TSTP Solution File: LAT010-1 by Matita---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : LAT010-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 05:55:34 EDT 2022
% Result : Unsatisfiable 114.89s 29.10s
% Output : CNFRefutation 114.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT010-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 30 01:36:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 1947: Facts:
% 0.12/0.34 1947: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
% 0.12/0.34 1947: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
% 0.12/0.34 1947: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
% 0.12/0.34 1947: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
% 0.12/0.34 1947: Id : 6, {_}:
% 0.12/0.34 meet ?12 ?13 =?= meet ?13 ?12
% 0.12/0.34 [13, 12] by commutativity_of_meet ?12 ?13
% 0.12/0.34 1947: Id : 7, {_}:
% 0.12/0.34 join ?15 ?16 =?= join ?16 ?15
% 0.12/0.34 [16, 15] by commutativity_of_join ?15 ?16
% 0.12/0.34 1947: Id : 8, {_}:
% 0.12/0.34 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
% 0.12/0.34 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
% 0.12/0.34 1947: Id : 9, {_}:
% 0.12/0.34 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
% 0.12/0.34 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
% 0.12/0.34 1947: Id : 10, {_}:
% 0.12/0.34 meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
% 0.12/0.34 =<=
% 0.12/0.34 join (meet ?26 (join ?27 (meet ?26 ?28)))
% 0.12/0.34 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29)))
% 0.12/0.34 [29, 28, 27, 26] by n5_1 ?26 ?27 ?28 ?29
% 0.12/0.34 1947: Id : 11, {_}:
% 0.12/0.34 join ?31 (meet ?32 (join ?33 (meet ?31 ?34)))
% 0.12/0.34 =<=
% 0.12/0.34 meet (join ?31 (meet ?32 (join ?31 ?33)))
% 0.12/0.34 (join ?31 (meet (join ?31 ?32) (join ?33 ?34)))
% 0.12/0.34 [34, 33, 32, 31] by n5_2 ?31 ?32 ?33 ?34
% 0.12/0.34 1947: Id : 12, {_}:
% 0.12/0.34 meet (join ?36 (meet ?37 ?38)) (join ?38 (meet ?36 ?37))
% 0.12/0.34 =<=
% 0.12/0.34 join (meet ?38 (join ?36 (meet ?37 ?38))) (meet ?36 (join ?37 ?38))
% 0.12/0.34 [38, 37, 36] by nr_3 ?36 ?37 ?38
% 0.12/0.34 1947: Goal:
% 0.12/0.34 1947: Id : 1, {_}:
% 0.12/0.34 meet a (meet (join b c) (join b d))
% 0.12/0.34 =<=
% 0.12/0.34 meet (meet a (meet (join b c) (join b d)))
% 0.12/0.34 (join (meet a (join b (meet c d))) (join (meet a c) (meet a d)))
% 0.12/0.34 [] by prove_this
% 114.89/29.10 Statistics :
% 114.89/29.10 Max weight : 26
% 114.89/29.10 Found proof, 28.762937s
% 114.89/29.10 % SZS status Unsatisfiable for theBenchmark.p
% 114.89/29.10 % SZS output start CNFRefutation for theBenchmark.p
% 114.89/29.10 Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
% 114.89/29.10 Id : 102, {_}: meet ?254 (join ?255 (meet ?256 (join ?254 ?257))) =<= join (meet ?254 (join ?255 (meet ?254 ?256))) (meet ?254 (join (meet ?254 ?255) (meet ?256 ?257))) [257, 256, 255, 254] by n5_1 ?254 ?255 ?256 ?257
% 114.89/29.10 Id : 12, {_}: meet (join ?36 (meet ?37 ?38)) (join ?38 (meet ?36 ?37)) =<= join (meet ?38 (join ?36 (meet ?37 ?38))) (meet ?36 (join ?37 ?38)) [38, 37, 36] by nr_3 ?36 ?37 ?38
% 114.89/29.10 Id : 79, {_}: join (join ?195 ?196) ?197 =>= join ?195 (join ?196 ?197) [197, 196, 195] by associativity_of_join ?195 ?196 ?197
% 114.89/29.10 Id : 8, {_}: meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
% 114.89/29.10 Id : 9, {_}: join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) [24, 23, 22] by associativity_of_join ?22 ?23 ?24
