TSTP Solution File: GRP180-1 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP180-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/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 : Sat Jul 16 10:29:25 EDT 2022
% Result : Unsatisfiable 283.54s 71.23s
% Output : CNFRefutation 283.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP180-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.15 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 14:04:54 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 14105: Facts:
% 0.15/0.37 14105: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.15/0.37 14105: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.15/0.37 14105: Id : 4, {_}:
% 0.15/0.37 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.15/0.37 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.15/0.37 14105: Id : 5, {_}:
% 0.15/0.37 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
% 0.15/0.37 [11, 10] by symmetry_of_glb ?10 ?11
% 0.15/0.37 14105: Id : 6, {_}:
% 0.15/0.37 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
% 0.15/0.37 [14, 13] by symmetry_of_lub ?13 ?14
% 0.15/0.37 14105: Id : 7, {_}:
% 0.15/0.37 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
% 0.15/0.37 =?=
% 0.15/0.37 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
% 0.15/0.37 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 0.15/0.37 14105: Id : 8, {_}:
% 0.15/0.37 least_upper_bound ?20 (least_upper_bound ?21 ?22)
% 0.15/0.37 =?=
% 0.15/0.37 least_upper_bound (least_upper_bound ?20 ?21) ?22
% 0.15/0.37 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 0.15/0.37 14105: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.15/0.37 14105: Id : 10, {_}:
% 0.15/0.37 greatest_lower_bound ?26 ?26 =>= ?26
% 0.15/0.37 [26] by idempotence_of_gld ?26
% 0.15/0.37 14105: Id : 11, {_}:
% 0.15/0.37 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
% 0.15/0.37 [29, 28] by lub_absorbtion ?28 ?29
% 0.15/0.37 14105: Id : 12, {_}:
% 0.15/0.37 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
% 0.15/0.37 [32, 31] by glb_absorbtion ?31 ?32
% 0.15/0.37 14105: Id : 13, {_}:
% 0.15/0.37 multiply ?34 (least_upper_bound ?35 ?36)
% 0.15/0.37 =<=
% 0.15/0.37 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
% 0.15/0.37 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 0.15/0.37 14105: Id : 14, {_}:
% 0.15/0.37 multiply ?38 (greatest_lower_bound ?39 ?40)
% 0.15/0.37 =<=
% 0.15/0.37 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
% 0.15/0.37 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 0.15/0.37 14105: Id : 15, {_}:
% 0.15/0.37 multiply (least_upper_bound ?42 ?43) ?44
% 0.15/0.37 =<=
% 0.15/0.37 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
% 0.15/0.37 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 0.15/0.37 14105: Id : 16, {_}:
% 0.15/0.37 multiply (greatest_lower_bound ?46 ?47) ?48
% 0.15/0.37 =<=
% 0.15/0.37 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
% 0.15/0.37 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 0.15/0.37 14105: Goal:
% 0.15/0.37 14105: Id : 1, {_}:
% 0.15/0.37 multiply a (multiply (inverse (greatest_lower_bound a b)) b)
% 0.15/0.37 =>=
% 0.15/0.37 least_upper_bound a b
% 0.15/0.37 [] by prove_p11
% 283.54/71.23 Statistics :
% 283.54/71.23 Max weight : 22
% 283.54/71.23 Found proof, 70.862285s
% 283.54/71.23 % SZS status Unsatisfiable for theBenchmark.p
% 283.54/71.23 % SZS output start CNFRefutation for theBenchmark.p
% 283.54/71.23 Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 283.54/71.23 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 283.54/71.23 Id : 10, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
% 283.54/71.23 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
% 283.54/71.23 Id : 132, {_}: greatest_lower_bound ?448 (least_upper_bound ?448 ?449) =>= ?448 [449, 448] by glb_absorbtion ?448 ?449
