TSTP Solution File: GRP167-2 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP167-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n017.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 10:29:18 EDT 2022
% Result : Unsatisfiable 17.86s 4.79s
% Output : CNFRefutation 17.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP167-2 : 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 : n017.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 03:26:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 11496: Facts:
% 0.12/0.34 11496: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.12/0.34 11496: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.12/0.34 11496: 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 11496: 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 11496: 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 11496: 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 11496: 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 11496: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.12/0.34 11496: 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 11496: 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 11496: 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 11496: 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 11496: 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 11496: 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 11496: 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 11496: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
% 0.12/0.34 11496: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
% 0.12/0.34 11496: Id : 19, {_}:
% 0.12/0.34 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
% 0.12/0.34 [54, 53] by lat4_3 ?53 ?54
% 0.12/0.34 11496: Id : 20, {_}:
% 0.12/0.34 positive_part ?56 =<= least_upper_bound ?56 identity
% 0.12/0.34 [56] by lat4_4 ?56
% 0.12/0.34 11496: Id : 21, {_}:
% 0.12/0.34 negative_part ?58 =<= greatest_lower_bound ?58 identity
% 0.12/0.34 [58] by lat4_5 ?58
% 0.12/0.34 11496: Id : 22, {_}:
% 0.12/0.34 least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
% 0.12/0.34 =<=
% 0.12/0.34 greatest_lower_bound (least_upper_bound ?60 ?61)
% 0.12/0.34 (least_upper_bound ?60 ?62)
% 0.12/0.34 [62, 61, 60] by lat4_6 ?60 ?61 ?62
% 0.12/0.34 11496: Id : 23, {_}:
% 0.12/0.34 greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
% 0.12/0.34 =<=
% 0.12/0.34 least_upper_bound (greatest_lower_bound ?64 ?65)
% 0.12/0.34 (greatest_lower_bound ?64 ?66)
% 0.12/0.34 [66, 65, 64] by lat4_7 ?64 ?65 ?66
% 0.12/0.34 11496: Goal:
% 0.12/0.34 11496: Id : 1, {_}:
% 0.12/0.34 a =<= multiply (positive_part a) (negative_part a)
% 0.12/0.34 [] by prove_lat4
% 17.86/4.79 Statistics :
% 17.86/4.79 Max weight : 16
% 17.86/4.79 Found proof, 4.454292s
% 17.86/4.79 % SZS status Unsatisfiable for theBenchmark.p
% 17.86/4.79 % SZS output start CNFRefutation for theBenchmark.p
% 17.86/4.79 Id : 28, {_}: multiply (multiply ?75 ?76) ?77 =?= multiply ?75 (multiply ?76 ?77) [77, 76, 75] by associativity ?75 ?76 ?77
