TSTP Solution File: REL018-1 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : REL018-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n005.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 19:42:09 EDT 2022
% Result : Unsatisfiable 6.36s 1.93s
% Output : CNFRefutation 6.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL018-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 16:00:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 20565: Facts:
% 0.14/0.36 20565: Id : 2, {_}:
% 0.14/0.36 join ?2 ?3 =?= join ?3 ?2
% 0.14/0.36 [3, 2] by maddux1_join_commutativity_1 ?2 ?3
% 0.14/0.36 20565: Id : 3, {_}:
% 0.14/0.36 join ?5 (join ?6 ?7) =?= join (join ?5 ?6) ?7
% 0.14/0.36 [7, 6, 5] by maddux2_join_associativity_2 ?5 ?6 ?7
% 0.14/0.36 20565: Id : 4, {_}:
% 0.14/0.36 ?9
% 0.14/0.36 =<=
% 0.14/0.36 join (complement (join (complement ?9) (complement ?10)))
% 0.14/0.36 (complement (join (complement ?9) ?10))
% 0.14/0.36 [10, 9] by maddux3_a_kind_of_de_Morgan_3 ?9 ?10
% 0.14/0.36 20565: Id : 5, {_}:
% 0.14/0.36 meet ?12 ?13 =<= complement (join (complement ?12) (complement ?13))
% 0.14/0.36 [13, 12] by maddux4_definiton_of_meet_4 ?12 ?13
% 0.14/0.36 20565: Id : 6, {_}:
% 0.14/0.36 composition ?15 (composition ?16 ?17)
% 0.14/0.36 =?=
% 0.14/0.36 composition (composition ?15 ?16) ?17
% 0.14/0.36 [17, 16, 15] by composition_associativity_5 ?15 ?16 ?17
% 0.14/0.36 20565: Id : 7, {_}: composition ?19 one =>= ?19 [19] by composition_identity_6 ?19
% 0.14/0.36 20565: Id : 8, {_}:
% 0.14/0.36 composition (join ?21 ?22) ?23
% 0.14/0.36 =<=
% 0.14/0.36 join (composition ?21 ?23) (composition ?22 ?23)
% 0.14/0.36 [23, 22, 21] by composition_distributivity_7 ?21 ?22 ?23
% 0.14/0.36 20565: Id : 9, {_}:
% 0.14/0.36 converse (converse ?25) =>= ?25
% 0.14/0.36 [25] by converse_idempotence_8 ?25
% 0.14/0.36 20565: Id : 10, {_}:
% 0.14/0.36 converse (join ?27 ?28) =<= join (converse ?27) (converse ?28)
% 0.14/0.36 [28, 27] by converse_additivity_9 ?27 ?28
% 0.14/0.36 20565: Id : 11, {_}:
% 0.14/0.36 converse (composition ?30 ?31)
% 0.14/0.36 =<=
% 0.14/0.36 composition (converse ?31) (converse ?30)
% 0.14/0.36 [31, 30] by converse_multiplicativity_10 ?30 ?31
% 0.14/0.36 20565: Id : 12, {_}:
% 0.14/0.36 join (composition (converse ?33) (complement (composition ?33 ?34)))
% 0.14/0.36 (complement ?34)
% 0.14/0.36 =>=
% 0.14/0.36 complement ?34
% 0.14/0.36 [34, 33] by converse_cancellativity_11 ?33 ?34
% 0.14/0.36 20565: Id : 13, {_}: top =<= join ?36 (complement ?36) [36] by def_top_12 ?36
% 0.14/0.36 20565: Id : 14, {_}: zero =<= meet ?38 (complement ?38) [38] by def_zero_13 ?38
% 0.14/0.36 20565: Id : 15, {_}: composition sk1 top =>= sk1 [] by goals_14
% 0.14/0.36 20565: Goal:
% 0.14/0.36 20565: Id : 1, {_}:
% 0.14/0.36 composition (complement sk1) top =>= complement sk1
% 0.14/0.36 [] by goals_15
% 6.36/1.93 Statistics :
% 6.36/1.93 Max weight : 20
% 6.36/1.93 Found proof, 1.566180s
% 6.36/1.93 % SZS status Unsatisfiable for theBenchmark.p
% 6.36/1.93 % SZS output start CNFRefutation for theBenchmark.p
