TSTP Solution File: GRP211-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP211-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:46:21 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP211-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.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 : Tue Jun 14 06:33:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 1049 clauses, backtracked 334 clauses, performed 11 splits and kept 740 clauses.
% 0.20/0.50 SPASS allocated 63795 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.07 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 5, length 411 :
% 0.20/0.50 % SZS output start Refutation
% 0.20/0.50 1[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.50 2[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.20/0.50 3[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.20/0.50 4[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.20/0.50 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.50 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c2).
% 0.20/0.50 7[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.50 8[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.50 9[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.50 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c2).
% 0.20/0.50 11[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.50 12[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.20/0.50 13[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.20/0.50 14[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.20/0.50 15[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.50 16[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 17[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.50 18[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.50 19[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.50 20[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 22[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 23[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c3,sk_c7),sk_c8).
% 0.20/0.50 24[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 26[0:Inp] || equal(multiply(u,v),sk_c8)** equal(inverse(u),v) equal(multiply(v,sk_c7),sk_c8)** equal(inverse(w),sk_c8) equal(multiply(w,sk_c7),sk_c8)** equal(inverse(x),sk_c8) equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(z,sk_c8),y)* equal(inverse(z),sk_c8) -> .
% 0.20/0.50 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.50 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.50 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.50 30[0:Con:26.5] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),y)* equal(multiply(x,sk_c7),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** -> .
% 0.20/0.50 31[1:Spt:30.0,30.3,30.6] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.50 32[2:Spt:10.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.50 34[3:Spt:6.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.50 37[1:SpL:27.0,31.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.20/0.50 38[4:Spt:9.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.50 43[5:Spt:8.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.50 46[6:Spt:7.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.50 52[2:SpR:32.0,28.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.20/0.50 53[3:SpR:34.0,28.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.50 56[2:SpL:52.0,31.1] || equal(inverse(sk_c8),sk_c5) equal(sk_c8,identity) equal(multiply(sk_c5,sk_c7),sk_c8)** -> .
% 0.20/0.50 58[3:SpL:53.0,31.1] || equal(inverse(sk_c8),sk_c4) equal(sk_c8,identity) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.50 65[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.50 68[2:SpR:52.0,29.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.20/0.50 71[2:Rew:27.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.20/0.50 73[0:Rew:27.0,65.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.50 77[4:SpR:38.0,71.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.50 78[2:SpL:71.0,31.1] || equal(multiply(sk_c5,u),inverse(sk_c8)) equal(u,sk_c8) equal(multiply(multiply(sk_c5,u),sk_c7),sk_c8)** -> .
% 0.20/0.50 79[5:Rew:43.0,77.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.50 82[5:Rew:79.0,34.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.50 83[5:Rew:79.0,38.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.20/0.50 84[5:Rew:79.0,43.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.50 85[6:Rew:79.0,46.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.20/0.50 86[5:Rew:79.0,52.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.20/0.50 87[5:Rew:79.0,53.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.50 113[2:Rew:29.0,78.2] || equal(multiply(sk_c5,u),inverse(sk_c8)) equal(u,sk_c8) equal(multiply(sk_c5,multiply(u,sk_c7)),sk_c8)** -> .
% 0.20/0.50 114[5:Rew:79.0,113.2,79.0,113.1,79.0,113.0] || equal(multiply(sk_c5,u),inverse(sk_c7)) equal(u,sk_c7) equal(multiply(sk_c5,multiply(u,sk_c7)),sk_c7)** -> .
% 0.20/0.50 134[0:SpR:73.0,73.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.50 136[0:SpR:27.0,73.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.20/0.50 137[0:SpR:28.0,73.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.50 141[5:SpR:84.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.50 142[5:SpR:86.0,73.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.20/0.50 143[5:SpR:87.0,73.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.20/0.50 149[5:Rew:28.0,141.0] || -> equal(identity,sk_c6)**.
