
278YESYESYESYES
279TIMEOUTTIMEOUTTIMEOUTTIMEOUT
284TIMEOUTTIMEOUTTIMEOUTTIMEOUT
285MAYBEMAYBEMAYBEMAYBE
286MAYBEMAYBEYESYES
287YESYESYESYES
288YESYESYESYES
289MAYBEMAYBEMAYBEMAYBE
292YESYESYESYES
293NONONONO
294YESYESYESYES
307YESYESYESYES
308YESYESYESYES
309NONONONO
310NONONONO
311NONONONO
312NONONONO
313MAYBEMAYBEMAYBEMAYBE
314NONONONO
315NONONONO
316YESYESYESYES
317YESYESYESYES
318NONONONO
319YESYESYESYES
320NONONONO
321NONONONO
322YESYESYESYES
323NONONONO
324MAYBEMAYBEMAYBEMAYBE
325NONONONO
326YESYESYESYES
327MAYBEMAYBEMAYBEMAYBE
328NONONONO
329YESYESYESYES
330NONONONO
332YESYESYESYES
333YESYESYESYES
334YESYESYESYES
335YESYESYESYES
336YESYESYESYES
337MAYBEMAYBEMAYBEMAYBE
339YESYESYESYES
340MAYBEYESMAYBEYES
341YESYESYESYES
342MAYBEMAYBEMAYBEMAYBE
343YESYESYESYES
344YESYESYESYES
345MAYBEMAYBEMAYBEMAYBE
346MAYBEMAYBEMAYBEMAYBE
347MAYBEMAYBEMAYBEMAYBE
348MAYBEMAYBEMAYBEMAYBE
349MAYBEMAYBEMAYBEMAYBE
350MAYBEMAYBEMAYBEMAYBE
351NONONONO
352NONONONO
353NONONONO
354YESYESYESYES
355YESYESYESYES
356YESYESYESYES
357NONONONO
358NONONONO
359YESYESYESYES
360NONONONO
361TIMEOUTYESTIMEOUTYES
362YESYESYESYES
363NONONONO
364YESYESYESYES
365MAYBEMAYBEMAYBEMAYBE
366NONONONO
367NONONONO
368NONONONO
369NONONONO
370YESYESYESYES
371YESYESYESYES
372NONONONO
373NONONONO
374NONONONO
375YESYESYESYES
376YESYESYESYES
377NONONONO
378TIMEOUTTIMEOUTYESYES
379NONONONO
380YESYESYESYES
381NONONONO
382NONONONO
383NONONONO
384NONONONO
385NONONONO
386YESYESYESYES
387MAYBEMAYBEMAYBEMAYBE
388YESYESYESYES
389MAYBEMAYBEMAYBEMAYBE
390YESYESYESYES
391NONONONO
403YESYESYESYES
404NONONONO
405MAYBEMAYBEMAYBEMAYBE
406MAYBEMAYBEMAYBEMAYBE
407MAYBEMAYBEMAYBEMAYBE
408YESYESYESYES
409MAYBEMAYBEMAYBEMAYBE
410NONONONO
411NONONONO
439YESYESYESYES
440MAYBETIMEOUTMAYBETIMEOUT
441NONONONO
488YESYESYESYES
489MAYBEMAYBEMAYBEMAYBE
490YESYESYESYES
491YESYESYESYES
492YESYESYESYES
493YESYESYESYES
494YESYESYESYES
495YESYESYESYES
499TIMEOUTTIMEOUTTIMEOUTTIMEOUT
522MAYBEMAYBEMAYBEMAYBE
523YESYESYESYES
524NONONONO
527YESYESYESYES
528YESYESYESYES
529TIMEOUTTIMEOUTTIMEOUTTIMEOUT
546YESYESYESYES
547YESYESYESYES
548YESYESYESYES
549YESYESYESYES
550YESYESYESYES
551YESYESYESYES
552YESYESYESYES
553MAYBEMAYBEMAYBEMAYBE
790MAYBEMAYBEMAYBEMAYBE
791MAYBEMAYBEMAYBEMAYBE
792YESYESYESYES
793MAYBEMAYBEYESYES
794YESYESYESYES
796NONONONO
798TIMEOUTTIMEOUTTIMEOUTTIMEOUT
799YESYESYESYES
805MAYBEMAYBEMAYBEMAYBE
806YESYESYESYES
807MAYBEMAYBEMAYBEMAYBE

Ordered Completion for Ground Completeness

The table below summarizes the results of our ordered completion experiments. File names are hyperlinked to the corresponding input and answers to proofs (pretty printed CPF certificates in case of "cert" columns and plain text files, otherwise).

