TSTP Solution File: GRP179-2 by Matita---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP179-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : n027.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 : Sat Jul 16 10:29:24 EDT 2022
% Result : Unsatisfiable 217.13s 54.62s
% Output : CNFRefutation 217.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP179-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 05:40:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 17719: Facts:
% 0.12/0.34 17719: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.12/0.34 17719: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.12/0.34 17719: Id : 4, {_}:
% 0.12/0.34 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.12/0.34 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.12/0.34 17719: Id : 5, {_}:
% 0.12/0.34 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
% 0.12/0.34 [11, 10] by symmetry_of_glb ?10 ?11
% 0.12/0.34 17719: Id : 6, {_}:
% 0.12/0.34 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
% 0.12/0.34 [14, 13] by symmetry_of_lub ?13 ?14
% 0.12/0.34 17719: Id : 7, {_}:
% 0.12/0.34 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
% 0.12/0.34 =?=
% 0.12/0.34 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
% 0.12/0.34 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 0.12/0.34 17719: Id : 8, {_}:
% 0.12/0.34 least_upper_bound ?20 (least_upper_bound ?21 ?22)
% 0.12/0.34 =?=
% 0.12/0.34 least_upper_bound (least_upper_bound ?20 ?21) ?22
% 0.12/0.34 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 0.12/0.34 17719: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.12/0.34 17719: Id : 10, {_}:
% 0.12/0.34 greatest_lower_bound ?26 ?26 =>= ?26
% 0.12/0.34 [26] by idempotence_of_gld ?26
% 0.12/0.34 17719: Id : 11, {_}:
% 0.12/0.34 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
% 0.12/0.34 [29, 28] by lub_absorbtion ?28 ?29
% 0.12/0.34 17719: Id : 12, {_}:
% 0.12/0.34 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
% 0.12/0.34 [32, 31] by glb_absorbtion ?31 ?32
% 0.12/0.34 17719: Id : 13, {_}:
% 0.12/0.34 multiply ?34 (least_upper_bound ?35 ?36)
% 0.12/0.34 =<=
% 0.12/0.34 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
% 0.12/0.34 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 0.12/0.34 17719: Id : 14, {_}:
% 0.12/0.34 multiply ?38 (greatest_lower_bound ?39 ?40)
% 0.12/0.34 =<=
% 0.12/0.34 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
% 0.12/0.34 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 0.12/0.34 17719: Id : 15, {_}:
% 0.12/0.34 multiply (least_upper_bound ?42 ?43) ?44
% 0.12/0.34 =<=
% 0.12/0.34 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
% 0.12/0.34 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 0.12/0.34 17719: Id : 16, {_}:
% 0.12/0.34 multiply (greatest_lower_bound ?46 ?47) ?48
% 0.12/0.34 =<=
% 0.12/0.34 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
% 0.12/0.34 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 0.12/0.34 17719: Goal:
% 0.12/0.34 17719: Id : 1, {_}:
% 0.12/0.34 least_upper_bound (inverse a) identity
% 0.12/0.34 =>=
% 0.12/0.34 inverse (greatest_lower_bound a identity)
% 0.12/0.34 [] by prove_p18
% 217.13/54.62 Statistics :