% 6.36/1.93 Id : 25, {_}: join ?72 (join ?73 ?74) =?= join (join ?72 ?73) ?74 [74, 73, 72] by maddux2_join_associativity_2 ?72 ?73 ?74
% 6.36/1.93 Id : 8, {_}: composition (join ?21 ?22) ?23 =<= join (composition ?21 ?23) (composition ?22 ?23) [23, 22, 21] by composition_distributivity_7 ?21 ?22 ?23
% 6.36/1.93 Id : 117, {_}: converse (join ?344 ?345) =<= join (converse ?344) (converse ?345) [345, 344] by converse_additivity_9 ?344 ?345
% 6.36/1.93 Id : 15, {_}: composition sk1 top =>= sk1 [] by goals_14
% 6.36/1.93 Id : 45, {_}: ?156 =<= join (complement (join (complement ?156) (complement ?157))) (complement (join (complement ?156) ?157)) [157, 156] by maddux3_a_kind_of_de_Morgan_3 ?156 ?157
% 6.36/1.93 Id : 13, {_}: top =<= join ?36 (complement ?36) [36] by def_top_12 ?36
% 6.36/1.93 Id : 3, {_}: join ?5 (join ?6 ?7) =?= join (join ?5 ?6) ?7 [7, 6, 5] by maddux2_join_associativity_2 ?5 ?6 ?7
% 6.36/1.93 Id : 9, {_}: converse (converse ?25) =>= ?25 [25] by converse_idempotence_8 ?25
% 6.36/1.93 Id : 130, {_}: converse (composition ?374 ?375) =<= composition (converse ?375) (converse ?374) [375, 374] by converse_multiplicativity_10 ?374 ?375
% 6.36/1.93 Id : 7, {_}: composition ?19 one =>= ?19 [19] by composition_identity_6 ?19
% 6.36/1.93 Id : 12, {_}: join (composition (converse ?33) (complement (composition ?33 ?34))) (complement ?34) =>= complement ?34 [34, 33] by converse_cancellativity_11 ?33 ?34
% 6.36/1.93 Id : 14, {_}: zero =<= meet ?38 (complement ?38) [38] by def_zero_13 ?38
% 6.36/1.93 Id : 2, {_}: join ?2 ?3 =?= join ?3 ?2 [3, 2] by maddux1_join_commutativity_1 ?2 ?3
% 6.36/1.93 Id : 5, {_}: meet ?12 ?13 =<= complement (join (complement ?12) (complement ?13)) [13, 12] by maddux4_definiton_of_meet_4 ?12 ?13
% 6.36/1.93 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
% 6.36/1.93 Id : 56, {_}: ?9 =<= join (meet ?9 ?10) (complement (join (complement ?9) ?10)) [10, 9] by Demod 4 with 5 at 1,3
% 6.36/1.93 Id : 57, {_}: ?9 =<= join (complement (join (complement ?9) ?10)) (meet ?9 ?10) [10, 9] by Demod 56 with 2 at 3
% 6.36/1.93 Id : 166, {_}: ?454 =<= join (complement (join (complement ?454) (complement ?454))) zero [454] by Super 57 with 14 at 2,3
% 6.36/1.93 Id : 170, {_}: ?454 =<= join zero (complement (join (complement ?454) (complement ?454))) [454] by Demod 166 with 2 at 3
% 6.36/1.93 Id : 171, {_}: ?454 =<= join zero (meet ?454 ?454) [454] by Demod 170 with 5 at 2,3
% 6.36/1.93 Id : 135, {_}: join (complement ?34) (composition (converse ?33) (complement (composition ?33 ?34))) =>= complement ?34 [33, 34] by Demod 12 with 2 at 2
% 6.36/1.93 Id : 1027, {_}: converse (composition (converse ?2614) ?2615) =>= composition (converse ?2615) ?2614 [2615, 2614] by Super 130 with 9 at 2,3
% 6.36/1.93 Id : 1032, {_}: converse (converse ?2632) =<= composition (converse one) ?2632 [2632] by Super 1027 with 7 at 1,2
% 6.36/1.93 Id : 1047, {_}: ?2632 =<= composition (converse one) ?2632 [2632] by Demod 1032 with 9 at 2
% 6.36/1.93 Id : 1054, {_}: one =<= converse one [] by Super 7 with 1047 at 2
% 6.36/1.93 Id : 1082, {_}: join (complement ?2686) (composition one (complement (composition one ?2686))) =>= complement ?2686 [2686] by Super 135 with 1054 at 1,2,2