% 283.54/71.23 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 283.54/71.23 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
% 283.54/71.23 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
% 283.54/71.23 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
% 283.54/71.23 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
% 283.54/71.23 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
% 283.54/71.23 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
% 283.54/71.23 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 283.54/71.23 Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =?= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
% 283.54/71.23 Id : 114, {_}: least_upper_bound ?393 (greatest_lower_bound ?393 ?394) =>= ?393 [394, 393] by lub_absorbtion ?393 ?394
% 283.54/71.23 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
% 283.54/71.23 Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
% 283.54/71.23 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 283.54/71.23 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 283.54/71.23 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
% 283.54/71.23 Id : 1289, {_}: 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
% 283.54/71.23 Id : 108, {_}: least_upper_bound (greatest_lower_bound ?371 ?372) ?371 =>= ?371 [372, 371] by Super 6 with 11 at 3
% 283.54/71.23 Id : 8324, {_}: multiply (inverse (greatest_lower_bound ?16236 ?16237)) ?16236 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?16236 ?16237)) ?16236) [16237, 16236] by Super 1289 with 108 at 2,2
% 283.54/71.23 Id : 8325, {_}: multiply (inverse (greatest_lower_bound ?16239 ?16240)) ?16239 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?16240 ?16239)) ?16239) [16240, 16239] by Super 8324 with 5 at 1,1,2,3
% 283.54/71.23 Id : 415, {_}: least_upper_bound (greatest_lower_bound ?1054 ?1055) ?1054 =>= ?1054 [1055, 1054] by Super 6 with 11 at 3
% 283.54/71.23 Id : 416, {_}: least_upper_bound (greatest_lower_bound ?1057 ?1058) ?1058 =>= ?1058 [1058, 1057] by Super 415 with 5 at 1,2
% 283.54/71.23 Id : 1299, {_}: multiply (inverse (greatest_lower_bound ?2539 ?2540)) ?2540 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2539 ?2540)) ?2540) [2540, 2539] by Super 1289 with 416 at 2,2
% 283.54/71.23 Id : 151295, {_}: multiply (inverse (greatest_lower_bound ?16239 ?16240)) ?16239 =?= multiply (inverse (greatest_lower_bound ?16240 ?16239)) ?16239 [16240, 16239] by Demod 8325 with 1299 at 3
% 283.54/71.23 Id : 115, {_}: least_upper_bound ?396 (greatest_lower_bound ?397 ?396) =>= ?396 [397, 396] by Super 114 with 5 at 2,2
% 283.54/71.23 Id : 23, {_}: multiply (multiply ?64 (inverse ?65)) ?65 =>= multiply ?64 identity [65, 64] by Super 21 with 3 at 2,3
% 283.54/71.23 Id : 1158, {_}: multiply (multiply ?2285 (inverse ?2286)) ?2286 =>= multiply ?2285 identity [2286, 2285] by Super 21 with 3 at 2,3
% 283.54/71.23 Id : 1161, {_}: multiply identity ?2292 =<= multiply (inverse (inverse ?2292)) identity [2292] by Super 1158 with 3 at 1,2
% 283.54/71.23 Id : 1174, {_}: ?2292 =<= multiply (inverse (inverse ?2292)) identity [2292] by Demod 1161 with 2 at 2
% 283.54/71.23 Id : 22, {_}: multiply (multiply ?61 identity) ?62 =>= multiply ?61 ?62 [62, 61] by Super 21 with 2 at 2,3
% 283.54/71.23 Id : 1179, {_}: multiply ?2313 ?2314 =<= multiply (inverse (inverse ?2313)) ?2314 [2314, 2313] by Super 22 with 1174 at 1,2
% 283.54/71.23 Id : 1194, {_}: ?2292 =<= multiply ?2292 identity [2292] by Demod 1174 with 1179 at 3
% 283.54/71.23 Id : 1195, {_}: multiply (multiply ?64 (inverse ?65)) ?65 =>= ?64 [65, 64] by Demod 23 with 1194 at 3
% 283.54/71.23 Id : 1210, {_}: inverse (inverse ?2400) =<= multiply ?2400 identity [2400] by Super 1194 with 1179 at 3
% 283.54/71.23 Id : 1216, {_}: inverse (inverse ?2400) =>= ?2400 [2400] by Demod 1210 with 1194 at 3