% 217.13/54.62 Max weight : 19
% 217.13/54.62 Found proof, 54.278901s
% 217.13/54.62 % SZS status Unsatisfiable for theBenchmark.p
% 217.13/54.62 % SZS output start CNFRefutation for theBenchmark.p
% 217.13/54.62 Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
% 217.13/54.62 Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 217.13/54.62 Id : 132, {_}: greatest_lower_bound ?448 (least_upper_bound ?448 ?449) =>= ?448 [449, 448] by glb_absorbtion ?448 ?449
% 217.13/54.62 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 217.13/54.62 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 217.13/54.62 Id : 151, {_}: multiply ?501 (least_upper_bound ?502 ?503) =<= least_upper_bound (multiply ?501 ?502) (multiply ?501 ?503) [503, 502, 501] by monotony_lub1 ?501 ?502 ?503
% 217.13/54.62 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
% 217.13/54.62 Id : 214, {_}: multiply (least_upper_bound ?646 ?647) ?648 =<= least_upper_bound (multiply ?646 ?648) (multiply ?647 ?648) [648, 647, 646] by monotony_lub2 ?646 ?647 ?648
% 217.13/54.62 Id : 181, {_}: multiply ?572 (greatest_lower_bound ?573 ?574) =<= greatest_lower_bound (multiply ?572 ?573) (multiply ?572 ?574) [574, 573, 572] by monotony_glb1 ?572 ?573 ?574
% 217.13/54.62 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
% 217.13/54.62 Id : 246, {_}: multiply (greatest_lower_bound ?723 ?724) ?725 =<= greatest_lower_bound (multiply ?723 ?725) (multiply ?724 ?725) [725, 724, 723] by monotony_glb2 ?723 ?724 ?725
% 217.13/54.62 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 217.13/54.62 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 217.13/54.62 Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =?= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
% 217.13/54.62 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
% 217.13/54.62 Id : 114, {_}: least_upper_bound ?393 (greatest_lower_bound ?393 ?394) =>= ?393 [394, 393] by lub_absorbtion ?393 ?394
% 217.13/54.62 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 217.13/54.62 Id : 115, {_}: least_upper_bound ?396 (greatest_lower_bound ?397 ?396) =>= ?396 [397, 396] by Super 114 with 5 at 2,2
% 217.13/54.62 Id : 23, {_}: multiply (multiply ?64 (inverse ?65)) ?65 =>= multiply ?64 identity [65, 64] by Super 21 with 3 at 2,3
% 217.13/54.62 Id : 1159, {_}: multiply (multiply ?2285 (inverse ?2286)) ?2286 =>= multiply ?2285 identity [2286, 2285] by Super 21 with 3 at 2,3
% 217.13/54.62 Id : 1162, {_}: multiply identity ?2292 =<= multiply (inverse (inverse ?2292)) identity [2292] by Super 1159 with 3 at 1,2
% 217.13/54.62 Id : 1175, {_}: ?2292 =<= multiply (inverse (inverse ?2292)) identity [2292] by Demod 1162 with 2 at 2
% 217.13/54.62 Id : 22, {_}: multiply (multiply ?61 identity) ?62 =>= multiply ?61 ?62 [62, 61] by Super 21 with 2 at 2,3
% 217.13/54.62 Id : 1180, {_}: multiply ?2313 ?2314 =<= multiply (inverse (inverse ?2313)) ?2314 [2314, 2313] by Super 22 with 1175 at 1,2
% 217.13/54.62 Id : 1195, {_}: ?2292 =<= multiply ?2292 identity [2292] by Demod 1175 with 1180 at 3
% 217.13/54.62 Id : 1196, {_}: multiply (multiply ?64 (inverse ?65)) ?65 =>= ?64 [65, 64] by Demod 23 with 1195 at 3
