TSTP Solution File: GRP328-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP328-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:46:52 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP328-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 10:23:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 1068 clauses, backtracked 355 clauses, performed 11 splits and kept 825 clauses.
% 0.19/0.47 SPASS allocated 63711 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.01 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 5, length 469 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.19/0.47 2[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 3[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.19/0.47 4[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.19/0.47 5[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 6[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 7[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 8[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 10[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.47 12[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 14[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 15[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 16[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 17[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 18[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 19[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.19/0.47 20[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 21[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 22[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 23[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 24[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 25[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 26[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.47 27[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 28[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 29[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 30[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 31[0:Inp] || equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(u,sk_c7),sk_c8)** equal(inverse(u),sk_c7) equal(multiply(sk_c8,v),sk_c7)** equal(multiply(w,sk_c8),v)* equal(inverse(w),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c8,x),sk_c7)** equal(multiply(y,sk_c8),x)* equal(inverse(y),sk_c8) -> .
% 0.19/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 35[0:Con:31.8] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(sk_c8),sk_c6) equal(multiply(u,sk_c8),w)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,w),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.19/0.47 36[1:Spt:35.0,35.3,35.5] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.19/0.47 38[2:Spt:2.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.19/0.47 40[3:Spt:1.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.47 42[4:Spt:5.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 45[1:SpL:32.0,36.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.47 46[5:Spt:4.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 51[6:Spt:3.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 54[2:SpR:38.0,33.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.19/0.47 55[4:SpR:42.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.47 56[1:SpL:33.0,36.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.47 57[2:Rew:38.0,56.0] || equal(inverse(sk_c6),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.47 64[2:SpR:54.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.19/0.47 65[6:SpR:51.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 66[4:SpR:55.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.47 67[3:SpR:40.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.47 69[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 71[2:Rew:32.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.19/0.47 72[4:Rew:32.0,66.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.19/0.47 73[0:Rew:32.0,69.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 78[4:SpR:55.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c4)**.
% 0.19/0.47 82[4:SpR:78.0,34.0] || -> equal(multiply(sk_c6,multiply(identity,u)),multiply(sk_c4,u))**.
% 0.19/0.47 84[4:Rew:32.0,82.0] || -> equal(multiply(sk_c4,u),multiply(sk_c6,u))**.
% 0.19/0.47 85[5:Rew:84.0,46.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.47 87[4:Rew:84.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.19/0.47 88[5:Rew:54.0,85.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 89[5:Rew:88.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 90[5:Rew:88.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 91[5:Rew:88.0,54.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.47 92[5:Rew:88.0,55.0] || -> equal(multiply(sk_c8,sk_c4),sk_c5)**.
% 0.19/0.47 93[5:Rew:88.0,78.0] || -> equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.19/0.47 94[5:Rew:88.0,45.0] || equal(inverse(sk_c5),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.47 95[5:Rew:88.0,57.1] || equal(inverse(sk_c6),sk_c8) equal(sk_c5,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.47 96[6:Rew:89.0,65.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.19/0.47 99[6:Rew:96.0,51.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.19/0.47 101[6:Rew:96.0,87.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.47 105[6:Rew:96.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.47 108[6:Rew:101.0,105.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 109[6:Rew:108.0,40.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 110[6:Rew:108.0,101.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 112[6:Rew:108.0,99.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 115[6:Rew:109.0,38.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 118[6:Rew:109.0,91.0] || -> equal(multiply(sk_c8,sk_c8),sk_c5)**.
% 0.19/0.47 123[6:Rew:112.0,90.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.47 126[6:Rew:109.0,110.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 129[6:Rew:126.0,118.0,112.0,118.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 130[6:Rew:129.0,109.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 131[6:Rew:129.0,115.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 143[6:Rew:108.0,95.2,129.0,95.2,112.0,95.1,131.0,95.0,130.0,95.0,129.0,95.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.47 144[6:Obv:143.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 145[6:UnC:144.0,123.0] || -> .
