TSTP Solution File: GRP331-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP331-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:46:53 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
% 0.04/0.13 % Problem : GRP331-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 18:19:07 EDT 2022
% 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 905 clauses, backtracked 316 clauses, performed 10 splits and kept 718 clauses.
% 0.20/0.49 SPASS allocated 63703 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 0:00:00.06 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 5, length 372 :
% 0.20/0.49 % SZS output start Refutation
% 0.20/0.49 1[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 2[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 3[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 5[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 6[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 7[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 8[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 9[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 10[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 11[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 12[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 14[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 16[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 17[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 18[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 19[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 20[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 21[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 22[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 23[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 24[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 25[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 26[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 27[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 28[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 29[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 30[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 31[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(inverse(y),sk_c7) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c6),sk_c7)** equal(multiply(y,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 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[1:Spt:31.4,31.9] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.20/0.49 36[2:Spt:5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 38[3:Spt:23.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 40[4:Spt:17.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 44[5:Spt:26.1] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 46[6:Spt:11.1] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 48[6:SpL:46.0,35.1] || equal(inverse(sk_c1),sk_c7)** equal(sk_c8,sk_c8) -> .
% 0.20/0.49 49[6:Obv:48.1] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.49 50[6:Rew:40.0,49.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 51[6:Obv:50.0] || -> .
% 0.20/0.49 52[6:Spt:51.0,11.1,46.0] || equal(multiply(sk_c1,sk_c7),sk_c8)** -> .
% 0.20/0.49 53[6:Spt:51.0,11.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 54[6:MRR:10.1,52.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 55[6:MRR:8.1,52.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 57[6:MRR:9.1,52.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 58[6:MRR:7.1,52.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 64[6:SpL:57.0,35.1] || equal(inverse(sk_c4),sk_c7)** equal(sk_c6,sk_c8) -> .
% 0.20/0.49 65[6:Rew:54.0,64.0] || equal(sk_c7,sk_c7)* equal(sk_c6,sk_c8) -> .
% 0.20/0.49 66[6:Obv:65.0] || equal(sk_c6,sk_c8)** -> .
% 0.20/0.49 69[3:SpR:38.0,33.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.20/0.49 70[4:SpR:40.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.20/0.49 72[6:SpR:54.0,33.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.49 73[6:SpR:55.0,33.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.20/0.49 74[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c8) -> .
% 0.20/0.49 82[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.49 85[0:Rew:32.0,82.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.49 87[3:SpR:69.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.20/0.49 89[3:Rew:32.0,87.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.20/0.49 104[5:SpR:44.0,89.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.49 117[0:SpR:85.0,85.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.49 120[2:SpR:36.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.20/0.49 123[0:SpR:32.0,85.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.20/0.49 124[0:SpR:33.0,85.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.49 127[3:SpR:69.0,85.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c2)**.
% 0.20/0.49 128[4:SpR:70.0,85.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.20/0.49 129[6:SpR:72.0,85.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.20/0.49 132[5:SpR:104.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.49 135[6:SpR:73.0,85.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.20/0.49 145[4:Rew:127.0,128.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.49 151[4:Rew:145.0,127.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.20/0.49 152[5:Rew:120.0,132.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 157[6:Rew:152.0,57.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.20/0.49 158[6:Rew:152.0,58.0] || -> equal(multiply(sk_c3,sk_c8),sk_c8)**.
% 0.20/0.49 166[6:Rew:152.0,129.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.20/0.49 186[6:Rew:135.0,166.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 188[6:Rew:186.0,157.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.49 190[6:Rew:158.0,188.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 191[6:MRR:190.0,66.0] || -> .
% 0.20/0.49 203[0:Rew:117.0,124.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.49 220[5:Spt:191.0,26.1,44.0] || equal(multiply(sk_c2,sk_c6),sk_c7)** -> .
% 0.20/0.49 221[5:Spt:191.0,26.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 222[4:Rew:203.0,151.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.49 223[4:Rew:222.0,120.0] || -> equal(multiply(sk_c1,sk_c6),sk_c8)**.
