TSTP Solution File: GRP014-1 by Matita---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : n013.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 10:28:25 EDT 2022
% Result : Unsatisfiable 5.46s 1.70s
% Output : CNFRefutation 5.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 23:42:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 5342: Facts:
% 0.13/0.35 5342: Id : 2, {_}:
% 0.13/0.35 multiply ?2
% 0.13/0.35 (inverse
% 0.13/0.35 (multiply
% 0.13/0.35 (multiply
% 0.13/0.35 (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
% 0.13/0.35 ?5) (inverse (multiply ?3 ?5))))
% 0.13/0.35 =>=
% 0.13/0.35 ?4
% 0.13/0.35 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
% 0.13/0.35 5342: Goal:
% 0.13/0.35 5342: Id : 1, {_}:
% 0.13/0.35 multiply a (multiply b c) =<= multiply (multiply a b) c
% 0.13/0.35 [] by prove_associativity
% 5.46/1.70 Statistics :
% 5.46/1.70 Max weight : 50
% 5.46/1.70 Found proof, 1.350743s
% 5.46/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 5.46/1.70 % SZS output start CNFRefutation for theBenchmark.p
% 5.46/1.70 Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
% 5.46/1.70 Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
% 5.46/1.70 Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2
% 5.46/1.70 Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
% 5.46/1.70 Id : 63, {_}: multiply (inverse ?569) (multiply ?569 (inverse (multiply (multiply (inverse (multiply (inverse ?570) ?571)) ?572) (inverse (multiply ?570 ?572))))) =>= ?571 [572, 571, 570, 569] by Super 2 with 5 at 2,2
% 5.46/1.70 Id : 64, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?574) (multiply (inverse (inverse ?575)) (multiply (inverse ?575) ?576)))) ?577) (inverse (multiply ?574 ?577))) =>= ?576 [577, 576, 575, 574] by Super 2 with 5 at 2
% 5.46/1.70 Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 63 with 64 at 2,2,2
% 5.46/1.70 Id : 188, {_}: multiply (inverse ?1656) (multiply ?1656 ?1657) =?= multiply (inverse (inverse ?1658)) (multiply (inverse ?1658) ?1657) [1658, 1657, 1656] by Super 63 with 64 at 2,2,2
% 5.46/1.70 Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 188 at 3
% 5.46/1.70 Id : 402, {_}: multiply (inverse ?2901) (multiply ?2901 (inverse (multiply (multiply (inverse (multiply (inverse ?2902) (multiply ?2902 ?2903))) ?2904) (inverse (multiply ?2905 ?2904))))) =>= multiply ?2905 ?2903 [2905, 2904, 2903, 2902, 2901] by Super 63 with 301 at 1,1,1,1,2,2,2
% 5.46/1.70 Id : 551, {_}: multiply ?3795 (inverse (multiply (multiply (inverse (multiply (inverse ?3796) (multiply ?3796 ?3797))) ?3798) (inverse (multiply (inverse ?3795) ?3798)))) =>= ?3797 [3798, 3797, 3796, 3795] by Super 2 with 301 at 1,1,1,1,2,2
% 5.46/1.70 Id : 1900, {_}: multiply ?13216 (inverse (multiply (multiply (inverse (multiply (inverse ?13217) (multiply ?13217 ?13218))) (multiply ?13216 ?13219)) (inverse (multiply (inverse ?13220) (multiply ?13220 ?13219))))) =>= ?13218 [13220, 13219, 13218, 13217, 13216] by Super 551 with 301 at 1,2,1,2,2
% 5.46/1.70 Id : 1975, {_}: multiply (multiply (inverse ?13848) (multiply ?13848 ?13849)) (inverse (multiply ?13850 (inverse (multiply (inverse ?13851) (multiply ?13851 (inverse (multiply (multiply (inverse (multiply (inverse ?13852) ?13850)) ?13853) (inverse (multiply ?13852 ?13853))))))))) =>= ?13849 [13853, 13852, 13851, 13850, 13849, 13848] by Super 1900 with 63 at 1,1,2,2
