TSTP Solution File: GRP281-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP281-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:46:40 EDT 2022
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP281-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 14:21:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 820 clauses, backtracked 361 clauses, performed 11 splits and kept 706 clauses.
% 0.18/0.47 SPASS allocated 63633 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.47 0:00:00.04 for the input.
% 0.18/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.01 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.07 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 5, length 354 :
% 0.18/0.47 % SZS output start Refutation
% 0.18/0.47 1[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.18/0.47 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 3[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.18/0.47 4[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.18/0.47 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 8[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 14[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 16[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.18/0.47 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 18[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.18/0.47 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 20[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.18/0.47 21[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 22[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 23[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 24[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 25[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 26[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 28[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 30[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 31[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(multiply(w,sk_c8),y)*+ equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c7)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.18/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.47 35[1:Spt:31.2,31.4,31.8] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.18/0.47 37[2:Spt:1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 40[3:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 42[4:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.47 45[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.18/0.47 46[5:Spt:5.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 48[6:Spt:3.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 51[3:SpR:40.0,33.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.18/0.47 52[4:SpR:42.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.18/0.47 53[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.18/0.47 59[4:SpR:52.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.18/0.47 61[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.47 62[5:SpR:46.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.18/0.47 64[3:SpR:51.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.18/0.47 66[4:Rew:32.0,59.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.18/0.47 67[3:Rew:32.0,64.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.18/0.47 68[0:Rew:32.0,61.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.47 72[6:SpR:48.0,66.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 79[5:SpR:46.0,67.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 84[0:SpR:68.0,68.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.47 86[2:SpR:37.0,68.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.18/0.47 87[4:SpR:52.0,68.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.18/0.47 91[0:SpR:33.0,68.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.47 94[3:SpR:51.0,68.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.18/0.47 96[5:SpR:79.0,68.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.47 102[5:Rew:86.0,96.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 104[5:Rew:102.0,37.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 109[6:Rew:102.0,72.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.18/0.47 114[5:Rew:102.0,86.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.18/0.47 115[5:Rew:102.0,94.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.18/0.47 117[5:Rew:102.0,53.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.18/0.47 118[5:Rew:102.0,45.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.18/0.47 120[5:Rew:102.0,62.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 126[6:Rew:104.0,109.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 130[6:Rew:126.0,114.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.18/0.47 131[6:Rew:33.0,130.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 132[6:Rew:131.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 134[6:Rew:131.0,52.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.18/0.47 139[6:Rew:132.0,134.0] || -> equal(sk_c4,sk_c8)**.
% 0.18/0.47 140[6:Rew:139.0,42.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 172[6:Rew:132.0,117.2,131.0,117.1,140.0,117.0,140.0,117.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.18/0.47 173[6:Obv:172.1] || equal(u,sk_c8)* -> .
% 0.18/0.47 174[6:UnC:173.0,68.0] || -> .
% 0.18/0.47 177[6:Spt:174.0,3.0,48.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.18/0.47 178[6:Spt:174.0,3.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 180[5:Rew:87.0,115.0] || -> equal(sk_c5,sk_c4)**.
% 0.18/0.47 184[6:Rew:102.0,177.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.18/0.47 185[0:Rew:84.0,91.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.47 186[4:Rew:185.0,87.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.18/0.47 194[5:Rew:102.0,13.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.18/0.47 195[6:MRR:194.1,184.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 196[5:Rew:180.0,120.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 201[5:Rew:102.0,8.1,102.0,8.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.18/0.47 202[6:MRR:201.0,184.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.18/0.47 210[4:SpR:186.0,68.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.18/0.47 239[6:SpR:202.0,68.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.18/0.47 241[6:Rew:104.0,239.0,195.0,239.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 245[6:Rew:241.0,196.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.18/0.47 249[6:Rew:210.0,245.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 251[6:Rew:249.0,52.0] || -> equal(identity,sk_c4)**.