% 114.89/29.10 Id : 11, {_}: join ?31 (meet ?32 (join ?33 (meet ?31 ?34))) =<= meet (join ?31 (meet ?32 (join ?31 ?33))) (join ?31 (meet (join ?31 ?32) (join ?33 ?34))) [34, 33, 32, 31] by n5_2 ?31 ?32 ?33 ?34
% 114.89/29.10 Id : 7, {_}: join ?15 ?16 =?= join ?16 ?15 [16, 15] by commutativity_of_join ?15 ?16
% 114.89/29.10 Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
% 114.89/29.10 Id : 55, {_}: meet (meet ?133 ?134) ?135 =>= meet ?133 (meet ?134 ?135) [135, 134, 133] by associativity_of_meet ?133 ?134 ?135
% 114.89/29.10 Id : 6, {_}: meet ?12 ?13 =?= meet ?13 ?12 [13, 12] by commutativity_of_meet ?12 ?13
% 114.89/29.10 Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
% 114.89/29.10 Id : 29, {_}: join ?66 (meet ?67 ?66) =>= ?66 [67, 66] by Super 5 with 6 at 2,2
% 114.89/29.10 Id : 57, {_}: meet ?140 ?141 =<= meet ?140 (meet (join ?140 ?142) ?141) [142, 141, 140] by Super 55 with 4 at 1,2
% 114.89/29.10 Id : 914, {_}: join (meet (join ?1608 ?1609) ?1610) (meet ?1608 ?1610) =>= meet (join ?1608 ?1609) ?1610 [1610, 1609, 1608] by Super 29 with 57 at 2,2
% 114.89/29.10 Id : 9034, {_}: join (meet ?16020 ?16021) (meet (join ?16020 ?16022) ?16021) =>= meet (join ?16020 ?16022) ?16021 [16022, 16021, 16020] by Demod 914 with 7 at 2
% 114.89/29.10 Id : 9096, {_}: join ?16312 (meet (join ?16312 ?16313) (join ?16312 ?16314)) =>= meet (join ?16312 ?16313) (join ?16312 ?16314) [16314, 16313, 16312] by Super 9034 with 4 at 1,2
% 114.89/29.10 Id : 76, {_}: join ?184 (join ?185 (meet (join ?184 ?185) ?186)) =>= join ?184 ?185 [186, 185, 184] by Super 5 with 9 at 2
% 114.89/29.10 Id : 39, {_}: meet ?90 (join ?91 ?90) =>= ?90 [91, 90] by Super 4 with 7 at 2,2
% 114.89/29.10 Id : 491, {_}: meet ?888 ?889 =<= meet ?888 (meet (join ?890 ?888) ?889) [890, 889, 888] by Super 8 with 39 at 1,2
% 114.89/29.10 Id : 1300, {_}: join (meet (join ?2329 ?2330) ?2331) (meet ?2330 ?2331) =>= meet (join ?2329 ?2330) ?2331 [2331, 2330, 2329] by Super 29 with 491 at 2,2
% 114.89/29.10 Id : 14457, {_}: join (meet ?26080 ?26081) (meet (join ?26082 ?26080) ?26081) =>= meet (join ?26082 ?26080) ?26081 [26082, 26081, 26080] by Demod 1300 with 7 at 2
% 114.89/29.10 Id : 14534, {_}: join ?26450 (meet (join ?26451 ?26450) (join ?26452 ?26450)) =>= meet (join ?26451 ?26450) (join ?26452 ?26450) [26452, 26451, 26450] by Super 14457 with 39 at 1,2
% 114.89/29.10 Id : 75444, {_}: join ?137779 (meet (join ?137779 ?137780) (join ?137781 ?137780)) =>= join ?137779 ?137780 [137781, 137780, 137779] by Super 76 with 14534 at 2,2
% 114.89/29.10 Id : 103915, {_}: join ?189295 (meet ?189296 (join ?189297 (meet ?189295 ?189296))) =<= meet (join ?189295 (meet ?189296 (join ?189295 ?189297))) (join ?189295 ?189296) [189297, 189296, 189295] by Super 11 with 75444 at 2,3
% 114.89/29.10 Id : 104424, {_}: join ?189295 (meet ?189296 (join ?189297 (meet ?189295 ?189296))) =<= meet (join ?189295 ?189296) (join ?189295 (meet ?189296 (join ?189295 ?189297))) [189297, 189296, 189295] by Demod 103915 with 6 at 3
% 114.89/29.10 Id : 1021, {_}: join ?1800 ?1801 =<= join ?1800 (join (meet ?1800 ?1802) ?1801) [1802, 1801, 1800] by Super 79 with 5 at 1,2
% 114.89/29.10 Id : 1036, {_}: join ?1861 ?1862 =<= join ?1861 (join ?1862 (meet ?1861 ?1863)) [1863, 1862, 1861] by Super 1021 with 7 at 2,3
% 114.89/29.10 Id : 2968, {_}: meet (join ?5106 (meet ?5107 ?5108)) (join ?5107 ?5106) =>= join ?5106 (meet ?5107 ?5108) [5108, 5107, 5106] by Super 39 with 1036 at 2,2
% 114.89/29.10 Id : 27814, {_}: meet (join ?52018 ?52019) (join ?52019 (meet ?52018 ?52020)) =>= join ?52019 (meet ?52018 ?52020) [52020, 52019, 52018] by Demod 2968 with 6 at 2
