TSTP Solution File: GRP296-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP296-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:46:44 EDT 2022
% Result : Unsatisfiable 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP296-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.11 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Tue Jun 14 06:32:12 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.40
% 0.15/0.40 SPASS V 3.9
% 0.15/0.40 SPASS beiseite: Proof found.
% 0.15/0.40 % SZS status Theorem
% 0.15/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 SPASS derived 866 clauses, backtracked 494 clauses, performed 13 splits and kept 836 clauses.
% 0.15/0.40 SPASS allocated 63612 KBytes.
% 0.15/0.40 SPASS spent 0:00:00.09 on the problem.
% 0.15/0.40 0:00:00.03 for the input.
% 0.15/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.40 0:00:00.00 for inferences.
% 0.15/0.40 0:00:00.00 for the backtracking.
% 0.15/0.40 0:00:00.04 for the reduction.
% 0.15/0.40
% 0.15/0.40
% 0.15/0.40 Here is a proof with depth 4, length 366 :
% 0.15/0.40 % SZS output start Refutation
% 0.15/0.40 1[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.15/0.40 2[0:Inp] || -> equal(multiply(sk_c8,sk_c4),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.15/0.40 3[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.15/0.40 4[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.15/0.40 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.15/0.40 6[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.15/0.40 7[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 8[0:Inp] || -> equal(multiply(sk_c8,sk_c4),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 9[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 10[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 11[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 12[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.15/0.40 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.15/0.40 15[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.15/0.40 16[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.40 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.15/0.40 18[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.40 19[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.15/0.40 21[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.15/0.40 22[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.40 23[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7).
% 0.15/0.40 24[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.40 25[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 26[0:Inp] || -> equal(multiply(sk_c8,sk_c4),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 27[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 28[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 29[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 30[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 31[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.15/0.40 32[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.15/0.40 33[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.15/0.40 34[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.40 35[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.15/0.40 36[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.40 37[0:Inp] || equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(v,sk_c8),sk_c6)** equal(inverse(v),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,w),sk_c7)** equal(multiply(x,sk_c8),w)* equal(inverse(x),sk_c8) equal(multiply(y,sk_c6),sk_c8)** equal(inverse(y),sk_c6) -> .
% 0.15/0.40 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.15/0.40 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.15/0.40 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.15/0.40 41[0:Con:37.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)**+ equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.15/0.40 42[1:Spt:41.2,41.5] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.15/0.40 43[2:Spt:19.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.15/0.40 45[2:SpL:43.0,42.1] || equal(inverse(sk_c6),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.15/0.40 46[2:Obv:45.1] || equal(inverse(sk_c6),sk_c8)** -> .
% 0.15/0.40 47[3:Spt:24.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.15/0.40 49[4:Spt:22.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.15/0.40 51[5:Spt:21.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.15/0.40 53[5:SpL:51.0,42.1] || equal(inverse(sk_c3),sk_c8)** equal(sk_c4,sk_c7) -> .
% 0.15/0.40 54[5:Rew:49.0,53.0] || equal(sk_c8,sk_c8) equal(sk_c4,sk_c7)** -> .
% 0.15/0.40 55[5:Obv:54.0] || equal(sk_c4,sk_c7)** -> .
% 0.15/0.40 56[6:Spt:23.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.15/0.40 61[1:SpL:38.0,42.1] || equal(inverse(identity),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.15/0.40 63[3:SpR:47.0,39.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.15/0.40 64[4:SpR:49.0,39.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.15/0.40 73[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.15/0.40 75[0:Rew:38.0,73.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.15/0.40 77[3:SpR:63.0,40.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.15/0.40 79[3:Rew:38.0,77.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.15/0.40 85[6:SpR:56.0,79.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.15/0.40 86[6:Rew:43.0,85.0] || -> equal(sk_c6,sk_c7)**.
% 0.15/0.40 87[6:Rew:86.0,43.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.15/0.40 90[6:Rew:86.0,46.0] || equal(inverse(sk_c7),sk_c8)** -> .
