TSTP Solution File: LAT009-1 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n019.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 44.22s 11.34s
% Output : CNFRefutation 44.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.11 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.32 % Computer : n019.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Wed Jun 29 22:23:09 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 17932: Facts:
% 0.12/0.33 17932: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
% 0.12/0.33 17932: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
% 0.12/0.33 17932: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
% 0.12/0.33 17932: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
% 0.12/0.33 17932: Id : 6, {_}:
% 0.12/0.33 meet ?12 ?13 =?= meet ?13 ?12
% 0.12/0.33 [13, 12] by commutativity_of_meet ?12 ?13
% 0.12/0.33 17932: Id : 7, {_}:
% 0.12/0.33 join ?15 ?16 =?= join ?16 ?15
% 0.12/0.33 [16, 15] by commutativity_of_join ?15 ?16
% 0.12/0.33 17932: Id : 8, {_}:
% 0.12/0.33 meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
% 0.12/0.33 [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
% 0.12/0.33 17932: Id : 9, {_}:
% 0.12/0.33 join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
% 0.12/0.33 [24, 23, 22] by associativity_of_join ?22 ?23 ?24
% 0.12/0.33 17932: Id : 10, {_}:
% 0.12/0.33 join (meet (join (meet ?26 ?27) ?28) ?27) (meet ?28 ?26)
% 0.12/0.33 =>=
% 0.12/0.33 meet (join (meet (join ?26 ?27) ?28) ?27) (join ?28 ?26)
% 0.12/0.33 [28, 27, 26] by distributivity_dual ?26 ?27 ?28
% 0.12/0.33 17932: Goal:
% 0.12/0.33 17932: Id : 1, {_}:
% 0.12/0.33 join a (meet b c) =<= meet (join a b) (join a c)
% 0.12/0.33 [] by prove_distributivity
% 44.22/11.34 Statistics :
% 44.22/11.34 Max weight : 31
% 44.22/11.34 Found proof, 11.016954s
% 44.22/11.34 % SZS status Unsatisfiable for theBenchmark.p
% 44.22/11.34 % SZS output start CNFRefutation for theBenchmark.p
% 44.22/11.34 Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
% 44.22/11.34 Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
% 44.22/11.34 Id : 73, {_}: join (join ?185 ?186) ?187 =>= join ?185 (join ?186 ?187) [187, 186, 185] by associativity_of_join ?185 ?186 ?187
% 44.22/11.34 Id : 10, {_}: join (meet (join (meet ?26 ?27) ?28) ?27) (meet ?28 ?26) =>= meet (join (meet (join ?26 ?27) ?28) ?27) (join ?28 ?26) [28, 27, 26] by distributivity_dual ?26 ?27 ?28
% 44.22/11.34 Id : 7, {_}: join ?15 ?16 =?= join ?16 ?15 [16, 15] by commutativity_of_join ?15 ?16
% 44.22/11.34 Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
% 44.22/11.34 Id : 9, {_}: join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) [24, 23, 22] by associativity_of_join ?22 ?23 ?24