Furthermore, we provide a ZIP archive with all required binaries and a README that describes how to reproduce our experiments.

TPTPcertnoncert
Ex4_12_ACgroups0YESYES
Ex4_1_commutativityYESYES
Ex4_2_ACYESYES
Ex4_4_ACUYESYES
Ex4_5_ACgroups_exp2YESYES
Ex4_6_ACgroups_exp2-2YESYES
Ex4_7_distributivityTIMEOUTTIMEOUT
Ex4_8_Boolean_ringsTIMEOUTYES
Ex4_9aTIMEOUTTIMEOUT
Ex4_9bYESYES
TRScertnoncert
AD93_Z22TIMEOUTTIMEOUT
ASK93_1YESYES
ASK93_2TIMEOUTYES
ASK93_5TIMEOUTTIMEOUT
ASK93_6YESYES
aufgabe3_2YESYES
aufgabe3_3YESYES
B91_ordered_ACgroupsYESYES
B91_ordered_ACIYESYES
B91_unfailing1YESYES
B91_unfailing_groupoidYESYES
BD94_collapseYESYES
BD94_peanoTIMEOUTYES
BD94_sqrtYESYES
BGK94_D08TIMEOUTYES
BGK94_D10TIMEOUTYES
BGK94_D12TIMEOUTTIMEOUT
BGK94_D16TIMEOUTTIMEOUT
BGK94_M08YESYES
BGK94_M10YESYES
BGK94_M12YESYES
BGK94_M14YESYES
BGK94_Z22WTIMEOUTTIMEOUT
BH96_fac8_theoryYESYES
Chr89_A24TIMEOUTTIMEOUT
Chr89_A2TIMEOUTYES
Chr89_A3TIMEOUTYES
fggxYESYES
fibTIMEOUTTIMEOUT
HR94_1TIMEOUTTIMEOUT
HR94_2TIMEOUTTIMEOUT
kb_fail1YESYES
kb_failYESYES
KK99_linear_assocYESYES
Les83_fibTIMEOUTYES
Les83_subsetTIMEOUTYES
lr_theoryTIMEOUTYES
LS06_CGE4TIMEOUTTIMEOUT
LS06_CGE5TIMEOUTTIMEOUT
LS06_CGE6TIMEOUTTIMEOUT
LS06_CGE7TIMEOUTTIMEOUT
LS94_G0TIMEOUTYES
LS94_G1TIMEOUTTIMEOUT
LS94_G2TIMEOUTTIMEOUT
LS94_G3TIMEOUTTIMEOUT
LS94_G4TIMEOUTTIMEOUT
LS94_G5TIMEOUTTIMEOUT
LS94_G6TIMEOUTTIMEOUT
LS94_G7TIMEOUTTIMEOUT
LS94_G8TIMEOUTTIMEOUT
LS94_G9TIMEOUTTIMEOUT
LS94_P1TIMEOUTTIMEOUT
LS94_P2TIMEOUTTIMEOUT
LS94_P3TIMEOUTTIMEOUT
LS94_P4TIMEOUTTIMEOUT
LS94_P5TIMEOUTTIMEOUT
LS94_P6TIMEOUTTIMEOUT
LS94_P7TIMEOUTTIMEOUT
LS94_P8TIMEOUTTIMEOUT
LS94_P9TIMEOUTTIMEOUT
MN90_distributivityTIMEOUTTIMEOUT
OKW95_dt1_theoryTIMEOUTTIMEOUT
rl_theoryTIMEOUTYES
Sim91_sims2TIMEOUTYES
SK90_3.01TIMEOUTYES
SK90_3.02YESYES
SK90_3.03TIMEOUTYES
SK90_3.04TIMEOUTYES
SK90_3.05YESYES
SK90_3.06TIMEOUTYES
SK90_3.07TIMEOUTYES
SK90_3.08YESYES
SK90_3.09TIMEOUTTIMEOUT
SK90_3.10YESYES
SK90_3.11YESYES
SK90_3.12TIMEOUTTIMEOUT
SK90_3.13YESYES
SK90_3.14TIMEOUTYES
SK90_3.15YESYES
SK90_3.16YESYES
SK90_3.17YESYES