% 0.15/0.40 91[6:Rew:86.0,63.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.15/0.40 110[0:SpR:75.0,75.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.15/0.40 113[6:SpR:87.0,75.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.15/0.40 115[4:SpR:64.0,75.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.15/0.40 117[0:SpR:39.0,75.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.15/0.40 120[6:SpR:91.0,75.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.15/0.40 140[6:Rew:39.0,113.0] || -> equal(identity,sk_c8)**.
% 0.15/0.40 141[6:Rew:140.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.15/0.40 143[6:Rew:140.0,64.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.15/0.40 149[6:Rew:141.0,143.0] || -> equal(sk_c3,sk_c8)**.
% 0.15/0.40 151[6:Rew:149.0,51.0] || -> equal(multiply(sk_c8,sk_c8),sk_c4)**.
% 0.15/0.40 158[6:Rew:141.0,151.0] || -> equal(sk_c4,sk_c8)**.
% 0.15/0.40 168[6:Rew:140.0,117.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.15/0.40 173[6:Rew:110.0,168.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.15/0.40 186[6:Rew:158.0,55.0] || equal(sk_c7,sk_c8)** -> .
% 0.15/0.40 194[6:Rew:173.0,120.0,140.0,120.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.15/0.40 195[6:Rew:194.0,90.0] || equal(sk_c5,sk_c8)** -> .
% 0.15/0.40 199[6:Rew:158.0,14.1,141.0,14.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c8).
% 0.15/0.40 200[6:MRR:199.1,186.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.40 208[6:Rew:173.0,8.1,158.0,8.0,141.0,8.0] || -> equal(sk_c7,sk_c8) equal(sk_c1,sk_c7)**.
% 0.15/0.40 209[6:MRR:208.0,186.0] || -> equal(sk_c1,sk_c7)**.
% 0.15/0.40 210[6:Rew:209.0,200.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.15/0.40 211[6:Rew:194.0,210.0] || -> equal(sk_c5,sk_c8)**.
% 0.15/0.40 212[6:MRR:211.0,195.0] || -> .
% 0.15/0.40 218[6:Spt:212.0,23.0,56.0] || equal(multiply(sk_c5,sk_c6),sk_c8)** -> .
% 0.15/0.40 219[6:Spt:212.0,23.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.40 221[0:Rew:110.0,117.0] || -> equal(multiply(u,identity),u)**.
% 0.15/0.40 222[4:Rew:221.0,115.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.15/0.40 223[6:MRR:35.1,218.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.40 224[6:MRR:17.1,218.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.40 225[6:MRR:29.0,218.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 226[6:MRR:11.0,218.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 227[6:MRR:5.0,218.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.15/0.40 232[6:SpR:219.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.15/0.40 234[6:Rew:222.0,232.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.15/0.40 239[4:SpR:222.0,75.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),u)**.
% 0.15/0.40 248[3:SpR:63.0,75.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c5)**.
% 0.15/0.40 250[3:Rew:221.0,248.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.15/0.40 251[3:Rew:250.0,46.0] || equal(sk_c5,sk_c8)** -> .
% 0.15/0.40 256[6:SpR:225.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.15/0.40 258[6:Rew:219.0,256.0,223.0,256.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 260[6:Rew:258.0,55.0] || equal(sk_c4,sk_c8)** -> .
% 0.15/0.40 266[6:Rew:258.0,226.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 267[6:Rew:258.0,227.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.15/0.40 270[6:Rew:258.0,234.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.15/0.40 271[6:Rew:51.0,270.0] || -> equal(sk_c4,sk_c6)**.
% 0.15/0.40 275[6:Rew:271.0,260.0] || equal(sk_c6,sk_c8)** -> .
% 0.15/0.40 296[6:SpR:266.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.15/0.40 298[6:Rew:224.0,296.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.15/0.40 299[6:Rew:267.0,298.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.40 300[6:MRR:299.0,275.0] || -> .
% 0.15/0.40 301[5:Spt:300.0,21.0,51.0] || equal(multiply(sk_c3,sk_c8),sk_c4)** -> .
