OKlibrary  0.2.1.6
Ramsey_2_4_4.hpp File Reference

On investigations into Ramsey problems of the form ramsey_2^2(4,4) More...

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## Detailed Description

On investigations into Ramsey problems of the form ramsey_2^2(4,4)

Todo:
General information
• Known is ramsey_2^2(4) = 18.
• So we get at most 6120 clauses.
• To generate an instance of SAT problem specifying "ramsey_2^2(4) > n?" use the following:
```Ramsey-O3-DNDEBUG 4 4 2 6 | ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_6.cnf
```
where n has been replaced by 6 in this example.
• To generate the additional clauses for each of the symmetry breaking techniques (see ComputerAlgebra/Satisfiability/Lisp/Generators/RamseyTheory/plans/RamseyProblems.hpp) and cardinality constraints, run the following in maxima (generating each of the additional clauses for a range of n values):
• Symmetry breaking by fixing colours/labels to break monochromatic k-subsets:
```for n : 5 thru 18 do output_ramsey2_symbr1_stdname(4,n);
```
• Symmetry breaking by fixing monochromatic cliques:
```for n : 5 thru 18 do output_ramsey2_symbr2_stdname(n);
```
• Symmetry breaking by recursive application of the pigeon hole principle:
```for n : 5 thru 18 do output_ramsey2_symbr3_stdname(n);
```
• Cardinality constraints:
```:lisp (ext:set-limit 'ext:heap-size 3000000000)
:lisp (ext:set-limit 'ext:frame-stack 10000)
:lisp (ext:set-limit 'ext:c-stack 200000)
:lisp (ext:set-limit 'ext:lisp-stack 200000)
for n : 5 thru 18 do block([n_e : binomial(n,2)],
output_fcs(
sconcat("Card ",n),
fcl2fcs(standardise_fcl(cl2fcl(unary_bb_crd2fcl([floor(n_e/2),create_list(i,i,1,n_e),ceiling(n_e/2)])))[1]),
sconcat("Card_n",n,".cnf")))\$
```
Todo:
Using DPLL and conflict-driven solvers
• Satisfiability for n=17:
1. Trivial for OKsolver.
2. Grasp aborts by default (10000s exceeded).
3. Trivial for minisat.
4. Trivial for march_pl.
• Unsatisfiability for n=18:
1. OKsolver
• Running it with
```> OKsolver_2002-O3-DNDEBUG -M -D14 -F Ramsey_4_2_18.cnf
```
seems to indicate that it will take roughly 15 days (on csltok).
• However, this seems to be too optimistic: The first 15 nodes at depth 14 (16384 nodes altogether) were solved all with around 100,000 nodes in the subtrees, however with node 16 the solver falls into a deep hole, and yet 500,000,000 nodes have been processed there.
• A still deeper hole waited at node 19, and after 16.35 days and 4,095,825,666 nodes (altogether; 3620490 single nodes, 16,220,739,545 2-reductions, 22,409,527 pure literals, 0 autarkies; 1,412,661.8 seconds) it was aborted.
• Interestingly it seems that cs-wsok here is quite a bit slower than csltok:
1. ```  1:110200,  208.1, 3408483.1
2:100554,  418.0, 3423838.0
```
but there is a lot of variability
```  1:110200,  161.6, 2647165.1
2:100554,  302.3, 2476385.0
```
(which is strange?) versus on csltok:
```  1:110200,   82.5, 1350942.2
2:100554,  162.8, 1333822.4
```
where actually csltok has a slower cpu??
2. After 3299m 19s, on csltok 487,747,031 nodes were processed, that makes 2460 nodes per second.
3. After 254392.7 s, on cs-wsok 740,136,935 nodes where processed, that makes 2900 nodes per second.
4. So it seems that cs-wsok was only initially that slow --- perhaps cache behaviour? But still, given that csltok runs with 1400 MHz and cs-wsok with 2100 MHz, executation on cs-wsok seems slow.
