TSTP Solution File: GRP359-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP359-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:47:01 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP359-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 13:41:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 1020 clauses, backtracked 352 clauses, performed 11 splits and kept 798 clauses.
% 0.20/0.49 SPASS allocated 63679 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.07 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 5, length 436 :
% 0.20/0.49 % SZS output start Refutation
% 0.20/0.49 1[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.20/0.49 2[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.20/0.49 3[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.49 4[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.20/0.49 5[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c8).
% 0.20/0.49 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.49 7[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 8[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 9[0:Inp] || -> equal(inverse(sk_c3),sk_c8)** equal(inverse(sk_c8),sk_c6).
% 0.20/0.49 10[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 11[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c8),sk_c6).
% 0.20/0.49 13[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 14[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c2),sk_c7).
% 0.20/0.49 15[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 16[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 17[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(multiply(sk_c8,sk_c2),sk_c7).
% 0.20/0.49 18[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 19[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 20[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 21[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 22[0:Inp] || -> equal(multiply(sk_c8,sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 23[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c5) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 24[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 25[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 26[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 27[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 28[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 29[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 30[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 31[0:Inp] || equal(multiply(sk_c7,sk_c6),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c8,u),sk_c7)** equal(multiply(v,sk_c8),u)* equal(inverse(v),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(sk_c8,x),sk_c7)** equal(multiply(y,sk_c8),x)* equal(inverse(y),sk_c8) -> .
% 0.20/0.49 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.49 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.49 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.49 35[0:Con:31.8] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(v,sk_c8),w)*+ equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,w),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.20/0.49 36[1:Spt:35.1,35.3,35.5] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.20/0.49 38[2:Spt:7.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.20/0.49 40[3:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.49 42[4:Spt:25.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 45[1:SpL:32.0,36.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.49 46[5:Spt:19.1] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 51[6:Spt:13.1] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 54[2:SpR:38.0,33.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.20/0.49 55[4:SpR:42.0,33.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.20/0.49 56[1:SpL:33.0,36.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.49 57[2:Rew:38.0,56.0] || equal(inverse(sk_c6),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.49 64[2:SpR:54.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.20/0.49 65[6:SpR:51.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),multiply(sk_c7,u))**.
% 0.20/0.49 66[4:SpR:55.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.20/0.49 67[3:SpR:40.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.49 69[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.49 71[2:Rew:32.0,64.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.20/0.49 72[4:Rew:32.0,66.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 73[0:Rew:32.0,69.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.49 78[4:SpR:55.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c1)**.
% 0.20/0.49 82[4:SpR:78.0,34.0] || -> equal(multiply(sk_c6,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.20/0.49 84[4:Rew:32.0,82.0] || -> equal(multiply(sk_c1,u),multiply(sk_c6,u))**.
% 0.20/0.49 85[5:Rew:84.0,46.0] || -> equal(multiply(sk_c6,sk_c8),sk_c2)**.
% 0.20/0.49 87[4:Rew:84.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.20/0.49 88[5:Rew:54.0,85.0] || -> equal(identity,sk_c2)**.
% 0.20/0.49 89[5:Rew:88.0,32.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.49 90[5:Rew:88.0,33.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.20/0.49 91[5:Rew:88.0,54.0] || -> equal(multiply(sk_c6,sk_c8),sk_c2)**.
% 0.20/0.49 93[5:Rew:88.0,78.0] || -> equal(multiply(sk_c6,sk_c2),sk_c1)**.
% 0.20/0.49 94[5:Rew:88.0,45.0] || equal(inverse(sk_c2),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.49 95[5:Rew:88.0,57.1] || equal(inverse(sk_c6),sk_c8) equal(sk_c2,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.49 96[6:Rew:89.0,65.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.20/0.49 99[6:Rew:96.0,51.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.20/0.49 101[6:Rew:96.0,87.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.20/0.49 105[6:Rew:96.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.49 108[6:Rew:101.0,105.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 109[6:Rew:108.0,40.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 110[6:Rew:108.0,101.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 112[6:Rew:108.0,99.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.49 115[6:Rew:109.0,38.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 117[6:Rew:109.0,91.0] || -> equal(multiply(sk_c6,sk_c6),sk_c2)**.
% 0.20/0.49 123[6:Rew:112.0,90.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.49 127[6:Rew:110.0,117.0,112.0,117.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 128[6:Rew:127.0,109.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 129[6:Rew:127.0,115.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 142[6:Rew:108.0,95.2,128.0,95.2,112.0,95.1,129.0,95.0,127.0,95.0,128.0,95.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.20/0.49 143[6:Obv:142.1] || equal(u,sk_c7)* -> .