% 17.86/4.79 Id : 23, {_}: greatest_lower_bound ?64 (least_upper_bound ?65 ?66) =<= least_upper_bound (greatest_lower_bound ?64 ?65) (greatest_lower_bound ?64 ?66) [66, 65, 64] by lat4_7 ?64 ?65 ?66
% 17.86/4.79 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 17.86/4.79 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
% 17.86/4.79 Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 17.86/4.79 Id : 253, {_}: multiply (greatest_lower_bound ?741 ?742) ?743 =<= greatest_lower_bound (multiply ?741 ?743) (multiply ?742 ?743) [743, 742, 741] by monotony_glb2 ?741 ?742 ?743
% 17.86/4.79 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
% 17.86/4.79 Id : 221, {_}: multiply (least_upper_bound ?664 ?665) ?666 =<= least_upper_bound (multiply ?664 ?666) (multiply ?665 ?666) [666, 665, 664] by monotony_lub2 ?664 ?665 ?666
% 17.86/4.79 Id : 354, {_}: least_upper_bound ?949 (greatest_lower_bound ?950 ?951) =<= greatest_lower_bound (least_upper_bound ?949 ?950) (least_upper_bound ?949 ?951) [951, 950, 949] by lat4_6 ?949 ?950 ?951
% 17.86/4.79 Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
% 17.86/4.79 Id : 22, {_}: least_upper_bound ?60 (greatest_lower_bound ?61 ?62) =<= greatest_lower_bound (least_upper_bound ?60 ?61) (least_upper_bound ?60 ?62) [62, 61, 60] by lat4_6 ?60 ?61 ?62
% 17.86/4.79 Id : 404, {_}: greatest_lower_bound ?1074 (least_upper_bound ?1075 ?1076) =<= least_upper_bound (greatest_lower_bound ?1074 ?1075) (greatest_lower_bound ?1074 ?1076) [1076, 1075, 1074] by lat4_7 ?1074 ?1075 ?1076
% 17.86/4.79 Id : 21, {_}: negative_part ?58 =<= greatest_lower_bound ?58 identity [58] by lat4_5 ?58
% 17.86/4.79 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
% 17.86/4.79 Id : 188, {_}: multiply ?590 (greatest_lower_bound ?591 ?592) =<= greatest_lower_bound (multiply ?590 ?591) (multiply ?590 ?592) [592, 591, 590] by monotony_glb1 ?590 ?591 ?592
% 17.86/4.79 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 17.86/4.79 Id : 20, {_}: positive_part ?56 =<= least_upper_bound ?56 identity [56] by lat4_4 ?56
% 17.86/4.79 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
% 17.86/4.79 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 17.86/4.79 Id : 17, {_}: inverse identity =>= identity [] by lat4_1
% 17.86/4.79 Id : 302, {_}: inverse (multiply ?849 ?850) =<= multiply (inverse ?850) (inverse ?849) [850, 849] by lat4_3 ?849 ?850
% 17.86/4.79 Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
% 17.86/4.79 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 17.86/4.79 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
% 17.86/4.79 Id : 285, {_}: multiply ?798 (inverse ?798) =>= identity [798] by Super 3 with 18 at 1,2
% 17.86/4.79 Id : 607, {_}: multiply (multiply ?1347 ?1348) (inverse ?1348) =>= multiply ?1347 identity [1348, 1347] by Super 4 with 285 at 2,3
% 17.86/4.79 Id : 303, {_}: inverse (multiply identity ?852) =<= multiply (inverse ?852) identity [852] by Super 302 with 17 at 2,3
% 17.86/4.79 Id : 543, {_}: inverse ?1286 =<= multiply (inverse ?1286) identity [1286] by Demod 303 with 2 at 1,2