% 0.20/0.50 158[5:Rew:149.0,136.0] || -> equal(multiply(inverse(sk_c6),u),u)**.
% 0.20/0.50 162[5:Rew:149.0,142.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.20/0.50 163[5:Rew:162.0,143.0,149.0,143.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.50 165[5:Rew:163.0,83.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.50 167[5:Rew:163.0,114.0] || equal(multiply(sk_c4,u),inverse(sk_c7)) equal(u,sk_c7) equal(multiply(sk_c5,multiply(u,sk_c7)),sk_c7)** -> .
% 0.20/0.50 169[5:Rew:163.0,162.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c4)**.
% 0.20/0.50 170[6:Rew:85.0,165.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.50 172[6:Rew:170.0,149.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 179[6:Rew:170.0,158.0] || -> equal(multiply(inverse(sk_c7),u),u)**.
% 0.20/0.50 180[6:Rew:179.0,169.0,170.0,169.0] || -> equal(sk_c7,sk_c4)**.
% 0.20/0.50 182[6:Rew:180.0,82.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.20/0.50 190[6:Rew:180.0,172.0] || -> equal(identity,sk_c4)**.
% 0.20/0.50 193[6:Rew:180.0,179.0] || -> equal(multiply(inverse(sk_c4),u),u)**.
% 0.20/0.50 196[6:Rew:182.0,193.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.50 197[6:Rew:190.0,137.0] || -> equal(multiply(inverse(inverse(u)),sk_c4),u)**.
% 0.20/0.50 203[6:Rew:134.0,197.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.20/0.50 219[6:Rew:196.0,167.2,163.0,167.2,203.0,167.2,180.0,167.2,180.0,167.1,196.0,167.0,182.0,167.0,180.0,167.0] || equal(u,sk_c4)* equal(u,sk_c4)* equal(u,sk_c4)* -> .
% 0.20/0.50 220[6:Obv:219.1] || equal(u,sk_c4)* -> .
% 0.20/0.50 221[6:UnC:220.0,73.0] || -> .
% 0.20/0.50 223[6:Spt:221.0,7.1,46.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.50 224[6:Spt:221.0,7.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.50 225[6:Rew:165.0,223.0,79.0,223.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.50 226[5:Rew:134.0,137.0,149.0,137.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.50 227[5:Rew:226.0,169.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.50 237[5:Rew:79.0,12.1,165.0,12.0,79.0,12.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.50 238[6:MRR:237.0,225.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.50 239[5:Rew:79.0,2.1,165.0,2.0,79.0,2.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c2),sk_c7)**.
% 0.20/0.50 240[6:MRR:239.0,225.0] || -> equal(multiply(sk_c1,sk_c2),sk_c7)**.
% 0.20/0.50 271[6:SpR:238.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.20/0.50 274[6:SpR:240.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c2)**.
% 0.20/0.50 276[6:Rew:238.0,274.0,224.0,274.0] || -> equal(sk_c7,sk_c2)**.
% 0.20/0.50 279[6:Rew:276.0,225.0] || equal(sk_c6,sk_c2)** -> .
% 0.20/0.50 280[6:Rew:276.0,227.0] || -> equal(inverse(sk_c2),sk_c4)**.
% 0.20/0.50 282[6:Rew:276.0,165.0] || -> equal(multiply(sk_c4,sk_c2),sk_c6)**.
% 0.20/0.50 297[6:Rew:276.0,271.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c2)**.
% 0.20/0.50 298[6:Rew:282.0,297.0,280.0,297.0] || -> equal(sk_c6,sk_c2)**.
% 0.20/0.50 299[6:MRR:298.0,279.0] || -> .
% 0.20/0.50 305[5:Spt:299.0,8.1,43.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.20/0.50 306[5:Spt:299.0,8.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.50 307[5:Rew:77.0,305.0] || equal(sk_c8,sk_c7)** -> .
% 0.20/0.50 308[0:Rew:134.0,137.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.50 309[4:Rew:77.0,18.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c8,sk_c7).
