TSTP Solution File: GRP186-2 by Matita---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP186-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : n028.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 10:29:31 EDT 2022
% Result : Unsatisfiable 129.05s 32.62s
% Output : CNFRefutation 129.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP186-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.12/0.34 % Computer : n028.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 : Mon Jun 13 18:59:08 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 8963: Facts:
% 0.12/0.35 8963: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.12/0.35 8963: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.12/0.35 8963: Id : 4, {_}:
% 0.12/0.35 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.12/0.35 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.12/0.35 8963: Id : 5, {_}:
% 0.12/0.35 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
% 0.12/0.35 [11, 10] by symmetry_of_glb ?10 ?11
% 0.12/0.35 8963: Id : 6, {_}:
% 0.12/0.35 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
% 0.12/0.35 [14, 13] by symmetry_of_lub ?13 ?14
% 0.12/0.35 8963: Id : 7, {_}:
% 0.12/0.35 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
% 0.12/0.35 =?=
% 0.12/0.35 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
% 0.12/0.35 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 0.12/0.35 8963: Id : 8, {_}:
% 0.12/0.35 least_upper_bound ?20 (least_upper_bound ?21 ?22)
% 0.12/0.35 =?=
% 0.12/0.35 least_upper_bound (least_upper_bound ?20 ?21) ?22
% 0.12/0.35 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 0.12/0.35 8963: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.12/0.35 8963: Id : 10, {_}:
% 0.12/0.35 greatest_lower_bound ?26 ?26 =>= ?26
% 0.12/0.35 [26] by idempotence_of_gld ?26
% 0.12/0.35 8963: Id : 11, {_}:
% 0.12/0.35 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
% 0.12/0.35 [29, 28] by lub_absorbtion ?28 ?29
% 0.12/0.35 8963: Id : 12, {_}:
% 0.12/0.35 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
% 0.12/0.35 [32, 31] by glb_absorbtion ?31 ?32
% 0.12/0.35 8963: Id : 13, {_}:
% 0.12/0.35 multiply ?34 (least_upper_bound ?35 ?36)
% 0.12/0.35 =<=
% 0.12/0.35 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
% 0.12/0.35 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 0.12/0.35 8963: Id : 14, {_}:
% 0.12/0.35 multiply ?38 (greatest_lower_bound ?39 ?40)
% 0.12/0.35 =<=
% 0.12/0.35 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
% 0.12/0.35 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 0.12/0.35 8963: Id : 15, {_}:
% 0.12/0.35 multiply (least_upper_bound ?42 ?43) ?44
% 0.12/0.35 =<=
% 0.12/0.35 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
% 0.12/0.35 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 0.12/0.35 8963: Id : 16, {_}:
% 0.12/0.35 multiply (greatest_lower_bound ?46 ?47) ?48
% 0.12/0.35 =<=
% 0.12/0.35 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
% 0.12/0.35 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 0.12/0.35 8963: Id : 17, {_}: inverse identity =>= identity [] by p23_1
% 0.12/0.35 8963: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
% 0.12/0.35 8963: Id : 19, {_}:
% 0.12/0.35 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
% 0.12/0.35 [54, 53] by p23_3 ?53 ?54
% 0.12/0.35 8963: Goal:
% 0.12/0.35 8963: Id : 1, {_}:
% 0.12/0.35 least_upper_bound (multiply a b) identity
% 0.12/0.35 =<=
% 0.12/0.35 multiply a (inverse (greatest_lower_bound a (inverse b)))
% 0.12/0.35 [] by prove_p23
% 129.05/32.62 Statistics :
% 129.05/32.62 Max weight : 20
% 129.05/32.62 Found proof, 32.274178s
% 129.05/32.62 % SZS status Unsatisfiable for theBenchmark.p
% 129.05/32.62 % SZS output start CNFRefutation for theBenchmark.p
% 129.05/32.62 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 129.05/32.62 Id : 117, {_}: least_upper_bound ?399 (greatest_lower_bound ?399 ?400) =>= ?399 [400, 399] by lub_absorbtion ?399 ?400
% 129.05/32.62 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
% 129.05/32.62 Id : 10, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
% 129.05/32.62 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
% 129.05/32.62 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
% 129.05/32.62 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
% 129.05/32.62 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