% 44.22/11.34 Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
% 44.22/11.34 Id : 8, {_}: meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
% 44.22/11.34 Id : 6, {_}: meet ?12 ?13 =?= meet ?13 ?12 [13, 12] by commutativity_of_meet ?12 ?13
% 44.22/11.34 Id : 52, {_}: meet (meet ?123 ?124) ?125 =>= meet ?123 (meet ?124 ?125) [125, 124, 123] by associativity_of_meet ?123 ?124 ?125
% 44.22/11.34 Id : 55, {_}: meet (meet ?134 ?135) ?136 =>= meet ?135 (meet ?134 ?136) [136, 135, 134] by Super 52 with 6 at 1,2
% 44.22/11.34 Id : 63, {_}: meet ?134 (meet ?135 ?136) =?= meet ?135 (meet ?134 ?136) [136, 135, 134] by Demod 55 with 8 at 2
% 44.22/11.34 Id : 4738, {_}: meet (join ?8758 ?8759) (join ?8758 (join ?8759 ?8760)) =>= join ?8758 ?8759 [8760, 8759, 8758] by Super 4 with 9 at 2,2
% 44.22/11.34 Id : 27, {_}: join ?56 (meet ?57 ?56) =>= ?56 [57, 56] by Super 5 with 6 at 2,2
% 44.22/11.34 Id : 37, {_}: meet ?80 (join ?81 ?80) =>= ?80 [81, 80] by Super 4 with 7 at 2,2
% 44.22/11.34 Id : 182, {_}: join (join ?390 ?391) ?391 =>= join ?390 ?391 [391, 390] by Super 27 with 37 at 2,2
% 44.22/11.34 Id : 194, {_}: join ?391 (join ?390 ?391) =>= join ?390 ?391 [390, 391] by Demod 182 with 7 at 2
% 44.22/11.34 Id : 4770, {_}: meet (join ?8890 ?8891) (join ?8891 ?8890) =>= join ?8890 ?8891 [8891, 8890] by Super 4738 with 194 at 2,2
% 44.22/11.34 Id : 5002, {_}: meet (join ?9169 ?9170) (meet ?9171 (join ?9170 ?9169)) =>= meet ?9171 (join ?9169 ?9170) [9171, 9170, 9169] by Super 63 with 4770 at 2,3
% 44.22/11.34 Id : 47, {_}: meet ?104 (meet ?105 ?106) =?= meet ?105 (meet ?106 ?104) [106, 105, 104] by Super 6 with 8 at 3
% 44.22/11.34 Id : 4995, {_}: meet (join ?9142 ?9143) (meet ?9144 (join ?9143 ?9142)) =>= meet ?9144 (join ?9143 ?9142) [9144, 9143, 9142] by Super 47 with 4770 at 2,3
% 44.22/11.34 Id : 49104, {_}: meet ?9171 (join ?9170 ?9169) =?= meet ?9171 (join ?9169 ?9170) [9169, 9170, 9171] by Demod 5002 with 4995 at 2
% 44.22/11.34 Id : 397, {_}: join ?787 (join ?788 ?787) =>= join ?788 ?787 [788, 787] by Demod 182 with 7 at 2
% 44.22/11.34 Id : 401, {_}: join ?798 (join ?799 (join ?800 ?798)) =>= join (join ?799 ?800) ?798 [800, 799, 798] by Super 397 with 9 at 2,2
% 44.22/11.34 Id : 422, {_}: join ?798 (join ?799 (join ?800 ?798)) =>= join ?799 (join ?800 ?798) [800, 799, 798] by Demod 401 with 9 at 3
% 44.22/11.34 Id : 1179, {_}: join (meet ?2175 ?2176) (meet ?2175 (meet ?2176 ?2177)) =>= meet ?2175 ?2176 [2177, 2176, 2175] by Super 5 with 8 at 2,2
% 44.22/11.34 Id : 183, {_}: meet ?393 (join ?394 ?393) =>= ?393 [394, 393] by Super 4 with 7 at 2,2
% 44.22/11.34 Id : 188, {_}: meet (meet ?408 ?409) ?409 =>= meet ?408 ?409 [409, 408] by Super 183 with 27 at 2,2
% 44.22/11.34 Id : 210, {_}: meet ?409 (meet ?408 ?409) =>= meet ?408 ?409 [408, 409] by Demod 188 with 6 at 2
