TSTP Solution File: GRP216-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP216-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:46:22 EDT 2022
% Result : Unsatisfiable 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP216-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 10:14:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.46
% 0.18/0.46 SPASS V 3.9
% 0.18/0.46 SPASS beiseite: Proof found.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 SPASS derived 736 clauses, backtracked 288 clauses, performed 10 splits and kept 552 clauses.
% 0.18/0.46 SPASS allocated 63600 KBytes.
% 0.18/0.46 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.46 0:00:00.03 for the input.
% 0.18/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.46 0:00:00.01 for inferences.
% 0.18/0.46 0:00:00.00 for the backtracking.
% 0.18/0.46 0:00:00.06 for the reduction.
% 0.18/0.46
% 0.18/0.46
% 0.18/0.46 Here is a proof with depth 5, length 367 :
% 0.18/0.46 % SZS output start Refutation
% 0.18/0.46 1[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.46 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.46 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.18/0.46 4[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.18/0.46 5[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.18/0.46 6[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.46 7[0:Inp] || -> equal(inverse(sk_c7),sk_c6)** equal(inverse(sk_c1),sk_c7).
% 0.18/0.46 8[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.18/0.46 9[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.18/0.46 10[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.46 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.46 12[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.18/0.46 13[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 14[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 15[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 16[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 17[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 18[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 19[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.18/0.46 20[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.18/0.46 21[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.18/0.46 22[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.46 23[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.46 24[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.18/0.46 25[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c7),y)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c7)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c7,y),sk_c6)** -> .
% 0.18/0.46 26[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.46 27[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.46 28[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.46 29[1:Spt:25.1,25.6] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.18/0.46 30[2:Spt:19.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.18/0.46 32[3:Spt:7.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.46 34[4:Spt:13.1] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.46 36[4:SpL:34.0,29.1] || equal(inverse(sk_c2),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.18/0.46 37[4:Obv:36.1] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.18/0.46 38[4:Rew:30.0,37.0] || equal(sk_c6,sk_c7)** -> .
% 0.18/0.46 44[2:SpR:30.0,27.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.18/0.46 45[3:SpR:32.0,27.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.18/0.46 46[1:SpL:27.0,29.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(identity,sk_c7) -> .
% 0.18/0.46 53[0:SpR:27.0,28.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.46 54[2:SpR:44.0,28.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.18/0.46 56[2:Rew:26.0,54.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.18/0.46 57[0:Rew:26.0,53.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.46 59[3:SpR:45.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.18/0.46 61[3:Rew:26.0,59.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.18/0.46 64[4:SpR:34.0,56.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.18/0.46 73[0:SpR:57.0,57.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.46 78[0:SpR:27.0,57.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.46 79[2:SpR:44.0,57.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c2)**.
% 0.18/0.46 81[4:SpR:64.0,57.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.18/0.46 83[3:SpR:45.0,57.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.18/0.46 89[4:Rew:27.0,81.0] || -> equal(identity,sk_c7)**.
% 0.18/0.46 90[4:Rew:89.0,26.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.46 93[4:Rew:89.0,45.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.18/0.46 96[4:Rew:89.0,79.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c2)**.
% 0.18/0.46 97[4:Rew:90.0,61.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.46 103[4:Rew:90.0,93.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.46 106[4:Rew:103.0,34.0] || -> equal(multiply(sk_c2,sk_c6),sk_c1)**.
% 0.18/0.46 107[4:Rew:103.0,38.0] || equal(sk_c6,sk_c1)** -> .
% 0.18/0.46 111[4:Rew:103.0,89.0] || -> equal(identity,sk_c1)**.
% 0.18/0.46 119[4:Rew:103.0,96.0] || -> equal(multiply(inverse(sk_c6),sk_c1),sk_c2)**.
% 0.18/0.46 120[4:Rew:111.0,78.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.18/0.46 139[4:Rew:73.0,120.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.46 149[4:Rew:139.0,119.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.18/0.46 154[4:Rew:103.0,6.1,97.0,6.1,103.0,6.0] || -> equal(inverse(sk_c4),sk_c1)** equal(sk_c6,sk_c1).