% 283.54/71.23 Id : 1782, {_}: multiply (multiply ?3260 ?3261) (inverse ?3261) =>= ?3260 [3261, 3260] by Super 1195 with 1216 at 2,1,2
% 283.54/71.23 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
% 283.54/71.23 Id : 1794, {_}: multiply (greatest_lower_bound identity (multiply ?3294 ?3295)) (inverse ?3295) =>= greatest_lower_bound (inverse ?3295) ?3294 [3295, 3294] by Super 1782 with 252 at 1,2
% 283.54/71.23 Id : 1149, {_}: multiply (multiply ?2250 (multiply ?2251 (inverse ?2252))) ?2252 =>= multiply ?2250 (multiply ?2251 identity) [2252, 2251, 2250] by Super 4 with 23 at 2,3
% 283.54/71.23 Id : 290554, {_}: multiply (multiply ?359403 (multiply ?359404 (inverse ?359405))) ?359405 =>= multiply ?359403 ?359404 [359405, 359404, 359403] by Demod 1149 with 1194 at 2,3
% 283.54/71.23 Id : 290640, {_}: multiply identity ?359756 =<= multiply (inverse (multiply ?359757 (inverse ?359756))) ?359757 [359757, 359756] by Super 290554 with 3 at 1,2
% 283.54/71.23 Id : 290961, {_}: ?360161 =<= multiply (inverse (multiply ?360162 (inverse ?360161))) ?360162 [360162, 360161] by Demod 290640 with 2 at 2
% 283.54/71.23 Id : 1242, {_}: multiply (multiply ?2416 ?2417) (inverse ?2417) =>= ?2416 [2417, 2416] by Super 1195 with 1216 at 2,1,2
% 283.54/71.23 Id : 292811, {_}: ?362795 =<= multiply (inverse ?362796) (multiply ?362796 ?362795) [362796, 362795] by Super 290961 with 1242 at 1,1,3
% 283.54/71.23 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
% 283.54/71.23 Id : 292817, {_}: greatest_lower_bound ?362812 ?362813 =<= multiply (inverse (inverse ?362812)) (greatest_lower_bound identity (multiply (inverse ?362812) ?362813)) [362813, 362812] by Super 292811 with 187 at 2,3
% 283.54/71.23 Id : 292964, {_}: greatest_lower_bound ?362812 ?362813 =<= multiply ?362812 (greatest_lower_bound identity (multiply (inverse ?362812) ?362813)) [362813, 362812] by Demod 292817 with 1216 at 1,3
% 283.54/71.23 Id : 290852, {_}: ?359756 =<= multiply (inverse (multiply ?359757 (inverse ?359756))) ?359757 [359757, 359756] by Demod 290640 with 2 at 2
% 283.54/71.23 Id : 291302, {_}: multiply ?360847 (inverse ?360848) =<= inverse (multiply ?360848 (inverse ?360847)) [360848, 360847] by Super 1242 with 290852 at 1,2
% 283.54/71.23 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
% 283.54/71.23 Id : 1792, {_}: multiply (least_upper_bound identity (multiply ?3288 ?3289)) (inverse ?3289) =>= least_upper_bound (inverse ?3289) ?3288 [3289, 3288] by Super 1782 with 220 at 1,2
% 283.54/71.23 Id : 336184, {_}: multiply ?402965 (inverse (least_upper_bound identity (multiply ?402966 ?402965))) =>= inverse (least_upper_bound (inverse ?402965) ?402966) [402966, 402965] by Super 291302 with 1792 at 1,3
% 283.54/71.23 Id : 336185, {_}: multiply ?402968 (inverse (least_upper_bound identity ?402968)) =>= inverse (least_upper_bound (inverse ?402968) identity) [402968] by Super 336184 with 2 at 2,1,2,2
% 283.54/71.23 Id : 485, {_}: greatest_lower_bound (least_upper_bound ?1191 ?1192) ?1191 =>= ?1191 [1192, 1191] by Super 5 with 12 at 3
% 283.54/71.23 Id : 486, {_}: greatest_lower_bound (least_upper_bound ?1194 ?1195) ?1195 =>= ?1195 [1195, 1194] by Super 485 with 6 at 1,2
% 283.54/71.23 Id : 1525, {_}: multiply (least_upper_bound identity (multiply ?2919 (inverse ?2920))) ?2920 =>= least_upper_bound (inverse (inverse ?2920)) ?2919 [2920, 2919] by Super 1195 with 220 at 1,2
% 283.54/71.23 Id : 65559, {_}: multiply (least_upper_bound identity (multiply ?79110 (inverse ?79111))) ?79111 =>= least_upper_bound ?79111 ?79110 [79111, 79110] by Demod 1525 with 1216 at 1,3
% 283.54/71.23 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
% 283.54/71.23 Id : 344, {_}: least_upper_bound (least_upper_bound ?890 ?891) ?890 =>= least_upper_bound ?890 ?891 [891, 890] by Super 6 with 92 at 3
% 283.54/71.23 Id : 1297, {_}: 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 1289 with 344 at 2,2