% 0.20/0.50 310[5:MRR:309.1,307.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 311[4:Rew:77.0,23.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 312[5:MRR:311.0,307.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 315[4:Rew:77.0,3.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.50 316[5:MRR:315.0,307.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.50 328[4:SpR:77.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.20/0.50 330[4:Rew:28.0,328.0] || -> equal(identity,sk_c6)**.
% 0.20/0.50 331[4:Rew:330.0,53.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.20/0.50 334[4:Rew:330.0,28.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.50 337[4:Rew:330.0,308.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.50 339[4:Rew:330.0,58.1] || equal(inverse(sk_c8),sk_c4) equal(sk_c8,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.50 345[5:SpR:312.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.20/0.50 347[5:Rew:310.0,345.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 357[5:SpR:316.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.20/0.50 359[5:Rew:306.0,357.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.20/0.50 361[4:SpR:331.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c4)**.
% 0.20/0.50 363[4:Rew:337.0,361.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.20/0.50 365[4:Rew:363.0,339.0] || equal(sk_c4,sk_c4) equal(sk_c8,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.50 368[4:Obv:365.0] || equal(sk_c8,sk_c6) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.50 393[5:SpR:347.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.50 395[5:Rew:363.0,393.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.50 396[5:Rew:395.0,368.1] || equal(sk_c8,sk_c6) equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 397[5:Obv:396.1] || equal(sk_c8,sk_c6)** -> .
% 0.20/0.50 409[5:SpR:359.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.20/0.50 411[5:Rew:334.0,409.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.50 412[5:MRR:411.0,397.0] || -> .
% 0.20/0.50 413[4:Spt:412.0,9.1,38.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.20/0.50 414[4:Spt:412.0,9.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.50 415[4:MRR:19.1,413.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 416[4:MRR:24.0,413.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 418[4:MRR:4.0,413.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.50 426[4:SpR:416.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.20/0.50 428[4:Rew:415.0,426.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 430[2:SpR:52.0,73.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.20/0.50 432[2:Rew:308.0,430.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.20/0.50 433[2:Rew:432.0,56.0] || equal(sk_c5,sk_c5) equal(sk_c8,identity) equal(multiply(sk_c5,sk_c7),sk_c8)** -> .
% 0.20/0.50 437[2:Obv:433.0] || equal(sk_c8,identity) equal(multiply(sk_c5,sk_c7),sk_c8)** -> .
% 0.20/0.50 441[3:SpR:53.0,73.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.20/0.50 443[3:Rew:432.0,441.0] || -> equal(multiply(sk_c5,identity),sk_c4)**.
% 0.20/0.50 444[3:Rew:308.0,443.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.50 447[3:Rew:444.0,432.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.20/0.50 450[3:Rew:444.0,437.1] || equal(sk_c8,identity) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.50 464[4:SpR:418.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.20/0.50 466[4:Rew:414.0,464.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.20/0.50 468[4:SpR:428.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.50 470[4:Rew:447.0,468.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.50 471[4:Rew:470.0,450.1] || equal(sk_c8,identity) equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 472[4:Obv:471.1] || equal(sk_c8,identity)** -> .
% 0.20/0.50 477[4:SpR:466.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.20/0.50 479[4:Rew:28.0,477.0] || -> equal(sk_c8,identity)**.
% 0.20/0.50 480[4:MRR:479.0,472.0] || -> .
% 0.20/0.50 481[3:Spt:480.0,6.0,34.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.50 482[3:Spt:480.0,6.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.50 483[3:MRR:16.0,481.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 484[3:MRR:21.0,481.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 486[3:MRR:1.0,481.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.50 501[3:SpR:484.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.20/0.50 503[3:Rew:483.0,501.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 508[3:SpR:486.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.20/0.50 510[3:Rew:482.0,508.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.20/0.50 521[3:SpR:503.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.50 523[3:Rew:432.0,521.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.20/0.50 524[3:Rew:523.0,437.1] || equal(sk_c8,identity) equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 525[3:Obv:524.1] || equal(sk_c8,identity)** -> .