2. Grasp aborts by default (10000s exceeded).
3. minisat seems hopeless:
```> minisat Ramsey_4_2_18.cnf
==================================[MINISAT]===================================
| Conflicts |     ORIGINAL     |              LEARNT              | Progress |
|           | Clauses Literals |   Limit Clauses Literals  Lit/Cl |          |
==============================================================================
|         0 |    6120    36720 |    2040       0        0     nan |  0.000 % |
|       101 |    6120    36720 |    2244     101     1575    15.6 |  0.004 % |
|       251 |    6120    36720 |    2468     251     5553    22.1 |  0.004 % |
|       477 |    6120    36720 |    2715     477    12466    26.1 |  0.004 % |
|       814 |    6120    36720 |    2986     814    21935    26.9 |  0.004 % |
|      1321 |    6120    36720 |    3285    1321    36858    27.9 |  0.004 % |
|      2081 |    6120    36720 |    3613    2081    59272    28.5 |  0.004 % |
|      3222 |    6120    36720 |    3975    3222    96072    29.8 |  0.004 % |
|      4930 |    6120    36720 |    4372    2911    89091    30.6 |  0.004 % |
|      7492 |    6120    36720 |    4810    3256    99003    30.4 |  0.004 % |
|     11336 |    6120    36720 |    5291    4661   155593    33.4 |  0.004 % |
|     17104 |    6120    36720 |    5820    5079   165609    32.6 |  0.004 % |
|     25753 |    6120    36720 |    6402    4923   157105    31.9 |  0.004 % |
|     38727 |    6120    36720 |    7042    4980   164881    33.1 |  0.004 % |
|     58188 |    6120    36720 |    7746    6702   218017    32.5 |  0.004 % |
|     87382 |    6120    36720 |    8521    4635   144895    31.3 |  0.004 % |
|    131171 |    6120    36720 |    9373    5516   180171    32.7 |  0.004 % |
|    196857 |    6120    36720 |   10311    5186   157778    30.4 |  0.004 % |
|    295383 |    6120    36720 |   11342    5205   153268    29.4 |  0.004 % |
|    443172 |    6120    36720 |   12476   10504   355910    33.9 |  0.004 % |
|    664855 |    6120    36720 |   13724    6638   206592    31.1 |  0.004 % |
|    997380 |    6120    36720 |   15096    8503   275191    32.4 |  0.004 % |
|   1496168 |    6120    36720 |   16606   14871   493709    33.2 |  0.004 % |
|   2244351 |    6120    36720 |   18266   13391   473701    35.4 |  0.004 % |
|   3366625 |    6120    36720 |   20093   18188   616966    33.9 |  0.004 % |
|   5050036 |    6120    36720 |   22102   19370   676586    34.9 |  0.004 % |
|   7575152 |    6120    36720 |   24313   18788   607228    32.3 |  0.004 % |
|  11362827 |    6120    36720 |   26744   15544   522901    33.6 |  0.004 % |
|  17044340 |    6120    36720 |   29418   14652   462997    31.6 |  0.004 % |
|  25566609 |    6120    36720 |   32360   19947   657932    33.0 |  0.004 % |
|  38350012 |    6120    36720 |   35596   29494  1047723    35.5 |  0.004 % |
|  57525118 |    6120    36720 |   39156   34447  1165683    33.8 |  0.004 % |
|  86287776 |    6120    36720 |   43072   35595  1309147    36.8 |  0.004 % |
| 129431764 |    6120    36720 |   47379   37529  1285937    34.3 |  0.004 % |
| 194147746 |    6120    36720 |   52117   39588  1369541    34.6 |  0.004 % |
| 291221720 |    6120    36720 |   57328   31103  1057264    34.0 |  0.004 % |
| 436832680 |    6120    36720 |   63061   46147  1656671    35.9 |  0.004 % |
| 655249120 |    6120    36720 |   69368   23145   770418    33.3 |  0.004 % |

*** INTERRUPTED ***
restarts              : 38
conflicts             : 669017040
decisions             : 771042110
propagations          : 11023313626
conflict literals     : 23997088233    (23.37 % deleted)
Memory used           : 43.93 MB
```
4. march_pl seems hopeless (after one hour).
