Solver Name | Answer | CPU time | Wall clock time |
---|---|---|---|
Sat4j Resolution 2011-06-08 | OPTIMUM | 1.26781 | 0.596834 |
Name | /PARTIAL-SMALLINT-LIN/wcsp/dimacs/ normalized-ssa2670-141_ext.wbo |
MD5SUM | 6ee94b597b3a6e422f7a3f5959080317 |
Bench Category | PARTIAL-SMALLINT-LIN (both soft and hard constraints, small integers, linear constraints) |
Best result obtained on this benchmark | MOPT |
Best cost obtained on this benchmark | 1 |
Best CPU time to get the best result obtained on this benchmark | 0.021996 |
Max-Satisfiable | |
Max-(Un)Satisfiability was proved | |
Best value of the cost | |
Optimality of the best cost was proved | |
Number of variables | 1972 |
Total number of constraints | 3301 |
Number of soft constraints | 2315 |
Number of constraints which are clauses | 2315 |
Number of constraints which are cardinality constraints (but not clauses) | 986 |
Number of constraints which are nor clauses,nor cardinality constraints | 0 |
Minimum length of a constraint | 1 |
Maximum length of a constraint | 5 |
Top cost | 2316 |
Min constraint cost | 1 |
Max constraint cost | 1 |
Sum of constraints costs | 2315 |
Biggest number in a constraint | 4 |
Number of bits of the biggest number in a constraint | 3 |
Biggest sum of numbers in a constraint | 9 |
Number of bits of the biggest sum of numbers | 4 |
Number of products (including duplicates) | 0 |
Sum of products size (including duplicates) | 0 |
Number of different products | 0 |
Sum of products size | 0 |
0.01/0.08 c SAT4J: a SATisfiability library for Java (c) 2004-2010 Daniel Le Berre 0.01/0.08 c This is free software under the dual EPL/GNU LGPL licenses. 0.01/0.08 c See www.sat4j.org for details. 0.01/0.08 c version 2.3.1.v20110525 0.01/0.08 c java.runtime.name Java(TM) SE Runtime Environment 0.01/0.08 c java.vm.name Java HotSpot(TM) 64-Bit Server VM 0.01/0.08 c java.vm.version 19.1-b02 0.01/0.08 c java.vm.vendor Sun Microsystems Inc. 0.01/0.08 c sun.arch.data.model 64 0.01/0.08 c java.version 1.6.0_24 0.01/0.08 c os.name Linux 0.01/0.08 c os.version 2.6.18-164.el5 0.01/0.08 c os.arch amd64 0.01/0.08 c Free memory 9996466904 0.01/0.08 c Max memory 10048897024 0.01/0.08 c Total memory 10048897024 0.01/0.08 c Number of processors 8 0.11/0.10 c Pseudo Boolean Optimization 0.11/0.10 c --- Begin Solver configuration --- 0.11/0.10 c org.sat4j.pb.constraints.CompetResolutionPBLongMixedWLClauseCardConstrDataStructure@13d4c61c 0.11/0.10 c Learn all clauses as in MiniSAT 0.11/0.10 c claDecay=0.999 varDecay=0.95 conflictBoundIncFactor=1.5 initConflictBound=100 0.11/0.10 c VSIDS like heuristics from MiniSAT using a heap lightweight component caching from RSAT taking into account the objective function 0.11/0.10 c Expensive reason simplification 0.11/0.10 c Armin Biere (Picosat) restarts strategy 0.11/0.10 c Glucose learned constraints deletion strategy 0.11/0.10 c timeout=2147483s 0.11/0.10 c DB Simplification allowed=false 0.11/0.10 c --- End Solver configuration --- 0.11/0.10 c solving HOME/instance-3492777-1307911815.wbo 0.11/0.10 c reading problem ... 