% 0.15/0.40 302[5:Spt:300.0,21.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.40 303[5:MRR:33.1,301.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.40 304[5:MRR:15.1,301.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.40 305[5:MRR:27.0,301.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 306[5:MRR:9.0,301.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 307[5:MRR:3.0,301.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.15/0.40 309[5:SpR:302.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.15/0.40 311[5:Rew:222.0,309.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.15/0.40 321[5:SpR:305.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.15/0.40 323[5:Rew:302.0,321.0,303.0,321.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 327[5:Rew:323.0,61.1] || equal(inverse(identity),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.15/0.40 330[5:Rew:323.0,306.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 331[5:Rew:323.0,307.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.15/0.40 334[5:Rew:323.0,311.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.15/0.40 337[5:Obv:327.1] || equal(inverse(identity),sk_c8)** -> .
% 0.15/0.40 345[5:SpR:330.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.15/0.40 347[5:Rew:304.0,345.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.15/0.40 348[5:Rew:331.0,347.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.40 361[5:Rew:348.0,334.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.15/0.40 385[5:SpR:361.0,40.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.15/0.40 389[5:Rew:239.0,385.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.15/0.40 390[5:Rew:389.0,64.0] || -> equal(identity,sk_c3)**.
% 0.15/0.40 398[5:Rew:390.0,337.0] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.15/0.40 403[5:Rew:49.0,398.0] || equal(sk_c8,sk_c8)* -> .
% 0.15/0.40 404[5:Obv:403.0] || -> .
% 0.15/0.40 406[4:Spt:404.0,22.0,49.0] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.15/0.40 407[4:Spt:404.0,22.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.40 408[4:MRR:34.0,406.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.40 409[4:MRR:16.0,406.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.40 410[4:MRR:28.0,406.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 411[4:MRR:10.0,406.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 412[4:MRR:4.0,406.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.15/0.40 414[4:SpR:407.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.15/0.40 438[4:SpR:410.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.15/0.40 440[4:Rew:407.0,438.0,408.0,438.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 448[4:Rew:440.0,411.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 449[4:Rew:440.0,412.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.15/0.40 453[4:Rew:440.0,414.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.40 454[4:Rew:39.0,453.0] || -> equal(identity,sk_c6)**.
% 0.15/0.40 455[4:Rew:454.0,63.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.15/0.40 456[4:Rew:454.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.15/0.40 461[4:Rew:456.0,455.0] || -> equal(sk_c5,sk_c6)**.
% 0.15/0.40 465[4:Rew:461.0,251.0] || equal(sk_c6,sk_c8)** -> .
% 0.15/0.40 477[4:SpR:448.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.15/0.40 479[4:Rew:409.0,477.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.15/0.40 480[4:Rew:449.0,479.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.40 481[4:MRR:480.0,465.0] || -> .
% 0.15/0.40 482[3:Spt:481.0,24.0,47.0] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.15/0.40 483[3:Spt:481.0,24.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.40 484[3:MRR:36.0,482.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.40 485[3:MRR:18.0,482.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.40 486[3:MRR:30.0,482.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 487[3:MRR:12.0,482.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.40 488[3:MRR:6.0,482.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.15/0.40 490[3:SpR:483.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.15/0.40 500[3:SpR:486.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.15/0.40 502[3:Rew:483.0,500.0,484.0,500.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 509[3:Rew:502.0,487.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 510[3:Rew:502.0,488.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.15/0.40 514[3:Rew:502.0,490.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.40 515[3:Rew:39.0,514.0] || -> equal(identity,sk_c6)**.
% 0.15/0.40 516[3:Rew:515.0,221.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.15/0.40 528[3:SpR:509.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.15/0.40 530[3:Rew:485.0,528.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.15/0.40 531[3:Rew:510.0,530.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.40 532[3:Rew:531.0,46.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.15/0.40 534[3:Rew:531.0,486.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.15/0.40 537[3:Rew:531.0,516.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.15/0.40 543[3:Rew:537.0,534.0] || -> equal(sk_c2,sk_c8)**.
% 0.15/0.40 548[3:Rew:543.0,484.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.15/0.40 552[3:MRR:548.0,532.0] || -> .
% 0.15/0.40 558[2:Spt:552.0,19.0,43.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.15/0.40 559[2:Spt:552.0,19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.40 560[2:MRR:31.1,558.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.40 562[2:MRR:25.0,558.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 566[2:SpR:559.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.15/0.40 573[2:SpR:562.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.15/0.40 575[2:Rew:559.0,573.0,560.0,573.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 577[2:Rew:575.0,558.0] || equal(multiply(sk_c6,sk_c8),sk_c8)** -> .