% 217.13/54.62 Id : 1211, {_}: inverse (inverse ?2400) =<= multiply ?2400 identity [2400] by Super 1195 with 1180 at 3
% 217.13/54.62 Id : 1217, {_}: inverse (inverse ?2400) =>= ?2400 [2400] by Demod 1211 with 1195 at 3
% 217.13/54.62 Id : 1783, {_}: multiply (multiply ?3260 ?3261) (inverse ?3261) =>= ?3260 [3261, 3260] by Super 1196 with 1217 at 2,1,2
% 217.13/54.62 Id : 252, {_}: multiply (greatest_lower_bound (inverse ?746) ?747) ?746 =>= greatest_lower_bound identity (multiply ?747 ?746) [747, 746] by Super 246 with 3 at 1,3
% 217.13/54.62 Id : 1795, {_}: multiply (greatest_lower_bound identity (multiply ?3294 ?3295)) (inverse ?3295) =>= greatest_lower_bound (inverse ?3295) ?3294 [3295, 3294] by Super 1783 with 252 at 1,2
% 217.13/54.62 Id : 1150, {_}: multiply (multiply ?2250 (multiply ?2251 (inverse ?2252))) ?2252 =>= multiply ?2250 (multiply ?2251 identity) [2252, 2251, 2250] by Super 4 with 23 at 2,3
% 217.13/54.62 Id : 290555, {_}: multiply (multiply ?359403 (multiply ?359404 (inverse ?359405))) ?359405 =>= multiply ?359403 ?359404 [359405, 359404, 359403] by Demod 1150 with 1195 at 2,3
% 217.13/54.62 Id : 290641, {_}: multiply identity ?359756 =<= multiply (inverse (multiply ?359757 (inverse ?359756))) ?359757 [359757, 359756] by Super 290555 with 3 at 1,2
% 217.13/54.62 Id : 290962, {_}: ?360161 =<= multiply (inverse (multiply ?360162 (inverse ?360161))) ?360162 [360162, 360161] by Demod 290641 with 2 at 2
% 217.13/54.62 Id : 1243, {_}: multiply (multiply ?2416 ?2417) (inverse ?2417) =>= ?2416 [2417, 2416] by Super 1196 with 1217 at 2,1,2
% 217.13/54.62 Id : 292812, {_}: ?362795 =<= multiply (inverse ?362796) (multiply ?362796 ?362795) [362796, 362795] by Super 290962 with 1243 at 1,1,3
% 217.13/54.62 Id : 187, {_}: multiply (inverse ?595) (greatest_lower_bound ?595 ?596) =>= greatest_lower_bound identity (multiply (inverse ?595) ?596) [596, 595] by Super 181 with 3 at 1,3
% 217.13/54.62 Id : 292818, {_}: greatest_lower_bound ?362812 ?362813 =<= multiply (inverse (inverse ?362812)) (greatest_lower_bound identity (multiply (inverse ?362812) ?362813)) [362813, 362812] by Super 292812 with 187 at 2,3
% 217.13/54.62 Id : 292965, {_}: greatest_lower_bound ?362812 ?362813 =<= multiply ?362812 (greatest_lower_bound identity (multiply (inverse ?362812) ?362813)) [362813, 362812] by Demod 292818 with 1217 at 1,3
% 217.13/54.62 Id : 290853, {_}: ?359756 =<= multiply (inverse (multiply ?359757 (inverse ?359756))) ?359757 [359757, 359756] by Demod 290641 with 2 at 2
% 217.13/54.62 Id : 291303, {_}: multiply ?360847 (inverse ?360848) =<= inverse (multiply ?360848 (inverse ?360847)) [360848, 360847] by Super 1243 with 290853 at 1,2
% 217.13/54.62 Id : 220, {_}: multiply (least_upper_bound (inverse ?669) ?670) ?669 =>= least_upper_bound identity (multiply ?670 ?669) [670, 669] by Super 214 with 3 at 1,3
% 217.13/54.62 Id : 1793, {_}: multiply (least_upper_bound identity (multiply ?3288 ?3289)) (inverse ?3289) =>= least_upper_bound (inverse ?3289) ?3288 [3289, 3288] by Super 1783 with 220 at 1,2
% 217.13/54.62 Id : 336185, {_}: multiply ?402965 (inverse (least_upper_bound identity (multiply ?402966 ?402965))) =>= inverse (least_upper_bound (inverse ?402965) ?402966) [402966, 402965] by Super 291303 with 1793 at 1,3