% 283.54/71.23 Id : 1326, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2533 ?2534)) ?2533) [2534, 2533] by Demod 1297 with 3 at 2
% 283.54/71.23 Id : 65595, {_}: multiply identity ?79215 =<= least_upper_bound ?79215 (inverse (least_upper_bound (inverse ?79215) ?79216)) [79216, 79215] by Super 65559 with 1326 at 1,2
% 283.54/71.23 Id : 65686, {_}: ?79215 =<= least_upper_bound ?79215 (inverse (least_upper_bound (inverse ?79215) ?79216)) [79216, 79215] by Demod 65595 with 2 at 2
% 283.54/71.23 Id : 89426, {_}: greatest_lower_bound ?98552 (inverse (least_upper_bound (inverse ?98552) ?98553)) =>= inverse (least_upper_bound (inverse ?98552) ?98553) [98553, 98552] by Super 486 with 65686 at 1,2
% 283.54/71.23 Id : 89428, {_}: greatest_lower_bound (inverse ?98557) (inverse (least_upper_bound ?98557 ?98558)) =>= inverse (least_upper_bound (inverse (inverse ?98557)) ?98558) [98558, 98557] by Super 89426 with 1216 at 1,1,2,2
% 283.54/71.23 Id : 102845, {_}: greatest_lower_bound (inverse ?112210) (inverse (least_upper_bound ?112210 ?112211)) =>= inverse (least_upper_bound ?112210 ?112211) [112211, 112210] by Demod 89428 with 1216 at 1,1,3
% 283.54/71.23 Id : 102846, {_}: greatest_lower_bound (inverse ?112213) (inverse (least_upper_bound ?112214 ?112213)) =>= inverse (least_upper_bound ?112213 ?112214) [112214, 112213] by Super 102845 with 6 at 1,2,2
% 283.54/71.23 Id : 133, {_}: greatest_lower_bound ?451 (least_upper_bound ?452 ?451) =>= ?451 [452, 451] by Super 132 with 6 at 2,2
% 283.54/71.23 Id : 518, {_}: least_upper_bound (least_upper_bound ?1240 ?1241) ?1241 =>= least_upper_bound ?1240 ?1241 [1241, 1240] by Super 115 with 133 at 2,2
% 283.54/71.23 Id : 1300, {_}: 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 1289 with 518 at 2,2
% 283.54/71.23 Id : 1328, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2542 ?2543)) ?2543) [2543, 2542] by Demod 1300 with 3 at 2
% 283.54/71.23 Id : 65596, {_}: multiply identity ?79218 =<= least_upper_bound ?79218 (inverse (least_upper_bound ?79219 (inverse ?79218))) [79219, 79218] by Super 65559 with 1328 at 1,2
% 283.54/71.23 Id : 65687, {_}: ?79218 =<= least_upper_bound ?79218 (inverse (least_upper_bound ?79219 (inverse ?79218))) [79219, 79218] by Demod 65596 with 2 at 2
% 283.54/71.23 Id : 95581, {_}: greatest_lower_bound ?103848 (inverse (least_upper_bound ?103849 (inverse ?103848))) =>= inverse (least_upper_bound ?103849 (inverse ?103848)) [103849, 103848] by Super 486 with 65687 at 1,2
% 283.54/71.23 Id : 95583, {_}: greatest_lower_bound (inverse ?103853) (inverse (least_upper_bound ?103854 ?103853)) =>= inverse (least_upper_bound ?103854 (inverse (inverse ?103853))) [103854, 103853] by Super 95581 with 1216 at 2,1,2,2
% 283.54/71.23 Id : 95957, {_}: greatest_lower_bound (inverse ?103853) (inverse (least_upper_bound ?103854 ?103853)) =>= inverse (least_upper_bound ?103854 ?103853) [103854, 103853] by Demod 95583 with 1216 at 2,1,3
% 283.54/71.23 Id : 105701, {_}: inverse (least_upper_bound ?112214 ?112213) =?= inverse (least_upper_bound ?112213 ?112214) [112213, 112214] by Demod 102846 with 95957 at 2
% 283.54/71.23 Id : 336451, {_}: multiply ?402968 (inverse (least_upper_bound identity ?402968)) =>= inverse (least_upper_bound identity (inverse ?402968)) [402968] by Demod 336185 with 105701 at 3
% 283.54/71.23 Id : 337052, {_}: multiply (inverse (least_upper_bound identity (inverse ?403500))) (least_upper_bound identity ?403500) =>= ?403500 [403500] by Super 1195 with 336451 at 1,2
% 283.54/71.23 Id : 436955, {_}: 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 292964 with 337052 at 2,2,3
% 283.54/71.23 Id : 437911, {_}: 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 1794 with 436955 at 2,1,2
% 283.54/71.23 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
% 283.54/71.23 Id : 438141, {_}: 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 437911 with 127 at 1,2