% 0.15/0.40 584[2:Rew:575.0,566.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.40 586[2:Rew:39.0,584.0] || -> equal(identity,sk_c6)**.
% 0.15/0.40 587[2:Rew:586.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.15/0.40 591[2:UnC:587.0,577.0] || -> .
% 0.15/0.40 595[1:Spt:591.0,41.0,41.1,41.3,41.4,41.6,41.7,41.8] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)**+ equal(multiply(v,sk_c8),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.15/0.40 597[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.15/0.40 598[2:Rew:597.0,595.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** equal(sk_c7,sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.15/0.40 600[2:Obv:598.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.15/0.40 603[2:SpR:597.0,75.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.15/0.40 605[3:Spt:22.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.40 607[3:Rew:605.0,600.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** equal(sk_c7,sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.15/0.40 608[3:Obv:607.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.15/0.40 611[3:SpR:605.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.15/0.40 613[4:Spt:6.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.15/0.40 615[4:Rew:613.0,608.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.15/0.40 616[4:Obv:615.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c8),sk_c6)** -> .
% 0.15/0.40 619[4:SpR:613.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.15/0.40 621[5:Spt:36.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.40 622[5:SpR:621.0,75.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.15/0.40 630[6:Spt:18.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.40 633[7:Spt:30.1] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.40 635[7:SpR:633.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.15/0.40 637[7:Rew:605.0,635.0,621.0,635.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 640[7:Rew:637.0,613.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.15/0.40 642[7:Rew:637.0,11.1] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 645[7:Rew:637.0,12.1] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 650[7:Rew:637.0,611.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.40 651[7:Rew:637.0,619.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.15/0.40 652[7:Rew:39.0,650.0] || -> equal(identity,sk_c6)**.
% 0.15/0.40 653[7:Rew:652.0,221.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.15/0.40 656[7:Rew:652.0,39.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.15/0.40 658[7:Rew:653.0,616.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c6)** -> .
% 0.15/0.40 659[7:Rew:653.0,651.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.15/0.40 664[7:Rew:653.0,642.0] || -> equal(sk_c5,sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 665[7:Rew:664.0,645.0] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 666[7:Rew:659.0,665.0] || -> equal(sk_c6,sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.40 691[7:SpR:630.0,656.0] || -> equal(multiply(sk_c8,sk_c1),sk_c6)**.
% 0.15/0.40 714[7:SpR:691.0,75.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c1)**.
% 0.15/0.40 716[7:Rew:653.0,714.0,659.0,714.0] || -> equal(sk_c1,sk_c8)**.
% 0.15/0.40 721[7:Rew:716.0,666.1] || -> equal(sk_c6,sk_c8) equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.15/0.40 725[7:Rew:640.0,721.1] || -> equal(sk_c6,sk_c8)** equal(sk_c6,sk_c8)**.
% 0.15/0.40 726[7:Obv:725.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.40 730[7:Rew:726.0,653.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.15/0.40 733[7:Rew:726.0,658.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c6)** -> .
% 0.15/0.40 736[7:Rew:730.0,733.3,726.0,733.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.15/0.40 737[7:Con:736.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.15/0.40 789[7:SpL:659.0,737.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.15/0.40 791[7:Obv:789.1] || -> .
% 0.15/0.40 792[7:Spt:791.0,30.1,633.0] || equal(multiply(sk_c2,sk_c8),sk_c6)** -> .
% 0.15/0.40 793[7:Spt:791.0,30.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.15/0.40 794[7:MRR:28.1,792.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.15/0.40 795[7:MRR:27.1,792.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.15/0.40 796[7:MRR:29.1,792.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.15/0.40 797[7:MRR:26.1,792.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.15/0.40 813[7:SpR:795.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c8)**.
% 0.15/0.40 815[7:Rew:794.0,813.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.15/0.40 816[7:Rew:797.0,815.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 820[7:Rew:816.0,619.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.15/0.40 821[7:Rew:816.0,611.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.40 827[7:Rew:39.0,821.0] || -> equal(identity,sk_c6)**.