% 17.86/4.79 Id : 545, {_}: inverse (inverse ?1289) =<= multiply ?1289 identity [1289] by Super 543 with 18 at 1,3
% 17.86/4.79 Id : 559, {_}: ?1289 =<= multiply ?1289 identity [1289] by Demod 545 with 18 at 2
% 17.86/4.79 Id : 15555, {_}: multiply (multiply ?17886 ?17887) (inverse ?17887) =>= ?17886 [17887, 17886] by Demod 607 with 559 at 3
% 17.86/4.79 Id : 564, {_}: multiply ?1300 (least_upper_bound ?1301 identity) =?= least_upper_bound (multiply ?1300 ?1301) ?1300 [1301, 1300] by Super 13 with 559 at 2,3
% 17.86/4.79 Id : 3444, {_}: multiply ?5108 (positive_part ?5109) =<= least_upper_bound (multiply ?5108 ?5109) ?5108 [5109, 5108] by Demod 564 with 20 at 2,2
% 17.86/4.79 Id : 3448, {_}: multiply ?5119 (positive_part (inverse ?5119)) =>= least_upper_bound identity ?5119 [5119] by Super 3444 with 285 at 1,3
% 17.86/4.79 Id : 320, {_}: least_upper_bound identity ?881 =>= positive_part ?881 [881] by Super 6 with 20 at 3
% 17.86/4.79 Id : 3485, {_}: multiply ?5119 (positive_part (inverse ?5119)) =>= positive_part ?5119 [5119] by Demod 3448 with 320 at 3
% 17.86/4.79 Id : 15572, {_}: multiply (positive_part ?17933) (inverse (positive_part (inverse ?17933))) =>= ?17933 [17933] by Super 15555 with 3485 at 1,2
% 17.86/4.79 Id : 588, {_}: multiply ?1300 (positive_part ?1301) =<= least_upper_bound (multiply ?1300 ?1301) ?1300 [1301, 1300] by Demod 564 with 20 at 2,2
% 17.86/4.79 Id : 190, {_}: multiply (inverse ?597) (greatest_lower_bound ?598 ?597) =>= greatest_lower_bound (multiply (inverse ?597) ?598) identity [598, 597] by Super 188 with 3 at 2,3
% 17.86/4.79 Id : 209, {_}: multiply (inverse ?597) (greatest_lower_bound ?598 ?597) =>= greatest_lower_bound identity (multiply (inverse ?597) ?598) [598, 597] by Demod 190 with 5 at 3
% 17.86/4.79 Id : 337, {_}: greatest_lower_bound identity ?912 =>= negative_part ?912 [912] by Super 5 with 21 at 3
% 17.86/4.79 Id : 8825, {_}: multiply (inverse ?597) (greatest_lower_bound ?598 ?597) =>= negative_part (multiply (inverse ?597) ?598) [598, 597] by Demod 209 with 337 at 3
% 17.86/4.79 Id : 423, {_}: greatest_lower_bound ?1156 (least_upper_bound identity ?1157) =<= least_upper_bound (negative_part ?1156) (greatest_lower_bound ?1156 ?1157) [1157, 1156] by Super 404 with 21 at 1,3
% 17.86/4.79 Id : 14712, {_}: greatest_lower_bound ?16994 (positive_part ?16995) =<= least_upper_bound (negative_part ?16994) (greatest_lower_bound ?16994 ?16995) [16995, 16994] by Demod 423 with 320 at 2,2
% 17.86/4.79 Id : 14713, {_}: greatest_lower_bound ?16997 (positive_part ?16998) =<= least_upper_bound (negative_part ?16997) (greatest_lower_bound ?16998 ?16997) [16998, 16997] by Super 14712 with 5 at 2,3
% 17.86/4.79 Id : 332, {_}: least_upper_bound ?898 (negative_part ?898) =>= ?898 [898] by Super 11 with 21 at 2,2
% 17.86/4.79 Id : 727, {_}: least_upper_bound (negative_part ?1509) ?1509 =>= ?1509 [1509] by Super 6 with 332 at 3
% 17.86/4.79 Id : 1057, {_}: least_upper_bound (negative_part ?1917) (greatest_lower_bound ?1918 ?1917) =>= greatest_lower_bound (least_upper_bound (negative_part ?1917) ?1918) ?1917 [1918, 1917] by Super 22 with 727 at 2,3