% 0.20/0.49 144[6:UnC:143.0,123.0] || -> .
% 0.20/0.49 147[6:Spt:144.0,13.1,51.0] || equal(multiply(sk_c8,sk_c2),sk_c7)** -> .
% 0.20/0.49 148[6:Spt:144.0,13.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 149[6:MRR:18.1,147.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 150[6:MRR:15.1,147.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 152[6:MRR:17.1,147.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 153[6:MRR:16.1,147.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 154[6:MRR:14.1,147.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 183[6:SpR:149.0,90.0] || -> equal(multiply(sk_c8,sk_c4),sk_c2)**.
% 0.20/0.49 186[6:SpR:150.0,90.0] || -> equal(multiply(sk_c8,sk_c3),sk_c2)**.
% 0.20/0.49 198[6:SpR:153.0,71.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.49 199[6:SpR:183.0,71.0] || -> equal(multiply(sk_c6,sk_c2),sk_c4)**.
% 0.20/0.49 200[6:SpR:186.0,71.0] || -> equal(multiply(sk_c6,sk_c2),sk_c3)**.
% 0.20/0.49 201[6:Rew:93.0,199.0] || -> equal(sk_c1,sk_c4)**.
% 0.20/0.49 204[6:Rew:201.0,93.0] || -> equal(multiply(sk_c6,sk_c2),sk_c4)**.
% 0.20/0.49 206[6:Rew:200.0,204.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 208[6:Rew:206.0,152.0] || -> equal(multiply(sk_c3,sk_c8),sk_c5)**.
% 0.20/0.49 213[6:Rew:154.0,208.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 214[6:Rew:213.0,153.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.20/0.49 216[6:Rew:213.0,198.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.20/0.49 217[6:Rew:148.0,214.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 219[6:Rew:217.0,38.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 220[6:Rew:217.0,40.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.20/0.49 221[6:Rew:217.0,91.0] || -> equal(multiply(sk_c7,sk_c8),sk_c2)**.
% 0.20/0.49 228[6:Rew:217.0,216.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.49 229[6:Rew:228.0,220.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 234[6:Rew:229.0,94.2] || equal(inverse(sk_c2),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.20/0.49 241[6:Rew:229.0,219.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 243[6:Rew:228.0,221.0,229.0,221.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.49 245[6:Rew:243.0,89.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 246[6:Rew:243.0,90.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.49 271[6:Rew:245.0,234.2,229.0,234.1,241.0,234.0,243.0,234.0,229.0,234.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.20/0.49 272[6:Obv:271.1] || equal(u,sk_c7)* -> .
% 0.20/0.49 273[6:UnC:272.0,246.0] || -> .
% 0.20/0.49 276[5:Spt:273.0,19.1,46.0] || equal(multiply(sk_c1,sk_c8),sk_c2)** -> .
% 0.20/0.49 277[5:Spt:273.0,19.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 278[5:Rew:84.0,276.0] || equal(multiply(sk_c6,sk_c8),sk_c2)** -> .
% 0.20/0.49 279[5:Rew:54.0,278.0] || equal(identity,sk_c2)** -> .
% 0.20/0.49 280[4:Rew:54.0,24.1,84.0,24.1] || -> equal(inverse(sk_c4),sk_c8)** equal(identity,sk_c2).
% 0.20/0.49 281[5:MRR:280.1,279.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 282[4:Rew:54.0,21.1,84.0,21.1] || -> equal(inverse(sk_c3),sk_c8)** equal(identity,sk_c2).
% 0.20/0.49 283[5:MRR:282.1,279.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 284[4:Rew:54.0,23.1,84.0,23.1] || -> equal(multiply(sk_c4,sk_c8),sk_c5)** equal(identity,sk_c2).
% 0.20/0.49 285[5:MRR:284.1,279.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 286[4:Rew:54.0,22.1,84.0,22.1] || -> equal(multiply(sk_c8,sk_c5),sk_c7)** equal(identity,sk_c2).
% 0.20/0.49 287[5:MRR:286.1,279.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 288[4:Rew:54.0,20.1,84.0,20.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(identity,sk_c2).
% 0.20/0.49 289[5:MRR:288.1,279.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 320[5:SpR:281.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.49 321[5:SpR:283.0,33.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.20/0.49 336[5:SpR:287.0,71.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.49 337[5:SpR:320.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c4)**.
