TSTP Solution File: GRP193-1 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n009.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 10:29:34 EDT 2022
% Result : Unsatisfiable 112.27s 28.40s
% Output : CNFRefutation 112.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 06:00:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 2685: Facts:
% 0.12/0.33 2685: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.12/0.33 2685: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.12/0.33 2685: Id : 4, {_}:
% 0.12/0.33 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.12/0.33 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.12/0.33 2685: Id : 5, {_}:
% 0.12/0.33 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
% 0.12/0.33 [11, 10] by symmetry_of_glb ?10 ?11
% 0.12/0.33 2685: Id : 6, {_}:
% 0.12/0.33 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
% 0.12/0.33 [14, 13] by symmetry_of_lub ?13 ?14
% 0.12/0.33 2685: Id : 7, {_}:
% 0.12/0.33 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
% 0.12/0.33 =?=
% 0.12/0.33 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
% 0.12/0.33 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 0.12/0.33 2685: Id : 8, {_}:
% 0.12/0.33 least_upper_bound ?20 (least_upper_bound ?21 ?22)
% 0.12/0.33 =?=
% 0.12/0.33 least_upper_bound (least_upper_bound ?20 ?21) ?22
% 0.12/0.33 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 0.12/0.33 2685: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.12/0.33 2685: Id : 10, {_}:
% 0.12/0.33 greatest_lower_bound ?26 ?26 =>= ?26
% 0.12/0.33 [26] by idempotence_of_gld ?26
% 0.12/0.33 2685: Id : 11, {_}:
% 0.12/0.33 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
% 0.12/0.33 [29, 28] by lub_absorbtion ?28 ?29
% 0.12/0.33 2685: Id : 12, {_}:
% 0.12/0.33 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
% 0.12/0.33 [32, 31] by glb_absorbtion ?31 ?32
% 0.12/0.33 2685: Id : 13, {_}:
% 0.12/0.33 multiply ?34 (least_upper_bound ?35 ?36)
% 0.12/0.33 =<=
% 0.12/0.33 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
% 0.12/0.33 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 0.12/0.33 2685: Id : 14, {_}:
% 0.12/0.33 multiply ?38 (greatest_lower_bound ?39 ?40)
% 0.12/0.33 =<=
% 0.12/0.33 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
% 0.12/0.33 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 0.12/0.33 2685: Id : 15, {_}:
% 0.12/0.33 multiply (least_upper_bound ?42 ?43) ?44
% 0.12/0.33 =<=
% 0.12/0.33 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
% 0.12/0.33 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 0.12/0.33 2685: Id : 16, {_}:
% 0.12/0.33 multiply (greatest_lower_bound ?46 ?47) ?48
% 0.12/0.33 =<=
% 0.12/0.33 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
% 0.12/0.33 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 0.12/0.33 2685: Id : 17, {_}: least_upper_bound identity a =>= a [] by p8_9a_1
% 0.12/0.33 2685: Id : 18, {_}: least_upper_bound identity b =>= b [] by p8_9a_2
% 0.12/0.33 2685: Id : 19, {_}: least_upper_bound identity c =>= c [] by p8_9a_3
% 0.12/0.33 2685: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p8_9a_4
% 0.12/0.33 2685: Id : 21, {_}:
% 0.12/0.33 least_upper_bound (greatest_lower_bound a (multiply b c))
% 0.12/0.33 (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
% 0.12/0.33 =>=
% 0.12/0.33 multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
% 0.12/0.33 [] by p8_9a_5
% 0.12/0.33 2685: Goal:
% 0.12/0.33 2685: Id : 1, {_}:
% 0.12/0.33 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
% 0.12/0.33 [] by prove_p8_9a
% 112.27/28.40 Statistics :
% 112.27/28.40 Max weight : 16
% 112.27/28.40 Found proof, 28.063768s
% 112.27/28.40 % SZS status Unsatisfiable for theBenchmark.p