% 17.86/4.79 Id : 372, {_}: least_upper_bound ?1026 (greatest_lower_bound identity ?1027) =<= greatest_lower_bound (positive_part ?1026) (least_upper_bound ?1026 ?1027) [1027, 1026] by Super 354 with 20 at 1,3
% 17.86/4.79 Id : 14465, {_}: least_upper_bound ?16745 (negative_part ?16746) =<= greatest_lower_bound (positive_part ?16745) (least_upper_bound ?16745 ?16746) [16746, 16745] by Demod 372 with 337 at 2,2
% 17.86/4.79 Id : 2496, {_}: least_upper_bound (greatest_lower_bound ?3877 ?3878) ?3877 =>= ?3877 [3878, 3877] by Super 6 with 11 at 3
% 17.86/4.79 Id : 2497, {_}: least_upper_bound (greatest_lower_bound ?3880 ?3881) ?3881 =>= ?3881 [3881, 3880] by Super 2496 with 5 at 1,2
% 17.86/4.79 Id : 14479, {_}: least_upper_bound (greatest_lower_bound ?16784 ?16785) (negative_part ?16785) =>= greatest_lower_bound (positive_part (greatest_lower_bound ?16784 ?16785)) ?16785 [16785, 16784] by Super 14465 with 2497 at 2,3
% 17.86/4.79 Id : 14586, {_}: least_upper_bound (negative_part ?16785) (greatest_lower_bound ?16784 ?16785) =>= greatest_lower_bound (positive_part (greatest_lower_bound ?16784 ?16785)) ?16785 [16784, 16785] by Demod 14479 with 6 at 2
% 17.86/4.79 Id : 33809, {_}: greatest_lower_bound (least_upper_bound (negative_part ?16785) ?16784) ?16785 =>= greatest_lower_bound (positive_part (greatest_lower_bound ?16784 ?16785)) ?16785 [16784, 16785] by Demod 14586 with 1057 at 2
% 17.86/4.79 Id : 33810, {_}: least_upper_bound (negative_part ?1917) (greatest_lower_bound ?1918 ?1917) =>= greatest_lower_bound (positive_part (greatest_lower_bound ?1918 ?1917)) ?1917 [1918, 1917] by Demod 1057 with 33809 at 3
% 17.86/4.79 Id : 34533, {_}: greatest_lower_bound ?16997 (positive_part ?16998) =<= greatest_lower_bound (positive_part (greatest_lower_bound ?16998 ?16997)) ?16997 [16998, 16997] by Demod 14713 with 33810 at 3
% 17.86/4.79 Id : 227, {_}: multiply (least_upper_bound (inverse ?687) ?688) ?687 =>= least_upper_bound identity (multiply ?688 ?687) [688, 687] by Super 221 with 3 at 1,3
% 17.86/4.79 Id : 8957, {_}: multiply (least_upper_bound (inverse ?12012) ?12013) ?12012 =>= positive_part (multiply ?12013 ?12012) [12013, 12012] by Demod 227 with 320 at 3
% 17.86/4.79 Id : 317, {_}: least_upper_bound ?872 (least_upper_bound ?873 identity) =>= positive_part (least_upper_bound ?872 ?873) [873, 872] by Super 8 with 20 at 3
% 17.86/4.79 Id : 329, {_}: least_upper_bound ?872 (positive_part ?873) =>= positive_part (least_upper_bound ?872 ?873) [873, 872] by Demod 317 with 20 at 2,2
% 17.86/4.79 Id : 82917, {_}: multiply (positive_part (least_upper_bound (inverse ?99380) ?99381)) ?99380 =>= positive_part (multiply (positive_part ?99381) ?99380) [99381, 99380] by Super 8957 with 329 at 1,2
% 17.86/4.79 Id : 306, {_}: inverse (multiply ?859 (inverse ?860)) =>= multiply ?860 (inverse ?859) [860, 859] by Super 302 with 18 at 1,3
% 17.86/4.79 Id : 259, {_}: multiply (greatest_lower_bound (inverse ?764) ?765) ?764 =>= greatest_lower_bound identity (multiply ?765 ?764) [765, 764] by Super 253 with 3 at 1,3