% 0.20/0.50 527[3:SpR:510.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.20/0.50 529[3:Rew:28.0,527.0] || -> equal(sk_c8,identity)**.
% 0.20/0.50 530[3:MRR:529.0,525.0] || -> .
% 0.20/0.50 531[2:Spt:530.0,10.0,32.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.20/0.50 532[2:Spt:530.0,10.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.50 533[2:MRR:20.0,531.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 534[2:MRR:25.0,531.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.50 535[2:MRR:15.0,531.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.50 536[2:MRR:5.0,531.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.50 538[2:SpR:532.0,28.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.20/0.50 541[2:SpR:533.0,28.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.20/0.50 544[2:SpR:534.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.20/0.50 546[2:Rew:533.0,544.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 555[2:SpR:538.0,73.0] || -> equal(multiply(inverse(sk_c2),identity),sk_c1)**.
% 0.20/0.50 557[2:Rew:308.0,555.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.20/0.50 561[2:SpR:541.0,73.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.20/0.50 563[2:Rew:308.0,561.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.20/0.50 566[2:SpR:557.0,28.0] || -> equal(multiply(sk_c1,sk_c2),identity)**.
% 0.20/0.50 568[2:Rew:536.0,566.0] || -> equal(sk_c8,identity)**.
% 0.20/0.50 569[2:Rew:568.0,533.0] || -> equal(inverse(sk_c3),identity)**.
% 0.20/0.50 572[2:Rew:568.0,535.0] || -> equal(multiply(sk_c2,sk_c7),identity)**.
% 0.20/0.50 574[2:Rew:568.0,541.0] || -> equal(multiply(identity,sk_c3),identity)**.
% 0.20/0.50 577[2:Rew:568.0,37.1] || equal(inverse(identity),u) equal(u,identity) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.20/0.50 580[2:Rew:568.0,546.0] || -> equal(multiply(identity,identity),sk_c7)**.
% 0.20/0.50 586[2:Rew:568.0,563.0] || -> equal(inverse(identity),sk_c3)**.
% 0.20/0.50 587[2:Rew:586.0,136.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.50 588[2:Rew:27.0,574.0] || -> equal(identity,sk_c3)**.
% 0.20/0.50 592[2:Rew:588.0,308.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.20/0.50 593[2:Rew:588.0,568.0] || -> equal(sk_c8,sk_c3)**.
% 0.20/0.50 594[2:Rew:588.0,569.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.20/0.50 598[2:Rew:588.0,572.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.20/0.50 600[2:Rew:588.0,580.0] || -> equal(multiply(sk_c3,sk_c3),sk_c7)**.
% 0.20/0.50 603[2:Rew:587.0,600.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.50 604[2:Rew:603.0,588.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 605[2:Rew:603.0,593.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.50 606[2:Rew:603.0,594.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.50 612[2:Rew:603.0,592.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.50 614[2:Rew:612.0,598.0,603.0,598.0] || -> equal(sk_c7,sk_c2)**.
% 0.20/0.50 616[2:Rew:614.0,604.0] || -> equal(identity,sk_c2)**.
% 0.20/0.50 617[2:Rew:614.0,605.0] || -> equal(sk_c8,sk_c2)**.
% 0.20/0.50 618[2:Rew:614.0,606.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.20/0.50 621[2:Rew:614.0,612.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.20/0.50 623[2:Rew:557.0,618.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.50 624[2:Rew:623.0,532.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 627[2:Rew:623.0,614.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.50 629[2:Rew:623.0,616.0] || -> equal(identity,sk_c1)**.
% 0.20/0.50 630[2:Rew:623.0,617.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.50 637[2:Rew:623.0,621.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.50 646[2:Rew:637.0,577.2,627.0,577.2,630.0,577.2,629.0,577.1,624.0,577.0,629.0,577.0] || equal(sk_c1,u)* equal(u,sk_c1)* equal(u,sk_c1)* -> .
