TSTP Solution File: GRP316-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP316-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:46:49 EDT 2022
% Result : Unsatisfiable 0.16s 0.43s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP316-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.11 % Command : run_spass %d %s
% 0.10/0.31 % Computer : n024.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Tue Jun 14 07:33:48 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.43
% 0.16/0.43 SPASS V 3.9
% 0.16/0.43 SPASS beiseite: Proof found.
% 0.16/0.43 % SZS status Theorem
% 0.16/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 SPASS derived 677 clauses, backtracked 361 clauses, performed 11 splits and kept 659 clauses.
% 0.16/0.43 SPASS allocated 63595 KBytes.
% 0.16/0.43 SPASS spent 0:00:00.11 on the problem.
% 0.16/0.43 0:00:00.03 for the input.
% 0.16/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.16/0.43 0:00:00.00 for inferences.
% 0.16/0.43 0:00:00.00 for the backtracking.
% 0.16/0.43 0:00:00.05 for the reduction.
% 0.16/0.43
% 0.16/0.43
% 0.16/0.43 Here is a proof with depth 5, length 342 :
% 0.16/0.43 % SZS output start Refutation
% 0.16/0.43 1[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.16/0.43 2[0:Inp] || -> equal(multiply(sk_c8,sk_c4),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.16/0.43 3[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.16/0.43 4[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.16/0.43 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.16/0.43 6[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.16/0.43 7[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.16/0.43 8[0:Inp] || -> equal(multiply(sk_c8,sk_c4),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.16/0.43 9[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.16/0.43 10[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.16/0.43 11[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.16/0.43 12[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.16/0.43 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 15[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 16[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.16/0.43 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 18[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c8)**.
% 0.16/0.43 19[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.16/0.43 20[0:Inp] || -> equal(multiply(sk_c8,sk_c4),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.16/0.43 21[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.16/0.43 22[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.16/0.43 23[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.16/0.43 24[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.16/0.43 25[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 26[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 27[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 28[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.16/0.43 29[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 30[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.16/0.43 31[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(v,sk_c8),y)*+ equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.16/0.43 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.16/0.43 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.16/0.43 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.16/0.43 35[1:Spt:31.1,31.4,31.8] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)* equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.16/0.43 37[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.16/0.43 40[3:Spt:25.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.16/0.43 42[4:Spt:13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.16/0.43 45[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.16/0.43 46[5:Spt:19.1] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.16/0.43 48[6:Spt:7.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.16/0.43 54[3:SpR:40.0,33.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.16/0.43 55[4:SpR:42.0,33.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.16/0.43 56[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.16/0.43 63[4:SpR:55.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.16/0.43 65[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.16/0.43 67[3:SpR:54.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.16/0.43 69[4:Rew:32.0,63.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.16/0.43 70[3:Rew:32.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.16/0.43 71[0:Rew:32.0,65.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.16/0.43 75[6:SpR:48.0,69.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.16/0.43 81[5:SpR:46.0,70.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.16/0.43 86[0:SpR:71.0,71.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.16/0.43 88[2:SpR:37.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.16/0.43 90[4:SpR:55.0,71.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.16/0.43 92[6:SpR:75.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.16/0.43 94[0:SpR:33.0,71.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.16/0.43 96[3:SpR:54.0,71.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c2)**.
% 0.16/0.43 98[5:SpR:81.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.16/0.43 103[6:Rew:33.0,92.0] || -> equal(identity,sk_c7)**.
% 0.16/0.43 104[6:Rew:103.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.16/0.43 106[6:Rew:103.0,54.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.16/0.43 109[6:Rew:103.0,56.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c7,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.16/0.43 111[6:Rew:104.0,81.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 113[6:Rew:104.0,37.0] || -> equal(sk_c6,sk_c8)**.
% 0.16/0.43 122[6:Rew:111.0,113.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 131[6:Rew:104.0,106.0] || -> equal(sk_c2,sk_c7)**.
