TSTP Solution File: REL004-2 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : REL004-2 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 19:41:50 EDT 2022
% Result : Unsatisfiable 4.38s 1.45s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL004-2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 08:53:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 7282: Facts:
% 0.13/0.34 7282: Id : 2, {_}:
% 0.13/0.34 join ?2 ?3 =?= join ?3 ?2
% 0.13/0.34 [3, 2] by maddux1_join_commutativity_1 ?2 ?3
% 0.13/0.34 7282: Id : 3, {_}:
% 0.13/0.34 join ?5 (join ?6 ?7) =?= join (join ?5 ?6) ?7
% 0.13/0.34 [7, 6, 5] by maddux2_join_associativity_2 ?5 ?6 ?7
% 0.13/0.34 7282: Id : 4, {_}:
% 0.13/0.34 ?9
% 0.13/0.34 =<=
% 0.13/0.34 join (complement (join (complement ?9) (complement ?10)))
% 0.13/0.34 (complement (join (complement ?9) ?10))
% 0.13/0.34 [10, 9] by maddux3_a_kind_of_de_Morgan_3 ?9 ?10
% 0.13/0.34 7282: Id : 5, {_}:
% 0.13/0.34 meet ?12 ?13 =<= complement (join (complement ?12) (complement ?13))
% 0.13/0.34 [13, 12] by maddux4_definiton_of_meet_4 ?12 ?13
% 0.13/0.34 7282: Id : 6, {_}:
% 0.13/0.34 composition ?15 (composition ?16 ?17)
% 0.13/0.34 =?=
% 0.13/0.34 composition (composition ?15 ?16) ?17
% 0.13/0.34 [17, 16, 15] by composition_associativity_5 ?15 ?16 ?17
% 0.13/0.34 7282: Id : 7, {_}: composition ?19 one =>= ?19 [19] by composition_identity_6 ?19
% 0.13/0.34 7282: Id : 8, {_}:
% 0.13/0.34 composition (join ?21 ?22) ?23
% 0.13/0.34 =<=
% 0.13/0.34 join (composition ?21 ?23) (composition ?22 ?23)
% 0.13/0.34 [23, 22, 21] by composition_distributivity_7 ?21 ?22 ?23
% 0.13/0.34 7282: Id : 9, {_}:
% 0.13/0.34 converse (converse ?25) =>= ?25
% 0.13/0.34 [25] by converse_idempotence_8 ?25
% 0.13/0.34 7282: Id : 10, {_}:
% 0.13/0.34 converse (join ?27 ?28) =<= join (converse ?27) (converse ?28)
% 0.13/0.34 [28, 27] by converse_additivity_9 ?27 ?28
% 0.13/0.34 7282: Id : 11, {_}:
% 0.13/0.34 converse (composition ?30 ?31)
% 0.13/0.34 =<=
% 0.13/0.34 composition (converse ?31) (converse ?30)
% 0.13/0.34 [31, 30] by converse_multiplicativity_10 ?30 ?31
% 0.13/0.34 7282: Id : 12, {_}:
% 0.13/0.34 join (composition (converse ?33) (complement (composition ?33 ?34)))
% 0.13/0.34 (complement ?34)
% 0.13/0.34 =>=
% 0.13/0.34 complement ?34
% 0.13/0.34 [34, 33] by converse_cancellativity_11 ?33 ?34
% 0.13/0.34 7282: Id : 13, {_}: top =<= join ?36 (complement ?36) [36] by def_top_12 ?36
% 0.13/0.34 7282: Id : 14, {_}: zero =<= meet ?38 (complement ?38) [38] by def_zero_13 ?38
% 0.13/0.34 7282: Id : 15, {_}:
% 0.13/0.34 join (meet (composition ?40 ?41) ?42)
% 0.13/0.34 (composition (meet ?40 (composition ?42 (converse ?41)))
% 0.13/0.34 (meet ?41 (composition (converse ?40) ?42)))
% 0.13/0.34 =>=
% 0.13/0.34 composition (meet ?40 (composition ?42 (converse ?41)))
% 0.13/0.34 (meet ?41 (composition (converse ?40) ?42))
% 0.13/0.34 [42, 41, 40] by dedekind_law_14 ?40 ?41 ?42
% 0.13/0.34 7282: Id : 16, {_}:
% 0.13/0.34 join (meet (composition ?44 ?45) ?46)
% 0.13/0.34 (meet (composition ?44 (meet ?45 (composition (converse ?44) ?46)))
% 0.13/0.34 ?46)
% 0.13/0.34 =>=