% 114.89/29.10 Id : 27888, {_}: meet (join ?52373 ?52374) (join ?52373 (meet ?52374 ?52375)) =>= join ?52373 (meet ?52374 ?52375) [52375, 52374, 52373] by Super 27814 with 7 at 1,2
% 114.89/29.10 Id : 104425, {_}: join ?189295 (meet ?189296 (join ?189297 (meet ?189295 ?189296))) =>= join ?189295 (meet ?189296 (join ?189295 ?189297)) [189297, 189296, 189295] by Demod 104424 with 27888 at 3
% 114.89/29.10 Id : 492, {_}: meet ?892 ?893 =<= meet ?892 (meet ?893 (join ?894 (meet ?892 ?893))) [894, 893, 892] by Super 8 with 39 at 2
% 114.89/29.10 Id : 431, {_}: join ?801 ?802 =<= join ?801 (join (meet ?803 ?801) ?802) [803, 802, 801] by Super 9 with 29 at 1,2
% 114.89/29.10 Id : 1099, {_}: meet (join (meet ?1914 ?1915) ?1916) (join ?1915 ?1916) =>= join (meet ?1914 ?1915) ?1916 [1916, 1915, 1914] by Super 39 with 431 at 2,2
% 114.89/29.10 Id : 10634, {_}: meet (join ?19050 ?19051) (join (meet ?19052 ?19050) ?19051) =>= join (meet ?19052 ?19050) ?19051 [19052, 19051, 19050] by Demod 1099 with 6 at 2
% 114.89/29.10 Id : 10703, {_}: meet ?19374 (join (meet ?19375 ?19374) (meet ?19376 ?19374)) =>= join (meet ?19375 ?19374) (meet ?19376 ?19374) [19376, 19375, 19374] by Super 10634 with 29 at 1,2
% 114.89/29.10 Id : 99458, {_}: meet ?182036 ?182037 =<= meet ?182036 (join (meet ?182038 ?182037) (meet ?182036 ?182037)) [182038, 182037, 182036] by Super 492 with 10703 at 2,3
% 114.89/29.10 Id : 99552, {_}: meet ?182522 (join ?182523 ?182524) =<= meet ?182522 (join ?182524 (meet ?182522 (join ?182523 ?182524))) [182524, 182523, 182522] by Super 99458 with 39 at 1,2,3
% 114.89/29.10 Id : 294, {_}: meet (join ?36 (meet ?37 ?38)) (join ?38 (meet ?36 ?37)) =<= join (meet ?36 (join ?37 ?38)) (meet ?38 (join ?36 (meet ?37 ?38))) [38, 37, 36] by Demod 12 with 7 at 3
% 114.89/29.10 Id : 439, {_}: join ?835 (meet ?836 ?835) =>= ?835 [836, 835] by Super 5 with 6 at 2,2
% 114.89/29.10 Id : 443, {_}: join ?846 (meet ?847 (meet ?848 ?846)) =>= ?846 [848, 847, 846] by Super 439 with 8 at 2,2
% 114.89/29.10 Id : 1208, {_}: meet (join ?2145 (meet ?2146 (meet ?2147 ?2145))) (join (meet ?2147 ?2145) (meet ?2145 ?2146)) =>= join (meet ?2145 (join ?2146 (meet ?2147 ?2145))) (meet (meet ?2147 ?2145) ?2145) [2147, 2146, 2145] by Super 294 with 443 at 2,2,3
% 114.89/29.10 Id : 1244, {_}: meet ?2145 (join (meet ?2147 ?2145) (meet ?2145 ?2146)) =<= join (meet ?2145 (join ?2146 (meet ?2147 ?2145))) (meet (meet ?2147 ?2145) ?2145) [2146, 2147, 2145] by Demod 1208 with 443 at 1,2
% 114.89/29.10 Id : 1245, {_}: meet ?2145 (join (meet ?2147 ?2145) (meet ?2145 ?2146)) =<= join (meet (meet ?2147 ?2145) ?2145) (meet ?2145 (join ?2146 (meet ?2147 ?2145))) [2146, 2147, 2145] by Demod 1244 with 7 at 3
% 114.89/29.10 Id : 1246, {_}: meet ?2145 (join (meet ?2147 ?2145) (meet ?2145 ?2146)) =<= join (meet ?2145 (meet ?2147 ?2145)) (meet ?2145 (join ?2146 (meet ?2147 ?2145))) [2146, 2147, 2145] by Demod 1245 with 6 at 1,3
% 114.89/29.10 Id : 498, {_}: meet ?918 (join ?919 ?918) =>= ?918 [919, 918] by Super 4 with 7 at 2,2
% 114.89/29.10 Id : 503, {_}: meet (meet ?933 ?934) ?934 =>= meet ?933 ?934 [934, 933] by Super 498 with 29 at 2,2
% 114.89/29.10 Id : 539, {_}: meet ?934 (meet ?933 ?934) =>= meet ?933 ?934 [933, 934] by Demod 503 with 6 at 2
% 114.89/29.10 Id : 1247, {_}: meet ?2145 (join (meet ?2147 ?2145) (meet ?2145 ?2146)) =<= join (meet ?2147 ?2145) (meet ?2145 (join ?2146 (meet ?2147 ?2145))) [2146, 2147, 2145] by Demod 1246 with 539 at 1,3