% 6.36/1.93 Id : 1073, {_}: ?2632 =<= composition one ?2632 [2632] by Demod 1047 with 1054 at 1,3
% 6.36/1.93 Id : 1088, {_}: join (complement ?2686) (complement (composition one ?2686)) =>= complement ?2686 [2686] by Demod 1082 with 1073 at 2,2
% 6.36/1.93 Id : 1089, {_}: join (complement ?2686) (complement ?2686) =>= complement ?2686 [2686] by Demod 1088 with 1073 at 1,2,2
% 6.36/1.93 Id : 2088, {_}: meet ?5117 ?5117 =>= complement (complement ?5117) [5117] by Super 5 with 1089 at 1,3
% 6.36/1.93 Id : 2170, {_}: ?454 =<= join zero (complement (complement ?454)) [454] by Demod 171 with 2088 at 2,3
% 6.36/1.93 Id : 2094, {_}: join (complement ?5134) (complement ?5134) =>= complement ?5134 [5134] by Demod 1088 with 1073 at 1,2,2
% 6.36/1.93 Id : 158, {_}: meet ?439 (complement ?439) =>= complement top [439] by Super 5 with 13 at 1,3
% 6.36/1.93 Id : 194, {_}: zero =<= complement top [] by Demod 158 with 14 at 2
% 6.36/1.93 Id : 2096, {_}: join (complement top) zero =>= complement top [] by Super 2094 with 194 at 2,2
% 6.36/1.93 Id : 2119, {_}: join zero (complement top) =>= complement top [] by Demod 2096 with 2 at 2
% 6.36/1.93 Id : 2120, {_}: join zero (complement top) =>= zero [] by Demod 2119 with 194 at 3
% 6.36/1.93 Id : 2121, {_}: join zero zero =>= zero [] by Demod 2120 with 194 at 2,2
% 6.36/1.93 Id : 2232, {_}: join zero (join zero ?5248) =>= join zero ?5248 [5248] by Super 3 with 2121 at 1,3
% 6.36/1.93 Id : 2241, {_}: join zero ?5265 =<= join zero (complement (complement ?5265)) [5265] by Super 2232 with 2170 at 2,2
% 6.36/1.93 Id : 2283, {_}: join zero ?5265 =>= ?5265 [5265] by Demod 2241 with 2170 at 3
% 6.36/1.93 Id : 2288, {_}: ?454 =<= complement (complement ?454) [454] by Demod 2170 with 2283 at 3
% 6.36/1.93 Id : 14179, {_}: join (complement ?14519) (complement ?14520) =<= join (complement (join (meet ?14519 ?14520) ?14521)) (meet (join (complement ?14519) (complement ?14520)) ?14521) [14521, 14520, 14519] by Super 57 with 5 at 1,1,1,3
% 6.36/1.93 Id : 14198, {_}: join (complement ?14587) (complement ?14588) =<= join (complement (join (meet ?14587 ?14588) (complement (join (complement ?14587) (complement ?14588))))) zero [14588, 14587] by Super 14179 with 14 at 2,3
% 6.36/1.93 Id : 14301, {_}: join (complement ?14587) (complement ?14588) =<= join zero (complement (join (meet ?14587 ?14588) (complement (join (complement ?14587) (complement ?14588))))) [14588, 14587] by Demod 14198 with 2 at 3
% 6.36/1.93 Id : 14302, {_}: join (complement ?14587) (complement ?14588) =<= complement (join (meet ?14587 ?14588) (complement (join (complement ?14587) (complement ?14588)))) [14588, 14587] by Demod 14301 with 2283 at 3
% 6.36/1.93 Id : 14303, {_}: join (complement ?14587) (complement ?14588) =<= complement (join (complement (join (complement ?14587) (complement ?14588))) (meet ?14587 ?14588)) [14588, 14587] by Demod 14302 with 2 at 1,3
% 6.36/1.93 Id : 14304, {_}: join (complement ?14587) (complement ?14588) =<= complement (join (meet ?14587 ?14588) (meet ?14587 ?14588)) [14588, 14587] by Demod 14303 with 5 at 1,1,3