% 283.54/71.23 Id : 438142, {_}: 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 438141 with 12 at 1,2
% 283.54/71.23 Id : 438143, {_}: 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 2 at 2
% 283.54/71.23 Id : 573559, {_}: 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 438143 at 2,2
% 283.54/71.23 Id : 574005, {_}: least_upper_bound (inverse (greatest_lower_bound identity ?568960)) (least_upper_bound identity (inverse ?568960)) =>= least_upper_bound identity (inverse ?568960) [568960] by Demod 573559 with 6 at 2
% 283.54/71.23 Id : 529, {_}: greatest_lower_bound ?1274 (least_upper_bound ?1275 ?1274) =>= ?1274 [1275, 1274] by Super 132 with 6 at 2,2
% 283.54/71.23 Id : 538, {_}: greatest_lower_bound ?1300 (least_upper_bound ?1301 (least_upper_bound ?1302 ?1300)) =>= ?1300 [1302, 1301, 1300] by Super 529 with 8 at 2,2
% 283.54/71.23 Id : 3974, {_}: 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 416 with 538 at 1,2
% 283.54/71.23 Id : 351, {_}: least_upper_bound ?915 (least_upper_bound ?915 ?916) =>= least_upper_bound ?915 ?916 [916, 915] by Super 8 with 9 at 1,3
% 283.54/71.23 Id : 723, {_}: least_upper_bound ?1581 (least_upper_bound ?1582 ?1581) =>= least_upper_bound ?1581 ?1582 [1582, 1581] by Super 351 with 6 at 2,2
% 283.54/71.23 Id : 734, {_}: 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 723 with 8 at 2,2
% 283.54/71.23 Id : 129691, {_}: least_upper_bound ?7595 (least_upper_bound ?7596 ?7597) =?= least_upper_bound ?7596 (least_upper_bound ?7597 ?7595) [7597, 7596, 7595] by Demod 3974 with 734 at 2
% 283.54/71.24 Id : 574006, {_}: least_upper_bound identity (least_upper_bound (inverse ?568960) (inverse (greatest_lower_bound identity ?568960))) =>= least_upper_bound identity (inverse ?568960) [568960] by Demod 574005 with 129691 at 2
% 283.54/71.24 Id : 8356, {_}: multiply (inverse (greatest_lower_bound identity ?16350)) identity =>= least_upper_bound identity (inverse (greatest_lower_bound identity ?16350)) [16350] by Super 8324 with 1194 at 2,3
% 283.54/71.24 Id : 8489, {_}: inverse (greatest_lower_bound identity ?16350) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?16350)) [16350] by Demod 8356 with 1194 at 2
% 283.54/71.24 Id : 9324, {_}: 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 8489 at 1,3
% 283.54/71.24 Id : 9342, {_}: 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 9324 with 6 at 2,2
% 283.54/71.24 Id : 574007, {_}: least_upper_bound (inverse (greatest_lower_bound identity ?568960)) (inverse ?568960) =>= least_upper_bound identity (inverse ?568960) [568960] by Demod 574006 with 9342 at 2
% 283.54/71.24 Id : 65594, {_}: 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 65559 with 1299 at 1,2
% 283.54/71.24 Id : 65683, {_}: 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 65594 with 4 at 2
% 283.54/71.24 Id : 65684, {_}: multiply (inverse (greatest_lower_bound ?79212 (inverse ?79213))) identity =?= least_upper_bound ?79213 (inverse (greatest_lower_bound ?79212 (inverse ?79213))) [79213, 79212] by Demod 65683 with 3 at 2,2
% 283.54/71.24 Id : 65685, {_}: inverse (greatest_lower_bound ?79212 (inverse ?79213)) =<= least_upper_bound ?79213 (inverse (greatest_lower_bound ?79212 (inverse ?79213))) [79213, 79212] by Demod 65684 with 1194 at 2
% 283.54/71.24 Id : 87593, {_}: least_upper_bound (inverse (greatest_lower_bound ?96746 (inverse ?96747))) ?96747 =>= inverse (greatest_lower_bound ?96746 (inverse ?96747)) [96747, 96746] by Super 6 with 65685 at 3
% 283.54/71.24 Id : 87595, {_}: least_upper_bound (inverse (greatest_lower_bound ?96751 ?96752)) (inverse ?96752) =>= inverse (greatest_lower_bound ?96751 (inverse (inverse ?96752))) [96752, 96751] by Super 87593 with 1216 at 2,1,1,2
% 283.54/71.24 Id : 87982, {_}: least_upper_bound (inverse (greatest_lower_bound ?96751 ?96752)) (inverse ?96752) =>= inverse (greatest_lower_bound ?96751 ?96752) [96752, 96751] by Demod 87595 with 1216 at 2,1,3