% 112.27/28.40 % SZS output start CNFRefutation for theBenchmark.p
% 112.27/28.40 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
% 112.27/28.40 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
% 112.27/28.40 Id : 19, {_}: least_upper_bound identity c =>= c [] by p8_9a_3
% 112.27/28.40 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
% 112.27/28.40 Id : 18, {_}: least_upper_bound identity b =>= b [] by p8_9a_2
% 112.27/28.40 Id : 48, {_}: greatest_lower_bound ?119 (greatest_lower_bound ?120 ?121) =<= greatest_lower_bound (greatest_lower_bound ?119 ?120) ?121 [121, 120, 119] by associativity_of_glb ?119 ?120 ?121
% 112.27/28.40 Id : 87, {_}: least_upper_bound ?222 (greatest_lower_bound ?222 ?223) =>= ?222 [223, 222] by lub_absorbtion ?222 ?223
% 112.27/28.40 Id : 119, {_}: multiply ?299 (least_upper_bound ?300 ?301) =<= least_upper_bound (multiply ?299 ?300) (multiply ?299 ?301) [301, 300, 299] by monotony_lub1 ?299 ?300 ?301
% 112.27/28.40 Id : 192, {_}: multiply (least_upper_bound ?424 ?425) ?426 =<= least_upper_bound (multiply ?424 ?426) (multiply ?425 ?426) [426, 425, 424] by monotony_lub2 ?424 ?425 ?426
% 112.27/28.40 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 112.27/28.40 Id : 26, {_}: multiply (multiply ?62 ?63) ?64 =>= multiply ?62 (multiply ?63 ?64) [64, 63, 62] by associativity ?62 ?63 ?64
% 112.27/28.40 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
% 112.27/28.40 Id : 10, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
% 112.27/28.40 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
% 112.27/28.40 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
% 112.27/28.40 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 112.27/28.40 Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p8_9a_4
% 112.27/28.40 Id : 21, {_}: least_upper_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) =>= multiply (greatest_lower_bound a b) (greatest_lower_bound a c) [] by p8_9a_5
% 112.27/28.40 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 112.27/28.40 Id : 101, {_}: greatest_lower_bound ?256 (least_upper_bound ?256 ?257) =>= ?256 [257, 256] by glb_absorbtion ?256 ?257
% 112.27/28.40 Id : 3405, {_}: greatest_lower_bound ?4554 (least_upper_bound ?4555 ?4554) =>= ?4554 [4555, 4554] by Super 101 with 6 at 2,2
% 112.27/28.40 Id : 283, {_}: least_upper_bound (greatest_lower_bound a (multiply b c)) (multiply identity (greatest_lower_bound a c)) =>= multiply (greatest_lower_bound a b) (greatest_lower_bound a c) [] by Demod 21 with 20 at 1,2,2
% 112.27/28.40 Id : 284, {_}: least_upper_bound (greatest_lower_bound a (multiply b c)) (multiply identity (greatest_lower_bound a c)) =>= multiply identity (greatest_lower_bound a c) [] by Demod 283 with 20 at 1,3
% 112.27/28.40 Id : 285, {_}: least_upper_bound (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c) =>= multiply identity (greatest_lower_bound a c) [] by Demod 284 with 2 at 2,2
% 112.27/28.40 Id : 286, {_}: least_upper_bound (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c) =>= greatest_lower_bound a c [] by Demod 285 with 2 at 3
% 112.27/28.40 Id : 287, {_}: least_upper_bound (greatest_lower_bound a c) (greatest_lower_bound a (multiply b c)) =>= greatest_lower_bound a c [] by Demod 286 with 6 at 2
% 112.27/28.40 Id : 3419, {_}: greatest_lower_bound (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c) =>= greatest_lower_bound a (multiply b c) [] by Super 3405 with 287 at 2,2
% 112.27/28.40 Id : 3480, {_}: greatest_lower_bound (greatest_lower_bound a c) (greatest_lower_bound a (multiply b c)) =>= greatest_lower_bound a (multiply b c) [] by Demod 3419 with 5 at 2
% 112.27/28.40 Id : 46, {_}: greatest_lower_bound ?111 (greatest_lower_bound ?112 ?113) =?= greatest_lower_bound ?112 (greatest_lower_bound ?113 ?111) [113, 112, 111] by Super 5 with 7 at 3