% 0.20/0.49 338[5:SpR:321.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c3)**.
% 0.20/0.49 339[5:Rew:78.0,337.0] || -> equal(sk_c1,sk_c4)**.
% 0.20/0.49 341[5:Rew:339.0,78.0] || -> equal(multiply(sk_c6,identity),sk_c4)**.
% 0.20/0.49 344[5:Rew:338.0,341.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 346[5:Rew:344.0,285.0] || -> equal(multiply(sk_c3,sk_c8),sk_c5)**.
% 0.20/0.49 352[5:Rew:289.0,346.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 353[5:Rew:352.0,287.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.20/0.49 355[5:Rew:352.0,336.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.20/0.49 356[5:Rew:277.0,353.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 358[5:Rew:356.0,38.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 359[5:Rew:356.0,40.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.20/0.49 360[5:Rew:356.0,54.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.20/0.49 368[5:Rew:356.0,355.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.49 369[5:Rew:368.0,359.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 373[5:Rew:369.0,45.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.20/0.49 379[5:Rew:369.0,358.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 381[5:Rew:368.0,360.0,369.0,360.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 383[5:Rew:381.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 384[5:Rew:381.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.49 407[5:Rew:383.0,373.2,369.0,373.1,379.0,373.0,381.0,373.0,369.0,373.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.20/0.49 408[5:Obv:407.1] || equal(u,sk_c7)* -> .
% 0.20/0.49 409[5:UnC:408.0,384.0] || -> .
% 0.20/0.49 412[4:Spt:409.0,25.0,42.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.20/0.49 413[4:Spt:409.0,25.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 414[4:MRR:30.1,412.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 415[4:MRR:27.1,412.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 416[4:MRR:29.0,412.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 417[4:MRR:28.0,412.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 418[4:MRR:26.0,412.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 440[4:SpR:414.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.49 442[4:SpR:415.0,33.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.20/0.49 453[4:SpR:417.0,71.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.49 454[4:SpR:440.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c4)**.
% 0.20/0.49 455[4:SpR:442.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c3)**.
% 0.20/0.49 456[4:Rew:454.0,455.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 458[4:Rew:456.0,416.0] || -> equal(multiply(sk_c3,sk_c8),sk_c5)**.
% 0.20/0.49 463[4:Rew:418.0,458.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 464[4:Rew:463.0,417.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.20/0.49 466[4:Rew:463.0,453.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.20/0.49 467[4:Rew:413.0,464.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 469[4:Rew:467.0,38.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 470[4:Rew:467.0,54.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.20/0.49 471[4:Rew:467.0,40.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.20/0.49 478[4:Rew:467.0,466.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.49 479[4:Rew:478.0,471.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 484[4:Rew:479.0,45.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.20/0.49 490[4:Rew:479.0,469.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 492[4:Rew:479.0,470.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.20/0.49 493[4:Rew:478.0,492.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 494[4:Rew:493.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 495[4:Rew:493.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.49 517[4:Rew:494.0,484.2,479.0,484.1,490.0,484.0,493.0,484.0,479.0,484.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.20/0.49 518[4:Obv:517.1] || equal(u,sk_c7)* -> .
% 0.20/0.49 519[4:UnC:518.0,495.0] || -> .
% 0.20/0.49 522[3:Spt:519.0,1.1,40.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.20/0.49 523[3:Spt:519.0,1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 524[3:MRR:6.1,522.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 525[3:MRR:3.1,522.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 526[3:MRR:5.1,522.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 527[3:MRR:4.1,522.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 528[3:MRR:2.1,522.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 549[3:SpR:524.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.49 550[3:SpR:525.0,33.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.20/0.49 561[3:SpR:527.0,71.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.49 562[3:SpR:549.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c4)**.
% 0.20/0.49 563[3:SpR:550.0,71.0] || -> equal(multiply(sk_c6,identity),sk_c3)**.
% 0.20/0.49 564[3:Rew:562.0,563.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 566[3:Rew:564.0,526.0] || -> equal(multiply(sk_c3,sk_c8),sk_c5)**.
% 0.20/0.49 570[3:Rew:564.0,562.0] || -> equal(multiply(sk_c6,identity),sk_c3)**.
% 0.20/0.49 571[3:Rew:528.0,566.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 572[3:Rew:571.0,527.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.20/0.49 574[3:Rew:571.0,561.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.20/0.49 575[3:Rew:523.0,572.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 577[3:Rew:575.0,38.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 580[3:Rew:575.0,71.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.20/0.49 581[3:Rew:575.0,57.0] || equal(inverse(sk_c7),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.49 584[3:Rew:575.0,570.0] || -> equal(multiply(sk_c7,identity),sk_c3)**.