% 0.20/0.49 224[5:Rew:223.0,220.0,145.0,220.0] || equal(sk_c7,sk_c8)** -> .
% 0.20/0.49 230[4:Rew:223.0,28.1,145.0,28.1] || -> equal(inverse(sk_c4),sk_c7)** equal(sk_c7,sk_c8).
% 0.20/0.49 231[5:MRR:230.1,224.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 234[4:Rew:223.0,27.1,145.0,27.1] || -> equal(multiply(sk_c4,sk_c7),sk_c6)** equal(sk_c7,sk_c8).
% 0.20/0.49 235[5:MRR:234.1,224.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 236[4:Rew:223.0,25.1,145.0,25.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(sk_c7,sk_c8).
% 0.20/0.49 237[5:MRR:236.1,224.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 238[4:Rew:40.0,74.0,222.0,74.0] || equal(sk_c7,sk_c7)* equal(identity,sk_c8) -> .
% 0.20/0.49 239[4:Obv:238.0] || equal(identity,sk_c8)** -> .
% 0.20/0.49 240[5:SpR:221.0,33.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.20/0.49 253[5:SpR:231.0,33.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.49 273[5:SpR:235.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.49 282[5:SpR:240.0,85.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.20/0.49 284[5:Rew:203.0,282.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.20/0.49 291[5:SpR:284.0,33.0] || -> equal(multiply(sk_c3,sk_c8),identity)**.
% 0.20/0.49 294[5:Rew:237.0,291.0] || -> equal(sk_c7,identity)**.
% 0.20/0.49 295[5:Rew:294.0,40.0] || -> equal(inverse(sk_c1),identity)**.
% 0.20/0.49 296[5:Rew:294.0,222.0] || -> equal(inverse(identity),sk_c1)**.
% 0.20/0.49 299[5:Rew:294.0,70.0] || -> equal(multiply(identity,sk_c1),identity)**.
% 0.20/0.49 309[5:Rew:294.0,273.0] || -> equal(multiply(sk_c4,multiply(identity,u)),multiply(sk_c6,u))**.
% 0.20/0.49 311[5:Rew:294.0,253.0] || -> equal(multiply(identity,sk_c4),identity)**.
% 0.20/0.49 315[5:Rew:296.0,123.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 316[5:Rew:32.0,299.0] || -> equal(identity,sk_c1)**.
% 0.20/0.49 317[5:Rew:316.0,32.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 319[5:Rew:316.0,239.0] || equal(sk_c1,sk_c8)** -> .
% 0.20/0.49 320[5:Rew:316.0,240.0] || -> equal(multiply(sk_c8,sk_c3),sk_c1)**.
% 0.20/0.49 324[5:Rew:316.0,295.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.49 331[5:Rew:316.0,311.0] || -> equal(multiply(sk_c1,sk_c4),sk_c1)**.
% 0.20/0.49 336[5:Rew:315.0,223.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 337[5:Rew:315.0,331.0] || -> equal(sk_c1,sk_c4)**.
% 0.20/0.49 348[5:Rew:337.0,316.0] || -> equal(identity,sk_c4)**.
% 0.20/0.49 350[5:Rew:337.0,319.0] || equal(sk_c4,sk_c8)** -> .
% 0.20/0.49 351[5:Rew:337.0,324.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.20/0.49 358[5:Rew:337.0,317.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.49 359[5:Rew:337.0,320.0] || -> equal(multiply(sk_c8,sk_c3),sk_c4)**.
% 0.20/0.49 374[5:Rew:358.0,309.0,358.0,309.0,348.0,309.0,336.0,309.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 376[5:Rew:374.0,359.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 382[5:Rew:376.0,350.0] || equal(sk_c3,sk_c8)** -> .
% 0.20/0.49 383[5:Rew:376.0,351.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.20/0.49 387[5:Rew:221.0,383.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 388[5:MRR:387.0,382.0] || -> .