% 112.27/28.40 Id : 3481, {_}: greatest_lower_bound a (greatest_lower_bound (multiply b c) (greatest_lower_bound a c)) =>= greatest_lower_bound a (multiply b c) [] by Demod 3480 with 46 at 2
% 112.27/28.40 Id : 3482, {_}: greatest_lower_bound a (greatest_lower_bound (greatest_lower_bound a c) (multiply b c)) =>= greatest_lower_bound a (multiply b c) [] by Demod 3481 with 5 at 2,2
% 112.27/28.40 Id : 3483, {_}: greatest_lower_bound a (greatest_lower_bound a (greatest_lower_bound c (multiply b c))) =>= greatest_lower_bound a (multiply b c) [] by Demod 3482 with 7 at 2,2
% 112.27/28.40 Id : 79, {_}: greatest_lower_bound ?198 (greatest_lower_bound ?198 ?199) =>= greatest_lower_bound ?198 ?199 [199, 198] by Super 7 with 10 at 1,3
% 112.27/28.40 Id : 3484, {_}: greatest_lower_bound a (greatest_lower_bound c (multiply b c)) =>= greatest_lower_bound a (multiply b c) [] by Demod 3483 with 79 at 2
% 112.27/28.40 Id : 28, {_}: multiply identity ?69 =<= multiply (inverse ?70) (multiply ?70 ?69) [70, 69] by Super 26 with 3 at 1,2
% 112.27/28.40 Id : 32, {_}: ?69 =<= multiply (inverse ?70) (multiply ?70 ?69) [70, 69] by Demod 28 with 2 at 2
% 112.27/28.40 Id : 168502, {_}: multiply (least_upper_bound identity ?125176) ?125177 =?= least_upper_bound ?125177 (multiply ?125176 ?125177) [125177, 125176] by Super 192 with 2 at 1,3
% 112.27/28.40 Id : 124, {_}: multiply (inverse ?317) (least_upper_bound ?317 ?318) =>= least_upper_bound identity (multiply (inverse ?317) ?318) [318, 317] by Super 119 with 3 at 1,3
% 112.27/28.40 Id : 88, {_}: least_upper_bound ?225 (greatest_lower_bound ?226 ?225) =>= ?225 [226, 225] by Super 87 with 5 at 2,2
% 112.27/28.40 Id : 49, {_}: greatest_lower_bound ?123 (greatest_lower_bound ?124 ?125) =<= greatest_lower_bound (greatest_lower_bound ?124 ?123) ?125 [125, 124, 123] by Super 48 with 5 at 1,3
% 112.27/28.40 Id : 55, {_}: greatest_lower_bound ?123 (greatest_lower_bound ?124 ?125) =?= greatest_lower_bound ?124 (greatest_lower_bound ?123 ?125) [125, 124, 123] by Demod 49 with 7 at 3
% 112.27/28.40 Id : 102, {_}: greatest_lower_bound ?259 (least_upper_bound ?260 ?259) =>= ?259 [260, 259] by Super 101 with 6 at 2,2
% 112.27/28.40 Id : 5006, {_}: multiply (inverse ?5898) (least_upper_bound ?5898 ?5899) =>= least_upper_bound identity (multiply (inverse ?5898) ?5899) [5899, 5898] by Super 119 with 3 at 1,3
% 112.27/28.40 Id : 257, {_}: least_upper_bound b identity =>= b [] by Demod 18 with 6 at 2
% 112.27/28.40 Id : 5016, {_}: multiply (inverse b) b =<= least_upper_bound identity (multiply (inverse b) identity) [] by Super 5006 with 257 at 2,2
% 112.27/28.40 Id : 5072, {_}: identity =<= least_upper_bound identity (multiply (inverse b) identity) [] by Demod 5016 with 3 at 2
% 112.27/28.40 Id : 364, {_}: ?640 =<= multiply (inverse ?641) (multiply ?641 ?640) [641, 640] by Demod 28 with 2 at 2
% 112.27/28.40 Id : 366, {_}: ?645 =<= multiply (inverse (inverse ?645)) identity [645] by Super 364 with 3 at 2,3
% 112.27/28.40 Id : 368, {_}: multiply ?651 ?652 =<= multiply (inverse (inverse ?651)) ?652 [652, 651] by Super 364 with 32 at 2,3
% 112.27/28.40 Id : 2852, {_}: ?645 =<= multiply ?645 identity [645] by Demod 366 with 368 at 3
% 112.27/28.40 Id : 5073, {_}: identity =<= least_upper_bound identity (inverse b) [] by Demod 5072 with 2852 at 2,3
% 112.27/28.40 Id : 5159, {_}: greatest_lower_bound (inverse b) identity =>= inverse b [] by Super 102 with 5073 at 2,2
% 112.27/28.40 Id : 5166, {_}: greatest_lower_bound identity (inverse b) =>= inverse b [] by Demod 5159 with 5 at 2
% 112.27/28.40 Id : 5408, {_}: greatest_lower_bound identity (greatest_lower_bound ?6196 (inverse b)) =>= greatest_lower_bound ?6196 (inverse b) [6196] by Super 55 with 5166 at 2,3
