Trace number 1517810

Some explanations

A solver is run under the control of another program named runsolver. runsolver is in charge of imposing the CPU time limit and the memory limit to the solver. It also monitors some information about the process. The trace of the execution of a solver is divided into four (or five) parts:
  1. SOLVER DATA
    This is the output of the solver (stdout and stderr).
    Note that some very long lines in this section may be truncated by your web browser ! In such a case, you may want to use the "Download as text" link to get the trace as a text file.

    When the --timestamp option is passed to the runsolver program, each line output by the solver is prepended with a timestamp which indicates at what time the line was output by the solver. Times are relative to the start of the program, given in seconds. The first timestamp (if present) is estimated CPU time. The last timestamp is wall clock time.

    As some 'v lines' may be very long (sometimes several megabytes), the 'v line' output by your solver may be split on several lines to help limit the size of the trace recorded in the database. In any case, the exact output of your solver is preserved in a trace file.
  2. VERIFIER DATA
    The output of the solver is piped to a verifier program which will search a value line "v " and, if found, will check that the given interpretation satisfies all constraints.
  3. CONVERSION SCRIPT DATA (Optionnal)
    When a conversion script is used, this section shows the messages that were output by the conversion script.
  4. WATCHER DATA
    This is the informations gathered by the runsolver program. It first prints the different limits. There's a first limit on CPU time set to X seconds (see the parameters in the trace). After this time has ellapsed, runsolver sends a SIGTERM and 2 seconds later a SIGKILL to the solver. For safety, there's also another limit set to X+30 seconds which will send a SIGXPU to the solver. The last limit is on the virtual memory used by the process (see the parameters in the trace).
    Every ten seconds, the runsolver process fetches the content of /proc/loadavg, /proc/pid/stat and /proc/pid/statm (see man proc) and prints it as raw data. This is only recorded in case we need to investigate the behaviour of a solver. The memory used by the solver (vsize) is also given every ten seconds.
    When the solver exits, runsolver prints some informations such as status and time. CPU usage is the ratio CPU Time/Real Time.
  5. LAUNCHER DATA
    These informations are related to the script which will launch the solver. The most important informations are the command line given to the solver, the md5sum of the different files and the dump of the /proc/cpuinfo and /proc/meminfo which provides some useful information on the computer.

Solver answer on this benchmark

Solver NameAnswerCPU timeWall clock time
march_nn nnUNSAT 39.8999 39.9137

General information on the benchmark

NameRANDOM/MEDIUM/3SAT/UNKNOWN/380/
unif-k3-r4.25-v380-c1615-S928666993-098.cnf
MD5SUMabbce28168cbe1770c6abedb21f913a2
Bench CategoryRANDOM (random instances)
Best result obtained on this benchmarkUNSAT
Best CPU time to get the best result obtained on this benchmark35.6896
Satisfiable
(Un)Satisfiability was proved
Number of variables380
Number of clauses1615
Sum of the clauses size4845
Maximum clause length3
Minimum clause length3
Number of clauses of size 10
Number of clauses of size 20
Number of clauses of size 31615
Number of clauses of size 40
Number of clauses of size 50
Number of clauses of size over 50