% 217.13/54.62 Id : 336186, {_}: multiply ?402968 (inverse (least_upper_bound identity ?402968)) =>= inverse (least_upper_bound (inverse ?402968) identity) [402968] by Super 336185 with 2 at 2,1,2,2
% 217.13/54.62 Id : 486, {_}: greatest_lower_bound (least_upper_bound ?1191 ?1192) ?1191 =>= ?1191 [1192, 1191] by Super 5 with 12 at 3
% 217.13/54.62 Id : 487, {_}: greatest_lower_bound (least_upper_bound ?1194 ?1195) ?1195 =>= ?1195 [1195, 1194] by Super 486 with 6 at 1,2
% 217.13/54.62 Id : 1526, {_}: multiply (least_upper_bound identity (multiply ?2919 (inverse ?2920))) ?2920 =>= least_upper_bound (inverse (inverse ?2920)) ?2919 [2920, 2919] by Super 1196 with 220 at 1,2
% 217.13/54.62 Id : 65560, {_}: multiply (least_upper_bound identity (multiply ?79110 (inverse ?79111))) ?79111 =>= least_upper_bound ?79111 ?79110 [79111, 79110] by Demod 1526 with 1217 at 1,3
% 217.13/54.62 Id : 1290, {_}: multiply (inverse ?2509) (least_upper_bound ?2509 ?2510) =>= least_upper_bound identity (multiply (inverse ?2509) ?2510) [2510, 2509] by Super 151 with 3 at 1,3
% 217.13/54.62 Id : 92, {_}: least_upper_bound ?327 (least_upper_bound ?327 ?328) =>= least_upper_bound ?327 ?328 [328, 327] by Super 8 with 9 at 1,3
% 217.13/54.62 Id : 345, {_}: least_upper_bound (least_upper_bound ?890 ?891) ?890 =>= least_upper_bound ?890 ?891 [891, 890] by Super 6 with 92 at 3
% 217.13/54.62 Id : 1298, {_}: multiply (inverse (least_upper_bound ?2533 ?2534)) (least_upper_bound ?2533 ?2534) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?2533 ?2534)) ?2533) [2534, 2533] by Super 1290 with 345 at 2,2
% 217.13/54.62 Id : 1327, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2533 ?2534)) ?2533) [2534, 2533] by Demod 1298 with 3 at 2
% 217.13/54.62 Id : 65596, {_}: multiply identity ?79215 =<= least_upper_bound ?79215 (inverse (least_upper_bound (inverse ?79215) ?79216)) [79216, 79215] by Super 65560 with 1327 at 1,2
% 217.13/54.62 Id : 65687, {_}: ?79215 =<= least_upper_bound ?79215 (inverse (least_upper_bound (inverse ?79215) ?79216)) [79216, 79215] by Demod 65596 with 2 at 2
% 217.13/54.62 Id : 89427, {_}: greatest_lower_bound ?98552 (inverse (least_upper_bound (inverse ?98552) ?98553)) =>= inverse (least_upper_bound (inverse ?98552) ?98553) [98553, 98552] by Super 487 with 65687 at 1,2
% 217.13/54.62 Id : 89429, {_}: greatest_lower_bound (inverse ?98557) (inverse (least_upper_bound ?98557 ?98558)) =>= inverse (least_upper_bound (inverse (inverse ?98557)) ?98558) [98558, 98557] by Super 89427 with 1217 at 1,1,2,2
% 217.13/54.62 Id : 102846, {_}: greatest_lower_bound (inverse ?112210) (inverse (least_upper_bound ?112210 ?112211)) =>= inverse (least_upper_bound ?112210 ?112211) [112211, 112210] by Demod 89429 with 1217 at 1,1,3
% 217.13/54.62 Id : 102847, {_}: greatest_lower_bound (inverse ?112213) (inverse (least_upper_bound ?112214 ?112213)) =>= inverse (least_upper_bound ?112213 ?112214) [112214, 112213] by Super 102846 with 6 at 1,2,2
% 217.13/54.62 Id : 133, {_}: greatest_lower_bound ?451 (least_upper_bound ?452 ?451) =>= ?451 [452, 451] by Super 132 with 6 at 2,2
% 217.13/54.62 Id : 519, {_}: least_upper_bound (least_upper_bound ?1240 ?1241) ?1241 =>= least_upper_bound ?1240 ?1241 [1241, 1240] by Super 115 with 133 at 2,2