% 112.27/28.40 Id : 98, {_}: greatest_lower_bound ?246 (greatest_lower_bound (least_upper_bound ?246 ?247) ?248) =>= greatest_lower_bound ?246 ?248 [248, 247, 246] by Super 7 with 12 at 1,3
% 112.27/28.40 Id : 14324, {_}: greatest_lower_bound identity (inverse b) =<= greatest_lower_bound (least_upper_bound identity ?13275) (inverse b) [13275] by Super 5408 with 98 at 2
% 112.27/28.40 Id : 14483, {_}: inverse b =<= greatest_lower_bound (least_upper_bound identity ?13275) (inverse b) [13275] by Demod 14324 with 5166 at 2
% 112.27/28.40 Id : 14484, {_}: inverse b =<= greatest_lower_bound (inverse b) (least_upper_bound identity ?13275) [13275] by Demod 14483 with 5 at 3
% 112.27/28.40 Id : 121, {_}: multiply (inverse ?306) (least_upper_bound ?307 ?306) =>= least_upper_bound (multiply (inverse ?306) ?307) identity [307, 306] by Super 119 with 3 at 2,3
% 112.27/28.40 Id : 33872, {_}: multiply (inverse ?28583) (least_upper_bound ?28584 ?28583) =>= least_upper_bound identity (multiply (inverse ?28583) ?28584) [28584, 28583] by Demod 121 with 6 at 3
% 112.27/28.40 Id : 266, {_}: least_upper_bound c identity =>= c [] by Demod 19 with 6 at 2
% 112.27/28.40 Id : 268, {_}: least_upper_bound c (least_upper_bound identity ?548) =>= least_upper_bound c ?548 [548] by Super 8 with 266 at 1,3
% 112.27/28.40 Id : 5149, {_}: least_upper_bound c identity =<= least_upper_bound c (inverse b) [] by Super 268 with 5073 at 2,2
% 112.27/28.40 Id : 5174, {_}: c =<= least_upper_bound c (inverse b) [] by Demod 5149 with 266 at 2
% 112.27/28.40 Id : 33953, {_}: multiply (inverse (inverse b)) c =<= least_upper_bound identity (multiply (inverse (inverse b)) c) [] by Super 33872 with 5174 at 2,2
% 112.27/28.40 Id : 2853, {_}: inverse (inverse ?3905) =<= multiply ?3905 identity [3905] by Super 2852 with 368 at 3
% 112.27/28.40 Id : 2892, {_}: inverse (inverse ?3905) =>= ?3905 [3905] by Demod 2853 with 2852 at 3
% 112.27/28.40 Id : 34126, {_}: multiply b c =<= least_upper_bound identity (multiply (inverse (inverse b)) c) [] by Demod 33953 with 2892 at 1,2
% 112.27/28.40 Id : 34127, {_}: multiply b c =<= least_upper_bound identity (multiply b c) [] by Demod 34126 with 2892 at 1,2,3
% 112.27/28.40 Id : 34508, {_}: inverse b =<= greatest_lower_bound (inverse b) (multiply b c) [] by Super 14484 with 34127 at 2,3
% 112.27/28.40 Id : 38026, {_}: least_upper_bound (multiply b c) (inverse b) =>= multiply b c [] by Super 88 with 34508 at 2,2
% 112.27/28.40 Id : 38049, {_}: least_upper_bound (inverse b) (multiply b c) =>= multiply b c [] by Demod 38026 with 6 at 2
% 112.27/28.40 Id : 42047, {_}: multiply (inverse (inverse b)) (multiply b c) =<= least_upper_bound identity (multiply (inverse (inverse b)) (multiply b c)) [] by Super 124 with 38049 at 2,2
% 112.27/28.40 Id : 42088, {_}: multiply b (multiply b c) =<= least_upper_bound identity (multiply (inverse (inverse b)) (multiply b c)) [] by Demod 42047 with 2892 at 1,2
% 112.27/28.40 Id : 42089, {_}: multiply b (multiply b c) =<= least_upper_bound identity (multiply b (multiply b c)) [] by Demod 42088 with 2892 at 1,2,3
% 112.27/28.40 Id : 135, {_}: multiply (inverse ?306) (least_upper_bound ?307 ?306) =>= least_upper_bound identity (multiply (inverse ?306) ?307) [307, 306] by Demod 121 with 6 at 3
% 112.27/28.40 Id : 259, {_}: least_upper_bound b (least_upper_bound identity ?542) =>= least_upper_bound b ?542 [542] by Super 8 with 257 at 1,3
% 112.27/28.40 Id : 5154, {_}: least_upper_bound b identity =<= least_upper_bound b (inverse b) [] by Super 259 with 5073 at 2,2
% 112.27/28.40 Id : 5169, {_}: b =<= least_upper_bound b (inverse b) [] by Demod 5154 with 257 at 2