% 0.16/0.43 132[6:Rew:131.0,40.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.16/0.43 166[6:Rew:104.0,109.2,122.0,109.2,132.0,109.0,132.0,109.0,122.0,109.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.16/0.43 167[6:Obv:166.1] || equal(u,sk_c7)* -> .
% 0.16/0.43 168[6:UnC:167.0,71.0] || -> .
% 0.16/0.43 171[6:Spt:168.0,7.1,48.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.16/0.43 172[6:Spt:168.0,7.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 174[5:Rew:33.0,98.0] || -> equal(identity,sk_c6)**.
% 0.16/0.43 177[5:Rew:174.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.16/0.43 179[5:Rew:174.0,90.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c1)**.
% 0.16/0.43 181[5:Rew:174.0,96.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c2)**.
% 0.16/0.43 182[6:Rew:177.0,172.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 183[6:Rew:182.0,42.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.16/0.43 184[6:Rew:182.0,37.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.16/0.43 185[6:Rew:182.0,88.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.16/0.43 187[6:Rew:182.0,171.0] || equal(multiply(sk_c1,sk_c7),sk_c7)** -> .
% 0.16/0.43 188[6:Rew:182.0,179.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c1)**.
% 0.16/0.43 189[6:Rew:188.0,181.0] || -> equal(sk_c2,sk_c1)**.
% 0.16/0.43 191[6:Rew:189.0,46.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.16/0.43 193[6:Rew:191.0,187.0] || equal(sk_c6,sk_c7)** -> .
% 0.16/0.43 194[6:Rew:188.0,185.0] || -> equal(sk_c1,sk_c7)**.
% 0.16/0.43 195[6:Rew:194.0,183.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.16/0.43 203[5:Rew:86.0,94.0,174.0,94.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.16/0.43 208[6:Rew:184.0,12.1,194.0,12.1,182.0,12.1] || -> equal(inverse(sk_c5),sk_c6)** equal(sk_c6,sk_c7).
% 0.16/0.43 209[6:MRR:208.1,193.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.43 215[6:Rew:184.0,11.1,194.0,11.1,182.0,11.1,203.0,11.0,182.0,11.0] || -> equal(sk_c5,sk_c7)** equal(sk_c6,sk_c7).
% 0.16/0.43 216[6:MRR:215.1,193.0] || -> equal(sk_c5,sk_c7)**.
% 0.16/0.43 217[6:Rew:216.0,209.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.16/0.43 218[6:Rew:195.0,217.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 219[6:MRR:218.0,193.0] || -> .
% 0.16/0.43 232[5:Spt:219.0,19.1,46.0] || equal(multiply(sk_c2,sk_c7),sk_c6)** -> .
% 0.16/0.43 233[5:Spt:219.0,19.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 234[0:Rew:86.0,94.0] || -> equal(multiply(u,identity),u)**.
% 0.16/0.43 236[3:Rew:234.0,96.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.16/0.43 237[3:Rew:236.0,88.0] || -> equal(multiply(sk_c2,sk_c6),sk_c8)**.
% 0.16/0.43 240[5:MRR:24.1,232.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.43 241[5:MRR:22.1,232.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.16/0.43 242[5:MRR:23.1,232.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 243[5:MRR:21.1,232.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 244[5:MRR:20.1,232.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 257[3:SpR:236.0,71.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),u)**.
% 0.16/0.43 278[5:SpR:242.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.16/0.43 280[5:Rew:233.0,278.0,240.0,278.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 285[5:Rew:280.0,232.0] || equal(multiply(sk_c2,sk_c7),sk_c7)** -> .
% 0.16/0.43 286[5:Rew:280.0,237.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.16/0.43 292[5:Rew:286.0,285.0] || equal(sk_c8,sk_c7)** -> .
% 0.16/0.43 299[5:SpR:243.0,71.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c8)**.
% 0.16/0.43 301[5:Rew:241.0,299.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.16/0.43 302[5:Rew:244.0,301.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 303[5:MRR:302.0,292.0] || -> .