% 129.05/32.62 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
% 129.05/32.62 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
% 129.05/32.62 Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
% 129.05/32.62 Id : 154, {_}: multiply ?507 (least_upper_bound ?508 ?509) =<= least_upper_bound (multiply ?507 ?508) (multiply ?507 ?509) [509, 508, 507] by monotony_lub1 ?507 ?508 ?509
% 129.05/32.62 Id : 217, {_}: multiply (least_upper_bound ?652 ?653) ?654 =<= least_upper_bound (multiply ?652 ?654) (multiply ?653 ?654) [654, 653, 652] by monotony_lub2 ?652 ?653 ?654
% 129.05/32.62 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
% 129.05/32.62 Id : 135, {_}: greatest_lower_bound ?454 (least_upper_bound ?454 ?455) =>= ?454 [455, 454] by glb_absorbtion ?454 ?455
% 129.05/32.62 Id : 249, {_}: multiply (greatest_lower_bound ?729 ?730) ?731 =<= greatest_lower_bound (multiply ?729 ?731) (multiply ?730 ?731) [731, 730, 729] by monotony_glb2 ?729 ?730 ?731
% 129.05/32.62 Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p23_3 ?53 ?54
% 129.05/32.62 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 129.05/32.62 Id : 17, {_}: inverse identity =>= identity [] by p23_1
% 129.05/32.62 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 129.05/32.62 Id : 24, {_}: multiply (multiply ?63 ?64) ?65 =?= multiply ?63 (multiply ?64 ?65) [65, 64, 63] by associativity ?63 ?64 ?65
% 129.05/32.62 Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
% 129.05/32.62 Id : 298, {_}: inverse (multiply ?837 ?838) =<= multiply (inverse ?838) (inverse ?837) [838, 837] by p23_3 ?837 ?838
% 129.05/32.62 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 129.05/32.62 Id : 302, {_}: inverse (multiply ?847 (inverse ?848)) =>= multiply ?848 (inverse ?847) [848, 847] by Super 298 with 18 at 1,3
% 129.05/32.62 Id : 26, {_}: multiply (multiply ?70 (inverse ?71)) ?71 =>= multiply ?70 identity [71, 70] by Super 24 with 3 at 2,3
% 129.05/32.62 Id : 299, {_}: inverse (multiply identity ?840) =<= multiply (inverse ?840) identity [840] by Super 298 with 17 at 2,3
% 129.05/32.62 Id : 323, {_}: inverse ?886 =<= multiply (inverse ?886) identity [886] by Demod 299 with 2 at 1,2
% 129.05/32.62 Id : 325, {_}: inverse (inverse ?889) =<= multiply ?889 identity [889] by Super 323 with 18 at 1,3
% 129.05/32.62 Id : 335, {_}: ?889 =<= multiply ?889 identity [889] by Demod 325 with 18 at 2
% 129.05/32.62 Id : 1187, {_}: multiply (multiply ?70 (inverse ?71)) ?71 =>= ?70 [71, 70] by Demod 26 with 335 at 3
% 129.05/32.62 Id : 1188, {_}: inverse ?2298 =<= multiply ?2299 (inverse (multiply ?2298 (inverse (inverse ?2299)))) [2299, 2298] by Super 302 with 1187 at 1,2
% 129.05/32.62 Id : 1219, {_}: inverse ?2298 =<= multiply ?2299 (multiply (inverse ?2299) (inverse ?2298)) [2299, 2298] by Demod 1188 with 302 at 2,3
% 129.05/32.62 Id : 1220, {_}: inverse ?2298 =<= multiply ?2299 (inverse (multiply ?2298 ?2299)) [2299, 2298] by Demod 1219 with 19 at 2,3
% 129.05/32.62 Id : 255, {_}: multiply (greatest_lower_bound (inverse ?752) ?753) ?752 =>= greatest_lower_bound identity (multiply ?753 ?752) [753, 752] by Super 249 with 3 at 1,3
% 129.05/32.62 Id : 1632, {_}: multiply (greatest_lower_bound identity (multiply ?3085 (inverse ?3086))) ?3086 =>= greatest_lower_bound (inverse (inverse ?3086)) ?3085 [3086, 3085] by Super 1187 with 255 at 1,2
% 129.05/32.62 Id : 110619, {_}: multiply (greatest_lower_bound identity (multiply ?120843 (inverse ?120844))) ?120844 =>= greatest_lower_bound ?120844 ?120843 [120844, 120843] by Demod 1632 with 18 at 1,3
% 129.05/32.62 Id : 110660, {_}: multiply (greatest_lower_bound identity (inverse (multiply ?120977 ?120978))) ?120977 =>= greatest_lower_bound ?120977 (inverse ?120978) [120978, 120977] by Super 110619 with 19 at 2,1,2
% 129.05/32.62 Id : 254899, {_}: inverse (greatest_lower_bound identity (inverse (multiply ?297090 ?297091))) =<= multiply ?297090 (inverse (greatest_lower_bound ?297090 (inverse ?297091))) [297091, 297090] by Super 1220 with 110660 at 1,2,3
% 129.05/32.62 Id : 136, {_}: greatest_lower_bound ?457 (least_upper_bound ?458 ?457) =>= ?457 [458, 457] by Super 135 with 6 at 2,2
% 129.05/32.62 Id : 281, {_}: multiply ?786 (inverse ?786) =>= identity [786] by Super 3 with 18 at 1,2
% 129.05/32.62 Id : 373, {_}: multiply (multiply ?947 ?948) (inverse ?948) =>= multiply ?947 identity [948, 947] by Super 4 with 281 at 2,3