% 0.20/0.49 393[4:Spt:388.0,17.1,40.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.49 394[4:Spt:388.0,17.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 395[3:Rew:203.0,127.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.20/0.49 398[4:MRR:16.1,393.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 399[4:MRR:14.1,393.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 402[4:MRR:15.0,393.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 403[4:MRR:13.0,393.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 404[3:Rew:38.0,74.0,395.0,74.0] || equal(sk_c7,sk_c7)* equal(identity,sk_c8) -> .
% 0.20/0.49 405[3:Obv:404.0] || equal(identity,sk_c8)** -> .
% 0.20/0.49 412[4:SpR:398.0,85.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.20/0.49 414[4:SpR:399.0,85.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.20/0.49 438[4:SpR:403.0,85.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.20/0.49 440[4:Rew:399.0,438.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.49 452[4:SpR:440.0,85.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.49 454[4:Rew:33.0,452.0] || -> equal(sk_c7,identity)**.
% 0.20/0.49 456[4:Rew:454.0,395.0] || -> equal(inverse(identity),sk_c2)**.
% 0.20/0.49 458[4:Rew:454.0,36.0] || -> equal(multiply(identity,sk_c8),sk_c6)**.
% 0.20/0.49 459[4:Rew:454.0,69.0] || -> equal(multiply(identity,sk_c2),identity)**.
% 0.20/0.49 461[4:Rew:454.0,402.0] || -> equal(multiply(sk_c4,identity),sk_c6)**.
% 0.20/0.49 462[4:Rew:454.0,403.0] || -> equal(multiply(sk_c3,sk_c8),identity)**.
% 0.20/0.49 473[4:Rew:454.0,412.0] || -> equal(multiply(identity,multiply(sk_c4,u)),u)**.
% 0.20/0.49 476[4:Rew:456.0,123.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.49 477[4:Rew:32.0,458.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 487[4:Rew:32.0,459.0] || -> equal(identity,sk_c2)**.
% 0.20/0.49 488[4:Rew:487.0,405.0] || equal(sk_c2,sk_c8)** -> .
% 0.20/0.49 490[4:Rew:487.0,203.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.20/0.49 497[4:Rew:487.0,461.0,477.0,461.0] || -> equal(multiply(sk_c4,sk_c2),sk_c8)**.
% 0.20/0.49 498[4:Rew:487.0,462.0] || -> equal(multiply(sk_c3,sk_c8),sk_c2)**.
% 0.20/0.49 506[4:Rew:490.0,497.0] || -> equal(sk_c4,sk_c8)**.
% 0.20/0.49 511[4:Rew:476.0,473.0,487.0,473.0,506.0,473.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 512[4:Rew:511.0,414.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.49 513[4:Rew:512.0,498.0] || -> equal(sk_c2,sk_c8)**.
% 0.20/0.49 514[4:MRR:513.0,488.0] || -> .
% 0.20/0.49 525[3:Spt:514.0,23.1,38.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.20/0.49 526[3:Spt:514.0,23.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 527[3:MRR:22.1,525.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 528[3:MRR:20.1,525.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 529[3:MRR:24.0,525.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 530[3:MRR:21.0,525.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 531[3:MRR:19.0,525.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 542[3:SpR:529.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 544[3:Rew:526.0,542.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 546[3:SpR:530.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 548[3:Rew:527.0,546.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 560[3:SpR:548.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 562[3:Rew:33.0,560.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 563[3:Rew:562.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 564[3:Rew:562.0,203.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 568[3:Rew:562.0,74.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c8) -> .
% 0.20/0.49 569[3:Rew:563.0,544.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 576[3:Rew:569.0,36.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.20/0.49 584[3:Rew:569.0,564.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 585[3:Rew:584.0,531.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.49 593[3:Rew:584.0,576.0,585.0,576.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 594[3:Rew:593.0,528.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.49 596[3:Rew:593.0,585.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 615[3:Rew:569.0,568.1,594.0,568.0,594.0,568.0,596.0,568.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.49 616[3:Obv:615.1] || -> .