% 0.15/0.40 828[7:Rew:827.0,221.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.15/0.40 829[7:Rew:827.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.15/0.40 832[7:Rew:828.0,820.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.15/0.40 834[7:Rew:828.0,796.0] || -> equal(sk_c5,sk_c8)**.
% 0.15/0.40 836[7:Rew:834.0,793.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.15/0.40 838[7:Rew:832.0,836.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.40 839[7:Rew:838.0,792.0] || equal(multiply(sk_c2,sk_c8),sk_c8)** -> .
% 0.15/0.40 844[7:Rew:838.0,829.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.15/0.40 848[7:Rew:844.0,622.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.15/0.40 853[7:Rew:848.0,839.0] || equal(sk_c8,sk_c8)* -> .
% 0.15/0.40 854[7:Obv:853.0] || -> .
% 0.15/0.40 864[6:Spt:854.0,18.1,630.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.15/0.40 865[6:Spt:854.0,18.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.15/0.40 866[6:MRR:16.1,864.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.15/0.40 867[6:MRR:15.0,864.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.15/0.40 868[6:MRR:17.0,864.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.15/0.40 869[6:MRR:14.0,864.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.15/0.40 870[6:SpR:865.0,75.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.15/0.40 884[6:SpR:867.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c8)**.
% 0.15/0.40 886[6:Rew:866.0,884.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.15/0.40 887[6:Rew:869.0,886.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 889[6:Rew:887.0,613.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.15/0.40 892[6:Rew:887.0,611.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.40 898[6:Rew:39.0,892.0] || -> equal(identity,sk_c6)**.
% 0.15/0.40 899[6:Rew:898.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.15/0.40 900[6:Rew:898.0,221.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.15/0.40 903[6:Rew:899.0,870.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.15/0.40 905[6:Rew:900.0,868.0] || -> equal(sk_c5,sk_c8)**.
% 0.15/0.40 906[6:Rew:900.0,616.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c6)** -> .
% 0.15/0.40 907[6:Rew:905.0,865.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.15/0.40 908[6:Rew:905.0,903.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.15/0.40 909[6:Rew:908.0,889.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.40 916[6:Rew:909.0,900.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.15/0.40 917[6:Rew:909.0,907.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.15/0.40 926[6:Rew:916.0,906.3,909.0,906.3,909.0,906.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.15/0.40 927[6:Con:926.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.15/0.40 970[6:SpL:917.0,927.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.15/0.40 971[6:Obv:970.1] || -> .
% 0.15/0.40 972[5:Spt:971.0,36.1,621.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.15/0.40 973[5:Spt:971.0,36.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.15/0.40 974[5:MRR:34.1,972.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.15/0.40 975[5:MRR:33.0,972.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.15/0.40 976[5:MRR:35.0,972.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.15/0.40 977[5:MRR:32.0,972.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.15/0.40 992[5:SpR:975.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c8)**.
% 0.15/0.40 994[5:Rew:974.0,992.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.15/0.40 995[5:Rew:977.0,994.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 999[5:Rew:995.0,619.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.15/0.40 1000[5:Rew:995.0,611.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.40 1006[5:Rew:39.0,1000.0] || -> equal(identity,sk_c6)**.
% 0.15/0.40 1007[5:Rew:1006.0,221.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.15/0.40 1011[5:Rew:1007.0,999.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.15/0.40 1013[5:Rew:1007.0,976.0] || -> equal(sk_c5,sk_c8)**.
% 0.15/0.40 1014[5:Rew:1007.0,616.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c6)** -> .
% 0.15/0.40 1015[5:Rew:1013.0,973.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.15/0.40 1017[5:Rew:1011.0,1015.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.40 1021[5:Rew:1017.0,1007.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.15/0.40 1034[5:Rew:1021.0,1014.3,1017.0,1014.3,1017.0,1014.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.15/0.40 1035[5:Con:1034.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.15/0.40 1105[5:SpL:1011.0,1035.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.15/0.40 1107[5:Obv:1105.1] || -> .