% 129.05/32.62 Id : 2200, {_}: multiply (multiply ?3921 ?3922) (inverse ?3922) =>= ?3921 [3922, 3921] by Demod 373 with 335 at 3
% 129.05/32.62 Id : 223, {_}: multiply (least_upper_bound (inverse ?675) ?676) ?675 =>= least_upper_bound identity (multiply ?676 ?675) [676, 675] by Super 217 with 3 at 1,3
% 129.05/32.62 Id : 2212, {_}: multiply (least_upper_bound identity (multiply ?3957 ?3958)) (inverse ?3958) =>= least_upper_bound (inverse ?3958) ?3957 [3958, 3957] by Super 2200 with 223 at 1,2
% 129.05/32.62 Id : 300, {_}: inverse (multiply (inverse ?842) ?843) =>= multiply (inverse ?843) ?842 [843, 842] by Super 298 with 18 at 2,3
% 129.05/32.62 Id : 1202, {_}: multiply (multiply ?2351 (inverse ?2352)) ?2352 =>= ?2351 [2352, 2351] by Demod 26 with 335 at 3
% 129.05/32.62 Id : 1212, {_}: multiply (inverse (multiply ?2380 ?2381)) ?2380 =>= inverse ?2381 [2381, 2380] by Super 1202 with 19 at 1,2
% 129.05/32.62 Id : 2425, {_}: inverse (inverse ?4293) =<= multiply (inverse ?4294) (multiply ?4294 ?4293) [4294, 4293] by Super 300 with 1212 at 1,2
% 129.05/32.62 Id : 2636, {_}: ?4605 =<= multiply (inverse ?4606) (multiply ?4606 ?4605) [4606, 4605] by Demod 2425 with 18 at 2
% 129.05/32.62 Id : 160, {_}: multiply (inverse ?530) (least_upper_bound ?530 ?531) =>= least_upper_bound identity (multiply (inverse ?530) ?531) [531, 530] by Super 154 with 3 at 1,3
% 129.05/32.62 Id : 2640, {_}: least_upper_bound ?4616 ?4617 =<= multiply (inverse (inverse ?4616)) (least_upper_bound identity (multiply (inverse ?4616) ?4617)) [4617, 4616] by Super 2636 with 160 at 2,3
% 129.05/32.62 Id : 2681, {_}: least_upper_bound ?4616 ?4617 =<= multiply ?4616 (least_upper_bound identity (multiply (inverse ?4616) ?4617)) [4617, 4616] by Demod 2640 with 18 at 1,3
% 129.05/32.62 Id : 1245, {_}: multiply (inverse ?2437) (least_upper_bound ?2437 ?2438) =>= least_upper_bound identity (multiply (inverse ?2437) ?2438) [2438, 2437] by Super 154 with 3 at 1,3
% 129.05/32.62 Id : 111, {_}: least_upper_bound (greatest_lower_bound ?377 ?378) ?377 =>= ?377 [378, 377] by Super 6 with 11 at 3
% 129.05/32.62 Id : 1251, {_}: multiply (inverse (greatest_lower_bound ?2455 ?2456)) ?2455 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?2455 ?2456)) ?2455) [2456, 2455] by Super 1245 with 111 at 2,2
% 129.05/32.62 Id : 622, {_}: greatest_lower_bound (least_upper_bound ?1381 ?1382) ?1381 =>= ?1381 [1382, 1381] by Super 5 with 12 at 3
% 129.05/32.62 Id : 623, {_}: greatest_lower_bound (least_upper_bound ?1384 ?1385) ?1385 =>= ?1385 [1385, 1384] by Super 622 with 6 at 1,2
% 129.05/32.62 Id : 9557, {_}: multiply (inverse (greatest_lower_bound ?18643 ?18644)) ?18643 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound ?18643 ?18644)) ?18643) [18644, 18643] by Super 1245 with 111 at 2,2
% 129.05/32.62 Id : 9590, {_}: multiply (inverse (greatest_lower_bound identity ?18760)) identity =>= least_upper_bound identity (inverse (greatest_lower_bound identity ?18760)) [18760] by Super 9557 with 335 at 2,3
% 129.05/32.62 Id : 9781, {_}: inverse (greatest_lower_bound identity ?18867) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?18867)) [18867] by Demod 9590 with 335 at 2
% 129.05/32.62 Id : 9782, {_}: inverse (greatest_lower_bound identity ?18869) =<= least_upper_bound identity (inverse (greatest_lower_bound ?18869 identity)) [18869] by Super 9781 with 5 at 1,2,3
% 129.05/32.62 Id : 12506, {_}: least_upper_bound identity (least_upper_bound (inverse (greatest_lower_bound ?21757 identity)) ?21758) =>= least_upper_bound (inverse (greatest_lower_bound identity ?21757)) ?21758 [21758, 21757] by Super 8 with 9782 at 1,3
% 129.05/32.62 Id : 12519, {_}: least_upper_bound identity (least_upper_bound ?21800 (inverse (greatest_lower_bound ?21801 identity))) =>= least_upper_bound (inverse (greatest_lower_bound identity ?21801)) ?21800 [21801, 21800] by Super 12506 with 6 at 2,2
% 129.05/32.62 Id : 1509, {_}: multiply (least_upper_bound identity (multiply ?2891 (inverse ?2892))) ?2892 =>= least_upper_bound (inverse (inverse ?2892)) ?2891 [2892, 2891] by Super 1187 with 223 at 1,2
% 129.05/32.63 Id : 68552, {_}: multiply (least_upper_bound identity (multiply ?82597 (inverse ?82598))) ?82598 =>= least_upper_bound ?82598 ?82597 [82598, 82597] by Demod 1509 with 18 at 1,3