% 5.46/1.70 Id : 2009, {_}: multiply (multiply (inverse ?13848) (multiply ?13848 ?13849)) (inverse (multiply ?13850 (inverse ?13850))) =>= ?13849 [13850, 13849, 13848] by Demod 1975 with 63 at 1,2,1,2,2
% 5.46/1.70 Id : 2038, {_}: multiply (inverse (multiply (inverse ?14074) (multiply ?14074 ?14075))) ?14075 =?= multiply (inverse (multiply (inverse ?14076) (multiply ?14076 ?14077))) ?14077 [14077, 14076, 14075, 14074] by Super 402 with 2009 at 2,2
% 5.46/1.70 Id : 2243, {_}: multiply (inverse (inverse (multiply (inverse ?15357) (multiply ?15357 (inverse (multiply (multiply (inverse (multiply (inverse ?15358) ?15359)) ?15360) (inverse (multiply ?15358 ?15360)))))))) (multiply (inverse (multiply (inverse ?15361) (multiply ?15361 ?15362))) ?15362) =>= ?15359 [15362, 15361, 15360, 15359, 15358, 15357] by Super 63 with 2038 at 2,2
% 5.46/1.70 Id : 2410, {_}: multiply (inverse (inverse ?15359)) (multiply (inverse (multiply (inverse ?15361) (multiply ?15361 ?15362))) ?15362) =>= ?15359 [15362, 15361, 15359] by Demod 2243 with 63 at 1,1,1,2
% 5.46/1.70 Id : 135, {_}: multiply (inverse ?1258) (multiply ?1258 (inverse (multiply (multiply (inverse (multiply (inverse ?1259) ?1260)) ?1261) (inverse (multiply ?1259 ?1261))))) =>= ?1260 [1261, 1260, 1259, 1258] by Super 2 with 5 at 2,2
% 5.46/1.70 Id : 154, {_}: multiply (inverse ?1413) (multiply ?1413 (multiply ?1414 (inverse (multiply (multiply (inverse (multiply (inverse ?1415) ?1416)) ?1417) (inverse (multiply ?1415 ?1417)))))) =>= multiply (inverse (inverse ?1414)) ?1416 [1417, 1416, 1415, 1414, 1413] by Super 135 with 5 at 2,2,2
% 5.46/1.70 Id : 2475, {_}: multiply (inverse (inverse (inverse ?16925))) ?16925 =?= multiply (inverse (inverse (inverse (multiply (inverse ?16926) (multiply ?16926 (inverse (multiply (multiply (inverse (multiply (inverse ?16927) ?16928)) ?16929) (inverse (multiply ?16927 ?16929))))))))) ?16928 [16929, 16928, 16927, 16926, 16925] by Super 154 with 2410 at 2,2
% 5.46/1.70 Id : 2558, {_}: multiply (inverse (inverse (inverse ?16925))) ?16925 =?= multiply (inverse (inverse (inverse ?16928))) ?16928 [16928, 16925] by Demod 2475 with 63 at 1,1,1,1,3
% 5.46/1.70 Id : 2724, {_}: multiply (inverse (inverse ?18143)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?18144)))) (multiply (inverse (inverse (inverse ?18145))) ?18145))) ?18144) =>= ?18143 [18145, 18144, 18143] by Super 2410 with 2558 at 2,1,1,2,2
% 5.46/1.70 Id : 386, {_}: multiply ?2785 (inverse (multiply (multiply (inverse ?2786) (multiply ?2786 ?2787)) (inverse (multiply ?2788 (multiply (multiply (inverse ?2788) (multiply (inverse ?2785) ?2789)) ?2787))))) =>= ?2789 [2789, 2788, 2787, 2786, 2785] by Super 2 with 301 at 1,1,2,2
% 5.46/1.70 Id : 190, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1668) (multiply (inverse (inverse ?1669)) (multiply (inverse ?1669) ?1670)))) ?1671) (inverse (multiply ?1668 ?1671))) =>= ?1670 [1671, 1670, 1669, 1668] by Super 2 with 5 at 2