Solver Data 

0.01/0.01	c main():: ***                                   [ march satisfiability solver ]                                   ***
0.01/0.01	c main()::  **                Copyright (C) 2001-2009 M.J.H. Heule, J.E. van Zwieten, and M. Dufour                 **
0.01/0.01	c main()::   *  This program may be redistributed and/or modified under the terms of the GNU Gereral Public License  *
0.01/0.01	c main()::
0.01/0.01	c initFormula():: searching for DIMACS p-line....
0.01/0.01	c initFormula():: the DIMACS p-line indicates a CNF of 380 variables and 1615 clauses.
0.01/0.01	c parseCNF():: parsing....
0.01/0.01	c parseCNF():: the CNF contains 0 unary clauses.
0.01/0.01	c runParser():: parsing was successful, warming up engines...
0.01/0.01	c simplify_formula():: removed 0 tautological, 14 satisfied and 0 duplicate clauses
0.01/0.01	c preprocessing fase I completed:: there are now 378 free variables and 1601 clauses.
0.01/0.01	c stat :: sign balance is biased by 0.467
0.01/0.01	c using 3-SAT heuristics (occurence based diff)
0.01/0.01	c simplify_formula():: removed 0 tautological, 0 satisfied and 0 duplicate clauses
0.01/0.01	c simplify_formula():: removed 0 tautological, 0 satisfied and 160 duplicate clauses
0.01/0.01	c resolvent_look() :: found 93 resolvents
0.01/0.01	c lessRedundantTransformation():: nothing to be done.
0.01/0.01	c transformTo3SAT():: you gave me 380 variables and 1694 clauses.
0.01/0.01	c transformTo3SAT():: by the way, the maximal clause length before transformation was 3.
0.01/0.01	c transformTo3SAT():: I will add 0 variables and 0 clauses!
0.01/0.01	c transformTo3SAT():: the transformation yielded 380 variabels and 1694 clauses.
0.01/0.01	c main():: clause / variable ratio: ( 1694 / 380 ) = 4.46
0.01/0.01	c longest clause has size 3
0.01/0.01	c simplify_formula():: removed 0 tautological, 0 satisfied and 0 duplicate clauses
0.01/0.01	c number of free variables = 378
0.01/0.01	c dynamic_preselect_setsize :: off
0.01/0.01	c main():: all systems go!
0.01/0.01	c |----------------------------------------------------------------|
c |*
c |**
c |****
c |********
c |****************
c |********************************
c |****************************************************************| ( 0/999) NodeCount: 24
0.01/0.02	c |----------------------------------------------------------------|
c |*
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c |****************************************************************| ( 1/999) NodeCount: 282
0.01/0.09	c |----------------------------------------------------------------|
c |*
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c |****************************************************************| ( 2/999) NodeCount: 1718
0.49/0.54	c |----------------------------------------------------------------|
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c |****************************************************************| ( 3/999) NodeCount: 6831
2.39/2.46	c |----------------------------------------------------------------|
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c |****************************************************************| ( 4/999) NodeCount: 18599
7.49/7.56	c |----------------------------------------------------------------|
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c |****************************************************************| ( 5/999) NodeCount: 36809
16.29/16.38	c |----------------------------------------------------------------|
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c |****************************************************************| ( 6/999) NodeCount: 55914
26.68/26.73	c |----------------------------------------------------------------|
c |*
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c |****************************************************************| ( 7/999) NodeCount: 69388
34.48/34.55	c |----------------------------------------------------------------|
c |*
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c |****************************************************************| ( 8/999) NodeCount: 75634
38.38/38.42	c |----------------------------------------------------------------|
c |*
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c |****************************************************************| ( 9/999) NodeCount: 77487
39.58/39.61	c |----------------------------------------------------------------|
c |*
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c |****************************************************************| (10/999) NodeCount: 77853
39.78/39.86	c |----------------------------------------------------------------|
c |********
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c |****************************************************************| (11/999) NodeCount: 77905
39.88/39.90	c |----------------------------------------------------------------|
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c |****************************************************************| (12/999) NodeCount: 77912
39.88/39.91	c |----------------------------------------------------------------|
c |
39.88/39.91	c
39.88/39.91	c main():: nodeCount: 77912
39.88/39.91	c main():: dead ends in main: 1478
39.88/39.91	c main():: lookAheadCount: 5220931
39.88/39.91	c main():: unitResolveCount: 1234933
39.88/39.91	c main():: time=39.900000
39.88/39.91	c main():: necessary_assignments: 15072
39.88/39.91	c main():: bin_sat: 0, bin_unsat 0
39.88/39.91	c main():: doublelook: #: 308038, succes #: 222852
39.88/39.91	c main():: doublelook: overall 6.101 of all possible doublelooks executed
39.88/39.91	c main():: doublelook: succesrate: 72.346, average DL_trigger: 48.263
39.88/39.91	s UNSATISFIABLE

Verifier Data 

No possible verification on an UNSAT instance

Watcher Data 

runsolver version 3.2.9 (svn:489) (c) roussel@cril.univ-artois.fr

command line: BIN/runsolver --timestamp -w /tmp/evaluation-result-1517810-1238291457/watcher-1517810-1238291457 -o /tmp/evaluation-result-1517810-1238291457/solver-1517810-1238291457 -C 1200 -W 1800 -M 1800 --output-limit 1,15 HOME/march_nn HOME/instance-1517810-1238291457.cnf 