% 114.89/29.10 Id : 10700, {_}: meet ?19361 (join (meet ?19362 ?19361) (meet ?19361 ?19363)) =>= join (meet ?19362 ?19361) (meet ?19361 ?19363) [19363, 19362, 19361] by Super 10634 with 5 at 1,2
% 114.89/29.10 Id : 154010, {_}: join (meet ?2147 ?2145) (meet ?2145 ?2146) =<= join (meet ?2147 ?2145) (meet ?2145 (join ?2146 (meet ?2147 ?2145))) [2146, 2145, 2147] by Demod 1247 with 10700 at 2
% 114.89/29.10 Id : 154210, {_}: meet ?280057 (join ?280058 (meet ?280059 ?280057)) =<= meet ?280057 (join (meet ?280059 ?280057) (meet ?280057 ?280058)) [280059, 280058, 280057] by Super 99552 with 154010 at 2,3
% 114.89/29.10 Id : 154587, {_}: meet ?280057 (join ?280058 (meet ?280059 ?280057)) =>= join (meet ?280059 ?280057) (meet ?280057 ?280058) [280059, 280058, 280057] by Demod 154210 with 10700 at 3
% 114.89/29.10 Id : 156058, {_}: join ?189295 (join (meet ?189295 ?189296) (meet ?189296 ?189297)) =>= join ?189295 (meet ?189296 (join ?189295 ?189297)) [189297, 189296, 189295] by Demod 104425 with 154587 at 2,2
% 114.89/29.10 Id : 81, {_}: join ?202 ?203 =<= join ?202 (join (meet ?202 ?204) ?203) [204, 203, 202] by Super 79 with 5 at 1,2
% 114.89/29.10 Id : 156059, {_}: join ?189295 (meet ?189296 ?189297) =<= join ?189295 (meet ?189296 (join ?189295 ?189297)) [189297, 189296, 189295] by Demod 156058 with 81 at 2
% 114.89/29.10 Id : 156065, {_}: join ?16312 (meet (join ?16312 ?16313) ?16314) =<= meet (join ?16312 ?16313) (join ?16312 ?16314) [16314, 16313, 16312] by Demod 9096 with 156059 at 2
% 114.89/29.10 Id : 52, {_}: meet ?122 (meet ?123 (join (meet ?122 ?123) ?124)) =>= meet ?122 ?123 [124, 123, 122] by Super 4 with 8 at 2
% 114.89/29.10 Id : 98288, {_}: meet ?180067 (join (meet ?180067 ?180068) (meet ?180068 ?180069)) =>= meet ?180067 ?180068 [180069, 180068, 180067] by Super 52 with 10700 at 2,2
% 114.89/29.10 Id : 5539, {_}: meet (join ?10193 ?10194) (join ?10193 (join ?10194 ?10195)) =>= join ?10193 ?10194 [10195, 10194, 10193] by Super 4 with 9 at 2,2
% 114.89/29.10 Id : 497, {_}: join (join ?915 ?916) ?916 =>= join ?915 ?916 [916, 915] by Super 29 with 39 at 2,2
% 114.89/29.10 Id : 510, {_}: join ?916 (join ?915 ?916) =>= join ?915 ?916 [915, 916] by Demod 497 with 7 at 2
% 114.89/29.10 Id : 5572, {_}: meet (join ?10331 ?10332) (join ?10332 ?10331) =>= join ?10331 ?10332 [10332, 10331] by Super 5539 with 510 at 2,2
% 114.89/29.10 Id : 5834, {_}: join (join ?10620 ?10621) (meet ?10622 (join ?10621 ?10620)) =>= join ?10620 ?10621 [10622, 10621, 10620] by Super 443 with 5572 at 2,2,2
% 114.89/29.10 Id : 5925, {_}: join ?10620 (join ?10621 (meet ?10622 (join ?10621 ?10620))) =>= join ?10620 ?10621 [10622, 10621, 10620] by Demod 5834 with 9 at 2
% 114.89/29.10 Id : 58062, {_}: join ?105421 (meet (join ?105422 ?105423) (join ?105422 ?105421)) =>= join ?105421 ?105422 [105423, 105422, 105421] by Super 5925 with 9096 at 2,2
% 114.89/29.10 Id : 98485, {_}: meet ?181008 (join (meet ?181008 (join ?181009 ?181010)) ?181009) =>= meet ?181008 (join ?181009 ?181010) [181010, 181009, 181008] by Super 98288 with 58062 at 2,2
% 114.89/29.10 Id : 1309, {_}: meet ?2367 ?2368 =<= meet ?2367 (meet (join ?2369 ?2367) ?2368) [2369, 2368, 2367] by Super 8 with 39 at 1,2
% 114.89/29.10 Id : 1311, {_}: meet (meet ?2374 ?2375) ?2376 =<= meet (meet ?2374 ?2375) (meet ?2374 ?2376) [2376, 2375, 2374] by Super 1309 with 5 at 1,2,3
% 114.89/29.10 Id : 1371, {_}: meet ?2374 (meet ?2375 ?2376) =<= meet (meet ?2374 ?2375) (meet ?2374 ?2376) [2376, 2375, 2374] by Demod 1311 with 8 at 2
% 114.89/29.10 Id : 1372, {_}: meet ?2374 (meet ?2375 ?2376) =<= meet ?2374 (meet ?2375 (meet ?2374 ?2376)) [2376, 2375, 2374] by Demod 1371 with 8 at 3