% 5.46/1.70 Id : 198, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1730) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1731) (multiply (inverse (inverse ?1732)) (multiply (inverse ?1732) ?1733)))) ?1734) (inverse (multiply ?1731 ?1734))))) (multiply ?1733 ?1735)))) ?1736) (inverse (multiply ?1730 ?1736))) =>= ?1735 [1736, 1735, 1734, 1733, 1732, 1731, 1730] by Super 190 with 64 at 1,2,2,1,1,1,1,2
% 5.46/1.70 Id : 224, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1730) (multiply (inverse ?1733) (multiply ?1733 ?1735)))) ?1736) (inverse (multiply ?1730 ?1736))) =>= ?1735 [1736, 1735, 1733, 1730] by Demod 198 with 64 at 1,1,2,1,1,1,1,2
% 5.46/1.70 Id : 638, {_}: multiply (inverse ?4392) (multiply ?4392 (multiply ?4393 (inverse (multiply (multiply (inverse (multiply (inverse ?4394) ?4395)) ?4396) (inverse (multiply ?4394 ?4396)))))) =>= multiply (inverse (inverse ?4393)) ?4395 [4396, 4395, 4394, 4393, 4392] by Super 135 with 5 at 2,2,2
% 5.46/1.70 Id : 671, {_}: multiply (inverse ?4676) (multiply ?4676 (multiply ?4677 ?4678)) =?= multiply (inverse (inverse ?4677)) (multiply (inverse ?4679) (multiply ?4679 ?4678)) [4679, 4678, 4677, 4676] by Super 638 with 224 at 2,2,2,2
% 5.46/1.70 Id : 763, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5282) (multiply ?5282 (multiply ?5283 ?5284)))) ?5285) (inverse (multiply (inverse ?5283) ?5285))) =>= ?5284 [5285, 5284, 5283, 5282] by Super 224 with 671 at 1,1,1,1,2
% 5.46/1.70 Id : 2217, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?15177) (multiply ?15177 ?15178))) ?15178) (inverse (multiply (inverse ?15179) (multiply ?15179 ?15180)))) =>= ?15180 [15180, 15179, 15178, 15177] by Super 763 with 2038 at 1,1,2
% 5.46/1.70 Id : 2596, {_}: multiply (multiply (inverse (inverse (inverse (inverse ?17397)))) (multiply (inverse (inverse (inverse ?17398))) ?17398)) (inverse (multiply ?17399 (inverse ?17399))) =>= ?17397 [17399, 17398, 17397] by Super 2009 with 2558 at 2,1,2
% 5.46/1.70 Id : 2474, {_}: multiply (inverse ?16918) (multiply ?16918 (multiply ?16919 (inverse (multiply (multiply (inverse ?16920) ?16921) (inverse (multiply (inverse ?16920) ?16921)))))) =?= multiply (inverse (inverse ?16919)) (multiply (inverse (multiply (inverse ?16922) (multiply ?16922 ?16923))) ?16923) [16923, 16922, 16921, 16920, 16919, 16918] by Super 154 with 2410 at 1,1,1,1,2,2,2,2
% 5.46/1.70 Id : 4107, {_}: multiply (inverse ?26136) (multiply ?26136 (multiply ?26137 (inverse (multiply (multiply (inverse ?26138) ?26139) (inverse (multiply (inverse ?26138) ?26139)))))) =>= ?26137 [26139, 26138, 26137, 26136] by Demod 2474 with 2410 at 3
% 5.46/1.70 Id : 4115, {_}: multiply (inverse ?26200) (multiply ?26200 (multiply ?26201 (inverse (multiply (multiply (inverse ?26202) (inverse (multiply (multiply (inverse (multiply (inverse ?26203) (multiply (inverse (inverse ?26202)) ?26204))) ?26205) (inverse (multiply ?26203 ?26205))))) (inverse ?26204))))) =>= ?26201 [26205, 26204, 26203, 26202, 26201, 26200] by Super 4107 with 2 at 1,2,1,2,2,2,2
% 5.46/1.70 Id : 4233, {_}: multiply (inverse ?26200) (multiply ?26200 (multiply ?26201 (inverse (multiply ?26204 (inverse ?26204))))) =>= ?26201 [26204, 26201, 26200] by Demod 4115 with 2 at 1,1,2,2,2,2
% 5.46/1.70 Id : 4286, {_}: multiply ?26895 (inverse (multiply ?26896 (inverse ?26896))) =?= multiply ?26895 (inverse (multiply ?26897 (inverse ?26897))) [26897, 26896, 26895] by Super 2596 with 4233 at 1,2