% 0.13/0.34 meet (composition ?44 (meet ?45 (composition (converse ?44) ?46)))
% 0.13/0.34 ?46
% 0.13/0.34 [46, 45, 44] by modular_law_1_15 ?44 ?45 ?46
% 0.13/0.34 7282: Id : 17, {_}:
% 0.13/0.34 join (meet (composition ?48 ?49) ?50)
% 0.13/0.34 (meet (composition (meet ?48 (composition ?50 (converse ?49))) ?49)
% 0.13/0.34 ?50)
% 0.13/0.34 =>=
% 0.13/0.34 meet (composition (meet ?48 (composition ?50 (converse ?49))) ?49)
% 0.13/0.34 ?50
% 0.13/0.34 [50, 49, 48] by modular_law_2_16 ?48 ?49 ?50
% 0.13/0.34 7282: Goal:
% 0.13/0.34 7282: Id : 1, {_}:
% 0.13/0.34 converse (complement sk1) =<= complement (converse sk1)
% 0.13/0.34 [] by goals_17
% 4.38/1.45 Statistics :
% 4.38/1.45 Max weight : 17
% 4.38/1.45 Found proof, 1.105491s
% 4.38/1.45 % SZS status Unsatisfiable for theBenchmark.p
% 4.38/1.45 % SZS output start CNFRefutation for theBenchmark.p
% 4.38/1.45 Id : 57, {_}: meet ?141 ?142 =<= complement (join (complement ?141) (complement ?142)) [142, 141] by maddux4_definiton_of_meet_4 ?141 ?142
% 4.38/1.45 Id : 10, {_}: converse (join ?27 ?28) =>= join (converse ?27) (converse ?28) [28, 27] by converse_additivity_9 ?27 ?28
% 4.38/1.45 Id : 13, {_}: top =<= join ?36 (complement ?36) [36] by def_top_12 ?36
% 4.38/1.45 Id : 3, {_}: join ?5 (join ?6 ?7) =<= join (join ?5 ?6) ?7 [7, 6, 5] by maddux2_join_associativity_2 ?5 ?6 ?7
% 4.38/1.45 Id : 14, {_}: zero =<= meet ?38 (complement ?38) [38] by def_zero_13 ?38
% 4.38/1.45 Id : 4, {_}: ?9 =<= join (complement (join (complement ?9) (complement ?10))) (complement (join (complement ?9) ?10)) [10, 9] by maddux3_a_kind_of_de_Morgan_3 ?9 ?10
% 4.38/1.45 Id : 119, {_}: converse (composition ?267 ?268) =>= composition (converse ?268) (converse ?267) [268, 267] by converse_multiplicativity_10 ?267 ?268
% 4.38/1.45 Id : 7, {_}: composition ?19 one =>= ?19 [19] by composition_identity_6 ?19
% 4.38/1.45 Id : 2, {_}: join ?2 ?3 =?= join ?3 ?2 [3, 2] by maddux1_join_commutativity_1 ?2 ?3
% 4.38/1.45 Id : 12, {_}: join (composition (converse ?33) (complement (composition ?33 ?34))) (complement ?34) =>= complement ?34 [34, 33] by converse_cancellativity_11 ?33 ?34
% 4.38/1.45 Id : 5, {_}: meet ?12 ?13 =<= complement (join (complement ?12) (complement ?13)) [13, 12] by maddux4_definiton_of_meet_4 ?12 ?13
% 4.38/1.45 Id : 9, {_}: converse (converse ?25) =>= ?25 [25] by converse_idempotence_8 ?25
% 4.38/1.45 Id : 130, {_}: join (complement ?34) (composition (converse ?33) (complement (composition ?33 ?34))) =>= complement ?34 [33, 34] by Demod 12 with 2 at 2
% 4.38/1.45 Id : 278, {_}: converse ?571 =<= composition (converse one) (converse ?571) [571] by Super 119 with 7 at 1,2
% 4.38/1.45 Id : 279, {_}: converse (converse ?573) =>= composition (converse one) ?573 [573] by Super 278 with 9 at 2,3
% 4.38/1.45 Id : 301, {_}: ?573 =<= composition (converse one) ?573 [573] by Demod 279 with 9 at 2
% 4.38/1.45 Id : 395, {_}: one =<= converse one [] by Super 7 with 301 at 2
% 4.38/1.45 Id : 428, {_}: join (complement ?837) (composition one (complement (composition one ?837))) =>= complement ?837 [837] by Super 130 with 395 at 1,2,2