% 114.89/29.10 Id : 714, {_}: meet (meet ?1200 ?1201) ?1202 =<= meet ?1201 (meet (meet ?1200 ?1201) ?1202) [1202, 1201, 1200] by Super 8 with 539 at 1,2
% 114.89/29.10 Id : 739, {_}: meet ?1200 (meet ?1201 ?1202) =<= meet ?1201 (meet (meet ?1200 ?1201) ?1202) [1202, 1201, 1200] by Demod 714 with 8 at 2
% 114.89/29.10 Id : 740, {_}: meet ?1200 (meet ?1201 ?1202) =<= meet ?1201 (meet ?1200 (meet ?1201 ?1202)) [1202, 1201, 1200] by Demod 739 with 8 at 2,3
% 114.89/29.10 Id : 3665, {_}: meet ?2374 (meet ?2375 ?2376) =?= meet ?2375 (meet ?2374 ?2376) [2376, 2375, 2374] by Demod 1372 with 740 at 3
% 114.89/29.10 Id : 5841, {_}: meet (join ?10646 ?10647) (meet ?10648 (join ?10647 ?10646)) =>= meet ?10648 (join ?10646 ?10647) [10648, 10647, 10646] by Super 3665 with 5572 at 2,3
% 114.89/29.10 Id : 50, {_}: meet ?114 (meet ?115 ?116) =?= meet ?115 (meet ?116 ?114) [116, 115, 114] by Super 6 with 8 at 3
% 114.89/29.10 Id : 5831, {_}: meet (join ?10608 ?10609) (meet ?10610 (join ?10609 ?10608)) =>= meet ?10610 (join ?10609 ?10608) [10610, 10609, 10608] by Super 50 with 5572 at 2,3
% 114.89/29.10 Id : 50020, {_}: meet ?10648 (join ?10647 ?10646) =?= meet ?10648 (join ?10646 ?10647) [10646, 10647, 10648] by Demod 5841 with 5831 at 2
% 114.89/29.10 Id : 99209, {_}: meet ?181008 (join ?181009 (meet ?181008 (join ?181009 ?181010))) =>= meet ?181008 (join ?181009 ?181010) [181010, 181009, 181008] by Demod 98485 with 50020 at 2
% 114.89/29.10 Id : 156069, {_}: meet ?181008 (join ?181009 (meet ?181008 ?181010)) =>= meet ?181008 (join ?181009 ?181010) [181010, 181009, 181008] by Demod 99209 with 156059 at 2,2
% 114.89/29.10 Id : 110, {_}: meet ?293 (join ?294 (meet ?295 (join ?293 ?296))) =<= join (meet ?293 (join ?294 (meet ?293 ?295))) (meet ?293 (join (meet ?294 ?293) (meet ?295 ?296))) [296, 295, 294, 293] by Super 102 with 6 at 1,2,2,3
% 114.89/29.10 Id : 1438, {_}: meet ?2604 (meet ?2605 (join (meet ?2604 ?2605) ?2606)) =>= meet ?2604 ?2605 [2606, 2605, 2604] by Super 4 with 8 at 2
% 114.89/29.10 Id : 1441, {_}: meet ?2615 (meet ?2616 (join (meet ?2616 ?2615) ?2617)) =>= meet ?2615 ?2616 [2617, 2616, 2615] by Super 1438 with 6 at 1,2,2,2
% 114.89/29.10 Id : 1018, {_}: meet (join (meet ?1788 ?1789) ?1790) (join ?1788 ?1790) =>= join (meet ?1788 ?1789) ?1790 [1790, 1789, 1788] by Super 39 with 81 at 2,2
% 114.89/29.10 Id : 10183, {_}: meet (join ?18319 ?18320) (join (meet ?18319 ?18321) ?18320) =>= join (meet ?18319 ?18321) ?18320 [18321, 18320, 18319] by Demod 1018 with 6 at 2
% 114.89/29.10 Id : 10251, {_}: meet ?18638 (join (meet ?18638 ?18639) (meet ?18640 ?18638)) =>= join (meet ?18638 ?18639) (meet ?18640 ?18638) [18640, 18639, 18638] by Super 10183 with 29 at 1,2
% 114.89/29.10 Id : 63411, {_}: meet ?114618 (join (meet ?114619 ?114618) (meet ?114620 ?114619)) =>= meet ?114618 ?114619 [114620, 114619, 114618] by Super 1441 with 10251 at 2,2
% 114.89/29.10 Id : 94500, {_}: meet ?174009 (join ?174010 (meet ?174011 (join ?174009 ?174010))) =<= join (meet ?174009 (join ?174010 (meet ?174009 ?174011))) (meet ?174009 ?174010) [174011, 174010, 174009] by Super 110 with 63411 at 2,3
% 114.89/29.10 Id : 94844, {_}: meet ?174009 (join ?174010 (meet ?174011 (join ?174009 ?174010))) =<= join (meet ?174009 ?174010) (meet ?174009 (join ?174010 (meet ?174009 ?174011))) [174011, 174010, 174009] by Demod 94500 with 7 at 3
% 114.89/29.10 Id : 2444, {_}: join (meet ?4298 ?4299) (meet ?4298 (meet ?4299 ?4300)) =>= meet ?4298 ?4299 [4300, 4299, 4298] by Super 5 with 8 at 2,2