% 0.20/0.49 619[2:Spt:616.0,5.1,36.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.49 620[2:Spt:616.0,5.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 621[2:MRR:4.1,619.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 622[2:MRR:2.1,619.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 623[2:MRR:6.1,619.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 624[2:MRR:3.1,619.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 625[2:MRR:1.1,619.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 633[2:SpR:623.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 635[2:Rew:620.0,633.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 637[2:SpR:624.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 639[2:Rew:621.0,637.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 641[2:SpR:625.0,85.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.20/0.49 643[2:Rew:622.0,641.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.49 648[2:SpR:639.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 650[2:Rew:33.0,648.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 651[2:Rew:650.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 652[2:Rew:650.0,203.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 656[2:Rew:650.0,74.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c8) -> .
% 0.20/0.49 657[2:Rew:651.0,635.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 669[2:Rew:657.0,651.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 670[2:Rew:657.0,652.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 671[2:Rew:670.0,625.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.49 677[2:Rew:671.0,643.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.20/0.49 680[2:Rew:669.0,677.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 681[2:Rew:680.0,622.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.49 682[2:Rew:680.0,671.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 700[2:Rew:657.0,656.1,681.0,656.0,681.0,656.0,682.0,656.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.49 701[2:Obv:700.1] || -> .
% 0.20/0.49 704[1:Spt:701.0,31.0,31.1,31.2,31.3,31.5,31.6,31.7,31.8,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.49 706[2:Spt:4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 707[2:Rew:706.0,704.8] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c6),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.49 709[2:Obv:707.8] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c6),sk_c7)** -> .
% 0.20/0.49 712[2:SpR:706.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.20/0.49 714[3:Spt:17.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 715[3:SpR:714.0,85.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.20/0.49 717[4:Spt:23.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 720[5:Spt:11.1] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 722[5:SpR:720.0,85.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.49 724[5:Rew:706.0,722.0,714.0,722.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 726[5:Rew:724.0,714.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.49 727[5:Rew:724.0,717.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 728[5:Rew:724.0,720.0] || -> equal(multiply(sk_c1,sk_c6),sk_c8)**.
% 0.20/0.49 730[5:Rew:724.0,25.1] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 732[5:Rew:724.0,30.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 733[5:Rew:724.0,26.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 734[5:Rew:724.0,29.1] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 735[5:Rew:724.0,709.1] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c6),sk_c7)** -> .
% 0.20/0.49 737[5:Rew:724.0,712.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 741[5:Rew:33.0,737.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 742[5:Rew:741.0,203.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 745[5:Rew:741.0,33.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.49 749[5:Rew:742.0,730.0,724.0,730.0] || -> equal(sk_c3,sk_c6) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 750[5:Rew:749.0,733.0] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 752[5:Rew:742.0,732.0] || -> equal(sk_c5,sk_c6) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 753[5:Rew:752.0,734.0] || -> equal(inverse(sk_c6),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 754[5:Rew:750.0,753.0] || -> equal(sk_c6,sk_c8) equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.20/0.49 762[5:Rew:724.0,735.7,742.0,735.6,724.0,735.6,724.0,735.5,742.0,735.4,724.0,735.3] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c8)** equal(inverse(x),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(w,sk_c6) equal(multiply(x,sk_c6),sk_c6)** -> .
% 0.20/0.49 763[5:Con:762.3] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c8)** equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(w,sk_c6) -> .
% 0.20/0.49 778[5:SpR:726.0,745.0] || -> equal(multiply(sk_c6,sk_c1),sk_c8)**.
% 0.20/0.49 779[5:SpR:727.0,745.0] || -> equal(multiply(sk_c6,sk_c2),sk_c8)**.
% 0.20/0.49 789[5:SpR:778.0,85.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c1)**.
% 0.20/0.49 791[5:Rew:742.0,789.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.20/0.49 797[5:SpR:779.0,85.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c2)**.