% 6.36/1.93 Id : 46, {_}: ?159 =<= join (complement (join (complement ?159) (complement ?160))) (complement (join ?160 (complement ?159))) [160, 159] by Super 45 with 2 at 1,2,3
% 6.36/1.93 Id : 3637, {_}: ?159 =<= join (meet ?159 ?160) (complement (join ?160 (complement ?159))) [160, 159] by Demod 46 with 5 at 1,3
% 6.36/1.93 Id : 3652, {_}: ?6688 =<= join (complement (join ?6689 (complement ?6688))) (meet ?6688 ?6689) [6689, 6688] by Demod 3637 with 2 at 3
% 6.36/1.93 Id : 155, {_}: join (complement ?433) ?433 =>= top [433] by Super 2 with 13 at 3
% 6.36/1.93 Id : 179, {_}: meet (complement ?471) ?471 =>= complement top [471] by Super 5 with 155 at 1,3
% 6.36/1.93 Id : 449, {_}: meet (complement ?471) ?471 =>= zero [471] by Demod 179 with 194 at 3
% 6.36/1.93 Id : 3653, {_}: complement ?6691 =<= join (complement (join ?6691 (complement (complement ?6691)))) zero [6691] by Super 3652 with 449 at 2,3
% 6.36/1.93 Id : 3691, {_}: complement ?6691 =<= join zero (complement (join ?6691 (complement (complement ?6691)))) [6691] by Demod 3653 with 2 at 3
% 6.36/1.93 Id : 3692, {_}: complement ?6691 =<= complement (join ?6691 (complement (complement ?6691))) [6691] by Demod 3691 with 2283 at 3
% 6.36/1.93 Id : 3693, {_}: complement ?6691 =<= complement (join ?6691 ?6691) [6691] by Demod 3692 with 2288 at 2,1,3
% 6.36/1.93 Id : 3738, {_}: join ?6781 ?6781 =>= complement (complement ?6781) [6781] by Super 2288 with 3693 at 1,3
% 6.36/1.93 Id : 3796, {_}: join ?6781 ?6781 =>= ?6781 [6781] by Demod 3738 with 2288 at 3
% 6.36/1.93 Id : 14568, {_}: join (complement ?14831) (complement ?14832) =>= complement (meet ?14831 ?14832) [14832, 14831] by Demod 14304 with 3796 at 1,3
% 6.36/1.93 Id : 14574, {_}: join ?14847 (complement ?14848) =<= complement (meet (complement ?14847) ?14848) [14848, 14847] by Super 14568 with 2288 at 1,2
% 6.36/1.93 Id : 14733, {_}: meet (complement ?15031) ?15032 =<= complement (join ?15031 (complement ?15032)) [15032, 15031] by Super 2288 with 14574 at 1,3
% 6.36/1.93 Id : 49, {_}: ?168 =<= join (complement (join (complement ?169) (complement ?168))) (complement (join (complement ?168) ?169)) [169, 168] by Super 45 with 2 at 1,1,3
% 6.36/1.93 Id : 4833, {_}: ?168 =<= join (meet ?169 ?168) (complement (join (complement ?168) ?169)) [169, 168] by Demod 49 with 5 at 1,3
% 6.36/1.93 Id : 4834, {_}: ?168 =<= join (complement (join (complement ?168) ?169)) (meet ?169 ?168) [169, 168] by Demod 4833 with 2 at 3
% 6.36/1.93 Id : 14570, {_}: join (complement ?14836) ?14837 =<= complement (meet ?14836 (complement ?14837)) [14837, 14836] by Super 14568 with 2288 at 2,2
% 6.36/1.93 Id : 14639, {_}: meet ?14893 (complement ?14894) =<= complement (join (complement ?14893) ?14894) [14894, 14893] by Super 2288 with 14570 at 1,3
% 6.36/1.93 Id : 15432, {_}: ?168 =<= join (meet ?168 (complement ?169)) (meet ?169 ?168) [169, 168] by Demod 4834 with 14639 at 1,3
% 6.36/1.93 Id : 15453, {_}: meet ?15608 (complement ?15609) =<= complement (join (complement ?15608) ?15609) [15609, 15608] by Super 2288 with 14570 at 1,3