SK90_3.18TIMEOUTYES
SK90_3.19YESYES
SK90_3.20TIMEOUTYES
SK90_3.21YESYES
SK90_3.22YESTIMEOUT
SK90_3.23TIMEOUTTIMEOUT
SK90_3.24YESYES
SK90_3.25YESYES
SK90_3.26TIMEOUTYES
SK90_3.27YESYES
SK90_3.28TIMEOUTTIMEOUT
SK90_3.29TIMEOUTYES
SK90_3.30YESYES
SK90_3.31YESYES
SK90_3.32YESYES
SK90_3.33YESYES
slothrop_ackermannTIMEOUTYES
slothrop_cge3TIMEOUTTIMEOUT
slothrop_cgeTIMEOUTTIMEOUT
slothrop_endoTIMEOUTTIMEOUT
slothrop_equiv_proofs_orTIMEOUTTIMEOUT
slothrop_equiv_proofsTIMEOUTTIMEOUT
slothrop_fghYESYES
slothrop_groups_conjYESYES
slothrop_groupsTIMEOUTYES
slothrop_hardYESYES
slothrop_nlp-2bTIMEOUTYES
TPDB_secret2006_torpa_secr10YESYES
TPDB_secret2006_torpa_secr4YESYES
TPDB_thiemann27TIMEOUTYES
TPDB_zantema_z115YESYES
TPTP_BOO027-1_theoryYESYES
TPTP_COL053-1_theoryYESYES
TPTP_COL056-1_theoryYESYES
TPTP_COL060-1_theoryYESYES
TPTP_COL085-1_theoryYESYES
TPTP_GRP010-4_theoryTIMEOUTYES
TPTP_GRP011-4_theoryTIMEOUTYES
TPTP_GRP012-4_theoryYESYES
TPTP_GRP393-2_theoryYESYES
TPTP_GRP394-3_theoryTIMEOUTYES
TPTP_GRP454-1_theoryTIMEOUTYES
TPTP_GRP457-1_theoryTIMEOUTYES
TPTP_GRP460-1_theoryTIMEOUTYES
TPTP_GRP463-1_theoryTIMEOUTYES
TPTP_GRP481-1_theoryTIMEOUTYES
TPTP_GRP484-1_theoryTIMEOUTTIMEOUT
TPTP_GRP487-1_theoryTIMEOUTYES
TPTP_GRP490-1_theoryTIMEOUTYES
TPTP_GRP493-1_theoryTIMEOUTYES
TPTP_GRP496-1_theoryTIMEOUTYES
TPTP_HWC004-1_theoryYESYES
TPTP_HWC004-2_theoryYESYES
TPTP_SWV262-2_theoryYESYES
unknot_culpritTIMEOUTTIMEOUT
unknot_trifoilTIMEOUTTIMEOUT
WS06_proofreductionTIMEOUTTIMEOUT

UEQ Satisfiability

The table below summarizes the results of our ordered completion experiments. File names are hyperlinked to the corresponding input and answers to proofs (pretty printed CPF certificates in case of "cert" columns and plain text files, otherwise).

Furthermore, we provide a ZIP archive with all required binaries and a README that describes how to reproduce our experiments.

TPTPcertnoncert
ALG299-1YESYES
ALG300-1YESYES
ALG302-1YESYES
BOO027-1YESYES
GRP393-2YESYES
GRP394-3YESYES
HWC004-1YESYES
HWC004-2YESYES
LCL407-2YESYES
LCL905-1YESYES
SYN552-1YESYES