Enforcing CPUTime limit (soft limit, will send SIGTERM then SIGKILL): 1200 seconds
Enforcing CPUTime limit (hard limit, will send SIGXCPU): 1230 seconds
Enforcing wall clock limit (soft limit, will send SIGTERM then SIGKILL): 1800 seconds
Enforcing VSIZE limit (soft limit, will send SIGTERM then SIGKILL): 1843200 KiB
Enforcing VSIZE limit (hard limit, stack expansion will fail with SIGSEGV, brk() and mmap() will return ENOMEM): 1894400 KiB
Solver output will be limited to a maximum of 15728640 bytes. The first 1048576 bytes and the last 14680064 bytes will be preserved
Current StackSize limit: 10240 KiB


[startup+0 s]
/proc/loadavg: 0.95 0.97 0.99 3/64 15871
/proc/meminfo: memFree=1082816/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=972 CPUtime=0
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 138 0 0 0 0 0 0 0 18 0 1 0 1101811753 995328 121 1992294400 134512640 135197250 4294956240 18446744073709551615 134535888 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 243 121 67 167 0 74 0

[startup+0.0121011 s]
/proc/loadavg: 0.95 0.97 0.99 3/64 15871
/proc/meminfo: memFree=1082816/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=972 CPUtime=0.01
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 160 0 0 0 1 0 0 0 18 0 1 0 1101811753 995328 143 1992294400 134512640 135197250 4294956240 18446744073709551615 134579323 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 243 143 83 167 0 74 0
Current children cumulated CPU time (s) 0.01
Current children cumulated vsize (KiB) 972

[startup+0.101116 s]
/proc/loadavg: 0.95 0.97 0.99 3/64 15871
/proc/meminfo: memFree=1082816/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=1536 CPUtime=0.09
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 250 0 0 0 9 0 0 0 18 0 1 0 1101811753 1572864 233 1992294400 134512640 135197250 4294956240 18446744073709551615 134525346 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 384 233 93 167 0 215 0
Current children cumulated CPU time (s) 0.09
Current children cumulated vsize (KiB) 1536

[startup+0.301152 s]
/proc/loadavg: 0.95 0.97 0.99 3/64 15871
/proc/meminfo: memFree=1082816/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=1536 CPUtime=0.29
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 261 0 0 0 29 0 0 0 19 0 1 0 1101811753 1572864 244 1992294400 134512640 135197250 4294956240 18446744073709551615 134617785 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 384 244 93 167 0 215 0
Current children cumulated CPU time (s) 0.29
Current children cumulated vsize (KiB) 1536

[startup+0.701224 s]
/proc/loadavg: 0.95 0.97 0.99 3/64 15871
/proc/meminfo: memFree=1082816/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=1668 CPUtime=0.69
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 279 0 0 0 69 0 0 0 22 0 1 0 1101811753 1708032 262 1992294400 134512640 135197250 4294956240 18446744073709551615 134542058 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 417 262 93 167 0 248 0
Current children cumulated CPU time (s) 0.69
Current children cumulated vsize (KiB) 1668

[startup+1.50137 s]
/proc/loadavg: 0.95 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1082040/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=1804 CPUtime=1.49
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 321 0 0 0 149 0 0 0 25 0 1 0 1101811753 1847296 304 1992294400 134512640 135197250 4294956240 18446744073709551615 134552743 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 451 304 93 167 0 282 0
Current children cumulated CPU time (s) 1.49
Current children cumulated vsize (KiB) 1804

[startup+3.10166 s]
/proc/loadavg: 0.95 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1081720/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=1872 CPUtime=3.09
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 345 0 0 0 309 0 0 0 25 0 1 0 1101811753 1916928 328 1992294400 134512640 135197250 4294956240 18446744073709551615 134552735 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 468 328 93 167 0 299 0
Current children cumulated CPU time (s) 3.09
Current children cumulated vsize (KiB) 1872