% 0.19/0.47 148[6:Spt:145.0,3.0,51.0] || equal(multiply(sk_c8,sk_c5),sk_c7)** -> .
% 0.19/0.47 149[6:Spt:145.0,3.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 150[6:MRR:28.1,148.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 151[6:MRR:13.1,148.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 153[6:MRR:23.0,148.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 154[6:MRR:18.0,148.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 176[6:SpR:154.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.19/0.47 184[6:SpR:150.0,90.0] || -> equal(multiply(sk_c8,sk_c2),sk_c5)**.
% 0.19/0.47 187[6:SpR:151.0,90.0] || -> equal(multiply(sk_c7,sk_c1),sk_c5)**.
% 0.19/0.47 199[6:SpR:184.0,71.0] || -> equal(multiply(sk_c6,sk_c5),sk_c2)**.
% 0.19/0.47 200[6:Rew:93.0,199.0] || -> equal(sk_c2,sk_c4)**.
% 0.19/0.47 202[6:Rew:200.0,153.0] || -> equal(multiply(sk_c4,sk_c8),sk_c3)**.
% 0.19/0.47 206[6:Rew:84.0,202.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.19/0.47 207[6:Rew:91.0,206.0] || -> equal(sk_c3,sk_c5)**.
% 0.19/0.47 209[6:Rew:207.0,176.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 215[6:Rew:89.0,209.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.19/0.47 218[6:Rew:215.0,92.0] || -> equal(multiply(sk_c7,sk_c4),sk_c5)**.
% 0.19/0.47 219[6:Rew:215.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.47 220[6:Rew:215.0,94.2] || equal(inverse(sk_c5),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.47 227[6:Rew:215.0,87.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.47 228[6:Rew:227.0,219.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 229[6:Rew:228.0,187.0] || -> equal(sk_c1,sk_c5)**.
% 0.19/0.47 235[6:Rew:228.0,218.0] || -> equal(sk_c4,sk_c5)**.
% 0.19/0.47 238[6:Rew:229.0,151.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.19/0.47 245[6:Rew:235.0,42.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.47 247[6:Rew:238.0,245.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 267[6:Rew:228.0,220.2,247.0,220.1,238.0,220.0,247.0,220.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.47 268[6:Obv:267.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 269[6:UnC:268.0,89.0] || -> .
% 0.19/0.47 272[5:Spt:269.0,4.0,46.0] || equal(multiply(sk_c4,sk_c8),sk_c5)** -> .
% 0.19/0.47 273[5:Spt:269.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 274[5:Rew:84.0,272.0] || equal(multiply(sk_c6,sk_c8),sk_c5)** -> .
% 0.19/0.47 275[5:Rew:54.0,274.0] || equal(identity,sk_c5)** -> .
% 0.19/0.47 276[4:Rew:54.0,29.1,84.0,29.1] || -> equal(inverse(sk_c2),sk_c8)** equal(identity,sk_c5).
% 0.19/0.47 277[5:MRR:276.1,275.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 278[4:Rew:54.0,14.1,84.0,14.1] || -> equal(inverse(sk_c1),sk_c7)** equal(identity,sk_c5).
% 0.19/0.47 279[5:MRR:278.1,275.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 280[4:Rew:54.0,24.0,84.0,24.0] || -> equal(identity,sk_c5) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 281[5:MRR:280.0,275.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 282[4:Rew:54.0,19.0,84.0,19.0] || -> equal(identity,sk_c5) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 283[5:MRR:282.0,275.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 306[5:SpR:283.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.19/0.47 316[5:SpR:277.0,33.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.19/0.47 317[5:SpR:279.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.47 329[5:SpR:316.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c2)**.
% 0.19/0.47 330[5:Rew:78.0,329.0] || -> equal(sk_c2,sk_c4)**.
% 0.19/0.47 332[5:Rew:330.0,281.0] || -> equal(multiply(sk_c4,sk_c8),sk_c3)**.