% 283.54/71.24 Id : 575239, {_}: inverse (greatest_lower_bound identity ?570230) =<= least_upper_bound identity (inverse ?570230) [570230] by Demod 574007 with 87982 at 2
% 283.54/71.24 Id : 291677, {_}: multiply (inverse ?361337) (inverse ?361338) =>= inverse (multiply ?361338 ?361337) [361338, 361337] by Super 291302 with 1216 at 2,1,3
% 283.54/71.24 Id : 291679, {_}: multiply (inverse ?361342) ?361343 =<= inverse (multiply (inverse ?361343) ?361342) [361343, 361342] by Super 291677 with 1216 at 2,2
% 283.54/71.24 Id : 604939, {_}: inverse (greatest_lower_bound identity (multiply (inverse ?587621) ?587622)) =>= least_upper_bound identity (multiply (inverse ?587622) ?587621) [587622, 587621] by Super 575239 with 291679 at 2,3
% 283.54/71.24 Id : 604980, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply (inverse ?587768) ?587769))) =?= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?587768 ?587769)) ?587768) [587769, 587768] by Super 604939 with 187 at 2,1,2
% 283.54/71.24 Id : 100, {_}: greatest_lower_bound ?349 (greatest_lower_bound ?349 ?350) =>= greatest_lower_bound ?349 ?350 [350, 349] by Super 7 with 10 at 1,3
% 283.54/71.24 Id : 605650, {_}: inverse (greatest_lower_bound identity (multiply (inverse ?587768) ?587769)) =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?587768 ?587769)) ?587768) [587769, 587768] by Demod 604980 with 100 at 1,2
% 283.54/71.24 Id : 1295, {_}: multiply (inverse (greatest_lower_bound ?2527 ?2528)) ?2527 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2527 ?2528)) ?2527) [2528, 2527] by Super 1289 with 108 at 2,2
% 283.54/71.24 Id : 605651, {_}: inverse (greatest_lower_bound identity (multiply (inverse ?587768) ?587769)) =?= multiply (inverse (greatest_lower_bound ?587768 ?587769)) ?587768 [587769, 587768] by Demod 605650 with 1295 at 3
% 283.54/71.24 Id : 575265, {_}: inverse (greatest_lower_bound identity (multiply (inverse ?570305) ?570306)) =>= least_upper_bound identity (multiply (inverse ?570306) ?570305) [570306, 570305] by Super 575239 with 291679 at 2,3
% 283.54/71.24 Id : 605652, {_}: least_upper_bound identity (multiply (inverse ?587769) ?587768) =<= multiply (inverse (greatest_lower_bound ?587768 ?587769)) ?587768 [587768, 587769] by Demod 605651 with 575265 at 2
% 283.54/71.24 Id : 644039, {_}: least_upper_bound identity (multiply (inverse ?16240) ?16239) =<= multiply (inverse (greatest_lower_bound ?16240 ?16239)) ?16239 [16239, 16240] by Demod 151295 with 605652 at 2
% 283.54/71.24 Id : 340602, {_}: multiply ?405818 (inverse (greatest_lower_bound identity (multiply ?405819 ?405818))) =>= inverse (greatest_lower_bound (inverse ?405818) ?405819) [405819, 405818] by Super 291302 with 1794 at 1,3
% 283.54/71.24 Id : 290963, {_}: inverse ?360166 =<= multiply (inverse (multiply ?360167 ?360166)) ?360167 [360167, 360166] by Super 290961 with 1216 at 2,1,1,3
% 283.54/71.24 Id : 340711, {_}: multiply ?406135 (inverse (greatest_lower_bound identity (inverse ?406136))) =<= inverse (greatest_lower_bound (inverse ?406135) (inverse (multiply ?406135 ?406136))) [406136, 406135] by Super 340602 with 290963 at 2,1,2,2
% 283.54/71.24 Id : 1241, {_}: multiply ?2414 (inverse ?2414) =>= identity [2414] by Super 3 with 1216 at 1,2
% 283.54/71.24 Id : 1257, {_}: multiply ?2450 (least_upper_bound (inverse ?2450) ?2451) =>= least_upper_bound identity (multiply ?2450 ?2451) [2451, 2450] by Super 13 with 1241 at 1,3
% 283.54/71.24 Id : 364896, {_}: least_upper_bound (inverse ?419141) ?419142 =<= multiply (inverse ?419141) (least_upper_bound identity (multiply ?419141 ?419142)) [419142, 419141] by Super 292811 with 1257 at 2,3
% 283.54/71.24 Id : 291304, {_}: multiply (inverse ?360852) (inverse ?360853) =>= inverse (multiply ?360853 ?360852) [360853, 360852] by Super 291302 with 1216 at 2,1,3