% 0.18/0.47 253[6:Rew:249.0,118.2] || equal(inverse(identity),sk_c8)** equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.18/0.47 277[6:Obv:253.1] || equal(inverse(identity),sk_c8)** equal(u,sk_c8)* -> .
% 0.18/0.47 278[6:Con:277.1] || equal(inverse(identity),sk_c8)** -> .
% 0.18/0.47 279[6:Rew:251.0,278.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.18/0.47 280[6:Rew:42.0,279.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 281[6:Obv:280.0] || -> .
% 0.18/0.47 285[5:Spt:281.0,5.0,46.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.18/0.47 286[5:Spt:281.0,5.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 287[3:Rew:185.0,94.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.18/0.47 288[3:Rew:287.0,86.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.18/0.47 289[5:Rew:288.0,285.0] || equal(sk_c7,sk_c8)** -> .
% 0.18/0.47 291[3:Rew:288.0,30.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c7,sk_c8).
% 0.18/0.47 292[5:MRR:291.1,289.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 295[3:Rew:288.0,25.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 296[5:MRR:295.0,289.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 297[3:Rew:288.0,20.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 298[5:MRR:297.0,289.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 310[3:SpR:287.0,68.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.18/0.47 322[5:SpR:296.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.47 324[5:Rew:292.0,322.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 325[5:Rew:298.0,324.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 326[5:MRR:325.0,289.0] || -> .
% 0.18/0.47 327[4:Spt:326.0,2.0,42.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.18/0.47 328[4:Spt:326.0,2.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 329[4:MRR:27.0,327.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 330[4:MRR:12.0,327.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 331[4:MRR:22.0,327.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 332[4:MRR:17.0,327.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 333[4:MRR:7.0,327.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 350[3:SpR:288.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 355[4:SpR:331.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.47 357[4:Rew:329.0,355.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 358[4:Rew:332.0,357.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 359[4:Rew:358.0,40.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.18/0.47 361[4:Rew:358.0,328.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 362[4:Rew:358.0,51.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.18/0.47 369[4:Rew:358.0,45.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.18/0.47 372[4:Rew:358.0,310.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.18/0.47 375[4:Rew:358.0,333.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.18/0.47 399[4:SpR:375.0,68.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.18/0.47 401[4:Rew:361.0,399.0,330.0,399.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 404[4:Rew:401.0,350.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.18/0.47 413[4:Rew:372.0,404.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 414[4:Rew:413.0,362.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 417[4:Rew:413.0,369.2] || equal(inverse(identity),sk_c8)** equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.18/0.47 431[4:Obv:417.1] || equal(inverse(identity),sk_c8)** equal(u,sk_c8)* -> .
% 0.18/0.47 432[4:Con:431.1] || equal(inverse(identity),sk_c8)** -> .
% 0.18/0.47 433[4:Rew:414.0,432.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.18/0.47 434[4:Rew:359.0,433.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 435[4:Obv:434.0] || -> .
% 0.18/0.47 439[3:Spt:435.0,4.0,40.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.18/0.47 440[3:Spt:435.0,4.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 441[3:MRR:29.0,439.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 442[3:MRR:14.0,439.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 443[3:MRR:24.0,439.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 444[3:MRR:19.0,439.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 445[3:MRR:9.0,439.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 457[3:SpR:443.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.47 459[3:Rew:441.0,457.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 460[3:Rew:444.0,459.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 461[3:Rew:460.0,440.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 464[3:Rew:460.0,86.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.18/0.47 467[3:Rew:460.0,444.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 468[3:Rew:460.0,445.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.18/0.47 470[3:Rew:460.0,53.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.18/0.47 482[3:SpR:467.0,68.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.18/0.47 484[3:Rew:33.0,482.0] || -> equal(identity,sk_c3)**.