% 5.46/1.70 Id : 4890, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?30017) (multiply ?30017 ?30018))) ?30018) (inverse (multiply (inverse ?30019) (multiply ?30019 (inverse (multiply ?30020 (inverse ?30020))))))) =?= inverse (multiply ?30021 (inverse ?30021)) [30021, 30020, 30019, 30018, 30017] by Super 2217 with 4286 at 2,1,2,1,2
% 5.46/1.70 Id : 4951, {_}: inverse (multiply ?30020 (inverse ?30020)) =?= inverse (multiply ?30021 (inverse ?30021)) [30021, 30020] by Demod 4890 with 2217 at 2
% 5.46/1.70 Id : 5227, {_}: multiply (inverse (inverse (multiply ?31553 (inverse ?31553)))) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?31554)))) (multiply (inverse (inverse (inverse ?31555))) ?31555))) ?31554) =?= multiply ?31556 (inverse ?31556) [31556, 31555, 31554, 31553] by Super 2724 with 4951 at 1,1,2
% 5.46/1.70 Id : 5284, {_}: multiply ?31553 (inverse ?31553) =?= multiply ?31556 (inverse ?31556) [31556, 31553] by Demod 5227 with 2724 at 2
% 5.46/1.70 Id : 5340, {_}: multiply (multiply (inverse ?31932) (multiply ?31933 (inverse ?31933))) (inverse (multiply ?31934 (inverse ?31934))) =>= inverse ?31932 [31934, 31933, 31932] by Super 2009 with 5284 at 2,1,2
% 5.46/1.70 Id : 5817, {_}: multiply ?34571 (inverse (multiply (multiply (inverse ?34572) (multiply ?34572 (inverse (multiply ?34573 (inverse ?34573))))) (inverse (multiply ?34574 (inverse ?34574))))) =>= inverse (inverse ?34571) [34574, 34573, 34572, 34571] by Super 386 with 5340 at 2,1,2,1,2,2
% 5.46/1.70 Id : 5892, {_}: multiply ?34571 (inverse (inverse (multiply ?34573 (inverse ?34573)))) =>= inverse (inverse ?34571) [34573, 34571] by Demod 5817 with 2009 at 1,2,2
% 5.46/1.70 Id : 5932, {_}: multiply (inverse (inverse ?35050)) (multiply (inverse (multiply (inverse ?35051) (inverse (inverse ?35051)))) (inverse (inverse (multiply ?35052 (inverse ?35052))))) =>= ?35050 [35052, 35051, 35050] by Super 2410 with 5892 at 2,1,1,2,2
% 5.46/1.70 Id : 6684, {_}: multiply (inverse (inverse ?38132)) (inverse (inverse (inverse (multiply (inverse ?38133) (inverse (inverse ?38133)))))) =>= ?38132 [38133, 38132] by Demod 5932 with 5892 at 2,2
% 5.46/1.70 Id : 6012, {_}: multiply ?35487 (inverse ?35487) =?= inverse (inverse (inverse (multiply ?35488 (inverse ?35488)))) [35488, 35487] by Super 5284 with 5892 at 3
% 5.46/1.70 Id : 6714, {_}: multiply (inverse (inverse ?38277)) (multiply ?38278 (inverse ?38278)) =>= ?38277 [38278, 38277] by Super 6684 with 6012 at 2,2
% 5.46/1.70 Id : 6844, {_}: multiply ?38788 (inverse (multiply ?38789 (inverse ?38789))) =>= inverse (inverse ?38788) [38789, 38788] by Super 2009 with 6714 at 1,2
% 5.46/1.70 Id : 7027, {_}: multiply (inverse (inverse ?39572)) (inverse (inverse (inverse (multiply (inverse (inverse (inverse (inverse (inverse (multiply ?39573 (inverse ?39573))))))) (multiply (inverse (inverse (inverse ?39574))) ?39574))))) =>= ?39572 [39574, 39573, 39572] by Super 2724 with 6844 at 2,2
% 5.46/1.70 Id : 6914, {_}: inverse (inverse (multiply (inverse (inverse (inverse (inverse ?17397)))) (multiply (inverse (inverse (inverse ?17398))) ?17398))) =>= ?17397 [17398, 17397] by Demod 2596 with 6844 at 2