% 0.19/0.47 333[5:Rew:330.0,316.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.47 336[5:Rew:84.0,332.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.19/0.47 337[5:Rew:54.0,336.0] || -> equal(identity,sk_c3)**.
% 0.19/0.47 342[5:Rew:337.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.47 343[5:Rew:337.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.47 344[5:Rew:337.0,317.0] || -> equal(multiply(sk_c7,sk_c1),sk_c3)**.
% 0.19/0.47 346[5:Rew:337.0,45.0] || equal(inverse(sk_c3),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.47 347[5:Rew:337.0,333.0] || -> equal(multiply(sk_c8,sk_c4),sk_c3)**.
% 0.19/0.47 348[5:Rew:342.0,306.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.19/0.47 351[5:Rew:348.0,283.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.47 352[5:Rew:348.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.47 355[5:Rew:348.0,347.0] || -> equal(multiply(sk_c7,sk_c4),sk_c3)**.
% 0.19/0.47 359[5:Rew:348.0,87.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.47 361[5:Rew:359.0,352.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 362[5:Rew:361.0,40.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 366[5:Rew:361.0,355.0] || -> equal(sk_c3,sk_c4)**.
% 0.19/0.47 367[5:Rew:361.0,351.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 368[5:Rew:361.0,344.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.47 371[5:Rew:362.0,38.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 379[5:Rew:366.0,343.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.19/0.47 380[5:Rew:366.0,367.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 381[5:Rew:380.0,42.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.47 383[5:Rew:380.0,366.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 385[5:Rew:368.0,383.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.47 386[5:Rew:385.0,279.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 388[5:Rew:385.0,368.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 390[5:Rew:381.0,386.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 392[5:Rew:390.0,371.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 403[5:Rew:380.0,379.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.47 413[5:Rew:361.0,346.2,390.0,346.2,390.0,346.1,392.0,346.0,388.0,346.0,390.0,346.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.47 414[5:Obv:413.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 415[5:UnC:414.0,403.0] || -> .
% 0.19/0.47 418[4:Spt:415.0,5.0,42.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.47 419[4:Spt:415.0,5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 420[4:MRR:30.0,418.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 421[4:MRR:15.0,418.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 422[4:MRR:25.0,418.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 423[4:MRR:20.0,418.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 438[4:SpR:423.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.19/0.47 447[4:SpR:420.0,33.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.19/0.47 448[4:SpR:421.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.47 450[4:SpR:447.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.47 452[4:Rew:32.0,450.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.19/0.47 459[4:SpR:447.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c2)**.
% 0.19/0.47 463[4:SpR:459.0,34.0] || -> equal(multiply(sk_c6,multiply(identity,u)),multiply(sk_c2,u))**.
% 0.19/0.47 465[4:Rew:32.0,463.0] || -> equal(multiply(sk_c2,u),multiply(sk_c6,u))**.
% 0.19/0.47 466[4:Rew:465.0,422.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.19/0.47 467[4:Rew:465.0,452.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.19/0.47 469[4:Rew:54.0,466.0] || -> equal(identity,sk_c3)**.
% 0.19/0.47 471[4:Rew:469.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.47 472[4:Rew:469.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.47 473[4:Rew:469.0,447.0] || -> equal(multiply(sk_c8,sk_c2),sk_c3)**.
% 0.19/0.47 474[4:Rew:469.0,448.0] || -> equal(multiply(sk_c7,sk_c1),sk_c3)**.
% 0.19/0.47 477[4:Rew:469.0,57.1] || equal(inverse(sk_c6),sk_c8) equal(sk_c3,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.47 478[4:Rew:471.0,438.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.19/0.47 481[4:Rew:478.0,423.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.47 482[4:Rew:478.0,473.0] || -> equal(multiply(sk_c7,sk_c2),sk_c3)**.
