Table 4.

General information of all benchmarks used

Instance	System Under Test (SUT)			Bounds for $t=2$					$PMSa{t}_{\mathit{CCX}}^{N,t=2,S,lb}$
	$S_P$	$S_{\phi }$	# lits $CNF(S_{\phi })$	$u{b}^{\mathit{ACTS}}$	$u{b}^{\simeq }$	lb	$|{\mathcal{T}}_a|$	$|{\mathcal{T}}_f|$	# vars	# clauses	# lits	size (MB)
Cohen et al. (2008)
1	$2^{86}{3}^3{4}^1{5}^5{6}^2$	$2^{20}{3}^3{4}^1$	53	48	37	35	23876	474	1158588	2620675	7463282	60.01
2	$2^{86}{3}^3{4}^3{5}^1{6}^1$	$2^{19}{3}^3$	47	32	30*	29	20331	237	657890	1371738	3984183	29.91
3	$2^{27}{4}^2$	$2^9{3}^1$	21	19	18*	15	1838	14	36217	79008	222390	1.47
4	$2^{51}{3}^4{4}^2{5}^1$	$2^{15}{3}^2$	36	22	20*	19	7530	386	168852	358291	1025536	7.33
5	$2^{155}{3}^7{4}^3{5}^5{6}^4$	$2^{32}{3}^6{4}^1$	86	54	45	35	76259	73	4142574	9720622	27451121	236.74
6	$2^{73}{4}^3{6}^1$	$2^{26}{3}^4$	64	25	24*	23	11382	1878	289001	597814	1730859	12.72
7	$2^{29}{3}^1$	$2^{13}{3}^2$	32	12	9	5	1567	231	19566	49758	132435	0.85
8	$2^{109}{3}^2{4}^2{5}^3{6}^3$	$2^{32}{3}^4{4}^1$	80	47	36*	35	33680	1098	1597165	3590459	10247230	84.50
9	$2^{57}{3}^1{4}^1{5}^1{6}^1$	$2^{30}{3}^7$	81	22	20*	19	6835	1720	153584	325984	932515	6.63
10	$2^{130}{3}^6{4}^5{5}^2{6}^4$	$2^{40}{3}^7$	101	47	41	35	52659	2029	2493173	5608369	16010703	135.34
11	$2^{84}{3}^4{4}^2{5}^2{6}^4$	$2^{28}{3}^4$	68	47	39	35	23636	707	1123311	2523897	7200149	57.70
12	$2^{136}{3}^4{4}^3{5}^1{6}^3$	$2^{23}{3}^4$	58	43	36*	35	49522	978	2144718	4675267	13461992	108.23
13	$2^{124}{3}^4{4}^1{5}^2{6}^2$	$2^{22}{3}^4$	56	40	36*	35	38862	1701	1567084	3319517	9632256	75.77
14	$2^{81}{3}^5{4}^3{6}^3$	$2^{13}{3}^2$	32	39	36*	35	20544	618	810618	1697204	4936072	37.18
15	$2^{50}{3}^4{4}^1{5}^2{6}^1$	$2^{20}{3}^2$	46	32	30*	29	8388	155	273410	569181	1650514	12.10
16	$2^{81}{3}^3{4}^2{6}^1$	$2^{30}{3}^4$	72	25	24*	23	14600	2303	370051	765960	2218422	16.44
17	$2^{128}{3}^3{4}^2{5}^1{6}^3$	$2^{25}{3}^4$	62	41	36*	35	43390	66	1792402	3835891	11100545	88.14
18	$2^{127}{3}^2{4}^4{5}^6{6}^2$	$2^{23}{3}^4{4}^1$	62	52	41	35	50128	28	2625808	6092947	17250882	146.38
19	$2^{172}{3}^9{4}^9{5}^3{6}^4$	$2^{38}{3}^5$	91	51	43	35	98778	114	5064366	11694341	33170488	287.31
20	$2^{138}{3}^4{4}^5{5}^4{6}^7$	$2^{42}{3}^6$	102	60	54	35	64620	3320	3903864	9411047	26386102	227.62
21	$2^{76}{3}^3{4}^2{5}^1{6}^3$	$2^{40}{3}^6$	98	39	36*	35	15442	2742	610938	1279170	3717471	27.90
22	$2^{72}{3}^4{4}^1{6}^2$	$2^{20}{3}^2$	46	37	36*	35	13405	1181	503127	1028139	3008516	22.48
23	$2^{25}{3}^1{6}^1$	$2^{13}{3}^2$	32	14	12*	11	1495	173	21856	47740	132915	0.85
24	$2^{110}{3}^2{5}^3{6}^4$	$2^{25}{3}^4$	62	48	41	35	34204	570	1656252	3748659	10679658	88.30
25	$2^{118}{3}^6{4}^2{5}^2{6}^6$	$2^{23}{3}^3{4}^1$	59	52	49	35	46968	52	2461280	5710735	16167454	136.81
26	$2^{87}{3}^1{4}^3{5}^4$	$2^{28}{3}^4$	68	34	26	24	20921	667	719347	1643461	4647485	36.52
27	$2^{55}{3}^2{4}^2{5}^1{6}^2$	$2^{17}{3}^3$	43	37	36*	35	9714	43	365524	746797	2183919	16.18
28	$2^{167}{3}^{16}{4}^2{5}^3{6}^6$	$2^{31}{3}^6$	80	57	50	35	96599	74	5535861	13181074	37087871	322.33