1. Again, since the problem is hard, we should run march_pl for, say, 2 weeks.
• Using the symmetry breaking by recursive application of the pigeon hole principle (see "ramsey2_symbr3_cs" in ComputerAlgebra/Satisfiability/Lisp/Generators/RamseyTheory/RamseyProblems.mac ) it seems several solvers can prove n=18 unsatisfiable:
• To generate, first in maxima:
```output_ramsey2_symbr3_stdname(18);
```
and then in the shell:
```Ramsey-O3-DNDEBUG 4 4 2 18 > Ramsey_4_4_2_18.ecnf
./merge_cnf.sh Ramsey_4_4_2_18.ecnf Ramsey_SB_PHP_18.ecnf > Ramsey_4_4_2_18_SB_PHP.ecnf
ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_18_SB_PHP.ecnf > Ramsey_4_4_2_18_SB_PHP.cnf
```
where "merge_cnf.sh" is defined as follows:
```#!/bin/bash

# Grab the number of clauses from each
CL1=`grep "^p" \$1  | cut -d " " -f "4"`
CL2=`grep "^p" \$2  | cut -d " " -f "4"`

NewCL=`expr \$CL1 + \$CL2`
cat \$1 | sed -e "s/p \+\([a-zA-Z]\+\) \+\([0-9]\+\).*\$/p \1 \2 \$NewCL/"
cat \$2 | grep -v "^c" | grep -v "^p"
```
• minisat2:
```\$ minisat2 Ramsey_4_4_2_18_SB_PHP.cnf
This is MiniSat 2.0 beta
WARNING: for repeatability, setting FPU to use double precision
============================[ Problem Statistics ]=============================
|                                                                             |
|  Number of variables:  153                                                  |
|  Number of clauses:    6222                                                 |
|  Parsing time:         0.01         s                                       |
============================[ Search Statistics ]==============================
| Conflicts |          ORIGINAL         |          LEARNT          | Progress |
|           |    Vars  Clauses Literals |    Limit  Clauses Lit/Cl |          |
===============================================================================
|         0 |     153     6222    35578 |     2074        0    nan |  0.000 % |
|       101 |     153     6222    35578 |     2281      101     12 |  0.038 % |
|       251 |     153     6222    35578 |     2509      251     18 |  0.004 % |
|       477 |     153     6222    35578 |     2760      477     21 |  0.004 % |
|       814 |     153     6222    35578 |     3036      814     21 |  0.004 % |
|      1320 |     153     6222    35578 |     3340     1320     21 |  0.004 % |
|      2080 |     153     6222    35578 |     3674     2080     21 |  0.004 % |
|      3222 |     153     6222    35578 |     4041     3222     19 |  0.004 % |
===============================================================================
restarts              : 8
conflicts             : 4647           (23234 /sec)
decisions             : 7230           (1.72 % random) (36148 /sec)
propagations          : 62907          (314516 /sec)
conflict literals     : 81530          (25.95 % deleted)
Memory used           : 2.63 MB
CPU time              : 0.200012 s

UNSATISFIABLE
```
• OKsolver:
```\$ OKsolver_2002-O3-DNDEBUG Ramsey_4_4_2_18_SB_PHP.cnf
s UNSATISFIABLE
c sat_status=0 initial_maximal_clause_length=6 initial_number_of_variables=153 initial_number_of_clauses=6222 initial_number_of_literal_occurrences=36924 running_time(s)=0.2 number_of_nodes=163 number_of_single_nodes=4 number_of_quasi_single_nodes=0 number_of_2-reductions=286 number_of_pure_literals=0 number_of_autarkies=0 number_of_missed_single_nodes=0 max_tree_depth=11 number_of_table_enlargements=0 reduced_maximal_clause_length=0 reduced_number_of_variables=0 reduced_number_of_clauses=0 reduced_number_of_literal_occurrences=0 number_of_1-autarkies=0 number_of_initial_unit-eliminations=0 number_of_new_2-clauses=0 maximal_number_of_added_2-clauses=0 initial_number_of_2-clauses=102 file_name=Ramsey_4_4_2_18_SB_PHP.cnf
```
• As a partial check the same symmetry breaking for n=17 yields satisfiable:
```\$ minisat2 Ramsey_4_4_2_17_SB_PHP.cnf
This is MiniSat 2.0 beta
WARNING: for repeatability, setting FPU to use double precision
============================[ Problem Statistics ]=============================
|                                                                             |
|  Number of variables:  136                                                  |
|  Number of clauses:    4844                                                 |
|  Parsing time:         0.01         s                                       |
============================[ Search Statistics ]==============================
| Conflicts |          ORIGINAL         |          LEARNT          | Progress |
|           |    Vars  Clauses Literals |    Limit  Clauses Lit/Cl |          |
===============================================================================
|         0 |     136     4844    27680 |     1614        0    nan |  0.000 % |
|       102 |     136     4844    27680 |     1776      102     12 |  0.043 % |
|       253 |     136     4844    27680 |     1953      253     15 |  0.005 % |
|       479 |     136     4844    27680 |     2149      479     17 |  0.005 % |
|       816 |     136     4844    27680 |     2364      816     15 |  0.005 % |
|      1323 |     136     4844    27680 |     2600     1323     17 |  0.011 % |
|      2085 |     136     4844    27680 |     2860     2085     18 |  0.005 % |
|      3225 |     136     4844    27680 |     3146     1768     20 |  0.005 % |
|      4934 |     136     4844    27680 |     3461     1881     17 |  0.005 % |
|      7497 |     136     4844    27680 |     3807     2694     22 |  0.065 % |
===============================================================================
restarts              : 10
conflicts             : 10812          (39172 /sec)
decisions             : 14637          (1.61 % random) (53029 /sec)
propagations          : 141515         (512704 /sec)
conflict literals     : 220783         (26.80 % deleted)
Memory used           : 2.62 MB
CPU time              : 0.276017 s

SATISFIABLE
```
• MG should finish providing a full proof that this symmetry breaking method is fully correct.