% 0.20/0.49 585[3:Rew:575.0,574.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.49 603[0:SpR:73.0,73.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.49 610[0:SpR:33.0,73.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.49 611[3:SpR:585.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.20/0.49 618[3:Rew:33.0,611.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 619[3:Rew:618.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 625[3:Rew:618.0,584.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.20/0.49 626[3:Rew:618.0,581.1] || equal(inverse(sk_c7),sk_c8) equal(sk_c7,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.49 628[3:Rew:619.0,580.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 633[3:Rew:619.0,625.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.49 634[3:Rew:633.0,525.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.49 657[3:Rew:628.0,626.2,634.0,626.0] || equal(sk_c8,sk_c8)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.20/0.49 658[3:Obv:657.1] || equal(u,sk_c7)* -> .
% 0.20/0.49 659[3:UnC:658.0,577.0] || -> .
% 0.20/0.49 660[2:Spt:659.0,7.0,38.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.20/0.49 661[2:Spt:659.0,7.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 662[0:Rew:603.0,610.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.49 663[2:MRR:12.1,660.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 664[2:MRR:9.1,660.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 665[2:MRR:11.0,660.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 666[2:MRR:10.0,660.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 667[2:MRR:8.0,660.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 669[2:SpR:661.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.49 676[2:SpR:665.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.20/0.49 678[2:Rew:663.0,676.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.20/0.49 679[2:Rew:666.0,678.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 680[2:Rew:679.0,661.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.49 681[2:Rew:679.0,663.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 682[2:Rew:679.0,664.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.49 683[2:Rew:679.0,660.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.20/0.49 684[2:Rew:679.0,665.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.49 685[2:Rew:679.0,669.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.49 686[2:Rew:679.0,666.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.20/0.49 687[2:Rew:679.0,667.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.49 715[2:SpR:686.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.20/0.49 717[2:Rew:33.0,715.0] || -> equal(identity,sk_c5)**.
% 0.20/0.49 719[2:Rew:717.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.49 722[2:Rew:717.0,662.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.49 728[2:SpR:687.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.20/0.49 730[2:Rew:680.0,728.0,682.0,728.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 732[2:Rew:730.0,683.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.20/0.49 733[2:Rew:730.0,685.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.20/0.49 735[2:Rew:719.0,733.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 736[2:Rew:735.0,684.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.20/0.49 739[2:Rew:735.0,722.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 751[2:Rew:739.0,736.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.49 753[2:Rew:751.0,681.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 755[2:MRR:753.0,732.0] || -> .
% 0.20/0.49 766[1:Spt:755.0,35.0,35.2,35.4,35.6,35.7] || equal(inverse(u),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(u,sk_c8),sk_c7)**+ equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.20/0.49 768[2:Spt:7.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.20/0.49 769[2:Rew:768.0,766.1] || equal(inverse(u),sk_c8) equal(sk_c6,sk_c6) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.20/0.49 771[2:Obv:769.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c8) -> .
% 0.20/0.49 773[2:SpR:768.0,73.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.20/0.49 775[3:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.49 777[3:Rew:775.0,771.3] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(sk_c8,sk_c8) -> .
% 0.20/0.49 778[3:Obv:777.3] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.20/0.49 780[3:SpR:775.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.49 781[3:SpR:775.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c6)**.
% 0.20/0.49 783[4:Spt:25.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 784[4:SpR:783.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 786[5:Spt:13.1] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 788[5:SpR:786.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c2)**.
% 0.20/0.49 790[5:Rew:768.0,788.0] || -> equal(multiply(sk_c6,sk_c7),sk_c2)**.
% 0.20/0.49 792[5:SpR:790.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c2),sk_c7)**.
% 0.20/0.49 794[6:Spt:19.1] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 796[6:SpR:794.0,73.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c8)**.
% 0.20/0.49 798[6:Rew:786.0,796.0,783.0,796.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 799[6:Rew:798.0,768.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.49 800[6:Rew:798.0,775.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 805[6:Rew:798.0,778.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.20/0.49 808[6:Rew:798.0,781.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 811[6:Rew:799.0,808.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 812[6:Rew:790.0,811.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 815[6:Rew:812.0,792.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.49 818[6:Rew:33.0,815.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 819[6:Rew:818.0,662.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 820[6:Rew:818.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 825[6:Rew:820.0,800.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 826[6:Rew:825.0,799.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 837[6:Rew:820.0,805.2,825.0,805.2,819.0,805.1,798.0,805.1,798.0,805.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.20/0.49 838[6:Obv:837.2] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.49 873[6:SpL:826.0,838.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 875[6:Obv:873.1] || -> .