29	$2^{134}{3}^7{5}^3$	$2^{19}{3}^3$	47	29	25*	24	45839	32	1338905	2899941	8321499	64.34
30	$2^{73}{3}^3{4}^3$	$2^{31}{3}^4$	74	22	16*	15	12453	1308	277976	640938	1792681	13.16
apache	$2^{158}{3}^8{4}^4{5}^1{6}^1$	$2^3{3}^1{4}^2{5}^1$	22	33	30*	29	66927	3	2221926	4701044	13619419	109.16
bugzilla	$2^{49}{3}^1{4}^2$	$2^4{3}^1$	11	19	16*	15	5818	4	112768	247130	697953	4.82
gcc	$2^{189}{3}^{10}$	$2^{37}{3}^3$	83	23	15	8	82770	39	1913568	5063264	13685896	112.78
spins	$2^{13}{4}^5$	$2^{13}$	26	26	19*	15	979	13	27050	64498	177169	1.23
spinv	$2^{42}{3}^2{4}^{11}$	$2^{47}{3}^2$	100	45	33	15	8741	56	401069	1063265	2888090	22.53
Segall et al. (2011)
Banking1	$3^4{4}^1$	$5^{112}$	560	15	13*	11	102	0	1938	5864	19573	0.11
Banking2	$2^{14}{4}^1$	$2^3$	6	11	10*	7	473	3	5591	12845	34672	0.21
CommProtocol	$2^{10}{7}^1$	$2^{10}{3}^{10}{4}^{12}{5}^{24}$ $6^{30}{7}^{30}{8}^{12}$	704	19	16*	13	285	35	6047	15914	50363	0.29
Concurrency	$2^5$	$2^4{3}^1{5}^2$	21	6	5*	3	36	4	278	667	1686	0.01
Healthcare1	$2^6{3}^2{5}^1{6}^1$	$2^3{3}^{18}$	60	30	30*	29	361	8	12090	24661	70619	0.44
Healthcare2	$2^5{3}^6{4}^1$	$2^1{3}^6{5}^{18}$	110	16	14	11	466	1	8212	18853	52268	0.31
Healthcare3	$2^{16}{3}^6{4}^5{5}^1{6}^1$	$2^{31}$	62	38	34*	29	3092	59	121950	271023	768538	5.38
Healthcare4	$2^{13}{3}^{12}{4}^6{5}^2{6}^1{7}^1$	$2^{22}$	44	49	46*	41	5707	38	287980	619634	1783211	13.14
Insurance	$2^6{3}^1{5}^1{6}^2{11}^1{13}^1{17}^1{31}^1$	–	0	527	527*	526	4573	0	2509047	5009492	14863678	122.95
NetworkMgmt	$2^2{4}^1{5}^3{10}^2{11}^1$	$2^{20}$	40	112	110*	109	1228	20	148402	301059	877206	6.28
ProcessorComm1	$2^3{3}^6{4}^6$	$2^{13}$	26	29	21	15	1058	13	32957	80475	219601	1.54
ProcessorComm2	$2^3{3}^{12}{4}^8{5}^2$	$1^4{2}^{121}$	246	32	25*	24	2525	854	85287	193248	541399	3.73
Services	$2^3{3}^4{5}^2{8}^2{10}^2$	$3^{386}{4}^2$	1166	106	100*	99	1819	16	204692	460866	1346965	9.78
Storage1	$2^1{3}^1{4}^1{5}^1$	$4^{95}$	380	17	17*	14	53	18	1294	4270	13468	0.07
Storage2	$3^4{6}^1$	–	0	18	18*	17	126	0	2826	5652	15552	0.09
Storage3	$2^9{3}^1{5}^3{6}^1{8}^1$	$2^{38}{3}^{10}$	106	50	50*	39	1020	120	54810	122009	344328	2.47
Storage4	$2^5{3}^7{4}^1{5}^2{6}^2{7}^1{10}^1{13}^1$	$2^{24}$	48	136	130*	129	3491	24	495046	1012862	2970799	22.45
Storage5	$2^5{3}^8{5}^3{6}^2{8}^1{9}^1{10}^2{11}^1$	$2^{151}$	302	218	215	109	5342	246	1206084	3020149	8366680	72.16
SystemMgmt	$2^5{3}^4{5}^1$	$2^{13}{3}^4$	38	17	15*	14	310	14	5935	12813	35376	0.21
Telecom	$2^5{3}^1{4}^2{5}^1{6}^1$	$2^{11}{3}^1{4}^9$	61	32	30*	29	440	11	15650	32761	93262	0.59
Yu et al. (2015)
RL-A	$2^5{3}^4{4}^7{5}^4{6}^5$ $7^4{8}^1{12}^3$	$1^{12}{2}^{491}{3}^{345}$	2029	155	153	143	7066	7156	1142671	2491775	7220414	59.32
RL-B	$2^8{3}^2{4}^3{5}^3{6}^1{9}^1$ ${10}^1{12}^2$	$1^8{2}^{1127}{3}^{277}$	27721	767	727	519	17018	5597	13365222	35733711	109278283	1026.60
	${14}^3{20}^1{24}^1{37}^1$	$4^{1755}{5}^{1064}{6}^{2048}$
Yamada et al. (2016)
Company2	$2^6{3}^4{8}^4$	$1^2{2}^{35}{3}^{89}{4}^{54}{5}^{34}$	1247	81	72	55	1149	261	100546	252543	744203	5.35
		$6^{20}{7}^{34}{8}^{16}{9}^4$