0.50/0.32 c ... done. Wall clock time 0.209s. 0.50/0.32 c #vars 4287 0.50/0.32 c #constraints 4287 0.50/0.32 c constraints type 0.50/0.32 c org.sat4j.minisat.constraints.cnf.OriginalWLClause => 2311 0.50/0.32 c org.sat4j.minisat.constraints.cnf.OriginalBinaryClause => 1976 1.05/0.51 c SATISFIABLE 1.05/0.51 c OPTIMIZING... 1.05/0.51 c Got one! Elapsed wall clock time (in seconds):0.407 1.05/0.51 o 84 1.05/0.54 c Got one! Elapsed wall clock time (in seconds):0.436 1.05/0.54 o 1 1.05/0.57 c starts : 5 1.05/0.57 c conflicts : 258 1.05/0.57 c decisions : 7866 1.05/0.57 c propagations : 66149 1.05/0.57 c inspects : 131155 1.05/0.57 c shortcuts : 0 1.05/0.57 c learnt literals : 5 1.05/0.57 c learnt binary clauses : 12 1.05/0.57 c learnt ternary clauses : 8 1.05/0.57 c learnt constraints : 252 1.05/0.57 c ignored constraints : 0 1.05/0.57 c root simplifications : 0 1.05/0.57 c removed literals (reason simplification) : 349 1.05/0.57 c reason swapping (by a shorter reason) : 0 1.05/0.57 c Calls to reduceDB : 0 1.05/0.57 c number of reductions to clauses (during analyze) : 0 1.05/0.57 c number of learned constraints concerned by reduction : 0 1.05/0.57 c number of learning phase by resolution : 0 1.05/0.57 c number of learning phase by cutting planes : 0 1.05/0.57 c speed (assignments/second) : 3006772.7272727275 1.05/0.57 c non guided choices 229 1.05/0.57 c learnt constraints type 1.05/0.57 c constraints type 1.05/0.57 c org.sat4j.minisat.constraints.cnf.OriginalWLClause => 2311 1.05/0.57 c org.sat4j.minisat.constraints.cnf.UnitClauses => 0 1.05/0.57 c org.sat4j.minisat.constraints.card.MinWatchCard => 0 1.05/0.57 c org.sat4j.minisat.constraints.cnf.OriginalBinaryClause => 1976 1.05/0.57 s OPTIMUM FOUND 1.05/0.57 v x1 -x2 x3 -x4 -x5 x6 x7 -x8 -x9 x10 -x11 x12 x13 -x14 x15 -x16 x17 -x18 x19 -x20 -x21 x22 x23 -x24 x25 -x26 x27 -x28 x29 -x30 x31 -x32 x33 -x34 x35 -x36 x37 -x38 -x39 x40 x41 -x42 x43 -x44 x45 -x46 x47 -x48 -x49 x50 x51 -x52 -x53 x54 x55 -x56 x57 -x58 x59 -x60 x61 -x62 -x63 x64 -x65 x66 x67 -x68 x69 -x70 x71 -x72 x73 -x74 x75 -x76 -x77 x78 x79 -x80 x81 -x82 -x83 x84 x85 -x86 -x87 x88 x89 -x90 x91 -x92 -x93 x94 -x95 x96 -x97 x98 -x99 x100 -x101 x102 -x103 x104 -x105 x106 -x107 x108 -x109 x110 -x111 x112 -x113 x114 -x115 x116 -x117 x118 x119 -x120 -x121 x122 -x123 x124 -x125 x126 -x127 x128 -x129 x130 x131 -x132 x133 -x134 -x135 x136 -x137 x138 x139 -x140 -x141 x142 x143 -x144 x145 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x1969 -x1970 -x1971 x1972 1.05/0.57 c objective function=1 1.05/0.58 c Total wall clock time (in seconds): 0.47
OK 1