% 0.18/0.47 485[3:Rew:484.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.18/0.47 486[3:Rew:484.0,185.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.18/0.47 487[3:Rew:484.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.18/0.47 490[3:Rew:484.0,470.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c3,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.18/0.47 495[3:SpR:468.0,68.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.18/0.47 497[3:Rew:461.0,495.0,442.0,495.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 499[3:Rew:497.0,464.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.18/0.47 502[3:Rew:487.0,499.0] || -> equal(sk_c3,sk_c8)**.
% 0.18/0.47 505[3:Rew:502.0,485.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 506[3:Rew:502.0,486.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 510[3:Rew:502.0,490.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.18/0.47 517[3:Rew:506.0,468.0] || -> equal(sk_c1,sk_c8)**.
% 0.18/0.47 519[3:Rew:517.0,442.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 534[3:Rew:505.0,510.2,519.0,510.0,519.0,510.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.18/0.47 535[3:Obv:534.1] || equal(u,sk_c8)* -> .
% 0.18/0.47 536[3:UnC:535.0,460.0] || -> .
% 0.18/0.47 538[2:Spt:536.0,1.0,37.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.18/0.47 539[2:Spt:536.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 540[2:MRR:26.1,538.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 542[2:MRR:21.0,538.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 543[2:MRR:16.0,538.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 553[2:SpR:542.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.47 555[2:Rew:540.0,553.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 556[2:Rew:543.0,555.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 557[2:Rew:556.0,539.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 558[2:Rew:556.0,538.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.18/0.47 568[2:Rew:557.0,558.0] || equal(sk_c6,sk_c6)* -> .
% 0.18/0.47 569[2:Obv:568.0] || -> .
% 0.18/0.47 570[1:Spt:569.0,31.0,31.1,31.3,31.5,31.6,31.7,31.9,31.10] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.18/0.47 572[2:Spt:1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 573[2:Rew:572.0,570.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c6,sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.18/0.47 575[2:Obv:573.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.18/0.47 578[2:SpR:572.0,68.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.18/0.47 580[3:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.47 583[4:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 584[4:SpR:583.0,68.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.18/0.47 586[5:Spt:3.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 588[5:SpR:586.0,68.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.18/0.47 590[5:Rew:580.0,588.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 592[5:SpR:590.0,68.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.18/0.47 594[6:Spt:5.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 596[6:SpR:594.0,68.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.18/0.47 598[6:Rew:583.0,596.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 603[6:SpR:598.0,68.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.47 605[6:Rew:578.0,603.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 606[6:Rew:605.0,572.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 607[6:Rew:605.0,583.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.18/0.47 609[6:Rew:605.0,590.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.18/0.47 610[6:Rew:605.0,594.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.18/0.47 613[6:Rew:605.0,575.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.18/0.47 614[6:Rew:605.0,578.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.18/0.47 621[6:Rew:606.0,609.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 623[6:Rew:621.0,610.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.18/0.47 625[6:Rew:33.0,614.0,621.0,614.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 626[6:Rew:625.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 627[6:Rew:625.0,185.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 631[6:Rew:627.0,623.0] || -> equal(sk_c5,sk_c8)**.
% 0.18/0.47 633[6:Rew:631.0,607.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 643[6:Rew:626.0,613.6,621.0,613.6,627.0,613.5,605.0,613.5,627.0,613.4,605.0,613.4,627.0,613.3,621.0,613.3,605.0,613.3,605.0,613.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.18/0.47 644[6:Obv:643.6] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.18/0.47 645[6:Con:644.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.47 706[6:SpL:633.0,645.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 708[6:Obv:706.1] || -> .
% 0.18/0.47 709[6:Spt:708.0,5.0,594.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.18/0.47 710[6:Spt:708.0,5.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 711[6:MRR:30.1,709.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 713[6:MRR:25.0,709.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 714[6:MRR:20.0,709.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 735[6:SpR:713.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.47 737[6:Rew:711.0,735.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 738[6:Rew:714.0,737.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 739[6:Rew:738.0,710.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 741[6:Rew:738.0,590.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.18/0.47 744[6:Rew:738.0,592.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.18/0.47 746[6:Rew:738.0,709.0] || equal(multiply(sk_c5,sk_c6),sk_c8)** -> .