% 5.46/1.70 Id : 7082, {_}: multiply (inverse (inverse ?39572)) (inverse (inverse (multiply ?39573 (inverse ?39573)))) =>= ?39572 [39573, 39572] by Demod 7027 with 6914 at 1,2,2
% 5.46/1.70 Id : 7083, {_}: inverse (inverse (inverse (inverse ?39572))) =>= ?39572 [39572] by Demod 7082 with 5892 at 2
% 5.46/1.70 Id : 896, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?6059) (multiply ?6059 (multiply ?6060 ?6061)))) ?6062) (inverse (multiply (inverse ?6060) ?6062))) =>= ?6061 [6062, 6061, 6060, 6059] by Super 224 with 671 at 1,1,1,1,2
% 5.46/1.70 Id : 917, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?6221) (multiply ?6221 (multiply (inverse ?6222) (multiply ?6222 ?6223))))) ?6224) (inverse (multiply (inverse (inverse ?6225)) ?6224))) =>= multiply ?6225 ?6223 [6225, 6224, 6223, 6222, 6221] by Super 896 with 301 at 2,2,1,1,1,1,2
% 5.46/1.70 Id : 6915, {_}: multiply (inverse ?26200) (multiply ?26200 (inverse (inverse ?26201))) =>= ?26201 [26201, 26200] by Demod 4233 with 6844 at 2,2,2
% 5.46/1.70 Id : 7304, {_}: multiply (inverse ?40285) (multiply ?40285 ?40286) =>= inverse (inverse ?40286) [40286, 40285] by Super 6915 with 7083 at 2,2,2
% 5.46/1.70 Id : 7717, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?6222) (multiply ?6222 ?6223))))) ?6224) (inverse (multiply (inverse (inverse ?6225)) ?6224))) =>= multiply ?6225 ?6223 [6225, 6224, 6223, 6222] by Demod 917 with 7304 at 1,1,1,1,2
% 5.46/1.70 Id : 7718, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?6223))))) ?6224) (inverse (multiply (inverse (inverse ?6225)) ?6224))) =>= multiply ?6225 ?6223 [6225, 6224, 6223] by Demod 7717 with 7304 at 1,1,1,1,1,1,2
% 5.46/1.70 Id : 7749, {_}: inverse (multiply (multiply (inverse ?6223) ?6224) (inverse (multiply (inverse (inverse ?6225)) ?6224))) =>= multiply ?6225 ?6223 [6225, 6224, 6223] by Demod 7718 with 7083 at 1,1,1,2
% 5.46/1.70 Id : 7207, {_}: multiply ?39810 (inverse (multiply (inverse (inverse (inverse ?39811))) ?39811)) =>= inverse (inverse ?39810) [39811, 39810] by Super 6844 with 7083 at 2,1,2,2
% 5.46/1.70 Id : 7899, {_}: inverse (inverse (inverse (multiply (inverse ?41635) ?41636))) =>= multiply (inverse ?41636) ?41635 [41636, 41635] by Super 7749 with 7207 at 1,2
% 5.46/1.70 Id : 8194, {_}: inverse (multiply (inverse ?42276) ?42277) =>= multiply (inverse ?42277) ?42276 [42277, 42276] by Super 7083 with 7899 at 1,2
% 5.46/1.70 Id : 8364, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 8194 at 1,1,1,2,1,2,1,2,2
% 5.46/1.70 Id : 8365, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 8364 with 8194 at 1,1,1,1,2,1,2,1,2,2
% 5.46/1.70 Id : 8366, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 8365 with 8194 at 2,1,1,1,1,2,1,2,1,2,2
% 5.46/1.70 Id : 8367, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 8366 with 8194 at 1,2,1,1,1,1,2,1,2,1,2,2
% 5.46/1.70 Id : 7729, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2902) (multiply ?2902 ?2903))) ?2904) (inverse (multiply ?2905 ?2904))))) =>= multiply ?2905 ?2903 [2905, 2904, 2903, 2902] by Demod 402 with 7304 at 2
% 5.46/1.70 Id : 7730, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2903))) ?2904) (inverse (multiply ?2905 ?2904))))) =>= multiply ?2905 ?2903 [2905, 2904, 2903] by Demod 7729 with 7304 at 1,1,1,1,1,1,2