% 0.16/0.43 304[4:Spt:303.0,13.0,42.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.16/0.43 305[4:Spt:303.0,13.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 306[4:MRR:18.1,304.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.43 307[4:MRR:16.1,304.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.16/0.43 308[4:MRR:17.0,304.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 309[4:MRR:15.0,304.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 310[4:MRR:14.0,304.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 316[4:SpR:307.0,71.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.16/0.43 322[3:SpR:237.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.16/0.43 327[4:SpR:308.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.16/0.43 329[4:Rew:305.0,327.0,306.0,327.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 336[4:Rew:329.0,322.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.16/0.43 343[4:Rew:257.0,336.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.16/0.43 344[4:Rew:343.0,310.0] || -> equal(sk_c4,sk_c7)**.
% 0.16/0.43 348[4:Rew:343.0,45.2] || equal(inverse(identity),sk_c8)** equal(sk_c8,u)* equal(u,sk_c7) -> .
% 0.16/0.43 351[4:Rew:343.0,316.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.16/0.43 353[4:Rew:344.0,309.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.16/0.43 354[4:Rew:351.0,353.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 360[4:Rew:354.0,343.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.16/0.43 361[4:Rew:360.0,54.0] || -> equal(identity,sk_c2)**.
% 0.16/0.43 373[4:Rew:354.0,348.1,361.0,348.0,354.0,348.0] || equal(inverse(sk_c2),sk_c7)** equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.16/0.43 374[4:Obv:373.1] || equal(inverse(sk_c2),sk_c7)** equal(u,sk_c7)* -> .
% 0.16/0.43 375[4:Con:374.1] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.16/0.43 376[4:Rew:40.0,375.0] || equal(sk_c7,sk_c7)* -> .
% 0.16/0.43 377[4:Obv:376.0] || -> .
% 0.16/0.43 386[3:Spt:377.0,25.0,40.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.16/0.43 387[3:Spt:377.0,25.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 388[3:MRR:30.1,386.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.43 389[3:MRR:28.1,386.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.16/0.43 390[3:MRR:29.0,386.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 391[3:MRR:27.0,386.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 392[3:MRR:26.0,386.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 394[3:SpR:387.0,71.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.16/0.43 404[3:SpR:390.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.16/0.43 406[3:Rew:387.0,404.0,388.0,404.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 411[3:Rew:406.0,88.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.16/0.43 414[3:Rew:406.0,394.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.16/0.43 417[3:Rew:33.0,411.0] || -> equal(identity,sk_c8)**.
% 0.16/0.43 418[3:Rew:417.0,234.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.16/0.43 419[3:Rew:417.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.16/0.43 423[3:Rew:417.0,56.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.16/0.43 427[3:Rew:418.0,391.0] || -> equal(sk_c3,sk_c4)**.
% 0.16/0.43 428[3:Rew:427.0,389.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.16/0.43 430[3:Rew:419.0,392.0] || -> equal(sk_c4,sk_c7)**.
% 0.16/0.43 432[3:Rew:430.0,428.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.16/0.43 433[3:Rew:419.0,414.0,432.0,414.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 437[3:Rew:433.0,419.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.16/0.43 438[3:Rew:433.0,432.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.16/0.43 456[3:Rew:437.0,423.2,433.0,423.2,433.0,423.1,438.0,423.0,438.0,423.0,433.0,423.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.16/0.43 457[3:Obv:456.1] || equal(u,sk_c7)* -> .
% 0.16/0.43 458[3:UnC:457.0,71.0] || -> .
% 0.16/0.43 460[2:Spt:458.0,1.1,37.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.16/0.43 461[2:Spt:458.0,1.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 462[2:MRR:6.1,460.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.43 463[2:MRR:4.1,460.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.16/0.43 464[2:MRR:5.1,460.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 465[2:MRR:3.1,460.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 466[2:MRR:2.1,460.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 468[2:SpR:461.0,71.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.16/0.43 472[2:SpR:463.0,71.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.16/0.43 475[2:SpR:464.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.16/0.43 477[2:Rew:461.0,475.0,462.0,475.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 479[2:Rew:477.0,462.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.16/0.43 480[2:Rew:477.0,464.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.16/0.43 482[2:Rew:477.0,468.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.16/0.43 487[2:Rew:33.0,482.0] || -> equal(identity,sk_c8)**.