% 44.22/11.34 Id : 1199, {_}: join (meet ?2253 ?2254) (meet ?2254 ?2253) =>= meet ?2253 ?2254 [2254, 2253] by Super 1179 with 210 at 2,2
% 44.22/11.34 Id : 3574, {_}: join (meet ?6720 ?6721) (join ?6722 (meet ?6721 ?6720)) =?= join ?6722 (join (meet ?6721 ?6720) (meet ?6720 ?6721)) [6722, 6721, 6720] by Super 422 with 1199 at 2,2,2
% 44.22/11.34 Id : 3632, {_}: join (meet ?6720 ?6721) (join ?6722 (meet ?6721 ?6720)) =>= join ?6722 (meet ?6721 ?6720) [6722, 6721, 6720] by Demod 3574 with 1199 at 2,3
% 44.22/11.34 Id : 804, {_}: join ?1451 ?1452 =<= join ?1451 (join (meet ?1453 ?1451) ?1452) [1453, 1452, 1451] by Super 9 with 27 at 1,2
% 44.22/11.34 Id : 806, {_}: join (join ?1458 ?1459) ?1460 =<= join (join ?1458 ?1459) (join ?1458 ?1460) [1460, 1459, 1458] by Super 804 with 4 at 1,2,3
% 44.22/11.34 Id : 855, {_}: join ?1458 (join ?1459 ?1460) =<= join (join ?1458 ?1459) (join ?1458 ?1460) [1460, 1459, 1458] by Demod 806 with 9 at 2
% 44.22/11.34 Id : 856, {_}: join ?1458 (join ?1459 ?1460) =<= join ?1458 (join ?1459 (join ?1458 ?1460)) [1460, 1459, 1458] by Demod 855 with 9 at 3
% 44.22/11.34 Id : 391, {_}: join (join ?768 ?769) ?770 =<= join ?769 (join (join ?768 ?769) ?770) [770, 769, 768] by Super 9 with 194 at 1,2
% 44.22/11.34 Id : 413, {_}: join ?768 (join ?769 ?770) =<= join ?769 (join (join ?768 ?769) ?770) [770, 769, 768] by Demod 391 with 9 at 2
% 44.22/11.34 Id : 414, {_}: join ?768 (join ?769 ?770) =<= join ?769 (join ?768 (join ?769 ?770)) [770, 769, 768] by Demod 413 with 9 at 2,3
% 44.22/11.35 Id : 2822, {_}: join ?1458 (join ?1459 ?1460) =?= join ?1459 (join ?1458 ?1460) [1460, 1459, 1458] by Demod 856 with 414 at 3
% 44.22/11.35 Id : 3553, {_}: join (meet ?6649 ?6650) (join ?6651 (meet ?6650 ?6649)) =>= join ?6651 (meet ?6649 ?6650) [6651, 6650, 6649] by Super 2822 with 1199 at 2,3
% 44.22/11.35 Id : 37898, {_}: join ?6722 (meet ?6720 ?6721) =?= join ?6722 (meet ?6721 ?6720) [6721, 6720, 6722] by Demod 3632 with 3553 at 2
% 44.22/11.35 Id : 89, {_}: join (meet ?28 ?26) (meet (join (meet ?26 ?27) ?28) ?27) =>= meet (join (meet (join ?26 ?27) ?28) ?27) (join ?28 ?26) [27, 26, 28] by Demod 10 with 7 at 2
% 44.22/11.35 Id : 90, {_}: join (meet ?28 ?26) (meet (join (meet ?26 ?27) ?28) ?27) =>= meet (join ?28 ?26) (join (meet (join ?26 ?27) ?28) ?27) [27, 26, 28] by Demod 89 with 6 at 3
% 44.22/11.35 Id : 91, {_}: join (meet ?28 ?26) (meet ?27 (join (meet ?26 ?27) ?28)) =>= meet (join ?28 ?26) (join (meet (join ?26 ?27) ?28) ?27) [27, 26, 28] by Demod 90 with 6 at 2,2
% 44.22/11.35 Id : 97, {_}: join (meet ?244 ?245) (meet ?246 (join (meet ?245 ?246) ?244)) =>= meet (join ?244 ?245) (join ?246 (meet (join ?245 ?246) ?244)) [246, 245, 244] by Demod 91 with 7 at 2,3