runsolver Copyright (C) 2010-2011 Olivier ROUSSEL This is runsolver version 3.3.1 (svn: 989) This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. command line: BIN/runsolver --timestamp -w /var/tmp/evaluation-result-3492777-1307911815/watcher-3492777-1307911815 -o /var/tmp/evaluation-result-3492777-1307911815/solver-3492777-1307911815 -C 1800 -W 1900 -M 15500 java -Xms10000m -Xmx10000m -jar sat4j-pb.jar Resolution HOME/instance-3492777-1307911815.wbo running on 4 cores: 1,3,5,7 Enforcing CPUTime limit (soft limit, will send SIGTERM then SIGKILL): 1800 seconds Enforcing CPUTime limit (hard limit, will send SIGXCPU): 1830 seconds Enforcing wall clock limit (soft limit, will send SIGTERM then SIGKILL): 1900 seconds Enforcing VSIZE limit (soft limit, will send SIGTERM then SIGKILL): 15872000 KiB Enforcing VSIZE limit (hard limit, stack expansion will fail with SIGSEGV, brk() and mmap() will return ENOMEM): 15923200 KiB Current StackSize limit: 10240 KiB [startup+0 s] /proc/loadavg: 2.25 2.09 2.03 3/195 14683 /proc/meminfo: memFree=1322776/32951124 swapFree=67054448/67111528 [pid=14683] ppid=14681 vsize=26088 CPUtime=0 cores=1,3,5,7 /proc/14683/stat : 14683 (java) S 14681 14683 8455 0 -1 4202496 1170 0 0 0 0 0 0 0 25 0 2 0 883597155 26714112 897 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 270350186469 0 0 4096 0 18446744073709551615 0 0 17 1 0 0 0 /proc/14683/statm: 6522 897 682 9 0 381 0 [pid=14683/tid=14684] ppid=14681 vsize=26088 CPUtime=0 cores=1,3,5,7 /proc/14683/task/14684/stat : 14684 (java) S 14681 14683 8455 0 -1 4202560 54 0 0 0 0 0 0 0 25 0 2 0 883597156 26714112 897 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 270333460103 0 2147483391 4096 0 18446744071699199166 0 0 -1 1 0 0 0 [startup+0.024129 s] /proc/loadavg: 2.25 2.09 2.03 3/195 14683 /proc/meminfo: memFree=1322776/32951124 swapFree=67054448/67111528 [pid=14683] ppid=14681 vsize=10521028 CPUtime=0.01 cores=1,3,5,7 /proc/14683/stat : 14683 (java) S 14681 14683 8455 0 -1 4202496 10208 0 1 0 0 1 0 0 25 0 10 0 883597155 10773532672 9905 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 270350186469 0 0 0 16784584 18446744073709551615 0 0 17 1 0 0 0 /proc/14683/statm: 2630257 9911 1090 9 0 2621005 0 [pid=14683/tid=14684] ppid=14681 vsize=10521028 CPUtime=0 cores=1,3,5,7 /proc/14683/task/14684/stat : 14684 (java) R 14681 14683 8455 0 -1 4202560 9092 0 1 0 0 0 0 0 25 0 10 0 883597156 10773532672 9914 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 46912504011048 0 4 0 16784584 0 0 0 -1 1 0 0 0 Current children cumulated CPU time (s) 0.01 Current children cumulated vsize (KiB) 10521028 [startup+0.10713 s] /proc/loadavg: 2.25 2.09 2.03 3/195 14683 /proc/meminfo: memFree=1322776/32951124 swapFree=67054448/67111528 [pid=14683] ppid=14681 vsize=10539584 CPUtime=0.11 cores=1,3,5,7 /proc/14683/stat : 14683 (java) S 14681 14683 8455 0 -1 4202496 13237 0 1 0 9 2 0 0 25 0 18 0 883597155 10792534016 12902 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 270350186469 0 0 0 16800975 18446744073709551615 0 0 17 1 0 0 0 /proc/14683/statm: 2634896 12903 2108 9 0 2625630 0 [pid=14683/tid=14684] ppid=14681 vsize=10539584 CPUtime=0.08 cores=1,3,5,7 /proc/14683/task/14684/stat : 14684 (java) R 14681 14683 8455 0 -1 4202560 11265 0 1 0 7 1 0 0 18 0 18 0 883597156 