% 6.36/1.93 Id : 131, {_}: converse (composition (converse ?377) ?378) =>= composition (converse ?378) ?377 [378, 377] by Super 130 with 9 at 2,3
% 6.36/1.93 Id : 175, {_}: join (complement top) (composition (converse sk1) (complement sk1)) =>= complement top [] by Super 135 with 15 at 1,2,2,2
% 6.36/1.93 Id : 4346, {_}: join zero (composition (converse sk1) (complement sk1)) =>= complement top [] by Demod 175 with 194 at 1,2
% 6.36/1.93 Id : 4347, {_}: join zero (composition (converse sk1) (complement sk1)) =>= zero [] by Demod 4346 with 194 at 3
% 6.36/1.93 Id : 4348, {_}: composition (converse sk1) (complement sk1) =>= zero [] by Demod 4347 with 2283 at 2
% 6.36/1.93 Id : 4353, {_}: converse zero =<= composition (converse (complement sk1)) sk1 [] by Super 131 with 4348 at 1,2
% 6.36/1.93 Id : 2321, {_}: join ?5311 zero =>= ?5311 [5311] by Super 2 with 2283 at 3
% 6.36/1.93 Id : 118, {_}: converse (join ?347 (converse ?348)) =>= join (converse ?347) ?348 [348, 347] by Super 117 with 9 at 2,3
% 6.36/1.93 Id : 2311, {_}: converse (converse ?5286) =<= join (converse zero) ?5286 [5286] by Super 118 with 2283 at 1,2
% 6.36/1.93 Id : 2345, {_}: ?5286 =<= join (converse zero) ?5286 [5286] by Demod 2311 with 9 at 2
% 6.36/1.93 Id : 2551, {_}: zero =<= converse zero [] by Super 2321 with 2345 at 2
% 6.36/1.93 Id : 4356, {_}: zero =<= composition (converse (complement sk1)) sk1 [] by Demod 4353 with 2551 at 2
% 6.36/1.93 Id : 4368, {_}: join (complement sk1) (composition (converse (converse (complement sk1))) (complement zero)) =>= complement sk1 [] by Super 135 with 4356 at 1,2,2,2
% 6.36/1.93 Id : 4377, {_}: join (complement sk1) (composition (complement sk1) (complement zero)) =>= complement sk1 [] by Demod 4368 with 9 at 1,2,2
% 6.36/1.93 Id : 2319, {_}: top =<= complement zero [] by Super 13 with 2283 at 3
% 6.36/1.93 Id : 4378, {_}: join (complement sk1) (composition (complement sk1) top) =>= complement sk1 [] by Demod 4377 with 2319 at 2,2,2
% 6.36/1.93 Id : 15467, {_}: meet sk1 (complement (composition (complement sk1) top)) =>= complement (complement sk1) [] by Super 15453 with 4378 at 1,3
% 6.36/1.93 Id : 15505, {_}: meet sk1 (complement (composition (complement sk1) top)) =>= sk1 [] by Demod 15467 with 2288 at 3
% 6.36/1.93 Id : 15944, {_}: complement (composition (complement sk1) top) =<= join (meet (complement (composition (complement sk1) top)) (complement sk1)) sk1 [] by Super 15432 with 15505 at 2,3
% 6.36/1.93 Id : 15978, {_}: complement (composition (complement sk1) top) =<= join sk1 (meet (complement (composition (complement sk1) top)) (complement sk1)) [] by Demod 15944 with 2 at 3
% 6.36/1.93 Id : 15455, {_}: meet (complement ?15613) (complement ?15614) =>= complement (join ?15613 ?15614) [15614, 15613] by Super 15453 with 2288 at 1,1,3
% 6.36/1.93 Id : 15979, {_}: complement (composition (complement sk1) top) =<= join sk1 (complement (join (composition (complement sk1) top) sk1)) [] by Demod 15978 with 15455 at 2,3
% 6.36/1.93 Id : 15980, {_}: complement (composition (complement sk1) top) =<= join sk1 (complement (join sk1 (composition (complement sk1) top))) [] by Demod 15979 with 2 at 1,2,3