% 0.19/0.47 485[4:Rew:478.0,467.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.47 487[4:Rew:478.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.47 491[4:Rew:485.0,487.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 492[4:Rew:491.0,40.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.47 494[4:Rew:491.0,482.0] || -> equal(sk_c2,sk_c3)**.
% 0.19/0.47 495[4:Rew:491.0,481.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 498[4:Rew:491.0,474.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.47 501[4:Rew:492.0,38.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.47 506[4:Rew:494.0,420.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 509[4:Rew:495.0,472.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.47 511[4:Rew:495.0,498.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.47 512[4:Rew:511.0,421.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 514[4:Rew:495.0,506.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.47 515[4:Rew:514.0,512.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 517[4:Rew:515.0,492.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 518[4:Rew:515.0,501.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 535[4:Rew:491.0,477.2,515.0,477.2,495.0,477.1,518.0,477.0,517.0,477.0,515.0,477.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.47 536[4:Obv:535.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 537[4:UnC:536.0,509.0] || -> .
% 0.19/0.47 540[3:Spt:537.0,1.0,40.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.19/0.47 541[3:Spt:537.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 542[3:MRR:26.1,540.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 543[3:MRR:11.1,540.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 544[3:MRR:21.0,540.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 545[3:MRR:16.0,540.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 546[3:MRR:6.0,540.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 557[3:SpR:545.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.19/0.47 565[3:SpR:542.0,33.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.19/0.47 567[3:SpR:543.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.47 572[3:SpR:567.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.47 574[3:Rew:32.0,572.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.47 578[3:SpR:565.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c2)**.
% 0.19/0.47 582[3:SpR:578.0,34.0] || -> equal(multiply(sk_c6,multiply(identity,u)),multiply(sk_c2,u))**.
% 0.19/0.47 584[3:Rew:32.0,582.0] || -> equal(multiply(sk_c2,u),multiply(sk_c6,u))**.
% 0.19/0.47 585[3:Rew:584.0,544.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.19/0.47 588[3:Rew:54.0,585.0] || -> equal(identity,sk_c3)**.
% 0.19/0.47 589[3:Rew:588.0,54.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.19/0.47 590[3:Rew:588.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.47 591[3:Rew:588.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.47 593[3:Rew:588.0,567.0] || -> equal(multiply(sk_c7,sk_c1),sk_c3)**.
% 0.19/0.47 596[3:Rew:588.0,45.0] || equal(inverse(sk_c3),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.47 597[3:Rew:590.0,557.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.19/0.47 610[3:Rew:597.0,596.2] || equal(inverse(sk_c3),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.47 639[3:SpR:546.0,574.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.47 640[3:Rew:541.0,639.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 641[3:Rew:640.0,541.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.47 645[3:Rew:640.0,589.0] || -> equal(multiply(sk_c7,sk_c8),sk_c3)**.
% 0.19/0.47 652[3:Rew:641.0,645.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 654[3:Rew:652.0,593.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.19/0.47 656[3:Rew:652.0,590.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 658[3:Rew:652.0,591.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.47 659[3:Rew:652.0,610.0] || equal(inverse(sk_c7),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.47 666[3:Rew:656.0,654.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.47 667[3:Rew:656.0,641.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 673[3:Rew:666.0,543.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 693[3:Rew:656.0,659.2,667.0,659.1,673.0,659.0,667.0,659.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.47 694[3:Obv:693.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 695[3:UnC:694.0,658.0] || -> .