% 17.86/4.79 Id : 12232, {_}: multiply (greatest_lower_bound (inverse ?14818) ?14819) ?14818 =>= negative_part (multiply ?14819 ?14818) [14819, 14818] by Demod 259 with 337 at 3
% 17.86/4.79 Id : 12246, {_}: multiply (negative_part (inverse ?14859)) ?14859 =>= negative_part (multiply identity ?14859) [14859] by Super 12232 with 21 at 1,2
% 17.86/4.79 Id : 12302, {_}: multiply (negative_part (inverse ?14859)) ?14859 =>= negative_part ?14859 [14859] by Demod 12246 with 2 at 1,3
% 17.86/4.79 Id : 12333, {_}: inverse (negative_part (inverse ?14889)) =<= multiply ?14889 (inverse (negative_part (inverse (inverse ?14889)))) [14889] by Super 306 with 12302 at 1,2
% 17.86/4.79 Id : 12378, {_}: inverse (negative_part (inverse ?14889)) =<= multiply ?14889 (inverse (negative_part ?14889)) [14889] by Demod 12333 with 18 at 1,1,2,3
% 17.86/4.79 Id : 12513, {_}: multiply ?15068 (positive_part (inverse (negative_part ?15068))) =>= least_upper_bound (inverse (negative_part (inverse ?15068))) ?15068 [15068] by Super 588 with 12378 at 1,3
% 17.86/4.79 Id : 570, {_}: multiply ?1314 (greatest_lower_bound ?1315 identity) =?= greatest_lower_bound (multiply ?1314 ?1315) ?1314 [1315, 1314] by Super 14 with 559 at 2,3
% 17.86/4.79 Id : 2850, {_}: multiply ?4414 (negative_part ?4415) =<= greatest_lower_bound (multiply ?4414 ?4415) ?4414 [4415, 4414] by Demod 570 with 21 at 2,2
% 17.86/4.79 Id : 2852, {_}: multiply (inverse ?4419) (negative_part ?4419) =>= greatest_lower_bound identity (inverse ?4419) [4419] by Super 2850 with 3 at 1,3
% 17.86/4.79 Id : 2904, {_}: multiply (inverse ?4491) (negative_part ?4491) =>= negative_part (inverse ?4491) [4491] by Demod 2852 with 337 at 3
% 17.86/4.79 Id : 654, {_}: greatest_lower_bound ?1405 (positive_part ?1405) =>= ?1405 [1405] by Super 12 with 20 at 2,2
% 17.86/4.79 Id : 488, {_}: least_upper_bound identity (negative_part ?1221) =>= identity [1221] by Super 11 with 337 at 2,2
% 17.86/4.79 Id : 506, {_}: positive_part (negative_part ?1221) =>= identity [1221] by Demod 488 with 320 at 2
% 17.86/4.79 Id : 656, {_}: greatest_lower_bound (negative_part ?1408) identity =>= negative_part ?1408 [1408] by Super 654 with 506 at 2,2
% 17.86/4.79 Id : 666, {_}: greatest_lower_bound identity (negative_part ?1408) =>= negative_part ?1408 [1408] by Demod 656 with 5 at 2
% 17.86/4.79 Id : 667, {_}: negative_part (negative_part ?1408) =>= negative_part ?1408 [1408] by Demod 666 with 337 at 2
% 17.86/4.79 Id : 2907, {_}: multiply (inverse (negative_part ?4496)) (negative_part ?4496) =>= negative_part (inverse (negative_part ?4496)) [4496] by Super 2904 with 667 at 2,2
% 17.86/4.79 Id : 2939, {_}: identity =<= negative_part (inverse (negative_part ?4496)) [4496] by Demod 2907 with 3 at 2
% 17.86/4.79 Id : 3011, {_}: least_upper_bound (inverse (negative_part ?4622)) identity =>= inverse (negative_part ?4622) [4622] by Super 332 with 2939 at 2,2
% 17.86/4.79 Id : 3036, {_}: least_upper_bound identity (inverse (negative_part ?4622)) =>= inverse (negative_part ?4622) [4622] by Demod 3011 with 6 at 2
% 17.86/4.79 Id : 3037, {_}: positive_part (inverse (negative_part ?4622)) =>= inverse (negative_part ?4622) [4622] by Demod 3036 with 320 at 2