% 129.05/32.63 Id : 68595, {_}: multiply (multiply (inverse (greatest_lower_bound (inverse ?82732) ?82733)) (inverse ?82732)) ?82732 =>= least_upper_bound ?82732 (inverse (greatest_lower_bound (inverse ?82732) ?82733)) [82733, 82732] by Super 68552 with 1251 at 1,2
% 129.05/32.63 Id : 68694, {_}: multiply (inverse (greatest_lower_bound (inverse ?82732) ?82733)) (multiply (inverse ?82732) ?82732) =>= least_upper_bound ?82732 (inverse (greatest_lower_bound (inverse ?82732) ?82733)) [82733, 82732] by Demod 68595 with 4 at 2
% 129.05/32.63 Id : 406, {_}: inverse (multiply (multiply (inverse ?980) ?981) ?982) =<= multiply (inverse ?982) (multiply (inverse ?981) ?980) [982, 981, 980] by Super 19 with 300 at 2,3
% 129.05/32.63 Id : 423, {_}: inverse (multiply (inverse ?980) (multiply ?981 ?982)) =<= multiply (inverse ?982) (multiply (inverse ?981) ?980) [982, 981, 980] by Demod 406 with 4 at 1,2
% 129.05/32.63 Id : 424, {_}: multiply (inverse (multiply ?981 ?982)) ?980 =<= multiply (inverse ?982) (multiply (inverse ?981) ?980) [980, 982, 981] by Demod 423 with 300 at 2
% 129.05/32.63 Id : 68695, {_}: multiply (inverse (multiply ?82732 (greatest_lower_bound (inverse ?82732) ?82733))) ?82732 =>= least_upper_bound ?82732 (inverse (greatest_lower_bound (inverse ?82732) ?82733)) [82733, 82732] by Demod 68694 with 424 at 2
% 129.05/32.63 Id : 68696, {_}: inverse (greatest_lower_bound (inverse ?82732) ?82733) =<= least_upper_bound ?82732 (inverse (greatest_lower_bound (inverse ?82732) ?82733)) [82733, 82732] by Demod 68695 with 1212 at 2
% 129.05/32.63 Id : 68735, {_}: least_upper_bound identity (inverse (greatest_lower_bound (inverse ?82821) identity)) =<= least_upper_bound (inverse (greatest_lower_bound identity (inverse ?82821))) ?82821 [82821] by Super 12519 with 68696 at 2,2
% 129.05/32.63 Id : 69071, {_}: inverse (greatest_lower_bound identity (inverse ?82821)) =<= least_upper_bound (inverse (greatest_lower_bound identity (inverse ?82821))) ?82821 [82821] by Demod 68735 with 9782 at 2
% 129.05/32.63 Id : 70928, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity (inverse ?84296))) ?84296 =>= ?84296 [84296] by Super 623 with 69071 at 1,2
% 129.05/32.63 Id : 70930, {_}: greatest_lower_bound (inverse (greatest_lower_bound identity ?84299)) (inverse ?84299) =>= inverse ?84299 [84299] by Super 70928 with 18 at 2,1,1,2
% 129.05/32.63 Id : 72861, {_}: multiply (inverse (greatest_lower_bound (inverse (greatest_lower_bound identity ?85521)) (inverse ?85521))) (inverse (greatest_lower_bound identity ?85521)) =>= least_upper_bound identity (multiply (inverse (inverse ?85521)) (inverse (greatest_lower_bound identity ?85521))) [85521] by Super 1251 with 70930 at 1,1,2,3
% 129.05/32.63 Id : 72969, {_}: inverse (multiply (greatest_lower_bound identity ?85521) (greatest_lower_bound (inverse (greatest_lower_bound identity ?85521)) (inverse ?85521))) =>= least_upper_bound identity (multiply (inverse (inverse ?85521)) (inverse (greatest_lower_bound identity ?85521))) [85521] by Demod 72861 with 19 at 2
% 129.05/32.63 Id : 72970, {_}: inverse (multiply (greatest_lower_bound identity ?85521) (greatest_lower_bound (inverse (greatest_lower_bound identity ?85521)) (inverse ?85521))) =>= least_upper_bound identity (inverse (multiply (greatest_lower_bound identity ?85521) (inverse ?85521))) [85521] by Demod 72969 with 19 at 2,3
% 129.05/32.63 Id : 372, {_}: multiply ?944 (greatest_lower_bound (inverse ?944) ?945) =>= greatest_lower_bound identity (multiply ?944 ?945) [945, 944] by Super 14 with 281 at 1,3
% 129.05/32.63 Id : 72971, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?85521) (inverse ?85521))) =<= least_upper_bound identity (inverse (multiply (greatest_lower_bound identity ?85521) (inverse ?85521))) [85521] by Demod 72970 with 372 at 1,2
% 129.05/32.63 Id : 72972, {_}: inverse (greatest_lower_bound identity (multiply (greatest_lower_bound identity ?85521) (inverse ?85521))) =>= least_upper_bound identity (multiply ?85521 (inverse (greatest_lower_bound identity ?85521))) [85521] by Demod 72971 with 302 at 2,3
% 129.05/32.63 Id : 369, {_}: multiply (greatest_lower_bound ?935 ?936) (inverse ?936) =>= greatest_lower_bound (multiply ?935 (inverse ?936)) identity [936, 935] by Super 16 with 281 at 2,3
% 129.05/32.63 Id : 396, {_}: multiply (greatest_lower_bound ?935 ?936) (inverse ?936) =>= greatest_lower_bound identity (multiply ?935 (inverse ?936)) [936, 935] by Demod 369 with 5 at 3