% 4.38/1.45 Id : 426, {_}: ?573 =<= composition one ?573 [573] by Demod 301 with 395 at 1,3
% 4.38/1.45 Id : 450, {_}: join (complement ?837) (complement (composition one ?837)) =>= complement ?837 [837] by Demod 428 with 426 at 2,2
% 4.38/1.45 Id : 451, {_}: join (complement ?837) (complement ?837) =>= complement ?837 [837] by Demod 450 with 426 at 1,2,2
% 4.38/1.45 Id : 471, {_}: meet ?868 ?868 =<= complement (complement ?868) [868] by Super 5 with 451 at 1,3
% 4.38/1.45 Id : 37, {_}: ?9 =<= join (complement (join (complement ?9) ?10)) (complement (join (complement ?9) (complement ?10))) [10, 9] by Demod 4 with 2 at 3
% 4.38/1.45 Id : 53, {_}: ?9 =<= join (complement (join (complement ?9) ?10)) (meet ?9 ?10) [10, 9] by Demod 37 with 5 at 2,3
% 4.38/1.45 Id : 54, {_}: ?9 =<= join (meet ?9 ?10) (complement (join (complement ?9) ?10)) [10, 9] by Demod 53 with 2 at 3
% 4.38/1.45 Id : 166, {_}: ?341 =<= join zero (complement (join (complement ?341) (complement ?341))) [341] by Super 54 with 14 at 1,3
% 4.38/1.45 Id : 170, {_}: ?341 =<= join zero (meet ?341 ?341) [341] by Demod 166 with 5 at 2,3
% 4.38/1.45 Id : 495, {_}: meet ?913 ?913 =<= complement (complement ?913) [913] by Super 5 with 451 at 1,3
% 4.38/1.45 Id : 614, {_}: meet (join (complement ?1243) (complement ?1244)) (join (complement ?1243) (complement ?1244)) =<= complement (meet ?1243 ?1244) [1244, 1243] by Super 495 with 5 at 1,3
% 4.38/1.45 Id : 615, {_}: meet (join (complement ?1246) (complement (complement ?1246))) (join (complement ?1246) (complement (complement ?1246))) =>= complement zero [1246] by Super 614 with 14 at 1,3
% 4.38/1.45 Id : 628, {_}: meet top (join (complement ?1246) (complement (complement ?1246))) =>= complement zero [1246] by Demod 615 with 13 at 1,2
% 4.38/1.45 Id : 629, {_}: meet top top =<= complement zero [] by Demod 628 with 13 at 2,2
% 4.38/1.45 Id : 638, {_}: meet zero zero =<= complement (meet top top) [] by Super 471 with 629 at 1,3
% 4.38/1.45 Id : 496, {_}: meet (join (complement ?915) (complement ?916)) (join (complement ?915) (complement ?916)) =<= complement (meet ?915 ?916) [916, 915] by Super 495 with 5 at 1,3
% 4.38/1.45 Id : 641, {_}: meet zero zero =<= meet (join (complement top) (complement top)) (join (complement top) (complement top)) [] by Demod 638 with 496 at 3
% 4.38/1.45 Id : 642, {_}: meet zero zero =<= meet (complement top) (join (complement top) (complement top)) [] by Demod 641 with 451 at 1,3
% 4.38/1.45 Id : 643, {_}: meet zero zero =<= meet (complement top) (complement top) [] by Demod 642 with 451 at 2,3
% 4.38/1.45 Id : 668, {_}: complement top =>= join zero (meet zero zero) [] by Super 170 with 643 at 2,3
% 4.38/1.45 Id : 681, {_}: complement top =>= zero [] by Demod 668 with 170 at 3
% 4.38/1.45 Id : 692, {_}: join (complement top) zero =>= complement top [] by Super 451 with 681 at 2,2
% 4.38/1.45 Id : 696, {_}: join zero (complement top) =>= complement top [] by Demod 692 with 2 at 2
% 4.38/1.45 Id : 697, {_}: join zero (complement top) =>= zero [] by Demod 696 with 681 at 3
% 4.38/1.45 Id : 698, {_}: join zero zero =>= zero [] by Demod 697 with 681 at 2,2