% 0.20/0.50 647[2:Obv:646.1] || equal(u,sk_c1)* -> .
% 0.20/0.50 648[2:UnC:647.0,73.0] || -> .
% 0.20/0.50 653[1:Spt:648.0,30.1,30.2,30.4,30.5,30.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),w)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,w),sk_c7)** -> .
% 0.20/0.50 654[1:EqR:653.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.50 656[2:Spt:6.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.50 657[2:SpR:656.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.50 659[3:Spt:20.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.50 662[4:Spt:7.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.50 664[4:SpR:662.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.20/0.50 666[4:Rew:656.0,664.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 668[4:SpR:666.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.50 671[5:Spt:8.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.50 673[5:SpR:671.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.20/0.50 675[5:Rew:668.0,673.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.50 677[5:Rew:675.0,656.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.50 678[5:Rew:675.0,659.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.50 679[5:Rew:675.0,662.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.50 680[5:Rew:675.0,666.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.20/0.50 683[5:Rew:675.0,4.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.20/0.50 684[5:Rew:675.0,14.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.20/0.50 686[5:Rew:675.0,9.1] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c6),sk_c6)**.
% 0.20/0.50 688[5:Rew:675.0,654.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.50 697[5:Rew:675.0,683.1] || -> equal(multiply(sk_c5,sk_c6),sk_c6)** equal(multiply(sk_c1,sk_c2),sk_c6).
% 0.20/0.50 698[5:Rew:675.0,684.1] || -> equal(multiply(sk_c5,sk_c6),sk_c6)** equal(multiply(sk_c2,sk_c7),sk_c6).
% 0.20/0.50 700[5:Rew:675.0,688.3,675.0,688.2,675.0,688.1] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c7)** -> .
% 0.20/0.50 727[0:SpR:28.0,73.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.50 728[0:SpR:28.0,308.0] || -> equal(inverse(identity),identity)**.
% 0.20/0.50 730[5:SpR:677.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.50 731[5:SpR:678.0,28.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.20/0.50 733[0:Rew:308.0,727.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.50 741[5:SpR:730.0,73.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.20/0.50 743[5:Rew:308.0,741.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.50 748[5:SpR:743.0,28.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.20/0.50 751[5:SpR:731.0,73.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c5)**.
% 0.20/0.50 753[5:Rew:308.0,751.0,743.0,751.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.50 758[5:Rew:753.0,698.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)** equal(multiply(sk_c2,sk_c7),sk_c6).
% 0.20/0.50 759[5:Rew:753.0,697.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)** equal(multiply(sk_c1,sk_c2),sk_c6).
% 0.20/0.50 760[5:Rew:753.0,686.1] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.20/0.50 764[5:Rew:748.0,760.1] || -> equal(inverse(sk_c1),sk_c2)** equal(identity,sk_c6).
% 0.20/0.50 767[5:Rew:748.0,758.0] || -> equal(identity,sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.50 768[5:Rew:748.0,759.0] || -> equal(identity,sk_c6) equal(multiply(sk_c1,sk_c2),sk_c6)**.
% 0.20/0.50 769[6:Spt:764.1] || -> equal(identity,sk_c6)**.
% 0.20/0.50 770[6:Rew:769.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.50 771[6:Rew:769.0,308.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.50 773[6:Rew:769.0,728.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.50 776[6:Rew:743.0,773.0] || -> equal(sk_c6,sk_c4)**.
% 0.20/0.50 778[6:Rew:776.0,677.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.20/0.50 779[6:Rew:776.0,679.0] || -> equal(multiply(sk_c4,sk_c7),sk_c4)**.
% 0.20/0.50 788[6:Rew:776.0,700.0] || equal(inverse(u),sk_c4) equal(inverse(v),sk_c6) equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c7)** -> .