% 0.20/0.49 876[6:Spt:875.0,19.1,794.0] || equal(multiply(sk_c1,sk_c8),sk_c2)** -> .
% 0.20/0.49 877[6:Spt:875.0,19.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 878[6:MRR:24.1,876.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 880[6:MRR:23.1,876.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 881[6:MRR:22.1,876.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 900[6:SpR:880.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.20/0.49 902[6:Rew:878.0,900.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.20/0.49 903[6:Rew:881.0,902.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 906[6:Rew:903.0,768.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.49 911[6:Rew:903.0,775.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 912[6:Rew:903.0,781.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 913[6:Rew:903.0,876.0] || equal(multiply(sk_c1,sk_c7),sk_c2)** -> .
% 0.20/0.49 914[6:Rew:903.0,784.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.20/0.49 925[6:Rew:790.0,912.0,906.0,912.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 927[6:Rew:925.0,792.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.49 930[6:Rew:925.0,913.0] || equal(multiply(sk_c1,sk_c7),sk_c6)** -> .
% 0.20/0.49 931[6:Rew:33.0,927.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 932[6:Rew:931.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 933[6:Rew:931.0,662.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 937[6:Rew:932.0,911.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 944[6:Rew:937.0,930.0] || equal(multiply(sk_c1,sk_c7),sk_c7)** -> .
% 0.20/0.49 950[6:Rew:933.0,944.0] || equal(sk_c1,sk_c7)** -> .
% 0.20/0.49 951[6:Rew:932.0,914.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 988[6:SpR:951.0,933.0] || -> equal(sk_c1,sk_c7)**.
% 0.20/0.49 990[6:MRR:988.0,950.0] || -> .
% 0.20/0.49 992[5:Spt:990.0,13.1,786.0] || equal(multiply(sk_c8,sk_c2),sk_c7)** -> .
% 0.20/0.49 993[5:Spt:990.0,13.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.49 994[5:MRR:18.1,992.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 995[5:MRR:15.1,992.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 996[5:MRR:17.1,992.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.49 997[5:MRR:16.1,992.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.49 998[5:MRR:14.1,992.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 999[5:Rew:993.0,778.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.49 1000[5:Obv:999.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.49 1019[5:SpR:996.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.20/0.49 1021[5:Rew:994.0,1019.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.20/0.49 1022[5:Rew:997.0,1021.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 1023[5:Rew:1022.0,993.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.49 1024[5:Rew:1022.0,768.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.49 1027[5:Rew:1022.0,995.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.50 1032[5:Rew:1022.0,773.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.20/0.50 1033[5:Rew:1022.0,780.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1036[5:Rew:1022.0,998.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.50 1037[5:Rew:1022.0,1000.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.50 1044[5:Rew:1022.0,1037.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.20/0.50 1080[5:SpR:1036.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.20/0.50 1082[5:Rew:1023.0,1080.0,1027.0,1080.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.50 1083[5:Rew:1082.0,1024.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.50 1088[5:Rew:1082.0,1032.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.20/0.50 1089[5:Rew:1082.0,1033.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1097[5:Rew:1088.0,1089.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 1121[5:SpR:1097.0,662.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 1124[5:Rew:1121.0,662.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.50 1128[5:Rew:1124.0,1044.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.50 1165[5:SpL:1083.0,1128.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.50 1166[5:Obv:1165.1] || -> .