% 0.20/0.49 799[5:Rew:791.0,797.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 800[5:Rew:742.0,799.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.49 808[5:Rew:800.0,754.1] || -> equal(sk_c6,sk_c8) equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.49 812[5:Rew:728.0,808.1] || -> equal(sk_c6,sk_c8)** equal(sk_c6,sk_c8)**.
% 0.20/0.49 813[5:Obv:812.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 815[5:Rew:813.0,726.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 816[5:Rew:813.0,728.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.49 821[5:Rew:813.0,763.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c8)** equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(w,sk_c6) -> .
% 0.20/0.49 823[5:Rew:742.0,816.0] || -> equal(sk_c1,sk_c8)**.
% 0.20/0.49 825[5:Rew:823.0,815.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.49 836[5:Con:821.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c6) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c6)** -> .
% 0.20/0.49 837[5:Rew:742.0,836.3,813.0,836.3,813.0,836.2,813.0,836.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.20/0.49 838[5:Con:837.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.49 847[5:SpL:825.0,838.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.49 848[5:Obv:847.1] || -> .
% 0.20/0.49 849[5:Spt:848.0,11.1,720.0] || equal(multiply(sk_c1,sk_c7),sk_c8)** -> .
% 0.20/0.49 850[5:Spt:848.0,11.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 851[5:MRR:10.1,849.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 853[5:MRR:12.1,849.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 854[5:MRR:9.1,849.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 855[5:MRR:7.1,849.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 867[5:SpR:853.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 869[5:Rew:850.0,867.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 874[5:SpR:854.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 876[5:Rew:851.0,874.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 888[5:SpR:876.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 890[5:Rew:33.0,888.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 891[5:Rew:890.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 892[5:Rew:890.0,203.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 895[5:Rew:891.0,869.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 903[5:Rew:895.0,706.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.20/0.49 911[5:Rew:895.0,891.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 912[5:Rew:895.0,892.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 913[5:Rew:912.0,855.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.49 917[5:Rew:913.0,849.0] || equal(multiply(sk_c1,sk_c3),sk_c8)** -> .
% 0.20/0.49 919[5:Rew:913.0,715.0] || -> equal(multiply(sk_c3,multiply(sk_c1,u)),u)**.
% 0.20/0.49 923[5:Rew:912.0,903.0,913.0,903.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 936[5:Rew:912.0,917.0,923.0,917.0] || equal(sk_c1,sk_c8)** -> .
% 0.20/0.49 942[5:Rew:911.0,919.0,923.0,919.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 1001[5:SpR:942.0,912.0] || -> equal(sk_c1,sk_c8)**.
% 0.20/0.49 1003[5:MRR:1001.0,936.0] || -> .
% 0.20/0.49 1005[4:Spt:1003.0,23.1,717.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.20/0.49 1006[4:Spt:1003.0,23.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 1007[4:MRR:22.1,1005.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 1008[4:MRR:20.1,1005.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 1009[4:MRR:24.0,1005.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 1010[4:MRR:21.0,1005.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 1011[4:MRR:19.0,1005.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 1024[4:SpR:1009.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 1026[4:Rew:1006.0,1024.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 1028[4:SpR:1010.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 1030[4:Rew:1007.0,1028.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 1039[4:SpR:1030.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 1041[4:Rew:33.0,1039.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 1042[4:Rew:1041.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 1043[4:Rew:1041.0,203.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1046[4:Rew:1042.0,1026.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 1053[4:Rew:1046.0,706.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.20/0.49 1058[4:Rew:1046.0,709.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c6),sk_c7)** -> .
% 0.20/0.49 1063[4:Rew:1046.0,1043.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 1064[4:Rew:1063.0,1011.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.49 1072[4:Rew:1063.0,1053.0,1064.0,1053.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 1073[4:Rew:1072.0,1008.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.49 1075[4:Rew:1072.0,1064.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 1094[4:Rew:1063.0,1058.7,1046.0,1058.7,1075.0,1058.7,1063.0,1058.6,1075.0,1058.6,1063.0,1058.5,1075.0,1058.5,1046.0,1058.5,1063.0,1058.4,1046.0,1058.4,1075.0,1058.3,1075.0,1058.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(inverse(x),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) equal(x,sk_c8) -> .