% 0.16/0.43 488[2:Rew:487.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.16/0.43 489[2:Rew:487.0,234.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.16/0.43 493[2:Rew:487.0,56.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.16/0.43 496[2:Rew:488.0,472.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.16/0.43 498[2:Rew:488.0,466.0] || -> equal(sk_c4,sk_c7)**.
% 0.16/0.43 499[2:Rew:498.0,465.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.16/0.43 500[2:Rew:496.0,499.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 502[2:Rew:500.0,480.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.16/0.43 504[2:Rew:500.0,488.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.16/0.43 505[2:Rew:500.0,489.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.16/0.43 506[2:Rew:505.0,502.0] || -> equal(sk_c5,sk_c7)**.
% 0.16/0.43 507[2:Rew:506.0,479.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.16/0.43 518[2:Rew:504.0,493.2,500.0,493.2,500.0,493.1,507.0,493.0,507.0,493.0,500.0,493.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.16/0.43 519[2:Obv:518.1] || equal(u,sk_c7)* -> .
% 0.16/0.43 520[2:UnC:519.0,71.0] || -> .
% 0.16/0.43 522[1:Spt:520.0,31.0,31.2,31.3,31.5,31.6,31.7,31.9,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.16/0.43 524[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.16/0.43 525[2:Rew:524.0,522.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.16/0.43 527[2:Obv:525.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.16/0.43 530[2:SpR:524.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.16/0.43 532[3:Spt:13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.16/0.43 533[3:SpR:532.0,71.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.16/0.43 535[4:Spt:25.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.16/0.43 536[4:SpR:535.0,71.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.16/0.43 538[5:Spt:7.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.16/0.43 540[5:SpR:538.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.16/0.43 542[5:Rew:532.0,540.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.16/0.43 544[5:SpR:542.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.16/0.43 546[5:Rew:33.0,544.0] || -> equal(identity,sk_c7)**.
% 0.16/0.43 547[5:Rew:546.0,234.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.16/0.43 548[5:Rew:546.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.16/0.43 549[5:Rew:546.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.16/0.43 552[5:Rew:547.0,527.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(v,sk_c6) equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.16/0.43 555[5:Rew:547.0,23.1] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(sk_c2,sk_c6).
% 0.16/0.43 558[5:Rew:547.0,24.1] || -> equal(inverse(sk_c5),sk_c6)** equal(sk_c2,sk_c6).
% 0.16/0.43 559[5:Rew:548.0,524.0] || -> equal(sk_c6,sk_c8)**.
% 0.16/0.43 561[5:Rew:548.0,536.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.16/0.43 565[5:Rew:559.0,558.1,559.0,558.0] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c2,sk_c8).
% 0.16/0.43 569[5:Rew:559.0,555.1,559.0,555.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)** equal(sk_c2,sk_c8).
% 0.16/0.43 572[5:Rew:559.0,552.6,559.0,552.4,559.0,552.3,559.0,552.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(v,sk_c8) equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.16/0.43 588[5:SpR:561.0,547.0] || -> equal(sk_c2,sk_c7)**.
% 0.16/0.43 590[5:Rew:588.0,535.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.16/0.43 593[5:Rew:588.0,569.1] || -> equal(multiply(sk_c5,sk_c8),sk_c8)** equal(sk_c8,sk_c7).
% 0.16/0.43 596[5:Rew:588.0,565.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c8,sk_c7).
% 0.16/0.43 602[5:SpR:549.0,71.0] || -> equal(multiply(inverse(inverse(u)),sk_c7),u)**.
% 0.16/0.43 605[5:SpR:532.0,549.0] || -> equal(multiply(sk_c8,sk_c1),sk_c7)**.