% 0.20/0.50 1167[4:Spt:1166.0,25.0,783.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.20/0.50 1168[4:Spt:1166.0,25.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.50 1169[4:MRR:30.1,1167.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.50 1170[4:MRR:27.1,1167.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 1171[4:MRR:29.0,1167.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.50 1172[4:MRR:28.0,1167.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.50 1173[4:MRR:26.0,1167.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 1174[4:Rew:1168.0,778.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.50 1175[4:Obv:1174.2] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.50 1192[4:SpR:1171.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.20/0.50 1194[4:Rew:1169.0,1192.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.20/0.50 1195[4:Rew:1172.0,1194.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.50 1196[4:Rew:1195.0,1168.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.50 1197[4:Rew:1195.0,768.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.50 1199[4:Rew:1195.0,1170.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.50 1204[4:Rew:1195.0,773.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.20/0.50 1205[4:Rew:1195.0,780.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1207[4:Rew:1195.0,1173.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.50 1208[4:Rew:1195.0,1175.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.50 1215[4:Rew:1195.0,1208.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.20/0.50 1250[4:SpR:1207.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.20/0.50 1252[4:Rew:1196.0,1250.0,1199.0,1250.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.50 1253[4:Rew:1252.0,1197.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.50 1259[4:Rew:1252.0,1204.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.20/0.50 1260[4:Rew:1252.0,1205.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1267[4:Rew:1259.0,1260.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 1289[4:SpR:1267.0,662.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 1292[4:Rew:1289.0,662.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.50 1296[4:Rew:1292.0,1215.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.50 1324[4:SpL:1253.0,1296.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.50 1325[4:Obv:1324.1] || -> .
% 0.20/0.50 1326[3:Spt:1325.0,1.1,775.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.20/0.50 1327[3:Spt:1325.0,1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.50 1328[3:MRR:6.1,1326.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.50 1329[3:MRR:3.1,1326.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 1330[3:MRR:5.1,1326.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.50 1331[3:MRR:4.1,1326.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.50 1332[3:MRR:2.1,1326.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 1334[3:SpR:1327.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.50 1336[3:Rew:768.0,1334.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.20/0.50 1344[3:SpR:1330.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.20/0.50 1346[3:Rew:1328.0,1344.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.20/0.50 1347[3:Rew:1331.0,1346.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.50 1348[3:Rew:1347.0,1327.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.50 1351[3:Rew:1347.0,1329.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.50 1353[3:Rew:1347.0,1326.0] || equal(multiply(sk_c7,sk_c6),sk_c7)** -> .
% 0.20/0.50 1356[3:Rew:1347.0,1332.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.50 1384[3:SpR:1356.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.20/0.50 1386[3:Rew:1348.0,1384.0,1351.0,1384.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.50 1388[3:Rew:1386.0,1336.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.50 1390[3:Rew:1386.0,1353.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.20/0.50 1401[3:Rew:1388.0,1390.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.50 1402[3:Obv:1401.0] || -> .
% 0.20/0.50 1409[2:Spt:1402.0,7.0,768.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.20/0.50 1410[2:Spt:1402.0,7.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.50 1411[2:MRR:12.1,1409.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.50 1412[2:MRR:9.1,1409.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 1413[2:MRR:11.0,1409.0] || -> equal(multiply(sk_c4,sk_c8),sk_c5)**.
% 0.20/0.50 1414[2:MRR:10.0,1409.0] || -> equal(multiply(sk_c8,sk_c5),sk_c7)**.
% 0.20/0.50 1415[2:MRR:8.0,1409.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 1417[2:SpR:1410.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.50 1424[2:SpR:1413.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c8)**.
% 0.20/0.50 1426[2:Rew:1411.0,1424.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.20/0.50 1427[2:Rew:1414.0,1426.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.50 1428[2:Rew:1427.0,1410.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.50 1429[2:Rew:1427.0,1411.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.50 1430[2:Rew:1427.0,1412.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.50 1431[2:Rew:1427.0,1409.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.20/0.50 1432[2:Rew:1427.0,1413.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.50 1433[2:Rew:1427.0,1417.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.50 1434[2:Rew:1427.0,1414.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.20/0.50 1435[2:Rew:1427.0,1415.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.50 1453[2:SpR:1434.0,73.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.20/0.50 1455[2:Rew:33.0,1453.0] || -> equal(identity,sk_c5)**.
% 0.20/0.50 1456[2:Rew:1455.0,662.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.50 1459[2:Rew:1455.0,33.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.50 1463[2:SpR:1435.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.20/0.50 1465[2:Rew:1428.0,1463.0,1430.0,1463.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.50 1467[2:Rew:1465.0,1431.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.20/0.50 1468[2:Rew:1465.0,1433.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.20/0.50 1470[2:Rew:1459.0,1468.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.50 1471[2:Rew:1470.0,1432.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.20/0.50 1473[2:Rew:1470.0,1456.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.50 1478[2:Rew:1473.0,1471.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.50 1481[2:Rew:1478.0,1429.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.50 1485[2:MRR:1481.0,1467.0] || -> .
% 0.20/0.50 % SZS output end Refutation
% 0.20/0.50 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 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.20/0.50
%------------------------------------------------------------------------------