% 44.22/11.35 Id : 105, {_}: join (meet ?275 ?276) (meet ?277 (join ?275 (meet ?276 ?277))) =>= meet (join ?275 ?276) (join ?277 (meet (join ?276 ?277) ?275)) [277, 276, 275] by Super 97 with 7 at 2,2,2
% 44.22/11.35 Id : 92, {_}: join (meet ?28 ?26) (meet ?27 (join (meet ?26 ?27) ?28)) =>= meet (join ?28 ?26) (join ?27 (meet (join ?26 ?27) ?28)) [27, 26, 28] by Demod 91 with 7 at 2,3
% 44.22/11.35 Id : 54, {_}: meet ?130 ?131 =<= meet ?130 (meet (join ?130 ?132) ?131) [132, 131, 130] by Super 52 with 4 at 1,2
% 44.22/11.35 Id : 519, {_}: join (meet (join ?966 ?967) ?968) (meet ?966 ?968) =>= meet (join ?966 ?967) ?968 [968, 967, 966] by Super 27 with 54 at 2,2
% 44.22/11.35 Id : 557, {_}: join (meet ?966 ?968) (meet (join ?966 ?967) ?968) =>= meet (join ?966 ?967) ?968 [967, 968, 966] by Demod 519 with 7 at 2
% 44.22/11.35 Id : 7508, {_}: join (meet (meet (join ?13120 ?13121) ?13122) ?13120) (meet ?13122 (meet (join ?13120 ?13121) ?13122)) =<= meet (join (meet (join ?13120 ?13121) ?13122) ?13120) (join ?13122 (meet (join ?13120 ?13122) (meet (join ?13120 ?13121) ?13122))) [13122, 13121, 13120] by Super 92 with 557 at 2,2,2
% 44.22/11.35 Id : 7681, {_}: join (meet ?13120 (meet (join ?13120 ?13121) ?13122)) (meet ?13122 (meet (join ?13120 ?13121) ?13122)) =<= meet (join (meet (join ?13120 ?13121) ?13122) ?13120) (join ?13122 (meet (join ?13120 ?13122) (meet (join ?13120 ?13121) ?13122))) [13122, 13121, 13120] by Demod 7508 with 6 at 1,2
% 44.22/11.35 Id : 7682, {_}: join (meet ?13120 (meet (join ?13120 ?13121) ?13122)) (meet (join ?13120 ?13121) ?13122) =<= meet (join (meet (join ?13120 ?13121) ?13122) ?13120) (join ?13122 (meet (join ?13120 ?13122) (meet (join ?13120 ?13121) ?13122))) [13122, 13121, 13120] by Demod 7681 with 210 at 2,2
% 44.22/11.35 Id : 7683, {_}: join (meet ?13120 (meet (join ?13120 ?13121) ?13122)) (meet (join ?13120 ?13121) ?13122) =<= meet (join ?13120 (meet (join ?13120 ?13121) ?13122)) (join ?13122 (meet (join ?13120 ?13122) (meet (join ?13120 ?13121) ?13122))) [13122, 13121, 13120] by Demod 7682 with 7 at 1,3
% 44.22/11.35 Id : 155, {_}: join ?338 (meet ?339 ?338) =>= ?338 [339, 338] by Super 5 with 6 at 2,2
% 44.22/11.35 Id : 159, {_}: join ?349 (meet ?350 (meet ?351 ?349)) =>= ?349 [351, 350, 349] by Super 155 with 8 at 2,2
% 44.22/11.35 Id : 7684, {_}: join (meet ?13120 (meet (join ?13120 ?13121) ?13122)) (meet (join ?13120 ?13121) ?13122) =>= meet (join ?13120 (meet (join ?13120 ?13121) ?13122)) ?13122 [13122, 13121, 13120] by Demod 7683 with 159 at 2,3
% 44.22/11.35 Id : 7685, {_}: join (meet (join ?13120 ?13121) ?13122) (meet ?13120 (meet (join ?13120 ?13121) ?13122)) =>= meet (join ?13120 (meet (join ?13120 ?13121) ?13122)) ?13122 [13122, 13121, 13120] by Demod 7684 with 7 at 2