% 5.46/1.70 Id : 7910, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?41680))) ?41681))))) =>= multiply (inverse (inverse (inverse ?41681))) ?41680 [41681, 41680] by Super 7730 with 7207 at 1,1,1,2
% 5.46/1.70 Id : 8095, {_}: inverse (multiply (inverse (inverse (inverse ?41680))) ?41681) =>= multiply (inverse (inverse (inverse ?41681))) ?41680 [41681, 41680] by Demod 7910 with 7083 at 2
% 5.46/1.70 Id : 8554, {_}: multiply (inverse ?41681) (inverse (inverse ?41680)) =?= multiply (inverse (inverse (inverse ?41681))) ?41680 [41680, 41681] by Demod 8095 with 8194 at 2
% 5.46/1.70 Id : 8646, {_}: multiply (inverse ?43671) (inverse (inverse (multiply (inverse (inverse ?43671)) ?43672))) =>= inverse (inverse ?43672) [43672, 43671] by Super 7304 with 8554 at 2
% 5.46/1.70 Id : 8772, {_}: multiply (inverse ?43671) (inverse (multiply (inverse ?43672) (inverse ?43671))) =>= inverse (inverse ?43672) [43672, 43671] by Demod 8646 with 8194 at 1,2,2
% 5.46/1.70 Id : 8773, {_}: multiply (inverse ?43671) (multiply (inverse (inverse ?43671)) ?43672) =>= inverse (inverse ?43672) [43672, 43671] by Demod 8772 with 8194 at 2,2
% 5.46/1.70 Id : 7732, {_}: multiply ?2785 (inverse (multiply (inverse (inverse ?2787)) (inverse (multiply ?2788 (multiply (multiply (inverse ?2788) (multiply (inverse ?2785) ?2789)) ?2787))))) =>= ?2789 [2789, 2788, 2787, 2785] by Demod 386 with 7304 at 1,1,2,2
% 5.46/1.70 Id : 8354, {_}: multiply ?2785 (multiply (inverse (inverse (multiply ?2788 (multiply (multiply (inverse ?2788) (multiply (inverse ?2785) ?2789)) ?2787)))) (inverse ?2787)) =>= ?2789 [2787, 2789, 2788, 2785] by Demod 7732 with 8194 at 2,2
% 5.46/1.70 Id : 404, {_}: multiply (inverse ?2913) (multiply ?2913 (inverse (multiply (multiply (inverse ?2914) (multiply ?2914 ?2915)) (inverse (multiply ?2916 (multiply (multiply (inverse ?2916) ?2917) ?2915)))))) =>= ?2917 [2917, 2916, 2915, 2914, 2913] by Super 63 with 301 at 1,1,2,2,2
% 5.46/1.70 Id : 7715, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2914) (multiply ?2914 ?2915)) (inverse (multiply ?2916 (multiply (multiply (inverse ?2916) ?2917) ?2915)))))) =>= ?2917 [2917, 2916, 2915, 2914] by Demod 404 with 7304 at 2
% 5.46/1.70 Id : 7716, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2915)) (inverse (multiply ?2916 (multiply (multiply (inverse ?2916) ?2917) ?2915)))))) =>= ?2917 [2917, 2916, 2915] by Demod 7715 with 7304 at 1,1,1,1,2
% 5.46/1.70 Id : 8164, {_}: multiply (inverse (inverse (multiply ?2916 (multiply (multiply (inverse ?2916) ?2917) ?2915)))) (inverse ?2915) =>= ?2917 [2915, 2917, 2916] by Demod 7716 with 7899 at 2
% 5.46/1.70 Id : 8372, {_}: multiply ?2785 (multiply (inverse ?2785) ?2789) =>= ?2789 [2789, 2785] by Demod 8354 with 8164 at 2,2
% 5.46/1.70 Id : 8774, {_}: ?43672 =<= inverse (inverse ?43672) [43672] by Demod 8773 with 8372 at 2
% 5.46/1.70 Id : 9179, {_}: inverse (multiply ?44503 ?44504) =<= multiply (inverse ?44504) (inverse ?44503) [44504, 44503] by Super 8194 with 8774 at 1,1,2
% 5.46/1.70 Id : 9196, {_}: inverse (multiply ?44575 (inverse ?44576)) =>= multiply ?44576 (inverse ?44575) [44576, 44575] by Super 9179 with 8774 at 1,3
% 5.46/1.70 Id : 9300, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 8367 with 9196 at 2,2