• Also for such a small instance, the symmetry breaking clauses can be checked manually to ensure they are as expected, and there is not a bug in the implementation.
• A more systematic investigation, involving each of the symmetry breaking techniques and cardinality constraints (see Experimentation/Investigations/RamseyTheory/RamseyProblems/plans/SymmetryBreaking.hpp) can be generated and run using the experiment system discussed at "General experiment system" in Experimentation/Investigations/Cryptography/AES/plans/BreakingAES.hpp), with the following "generate_exp.sh" script:
```# Generates Ramsey experiments for "ramsey_2^2(4,4) > n?" for 5 <= n <= 49.

for n in `seq 5 49`; do
# No Symmetry breaking
echo "PICOSAT_"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./solvers/picosat913 -v Ramsey_exp.cnf > Ramsey_4_4_2_\${n}.cnf.result.picosat 2>&1 && rm Ramsey_4_4_2_\${n}.cnf" >> experiments;
echo "MINISAT2_"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./solvers/minisat2 Ramsey_4_4_2_\${n}.cnf minisat-temp > Ramsey_4_4_2_\${n}.cnf.result.minisat2 2>&1; cat minisat-temp >> Ramsey_4_4_2_\${n}.cnf.result.minisat2;rm Ramsey_4_4_2_\${n}.cnf" >> experiments;
echo "MARCH_PL_"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./solvers/march_pl Ramsey_4_4_2_\${n}.cnf > Ramsey_4_4_2_\${n}.cnf.result.march_pl 2>&1;rm Ramsey_4_4_2_\${n}.cnf" >> experiments;
echo "OKSOLVER_"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./solvers/OKsolver_2002-O3-DNDEBUG -O -D20 -M -F Ramsey_4_4_2_\${n}.cnf > Ramsey_4_4_2_\${n}.cnf.result.OKsolver 2>&1; mv Ramsey_4_4_2_\${n}.cnf.mo Ramsey_4_4_2_\${n}.cnf.mo.OKsolver;mv Ramsey_4_4_2_\${n}.cnf.pa Ramsey_4_4_2_\${n}.cnf.pa.OKsolver;rm Ramsey_4_4_2_\${n}.cnf" >> experiments;
echo "OKSOLVERM2PP_"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./solvers/OKsolver_2002-m2pp -O -D20 -M -F Ramsey_4_4_2_\${n}.cnf > Ramsey_4_4_2_\${n}.cnf.result.OKsolver-m2pp 2>&1; mv Ramsey_4_4_2_\${n}.cnf_m2pp_*.mo Ramsey_4_4_2_\${n}.cnf.mo.OKsolver-m2pp;mv Ramsey_4_4_2_\${n}.cnf_m2pp_*.pa Ramsey_4_4_2_\${n}.cnf.pa.OKsolver-m2pp;rm Ramsey_4_4_2_\${n}.cnf" >> experiments;
# Symmetry breaking 1
echo "PICOSAT_FC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_FC_4_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_FC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_FC.ecnf > Ramsey_4_4_2_\${n}_SB_FC.cnf && ./solvers/picosat913 -v Ramsey_exp.cnf > Ramsey_4_4_2_\${n}_SB_FC.cnf.result.picosat 2>&1 && rm -f Ramsey_4_4_2_\${n}{,_SB_FC}.{e,}cnf" >> experiments;
echo "MINISAT2_FC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_FC_4_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_FC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_FC.ecnf > Ramsey_4_4_2_\${n}_SB_FC.cnf && ./solvers/minisat2 Ramsey_4_4_2_\${n}_SB_FC.cnf minisat-temp > Ramsey_4_4_2_\${n}_SB_FC.cnf.result.minisat2 2>&1; cat minisat-temp >> Ramsey_4_4_2_\${n}_SB_FC.cnf.result.minisat2;rm -f Ramsey_4_4_2_\${n}{,_SB_FC}.{e,}cnf" >> experiments;