[startup+6.30124 s]
/proc/loadavg: 0.95 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1081400/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=2324 CPUtime=6.29
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 408 0 0 0 629 0 0 0 25 0 1 0 1101811753 2379776 391 1992294400 134512640 135197250 4294956240 18446744073709551615 134542152 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 581 391 93 167 0 412 0
Current children cumulated CPU time (s) 6.29
Current children cumulated vsize (KiB) 2324

[startup+12.7014 s]
/proc/loadavg: 0.96 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1080960/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=2892 CPUtime=12.69
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 509 0 0 0 1269 0 0 0 25 0 1 0 1101811753 2961408 492 1992294400 134512640 135197250 4294956240 18446744073709551615 134548478 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 723 492 93 167 0 554 0
Current children cumulated CPU time (s) 12.69
Current children cumulated vsize (KiB) 2892

[startup+25.5017 s]
/proc/loadavg: 0.97 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1080064/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=3656 CPUtime=25.48
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 727 0 0 0 2548 0 0 0 25 0 1 0 1101811753 3743744 700 1992294400 134512640 135197250 4294956240 18446744073709551615 134594007 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 914 700 93 167 0 745 0
Current children cumulated CPU time (s) 25.48
Current children cumulated vsize (KiB) 3656

Solver just ended. Dumping a history of the last processes samples

[startup+31.9059 s]
/proc/loadavg: 0.97 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1079744/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=3996 CPUtime=31.89
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 809 0 0 0 3189 0 0 0 25 0 1 0 1101811753 4091904 782 1992294400 134512640 135197250 4294956240 18446744073709551615 134542099 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 999 782 93 167 0 830 0
Current children cumulated CPU time (s) 31.89
Current children cumulated vsize (KiB) 3996

[startup+35.1015 s]
/proc/loadavg: 0.97 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1079552/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=4760 CPUtime=35.08
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 847 0 0 0 3508 0 0 0 25 0 1 0 1101811753 4874240 820 1992294400 134512640 135197250 4294956240 18446744073709551615 134539276 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 1190 820 93 167 0 1021 0
Current children cumulated CPU time (s) 35.08
Current children cumulated vsize (KiB) 4760

[startup+38.301 s]
/proc/loadavg: 0.97 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1079488/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=4760 CPUtime=38.28
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 884 0 0 0 3828 0 0 0 25 0 1 0 1101811753 4874240 857 1992294400 134512640 135197250 4294956240 18446744073709551615 134541957 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 1190 857 93 167 0 1021 0
Current children cumulated CPU time (s) 38.28
Current children cumulated vsize (KiB) 4760

[startup+39.1022 s]
/proc/loadavg: 0.97 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1079424/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=4760 CPUtime=39.08
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 894 0 0 0 3908 0 0 0 25 0 1 0 1101811753 4874240 867 1992294400 134512640 135197250 4294956240 18446744073709551615 134592379 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 1190 867 93 167 0 1021 0
Current children cumulated CPU time (s) 39.08
Current children cumulated vsize (KiB) 4760

[startup+39.5013 s]
/proc/loadavg: 0.97 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1079360/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=4760 CPUtime=39.48
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 899 0 0 0 3948 0 0 0 25 0 1 0 1101811753 4874240 872 1992294400 134512640 135197250 4294956240 18446744073709551615 134552521 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 1190 872 93 167 0 1021 0
Current children cumulated CPU time (s) 39.48
Current children cumulated vsize (KiB) 4760

[startup+39.9013 s]
/proc/loadavg: 0.97 0.97 0.99 2/65 15872
/proc/meminfo: memFree=1079360/2055920 swapFree=4174052/4192956
[pid=15871] ppid=15869 vsize=4760 CPUtime=39.88
/proc/15871/stat : 15871 (march_nn) R 15869 15871 15579 0 -1 4194304 902 0 0 0 3988 0 0 0 25 0 1 0 1101811753 4874240 875 1992294400 134512640 135197250 4294956240 18446744073709551615 134593998 0 0 4096 0 0 0 0 17 1 0 0
/proc/15871/statm: 1190 875 93 167 0 1021 0
Current children cumulated CPU time (s) 39.88
Current children cumulated vsize (KiB) 4760