% 283.54/71.24 Id : 364978, {_}: least_upper_bound (inverse (inverse ?419376)) (inverse ?419377) =<= multiply (inverse (inverse ?419376)) (least_upper_bound identity (inverse (multiply ?419377 ?419376))) [419377, 419376] by Super 364896 with 291304 at 2,2,3
% 283.54/71.24 Id : 365361, {_}: least_upper_bound ?419376 (inverse ?419377) =<= multiply (inverse (inverse ?419376)) (least_upper_bound identity (inverse (multiply ?419377 ?419376))) [419377, 419376] by Demod 364978 with 1216 at 1,2
% 283.54/71.24 Id : 365362, {_}: least_upper_bound ?419376 (inverse ?419377) =<= multiply ?419376 (least_upper_bound identity (inverse (multiply ?419377 ?419376))) [419377, 419376] by Demod 365361 with 1216 at 1,3
% 283.54/71.24 Id : 574008, {_}: inverse (greatest_lower_bound identity ?568960) =<= least_upper_bound identity (inverse ?568960) [568960] by Demod 574007 with 87982 at 2
% 283.54/71.24 Id : 574838, {_}: least_upper_bound ?419376 (inverse ?419377) =<= multiply ?419376 (inverse (greatest_lower_bound identity (multiply ?419377 ?419376))) [419377, 419376] by Demod 365362 with 574008 at 2,3
% 283.54/71.24 Id : 291340, {_}: multiply ?360977 (inverse (greatest_lower_bound identity (multiply ?360978 ?360977))) =>= inverse (greatest_lower_bound (inverse ?360977) ?360978) [360978, 360977] by Super 291302 with 1794 at 1,3
% 283.54/71.24 Id : 574845, {_}: least_upper_bound ?419376 (inverse ?419377) =<= inverse (greatest_lower_bound (inverse ?419376) ?419377) [419377, 419376] by Demod 574838 with 291340 at 3
% 283.54/71.24 Id : 574859, {_}: multiply ?406135 (inverse (greatest_lower_bound identity (inverse ?406136))) =?= least_upper_bound ?406135 (inverse (inverse (multiply ?406135 ?406136))) [406136, 406135] by Demod 340711 with 574845 at 3
% 283.54/71.24 Id : 574869, {_}: multiply ?406135 (inverse (greatest_lower_bound identity (inverse ?406136))) =?= least_upper_bound ?406135 (multiply ?406135 ?406136) [406136, 406135] by Demod 574859 with 1216 at 2,3
% 283.54/71.24 Id : 1828, {_}: multiply (greatest_lower_bound ?3367 ?3368) (inverse ?3367) =>= greatest_lower_bound identity (multiply ?3368 (inverse ?3367)) [3368, 3367] by Super 16 with 1241 at 1,3
% 283.54/71.24 Id : 125, {_}: greatest_lower_bound (least_upper_bound ?424 ?425) ?424 =>= ?424 [425, 424] by Super 5 with 12 at 3
% 283.54/71.24 Id : 108051, {_}: multiply ?118031 (inverse (least_upper_bound ?118031 ?118032)) =<= greatest_lower_bound identity (multiply ?118031 (inverse (least_upper_bound ?118031 ?118032))) [118032, 118031] by Super 1828 with 125 at 1,2
% 283.54/71.24 Id : 108052, {_}: multiply ?118034 (inverse (least_upper_bound ?118034 ?118035)) =<= greatest_lower_bound identity (multiply ?118034 (inverse (least_upper_bound ?118035 ?118034))) [118035, 118034] by Super 108051 with 6 at 1,2,2,3
% 283.54/71.24 Id : 1840, {_}: multiply ?3402 (inverse (least_upper_bound ?3403 ?3402)) =<= greatest_lower_bound identity (multiply ?3402 (inverse (least_upper_bound ?3403 ?3402))) [3403, 3402] by Super 1828 with 486 at 1,2
% 283.54/71.24 Id : 213345, {_}: multiply ?118034 (inverse (least_upper_bound ?118034 ?118035)) =?= multiply ?118034 (inverse (least_upper_bound ?118035 ?118034)) [118035, 118034] by Demod 108052 with 1840 at 3
% 283.54/71.24 Id : 575188, {_}: multiply (inverse ?570109) (inverse (least_upper_bound (inverse ?570109) identity)) =>= multiply (inverse ?570109) (inverse (inverse (greatest_lower_bound identity ?570109))) [570109] by Super 213345 with 574008 at 1,2,2
% 283.54/71.24 Id : 575440, {_}: multiply (inverse ?570109) (inverse (least_upper_bound identity (inverse ?570109))) =>= multiply (inverse ?570109) (inverse (inverse (greatest_lower_bound identity ?570109))) [570109] by Demod 575188 with 213345 at 2
% 283.54/71.24 Id : 575441, {_}: multiply (inverse ?570109) (inverse (least_upper_bound identity (inverse ?570109))) =>= inverse (multiply (inverse (greatest_lower_bound identity ?570109)) ?570109) [570109] by Demod 575440 with 291304 at 3