% 0.18/0.47 747[6:Rew:738.0,584.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.18/0.47 757[6:Rew:739.0,741.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 760[6:Rew:33.0,744.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 761[6:Rew:760.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 762[6:Rew:760.0,185.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 777[6:Rew:762.0,746.0,757.0,746.0] || equal(sk_c5,sk_c8)** -> .
% 0.18/0.47 780[6:Rew:761.0,747.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.47 824[6:SpR:780.0,762.0] || -> equal(sk_c5,sk_c8)**.
% 0.18/0.47 826[6:MRR:824.0,777.0] || -> .
% 0.18/0.47 828[5:Spt:826.0,3.0,586.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.18/0.47 829[5:Spt:826.0,3.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 830[5:MRR:28.1,828.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 831[5:MRR:13.1,828.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 832[5:MRR:23.0,828.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 833[5:MRR:18.0,828.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 834[5:MRR:8.0,828.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 854[5:SpR:832.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.47 856[5:Rew:830.0,854.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 857[5:Rew:833.0,856.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 858[5:Rew:857.0,829.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 861[5:Rew:857.0,578.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.18/0.47 862[5:Rew:857.0,828.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.18/0.47 865[5:Rew:857.0,833.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 866[5:Rew:857.0,834.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.18/0.47 882[5:SpR:865.0,68.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.18/0.47 884[5:Rew:33.0,882.0] || -> equal(identity,sk_c3)**.
% 0.18/0.47 885[5:Rew:884.0,185.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.18/0.47 886[5:Rew:884.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.18/0.47 888[5:Rew:884.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.18/0.47 892[5:SpR:866.0,68.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.18/0.47 894[5:Rew:858.0,892.0,831.0,892.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 896[5:Rew:894.0,861.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.18/0.47 900[5:Rew:888.0,896.0] || -> equal(sk_c3,sk_c8)**.
% 0.18/0.47 903[5:Rew:900.0,885.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 904[5:Rew:900.0,886.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 906[5:Rew:900.0,888.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.47 909[5:Rew:903.0,862.0] || equal(sk_c4,sk_c8)** -> .
% 0.18/0.47 949[5:SpR:580.0,906.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.18/0.47 952[5:Rew:904.0,949.0] || -> equal(sk_c4,sk_c8)**.
% 0.18/0.47 953[5:MRR:952.0,909.0] || -> .
% 0.18/0.47 960[4:Spt:953.0,4.0,583.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.18/0.47 961[4:Spt:953.0,4.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 962[4:MRR:29.0,960.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 963[4:MRR:14.0,960.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 964[4:MRR:24.0,960.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 965[4:MRR:19.0,960.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 966[4:MRR:9.0,960.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 967[4:Rew:961.0,575.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.18/0.47 968[4:Obv:967.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.18/0.47 982[4:SpR:964.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.47 984[4:Rew:962.0,982.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 985[4:Rew:965.0,984.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 986[4:Rew:985.0,961.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 989[4:Rew:985.0,578.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.18/0.47 991[4:Rew:985.0,965.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.47 992[4:Rew:985.0,966.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.18/0.47 993[4:Rew:985.0,968.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.18/0.47 997[4:Rew:985.0,993.5,985.0,993.4,985.0,993.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.18/0.47 998[4:Con:997.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.18/0.47 1006[4:SpR:991.0,68.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.18/0.47 1008[4:Rew:33.0,1006.0] || -> equal(identity,sk_c3)**.