% 44.22/11.35 Id : 7686, {_}: join (meet (join ?13120 ?13121) ?13122) (meet ?13120 (meet (join ?13120 ?13121) ?13122)) =>= meet ?13122 (join ?13120 (meet (join ?13120 ?13121) ?13122)) [13122, 13121, 13120] by Demod 7685 with 6 at 3
% 44.22/11.35 Id : 7687, {_}: meet (join ?13120 ?13121) ?13122 =<= meet ?13122 (join ?13120 (meet (join ?13120 ?13121) ?13122)) [13122, 13121, 13120] by Demod 7686 with 27 at 2
% 44.22/11.35 Id : 58799, {_}: join (meet ?104353 (join ?104353 ?104354)) (meet (join ?104353 ?104354) ?104355) =<= meet (join ?104353 (join ?104353 ?104354)) (join ?104355 (meet (join (join ?104353 ?104354) ?104355) ?104353)) [104355, 104354, 104353] by Super 105 with 7687 at 2,2
% 44.22/11.35 Id : 59291, {_}: join ?104353 (meet (join ?104353 ?104354) ?104355) =<= meet (join ?104353 (join ?104353 ?104354)) (join ?104355 (meet (join (join ?104353 ?104354) ?104355) ?104353)) [104355, 104354, 104353] by Demod 58799 with 4 at 1,2
% 44.22/11.35 Id : 74, {_}: join ?189 ?190 =<= join ?189 (join ?189 ?190) [190, 189] by Super 73 with 3 at 1,2
% 44.22/11.35 Id : 59292, {_}: join ?104353 (meet (join ?104353 ?104354) ?104355) =<= meet (join ?104353 ?104354) (join ?104355 (meet (join (join ?104353 ?104354) ?104355) ?104353)) [104355, 104354, 104353] by Demod 59291 with 74 at 1,3
% 44.22/11.35 Id : 59293, {_}: join ?104353 (meet (join ?104353 ?104354) ?104355) =<= meet (join ?104353 ?104354) (join ?104355 (meet ?104353 (join (join ?104353 ?104354) ?104355))) [104355, 104354, 104353] by Demod 59292 with 37898 at 2,3
% 44.22/11.35 Id : 59294, {_}: join ?104353 (meet (join ?104353 ?104354) ?104355) =<= meet (join ?104353 ?104354) (join ?104355 (meet ?104353 (join ?104353 (join ?104354 ?104355)))) [104355, 104354, 104353] by Demod 59293 with 9 at 2,2,2,3
% 44.22/11.35 Id : 59295, {_}: join ?104353 (meet (join ?104353 ?104354) ?104355) =>= meet (join ?104353 ?104354) (join ?104355 ?104353) [104355, 104354, 104353] by Demod 59294 with 4 at 2,2,3
% 44.22/11.35 Id : 59847, {_}: join ?106258 (meet ?106259 (join ?106258 ?106260)) =>= meet (join ?106258 ?106260) (join ?106259 ?106258) [106260, 106259, 106258] by Super 37898 with 59295 at 3
% 44.22/11.35 Id : 108, {_}: join (meet ?287 ?288) (meet ?289 (meet ?290 (join (meet ?288 (meet ?289 ?290)) ?287))) =>= meet (join ?287 ?288) (join (meet ?289 ?290) (meet (join ?288 (meet ?289 ?290)) ?287)) [290, 289, 288, 287] by Super 97 with 8 at 2,2
% 44.22/11.35 Id : 59861, {_}: join ?106329 (meet (join ?106329 ?106330) ?106331) =>= meet (join ?106329 ?106330) (join ?106331 ?106329) [106331, 106330, 106329] by Demod 59294 with 4 at 2,2,3
% 44.22/11.35 Id : 59864, {_}: join ?106340 (meet (join ?106341 ?106340) ?106342) =>= meet (join ?106340 ?106341) (join ?106342 ?106340) [106342, 106341, 106340] by Super 59861 with 7 at 1,2,2