% 5.46/1.70 Id : 9301, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 9300 with 9196 at 2,1,2,2
% 5.46/1.70 Id : 9069, {_}: inverse (multiply ?44136 ?44137) =<= multiply (inverse ?44137) (inverse ?44136) [44137, 44136] by Super 8194 with 8774 at 1,1,2
% 5.46/1.70 Id : 9428, {_}: multiply ?45019 (inverse (multiply ?45020 ?45019)) =>= inverse ?45020 [45020, 45019] by Super 8372 with 9069 at 2,2
% 5.46/1.71 Id : 9161, {_}: multiply ?44439 (inverse (multiply ?44440 ?44439)) =>= inverse ?44440 [44440, 44439] by Super 8372 with 9069 at 2,2
% 5.46/1.71 Id : 9437, {_}: multiply (inverse (multiply ?45049 ?45050)) (inverse (inverse ?45049)) =>= inverse ?45050 [45050, 45049] by Super 9428 with 9161 at 1,2,2
% 5.46/1.71 Id : 9509, {_}: inverse (multiply (inverse ?45049) (multiply ?45049 ?45050)) =>= inverse ?45050 [45050, 45049] by Demod 9437 with 9069 at 2
% 5.46/1.71 Id : 9743, {_}: multiply (inverse (multiply ?45603 ?45604)) ?45603 =>= inverse ?45604 [45604, 45603] by Demod 9509 with 8194 at 2
% 5.46/1.71 Id : 7723, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?570) ?571)) ?572) (inverse (multiply ?570 ?572))))) =>= ?571 [572, 571, 570] by Demod 63 with 7304 at 2
% 5.46/1.71 Id : 8353, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?571) ?570) ?572) (inverse (multiply ?570 ?572))))) =>= ?571 [572, 570, 571] by Demod 7723 with 8194 at 1,1,1,1,1,2
% 5.46/1.71 Id : 9054, {_}: inverse (multiply (multiply (multiply (inverse ?571) ?570) ?572) (inverse (multiply ?570 ?572))) =>= ?571 [572, 570, 571] by Demod 8353 with 8774 at 2
% 5.46/1.71 Id : 9304, {_}: multiply (multiply ?570 ?572) (inverse (multiply (multiply (inverse ?571) ?570) ?572)) =>= ?571 [571, 572, 570] by Demod 9054 with 9196 at 2
% 5.46/1.71 Id : 9756, {_}: multiply (inverse ?45655) (multiply ?45656 ?45657) =<= inverse (inverse (multiply (multiply (inverse ?45655) ?45656) ?45657)) [45657, 45656, 45655] by Super 9743 with 9304 at 1,1,2
% 5.46/1.71 Id : 9819, {_}: multiply (inverse ?45655) (multiply ?45656 ?45657) =<= multiply (multiply (inverse ?45655) ?45656) ?45657 [45657, 45656, 45655] by Demod 9756 with 8774 at 3
% 5.46/1.71 Id : 10202, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 9301 with 9819 at 1,1,2,2,1,2,2
% 5.46/1.71 Id : 10203, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 10202 with 9819 at 1,2,2,1,2,2
% 5.46/1.71 Id : 10204, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 10203 with 9819 at 1,1,2,1,2,2,1,2,2
% 5.46/1.71 Id : 10205, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 10204 with 9819 at 1,2,1,2,2,1,2,2
% 5.46/1.71 Id : 10206, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 10205 with 9819 at 2,1,2,2,1,2,2
% 5.46/1.71 Id : 10223, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 10206 with 8194 at 2,2,1,2,2
% 5.46/1.71 Id : 10224, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 10223 with 8194 at 1,2,2,1,2,2
% 5.46/1.71 Id : 10225, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 10224 with 9819 at 2,2,1,2,2
% 5.46/1.71 Id : 2726, {_}: multiply (inverse (inverse (inverse ?18151))) ?18151 =?= inverse (multiply (inverse (multiply (inverse ?18152) (multiply ?18152 ?18153))) ?18153) [18153, 18152, 18151] by Super 2410 with 2558 at 2