% 0.19/0.47 698[2:Spt:695.0,2.0,38.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.19/0.47 699[2:Spt:695.0,2.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 700[2:MRR:27.0,698.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 701[2:MRR:12.0,698.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 702[2:MRR:22.0,698.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 703[2:MRR:17.0,698.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 704[2:MRR:7.0,698.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 719[2:SpR:700.0,33.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.19/0.47 720[2:SpR:701.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.47 722[2:SpR:719.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.47 724[2:Rew:32.0,722.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.19/0.47 725[2:SpR:720.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.47 727[2:Rew:32.0,725.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.47 730[2:SpR:702.0,724.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.47 731[2:Rew:703.0,730.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 732[2:Rew:731.0,699.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 733[2:Rew:731.0,700.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 734[2:Rew:731.0,698.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.19/0.47 736[2:Rew:731.0,703.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.47 737[2:Rew:731.0,704.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 738[2:Rew:731.0,719.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.19/0.47 772[2:SpR:737.0,727.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 773[2:Rew:732.0,772.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 774[2:Rew:773.0,732.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 775[2:Rew:773.0,734.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.47 786[0:SpR:73.0,73.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 790[0:SpR:33.0,73.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 792[2:SpR:736.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.47 798[2:SpR:774.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.47 801[2:Rew:33.0,792.0] || -> equal(identity,sk_c3)**.
% 0.19/0.47 802[2:Rew:801.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.47 803[2:Rew:801.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.47 805[2:Rew:801.0,738.0] || -> equal(multiply(sk_c7,sk_c2),sk_c3)**.
% 0.19/0.47 815[2:Rew:803.0,798.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 819[2:Rew:815.0,802.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 821[2:Rew:815.0,805.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.19/0.47 834[2:Rew:819.0,821.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.47 835[2:Rew:834.0,733.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 837[2:MRR:835.0,775.0] || -> .
% 0.19/0.47 861[1:Spt:837.0,35.1,35.2,35.4,35.6,35.7] || equal(inverse(u),sk_c7) equal(inverse(sk_c8),sk_c6) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.19/0.47 862[0:Rew:786.0,790.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 864[2:Spt:2.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.19/0.47 865[2:Rew:864.0,861.1] || equal(inverse(u),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.19/0.47 867[2:Obv:865.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.19/0.47 869[2:SpR:864.0,73.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.19/0.47 871[3:Spt:1.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.19/0.47 873[3:Rew:871.0,867.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(sk_c8,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.19/0.47 874[3:Obv:873.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.19/0.47 876[3:SpR:871.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.19/0.47 877[3:SpR:871.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c6)**.
% 0.19/0.47 879[4:Spt:5.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 880[4:SpR:879.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.19/0.47 882[5:Spt:3.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.19/0.47 884[5:SpR:882.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c5)**.
% 0.19/0.47 886[5:Rew:864.0,884.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 888[5:SpR:886.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.47 890[6:Spt:4.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.19/0.47 892[6:SpR:890.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.19/0.47 894[6:Rew:882.0,892.0,879.0,892.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 895[6:Rew:894.0,864.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 896[6:Rew:894.0,871.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 901[6:Rew:894.0,874.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.19/0.47 904[6:Rew:894.0,877.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 907[6:Rew:895.0,904.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.47 908[6:Rew:886.0,907.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 911[6:Rew:908.0,888.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.47 914[6:Rew:33.0,911.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 915[6:Rew:914.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 918[6:Rew:914.0,862.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 919[6:Rew:915.0,896.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 920[6:Rew:919.0,895.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 933[6:Rew:915.0,901.2,919.0,901.2,918.0,901.1,894.0,901.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.19/0.47 934[6:Obv:933.2] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 969[6:SpL:920.0,934.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 971[6:Obv:969.1] || -> .
% 0.19/0.47 972[6:Spt:971.0,4.0,890.0] || equal(multiply(sk_c4,sk_c8),sk_c5)** -> .
% 0.19/0.47 973[6:Spt:971.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 974[6:MRR:29.1,972.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 976[6:MRR:24.0,972.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 977[6:MRR:19.0,972.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 995[6:SpR:976.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.47 997[6:Rew:974.0,995.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.47 998[6:Rew:977.0,997.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 999[6:Rew:998.0,973.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 1001[6:Rew:998.0,864.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 1006[6:Rew:998.0,877.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 1007[6:Rew:998.0,972.0] || equal(multiply(sk_c4,sk_c7),sk_c5)** -> .