% 114.89/29.10 Id : 23443, {_}: join (meet ?43488 ?43489) (meet ?43488 (meet ?43490 ?43489)) =>= meet ?43488 ?43489 [43490, 43489, 43488] by Super 2444 with 6 at 2,2,2
% 114.89/29.10 Id : 23445, {_}: join (meet ?43495 (join ?43496 ?43497)) (meet ?43495 ?43496) =>= meet ?43495 (join ?43496 ?43497) [43497, 43496, 43495] by Super 23443 with 4 at 2,2,2
% 114.89/29.10 Id : 23796, {_}: join (meet ?43495 ?43496) (meet ?43495 (join ?43496 ?43497)) =>= meet ?43495 (join ?43496 ?43497) [43497, 43496, 43495] by Demod 23445 with 7 at 2
% 114.89/29.10 Id : 111532, {_}: meet ?201800 (join ?201801 (meet ?201802 (join ?201800 ?201801))) =>= meet ?201800 (join ?201801 (meet ?201800 ?201802)) [201802, 201801, 201800] by Demod 94844 with 23796 at 3
% 114.89/29.10 Id : 111535, {_}: meet ?201811 (join ?201812 (meet ?201813 (join ?201812 ?201811))) =>= meet ?201811 (join ?201812 (meet ?201811 ?201813)) [201813, 201812, 201811] by Super 111532 with 7 at 2,2,2,2
% 114.89/29.10 Id : 156070, {_}: meet ?201811 (join ?201812 (meet ?201813 ?201811)) =?= meet ?201811 (join ?201812 (meet ?201811 ?201813)) [201813, 201812, 201811] by Demod 111535 with 156059 at 2,2
% 114.89/29.10 Id : 156073, {_}: join (meet ?201813 ?201811) (meet ?201811 ?201812) =<= meet ?201811 (join ?201812 (meet ?201811 ?201813)) [201812, 201811, 201813] by Demod 156070 with 154587 at 2
% 114.89/29.10 Id : 156119, {_}: join (meet ?181010 ?181008) (meet ?181008 ?181009) =>= meet ?181008 (join ?181009 ?181010) [181009, 181008, 181010] by Demod 156069 with 156073 at 2
% 114.89/29.10 Id : 156131, {_}: meet ?280057 (join ?280058 (meet ?280059 ?280057)) =>= meet ?280057 (join ?280058 ?280059) [280059, 280058, 280057] by Demod 154587 with 156119 at 3
% 114.89/29.10 Id : 156276, {_}: join ?281693 (meet (join ?281693 ?281694) (meet ?281695 (join ?281693 ?281694))) =>= meet (join ?281693 ?281694) (join ?281693 ?281695) [281695, 281694, 281693] by Super 156065 with 156131 at 3
% 114.89/29.10 Id : 156748, {_}: join ?281693 (meet ?281695 (join ?281693 ?281694)) =<= meet (join ?281693 ?281694) (join ?281693 ?281695) [281694, 281695, 281693] by Demod 156276 with 539 at 2,2
% 114.89/29.10 Id : 156749, {_}: join ?281693 (meet ?281695 (join ?281693 ?281694)) =?= join ?281693 (meet (join ?281693 ?281694) ?281695) [281694, 281695, 281693] by Demod 156748 with 156065 at 3
% 114.89/29.10 Id : 156750, {_}: join ?281693 (meet ?281695 ?281694) =<= join ?281693 (meet (join ?281693 ?281694) ?281695) [281694, 281695, 281693] by Demod 156749 with 156059 at 2
% 114.89/29.10 Id : 157998, {_}: join ?16312 (meet ?16314 ?16313) =<= meet (join ?16312 ?16313) (join ?16312 ?16314) [16313, 16314, 16312] by Demod 156065 with 156750 at 2
% 114.89/29.10 Id : 103, {_}: meet ?259 (join ?260 (meet ?261 (join ?259 ?261))) =<= join (meet ?259 (join ?260 (meet ?259 ?261))) (meet ?259 (join (meet ?259 ?260) ?261)) [261, 260, 259] by Super 102 with 2 at 2,2,2,3
% 114.89/29.10 Id : 12153, {_}: meet ?259 (join ?260 ?261) =<= join (meet ?259 (join ?260 (meet ?259 ?261))) (meet ?259 (join (meet ?259 ?260) ?261)) [261, 260, 259] by Demod 103 with 39 at 2,2,2
% 114.89/29.10 Id : 156083, {_}: meet ?259 (join ?260 ?261) =<= join (join (meet ?261 ?259) (meet ?259 ?260)) (meet ?259 (join (meet ?259 ?260) ?261)) [261, 260, 259] by Demod 12153 with 156073 at 1,3
% 114.89/29.10 Id : 156098, {_}: meet ?259 (join ?260 ?261) =<= join (meet ?261 ?259) (join (meet ?259 ?260) (meet ?259 (join (meet ?259 ?260) ?261))) [261, 260, 259] by Demod 156083 with 9 at 3