% 44.22/11.35 Id : 61398, {_}: join (meet ?287 ?288) (meet ?289 (meet ?290 (join (meet ?288 (meet ?289 ?290)) ?287))) =>= meet (join ?287 ?288) (meet (join (meet ?289 ?290) ?288) (join ?287 (meet ?289 ?290))) [290, 289, 288, 287] by Demod 108 with 59864 at 2,3
% 44.22/11.35 Id : 61527, {_}: join ?108783 (meet (join ?108784 ?108783) ?108785) =>= meet (join ?108783 ?108784) (join ?108785 ?108783) [108785, 108784, 108783] by Super 59861 with 7 at 1,2,2
% 44.22/11.35 Id : 61532, {_}: join (meet ?108803 ?108804) (meet ?108804 ?108805) =<= meet (join (meet ?108803 ?108804) ?108804) (join ?108805 (meet ?108803 ?108804)) [108805, 108804, 108803] by Super 61527 with 27 at 1,2,2
% 44.22/11.35 Id : 7532, {_}: join (meet ?13230 ?13231) (meet (join ?13230 ?13232) ?13231) =>= meet (join ?13230 ?13232) ?13231 [13232, 13231, 13230] by Demod 519 with 7 at 2
% 44.22/11.35 Id : 7535, {_}: join (meet ?13241 ?13242) (meet (join ?13243 ?13241) ?13242) =>= meet (join ?13241 ?13243) ?13242 [13243, 13242, 13241] by Super 7532 with 7 at 1,2,2
% 44.22/11.35 Id : 180, {_}: meet ?382 ?383 =<= meet ?382 (meet (join ?384 ?382) ?383) [384, 383, 382] by Super 8 with 37 at 1,2
% 44.22/11.35 Id : 952, {_}: join (meet (join ?1740 ?1741) ?1742) (meet ?1741 ?1742) =>= meet (join ?1740 ?1741) ?1742 [1742, 1741, 1740] by Super 27 with 180 at 2,2
% 44.22/11.35 Id : 1017, {_}: join (meet ?1741 ?1742) (meet (join ?1740 ?1741) ?1742) =>= meet (join ?1740 ?1741) ?1742 [1740, 1742, 1741] by Demod 952 with 7 at 2
% 44.22/11.35 Id : 55691, {_}: meet (join ?13243 ?13241) ?13242 =?= meet (join ?13241 ?13243) ?13242 [13242, 13241, 13243] by Demod 7535 with 1017 at 2
% 44.22/11.35 Id : 61991, {_}: join (meet ?108803 ?108804) (meet ?108804 ?108805) =<= meet (join ?108804 (meet ?108803 ?108804)) (join ?108805 (meet ?108803 ?108804)) [108805, 108804, 108803] by Demod 61532 with 55691 at 3
% 44.22/11.35 Id : 61992, {_}: join (meet ?108803 ?108804) (meet ?108804 ?108805) =>= meet ?108804 (join ?108805 (meet ?108803 ?108804)) [108805, 108804, 108803] by Demod 61991 with 27 at 1,3
% 44.22/11.35 Id : 64280, {_}: meet ?112078 (join (meet ?112079 (join (meet ?112078 (meet ?112078 ?112079)) ?112080)) (meet ?112080 ?112078)) =<= meet (join ?112080 ?112078) (meet (join (meet ?112078 ?112079) ?112078) (join ?112080 (meet ?112078 ?112079))) [112080, 112079, 112078] by Super 61398 with 61992 at 2
% 44.22/11.35 Id : 64835, {_}: meet ?112078 (join (meet ?112080 ?112078) (meet ?112079 (join (meet ?112078 (meet ?112078 ?112079)) ?112080))) =<= meet (join ?112080 ?112078) (meet (join (meet ?112078 ?112079) ?112078) (join ?112080 (meet ?112078 ?112079))) [112079, 112080, 112078] by Demod 64280 with 49104 at 2