% 4.38/1.45 Id : 1175, {_}: join zero (join zero ?1806) =>= join zero ?1806 [1806] by Super 3 with 698 at 1,3
% 4.38/1.45 Id : 1186, {_}: join zero ?1830 =<= join zero (meet ?1830 ?1830) [1830] by Super 1175 with 170 at 2,2
% 4.38/1.45 Id : 1207, {_}: join zero ?1830 =>= ?1830 [1830] by Demod 1186 with 170 at 3
% 4.38/1.45 Id : 1215, {_}: ?341 =<= meet ?341 ?341 [341] by Demod 170 with 1207 at 3
% 4.38/1.45 Id : 1219, {_}: ?868 =<= complement (complement ?868) [868] by Demod 471 with 1215 at 2
% 4.38/1.45 Id : 1220, {_}: join (complement ?915) (complement ?916) =<= complement (meet ?915 ?916) [916, 915] by Demod 496 with 1215 at 2
% 4.38/1.45 Id : 1719, {_}: converse top =<= join (converse ?2396) (converse (complement ?2396)) [2396] by Super 10 with 13 at 1,2
% 4.38/1.45 Id : 1725, {_}: converse top =<= join ?2408 (converse (complement (converse ?2408))) [2408] by Super 1719 with 9 at 1,3
% 4.38/1.45 Id : 630, {_}: join (complement zero) (meet top top) =>= complement zero [] by Super 451 with 629 at 2,2
% 4.38/1.45 Id : 647, {_}: join (meet top top) (complement zero) =>= complement zero [] by Demod 630 with 2 at 2
% 4.38/1.45 Id : 648, {_}: join (meet top top) (complement zero) =>= meet top top [] by Demod 647 with 629 at 3
% 4.38/1.45 Id : 649, {_}: join (meet top top) (meet top top) =>= meet top top [] by Demod 648 with 629 at 2,2
% 4.38/1.45 Id : 689, {_}: meet top ?1281 =<= complement (join zero (complement ?1281)) [1281] by Super 5 with 681 at 1,1,3
% 4.38/1.45 Id : 1213, {_}: meet top ?1281 =<= complement (complement ?1281) [1281] by Demod 689 with 1207 at 1,3
% 4.38/1.45 Id : 1222, {_}: meet top ?1281 =>= ?1281 [1281] by Demod 1213 with 1219 at 3
% 4.38/1.45 Id : 1492, {_}: join top (meet top top) =>= meet top top [] by Demod 649 with 1222 at 1,2
% 4.38/1.45 Id : 1493, {_}: join top top =>= meet top top [] by Demod 1492 with 1222 at 2,2
% 4.38/1.45 Id : 1494, {_}: join top top =>= top [] by Demod 1493 with 1222 at 3
% 4.38/1.45 Id : 1498, {_}: converse top =<= join (converse top) (converse top) [] by Super 10 with 1494 at 1,2
% 4.38/1.45 Id : 2405, {_}: join (converse top) (join (converse top) ?2964) =>= join (converse top) ?2964 [2964] by Super 3 with 1498 at 1,3
% 4.38/1.45 Id : 2413, {_}: join (converse top) top =<= join (converse top) (complement (converse top)) [] by Super 2405 with 13 at 2,2
% 4.38/1.45 Id : 2444, {_}: join top (converse top) =<= join (converse top) (complement (converse top)) [] by Demod 2413 with 2 at 2
% 4.38/1.45 Id : 2445, {_}: join top (converse top) =>= top [] by Demod 2444 with 13 at 3
% 4.38/1.45 Id : 2460, {_}: converse top =<= join (converse top) (converse (converse top)) [] by Super 10 with 2445 at 1,2
% 4.38/1.45 Id : 2470, {_}: converse top =<= join (converse top) top [] by Demod 2460 with 9 at 2,3
% 4.38/1.45 Id : 2471, {_}: converse top =<= join top (converse top) [] by Demod 2470 with 2 at 3
% 4.38/1.45 Id : 2472, {_}: converse top =>= top [] by Demod 2471 with 2445 at 3
% 4.38/1.45 Id : 2536, {_}: top =<= join ?2408 (converse (complement (converse ?2408))) [2408] by Demod 1725 with 2472 at 2