% 129.05/32.63 Id : 72973, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound identity (multiply identity (inverse ?85521)))) =?= least_upper_bound identity (multiply ?85521 (inverse (greatest_lower_bound identity ?85521))) [85521] by Demod 72972 with 396 at 2,1,2
% 129.05/32.63 Id : 103, {_}: greatest_lower_bound ?355 (greatest_lower_bound ?355 ?356) =>= greatest_lower_bound ?355 ?356 [356, 355] by Super 7 with 10 at 1,3
% 129.05/32.63 Id : 72974, {_}: inverse (greatest_lower_bound identity (multiply identity (inverse ?85521))) =<= least_upper_bound identity (multiply ?85521 (inverse (greatest_lower_bound identity ?85521))) [85521] by Demod 72973 with 103 at 1,2
% 129.05/32.63 Id : 72975, {_}: inverse (greatest_lower_bound identity (inverse ?85521)) =<= least_upper_bound identity (multiply ?85521 (inverse (greatest_lower_bound identity ?85521))) [85521] by Demod 72974 with 2 at 2,1,2
% 129.05/32.63 Id : 376, {_}: multiply ?954 (least_upper_bound ?955 (inverse ?954)) =>= least_upper_bound (multiply ?954 ?955) identity [955, 954] by Super 13 with 281 at 2,3
% 129.05/32.63 Id : 391, {_}: multiply ?954 (least_upper_bound ?955 (inverse ?954)) =>= least_upper_bound identity (multiply ?954 ?955) [955, 954] by Demod 376 with 6 at 3
% 129.05/32.63 Id : 69375, {_}: multiply ?83445 (inverse (greatest_lower_bound identity (inverse (inverse ?83445)))) =<= least_upper_bound identity (multiply ?83445 (inverse (greatest_lower_bound identity (inverse (inverse ?83445))))) [83445] by Super 391 with 69071 at 2,2
% 129.05/32.63 Id : 69769, {_}: multiply ?83445 (inverse (greatest_lower_bound identity ?83445)) =<= least_upper_bound identity (multiply ?83445 (inverse (greatest_lower_bound identity (inverse (inverse ?83445))))) [83445] by Demod 69375 with 18 at 2,1,2,2
% 129.05/32.63 Id : 69770, {_}: multiply ?83445 (inverse (greatest_lower_bound identity ?83445)) =<= least_upper_bound identity (multiply ?83445 (inverse (greatest_lower_bound identity ?83445))) [83445] by Demod 69769 with 18 at 2,1,2,2,3
% 129.05/32.63 Id : 89953, {_}: inverse (greatest_lower_bound identity (inverse ?85521)) =<= multiply ?85521 (inverse (greatest_lower_bound identity ?85521)) [85521] by Demod 72975 with 69770 at 3
% 129.05/32.63 Id : 89977, {_}: multiply (inverse (greatest_lower_bound identity (inverse ?99534))) (greatest_lower_bound identity ?99534) =>= ?99534 [99534] by Super 1187 with 89953 at 1,2
% 129.05/32.63 Id : 221505, {_}: least_upper_bound (greatest_lower_bound identity (inverse ?272954)) (greatest_lower_bound identity ?272954) =<= multiply (greatest_lower_bound identity (inverse ?272954)) (least_upper_bound identity ?272954) [272954] by Super 2681 with 89977 at 2,2,3
% 129.05/32.63 Id : 222047, {_}: multiply (least_upper_bound identity (least_upper_bound (greatest_lower_bound identity (inverse ?273420)) (greatest_lower_bound identity ?273420))) (inverse (least_upper_bound identity ?273420)) =>= least_upper_bound (inverse (least_upper_bound identity ?273420)) (greatest_lower_bound identity (inverse ?273420)) [273420] by Super 2212 with 221505 at 2,1,2
% 129.05/32.63 Id : 113, {_}: least_upper_bound ?383 (least_upper_bound (greatest_lower_bound ?383 ?384) ?385) =>= least_upper_bound ?383 ?385 [385, 384, 383] by Super 8 with 11 at 1,3
% 129.05/32.63 Id : 222181, {_}: multiply (least_upper_bound identity (greatest_lower_bound identity ?273420)) (inverse (least_upper_bound identity ?273420)) =>= least_upper_bound (inverse (least_upper_bound identity ?273420)) (greatest_lower_bound identity (inverse ?273420)) [273420] by Demod 222047 with 113 at 1,2
% 129.05/32.63 Id : 222182, {_}: multiply identity (inverse (least_upper_bound identity ?273420)) =<= least_upper_bound (inverse (least_upper_bound identity ?273420)) (greatest_lower_bound identity (inverse ?273420)) [273420] by Demod 222181 with 11 at 1,2
% 129.05/32.63 Id : 222183, {_}: inverse (least_upper_bound identity ?273420) =<= least_upper_bound (inverse (least_upper_bound identity ?273420)) (greatest_lower_bound identity (inverse ?273420)) [273420] by Demod 222182 with 2 at 2
% 129.05/32.63 Id : 403579, {_}: greatest_lower_bound (greatest_lower_bound identity (inverse ?438811)) (inverse (least_upper_bound identity ?438811)) =>= greatest_lower_bound identity (inverse ?438811) [438811] by Super 136 with 222183 at 2,2