% 0.20/0.50 791[6:Rew:776.0,770.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.50 792[6:Rew:776.0,771.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.20/0.50 793[6:Rew:791.0,779.0] || -> equal(sk_c7,sk_c4)**.
% 0.20/0.50 800[6:Rew:792.0,788.3,791.0,788.3,776.0,788.3,793.0,788.3,792.0,788.2,793.0,788.2,776.0,788.2,776.0,788.1] || equal(inverse(u),sk_c4)** equal(inverse(v),sk_c4)** equal(v,sk_c4) equal(u,sk_c4) -> .
% 0.20/0.50 801[6:Con:800.0] || equal(inverse(u),sk_c4)** equal(u,sk_c4) -> .
% 0.20/0.50 819[0:SpR:733.0,73.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.20/0.50 863[6:SpL:778.0,801.0] || equal(sk_c4,sk_c4)* equal(sk_c4,sk_c4)* -> .
% 0.20/0.50 865[6:Obv:863.1] || -> .
% 0.20/0.50 866[6:Spt:865.0,764.1,769.0] || equal(identity,sk_c6)** -> .
% 0.20/0.50 867[6:Spt:865.0,764.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.50 870[6:MRR:767.0,866.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.50 871[6:MRR:768.0,866.0] || -> equal(multiply(sk_c1,sk_c2),sk_c6)**.
% 0.20/0.50 873[6:SpR:867.0,733.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.20/0.50 874[6:SpR:867.0,819.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.20/0.50 919[6:SpR:871.0,29.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c6,u))**.
% 0.20/0.50 920[6:SpR:871.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c2)**.
% 0.20/0.50 922[6:Rew:867.0,920.0] || -> equal(multiply(sk_c2,sk_c6),sk_c2)**.
% 0.20/0.50 923[6:Rew:874.0,919.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.50 924[6:Rew:923.0,730.0] || -> equal(identity,sk_c4)**.
% 0.20/0.50 925[6:Rew:923.0,680.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.50 935[6:Rew:924.0,866.0] || equal(sk_c6,sk_c4)** -> .
% 0.20/0.50 936[6:Rew:924.0,728.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.20/0.50 942[6:Rew:925.0,743.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.50 944[6:Rew:925.0,870.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.50 948[6:Rew:925.0,922.0] || -> equal(multiply(sk_c2,sk_c7),sk_c2)**.
% 0.20/0.50 950[6:Rew:925.0,935.0] || equal(sk_c7,sk_c4)** -> .
% 0.20/0.50 955[6:Rew:944.0,948.0] || -> equal(sk_c7,sk_c2)**.
% 0.20/0.50 958[6:Rew:955.0,950.0] || equal(sk_c4,sk_c2)** -> .
% 0.20/0.50 959[6:Rew:955.0,942.0] || -> equal(inverse(sk_c2),sk_c4)**.
% 0.20/0.50 963[6:Rew:873.0,959.0] || -> equal(sk_c4,sk_c1)**.
% 0.20/0.50 967[6:Rew:963.0,936.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 970[6:Rew:963.0,958.0] || equal(sk_c2,sk_c1)** -> .
% 0.20/0.50 971[6:Rew:867.0,967.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.50 979[6:Rew:971.0,970.0] || equal(sk_c1,sk_c1)* -> .
% 0.20/0.50 980[6:Obv:979.0] || -> .
% 0.20/0.50 997[5:Spt:980.0,8.1,671.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.20/0.50 998[5:Spt:980.0,8.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.50 1001[5:MRR:13.0,997.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.50 1002[5:MRR:3.0,997.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.50 1005[5:SpR:998.0,819.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.20/0.50 1014[3:SpR:659.0,733.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.20/0.50 1020[2:SpR:656.0,733.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.20/0.50 1023[3:Rew:1014.0,1020.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.50 1026[3:Rew:1023.0,1014.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.20/0.50 1061[5:SpR:1002.0,29.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.20/0.50 1062[5:SpR:1002.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.20/0.50 1064[5:Rew:998.0,1062.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.20/0.50 1065[5:Rew:1005.0,1061.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.50 1066[5:Rew:1065.0,666.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.50 1074[5:Rew:1065.0,654.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.50 1079[5:Rew:1066.0,1001.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.50 1083[5:Rew:1066.0,1064.0] || -> equal(multiply(sk_c2,sk_c7),sk_c2)**.
