## Octopus Results

Monty Newborn

Octopus solved 116 of the 200 MIX division problems of CASC-J2. It produced a proof for 115 of the 200 problems. For SYN353-1, a proof was found to exist, but there was not time to put it together. THEO (the underlying sequential system) was able to solve 83 theorems, 33 less than Octopus. Each was unable to construct the proof of one theorem for which a proof was known to exist.

Octopus ran on a network of 120 computers (PCs). Because it got a later start in the competition, it was given only 400 seconds per theorem. The MIX division problem solvers all were given 600 seconds per theorem. Given the spread on times to find a proof, if Octopus had been given the additional 200 seconds per theorem, it might have proved 2-3 more.

A bug may have come up near the end of the test when the master solved a number of the theorems by itself. Essentially, copies of octopus were not being killed on the slaves between problems. The program was stopped and restarted on GEO008-1 (Problem 192) and when restarted, the slaves again solved problems before the master. If the version of Octopus running on the slaves is not properly killed between problems, eventually, the slaves are brought to a standstill. The problem seemed to begin around Problem 184-185.

The 200 problems follow.

```ALG004-1
ALG012-1
ANA002-1            solved by slave  27 in 7 sec. (66)
ANA003-1            solved by slave  34 in 44 sec. (21)
ANA003-2            solved by slave  34 in 26 sec. (25)
ANA003-4            solved by slave  37 in 3 sec.  (2)
ANA004-1            solved by slave  57 in 84 sec. (38)
ANA004-4            solved by slave  53 in 5 sec. (53)
ANA005-1
BOO038-1
CAT004-3            solved by slave   3 in 0 sec. (95)
CAT009-3            solved by slave  22 in 2 sec. (94)
COL003-7            solved by slave  30 in 324 sec. (46)
COL003-9            solved by slave 106 in 238 sec. (72)
COL003-10
COL006-2
COL006-3
COL006-4
COL043-2
COL044-2
COL044-3
COL044-4
COL076-2
COL078-1
COL079-2            solved by slave  40 in 7 sec. (8)
COL088-2            solved by slave  12 in 2 sec. (85)
COL089-1            solved by slave   3 in 0 sec. (44)
COL089-2            solved by slave  51 in 3 sec. (23)
COL090-2            solved by slave  12 in 6 sec. (65)
COL090-3            solved by master    in 0 sec. (103)
COL091-1            solved by master    in 0 sec. (102)
COL091-2            solved by slave  32 in 1 sec. (100)
COL092-1            solved by slave  28 in 1 sec. (61)
COL092-2            solved by slave  28 in 6 sec. (91)
COL093-1            solved by slave  28 in 2 sec. (14)
COL093-2            solved by slave  12 in 258 sec. (111)
COL098-2            solved by slave  17 in 8 sec. (41)
COL099-2            solved by master    in 0 sec. (104)
COM003-1
COM005-1
FLD007-1            solved by master    in 26 sec. (45)
FLD009-1            solved by slave  77 in 2 sec.  (5)
FLD023-1            solved by master    in 0 sec. (69)
FLD031-1            solved by slave  22 in 0 sec. (56)
FLD047-4            solved by slave  12 in 13 sec. (59)
FLD050-4            solved by slave  15 in 1 sec. (58)
FLD060-2            solved by slave   9 in 3 sec. (48)
FLD062-3            solved by slave  45 in 1 sec. (24)
FLD063-1            solved by slave  29 in 13 sec. (83)
GEO006-1            solved by slave  23 in 1 sec. (90)
GEO007-1            solved by slave  94 in 48 sec. (29)
GEO008-1
GEO026-2            solved by slave  15 in 0 sec. (101)
GEO030-3            solved by master    in 0 sec.  (4)
GEO036-2            solved by slave   1 in 0 sec. (99)
GEO043-3            solved by slave   7 in 0 sec. (52)
GEO045-2
GEO083-1            solved by slave   3 in 1 sec. (96)
GEO146-1            solved by slave   6 in 0 sec. (49)
GRP039-1            solved by slave  32 in 4 sec. (86)
GRP039-2            solved by slave   7 in 33 sec. (112)
GRP039-4            solved by slave  17 in 6 sec. (68)
GRP039-5            solved by slave  55 in 105 sec. (93)
GRP039-6            solved by slave  18 in 1 sec. (78)
GRP039-7            solved by slave   3 in 77 sec. (105)
GRP040-3            solved by slave  28 in 3 sec. (98)
GRP040-4            solved by slave  12 in 0 sec. (82)
GRP054-1
GRP084-1
GRP086-1
GRP113-1
GRP197-1
GRP198-1