Child status: 20
Real time (s): 39.9137
CPU time (s): 39.8999
CPU user time (s): 39.8939
CPU system time (s): 0.005999
CPU usage (%): 99.9656
Max. virtual memory (cumulated for all children) (KiB): 4760

getrusage(RUSAGE_CHILDREN,...) data:
user time used= 39.8939
system time used= 0.005999
maximum resident set size= 0
integral shared memory size= 0
integral unshared data size= 0
integral unshared stack size= 0
page reclaims= 904
page faults= 0
swaps= 0
block input operations= 0
block output operations= 0
messages sent= 0
messages received= 0
signals received= 0
voluntary context switches= 2
involuntary context switches= 65

runsolver used 0.029995 second user time and 0.102984 second system time

The end

Launcher Data 

Begin job on node17 at 2009-03-29 03:50:57
IDJOB=1517810
IDBENCH=70627
IDSOLVER=522
FILE ID=node17/1517810-1238291457
PBS_JOBID= 9060939
Free space on /tmp= 66332 MiB

SOLVER NAME= march_nn nn
BENCH NAME= SAT09/RANDOM/MEDIUM/3SAT/UNKNOWN/380/unif-k3-r4.25-v380-c1615-S928666993-098.cnf
COMMAND LINE= HOME/march_nn BENCHNAME
RUNSOLVER COMMAND LINE= BIN/runsolver --timestamp -w /tmp/evaluation-result-1517810-1238291457/watcher-1517810-1238291457 -o /tmp/evaluation-result-1517810-1238291457/solver-1517810-1238291457 -C 1200 -W 1800 -M 1800 --output-limit 1,15  HOME/march_nn HOME/instance-1517810-1238291457.cnf

TIME LIMIT= 1200 seconds
MEMORY LIMIT= 1800 MiB
MAX NB THREAD= 0

MD5SUM BENCH= abbce28168cbe1770c6abedb21f913a2
RANDOM SEED=1854644313

node17.alineos.net Linux 2.6.9-22.EL.rootsmp #1 SMP Mon Oct 3 08:59:52 CEST 2005

/proc/cpuinfo:
processor	: 0
vendor_id	: GenuineIntel
cpu family	: 15
model		: 4
model name	:                   Intel(R) Xeon(TM) CPU 3.00GHz
stepping	: 3
cpu MHz		: 3000.265
cache size	: 2048 KB
fpu		: yes
fpu_exception	: yes
cpuid level	: 5
wp		: yes
flags		: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm syscall nx lm pni monitor ds_cpl cid cx16 xtpr
bogomips	: 5914.62
clflush size	: 64
cache_alignment	: 128
address sizes	: 36 bits physical, 48 bits virtual
power management:

processor	: 1
vendor_id	: GenuineIntel
cpu family	: 15
model		: 4
model name	:                   Intel(R) Xeon(TM) CPU 3.00GHz
stepping	: 3
cpu MHz		: 3000.265
cache size	: 2048 KB
fpu		: yes
fpu_exception	: yes
cpuid level	: 5
wp		: yes
flags		: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm syscall nx lm pni monitor ds_cpl cid cx16 xtpr
bogomips	: 5586.94
clflush size	: 64
cache_alignment	: 128
address sizes	: 36 bits physical, 48 bits virtual
power management:


/proc/meminfo:
MemTotal:      2055920 kB
MemFree:       1083232 kB
Buffers:         82388 kB
Cached:         797632 kB
SwapCached:      12684 kB
Active:          64372 kB
Inactive:       829852 kB
HighTotal:           0 kB
HighFree:            0 kB
LowTotal:      2055920 kB
LowFree:       1083232 kB
SwapTotal:     4192956 kB
SwapFree:      4174052 kB
Dirty:             796 kB
Writeback:           0 kB
Mapped:          19756 kB
Slab:            64412 kB
Committed_AS:  2880280 kB
PageTables:       1464 kB
VmallocTotal: 536870911 kB
VmallocUsed:    264952 kB
VmallocChunk: 536605679 kB
HugePages_Total:     0
HugePages_Free:      0
Hugepagesize:     2048 kB

Free space on /tmp at the end= 66328 MiB
End job on node17 at 2009-03-29 03:51:37