% 0.19/0.47 1008[6:Rew:998.0,880.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.19/0.47 1019[6:Rew:886.0,1006.0,1001.0,1006.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 1021[6:Rew:1019.0,888.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.47 1024[6:Rew:1019.0,1007.0] || equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.19/0.47 1026[6:Rew:33.0,1021.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 1027[6:Rew:1026.0,862.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 1028[6:Rew:1026.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 1031[6:Rew:1027.0,1024.0] || equal(sk_c4,sk_c6)** -> .
% 0.19/0.47 1034[6:Rew:1027.0,999.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1042[6:Rew:1034.0,1031.0] || equal(sk_c4,sk_c7)** -> .
% 0.19/0.47 1047[6:Rew:1028.0,1008.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.47 1084[6:SpR:1047.0,1027.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 1086[6:MRR:1084.0,1042.0] || -> .
% 0.19/0.47 1088[5:Spt:1086.0,3.0,882.0] || equal(multiply(sk_c8,sk_c5),sk_c7)** -> .
% 0.19/0.47 1089[5:Spt:1086.0,3.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 1090[5:MRR:28.1,1088.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 1091[5:MRR:13.1,1088.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 1092[5:MRR:23.0,1088.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 1093[5:MRR:18.0,1088.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 1094[5:MRR:8.0,1088.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 1095[5:Rew:1089.0,874.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 1096[5:Obv:1095.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 1114[5:SpR:1092.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.47 1116[5:Rew:1090.0,1114.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.47 1117[5:Rew:1093.0,1116.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 1118[5:Rew:1117.0,1089.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 1119[5:Rew:1117.0,864.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 1121[5:Rew:1117.0,879.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.47 1126[5:Rew:1117.0,869.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.47 1127[5:Rew:1117.0,876.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.47 1131[5:Rew:1117.0,1094.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 1132[5:Rew:1117.0,1096.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.47 1169[5:SpR:1131.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 1171[5:Rew:1118.0,1169.0,1091.0,1169.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1172[5:Rew:1171.0,1119.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 1178[5:Rew:1171.0,1126.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.47 1179[5:Rew:1171.0,1127.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.47 1183[5:Rew:1178.0,1179.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 1201[5:SpR:1091.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.47 1203[5:SpR:1121.0,33.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.47 1204[5:SpR:1172.0,33.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.47 1205[5:Rew:1183.0,1201.0] || -> equal(identity,sk_c1)**.
% 0.19/0.47 1208[5:Rew:1205.0,862.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.47 1213[5:Rew:1183.0,1203.0,1205.0,1203.0] || -> equal(sk_c1,sk_c4)**.
% 0.19/0.47 1216[5:Rew:1213.0,1205.0] || -> equal(identity,sk_c4)**.
% 0.19/0.47 1218[5:Rew:1183.0,1204.0,1216.0,1204.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 1221[5:Rew:1218.0,1213.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.47 1225[5:Rew:1221.0,1208.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 1227[5:Rew:1225.0,1132.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 1258[5:SpL:1172.0,1227.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 1259[5:Obv:1258.1] || -> .
% 0.19/0.47 1260[4:Spt:1259.0,5.0,879.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.47 1261[4:Spt:1259.0,5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 1263[4:MRR:30.0,1260.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 1264[4:MRR:15.0,1260.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 1265[4:MRR:25.0,1260.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 1266[4:MRR:20.0,1260.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 1267[4:MRR:10.0,1260.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 1269[4:Rew:1261.0,874.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 1270[4:Obv:1269.2] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 1286[4:SpR:1265.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.47 1288[4:Rew:1263.0,1286.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.47 1289[4:Rew:1266.0,1288.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 1290[4:Rew:1289.0,1261.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 1291[4:Rew:1289.0,864.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.47 1297[4:Rew:1289.0,869.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.47 1298[4:Rew:1289.0,876.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.47 1301[4:Rew:1289.0,1267.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 1302[4:Rew:1289.0,1270.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.47 1337[4:SpR:1301.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 1339[4:Rew:1290.0,1337.0,1264.0,1337.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1340[4:Rew:1339.0,1291.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 1346[4:Rew:1339.0,1297.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.47 1347[4:Rew:1339.0,1298.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.47 1351[4:Rew:1346.0,1347.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 1373[0:SpR:33.0,862.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.47 1375[4:SpR:1264.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.47 1379[4:Rew:1351.0,1375.0] || -> equal(identity,sk_c1)**.