% 217.13/54.62 Id : 1301, {_}: multiply (inverse (least_upper_bound ?2542 ?2543)) (least_upper_bound ?2542 ?2543) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?2542 ?2543)) ?2543) [2543, 2542] by Super 1290 with 519 at 2,2
% 217.13/54.62 Id : 1329, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2542 ?2543)) ?2543) [2543, 2542] by Demod 1301 with 3 at 2
% 217.13/54.62 Id : 65597, {_}: multiply identity ?79218 =<= least_upper_bound ?79218 (inverse (least_upper_bound ?79219 (inverse ?79218))) [79219, 79218] by Super 65560 with 1329 at 1,2
% 217.13/54.62 Id : 65688, {_}: ?79218 =<= least_upper_bound ?79218 (inverse (least_upper_bound ?79219 (inverse ?79218))) [79219, 79218] by Demod 65597 with 2 at 2
% 217.13/54.62 Id : 95582, {_}: greatest_lower_bound ?103848 (inverse (least_upper_bound ?103849 (inverse ?103848))) =>= inverse (least_upper_bound ?103849 (inverse ?103848)) [103849, 103848] by Super 487 with 65688 at 1,2
% 217.13/54.62 Id : 95584, {_}: greatest_lower_bound (inverse ?103853) (inverse (least_upper_bound ?103854 ?103853)) =>= inverse (least_upper_bound ?103854 (inverse (inverse ?103853))) [103854, 103853] by Super 95582 with 1217 at 2,1,2,2
% 217.13/54.62 Id : 95958, {_}: greatest_lower_bound (inverse ?103853) (inverse (least_upper_bound ?103854 ?103853)) =>= inverse (least_upper_bound ?103854 ?103853) [103854, 103853] by Demod 95584 with 1217 at 2,1,3
% 217.13/54.62 Id : 105702, {_}: inverse (least_upper_bound ?112214 ?112213) =?= inverse (least_upper_bound ?112213 ?112214) [112213, 112214] by Demod 102847 with 95958 at 2
% 217.13/54.62 Id : 336452, {_}: multiply ?402968 (inverse (least_upper_bound identity ?402968)) =>= inverse (least_upper_bound identity (inverse ?402968)) [402968] by Demod 336186 with 105702 at 3
% 217.13/54.62 Id : 337053, {_}: multiply (inverse (least_upper_bound identity (inverse ?403500))) (least_upper_bound identity ?403500) =>= ?403500 [403500] by Super 1196 with 336452 at 1,2
% 217.13/54.62 Id : 436956, {_}: greatest_lower_bound (least_upper_bound identity (inverse ?473585)) (least_upper_bound identity ?473585) =<= multiply (least_upper_bound identity (inverse ?473585)) (greatest_lower_bound identity ?473585) [473585] by Super 292965 with 337053 at 2,2,3
% 217.13/54.62 Id : 437912, {_}: multiply (greatest_lower_bound identity (greatest_lower_bound (least_upper_bound identity (inverse ?474150)) (least_upper_bound identity ?474150))) (inverse (greatest_lower_bound identity ?474150)) =>= greatest_lower_bound (inverse (greatest_lower_bound identity ?474150)) (least_upper_bound identity (inverse ?474150)) [474150] by Super 1795 with 436956 at 2,1,2
% 217.13/54.62 Id : 127, {_}: greatest_lower_bound ?430 (greatest_lower_bound (least_upper_bound ?430 ?431) ?432) =>= greatest_lower_bound ?430 ?432 [432, 431, 430] by Super 7 with 12 at 1,3
% 217.13/54.62 Id : 438142, {_}: multiply (greatest_lower_bound identity (least_upper_bound identity ?474150)) (inverse (greatest_lower_bound identity ?474150)) =>= greatest_lower_bound (inverse (greatest_lower_bound identity ?474150)) (least_upper_bound identity (inverse ?474150)) [474150] by Demod 437912 with 127 at 1,2