% 4.38/1.45 Id : 2547, {_}: ?3056 =<= join (meet ?3056 (converse (complement (converse (complement ?3056))))) (complement top) [3056] by Super 54 with 2536 at 1,2,3
% 4.38/1.45 Id : 2572, {_}: ?3056 =<= join (complement top) (meet ?3056 (converse (complement (converse (complement ?3056))))) [3056] by Demod 2547 with 2 at 3
% 4.38/1.45 Id : 2573, {_}: ?3056 =<= join zero (meet ?3056 (converse (complement (converse (complement ?3056))))) [3056] by Demod 2572 with 681 at 1,3
% 4.38/1.45 Id : 11891, {_}: ?10044 =<= meet ?10044 (converse (complement (converse (complement ?10044)))) [10044] by Demod 2573 with 1207 at 3
% 4.38/1.45 Id : 11894, {_}: complement ?10048 =<= meet (complement ?10048) (converse (complement (converse ?10048))) [10048] by Super 11891 with 1219 at 1,1,1,2,3
% 4.38/1.45 Id : 12426, {_}: join (complement (complement ?10786)) (complement (converse (complement (converse ?10786)))) =>= complement (complement ?10786) [10786] by Super 1220 with 11894 at 1,3
% 4.38/1.45 Id : 12456, {_}: join ?10786 (complement (converse (complement (converse ?10786)))) =>= complement (complement ?10786) [10786] by Demod 12426 with 1219 at 1,2
% 4.38/1.45 Id : 12457, {_}: join ?10786 (complement (converse (complement (converse ?10786)))) =>= ?10786 [10786] by Demod 12456 with 1219 at 3
% 4.38/1.45 Id : 12816, {_}: converse ?11120 =<= join (converse ?11120) (converse (complement (converse (complement (converse ?11120))))) [11120] by Super 10 with 12457 at 1,2
% 4.38/1.45 Id : 10890, {_}: converse (complement ?8758) =<= join (converse (complement ?8758)) (converse (complement ?8758)) [8758] by Super 10 with 451 at 1,2
% 4.38/1.45 Id : 10893, {_}: converse (complement (complement ?8762)) =<= join (converse (complement (complement ?8762))) (converse ?8762) [8762] by Super 10890 with 1219 at 1,2,3
% 4.38/1.45 Id : 10922, {_}: converse ?8762 =<= join (converse (complement (complement ?8762))) (converse ?8762) [8762] by Demod 10893 with 1219 at 1,2
% 4.38/1.45 Id : 10923, {_}: converse ?8762 =<= join (converse ?8762) (converse (complement (complement ?8762))) [8762] by Demod 10922 with 2 at 3
% 4.38/1.45 Id : 10971, {_}: converse ?8803 =<= join (converse ?8803) (converse ?8803) [8803] by Demod 10923 with 1219 at 1,2,3
% 4.38/1.45 Id : 10972, {_}: converse (converse ?8805) =<= join (converse (converse ?8805)) ?8805 [8805] by Super 10971 with 9 at 2,3
% 4.38/1.45 Id : 10991, {_}: ?8805 =<= join (converse (converse ?8805)) ?8805 [8805] by Demod 10972 with 9 at 2
% 4.38/1.45 Id : 10992, {_}: ?8805 =<= join ?8805 (converse (converse ?8805)) [8805] by Demod 10991 with 2 at 3
% 4.38/1.45 Id : 10993, {_}: ?8805 =<= join ?8805 ?8805 [8805] by Demod 10992 with 9 at 2,3
% 4.38/1.45 Id : 11284, {_}: join ?9160 (join ?9160 ?9161) =>= join ?9160 ?9161 [9161, 9160] by Super 3 with 10993 at 1,3
% 4.38/1.45 Id : 40, {_}: ?111 =<= join (complement (join (complement ?111) ?112)) (complement (join (complement ?111) (complement ?112))) [112, 111] by Demod 4 with 2 at 3
% 4.38/1.45 Id : 41, {_}: ?114 =<= join (complement (join (complement ?114) ?115)) (complement (join (complement ?115) (complement ?114))) [115, 114] by Super 40 with 2 at 1,2,3