% 0.18/0.47 1010[4:Rew:1008.0,185.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.18/0.47 1011[4:Rew:1008.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.18/0.47 1016[4:SpR:992.0,68.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.18/0.47 1018[4:Rew:986.0,1016.0,963.0,1016.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 1020[4:Rew:1018.0,989.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.18/0.47 1022[4:Rew:1018.0,998.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.18/0.47 1024[4:Rew:1011.0,1020.0] || -> equal(sk_c3,sk_c8)**.
% 0.18/0.47 1028[4:Rew:1024.0,1010.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 1035[4:Rew:1028.0,992.0] || -> equal(sk_c1,sk_c8)**.
% 0.18/0.47 1037[4:Rew:1035.0,963.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 1044[4:Con:1022.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.18/0.47 1045[4:Rew:1028.0,1044.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.47 1115[4:SpL:1037.0,1045.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 1117[4:Obv:1115.1] || -> .
% 0.18/0.47 1118[3:Spt:1117.0,2.0,580.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.18/0.47 1119[3:Spt:1117.0,2.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.47 1120[3:MRR:27.0,1118.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.47 1121[3:MRR:12.0,1118.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 1122[3:MRR:22.0,1118.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.47 1123[3:MRR:17.0,1118.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.47 1124[3:MRR:7.0,1118.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 1125[3:Rew:1119.0,575.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.18/0.47 1126[3:Obv:1125.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.18/0.48 1140[3:SpR:1122.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.48 1142[3:Rew:1120.0,1140.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.48 1143[3:Rew:1123.0,1142.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.48 1144[3:Rew:1143.0,1119.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.48 1146[3:Rew:1143.0,578.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.18/0.48 1148[3:Rew:1143.0,1123.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.48 1149[3:Rew:1143.0,1124.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.18/0.48 1150[3:Rew:1143.0,1126.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.18/0.48 1154[3:Rew:1143.0,1150.5,1143.0,1150.4,1143.0,1150.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.18/0.48 1155[3:Con:1154.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.18/0.48 1163[3:SpR:1148.0,68.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.18/0.48 1165[3:Rew:33.0,1163.0] || -> equal(identity,sk_c3)**.
% 0.18/0.48 1166[3:Rew:1165.0,185.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.18/0.48 1169[3:Rew:1165.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.18/0.48 1174[3:SpR:1149.0,68.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.18/0.48 1176[3:Rew:1144.0,1174.0,1121.0,1174.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.48 1178[3:Rew:1176.0,1146.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.18/0.48 1180[3:Rew:1176.0,1155.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.18/0.48 1182[3:Rew:1169.0,1178.0] || -> equal(sk_c3,sk_c8)**.
% 0.18/0.48 1185[3:Rew:1182.0,1166.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.48 1189[3:Rew:1185.0,1149.0] || -> equal(sk_c1,sk_c8)**.
% 0.18/0.48 1191[3:Rew:1189.0,1121.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.48 1201[3:Con:1180.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.18/0.48 1202[3:Rew:1185.0,1201.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.48 1232[3:SpL:1191.0,1202.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.48 1233[3:Obv:1232.1] || -> .
% 0.18/0.48 1234[2:Spt:1233.0,1.0,572.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.18/0.48 1235[2:Spt:1233.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.18/0.48 1236[2:MRR:26.1,1234.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.18/0.48 1238[2:MRR:21.0,1234.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.18/0.48 1239[2:MRR:16.0,1234.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.18/0.48 1249[2:SpR:1238.0,68.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.18/0.48 1251[2:Rew:1236.0,1249.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.18/0.48 1252[2:Rew:1239.0,1251.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.48 1253[2:Rew:1252.0,1235.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.48 1254[2:Rew:1252.0,1234.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.18/0.48 1259[2:Rew:1253.0,1254.0] || equal(sk_c6,sk_c6)* -> .
% 0.18/0.48 1260[2:Obv:1259.0] || -> .
% 0.18/0.48 % SZS output end Refutation
% 0.18/0.48 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_7 prove_this_8 prove_this_9 prove_this_12 prove_this_13 prove_this_14 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.18/0.48
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