% 217.13/54.62 Id : 438143, {_}: multiply identity (inverse (greatest_lower_bound identity ?474150)) =<= greatest_lower_bound (inverse (greatest_lower_bound identity ?474150)) (least_upper_bound identity (inverse ?474150)) [474150] by Demod 438142 with 12 at 1,2
% 217.13/54.62 Id : 438144, {_}: inverse (greatest_lower_bound identity ?474150) =<= greatest_lower_bound (inverse (greatest_lower_bound identity ?474150)) (least_upper_bound identity (inverse ?474150)) [474150] by Demod 438143 with 2 at 2
% 217.13/54.62 Id : 573560, {_}: least_upper_bound (least_upper_bound identity (inverse ?568960)) (inverse (greatest_lower_bound identity ?568960)) =>= least_upper_bound identity (inverse ?568960) [568960] by Super 115 with 438144 at 2,2
% 217.13/54.62 Id : 574006, {_}: least_upper_bound (inverse (greatest_lower_bound identity ?568960)) (least_upper_bound identity (inverse ?568960)) =>= least_upper_bound identity (inverse ?568960) [568960] by Demod 573560 with 6 at 2
% 217.13/54.62 Id : 416, {_}: least_upper_bound (greatest_lower_bound ?1054 ?1055) ?1054 =>= ?1054 [1055, 1054] by Super 6 with 11 at 3
% 217.13/54.62 Id : 417, {_}: least_upper_bound (greatest_lower_bound ?1057 ?1058) ?1058 =>= ?1058 [1058, 1057] by Super 416 with 5 at 1,2
% 217.13/54.62 Id : 530, {_}: greatest_lower_bound ?1274 (least_upper_bound ?1275 ?1274) =>= ?1274 [1275, 1274] by Super 132 with 6 at 2,2
% 217.13/54.62 Id : 539, {_}: greatest_lower_bound ?1300 (least_upper_bound ?1301 (least_upper_bound ?1302 ?1300)) =>= ?1300 [1302, 1301, 1300] by Super 530 with 8 at 2,2
% 217.13/54.62 Id : 3975, {_}: least_upper_bound ?7595 (least_upper_bound ?7596 (least_upper_bound ?7597 ?7595)) =>= least_upper_bound ?7596 (least_upper_bound ?7597 ?7595) [7597, 7596, 7595] by Super 417 with 539 at 1,2
% 217.13/54.62 Id : 352, {_}: least_upper_bound ?915 (least_upper_bound ?915 ?916) =>= least_upper_bound ?915 ?916 [916, 915] by Super 8 with 9 at 1,3
% 217.13/54.62 Id : 724, {_}: least_upper_bound ?1581 (least_upper_bound ?1582 ?1581) =>= least_upper_bound ?1581 ?1582 [1582, 1581] by Super 352 with 6 at 2,2
% 217.13/54.62 Id : 735, {_}: least_upper_bound ?1614 (least_upper_bound ?1615 (least_upper_bound ?1616 ?1614)) =>= least_upper_bound ?1614 (least_upper_bound ?1615 ?1616) [1616, 1615, 1614] by Super 724 with 8 at 2,2
% 217.13/54.62 Id : 129692, {_}: least_upper_bound ?7595 (least_upper_bound ?7596 ?7597) =?= least_upper_bound ?7596 (least_upper_bound ?7597 ?7595) [7597, 7596, 7595] by Demod 3975 with 735 at 2
% 217.13/54.62 Id : 574007, {_}: least_upper_bound identity (least_upper_bound (inverse ?568960) (inverse (greatest_lower_bound identity ?568960))) =>= least_upper_bound identity (inverse ?568960) [568960] by Demod 574006 with 129692 at 2
% 217.13/54.62 Id : 108, {_}: least_upper_bound (greatest_lower_bound ?371 ?372) ?371 =>= ?371 [372, 371] by Super 6 with 11 at 3
% 217.13/54.62 Id : 8325, {_}: multiply (inverse (greatest_lower_bound ?16236 ?16237)) ?16236 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?16236 ?16237)) ?16236) [16237, 16236] by Super 1290 with 108 at 2,2
% 217.13/54.62 Id : 8357, {_}: multiply (inverse (greatest_lower_bound identity ?16350)) identity =>= least_upper_bound identity (inverse (greatest_lower_bound identity ?16350)) [16350] by Super 8325 with 1195 at 2,3