% 112.27/28.40 Id : 33951, {_}: multiply (inverse (inverse b)) b =<= least_upper_bound identity (multiply (inverse (inverse b)) b) [] by Super 33872 with 5169 at 2,2
% 112.27/28.40 Id : 34122, {_}: multiply b b =<= least_upper_bound identity (multiply (inverse (inverse b)) b) [] by Demod 33951 with 2892 at 1,2
% 112.27/28.40 Id : 34123, {_}: multiply b b =<= least_upper_bound identity (multiply b b) [] by Demod 34122 with 2892 at 1,2,3
% 112.27/28.40 Id : 34378, {_}: multiply (inverse (multiply b b)) (multiply b b) =>= least_upper_bound identity (multiply (inverse (multiply b b)) identity) [] by Super 135 with 34123 at 2,2
% 112.27/28.40 Id : 34432, {_}: identity =<= least_upper_bound identity (multiply (inverse (multiply b b)) identity) [] by Demod 34378 with 3 at 2
% 112.27/28.40 Id : 34433, {_}: identity =<= least_upper_bound identity (inverse (multiply b b)) [] by Demod 34432 with 2852 at 2,3
% 112.27/28.40 Id : 36871, {_}: least_upper_bound c identity =<= least_upper_bound c (inverse (multiply b b)) [] by Super 268 with 34433 at 2,2
% 112.27/28.40 Id : 36907, {_}: c =<= least_upper_bound c (inverse (multiply b b)) [] by Demod 36871 with 266 at 2
% 112.27/28.40 Id : 41206, {_}: multiply (inverse (inverse (multiply b b))) c =<= least_upper_bound identity (multiply (inverse (inverse (multiply b b))) c) [] by Super 135 with 36907 at 2,2
% 112.27/28.40 Id : 41222, {_}: multiply (multiply b b) c =<= least_upper_bound identity (multiply (inverse (inverse (multiply b b))) c) [] by Demod 41206 with 2892 at 1,2
% 112.27/28.40 Id : 41223, {_}: multiply (multiply b b) c =<= least_upper_bound identity (multiply (multiply b b) c) [] by Demod 41222 with 2892 at 1,2,3
% 112.27/28.40 Id : 41224, {_}: multiply b (multiply b c) =<= least_upper_bound identity (multiply (multiply b b) c) [] by Demod 41223 with 4 at 2
% 112.27/28.40 Id : 41225, {_}: multiply b (multiply b c) =<= least_upper_bound identity (multiply b (multiply b c)) [] by Demod 41224 with 4 at 2,3
% 112.27/28.40 Id : 48916, {_}: multiply b (multiply b c) =?= multiply b (multiply b c) [] by Demod 42089 with 41225 at 3
% 112.27/28.40 Id : 168524, {_}: multiply (least_upper_bound identity b) (multiply b c) =<= least_upper_bound (multiply b c) (multiply b (multiply b c)) [] by Super 168502 with 48916 at 2,3
% 112.27/28.40 Id : 168839, {_}: multiply (least_upper_bound b identity) (multiply b c) =<= least_upper_bound (multiply b c) (multiply b (multiply b c)) [] by Demod 168524 with 6 at 1,2
% 112.27/28.40 Id : 168840, {_}: multiply (least_upper_bound b identity) (multiply b c) =>= multiply b (least_upper_bound c (multiply b c)) [] by Demod 168839 with 13 at 3
% 112.27/28.40 Id : 168841, {_}: multiply b (multiply b c) =<= multiply b (least_upper_bound c (multiply b c)) [] by Demod 168840 with 257 at 1,2
% 112.27/28.40 Id : 171081, {_}: least_upper_bound c (multiply b c) =<= multiply (inverse b) (multiply b (multiply b c)) [] by Super 32 with 168841 at 2,3
% 112.27/28.40 Id : 171114, {_}: least_upper_bound c (multiply b c) =>= multiply b c [] by Demod 171081 with 32 at 3
% 112.27/28.40 Id : 171190, {_}: greatest_lower_bound c (multiply b c) =>= c [] by Super 12 with 171114 at 2,2
% 112.27/28.40 Id : 171317, {_}: greatest_lower_bound a c =<= greatest_lower_bound a (multiply b c) [] by Demod 3484 with 171190 at 2,2
% 112.27/28.40 Id : 171408, {_}: greatest_lower_bound a c =?= greatest_lower_bound a c [] by Demod 1 with 171317 at 2
% 112.27/28.40 Id : 1, {_}: greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c [] by prove_p8_9a
% 112.27/28.40 % SZS output end CNFRefutation for theBenchmark.p
% 112.27/28.40 2686: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 28.062167 using kbo
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