% 0.20/0.49 1095[4:Con:1094.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.49 1151[4:SpL:1073.0,1095.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.49 1152[4:Obv:1151.1] || -> .
% 0.20/0.49 1153[3:Spt:1152.0,17.1,714.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.20/0.49 1154[3:Spt:1152.0,17.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 1155[3:MRR:16.1,1153.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 1156[3:MRR:14.1,1153.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 1157[3:MRR:18.0,1153.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 1158[3:MRR:15.0,1153.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 1159[3:MRR:13.0,1153.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 1170[3:SpR:1157.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.50 1172[3:Rew:1154.0,1170.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.50 1174[3:SpR:1158.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.50 1176[3:Rew:1155.0,1174.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.50 1178[3:SpR:1159.0,85.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.20/0.50 1180[3:Rew:1156.0,1178.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.50 1185[3:SpR:1176.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.50 1187[3:Rew:33.0,1185.0] || -> equal(identity,sk_c6)**.
% 0.20/0.50 1188[3:Rew:1187.0,203.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.50 1189[3:Rew:1187.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.50 1192[3:Rew:1188.0,1172.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 1194[3:Rew:1188.0,709.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7)** equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(x,sk_c7) -> .
% 0.20/0.50 1195[3:Rew:1188.0,712.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.50 1207[3:Rew:1192.0,1188.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.50 1208[3:Rew:1192.0,1189.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.50 1209[3:Rew:1208.0,1180.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.50 1216[3:Rew:1209.0,1195.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.50 1232[3:Rew:1209.0,1194.7,1207.0,1194.6,1209.0,1194.6,1207.0,1194.5,1209.0,1194.5,1192.0,1194.5,1207.0,1194.4,1192.0,1194.4,1209.0,1194.3,1209.0,1194.1,1192.0,1194.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(inverse(x),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) equal(x,sk_c8) -> .
% 0.20/0.50 1233[3:Con:1232.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 1303[3:SpL:1216.0,1233.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 1305[3:Obv:1303.1] || -> .
% 0.20/0.50 1306[2:Spt:1305.0,4.1,706.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.50 1307[2:Spt:1305.0,4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.50 1308[2:MRR:2.1,1306.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.50 1309[2:MRR:5.1,1306.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.50 1310[2:MRR:6.1,1306.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.50 1311[2:MRR:3.1,1306.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.50 1312[2:MRR:1.1,1306.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 1320[2:SpR:1310.0,85.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.50 1322[2:Rew:1309.0,1320.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.50 1324[2:SpR:1311.0,85.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.50 1326[2:Rew:1307.0,1324.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.50 1328[2:SpR:1312.0,85.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.20/0.50 1330[2:Rew:1308.0,1328.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.50 1335[2:SpR:1326.0,85.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.50 1337[2:Rew:33.0,1335.0] || -> equal(identity,sk_c6)**.
% 0.20/0.50 1338[2:Rew:1337.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.50 1339[2:Rew:1337.0,203.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.50 1342[2:Rew:1338.0,1322.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 1351[2:Rew:1342.0,1306.0] || equal(multiply(sk_c7,sk_c8),sk_c8)** -> .
% 0.20/0.50 1354[2:Rew:1342.0,1338.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.50 1355[2:Rew:1342.0,1339.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.50 1356[2:Rew:1355.0,1312.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.50 1360[2:Rew:1356.0,1330.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.20/0.50 1363[2:Rew:1354.0,1360.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.50 1365[2:Rew:1363.0,1356.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.50 1373[2:Rew:1354.0,1351.0,1365.0,1351.0] || equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 1374[2:Obv:1373.0] || -> .
% 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
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