GRP199-1
GRP273-1
GRP401-1
HWC003-1
HWC003-2
HWV002-1
HWV003-1
HWV017-2            solved by slave  25 in 61 sec. (115)
HWV018-2            solved by slave  28 in 0 sec. (77)
HWV029-1
HWV033-1            solved by slave   3 in 0 sec. (62)
LAT001-1
LAT002-1
LAT003-1
LAT015-1
LAT036-1
LAT041-1
LAT066-1
LCL012-1            solved by slave  25 in 120 sec. (13)
LCL018-1            solved by slave  60 in 230 sec. (6)
LCL052-1            solved by slave  45 in 363 sec. (81)
LCL068-1            solved by slave  31 in 2 sec. (73)
LCL109-3            solved by slave  84 in 4 sec. (12)
LCL109-4
LCL152-1
LCL166-1
LCL191-1
LCL195-1            solved by slave   3 in 1 sec. (71)
LCL221-1            solved by slave  41 in 11 sec. (28)
LCL222-3
LCL225-1            solved by slave  19 in 275 sec. (79)
LCL227-1            solved by slave  12 in 331 sec. (57)
LCL237-3            solved by slave   6 in 5 sec. (75)
LCL243-3
LCL249-3
LCL253-1
LCL253-3
LCL278-3
LCL324-3
LCL341-3
MGT029-1
MGT035-1
MGT039-2            solved by slave 106 in 80 sec. (108)
MGT051-1            solved by slave  25 in 3 sec. (16)
MGT060-1            solved by master    in 0 sec. (10)
MGT063-1
NUM007-1            solved by master    in 7 sec. (113)
NUM011-1
PLA004-2            solved by slave   4 in 3 sec. (70)
PLA005-2            solved by slave   6 in 4 sec. (36)
PLA009-2            solved by slave   9 in 1 sec. (67)
PLA011-1            solved by slave  29 in 2 sec. (17)
PLA012-1            solved by slave  39 in 31 sec. (20)
PLA021-1            solved by slave 119 in 2 sec. (30)
PLA023-1
PUZ035-7            solved by master    in 0 sec. (32)
PUZ039-1
PUZ040-1
PUZ042-1
PUZ056-1
RNG001-2            solved by slave  19 in 8 sec. (54)
RNG001-5            solved by slave   7 in 1 sec. (64)
RNG004-3            solved by slace  15 in 0 sec. (22)
RNG025-1
RNG029-3
ROB014-1
ROB015-2
ROB018-1
ROB019-1
SET010-1            solved by slave   6 in 0 sec. (35)
SET012-3            solved by slave   3 in 5 sec. (109)
SET013-1            solved by master    in 9 sec. (63)
SET013-2            solved by slave   5 in 139 sec. (37)
SET014-3            solved by slave   3 in 1 sec. (89)
SET014-4            solved by slave   1 in 0 sec. (55)
SET015-1            solved by master    in 32 sec. (19)
SET016-3
SET019-4            solved by slave  25 in 4 sec. (33)
SET021-3
SET022-3            solved by slave  16 in 1 sec. (84)
SET025-8            solved by slave   1 in 0 sec. (31)
SET031-3            solved by slave  43 in 1 sec. (26)
SET041-3            solved by slave   3 in 1 sec. (110)
SET082-6            solved by slave   9 in 1 sec. (34)
SET121-7            solved by slave   5 in 4 sec. (18)
SET199-6            solved by master    in 0 sec. (106)
SET215-6            solved by slave   3 in 148 sec. (107)
SET230-6
SET235-6            solved by slave   3 in 1 sec. (114)
SET260-6            solved by slave 101 in 247 sec. (7)
SET386-6            solved by slave  35 in 1 sec. (47)
SET787-1            solved by slave   3 in 0 sec. (74)
SET787-2            solved by slave  15 in 3 sec. (87)
SWC113-1
SWC123-1
SWC166-1
SWC286-1            solved by slave  71 in 12 sec. (116)
SWC293-1            solved by slave   1 in 2 sec. (97)
SWC295-1
SWC375-1            solved by slave  10 in 2 sec. (92)
SWV014-1            solved by slave  22 in 0 sec. (43)
SYN036-1
SYN036-4
SYN067-1
SYN067-2
SYN076-1
SYN077-1            solved by slave  32 in 0 sec. (88)
SYN311-1            solved by slave   3 in 0 sec. (76)
SYN312-1            solved by slave  23 in 0 sec. (15)
SYN314-1.002.001
SYN353-1            solved by slave  82 -- no proof constructed (50)
SYN597-1            solved by slave   6 in 1 sec. (9)
SYN602-1            solved by slave   3 in 0 sec. (40)
SYN603-1            solved by slave   4 in 0 sec. (60)
SYN609-1            solved by slave  15 in 0 sec. (80)
SYN610-1            solved by slave  16 in 1 sec. (39)
SYN611-1            solved by slave   1 in o sec. (27)
SYN612-1            solved by slave   9 in 0 sec. (42)
SYN650-1            solved by slave 110 in 1 sec. (11)
SYN653-1            solved by slave 107 in 0 sec. (51)
SYN704-1            solved by slave  18 in 1 sec.  (1)
SYN708-1            solved by slave  19 in 0 sec.  (3)
SYN755-1
SYN758-1
SYN796-1
SYN802-1
```