% 0.16/0.43 606[5:Rew:547.0,602.0] || -> equal(inverse(inverse(u)),u)**.
% 0.16/0.43 615[5:SpR:605.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c1)**.
% 0.16/0.43 617[5:Rew:547.0,615.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.16/0.43 622[6:Spt:596.1] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 631[6:Rew:622.0,572.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(v,sk_c8) equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.16/0.43 640[6:Rew:548.0,631.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(v,sk_c8) equal(multiply(w,sk_c8),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.16/0.43 641[6:Obv:640.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(v,sk_c8) equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.16/0.43 642[6:Rew:622.0,641.5,622.0,641.4,622.0,641.3,622.0,641.2,622.0,641.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(v,sk_c7) equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.16/0.43 643[6:Con:642.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** equal(v,sk_c7) -> .
% 0.16/0.43 644[6:Rew:547.0,643.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.16/0.43 645[6:Con:644.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.16/0.43 665[6:SpL:590.0,645.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.16/0.43 667[6:Obv:665.1] || -> .
% 0.16/0.43 668[6:Spt:667.0,596.1,622.0] || equal(sk_c8,sk_c7)** -> .
% 0.16/0.43 669[6:Spt:667.0,596.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.16/0.43 672[6:MRR:593.1,668.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.16/0.43 681[6:SpR:669.0,606.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.16/0.43 684[6:Rew:617.0,681.0] || -> equal(sk_c1,sk_c5)**.
% 0.16/0.43 688[6:Rew:684.0,538.0] || -> equal(multiply(sk_c5,sk_c8),sk_c7)**.
% 0.16/0.43 693[6:Rew:672.0,688.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 694[6:MRR:693.0,668.0] || -> .
% 0.16/0.43 695[5:Spt:694.0,7.1,538.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.16/0.43 696[5:Spt:694.0,7.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 697[5:MRR:12.1,695.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.43 698[5:MRR:10.1,695.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.16/0.43 699[5:MRR:11.1,695.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 700[5:MRR:9.1,695.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 701[5:MRR:8.1,695.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 715[5:SpR:698.0,71.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.16/0.43 718[5:SpR:699.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.16/0.43 720[5:Rew:696.0,718.0,697.0,718.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 725[5:Rew:720.0,530.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.16/0.43 732[5:Rew:33.0,725.0] || -> equal(identity,sk_c8)**.
% 0.16/0.43 733[5:Rew:732.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.16/0.43 734[5:Rew:732.0,234.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.16/0.43 737[5:Rew:733.0,701.0] || -> equal(sk_c4,sk_c7)**.
% 0.16/0.43 738[5:Rew:733.0,715.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.16/0.43 739[5:Rew:733.0,533.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.16/0.43 740[5:Rew:737.0,700.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.16/0.43 741[5:Rew:734.0,695.0] || equal(sk_c1,sk_c7)** -> .
% 0.16/0.43 742[5:Rew:738.0,740.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 748[5:Rew:742.0,734.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.16/0.43 795[5:SpR:748.0,739.0] || -> equal(sk_c1,sk_c7)**.
% 0.16/0.43 798[5:MRR:795.0,741.0] || -> .
% 0.16/0.43 801[4:Spt:798.0,25.0,535.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.16/0.43 802[4:Spt:798.0,25.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 803[4:MRR:30.1,801.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.43 804[4:MRR:28.1,801.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.16/0.43 805[4:MRR:29.0,801.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 806[4:MRR:27.0,801.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 807[4:MRR:26.0,801.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 808[4:Rew:802.0,527.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.16/0.43 809[4:Obv:808.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.16/0.43 813[4:SpR:802.0,71.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.16/0.43 825[4:SpR:805.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.16/0.43 827[4:Rew:802.0,825.0,803.0,825.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 832[4:Rew:827.0,530.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.16/0.43 834[4:Rew:827.0,809.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.16/0.43 836[4:Rew:827.0,813.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.16/0.43 839[4:Rew:33.0,832.0] || -> equal(identity,sk_c8)**.