% 6.36/1.93 Id : 173, {_}: composition (join sk1 ?464) top =<= join sk1 (composition ?464 top) [464] by Super 8 with 15 at 1,3
% 6.36/1.93 Id : 15981, {_}: complement (composition (complement sk1) top) =<= join sk1 (complement (composition (join sk1 (complement sk1)) top)) [] by Demod 15980 with 173 at 1,2,3
% 6.36/1.93 Id : 15982, {_}: complement (composition (complement sk1) top) =<= join sk1 (complement (composition top top)) [] by Demod 15981 with 13 at 1,1,2,3
% 6.36/1.93 Id : 15985, {_}: meet (complement sk1) (composition top top) =>= complement (complement (composition (complement sk1) top)) [] by Super 14733 with 15982 at 1,3
% 6.36/1.93 Id : 16014, {_}: meet (complement sk1) (composition top top) =>= composition (complement sk1) top [] by Demod 15985 with 2288 at 3
% 6.36/1.93 Id : 1058, {_}: composition (join sk1 (converse one)) top =>= join sk1 top [] by Super 173 with 1047 at 2,3
% 6.36/1.93 Id : 1237, {_}: composition (join sk1 one) top =>= join sk1 top [] by Demod 1058 with 1054 at 2,1,2
% 6.36/1.93 Id : 1239, {_}: composition (join (join sk1 one) ?2836) top =<= join (join sk1 top) (composition ?2836 top) [2836] by Super 8 with 1237 at 1,3
% 6.36/1.93 Id : 1253, {_}: composition (join sk1 (join one ?2836)) top =<= join (join sk1 top) (composition ?2836 top) [2836] by Demod 1239 with 3 at 1,2
% 6.36/1.93 Id : 1254, {_}: composition (join sk1 (join one ?2836)) top =<= join (composition ?2836 top) (join sk1 top) [2836] by Demod 1253 with 2 at 3
% 6.36/1.93 Id : 22, {_}: join ?60 (join ?61 ?62) =?= join ?61 (join ?62 ?60) [62, 61, 60] by Super 2 with 3 at 3
% 6.36/1.93 Id : 1255, {_}: composition (join sk1 (join one ?2836)) top =<= join sk1 (join top (composition ?2836 top)) [2836] by Demod 1254 with 22 at 3
% 6.36/1.93 Id : 1238, {_}: composition (join ?2834 (join sk1 one)) top =<= join (composition ?2834 top) (join sk1 top) [2834] by Super 8 with 1237 at 2,3
% 6.36/1.93 Id : 1252, {_}: composition (join ?2834 (join sk1 one)) top =<= join sk1 (join top (composition ?2834 top)) [2834] by Demod 1238 with 22 at 3
% 6.36/1.93 Id : 13420, {_}: composition (join sk1 (join one ?2836)) top =?= composition (join ?2836 (join sk1 one)) top [2836] by Demod 1255 with 1252 at 3
% 6.36/1.93 Id : 51, {_}: join (complement ?174) (complement ?175) =<= join (complement ?174) (complement (join (complement (join (complement ?174) (complement ?175))) (join (complement ?174) ?175))) [175, 174] by Super 45 with 4 at 1,1,3
% 6.36/1.93 Id : 6170, {_}: join (complement ?174) (complement ?175) =<= join (complement ?174) (complement (join (meet ?174 ?175) (join (complement ?174) ?175))) [175, 174] by Demod 51 with 5 at 1,1,2,3
% 6.36/1.93 Id : 6188, {_}: join (complement ?9014) (complement ?9015) =<= join (complement ?9014) (complement (join (complement ?9014) (join ?9015 (meet ?9014 ?9015)))) [9015, 9014] by Demod 6170 with 22 at 1,2,3
% 6.36/1.93 Id : 2362, {_}: meet ?5349 zero =<= complement (join (complement ?5349) top) [5349] by Super 5 with 2319 at 2,1,3