% 44.22/11.35 Id : 64836, {_}: meet ?112078 (join (meet ?112080 ?112078) (meet ?112079 (join (meet ?112078 (meet ?112078 ?112079)) ?112080))) =<= meet (join ?112080 ?112078) (meet (join ?112078 (meet ?112078 ?112079)) (join ?112080 (meet ?112078 ?112079))) [112079, 112080, 112078] by Demod 64835 with 55691 at 2,3
% 44.22/11.35 Id : 53, {_}: meet ?127 ?128 =<= meet ?127 (meet ?127 ?128) [128, 127] by Super 52 with 2 at 1,2
% 44.22/11.35 Id : 64837, {_}: meet ?112078 (join (meet ?112080 ?112078) (meet ?112079 (join (meet ?112078 ?112079) ?112080))) =<= meet (join ?112080 ?112078) (meet (join ?112078 (meet ?112078 ?112079)) (join ?112080 (meet ?112078 ?112079))) [112079, 112080, 112078] by Demod 64836 with 53 at 1,2,2,2,2
% 44.22/11.35 Id : 64838, {_}: meet ?112078 (join (meet ?112080 ?112078) (meet ?112079 (join (meet ?112078 ?112079) ?112080))) =>= meet (join ?112080 ?112078) (meet ?112078 (join ?112080 (meet ?112078 ?112079))) [112079, 112080, 112078] by Demod 64837 with 5 at 1,2,3
% 44.22/11.35 Id : 61395, {_}: join (meet ?28 ?26) (meet ?27 (join (meet ?26 ?27) ?28)) =>= meet (join ?28 ?26) (meet (join ?27 ?26) (join ?28 ?27)) [27, 26, 28] by Demod 92 with 59864 at 2,3
% 44.22/11.35 Id : 64839, {_}: meet ?112078 (meet (join ?112080 ?112078) (meet (join ?112079 ?112078) (join ?112080 ?112079))) =>= meet (join ?112080 ?112078) (meet ?112078 (join ?112080 (meet ?112078 ?112079))) [112079, 112080, 112078] by Demod 64838 with 61395 at 2,2
% 44.22/11.35 Id : 64840, {_}: meet ?112078 (meet (join ?112080 ?112078) (meet (join ?112079 ?112078) (join ?112080 ?112079))) =>= meet ?112078 (meet (join ?112080 (meet ?112078 ?112079)) (join ?112080 ?112078)) [112079, 112080, 112078] by Demod 64839 with 47 at 3
% 44.22/11.35 Id : 64841, {_}: meet ?112078 (meet (join ?112079 ?112078) (join ?112080 ?112079)) =?= meet ?112078 (meet (join ?112080 (meet ?112078 ?112079)) (join ?112080 ?112078)) [112080, 112079, 112078] by Demod 64840 with 180 at 2
% 44.22/11.35 Id : 968, {_}: meet ?1809 ?1810 =<= meet ?1809 (meet (join ?1811 ?1809) ?1810) [1811, 1810, 1809] by Super 8 with 37 at 1,2
% 44.22/11.35 Id : 970, {_}: meet (meet ?1816 ?1817) ?1818 =<= meet (meet ?1816 ?1817) (meet ?1816 ?1818) [1818, 1817, 1816] by Super 968 with 5 at 1,2,3
% 44.22/11.35 Id : 1036, {_}: meet ?1816 (meet ?1817 ?1818) =<= meet (meet ?1816 ?1817) (meet ?1816 ?1818) [1818, 1817, 1816] by Demod 970 with 8 at 2
% 44.22/11.35 Id : 1037, {_}: meet ?1816 (meet ?1817 ?1818) =<= meet ?1816 (meet ?1817 (meet ?1816 ?1818)) [1818, 1817, 1816] by Demod 1036 with 8 at 3
% 44.22/11.35 Id : 274, {_}: meet ?564 (meet ?565 ?566) =<= meet ?564 (meet ?566 (meet ?564 ?565)) [566, 565, 564] by Super 53 with 47 at 2,3
% 44.22/11.35 Id : 3223, {_}: meet ?1816 (meet ?1817 ?1818) =?= meet ?1816 (meet ?1818 ?1817) [1818, 1817, 1816] by Demod 1037 with 274 at 3