echo "MARCH_PL_FC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_FC_4_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_FC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_FC.ecnf > Ramsey_4_4_2_\${n}_SB_FC.cnf && ./solvers/march_pl Ramsey_4_4_2_\${n}_SB_FC.cnf > Ramsey_4_4_2_\${n}_SB_FC.cnf.result.march_pl 2>&1;rm -f Ramsey_4_4_2_\${n}{_SB_FC,}.{e,}cnf" >> experiments;
echo "OKSOLVER_FC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_FC_4_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_FC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_FC.ecnf > Ramsey_4_4_2_\${n}_SB_FC.cnf && ./solvers/OKsolver_2002-O3-DNDEBUG -O -D20 -M -F Ramsey_4_4_2_\${n}_SB_FC.cnf > Ramsey_4_4_2_\${n}_SB_FC.cnf.result.OKsolver 2>&1; mv Ramsey_4_4_2_\${n}_SB_FC.cnf.mo Ramsey_4_4_2_\${n}_SB_FC.cnf.mo.OKsolver;mv Ramsey_4_4_2_\${n}_SB_FC.cnf.pa Ramsey_4_4_2_\${n}_SB_FC.cnf.pa.OKsolver;rm -f Ramsey_4_4_2_\${n}{,_SB_FC}.{e,}cnf" >> experiments;
echo "OKSOLVERM2PP_FC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_FC_4_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_FC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_FC.ecnf > Ramsey_4_4_2_\${n}_SB_FC.cnf && ./solvers/OKsolver_2002-m2pp -O -D20 -M -F Ramsey_4_4_2_\${n}_SB_FC.cnf > Ramsey_4_4_2_\${n}_SB_FC.cnf.result.OKsolver-m2pp 2>&1; mv Ramsey_4_4_2_\${n}_SB_FC.cnf_m2pp_*.mo Ramsey_4_4_2_\${n}_SB_FC.cnf.mo.OKsolver-m2pp;mv Ramsey_4_4_2_\${n}_SB_FC.cnf_m2pp_*.pa Ramsey_4_4_2_\${n}_SB_FC.cnf.pa.OKsolver-m2pp;rm -f Ramsey_4_4_2_\${n}{,_SB_FC}.{e,}cnf" >> experiments;
# Symmetry breaking 2
echo "PICOSAT_MC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_MC_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_MC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_MC.ecnf > Ramsey_4_4_2_\${n}_SB_MC.cnf && ./solvers/picosat913 -v Ramsey_4_4_2_\${n}_SB_MC.cnf > Ramsey_4_4_2_\${n}_SB_MC.cnf.result.picosat 2>&1 && rm -f Ramsey_4_4_2_\${n}{,_SB_MC}.{e,}cnf" >> experiments;
echo "MINISAT2_MC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_MC_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_MC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_MC.ecnf > Ramsey_4_4_2_\${n}_SB_MC.cnf && ./solvers/minisat2 Ramsey_4_4_2_\${n}_SB_MC.cnf minisat-temp > Ramsey_4_4_2_\${n}_SB_MC.cnf.result.minisat2 2>&1; cat minisat-temp >> Ramsey_4_4_2_\${n}_SB_MC.cnf.result.minisat2;rm -f Ramsey_4_4_2_\${n}{,_SB_MC}.{e,}cnf" >> experiments;
echo "MARCH_PL_MC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_MC_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_MC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_MC.ecnf > Ramsey_4_4_2_\${n}_SB_MC.cnf && ./solvers/march_pl Ramsey_4_4_2_\${n}_SB_MC.cnf > Ramsey_4_4_2_\${n}_SB_MC.cnf.result.march_pl 2>&1;rm -f Ramsey_4_4_2_\${n}{_SB_MC,}.{e,}cnf" >> experiments;