% 6.36/1.93 Id : 2379, {_}: meet ?5349 zero =<= complement (join top (complement ?5349)) [5349] by Demod 2362 with 2 at 1,3
% 6.36/1.93 Id : 2363, {_}: meet zero ?5351 =<= complement (join top (complement ?5351)) [5351] by Super 5 with 2319 at 1,1,3
% 6.36/1.93 Id : 2844, {_}: join top (complement ?5951) =>= complement (meet zero ?5951) [5951] by Super 2288 with 2363 at 1,3
% 6.36/1.93 Id : 2949, {_}: meet ?5349 zero =<= complement (complement (meet zero ?5349)) [5349] by Demod 2379 with 2844 at 1,3
% 6.36/1.93 Id : 2950, {_}: meet ?5349 zero =?= meet zero ?5349 [5349] by Demod 2949 with 2288 at 3
% 6.36/1.93 Id : 6196, {_}: join (complement zero) (complement ?9031) =<= join (complement zero) (complement (join (complement zero) (join ?9031 (meet ?9031 zero)))) [9031] by Super 6188 with 2950 at 2,2,1,2,3
% 6.36/1.93 Id : 6287, {_}: join top (complement ?9031) =<= join (complement zero) (complement (join (complement zero) (join ?9031 (meet ?9031 zero)))) [9031] by Demod 6196 with 2319 at 1,2
% 6.36/1.93 Id : 6288, {_}: join top (complement ?9031) =<= join top (complement (join (complement zero) (join ?9031 (meet ?9031 zero)))) [9031] by Demod 6287 with 2319 at 1,3
% 6.36/1.93 Id : 6289, {_}: join top (complement ?9031) =<= join top (complement (join top (join ?9031 (meet ?9031 zero)))) [9031] by Demod 6288 with 2319 at 1,1,2,3
% 6.36/1.93 Id : 2428, {_}: ?5446 =<= join (complement (complement ?5446)) (meet ?5446 zero) [5446] by Super 57 with 2321 at 1,1,3
% 6.36/1.93 Id : 2484, {_}: ?5446 =<= join ?5446 (meet ?5446 zero) [5446] by Demod 2428 with 2288 at 1,3
% 6.36/1.93 Id : 6290, {_}: join top (complement ?9031) =<= join top (complement (join top ?9031)) [9031] by Demod 6289 with 2484 at 2,1,2,3
% 6.36/1.93 Id : 6291, {_}: complement (meet zero ?9031) =<= join top (complement (join top ?9031)) [9031] by Demod 6290 with 2844 at 2
% 6.36/1.93 Id : 9167, {_}: complement (meet zero ?11101) =<= complement (meet zero (join top ?11101)) [11101] by Demod 6291 with 2844 at 3
% 6.36/1.93 Id : 9173, {_}: complement (meet zero (complement ?11113)) =<= complement (meet zero (complement (meet zero ?11113))) [11113] by Super 9167 with 2844 at 2,1,3
% 6.36/1.93 Id : 2855, {_}: meet zero ?5977 =<= complement (join top (complement ?5977)) [5977] by Super 5 with 2319 at 1,1,3
% 6.36/1.93 Id : 2858, {_}: meet zero (complement ?5983) =>= complement (join top ?5983) [5983] by Super 2855 with 2288 at 2,1,3
% 6.36/1.93 Id : 9197, {_}: complement (complement (join top ?11113)) =<= complement (meet zero (complement (meet zero ?11113))) [11113] by Demod 9173 with 2858 at 1,2
% 6.36/1.93 Id : 9198, {_}: complement (complement (join top ?11113)) =<= complement (complement (join top (meet zero ?11113))) [11113] by Demod 9197 with 2858 at 1,3
% 6.36/1.93 Id : 9199, {_}: join top ?11113 =<= complement (complement (join top (meet zero ?11113))) [11113] by Demod 9198 with 2288 at 2
% 6.36/1.93 Id : 9200, {_}: join top ?11113 =<= join top (meet zero ?11113) [11113] by Demod 9199 with 2288 at 3
% 6.36/1.93 Id : 9168, {_}: complement (meet zero ?11103) =<= complement (meet zero (join ?11103 top)) [11103] by Super 9167 with 2 at 2,1,3