% 0.20/0.50 1084[5:Rew:1066.0,1065.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 1085[5:Rew:1079.0,1083.0] || -> equal(sk_c7,sk_c2)**.
% 0.20/0.50 1086[5:Rew:1085.0,1066.0] || -> equal(sk_c8,sk_c2)**.
% 0.20/0.50 1098[5:Rew:1085.0,1084.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.50 1104[5:Rew:1086.0,1074.3,1085.0,1074.3,1085.0,1074.2,1086.0,1074.2,1086.0,1074.1,1086.0,1074.0] || equal(inverse(u),sk_c2) equal(inverse(v),sk_c2) equal(multiply(v,sk_c2),sk_c2)** equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.50 1105[5:Con:1104.0] || equal(inverse(u),sk_c2) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.50 1127[5:SpR:998.0,28.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.20/0.51 1130[5:Rew:1098.0,1127.0] || -> equal(identity,sk_c1)**.
% 0.20/0.51 1131[5:Rew:1130.0,728.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1134[5:Rew:1130.0,308.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.51 1135[5:Rew:998.0,1131.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.51 1136[5:Rew:1135.0,998.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1142[5:Rew:1135.0,1105.0] || equal(inverse(u),sk_c1) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.51 1150[5:Rew:1134.0,1142.1,1135.0,1142.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.51 1195[5:SpL:1136.0,1150.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.51 1196[5:Obv:1195.1] || -> .
% 0.20/0.51 1197[4:Spt:1196.0,7.1,662.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.51 1198[4:Spt:1196.0,7.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.51 1201[4:MRR:17.1,1197.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.51 1206[4:MRR:22.0,1197.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 1223[4:SpR:1201.0,733.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.20/0.51 1226[4:Rew:1026.0,1223.0] || -> equal(sk_c3,sk_c4)**.
% 0.20/0.51 1228[4:Rew:1226.0,1206.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.51 1229[4:MRR:1228.0,1197.0] || -> .
% 0.20/0.51 1232[3:Spt:1229.0,20.0,659.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.20/0.51 1233[3:Spt:1229.0,20.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.51 1234[3:MRR:10.0,1232.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.51 1235[3:MRR:25.0,1232.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 1236[3:MRR:15.0,1232.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.51 1237[3:MRR:5.0,1232.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.51 1239[3:SpR:1233.0,733.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.20/0.51 1242[3:Rew:1020.0,1239.0] || -> equal(sk_c3,sk_c4)**.
% 0.20/0.51 1244[3:Rew:1242.0,1235.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.51 1260[3:SpR:1234.0,819.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.20/0.51 1270[3:SpR:1237.0,29.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.20/0.51 1271[3:SpR:1237.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.20/0.51 1273[3:Rew:1234.0,1271.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.20/0.51 1274[3:Rew:1260.0,1270.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.51 1277[3:Rew:1274.0,654.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.51 1278[3:Rew:1274.0,657.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.51 1281[3:Rew:1278.0,1244.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.51 1285[3:Rew:1281.0,1236.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.51 1288[3:Rew:1281.0,1273.0] || -> equal(multiply(sk_c2,sk_c7),sk_c2)**.
% 0.20/0.51 1289[3:Rew:1281.0,1274.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 1290[3:Rew:1285.0,1288.0] || -> equal(sk_c7,sk_c2)**.
% 0.20/0.51 1291[3:Rew:1290.0,1281.0] || -> equal(sk_c8,sk_c2)**.