10792534016 12905 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 47979989246564 0 4 0 16800975 0 0 0 -1 5 0 0 0 Current children cumulated CPU time (s) 0.11 Current children cumulated vsize (KiB) 10539584 [startup+0.305049 s] /proc/loadavg: 2.25 2.09 2.03 3/195 14683 /proc/meminfo: memFree=1322776/32951124 swapFree=67054448/67111528 [pid=14683] ppid=14681 vsize=10541632 CPUtime=0.5 cores=1,3,5,7 /proc/14683/stat : 14683 (java) S 14681 14683 8455 0 -1 4202496 16409 0 1 0 47 3 0 0 25 0 18 0 883597155 10794631168 15776 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 270350186469 0 0 0 16800975 18446744073709551615 0 0 17 1 0 0 0 /proc/14683/statm: 2635408 15777 2201 9 0 2626142 0 [pid=14683/tid=14684] ppid=14681 vsize=10541632 CPUtime=0.29 cores=1,3,5,7 /proc/14683/task/14684/stat : 14684 (java) R 14681 14683 8455 0 -1 4202560 13285 0 1 0 27 2 0 0 18 0 18 0 883597156 10794631168 15777 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 46912505219208 0 4 0 16800975 0 0 0 -1 3 0 0 0 Current children cumulated CPU time (s) 0.5 Current children cumulated vsize (KiB) 10541632 Solver just ended. Dumping a history of the last processes samples [startup+0.501013 s] /proc/loadavg: 2.25 2.09 2.03 3/195 14683 /proc/meminfo: memFree=1322776/32951124 swapFree=67054448/67111528 [pid=14683] ppid=14681 vsize=10547780 CPUtime=1.05 cores=1,3,5,7 /proc/14683/stat : 14683 (java) S 14681 14683 8455 0 -1 4202496 20635 0 1 0 102 3 0 0 25 0 19 0 883597155 10800926720 18791 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 270350186469 0 0 0 16800975 18446744073709551615 0 0 17 1 0 0 0 /proc/14683/statm: 2636945 18791 2221 9 0 2627679 0 [pid=14683/tid=14684] ppid=14681 vsize=10547780 CPUtime=0.48 cores=1,3,5,7 /proc/14683/task/14684/stat : 14684 (java) R 14681 14683 8455 0 -1 4202560 13683 0 1 0 46 2 0 0 19 0 19 0 883597156 10800926720 18791 33554432000 1073741824 1073778376 140734364120208 18446744073709551615 47979987694421 0 4 0 16800975 0 0 0 -1 3 0 0 0 Current children cumulated CPU time (s) 1.05 Current children cumulated vsize (KiB) 10547780 Child status: 30 Real time (s): 0.596834 CPU time (s): 1.26781 CPU user time (s): 1.22381 CPU system time (s): 0.043993 CPU usage (%): 212.422 Max. virtual memory (cumulated for all children) (KiB): 10547780 getrusage(RUSAGE_CHILDREN,...) data: user time used= 1.22381 system time used= 0.043993 maximum resident set size= 0 integral shared memory size= 0 integral unshared data size= 0 integral unshared stack size= 0 page reclaims= 21084 page faults= 1 swaps= 0 block input operations= 0 block output operations= 0 messages sent= 0 messages received= 0 signals received= 0 voluntary context switches= 185 involuntary context switches= 15 runsolver used 0.001999 second user time and 0.003999 second system time The end