% 0.19/0.47 1381[4:Rew:1379.0,862.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.47 1383[4:Rew:1379.0,1373.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 1384[4:Rew:1264.0,1383.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.47 1394[4:Rew:1384.0,1381.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 1396[4:Rew:1394.0,1302.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 1422[4:SpL:1340.0,1396.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 1423[4:Obv:1422.1] || -> .
% 0.19/0.47 1424[3:Spt:1423.0,1.0,871.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.19/0.47 1425[3:Spt:1423.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 1427[3:MRR:26.1,1424.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 1428[3:MRR:11.1,1424.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 1430[3:MRR:21.0,1424.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 1431[3:MRR:16.0,1424.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 1432[3:MRR:6.0,1424.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 1446[3:SpR:1430.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.47 1448[3:Rew:1427.0,1446.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.47 1449[3:Rew:1431.0,1448.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 1450[3:Rew:1449.0,1425.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 1454[3:Rew:1449.0,1424.0] || equal(multiply(sk_c7,sk_c6),sk_c7)** -> .
% 0.19/0.47 1458[3:Rew:1449.0,1432.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 1481[3:SpR:1458.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 1483[3:Rew:1450.0,1481.0,1428.0,1481.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1485[3:Rew:1483.0,1450.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 1486[3:Rew:1483.0,1454.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.19/0.47 1496[3:Rew:1485.0,1486.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 1497[3:Obv:1496.0] || -> .
% 0.19/0.47 1503[2:Spt:1497.0,2.0,864.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.19/0.47 1504[2:Spt:1497.0,2.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 1505[2:MRR:27.0,1503.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.47 1506[2:MRR:12.0,1503.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 1507[2:MRR:22.0,1503.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.47 1508[2:MRR:17.0,1503.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.47 1509[2:MRR:7.0,1503.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.47 1511[2:SpR:1504.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.19/0.47 1518[2:SpR:1507.0,73.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.47 1520[2:Rew:1505.0,1518.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.47 1521[2:Rew:1508.0,1520.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 1522[2:Rew:1521.0,1504.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 1523[2:Rew:1521.0,1505.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 1524[2:Rew:1521.0,1503.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.19/0.47 1525[2:Rew:1521.0,1507.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.19/0.47 1526[2:Rew:1521.0,1508.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.47 1527[2:Rew:1521.0,1509.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 1528[2:Rew:1521.0,1511.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.19/0.47 1543[2:SpR:1526.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.47 1545[2:Rew:33.0,1543.0] || -> equal(identity,sk_c3)**.
% 0.19/0.47 1547[2:Rew:1545.0,862.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.47 1549[2:Rew:1545.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.47 1553[2:SpR:1527.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 1555[2:Rew:1522.0,1553.0,1506.0,1553.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1557[2:Rew:1555.0,1524.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.47 1558[2:Rew:1555.0,1528.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.47 1560[2:Rew:1549.0,1558.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 1561[2:Rew:1560.0,1525.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.47 1564[2:Rew:1560.0,1547.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 1569[2:Rew:1564.0,1561.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.47 1572[2:Rew:1569.0,1523.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 1576[2:MRR:1572.0,1557.0] || -> .
% 0.19/0.47 % SZS output end Refutation
% 0.19/0.47 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_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 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.19/0.47
%------------------------------------------------------------------------------