% 0.15/0.40 1108[4:Spt:1107.0,6.1,613.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.15/0.40 1109[4:Spt:1107.0,6.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.15/0.40 1110[4:MRR:4.1,1108.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.15/0.40 1111[4:MRR:3.1,1108.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.15/0.40 1112[4:MRR:5.1,1108.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.15/0.40 1113[4:MRR:2.1,1108.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.15/0.40 1114[4:SpR:1109.0,75.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.15/0.40 1125[4:SpR:1111.0,75.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c8)**.
% 0.15/0.40 1127[4:Rew:1110.0,1125.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.15/0.40 1128[4:Rew:1113.0,1127.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.40 1132[4:Rew:1128.0,611.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.15/0.40 1133[4:Rew:1128.0,1108.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.15/0.40 1137[4:Rew:39.0,1132.0] || -> equal(identity,sk_c6)**.
% 0.15/0.40 1138[4:Rew:1137.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.15/0.40 1139[4:Rew:1137.0,221.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.15/0.40 1142[4:Rew:1138.0,1114.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.15/0.40 1143[4:Rew:1139.0,1112.0] || -> equal(sk_c5,sk_c8)**.
% 0.15/0.41 1145[4:Rew:1143.0,1142.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.15/0.41 1149[4:Rew:1145.0,1133.0] || equal(sk_c6,sk_c8)** -> .
% 0.15/0.41 1171[4:SpR:1145.0,1139.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.41 1173[4:MRR:1171.0,1149.0] || -> .
% 0.15/0.41 1175[3:Spt:1173.0,22.1,605.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.15/0.41 1176[3:Spt:1173.0,22.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.15/0.41 1177[3:MRR:24.1,1175.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.15/0.41 1179[3:MRR:23.1,1175.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.15/0.41 1192[3:SpR:1179.0,75.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.15/0.41 1194[3:Rew:597.0,1192.0,1177.0,1192.0] || -> equal(sk_c6,sk_c7)**.
% 0.15/0.41 1198[3:Rew:1194.0,603.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.15/0.41 1199[3:Rew:1194.0,1175.0] || equal(multiply(sk_c8,sk_c7),sk_c7)** -> .
% 0.15/0.41 1202[3:Rew:39.0,1198.0] || -> equal(identity,sk_c8)**.
% 0.15/0.41 1204[3:Rew:1202.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.15/0.41 1215[3:Rew:1204.0,1199.0] || equal(sk_c7,sk_c7)* -> .
% 0.15/0.41 1216[3:Obv:1215.0] || -> .
% 0.15/0.41 1230[2:Spt:1216.0,1.0,597.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.15/0.41 1231[2:Spt:1216.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.15/0.41 1232[2:MRR:31.1,1230.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.15/0.41 1233[2:MRR:13.1,1230.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.15/0.41 1234[2:MRR:25.0,1230.0] || -> equal(multiply(sk_c2,sk_c8),sk_c6)**.
% 0.15/0.41 1235[2:MRR:7.0,1230.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.15/0.41 1236[2:MRR:19.0,1230.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.15/0.41 1245[2:SpR:1234.0,75.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c8)**.
% 0.15/0.41 1247[2:Rew:1232.0,1245.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.15/0.41 1248[2:Rew:1236.0,1247.0] || -> equal(sk_c7,sk_c8)**.
% 0.15/0.41 1249[2:Rew:1248.0,1231.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.15/0.41 1250[2:Rew:1248.0,1230.0] || equal(multiply(sk_c6,sk_c8),sk_c8)** -> .
% 0.15/0.41 1251[2:Rew:1248.0,1235.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.15/0.41 1260[2:SpR:1251.0,75.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.15/0.41 1262[2:Rew:1249.0,1260.0,1233.0,1260.0] || -> equal(sk_c6,sk_c8)**.
% 0.15/0.41 1264[2:Rew:1262.0,1249.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.15/0.41 1266[2:Rew:1262.0,1250.0] || equal(multiply(sk_c8,sk_c8),sk_c8)** -> .
% 0.15/0.41 1270[2:Rew:1264.0,1266.0] || equal(sk_c8,sk_c8)* -> .
% 0.15/0.41 1271[2:Obv:1270.0] || -> .
% 0.15/0.41 % SZS output end Refutation
% 0.15/0.41 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_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 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.15/0.41
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