% 114.89/29.10 Id : 156099, {_}: meet ?259 (join ?260 ?261) =<= join (meet ?261 ?259) (join (meet ?259 ?260) (meet ?259 ?261)) [261, 260, 259] by Demod 156098 with 156059 at 2,3
% 114.89/29.10 Id : 1112, {_}: join ?1973 ?1974 =<= join ?1973 (join (meet ?1975 ?1973) ?1974) [1975, 1974, 1973] by Super 9 with 29 at 1,2
% 114.89/29.10 Id : 1114, {_}: join (join ?1980 ?1981) ?1982 =<= join (join ?1980 ?1981) (join ?1980 ?1982) [1982, 1981, 1980] by Super 1112 with 4 at 1,2,3
% 114.89/29.10 Id : 1165, {_}: join ?1980 (join ?1981 ?1982) =<= join (join ?1980 ?1981) (join ?1980 ?1982) [1982, 1981, 1980] by Demod 1114 with 9 at 2
% 114.89/29.10 Id : 1166, {_}: join ?1980 (join ?1981 ?1982) =<= join ?1980 (join ?1981 (join ?1980 ?1982)) [1982, 1981, 1980] by Demod 1165 with 9 at 3
% 114.89/29.10 Id : 654, {_}: join (join ?1110 ?1111) ?1112 =<= join ?1111 (join (join ?1110 ?1111) ?1112) [1112, 1111, 1110] by Super 9 with 510 at 1,2
% 114.89/29.10 Id : 685, {_}: join ?1110 (join ?1111 ?1112) =<= join ?1111 (join (join ?1110 ?1111) ?1112) [1112, 1111, 1110] by Demod 654 with 9 at 2
% 114.89/29.10 Id : 686, {_}: join ?1110 (join ?1111 ?1112) =<= join ?1111 (join ?1110 (join ?1111 ?1112)) [1112, 1111, 1110] by Demod 685 with 9 at 2,3
% 114.89/29.10 Id : 3243, {_}: join ?1980 (join ?1981 ?1982) =?= join ?1981 (join ?1980 ?1982) [1982, 1981, 1980] by Demod 1166 with 686 at 3
% 114.89/29.10 Id : 2467, {_}: join (meet ?4392 ?4393) (meet ?4393 ?4392) =>= meet ?4392 ?4393 [4393, 4392] by Super 2444 with 539 at 2,2
% 114.89/29.10 Id : 4948, {_}: join (meet ?9362 ?9363) (join ?9364 (meet ?9363 ?9362)) =>= join ?9364 (meet ?9362 ?9363) [9364, 9363, 9362] by Super 3243 with 2467 at 2,3
% 114.89/29.10 Id : 156100, {_}: meet ?259 (join ?260 ?261) =<= join (meet ?259 ?260) (meet ?261 ?259) [261, 260, 259] by Demod 156099 with 4948 at 3
% 114.89/29.10 Id : 158020, {_}: meet ?284546 (join ?284547 (join (meet ?284546 ?284547) ?284548)) =>= join (meet ?284546 ?284547) (meet ?284546 ?284548) [284548, 284547, 284546] by Super 156100 with 156750 at 3
% 114.89/29.10 Id : 158526, {_}: meet ?284546 (join ?284547 ?284548) =<= join (meet ?284546 ?284547) (meet ?284546 ?284548) [284548, 284547, 284546] by Demod 158020 with 431 at 2,2
% 114.89/29.10 Id : 1967, {_}: meet ?3528 (meet ?3529 ?3530) =<= meet ?3529 (meet ?3528 (meet ?3529 ?3530)) [3530, 3529, 3528] by Demod 739 with 8 at 2,3
% 114.89/29.10 Id : 1979, {_}: meet ?3581 (meet ?3582 (meet ?3583 ?3584)) =<= meet ?3582 (meet ?3581 (meet ?3584 (meet ?3582 ?3583))) [3584, 3583, 3582, 3581] by Super 1967 with 50 at 2,2,3
% 114.89/29.10 Id : 2981, {_}: join ?5160 ?5161 =<= join ?5160 (join ?5161 (meet ?5160 ?5162)) [5162, 5161, 5160] by Super 1021 with 7 at 2,3
% 114.89/29.10 Id : 3004, {_}: join ?5251 (join ?5252 ?5253) =<= join ?5251 (join ?5252 (join ?5253 (meet ?5251 ?5254))) [5254, 5253, 5252, 5251] by Super 2981 with 9 at 2,3
% 114.89/29.10 Id : 1709, {_}: join ?3052 (join ?3053 ?3054) =<= join ?3053 (join ?3052 (join ?3053 ?3054)) [3054, 3053, 3052] by Demod 685 with 9 at 2,3
% 114.89/29.10 Id : 1712, {_}: join ?3063 (join ?3064 ?3065) =<= join ?3064 (join ?3063 (join ?3065 ?3064)) [3065, 3064, 3063] by Super 1709 with 7 at 2,2,3
% 114.89/29.10 Id : 663, {_}: join ?1145 (join ?1146 ?1145) =>= join ?1146 ?1145 [1146, 1145] by Demod 497 with 7 at 2
% 114.89/29.10 Id : 667, {_}: join ?1156 (join ?1157 (join ?1158 ?1156)) =>= join (join ?1157 ?1158) ?1156 [1158, 1157, 1156] by Super 663 with 9 at 2,2
% 114.89/29.10 Id : 694, {_}: join ?1156 (join ?1157 (join ?1158 ?1156)) =>= join ?1157 (join ?1158 ?1156) [1158, 1157, 1156] by Demod 667 with 9 at 3