% 0.20/0.51 1302[3:Rew:1290.0,1289.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.51 1306[3:Rew:1291.0,1277.3,1290.0,1277.3,1290.0,1277.2,1291.0,1277.2,1291.0,1277.1,1291.0,1277.0] || equal(inverse(u),sk_c2) equal(inverse(v),sk_c2) equal(multiply(v,sk_c2),sk_c2)** equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.51 1307[3:Con:1306.0] || equal(inverse(u),sk_c2) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.51 1326[3:SpR:1234.0,28.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.20/0.51 1328[3:Rew:1302.0,1326.0] || -> equal(identity,sk_c1)**.
% 0.20/0.51 1329[3:Rew:1328.0,728.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1332[3:Rew:1328.0,308.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.51 1334[3:Rew:1234.0,1329.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.51 1335[3:Rew:1334.0,1234.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1341[3:Rew:1334.0,1307.0] || equal(inverse(u),sk_c1) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.51 1348[3:Rew:1332.0,1341.1,1334.0,1341.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.51 1393[3:SpL:1335.0,1348.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.51 1394[3:Obv:1393.1] || -> .
% 0.20/0.51 1395[2:Spt:1394.0,6.0,656.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.51 1396[2:Spt:1394.0,6.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.51 1398[2:MRR:16.0,1395.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.51 1399[2:MRR:21.0,1395.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 1400[2:MRR:11.0,1395.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.51 1401[2:MRR:1.0,1395.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.51 1405[2:SpR:1396.0,819.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.20/0.51 1426[2:SpR:1399.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.20/0.51 1428[2:Rew:1398.0,1426.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.51 1433[2:SpR:1401.0,29.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.20/0.51 1434[2:SpR:1401.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.20/0.51 1436[2:Rew:1396.0,1434.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.20/0.51 1437[2:Rew:1405.0,1433.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.51 1439[2:Rew:1437.0,1428.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.51 1445[2:Rew:1437.0,654.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.51 1450[2:Rew:1439.0,1400.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.51 1453[2:Rew:1439.0,1436.0] || -> equal(multiply(sk_c2,sk_c7),sk_c2)**.
% 0.20/0.51 1454[2:Rew:1439.0,1437.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 1455[2:Rew:1450.0,1453.0] || -> equal(sk_c7,sk_c2)**.
% 0.20/0.51 1456[2:Rew:1455.0,1439.0] || -> equal(sk_c8,sk_c2)**.
% 0.20/0.51 1466[2:Rew:1455.0,1454.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.51 1471[2:Rew:1456.0,1445.3,1455.0,1445.3,1455.0,1445.2,1456.0,1445.2,1456.0,1445.1,1456.0,1445.0] || equal(inverse(u),sk_c2) equal(inverse(v),sk_c2) equal(multiply(v,sk_c2),sk_c2)** equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.51 1472[2:Con:1471.0] || equal(inverse(u),sk_c2) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.51 1489[2:SpR:1396.0,28.0] || -> equal(multiply(sk_c2,sk_c1),identity)**.
% 0.20/0.51 1492[2:Rew:1466.0,1489.0] || -> equal(identity,sk_c1)**.
% 0.20/0.51 1493[2:Rew:1492.0,728.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1496[2:Rew:1492.0,308.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.51 1498[2:Rew:1396.0,1493.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.51 1499[2:Rew:1498.0,1396.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1505[2:Rew:1498.0,1472.0] || equal(inverse(u),sk_c1) equal(multiply(u,sk_c2),sk_c2)** -> .
% 0.20/0.51 1513[2:Rew:1496.0,1505.1,1498.0,1505.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.51 1558[2:SpL:1499.0,1513.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.51 1559[2:Obv:1558.1] || -> .
% 0.20/0.51 % SZS output end Refutation
% 0.20/0.51 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 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 left_identity left_inverse associativity
% 0.20/0.51
%------------------------------------------------------------------------------