% 17.86/4.79 Id : 12578, {_}: multiply ?15068 (inverse (negative_part ?15068)) =<= least_upper_bound (inverse (negative_part (inverse ?15068))) ?15068 [15068] by Demod 12513 with 3037 at 2,2
% 17.86/4.79 Id : 12579, {_}: inverse (negative_part (inverse ?15068)) =<= least_upper_bound (inverse (negative_part (inverse ?15068))) ?15068 [15068] by Demod 12578 with 12378 at 2
% 17.86/4.79 Id : 82957, {_}: multiply (positive_part (inverse (negative_part (inverse ?99500)))) (negative_part (inverse ?99500)) =>= positive_part (multiply (positive_part ?99500) (negative_part (inverse ?99500))) [99500] by Super 82917 with 12579 at 1,1,2
% 17.86/4.79 Id : 8971, {_}: multiply (positive_part (inverse ?12053)) ?12053 =>= positive_part (multiply identity ?12053) [12053] by Super 8957 with 20 at 1,2
% 17.86/4.79 Id : 9017, {_}: multiply (positive_part (inverse ?12053)) ?12053 =>= positive_part ?12053 [12053] by Demod 8971 with 2 at 1,3
% 17.86/4.79 Id : 83149, {_}: positive_part (negative_part (inverse ?99500)) =<= positive_part (multiply (positive_part ?99500) (negative_part (inverse ?99500))) [99500] by Demod 82957 with 9017 at 2
% 17.86/4.80 Id : 571, {_}: multiply ?1317 (greatest_lower_bound identity ?1318) =?= greatest_lower_bound ?1317 (multiply ?1317 ?1318) [1318, 1317] by Super 14 with 559 at 1,3
% 17.86/4.80 Id : 584, {_}: multiply ?1317 (negative_part ?1318) =<= greatest_lower_bound ?1317 (multiply ?1317 ?1318) [1318, 1317] by Demod 571 with 337 at 2,2
% 17.86/4.80 Id : 9044, {_}: multiply (positive_part (inverse ?12115)) ?12115 =>= positive_part ?12115 [12115] by Demod 8971 with 2 at 1,3
% 17.86/4.80 Id : 9046, {_}: multiply (positive_part ?12118) (inverse ?12118) =>= positive_part (inverse ?12118) [12118] by Super 9044 with 18 at 1,1,2
% 17.86/4.80 Id : 9113, {_}: multiply (positive_part ?12173) (negative_part (inverse ?12173)) =>= greatest_lower_bound (positive_part ?12173) (positive_part (inverse ?12173)) [12173] by Super 584 with 9046 at 2,3
% 17.86/4.80 Id : 454, {_}: least_upper_bound identity (greatest_lower_bound ?1183 ?1184) =<= greatest_lower_bound (least_upper_bound identity ?1183) (positive_part ?1184) [1184, 1183] by Super 22 with 320 at 2,3
% 17.86/4.80 Id : 474, {_}: positive_part (greatest_lower_bound ?1183 ?1184) =<= greatest_lower_bound (least_upper_bound identity ?1183) (positive_part ?1184) [1184, 1183] by Demod 454 with 320 at 2
% 17.86/4.80 Id : 475, {_}: positive_part (greatest_lower_bound ?1183 ?1184) =<= greatest_lower_bound (positive_part ?1184) (least_upper_bound identity ?1183) [1184, 1183] by Demod 474 with 5 at 3
% 17.86/4.80 Id : 476, {_}: positive_part (greatest_lower_bound ?1183 ?1184) =<= greatest_lower_bound (positive_part ?1184) (positive_part ?1183) [1184, 1183] by Demod 475 with 320 at 2,3
% 17.86/4.80 Id : 9142, {_}: multiply (positive_part ?12173) (negative_part (inverse ?12173)) =>= positive_part (greatest_lower_bound (inverse ?12173) ?12173) [12173] by Demod 9113 with 476 at 3
% 17.86/4.80 Id : 83150, {_}: positive_part (negative_part (inverse ?99500)) =<= positive_part (positive_part (greatest_lower_bound (inverse ?99500) ?99500)) [99500] by Demod 83149 with 9142 at 1,3