% 0.18/0.46 155[4:MRR:154.1,107.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.18/0.46 158[4:Rew:103.0,5.1,97.0,5.1,139.0,5.0,103.0,5.0] || -> equal(sk_c4,sk_c5)** equal(sk_c6,sk_c1).
% 0.18/0.46 159[4:MRR:158.1,107.0] || -> equal(sk_c4,sk_c5)**.
% 0.18/0.46 160[4:Rew:159.0,155.0] || -> equal(inverse(sk_c5),sk_c1)**.
% 0.18/0.46 161[4:Rew:103.0,4.1,97.0,4.1,97.0,4.0,103.0,4.0] || -> equal(sk_c5,sk_c6)** equal(sk_c6,sk_c1).
% 0.18/0.46 162[4:MRR:161.1,107.0] || -> equal(sk_c5,sk_c6)**.
% 0.18/0.46 164[4:Rew:162.0,160.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.18/0.46 165[4:Rew:149.0,164.0] || -> equal(sk_c2,sk_c1)**.
% 0.18/0.46 168[4:Rew:165.0,106.0] || -> equal(multiply(sk_c1,sk_c6),sk_c1)**.
% 0.18/0.46 176[4:Rew:97.0,168.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.46 177[4:MRR:176.0,107.0] || -> .
% 0.18/0.46 182[4:Spt:177.0,13.1,34.0] || equal(multiply(sk_c2,sk_c6),sk_c7)** -> .
% 0.18/0.46 183[4:Spt:177.0,13.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.18/0.46 184[4:Rew:183.0,83.0] || -> equal(multiply(sk_c6,identity),sk_c1)**.
% 0.18/0.46 185[0:Rew:73.0,78.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.46 186[4:Rew:185.0,184.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.46 187[2:Rew:185.0,79.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.18/0.46 191[4:Rew:186.0,182.0] || equal(multiply(sk_c2,sk_c1),sk_c7)** -> .
% 0.18/0.46 192[4:Rew:32.0,187.0,186.0,187.0] || -> equal(sk_c2,sk_c7)**.
% 0.18/0.46 195[4:Rew:45.0,191.0,192.0,191.0] || equal(identity,sk_c7)** -> .
% 0.18/0.46 200[4:Rew:45.0,18.1,192.0,18.1,186.0,18.1] || -> equal(inverse(sk_c4),sk_c7)** equal(identity,sk_c7).
% 0.18/0.46 201[4:MRR:200.1,195.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.46 202[4:Rew:45.0,14.1,192.0,14.1,186.0,14.1] || -> equal(inverse(sk_c3),sk_c7)** equal(identity,sk_c7).
% 0.18/0.46 203[4:MRR:202.1,195.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.18/0.46 205[4:Rew:45.0,17.1,192.0,17.1,186.0,17.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(identity,sk_c7).
% 0.18/0.46 206[4:MRR:205.1,195.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.46 207[4:Rew:45.0,16.1,192.0,16.1,186.0,16.1,186.0,16.0] || -> equal(multiply(sk_c7,sk_c5),sk_c1)** equal(identity,sk_c7).
% 0.18/0.46 208[4:MRR:207.1,195.0] || -> equal(multiply(sk_c7,sk_c5),sk_c1)**.
% 0.18/0.46 209[4:Rew:45.0,15.1,192.0,15.1,186.0,15.1,186.0,15.0] || -> equal(multiply(sk_c3,sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.18/0.46 210[4:MRR:209.1,195.0] || -> equal(multiply(sk_c3,sk_c1),sk_c7)**.
% 0.18/0.46 236[4:SpR:206.0,57.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.18/0.46 238[4:Rew:201.0,236.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.18/0.46 239[4:Rew:208.0,238.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.46 241[4:Rew:239.0,32.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.46 243[4:Rew:239.0,195.0] || equal(identity,sk_c1)** -> .