% 4.38/1.45 Id : 957, {_}: ?114 =<= join (complement (join (complement ?114) ?115)) (meet ?115 ?114) [115, 114] by Demod 41 with 5 at 2,3
% 4.38/1.45 Id : 958, {_}: ?114 =<= join (meet ?115 ?114) (complement (join (complement ?114) ?115)) [115, 114] by Demod 957 with 2 at 3
% 4.38/1.45 Id : 6018, {_}: meet ?5562 (join (complement ?5563) (complement ?5564)) =<= complement (join (complement ?5562) (meet ?5563 ?5564)) [5564, 5563, 5562] by Super 57 with 5 at 2,1,3
% 4.38/1.45 Id : 6019, {_}: meet ?5566 (join (complement top) (complement ?5567)) =<= complement (join (complement ?5566) ?5567) [5567, 5566] by Super 6018 with 1222 at 2,1,3
% 4.38/1.45 Id : 6089, {_}: meet ?5566 (join zero (complement ?5567)) =<= complement (join (complement ?5566) ?5567) [5567, 5566] by Demod 6019 with 681 at 1,2,2
% 4.38/1.45 Id : 6090, {_}: meet ?5566 (complement ?5567) =<= complement (join (complement ?5566) ?5567) [5567, 5566] by Demod 6089 with 1207 at 2,2
% 4.38/1.45 Id : 6213, {_}: ?114 =<= join (meet ?115 ?114) (meet ?114 (complement ?115)) [115, 114] by Demod 958 with 6090 at 2,3
% 4.38/1.45 Id : 11308, {_}: join (meet ?9236 ?9237) ?9237 =<= join (meet ?9236 ?9237) (meet ?9237 (complement ?9236)) [9237, 9236] by Super 11284 with 6213 at 2,2
% 4.38/1.45 Id : 11381, {_}: join ?9237 (meet ?9236 ?9237) =<= join (meet ?9236 ?9237) (meet ?9237 (complement ?9236)) [9236, 9237] by Demod 11308 with 2 at 2
% 4.38/1.45 Id : 11382, {_}: join ?9237 (meet ?9236 ?9237) =>= ?9237 [9236, 9237] by Demod 11381 with 6213 at 3
% 4.38/1.45 Id : 2574, {_}: ?3056 =<= meet ?3056 (converse (complement (converse (complement ?3056)))) [3056] by Demod 2573 with 1207 at 3
% 4.38/1.45 Id : 11890, {_}: join (converse (complement (converse (complement ?10042)))) ?10042 =>= converse (complement (converse (complement ?10042))) [10042] by Super 11382 with 2574 at 2,2
% 4.38/1.45 Id : 11901, {_}: join ?10042 (converse (complement (converse (complement ?10042)))) =>= converse (complement (converse (complement ?10042))) [10042] by Demod 11890 with 2 at 2
% 4.38/1.45 Id : 12852, {_}: converse ?11120 =<= converse (complement (converse (complement (converse ?11120)))) [11120] by Demod 12816 with 11901 at 3
% 4.38/1.45 Id : 12904, {_}: converse (converse ?11211) =<= complement (converse (complement (converse ?11211))) [11211] by Super 9 with 12852 at 1,2
% 4.38/1.45 Id : 12937, {_}: ?11211 =<= complement (converse (complement (converse ?11211))) [11211] by Demod 12904 with 9 at 2
% 4.38/1.45 Id : 13010, {_}: converse (complement (converse ?11282)) =>= complement ?11282 [11282] by Super 1219 with 12937 at 1,3
% 4.38/1.45 Id : 13111, {_}: converse (complement ?11359) =<= complement (converse ?11359) [11359] by Super 9 with 13010 at 1,2
% 4.38/1.45 Id : 13206, {_}: converse (complement sk1) === converse (complement sk1) [] by Demod 1 with 13111 at 3
% 4.38/1.45 Id : 1, {_}: converse (complement sk1) =<= complement (converse sk1) [] by goals_17
% 4.38/1.45 % SZS output end CNFRefutation for theBenchmark.p
% 4.38/1.45 7284: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 1.109847 using lpo
%------------------------------------------------------------------------------