% 17.86/4.80 Id : 83151, {_}: identity =<= positive_part (positive_part (greatest_lower_bound (inverse ?99500) ?99500)) [99500] by Demod 83150 with 506 at 2
% 17.86/4.80 Id : 689, {_}: least_upper_bound ?1468 (positive_part ?1469) =>= positive_part (least_upper_bound ?1468 ?1469) [1469, 1468] by Demod 317 with 20 at 2,2
% 17.86/4.80 Id : 322, {_}: positive_part identity =>= identity [] by Super 9 with 20 at 2
% 17.86/4.80 Id : 690, {_}: least_upper_bound ?1471 identity =<= positive_part (least_upper_bound ?1471 identity) [1471] by Super 689 with 322 at 2,2
% 17.86/4.80 Id : 704, {_}: positive_part ?1471 =<= positive_part (least_upper_bound ?1471 identity) [1471] by Demod 690 with 20 at 2
% 17.86/4.80 Id : 705, {_}: positive_part ?1471 =<= positive_part (positive_part ?1471) [1471] by Demod 704 with 20 at 1,3
% 17.86/4.80 Id : 83152, {_}: identity =<= positive_part (greatest_lower_bound (inverse ?99500) ?99500) [99500] by Demod 83151 with 705 at 3
% 17.86/4.80 Id : 83301, {_}: greatest_lower_bound ?99803 (positive_part (inverse ?99803)) =>= greatest_lower_bound identity ?99803 [99803] by Super 34533 with 83152 at 1,3
% 17.86/4.80 Id : 83424, {_}: greatest_lower_bound ?99803 (positive_part (inverse ?99803)) =>= negative_part ?99803 [99803] by Demod 83301 with 337 at 3
% 17.86/4.80 Id : 84238, {_}: multiply (inverse (positive_part (inverse ?100380))) (negative_part ?100380) =>= negative_part (multiply (inverse (positive_part (inverse ?100380))) ?100380) [100380] by Super 8825 with 83424 at 2,2
% 17.86/4.80 Id : 91696, {_}: multiply (inverse (positive_part (inverse ?107282))) (positive_part (negative_part ?107282)) =<= least_upper_bound (negative_part (multiply (inverse (positive_part (inverse ?107282))) ?107282)) (inverse (positive_part (inverse ?107282))) [107282] by Super 588 with 84238 at 1,3
% 17.86/4.80 Id : 91838, {_}: multiply (inverse (positive_part (inverse ?107282))) identity =<= least_upper_bound (negative_part (multiply (inverse (positive_part (inverse ?107282))) ?107282)) (inverse (positive_part (inverse ?107282))) [107282] by Demod 91696 with 506 at 2,2
% 17.86/4.80 Id : 485, {_}: greatest_lower_bound identity (least_upper_bound ?1214 ?1215) =<= least_upper_bound (greatest_lower_bound identity ?1214) (negative_part ?1215) [1215, 1214] by Super 23 with 337 at 2,3
% 17.86/4.80 Id : 507, {_}: negative_part (least_upper_bound ?1214 ?1215) =<= least_upper_bound (greatest_lower_bound identity ?1214) (negative_part ?1215) [1215, 1214] by Demod 485 with 337 at 2
% 17.86/4.80 Id : 508, {_}: negative_part (least_upper_bound ?1214 ?1215) =<= least_upper_bound (negative_part ?1215) (greatest_lower_bound identity ?1214) [1215, 1214] by Demod 507 with 6 at 3
% 17.86/4.80 Id : 509, {_}: negative_part (least_upper_bound ?1214 ?1215) =<= least_upper_bound (negative_part ?1215) (negative_part ?1214) [1215, 1214] by Demod 508 with 337 at 2,3
% 17.86/4.80 Id : 493, {_}: negative_part (least_upper_bound identity ?1231) =>= identity [1231] by Super 12 with 337 at 2