% 0.16/0.43 840[4:Rew:839.0,234.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.16/0.43 841[4:Rew:839.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.16/0.43 844[4:Rew:840.0,806.0] || -> equal(sk_c3,sk_c4)**.
% 0.16/0.43 845[4:Rew:844.0,804.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.16/0.43 847[4:Rew:841.0,807.0] || -> equal(sk_c4,sk_c7)**.
% 0.16/0.43 850[4:Rew:847.0,845.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.16/0.43 851[4:Rew:841.0,836.0,850.0,836.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.43 855[4:Rew:851.0,840.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.16/0.43 857[4:Rew:851.0,850.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.16/0.43 867[4:Rew:855.0,834.5,851.0,834.5,855.0,834.4,827.0,834.4,855.0,834.3,827.0,834.3,851.0,834.3,851.0,834.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.16/0.43 868[4:Con:867.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.16/0.43 923[4:SpL:857.0,868.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.16/0.43 925[4:Obv:923.1] || -> .
% 0.16/0.43 926[3:Spt:925.0,13.0,532.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.16/0.43 927[3:Spt:925.0,13.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.43 928[3:MRR:18.1,926.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.43 929[3:MRR:16.1,926.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.16/0.43 930[3:MRR:17.0,926.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.43 931[3:MRR:15.0,926.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.16/0.43 932[3:MRR:14.0,926.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.16/0.43 933[3:Rew:927.0,527.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.16/0.43 934[3:Obv:933.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.16/0.43 942[3:SpR:929.0,71.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.16/0.43 948[3:SpR:930.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.16/0.43 950[3:Rew:927.0,948.0,928.0,948.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.43 952[3:Rew:950.0,928.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.16/0.44 954[3:Rew:950.0,930.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.16/0.44 955[3:Rew:950.0,530.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.16/0.44 957[3:Rew:950.0,934.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.16/0.44 962[3:Rew:33.0,955.0] || -> equal(identity,sk_c8)**.
% 0.16/0.44 963[3:Rew:962.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.16/0.44 964[3:Rew:962.0,234.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.16/0.44 967[3:Rew:963.0,932.0] || -> equal(sk_c4,sk_c7)**.
% 0.16/0.44 968[3:Rew:963.0,942.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.16/0.44 969[3:Rew:967.0,931.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.16/0.44 970[3:Rew:968.0,969.0] || -> equal(sk_c8,sk_c7)**.
% 0.16/0.44 973[3:Rew:970.0,954.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.16/0.44 976[3:Rew:970.0,964.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.16/0.44 977[3:Rew:976.0,973.0] || -> equal(sk_c5,sk_c7)**.
% 0.16/0.44 978[3:Rew:977.0,952.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.16/0.44 986[3:Rew:976.0,957.5,970.0,957.5,976.0,957.4,950.0,957.4,976.0,957.3,950.0,957.3,970.0,957.3,970.0,957.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.16/0.44 987[3:Con:986.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.16/0.44 1033[3:SpL:978.0,987.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.16/0.44 1035[3:Obv:1033.1] || -> .
% 0.16/0.44 1036[2:Spt:1035.0,1.1,524.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.16/0.44 1037[2:Spt:1035.0,1.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.16/0.44 1038[2:MRR:6.1,1036.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.16/0.44 1040[2:MRR:5.1,1036.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.16/0.44 1051[2:SpR:1040.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.16/0.44 1053[2:Rew:1037.0,1051.0,1038.0,1051.0] || -> equal(sk_c6,sk_c7)**.
% 0.16/0.44 1054[2:Rew:1053.0,1037.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.16/0.44 1057[2:Rew:1053.0,1036.0] || equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.16/0.44 1061[2:Rew:1054.0,1057.0] || equal(sk_c7,sk_c7)* -> .
% 0.16/0.44 1062[2:Obv:1061.0] || -> .
% 0.16/0.44 % SZS output end Refutation
% 0.16/0.44 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
% 0.16/0.44
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