% 5.46/1.71 Id : 7736, {_}: multiply (inverse (inverse (inverse ?18151))) ?18151 =?= inverse (multiply (inverse (inverse (inverse ?18153))) ?18153) [18153, 18151] by Demod 2726 with 7304 at 1,1,1,3
% 5.46/1.71 Id : 8368, {_}: multiply (inverse (inverse (inverse ?18151))) ?18151 =?= multiply (inverse ?18153) (inverse (inverse ?18153)) [18153, 18151] by Demod 7736 with 8194 at 3
% 5.46/1.71 Id : 9052, {_}: multiply (inverse ?18151) ?18151 =?= multiply (inverse ?18153) (inverse (inverse ?18153)) [18153, 18151] by Demod 8368 with 8774 at 1,2
% 5.46/1.71 Id : 9053, {_}: multiply (inverse ?18151) ?18151 =?= multiply (inverse ?18153) ?18153 [18153, 18151] by Demod 9052 with 8774 at 2,3
% 5.46/1.71 Id : 9066, {_}: multiply (inverse ?44126) ?44126 =?= multiply ?44127 (inverse ?44127) [44127, 44126] by Super 9053 with 8774 at 1,3
% 5.46/1.71 Id : 11435, {_}: multiply ?48234 (multiply (multiply ?48235 (multiply (multiply ?48236 ?48237) (multiply ?48238 (inverse ?48238)))) (inverse ?48237)) =>= multiply (multiply ?48234 ?48235) ?48236 [48238, 48237, 48236, 48235, 48234] by Super 10225 with 9066 at 2,2,1,2,2
% 5.46/1.71 Id : 7215, {_}: multiply ?39837 (multiply ?39838 (inverse ?39838)) =>= inverse (inverse ?39837) [39838, 39837] by Super 6714 with 7083 at 1,2
% 5.46/1.71 Id : 9042, {_}: multiply ?39837 (multiply ?39838 (inverse ?39838)) =>= ?39837 [39838, 39837] by Demod 7215 with 8774 at 3
% 5.46/1.71 Id : 11665, {_}: multiply ?48234 (multiply (multiply ?48235 (multiply ?48236 ?48237)) (inverse ?48237)) =>= multiply (multiply ?48234 ?48235) ?48236 [48237, 48236, 48235, 48234] by Demod 11435 with 9042 at 2,1,2,2
% 5.46/1.71 Id : 9030, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2903))) ?2904) (inverse (multiply ?2905 ?2904))) =>= multiply ?2905 ?2903 [2905, 2904, 2903] by Demod 7730 with 8774 at 2
% 5.46/1.71 Id : 9031, {_}: inverse (multiply (multiply (inverse ?2903) ?2904) (inverse (multiply ?2905 ?2904))) =>= multiply ?2905 ?2903 [2905, 2904, 2903] by Demod 9030 with 8774 at 1,1,1,2
% 5.46/1.71 Id : 9306, {_}: multiply (multiply ?2905 ?2904) (inverse (multiply (inverse ?2903) ?2904)) =>= multiply ?2905 ?2903 [2903, 2904, 2905] by Demod 9031 with 9196 at 2
% 5.46/1.71 Id : 9307, {_}: multiply (multiply ?2905 ?2904) (multiply (inverse ?2904) ?2903) =>= multiply ?2905 ?2903 [2903, 2904, 2905] by Demod 9306 with 8194 at 2,2
% 5.46/1.71 Id : 9510, {_}: multiply (inverse (multiply ?45049 ?45050)) ?45049 =>= inverse ?45050 [45050, 45049] by Demod 9509 with 8194 at 2
% 5.46/1.71 Id : 9734, {_}: multiply (multiply ?45558 (multiply ?45559 ?45560)) (inverse ?45560) =>= multiply ?45558 ?45559 [45560, 45559, 45558] by Super 9307 with 9510 at 2,2
% 5.46/1.71 Id : 20647, {_}: multiply ?48234 (multiply ?48235 ?48236) =?= multiply (multiply ?48234 ?48235) ?48236 [48236, 48235, 48234] by Demod 11665 with 9734 at 2,2
% 5.46/1.71 Id : 21104, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 1 with 20647 at 3
% 5.46/1.71 Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
% 5.46/1.71 % SZS output end CNFRefutation for theBenchmark.p
% 5.46/1.71 5345: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 1.359253 using nrkbo
%------------------------------------------------------------------------------