Begin job on node143 at 2011-06-12 22:50:15 IDJOB=3492777 IDBENCH=79384 IDSOLVER=1982 FILE ID=node143/3492777-1307911815 RUNJOBID= node143-1307908050-12755 PBS_JOBID= 13559565 Free space on /var/tmp= 2916 MiB SOLVER NAME= Sat4j Resolution 2011-06-08 BENCH NAME= PB10/normalized-PB10/PARTIAL-SMALLINT-LIN/wcsp/dimacs/normalized-ssa2670-141_ext.wbo COMMAND LINE= java -Xms10000m -Xmx10000m -jar sat4j-pb.jar Resolution BENCHNAME RUNSOLVER COMMAND LINE= BIN/runsolver --timestamp -w /var/tmp/evaluation-result-3492777-1307911815/watcher-3492777-1307911815 -o /var/tmp/evaluation-result-3492777-1307911815/solver-3492777-1307911815 -C 1800 -W 1900 -M 15500 java -Xms10000m -Xmx10000m -jar sat4j-pb.jar Resolution HOME/instance-3492777-1307911815.wbo TIME LIMIT= 1800 seconds MEMORY LIMIT= 15500 MiB NBCORE= 4 MD5SUM BENCH= 6ee94b597b3a6e422f7a3f5959080317 RANDOM SEED=1675366129 node143.alineos.net Linux 2.6.18-164.el5 #1 SMP Thu Sep 3 03:28:30 EDT 2009 /proc/cpuinfo: processor : 0 vendor_id : GenuineIntel cpu family : 6 model : 26 model name : Intel(R) Xeon(R) CPU X5550 @ 2.67GHz stepping : 5 cpu MHz : 2666.846 cache size : 8192 KB physical id : 0 siblings : 4 core id : 0 cpu cores : 4 apicid : 0 fpu : yes fpu_exception : yes cpuid level : 11 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 rdtscp lm constant_tsc ida nonstop_tsc pni monitor ds_cpl vmx est tm2 cx16 xtpr popcnt lahf_lm bogomips : 5333.69 clflush size : 64 cache_alignment : 64 address sizes : 40 bits physical, 48 bits virtual power management: [8] processor : 1 vendor_id : GenuineIntel cpu family : 6 model : 26 model name : Intel(R) Xeon(R) CPU X5550 @ 2.67GHz stepping : 5 cpu MHz : 2666.846 cache size : 8192 KB physical id : 1 siblings : 4 core id : 0 cpu cores : 4 apicid : 16 fpu : yes fpu_exception : yes cpuid level : 11 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 rdtscp lm constant_tsc ida nonstop_tsc pni monitor ds_cpl vmx est tm2 cx16 xtpr popcnt lahf_lm bogomips : 5226.15 clflush size : 64 cache_alignment : 64 address sizes : 40 bits physical, 48 bits virtual power management: [8] processor : 2 vendor_id : GenuineIntel cpu family : 6 model : 26 model name : Intel(R) Xeon(R) CPU X5550 @ 2.67GHz stepping : 5 cpu MHz : 2666.846 cache size : 8192 KB physical id : 0 siblings : 4 core id : 1 cpu cores : 4 apicid : 2 fpu : yes fpu_exception : yes cpuid level : 11 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 rdtscp lm constant_tsc ida nonstop_tsc pni monitor ds_cpl vmx est tm2 cx16 xtpr popcnt lahf_lm bogomips : 5332.74 clflush size : 64 cache_alignment : 64 address sizes : 40 bits physical, 48 bits virtual power management: [8] processor : 3 vendor_id : GenuineIntel cpu family : 6 model : 26 model name : Intel(R) Xeon(R) CPU X5550 @ 2.67GHz stepping : 5 cpu MHz : 2666.846 cache size : 8192 KB physical id : 1 siblings : 4 core id : 1 cpu cores : 4 apicid : 18 fpu : yes fpu_exception : yes cpuid level : 11 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 rdtscp lm constant_tsc ida nonstop_tsc pni monitor ds_cpl vmx est tm2 cx16 xtpr popcnt lahf_lm bogomips : 5332.83 clflush size : 64 cache_alignment : 64 address sizes : 40 bits physical, 