% 217.13/54.62 Id : 8490, {_}: inverse (greatest_lower_bound identity ?16350) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?16350)) [16350] by Demod 8357 with 1195 at 2
% 217.13/54.62 Id : 9325, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound identity ?17213)) ?17214) =>= least_upper_bound (inverse (greatest_lower_bound identity ?17213)) ?17214 [17214, 17213] by Super 8 with 8490 at 1,3
% 217.13/54.62 Id : 9343, {_}: least_upper_bound identity (least_upper_bound ?17274 (inverse (greatest_lower_bound identity ?17275))) =>= least_upper_bound (inverse (greatest_lower_bound identity ?17275)) ?17274 [17275, 17274] by Super 9325 with 6 at 2,2
% 217.13/54.62 Id : 574008, {_}: least_upper_bound (inverse (greatest_lower_bound identity ?568960)) (inverse ?568960) =>= least_upper_bound identity (inverse ?568960) [568960] by Demod 574007 with 9343 at 2
% 217.13/54.62 Id : 1300, {_}: multiply (inverse (greatest_lower_bound ?2539 ?2540)) ?2540 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2539 ?2540)) ?2540) [2540, 2539] by Super 1290 with 417 at 2,2
% 217.13/54.62 Id : 65595, {_}: multiply (multiply (inverse (greatest_lower_bound ?79212 (inverse ?79213))) (inverse ?79213)) ?79213 =>= least_upper_bound ?79213 (inverse (greatest_lower_bound ?79212 (inverse ?79213))) [79213, 79212] by Super 65560 with 1300 at 1,2
% 217.13/54.62 Id : 65684, {_}: multiply (inverse (greatest_lower_bound ?79212 (inverse ?79213))) (multiply (inverse ?79213) ?79213) =>= least_upper_bound ?79213 (inverse (greatest_lower_bound ?79212 (inverse ?79213))) [79213, 79212] by Demod 65595 with 4 at 2
% 217.13/54.62 Id : 65685, {_}: multiply (inverse (greatest_lower_bound ?79212 (inverse ?79213))) identity =?= least_upper_bound ?79213 (inverse (greatest_lower_bound ?79212 (inverse ?79213))) [79213, 79212] by Demod 65684 with 3 at 2,2
% 217.13/54.62 Id : 65686, {_}: inverse (greatest_lower_bound ?79212 (inverse ?79213)) =<= least_upper_bound ?79213 (inverse (greatest_lower_bound ?79212 (inverse ?79213))) [79213, 79212] by Demod 65685 with 1195 at 2
% 217.13/54.62 Id : 87594, {_}: least_upper_bound (inverse (greatest_lower_bound ?96746 (inverse ?96747))) ?96747 =>= inverse (greatest_lower_bound ?96746 (inverse ?96747)) [96747, 96746] by Super 6 with 65686 at 3
% 217.13/54.62 Id : 87596, {_}: least_upper_bound (inverse (greatest_lower_bound ?96751 ?96752)) (inverse ?96752) =>= inverse (greatest_lower_bound ?96751 (inverse (inverse ?96752))) [96752, 96751] by Super 87594 with 1217 at 2,1,1,2
% 217.13/54.62 Id : 87983, {_}: least_upper_bound (inverse (greatest_lower_bound ?96751 ?96752)) (inverse ?96752) =>= inverse (greatest_lower_bound ?96751 ?96752) [96752, 96751] by Demod 87596 with 1217 at 2,1,3
% 217.13/54.62 Id : 574009, {_}: inverse (greatest_lower_bound identity ?568960) =<= least_upper_bound identity (inverse ?568960) [568960] by Demod 574008 with 87983 at 2
% 217.13/54.62 Id : 1296, {_}: multiply (inverse (greatest_lower_bound ?2527 ?2528)) ?2527 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2527 ?2528)) ?2527) [2528, 2527] by Super 1290 with 108 at 2,2