echo "OKSOLVER_MC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_MC_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_MC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_MC.ecnf > Ramsey_4_4_2_\${n}_SB_MC.cnf && ./solvers/OKsolver_2002-O3-DNDEBUG -O -D20 -M -F Ramsey_4_4_2_\${n}_SB_MC.cnf > Ramsey_4_4_2_\${n}_SB_MC.cnf.result.OKsolver 2>&1; mv Ramsey_4_4_2_\${n}_SB_MC.cnf.mo Ramsey_4_4_2_\${n}_SB_MC.cnf.mo.OKsolver;mv Ramsey_4_4_2_\${n}_SB_MC.cnf.pa Ramsey_4_4_2_\${n}_SB_MC.cnf.pa.OKsolver;rm -f Ramsey_4_4_2_\${n}{,_SB_MC}.{e,}cnf" >> experiments;
echo "OKSOLVERM2PP_MC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_MC_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_MC.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_MC.ecnf > Ramsey_4_4_2_\${n}_SB_MC.cnf && ./solvers/OKsolver_2002-m2pp -O -D20 -M -F Ramsey_4_4_2_\${n}_SB_MC.cnf > Ramsey_4_4_2_\${n}_SB_MC.cnf.result.OKsolver-m2pp 2>&1; mv Ramsey_4_4_2_\${n}_SB_MC.cnf_m2pp_*.mo Ramsey_4_4_2_\${n}_SB_MC.cnf.mo.OKsolver-m2pp;mv Ramsey_4_4_2_\${n}_SB_MC.cnf_m2pp_*.pa Ramsey_4_4_2_\${n}_SB_MC.cnf.pa.OKsolver-m2pp;rm -f Ramsey_4_4_2_\${n}{,_SB_MC}.{e,}cnf" >> experiments;
# Symmetry breaking 3
echo "PICOSAT_PHP"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_PHP_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_PHP.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf && ./solvers/picosat913 -v Ramsey_4_4_2_\${n}_SB_PHP.cnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf.result.picosat 2>&1 && rm -f Ramsey_4_4_2_\${n}{,_SB_PHP}.{e,}cnf" >> experiments;
echo "MINISAT2_PHP"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_PHP_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_PHP.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf && ./solvers/minisat2 Ramsey_4_4_2_\${n}_SB_PHP.cnf minisat-temp > Ramsey_4_4_2_\${n}_SB_PHP.cnf.result.minisat2 2>&1; cat minisat-temp >> Ramsey_4_4_2_\${n}_SB_PHP.cnf.result.minisat2;rm -f Ramsey_4_4_2_\${n}{,_SB_PHP}.{e,}cnf" >> experiments;
echo "MARCH_PL_PHP"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_PHP_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_PHP.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf && ./solvers/march_pl Ramsey_4_4_2_\${n}_SB_PHP.cnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf.result.march_pl 2>&1;rm -f Ramsey_4_4_2_\${n}{_SB_PHP,}.{e,}cnf" >> experiments;
echo "OKSOLVER_PHP"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_PHP_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_PHP.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf && ./solvers/OKsolver_2002-O3-DNDEBUG -O -D20 -M -F Ramsey_4_4_2_\${n}_SB_PHP.cnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf.result.OKsolver 2>&1; mv Ramsey_4_4_2_\${n}_SB_PHP.cnf.mo Ramsey_4_4_2_\${n}_SB_PHP.cnf.mo.OKsolver;mv Ramsey_4_4_2_\${n}_SB_PHP.cnf.pa Ramsey_4_4_2_\${n}_SB_PHP.cnf.pa.OKsolver;rm -f Ramsey_4_4_2_\${n}{,_SB_PHP}.{e,}cnf" >> experiments;