% 17.86/4.80 Id : 501, {_}: negative_part (positive_part ?1231) =>= identity [1231] by Demod 493 with 320 at 1,2
% 17.86/4.80 Id : 2906, {_}: multiply (inverse (positive_part ?4494)) identity =>= negative_part (inverse (positive_part ?4494)) [4494] by Super 2904 with 501 at 2,2
% 17.86/4.80 Id : 2938, {_}: inverse (positive_part ?4494) =<= negative_part (inverse (positive_part ?4494)) [4494] by Demod 2906 with 559 at 2
% 17.86/4.80 Id : 2957, {_}: negative_part (least_upper_bound (inverse (positive_part ?4556)) ?4557) =<= least_upper_bound (negative_part ?4557) (inverse (positive_part ?4556)) [4557, 4556] by Super 509 with 2938 at 2,3
% 17.86/4.80 Id : 91839, {_}: multiply (inverse (positive_part (inverse ?107282))) identity =<= negative_part (least_upper_bound (inverse (positive_part (inverse ?107282))) (multiply (inverse (positive_part (inverse ?107282))) ?107282)) [107282] by Demod 91838 with 2957 at 3
% 17.86/4.80 Id : 91840, {_}: inverse (positive_part (inverse ?107282)) =<= negative_part (least_upper_bound (inverse (positive_part (inverse ?107282))) (multiply (inverse (positive_part (inverse ?107282))) ?107282)) [107282] by Demod 91839 with 559 at 2
% 17.86/4.80 Id : 565, {_}: multiply ?1303 (least_upper_bound identity ?1304) =?= least_upper_bound ?1303 (multiply ?1303 ?1304) [1304, 1303] by Super 13 with 559 at 1,3
% 17.86/4.80 Id : 589, {_}: multiply ?1303 (positive_part ?1304) =<= least_upper_bound ?1303 (multiply ?1303 ?1304) [1304, 1303] by Demod 565 with 320 at 2,2
% 17.86/4.80 Id : 91841, {_}: inverse (positive_part (inverse ?107282)) =<= negative_part (multiply (inverse (positive_part (inverse ?107282))) (positive_part ?107282)) [107282] by Demod 91840 with 589 at 1,3
% 17.86/4.80 Id : 30, {_}: multiply (multiply ?82 (inverse ?83)) ?83 =>= multiply ?82 identity [83, 82] by Super 28 with 3 at 2,3
% 17.86/4.80 Id : 8447, {_}: multiply (multiply ?82 (inverse ?83)) ?83 =>= ?82 [83, 82] by Demod 30 with 559 at 3
% 17.86/4.80 Id : 9040, {_}: inverse (positive_part (inverse ?12107)) =<= multiply ?12107 (inverse (positive_part (inverse (inverse ?12107)))) [12107] by Super 306 with 9017 at 1,2
% 17.86/4.80 Id : 9061, {_}: inverse (positive_part (inverse ?12107)) =<= multiply ?12107 (inverse (positive_part ?12107)) [12107] by Demod 9040 with 18 at 1,1,2,3
% 17.86/4.80 Id : 9208, {_}: multiply (inverse (positive_part (inverse ?12293))) (positive_part ?12293) =>= ?12293 [12293] by Super 8447 with 9061 at 1,2
% 17.86/4.80 Id : 91842, {_}: inverse (positive_part (inverse ?107282)) =>= negative_part ?107282 [107282] by Demod 91841 with 9208 at 1,3
% 17.86/4.80 Id : 92187, {_}: multiply (positive_part ?17933) (negative_part ?17933) =>= ?17933 [17933] by Demod 15572 with 91842 at 2,2
% 17.86/4.80 Id : 92848, {_}: a === a [] by Demod 1 with 92187 at 3
% 17.86/4.80 Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
% 17.86/4.80 % SZS output end CNFRefutation for theBenchmark.p
% 17.86/4.80 11499: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 4.449125 using nrkbo
%------------------------------------------------------------------------------