% 283.54/71.24 Id : 575442, {_}: inverse (multiply (least_upper_bound identity (inverse ?570109)) ?570109) =>= inverse (multiply (inverse (greatest_lower_bound identity ?570109)) ?570109) [570109] by Demod 575441 with 291304 at 2
% 283.54/71.24 Id : 575443, {_}: inverse (multiply (least_upper_bound identity (inverse ?570109)) ?570109) =>= multiply (inverse ?570109) (greatest_lower_bound identity ?570109) [570109] by Demod 575442 with 291679 at 3
% 283.54/71.24 Id : 216, {_}: multiply (least_upper_bound ?653 (inverse ?654)) ?654 =>= least_upper_bound (multiply ?653 ?654) identity [654, 653] by Super 214 with 3 at 2,3
% 283.54/71.24 Id : 234, {_}: multiply (least_upper_bound ?653 (inverse ?654)) ?654 =>= least_upper_bound identity (multiply ?653 ?654) [654, 653] by Demod 216 with 6 at 3
% 283.54/71.24 Id : 575444, {_}: inverse (least_upper_bound identity (multiply identity ?570109)) =<= multiply (inverse ?570109) (greatest_lower_bound identity ?570109) [570109] by Demod 575443 with 234 at 1,2
% 283.54/71.24 Id : 183, {_}: multiply (inverse ?579) (greatest_lower_bound ?580 ?579) =>= greatest_lower_bound (multiply (inverse ?579) ?580) identity [580, 579] by Super 181 with 3 at 2,3
% 283.54/71.24 Id : 202, {_}: multiply (inverse ?579) (greatest_lower_bound ?580 ?579) =>= greatest_lower_bound identity (multiply (inverse ?579) ?580) [580, 579] by Demod 183 with 5 at 3
% 283.54/71.24 Id : 575445, {_}: inverse (least_upper_bound identity (multiply identity ?570109)) =<= greatest_lower_bound identity (multiply (inverse ?570109) identity) [570109] by Demod 575444 with 202 at 3
% 283.54/71.24 Id : 575446, {_}: inverse (least_upper_bound identity ?570109) =<= greatest_lower_bound identity (multiply (inverse ?570109) identity) [570109] by Demod 575445 with 2 at 2,1,2
% 283.54/71.24 Id : 575447, {_}: inverse (least_upper_bound identity ?570109) =<= greatest_lower_bound identity (inverse ?570109) [570109] by Demod 575446 with 1194 at 2,3
% 283.54/71.24 Id : 576187, {_}: multiply ?406135 (inverse (inverse (least_upper_bound identity ?406136))) =?= least_upper_bound ?406135 (multiply ?406135 ?406136) [406136, 406135] by Demod 574869 with 575447 at 1,2,2
% 283.54/71.24 Id : 576344, {_}: multiply ?406135 (least_upper_bound identity ?406136) =?= least_upper_bound ?406135 (multiply ?406135 ?406136) [406136, 406135] by Demod 576187 with 1216 at 2,2
% 283.54/71.24 Id : 290930, {_}: multiply ?360064 (inverse ?360065) =<= inverse (multiply ?360065 (inverse ?360064)) [360065, 360064] by Super 1242 with 290852 at 1,2
% 283.54/71.24 Id : 292450, {_}: multiply ?362383 (inverse (inverse (multiply (inverse ?362383) ?362384))) =>= inverse (inverse ?362384) [362384, 362383] by Super 290930 with 290963 at 1,3
% 283.54/71.24 Id : 292567, {_}: multiply ?362383 (multiply (inverse ?362383) ?362384) =>= inverse (inverse ?362384) [362384, 362383] by Demod 292450 with 1216 at 2,2
% 283.54/71.24 Id : 292568, {_}: multiply ?362383 (multiply (inverse ?362383) ?362384) =>= ?362384 [362384, 362383] by Demod 292567 with 1216 at 3
% 283.54/71.24 Id : 645505, {_}: least_upper_bound a b === least_upper_bound a b [] by Demod 645504 with 292568 at 2,2
% 283.54/71.24 Id : 645504, {_}: least_upper_bound a (multiply a (multiply (inverse a) b)) =>= least_upper_bound a b [] by Demod 645503 with 576344 at 2
% 283.54/71.24 Id : 645503, {_}: multiply a (least_upper_bound identity (multiply (inverse a) b)) =>= least_upper_bound a b [] by Demod 1 with 644039 at 2,2
% 283.54/71.24 Id : 1, {_}: multiply a (multiply (inverse (greatest_lower_bound a b)) b) =>= least_upper_bound a b [] by prove_p11
% 283.54/71.24 % SZS output end CNFRefutation for theBenchmark.p
% 283.54/71.24 14108: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 70.821789 using nrkbo
%------------------------------------------------------------------------------