% 129.05/32.63 Id : 403976, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?438811)) (greatest_lower_bound identity (inverse ?438811)) =>= greatest_lower_bound identity (inverse ?438811) [438811] by Demod 403579 with 5 at 2
% 129.05/32.63 Id : 586, {_}: least_upper_bound ?1313 (greatest_lower_bound ?1314 ?1313) =>= ?1313 [1314, 1313] by Super 117 with 5 at 2,2
% 129.05/32.63 Id : 593, {_}: least_upper_bound ?1334 (greatest_lower_bound ?1335 (greatest_lower_bound ?1336 ?1334)) =>= ?1334 [1336, 1335, 1334] by Super 586 with 7 at 2,2
% 129.05/32.63 Id : 4682, {_}: greatest_lower_bound ?8735 (greatest_lower_bound ?8736 (greatest_lower_bound ?8737 ?8735)) =>= greatest_lower_bound ?8736 (greatest_lower_bound ?8737 ?8735) [8737, 8736, 8735] by Super 623 with 593 at 1,2
% 129.05/32.63 Id : 521, {_}: greatest_lower_bound ?1179 (greatest_lower_bound ?1179 ?1180) =>= greatest_lower_bound ?1179 ?1180 [1180, 1179] by Super 7 with 10 at 1,3
% 129.05/32.63 Id : 873, {_}: greatest_lower_bound ?1837 (greatest_lower_bound ?1838 ?1837) =>= greatest_lower_bound ?1837 ?1838 [1838, 1837] by Super 521 with 5 at 2,2
% 129.05/32.63 Id : 884, {_}: greatest_lower_bound ?1870 (greatest_lower_bound ?1871 (greatest_lower_bound ?1872 ?1870)) =>= greatest_lower_bound ?1870 (greatest_lower_bound ?1871 ?1872) [1872, 1871, 1870] by Super 873 with 7 at 2,2
% 129.05/32.63 Id : 135601, {_}: greatest_lower_bound ?8735 (greatest_lower_bound ?8736 ?8737) =?= greatest_lower_bound ?8736 (greatest_lower_bound ?8737 ?8735) [8737, 8736, 8735] by Demod 4682 with 884 at 2
% 129.05/32.63 Id : 403977, {_}: greatest_lower_bound identity (greatest_lower_bound (inverse ?438811) (inverse (least_upper_bound identity ?438811))) =>= greatest_lower_bound identity (inverse ?438811) [438811] by Demod 403976 with 135601 at 2
% 129.05/32.63 Id : 666, {_}: greatest_lower_bound ?1464 (least_upper_bound ?1465 ?1464) =>= ?1464 [1465, 1464] by Super 135 with 6 at 2,2
% 129.05/32.63 Id : 118, {_}: least_upper_bound ?402 (greatest_lower_bound ?403 ?402) =>= ?402 [403, 402] by Super 117 with 5 at 2,2
% 129.05/32.63 Id : 673, {_}: greatest_lower_bound (greatest_lower_bound ?1484 ?1485) ?1485 =>= greatest_lower_bound ?1484 ?1485 [1485, 1484] by Super 666 with 118 at 2,2
% 129.05/32.63 Id : 660, {_}: greatest_lower_bound ?1444 (greatest_lower_bound (least_upper_bound ?1445 ?1444) ?1446) =>= greatest_lower_bound ?1444 ?1446 [1446, 1445, 1444] by Super 7 with 136 at 1,3
% 129.05/32.63 Id : 156, {_}: multiply (inverse ?514) (least_upper_bound ?515 ?514) =>= least_upper_bound (multiply (inverse ?514) ?515) identity [515, 514] by Super 154 with 3 at 2,3
% 129.05/32.63 Id : 173, {_}: multiply (inverse ?514) (least_upper_bound ?515 ?514) =>= least_upper_bound identity (multiply (inverse ?514) ?515) [515, 514] by Demod 156 with 6 at 3
% 129.05/32.63 Id : 9741, {_}: inverse (greatest_lower_bound identity ?18760) =<= least_upper_bound identity (inverse (greatest_lower_bound identity ?18760)) [18760] by Demod 9590 with 335 at 2
% 129.05/32.63 Id : 9940, {_}: greatest_lower_bound identity (inverse (greatest_lower_bound identity ?18997)) =>= identity [18997] by Super 12 with 9741 at 2,2
% 129.05/32.63 Id : 9941, {_}: greatest_lower_bound identity (inverse (greatest_lower_bound ?18999 identity)) =>= identity [18999] by Super 9940 with 5 at 1,2,2
% 129.05/32.63 Id : 10226, {_}: least_upper_bound (inverse (greatest_lower_bound ?19200 identity)) identity =>= inverse (greatest_lower_bound ?19200 identity) [19200] by Super 118 with 9941 at 2,2
% 129.05/32.63 Id : 10297, {_}: least_upper_bound identity (inverse (greatest_lower_bound ?19200 identity)) =>= inverse (greatest_lower_bound ?19200 identity) [19200] by Demod 10226 with 6 at 2
% 129.05/32.63 Id : 10298, {_}: inverse (greatest_lower_bound identity ?19200) =?= inverse (greatest_lower_bound ?19200 identity) [19200] by Demod 10297 with 9782 at 2
% 129.05/32.63 Id : 14763, {_}: multiply (inverse (greatest_lower_bound ?24329 identity)) ?24329 =<= least_upper_bound identity (multiply (inverse (greatest_lower_bound identity ?24329)) ?24329) [24329] by Super 1251 with 10298 at 1,2,3
% 129.05/32.63 Id : 10091, {_}: inverse (greatest_lower_bound identity ?19122) =<= least_upper_bound identity (inverse (greatest_lower_bound ?19122 identity)) [19122] by Super 9781 with 5 at 1,2,3