% 6.36/1.93 Id : 9991, {_}: meet zero (join ?11684 top) =>= complement (complement (meet zero ?11684)) [11684] by Super 2288 with 9168 at 1,3
% 6.36/1.93 Id : 10045, {_}: meet zero (join ?11684 top) =>= meet zero ?11684 [11684] by Demod 9991 with 2288 at 3
% 6.36/1.93 Id : 26, {_}: join ?76 (join ?77 ?78) =?= join (join ?77 ?76) ?78 [78, 77, 76] by Super 25 with 2 at 1,3
% 6.36/1.93 Id : 18694, {_}: join ?18043 (join ?18043 ?18044) =>= join ?18043 ?18044 [18044, 18043] by Super 26 with 3796 at 1,3
% 6.36/1.93 Id : 18733, {_}: join ?18151 top =<= join ?18151 (complement ?18151) [18151] by Super 18694 with 13 at 2,2
% 6.36/1.93 Id : 18910, {_}: join ?18151 top =>= top [18151] by Demod 18733 with 13 at 3
% 6.36/1.93 Id : 19027, {_}: meet zero top =?= meet zero ?11684 [11684] by Demod 10045 with 18910 at 2,2
% 6.36/1.93 Id : 198, {_}: meet ?496 top =<= complement (join (complement ?496) zero) [496] by Super 5 with 194 at 2,1,3
% 6.36/1.93 Id : 204, {_}: meet ?496 top =<= complement (join zero (complement ?496)) [496] by Demod 198 with 2 at 1,3
% 6.36/1.93 Id : 199, {_}: meet top ?498 =<= complement (join zero (complement ?498)) [498] by Super 5 with 194 at 1,1,3
% 6.36/1.93 Id : 498, {_}: meet ?496 top =?= meet top ?496 [496] by Demod 204 with 199 at 3
% 6.36/1.93 Id : 2292, {_}: meet top ?498 =>= complement (complement ?498) [498] by Demod 199 with 2283 at 1,3
% 6.36/1.93 Id : 2297, {_}: meet ?496 top =>= complement (complement ?496) [496] by Demod 498 with 2292 at 3
% 6.36/1.93 Id : 2306, {_}: meet ?496 top =>= ?496 [496] by Demod 2297 with 2288 at 3
% 6.36/1.93 Id : 19028, {_}: zero =<= meet zero ?11684 [11684] by Demod 19027 with 2306 at 2
% 6.36/1.93 Id : 19059, {_}: join top ?11113 =?= join top zero [11113] by Demod 9200 with 19028 at 2,3
% 6.36/1.93 Id : 19083, {_}: join top ?11113 =>= top [11113] by Demod 19059 with 2321 at 3
% 6.36/1.93 Id : 19108, {_}: composition (join ?2834 (join sk1 one)) top =>= join sk1 top [2834] by Demod 1252 with 19083 at 2,3
% 6.36/1.93 Id : 19119, {_}: composition (join ?2834 (join sk1 one)) top =>= top [2834] by Demod 19108 with 18910 at 3
% 6.36/1.93 Id : 19120, {_}: composition (join sk1 (join one ?2836)) top =>= top [2836] by Demod 13420 with 19119 at 3
% 6.36/1.93 Id : 19162, {_}: composition (join sk1 top) top =>= top [] by Super 19120 with 18910 at 2,1,2
% 6.36/1.93 Id : 19343, {_}: composition top top =>= top [] by Demod 19162 with 18910 at 1,2
% 6.36/1.93 Id : 19388, {_}: meet (complement sk1) top =<= composition (complement sk1) top [] by Demod 16014 with 19343 at 2,2
% 6.36/1.93 Id : 19389, {_}: complement sk1 =<= composition (complement sk1) top [] by Demod 19388 with 2306 at 2
% 6.36/1.93 Id : 19460, {_}: complement sk1 === complement sk1 [] by Demod 1 with 19389 at 2
% 6.36/1.93 Id : 1, {_}: composition (complement sk1) top =>= complement sk1 [] by goals_15
% 6.36/1.93 % SZS output end CNFRefutation for theBenchmark.p
% 6.36/1.93 20565: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 1.572601 using nrkbo
%------------------------------------------------------------------------------