% 217.13/54.62 Id : 65594, {_}: multiply (multiply (inverse (greatest_lower_bound (inverse ?79209) ?79210)) (inverse ?79209)) ?79209 =>= least_upper_bound ?79209 (inverse (greatest_lower_bound (inverse ?79209) ?79210)) [79210, 79209] by Super 65560 with 1296 at 1,2
% 217.13/54.62 Id : 65681, {_}: multiply (inverse (greatest_lower_bound (inverse ?79209) ?79210)) (multiply (inverse ?79209) ?79209) =>= least_upper_bound ?79209 (inverse (greatest_lower_bound (inverse ?79209) ?79210)) [79210, 79209] by Demod 65594 with 4 at 2
% 217.13/54.62 Id : 65682, {_}: multiply (inverse (greatest_lower_bound (inverse ?79209) ?79210)) identity =?= least_upper_bound ?79209 (inverse (greatest_lower_bound (inverse ?79209) ?79210)) [79210, 79209] by Demod 65681 with 3 at 2,2
% 217.13/54.62 Id : 65806, {_}: inverse (greatest_lower_bound (inverse ?79589) ?79590) =<= least_upper_bound ?79589 (inverse (greatest_lower_bound (inverse ?79589) ?79590)) [79590, 79589] by Demod 65682 with 1195 at 2
% 217.13/54.62 Id : 65808, {_}: inverse (greatest_lower_bound (inverse (inverse ?79594)) ?79595) =<= least_upper_bound (inverse ?79594) (inverse (greatest_lower_bound ?79594 ?79595)) [79595, 79594] by Super 65806 with 1217 at 1,1,2,3
% 217.13/54.62 Id : 84264, {_}: inverse (greatest_lower_bound ?93876 ?93877) =<= least_upper_bound (inverse ?93876) (inverse (greatest_lower_bound ?93876 ?93877)) [93877, 93876] by Demod 65808 with 1217 at 1,1,2
% 217.13/54.62 Id : 84265, {_}: inverse (greatest_lower_bound ?93879 ?93880) =<= least_upper_bound (inverse ?93879) (inverse (greatest_lower_bound ?93880 ?93879)) [93880, 93879] by Super 84264 with 5 at 1,2,3
% 217.13/54.62 Id : 72083, {_}: inverse (greatest_lower_bound ?83714 (inverse ?83715)) =<= least_upper_bound ?83715 (inverse (greatest_lower_bound ?83714 (inverse ?83715))) [83715, 83714] by Demod 65685 with 1195 at 2
% 217.13/54.62 Id : 72085, {_}: inverse (greatest_lower_bound ?83719 (inverse (inverse ?83720))) =<= least_upper_bound (inverse ?83720) (inverse (greatest_lower_bound ?83719 ?83720)) [83720, 83719] by Super 72083 with 1217 at 2,1,2,3
% 217.13/54.62 Id : 72388, {_}: inverse (greatest_lower_bound ?83719 ?83720) =<= least_upper_bound (inverse ?83720) (inverse (greatest_lower_bound ?83719 ?83720)) [83720, 83719] by Demod 72085 with 1217 at 2,1,2
% 217.13/54.62 Id : 98554, {_}: inverse (greatest_lower_bound ?93879 ?93880) =?= inverse (greatest_lower_bound ?93880 ?93879) [93880, 93879] by Demod 84265 with 72388 at 3
% 217.13/54.62 Id : 576184, {_}: inverse (greatest_lower_bound a identity) === inverse (greatest_lower_bound a identity) [] by Demod 576183 with 98554 at 2
% 217.13/54.62 Id : 576183, {_}: inverse (greatest_lower_bound identity a) =>= inverse (greatest_lower_bound a identity) [] by Demod 274 with 574009 at 2
% 217.13/54.62 Id : 274, {_}: least_upper_bound identity (inverse a) =>= inverse (greatest_lower_bound a identity) [] by Demod 1 with 6 at 2
% 217.13/54.62 Id : 1, {_}: least_upper_bound (inverse a) identity =>= inverse (greatest_lower_bound a identity) [] by prove_p18
% 217.13/54.62 % SZS output end CNFRefutation for theBenchmark.p
% 217.13/54.62 17722: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 54.26211 using nrkbo
%------------------------------------------------------------------------------