% 129.05/32.63 Id : 12752, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound ?22003 ?22004)) =<= least_upper_bound identity (inverse (greatest_lower_bound ?22003 (greatest_lower_bound ?22004 identity))) [22004, 22003] by Super 10091 with 7 at 1,2,3
% 129.05/32.63 Id : 128, {_}: greatest_lower_bound (least_upper_bound ?430 ?431) ?430 =>= ?430 [431, 430] by Super 5 with 12 at 3
% 129.05/32.63 Id : 12755, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound ?22011 (least_upper_bound identity ?22012))) =>= least_upper_bound identity (inverse (greatest_lower_bound ?22011 identity)) [22012, 22011] by Super 12752 with 128 at 2,1,2,3
% 129.05/32.63 Id : 18253, {_}: inverse (greatest_lower_bound identity (greatest_lower_bound ?28575 (least_upper_bound identity ?28576))) =>= inverse (greatest_lower_bound identity ?28575) [28576, 28575] by Demod 12755 with 9782 at 3
% 129.05/32.63 Id : 18284, {_}: inverse (greatest_lower_bound identity (least_upper_bound identity ?28670)) =<= inverse (greatest_lower_bound identity (least_upper_bound ?28671 (least_upper_bound identity ?28670))) [28671, 28670] by Super 18253 with 623 at 2,1,2
% 129.05/32.63 Id : 18386, {_}: inverse identity =<= inverse (greatest_lower_bound identity (least_upper_bound ?28671 (least_upper_bound identity ?28670))) [28670, 28671] by Demod 18284 with 12 at 1,2
% 129.05/32.63 Id : 18387, {_}: identity =<= inverse (greatest_lower_bound identity (least_upper_bound ?28671 (least_upper_bound identity ?28670))) [28670, 28671] by Demod 18386 with 17 at 2
% 129.05/32.63 Id : 22982, {_}: multiply (inverse (greatest_lower_bound (least_upper_bound ?33937 (least_upper_bound identity ?33938)) identity)) (least_upper_bound ?33937 (least_upper_bound identity ?33938)) =>= least_upper_bound identity (multiply identity (least_upper_bound ?33937 (least_upper_bound identity ?33938))) [33938, 33937] by Super 14763 with 18387 at 1,2,3
% 129.05/32.63 Id : 23049, {_}: multiply (inverse (greatest_lower_bound identity (least_upper_bound ?33937 (least_upper_bound identity ?33938)))) (least_upper_bound ?33937 (least_upper_bound identity ?33938)) =>= least_upper_bound identity (multiply identity (least_upper_bound ?33937 (least_upper_bound identity ?33938))) [33938, 33937] by Demod 22982 with 10298 at 1,2
% 129.05/32.63 Id : 23050, {_}: multiply (inverse (greatest_lower_bound identity (least_upper_bound ?33937 (least_upper_bound identity ?33938)))) (least_upper_bound ?33937 (least_upper_bound identity ?33938)) =>= least_upper_bound identity (least_upper_bound ?33937 (least_upper_bound identity ?33938)) [33938, 33937] by Demod 23049 with 2 at 2,3
% 129.05/32.63 Id : 23051, {_}: multiply identity (least_upper_bound ?33937 (least_upper_bound identity ?33938)) =>= least_upper_bound identity (least_upper_bound ?33937 (least_upper_bound identity ?33938)) [33938, 33937] by Demod 23050 with 18387 at 1,2
% 129.05/32.63 Id : 23052, {_}: least_upper_bound ?33937 (least_upper_bound identity ?33938) =<= least_upper_bound identity (least_upper_bound ?33937 (least_upper_bound identity ?33938)) [33938, 33937] by Demod 23051 with 2 at 2
% 129.05/32.63 Id : 23259, {_}: multiply (inverse (least_upper_bound ?34225 (least_upper_bound identity ?34226))) (least_upper_bound ?34225 (least_upper_bound identity ?34226)) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?34225 (least_upper_bound identity ?34226))) identity) [34226, 34225] by Super 173 with 23052 at 2,2
% 129.05/32.63 Id : 23371, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?34225 (least_upper_bound identity ?34226))) identity) [34226, 34225] by Demod 23259 with 3 at 2
% 129.05/32.63 Id : 26301, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound ?37790 (least_upper_bound identity ?37791))) [37791, 37790] by Demod 23371 with 335 at 2,3
% 129.05/32.63 Id : 26334, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound identity ?37892)) [37892] by Super 26301 with 9 at 1,2,3
% 129.05/32.63 Id : 26673, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?38140)) (greatest_lower_bound identity ?38141) =>= greatest_lower_bound (inverse (least_upper_bound identity ?38140)) ?38141 [38141, 38140] by Super 660 with 26334 at 1,2,2
% 129.05/32.63 Id : 33749, {_}: greatest_lower_bound (greatest_lower_bound (inverse (least_upper_bound identity ?46128)) ?46129) (greatest_lower_bound identity ?46129) =>= greatest_lower_bound (inverse (least_upper_bound identity ?46128)) (greatest_lower_bound identity ?46129) [46129, 46128] by Super 673 with 26673 at 1,2