echo "OKSOLVERM2PP_PHP"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} > Ramsey_4_4_2_\${n}.ecnf && ./merge_cnf.sh Ramsey_4_4_2_\${n}.ecnf Ramsey_SB_PHP_\${n}.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.ecnf && ./ExtendedToStrictDimacs-O3-DNDEBUG < Ramsey_4_4_2_\${n}_SB_PHP.ecnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf && ./solvers/OKsolver_2002-m2pp -O -D20 -M -F Ramsey_4_4_2_\${n}_SB_PHP.cnf > Ramsey_4_4_2_\${n}_SB_PHP.cnf.result.OKsolver-m2pp 2>&1; mv Ramsey_4_4_2_\${n}_SB_PHP.cnf_m2pp_*.mo Ramsey_4_4_2_\${n}_SB_PHP.cnf.mo.OKsolver-m2pp;mv Ramsey_4_4_2_\${n}_SB_PHP.cnf_m2pp_*.pa Ramsey_4_4_2_\${n}_SB_PHP.cnf.pa.OKsolver-m2pp;rm -f Ramsey_4_4_2_\${n}{,_SB_PHP}.{e,}cnf" >> experiments;
# Cardinality Constraints
echo "PICOSAT_CC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./merge_cnf.sh Card/Card_n\${n}.cnf Ramsey_4_4_2_\${n}.cnf > Ramsey_4_4_2_\${n}_CC.cnf && ./solvers/picosat913 -v Ramsey_4_4_2_\${n}_CC.cnf > Ramsey_4_4_2_\${n}_CC.cnf.result.picosat 2>&1 && rm -f Ramsey_4_4_2_\${n}{,_CC}.{e,}cnf" >> experiments;
echo "MINISAT2_CC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./merge_cnf.sh Card/Card_n\${n}.cnf Ramsey_4_4_2_\${n}.cnf > Ramsey_4_4_2_\${n}_CC.cnf && ./solvers/minisat2 Ramsey_4_4_2_\${n}_CC.cnf minisat-temp > Ramsey_4_4_2_\${n}_CC.cnf.result.minisat2 2>&1; cat minisat-temp >> Ramsey_4_4_2_\${n}_CC.cnf.result.minisat2;rm -f Ramsey_4_4_2_\${n}{,_CC}.{e,}cnf" >> experiments;
#    echo "MARCH_PL_CC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./merge_cnf.sh Card/Card_n\${n}.cnf Ramsey_4_4_2_\${n}.cnf > Ramsey_4_4_2_\${n}_CC.cnf && ./solvers/march_pl Ramsey_4_4_2_\${n}_CC.cnf > Ramsey_4_4_2_\${n}_CC.cnf.result.march_pl 2>&1;rm -f Ramsey_4_4_2_\${n}{_CC,}.{e,}cnf" >> experiments;
echo "OKSOLVER_CC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./merge_cnf.sh Card/Card_n\${n}.cnf Ramsey_4_4_2_\${n}.cnf > Ramsey_4_4_2_\${n}_CC.cnf && ./solvers/OKsolver_2002-O3-DNDEBUG -O -D20 -M -F Ramsey_4_4_2_\${n}_CC.cnf > Ramsey_4_4_2_\${n}_CC.cnf.result.OKsolver 2>&1; mv Ramsey_4_4_2_\${n}_CC.cnf.mo Ramsey_4_4_2_\${n}_CC.cnf.mo.OKsolver;mv Ramsey_4_4_2_\${n}_CC.cnf.pa Ramsey_4_4_2_\${n}_CC.cnf.pa.OKsolver;rm -f Ramsey_4_4_2_\${n}{,_CC}.{e,}cnf" >> experiments;
echo "OKSOLVERM2PP_CC"\$n "./Ramsey-O3-DNDEBUG 4 4 2 \${n} | ./ExtendedToStrictDimacs-O3-DNDEBUG > Ramsey_4_4_2_\${n}.cnf && ./merge_cnf.sh Card/Card_n\${n}.cnf Ramsey_4_4_2_\${n}.cnf > Ramsey_4_4_2_\${n}_CC.cnf && ./solvers/OKsolver_2002-m2pp -O -D20 -M -F Ramsey_4_4_2_\${n}_CC.cnf > Ramsey_4_4_2_\${n}_CC.cnf.result.OKsolver-m2pp 2>&1; mv Ramsey_4_4_2_\${n}_CC.cnf_m2pp_*.mo Ramsey_4_4_2_\${n}_CC.cnf.mo.OKsolver-m2pp;mv Ramsey_4_4_2_\${n}_CC.cnf_m2pp_*.pa Ramsey_4_4_2_\${n}_CC.cnf.pa.OKsolver-m2pp;rm -f Ramsey_4_4_2_\${n}{,_CC}.{e,}cnf" >> experiments;
done
```
• The above experiment (in the generation script) is currently running on cssinope with a timeout of 2 hours.
• Combining all such investigations (different symmetry breaking techniques, cardinality contraints etc) into a single experiment allows one to run through all such investigations for a short time and then split the experiments if certain aspects are slowing the entire experiment set down or it makes more sense to run certain parts, or solvers in parallel.

Definition in file Ramsey_2_4_4.hpp.