% 44.22/11.35 Id : 64842, {_}: meet ?112078 (meet (join ?112079 ?112078) (join ?112080 ?112079)) =?= meet ?112078 (meet (join ?112080 ?112078) (join ?112080 (meet ?112078 ?112079))) [112080, 112079, 112078] by Demod 64841 with 3223 at 3
% 44.22/11.35 Id : 64843, {_}: meet ?112078 (join ?112080 ?112079) =<= meet ?112078 (meet (join ?112080 ?112078) (join ?112080 (meet ?112078 ?112079))) [112079, 112080, 112078] by Demod 64842 with 180 at 2
% 44.22/11.35 Id : 64844, {_}: meet ?112078 (join ?112080 ?112079) =<= meet ?112078 (join ?112080 (meet ?112078 ?112079)) [112079, 112080, 112078] by Demod 64843 with 180 at 3
% 44.22/11.35 Id : 71917, {_}: join ?123979 (meet ?123980 (join ?123979 ?123981)) =<= meet (join ?123979 (meet ?123980 ?123981)) (join ?123980 ?123979) [123981, 123980, 123979] by Super 59847 with 64844 at 2,2
% 44.22/11.35 Id : 72084, {_}: meet (join ?123979 ?123981) (join ?123980 ?123979) =<= meet (join ?123979 (meet ?123980 ?123981)) (join ?123980 ?123979) [123980, 123981, 123979] by Demod 71917 with 59847 at 2
% 44.22/11.35 Id : 72085, {_}: meet (join ?123979 ?123981) (join ?123980 ?123979) =<= meet (join ?123980 ?123979) (join ?123979 (meet ?123980 ?123981)) [123980, 123981, 123979] by Demod 72084 with 6 at 3
% 44.22/11.35 Id : 721, {_}: join ?1299 ?1300 =<= join ?1299 (join (meet ?1299 ?1301) ?1300) [1301, 1300, 1299] by Super 73 with 5 at 1,2
% 44.22/11.35 Id : 736, {_}: join ?1358 ?1359 =<= join ?1358 (join ?1359 (meet ?1358 ?1360)) [1360, 1359, 1358] by Super 721 with 7 at 2,3
% 44.22/11.35 Id : 2565, {_}: meet (join ?4626 (meet ?4627 ?4628)) (join ?4627 ?4626) =>= join ?4626 (meet ?4627 ?4628) [4628, 4627, 4626] by Super 37 with 736 at 2,2
% 44.22/11.35 Id : 2647, {_}: meet (join ?4627 ?4626) (join ?4626 (meet ?4627 ?4628)) =>= join ?4626 (meet ?4627 ?4628) [4628, 4626, 4627] by Demod 2565 with 6 at 2
% 44.22/11.35 Id : 72086, {_}: meet (join ?123979 ?123981) (join ?123980 ?123979) =>= join ?123979 (meet ?123980 ?123981) [123980, 123981, 123979] by Demod 72085 with 2647 at 3
% 44.22/11.35 Id : 73276, {_}: meet (join ?126330 ?126331) (join ?126330 ?126332) =>= join ?126330 (meet ?126332 ?126331) [126332, 126331, 126330] by Super 49104 with 72086 at 3
% 44.22/11.35 Id : 77946, {_}: join a (meet b c) =?= join a (meet b c) [] by Demod 77945 with 6 at 2,3
% 44.22/11.35 Id : 77945, {_}: join a (meet b c) =?= join a (meet c b) [] by Demod 1 with 73276 at 3
% 44.22/11.35 Id : 1, {_}: join a (meet b c) =<= meet (join a b) (join a c) [] by prove_distributivity
% 44.22/11.35 % SZS output end CNFRefutation for theBenchmark.p
% 44.22/11.35 17933: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 11.02077 using kbo
%------------------------------------------------------------------------------