48 bits virtual power management: [8] processor : 4 vendor_id : GenuineIntel cpu family : 6 model : 26 model name : Intel(R) Xeon(R) CPU X5550 @ 2.67GHz stepping : 5 cpu MHz : 2666.846 cache size : 8192 KB physical id : 0 siblings : 4 core id : 2 cpu cores : 4 apicid : 4 fpu : yes fpu_exception : yes cpuid level : 11 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 rdtscp lm constant_tsc ida nonstop_tsc pni monitor ds_cpl vmx est tm2 cx16 xtpr popcnt lahf_lm bogomips : 5332.75 clflush size : 64 cache_alignment : 64 address sizes : 40 bits physical, 48 bits virtual power management: [8] processor : 5 vendor_id : GenuineIntel cpu family : 6 model : 26 model name : Intel(R) Xeon(R) CPU X5550 @ 2.67GHz stepping : 5 cpu MHz : 2666.846 cache size : 8192 KB physical id : 1 siblings : 4 core id : 2 cpu cores : 4 apicid : 20 fpu : yes fpu_exception : yes cpuid level : 11 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 rdtscp lm constant_tsc ida nonstop_tsc pni monitor ds_cpl vmx est tm2 cx16 xtpr popcnt lahf_lm bogomips : 5332.83 clflush size : 64 cache_alignment : 64 address sizes : 40 bits physical, 48 bits virtual power management: [8] processor : 6 vendor_id : GenuineIntel cpu family : 6 model : 26 model name : Intel(R) Xeon(R) CPU X5550 @ 2.67GHz stepping : 5 cpu MHz : 2666.846 cache size : 8192 KB physical id : 0 siblings : 4 core id : 3 cpu cores : 4 apicid : 6 fpu : yes fpu_exception : yes cpuid level : 11 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 rdtscp lm constant_tsc ida nonstop_tsc pni monitor ds_cpl vmx est tm2 cx16 xtpr popcnt lahf_lm bogomips : 5332.74 clflush size : 64 cache_alignment : 64 address sizes : 40 bits physical, 48 bits virtual power management: [8] processor : 7 vendor_id : GenuineIntel cpu family : 6 model : 26 model name : Intel(R) Xeon(R) CPU X5550 @ 2.67GHz stepping : 5 cpu MHz : 2666.846 cache size : 8192 KB physical id : 1 siblings : 4 core id : 3 cpu cores : 4 apicid : 22 fpu : yes fpu_exception : yes cpuid level : 11 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 rdtscp lm constant_tsc ida nonstop_tsc pni monitor ds_cpl vmx est tm2 cx16 xtpr popcnt lahf_lm bogomips : 5332.83 clflush size : 64 cache_alignment : 64 address sizes : 40 bits physical, 48 bits virtual power management: [8] /proc/meminfo: MemTotal: 32951124 kB MemFree: 1323444 kB Buffers: 66272 kB Cached: 30491084 kB SwapCached: 9484 kB Active: 15928604 kB Inactive: 14752976 kB HighTotal: 0 kB HighFree: 0 kB LowTotal: 32951124 kB LowFree: 1323444 kB SwapTotal: 67111528 kB SwapFree: 67054448 kB Dirty: 436 kB Writeback: 0 kB AnonPages: 121828 kB Mapped: 21264 kB Slab: 882924 kB PageTables: 4784 kB NFS_Unstable: 0 kB Bounce: 0 kB CommitLimit: 83587088 kB Committed_AS: 10553688 kB VmallocTotal: 34359738367 kB VmallocUsed: 296008 kB VmallocChunk: 34359440975 kB HugePages_Total: 0 HugePages_Free: 0 HugePages_Rsvd: 0 Hugepagesize: 2048 kB Free space on /var/tmp at the end= 2912 MiB End job on node143 at 2011-06-12 22:50:16