% 129.05/32.63 Id : 33920, {_}: greatest_lower_bound (greatest_lower_bound identity ?46129) (greatest_lower_bound (inverse (least_upper_bound identity ?46128)) ?46129) =>= greatest_lower_bound (inverse (least_upper_bound identity ?46128)) (greatest_lower_bound identity ?46129) [46128, 46129] by Demod 33749 with 5 at 2
% 129.05/32.63 Id : 33921, {_}: greatest_lower_bound (greatest_lower_bound identity ?46129) (greatest_lower_bound (inverse (least_upper_bound identity ?46128)) ?46129) =>= greatest_lower_bound (inverse (least_upper_bound identity ?46128)) ?46129 [46128, 46129] by Demod 33920 with 26673 at 3
% 129.05/32.63 Id : 33922, {_}: greatest_lower_bound identity (greatest_lower_bound ?46129 (greatest_lower_bound (inverse (least_upper_bound identity ?46128)) ?46129)) =>= greatest_lower_bound (inverse (least_upper_bound identity ?46128)) ?46129 [46128, 46129] by Demod 33921 with 7 at 2
% 129.05/32.63 Id : 522, {_}: greatest_lower_bound ?1182 (greatest_lower_bound ?1183 ?1182) =>= greatest_lower_bound ?1182 ?1183 [1183, 1182] by Super 521 with 5 at 2,2
% 129.05/32.63 Id : 33923, {_}: greatest_lower_bound identity (greatest_lower_bound ?46129 (inverse (least_upper_bound identity ?46128))) =>= greatest_lower_bound (inverse (least_upper_bound identity ?46128)) ?46129 [46128, 46129] by Demod 33922 with 522 at 2,2
% 129.05/32.63 Id : 403978, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?438811)) (inverse ?438811) =>= greatest_lower_bound identity (inverse ?438811) [438811] by Demod 403977 with 33923 at 2
% 129.05/32.63 Id : 655, {_}: least_upper_bound (least_upper_bound ?1430 ?1431) ?1431 =>= least_upper_bound ?1430 ?1431 [1431, 1430] by Super 118 with 136 at 2,2
% 129.05/32.63 Id : 1256, {_}: multiply (inverse (least_upper_bound ?2470 ?2471)) (least_upper_bound ?2470 ?2471) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?2470 ?2471)) ?2471) [2471, 2470] by Super 1245 with 655 at 2,2
% 129.05/32.63 Id : 1286, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?2470 ?2471)) ?2471) [2471, 2470] by Demod 1256 with 3 at 2
% 129.05/32.63 Id : 68598, {_}: multiply identity ?82741 =<= least_upper_bound ?82741 (inverse (least_upper_bound ?82742 (inverse ?82741))) [82742, 82741] by Super 68552 with 1286 at 1,2
% 129.05/32.63 Id : 68701, {_}: ?82741 =<= least_upper_bound ?82741 (inverse (least_upper_bound ?82742 (inverse ?82741))) [82742, 82741] by Demod 68598 with 2 at 2
% 129.05/32.63 Id : 98583, {_}: greatest_lower_bound (inverse (least_upper_bound ?107136 (inverse ?107137))) ?107137 =>= inverse (least_upper_bound ?107136 (inverse ?107137)) [107137, 107136] by Super 136 with 68701 at 2,2
% 129.05/32.63 Id : 98585, {_}: greatest_lower_bound (inverse (least_upper_bound ?107141 ?107142)) (inverse ?107142) =>= inverse (least_upper_bound ?107141 (inverse (inverse ?107142))) [107142, 107141] by Super 98583 with 18 at 2,1,1,2
% 129.05/32.63 Id : 98989, {_}: greatest_lower_bound (inverse (least_upper_bound ?107141 ?107142)) (inverse ?107142) =>= inverse (least_upper_bound ?107141 ?107142) [107142, 107141] by Demod 98585 with 18 at 2,1,3
% 129.05/32.63 Id : 403979, {_}: inverse (least_upper_bound identity ?438811) =<= greatest_lower_bound identity (inverse ?438811) [438811] by Demod 403978 with 98989 at 2
% 129.05/32.63 Id : 404759, {_}: inverse (inverse (least_upper_bound identity (multiply ?297090 ?297091))) =<= multiply ?297090 (inverse (greatest_lower_bound ?297090 (inverse ?297091))) [297091, 297090] by Demod 254899 with 403979 at 1,2
% 129.05/32.63 Id : 404779, {_}: least_upper_bound identity (multiply ?297090 ?297091) =<= multiply ?297090 (inverse (greatest_lower_bound ?297090 (inverse ?297091))) [297091, 297090] by Demod 404759 with 18 at 2
% 129.05/32.63 Id : 405734, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 311 with 404779 at 3
% 129.05/32.63 Id : 311, {_}: least_upper_bound identity (multiply a b) =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by Demod 1 with 6 at 2
% 129.05/32.63 Id : 1, {_}: least_upper_bound (multiply a b) identity =<= multiply a (inverse (greatest_lower_bound a (inverse b))) [] by prove_p23
% 129.05/32.63 % SZS output end CNFRefutation for theBenchmark.p
% 129.05/32.63 8966: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 32.278571 using nrkbo
%------------------------------------------------------------------------------