% 114.89/29.10 Id : 4231, {_}: join ?3063 (join ?3064 ?3065) =?= join ?3063 (join ?3065 ?3064) [3065, 3064, 3063] by Demod 1712 with 694 at 3
% 114.89/29.10 Id : 4276, {_}: meet (join ?8037 ?8038) (join ?8039 (join ?8038 ?8037)) =>= join ?8037 ?8038 [8039, 8038, 8037] by Super 39 with 4231 at 2,2
% 114.89/29.10 Id : 160630, {_}: meet a (join b (meet c d)) =?= meet a (join b (meet c d)) [] by Demod 160629 with 6 at 2,2,3
% 114.89/29.10 Id : 160629, {_}: meet a (join b (meet c d)) =?= meet a (join b (meet d c)) [] by Demod 160628 with 157998 at 2,3
% 114.89/29.10 Id : 160628, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (join b d)) [] by Demod 160627 with 4276 at 2,2,3
% 114.89/29.10 Id : 160627, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (meet (join b d) (join c (join d b)))) [] by Demod 160626 with 3004 at 2,2,2,3
% 114.89/29.10 Id : 160626, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (meet (join b d) (join c (join d (join b (meet c d)))))) [] by Demod 160625 with 6 at 2,2,3
% 114.89/29.10 Id : 160625, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (meet (join c (join d (join b (meet c d)))) (join b d))) [] by Demod 160624 with 6 at 2,3
% 114.89/29.10 Id : 160624, {_}: meet a (join b (meet c d)) =<= meet a (meet (meet (join c (join d (join b (meet c d)))) (join b d)) (join b c)) [] by Demod 160623 with 50 at 3
% 114.89/29.10 Id : 160623, {_}: meet a (join b (meet c d)) =<= meet (join b c) (meet a (meet (join c (join d (join b (meet c d)))) (join b d))) [] by Demod 160622 with 1979 at 3
% 114.89/29.10 Id : 160622, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (meet (join b d) (meet a (join c (join d (join b (meet c d))))))) [] by Demod 160621 with 158526 at 2,2,2,3
% 114.89/29.10 Id : 160621, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (meet (join b d) (join (meet a c) (meet a (join d (join b (meet c d))))))) [] by Demod 160620 with 158526 at 2,2,2,2,3
% 114.89/29.10 Id : 160620, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (meet (join b d) (join (meet a c) (join (meet a d) (meet a (join b (meet c d))))))) [] by Demod 160619 with 9 at 2,2,2,3
% 114.89/29.10 Id : 160619, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (meet (join b d) (join (join (meet a c) (meet a d)) (meet a (join b (meet c d)))))) [] by Demod 160618 with 7 at 2,2,2,3
% 114.89/29.10 Id : 160618, {_}: meet a (join b (meet c d)) =<= meet a (meet (join b c) (meet (join b d) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d))))) [] by Demod 160617 with 8 at 2,3
% 114.89/29.10 Id : 160617, {_}: meet a (join b (meet c d)) =<= meet a (meet (meet (join b c) (join b d)) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d)))) [] by Demod 160616 with 6 at 2,2,2
% 114.89/29.10 Id : 160616, {_}: meet a (join b (meet d c)) =<= meet a (meet (meet (join b c) (join b d)) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d)))) [] by Demod 160615 with 8 at 3
% 114.89/29.10 Id : 160615, {_}: meet a (join b (meet d c)) =<= meet (meet a (meet (join b c) (join b d))) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d))) [] by Demod 1 with 157998 at 2,2
% 114.89/29.10 Id : 1, {_}: meet a (meet (join b c) (join b d)) =<= meet (meet a (meet (join b c) (join b d))) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d))) [] by prove_this
% 114.89/29.10 % SZS output end CNFRefutation for theBenchmark.p
% 114.89/29.10 1948: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 28.768633 using kbo
%------------------------------------------------------------------------------