% 0.18/0.46 245[4:Rew:239.0,203.0] || -> equal(inverse(sk_c3),sk_c1)**.
% 0.18/0.46 246[4:Rew:239.0,45.0] || -> equal(multiply(sk_c1,sk_c1),identity)**.
% 0.18/0.46 252[4:Rew:239.0,208.0] || -> equal(multiply(sk_c1,sk_c5),sk_c1)**.
% 0.18/0.46 253[4:Rew:239.0,210.0] || -> equal(multiply(sk_c3,sk_c1),sk_c1)**.
% 0.18/0.46 281[4:SpR:252.0,57.0] || -> equal(multiply(inverse(sk_c1),sk_c1),sk_c5)**.
% 0.18/0.46 283[4:Rew:246.0,281.0,241.0,281.0] || -> equal(identity,sk_c5)**.
% 0.18/0.46 284[4:Rew:283.0,243.0] || equal(sk_c5,sk_c1)** -> .
% 0.18/0.46 285[4:Rew:283.0,246.0] || -> equal(multiply(sk_c1,sk_c1),sk_c5)**.
% 0.18/0.46 295[4:SpR:253.0,57.0] || -> equal(multiply(inverse(sk_c3),sk_c1),sk_c1)**.
% 0.18/0.46 297[4:Rew:245.0,295.0] || -> equal(multiply(sk_c1,sk_c1),sk_c1)**.
% 0.18/0.46 298[4:Rew:285.0,297.0] || -> equal(sk_c5,sk_c1)**.
% 0.18/0.46 299[4:MRR:298.0,284.0] || -> .
% 0.18/0.46 300[3:Spt:299.0,7.1,32.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.18/0.46 301[3:Spt:299.0,7.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.18/0.46 303[3:MRR:12.1,300.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.46 304[3:MRR:8.1,300.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.18/0.46 305[3:MRR:11.0,300.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.46 306[3:MRR:10.0,300.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.46 307[3:MRR:9.0,300.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.18/0.46 308[2:Rew:30.0,46.0,187.0,46.0] || equal(sk_c6,sk_c7) equal(identity,sk_c7)** -> .
% 0.18/0.46 325[3:SpR:305.0,57.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.18/0.46 327[3:Rew:303.0,325.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.18/0.46 328[3:Rew:306.0,327.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.46 329[3:Rew:328.0,301.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.18/0.46 331[3:Rew:328.0,187.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.18/0.46 332[3:Rew:328.0,44.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.18/0.46 334[3:Rew:328.0,308.0] || equal(sk_c7,sk_c7) equal(identity,sk_c7)** -> .
% 0.18/0.46 336[3:Rew:328.0,306.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.18/0.46 337[3:Rew:328.0,307.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.18/0.46 342[3:Rew:329.0,331.0] || -> equal(sk_c2,sk_c7)**.
% 0.18/0.46 344[3:Rew:342.0,332.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.18/0.46 347[3:Obv:334.0] || equal(identity,sk_c7)** -> .
% 0.18/0.46 350[3:SpR:336.0,57.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.18/0.46 352[3:Rew:344.0,350.0,329.0,350.0] || -> equal(identity,sk_c5)**.
% 0.18/0.46 358[3:Rew:352.0,344.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.18/0.46 359[3:Rew:352.0,347.0] || equal(sk_c5,sk_c7)** -> .
% 0.18/0.46 368[3:SpR:337.0,57.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.18/0.46 370[3:Rew:304.0,368.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.18/0.46 371[3:Rew:358.0,370.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.46 372[3:MRR:371.0,359.0] || -> .
% 0.18/0.46 373[2:Spt:372.0,19.1,30.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.18/0.46 374[2:Spt:372.0,19.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.18/0.46 375[2:MRR:24.1,373.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.46 376[2:MRR:20.1,373.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.18/0.46 377[2:MRR:23.0,373.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.46 378[2:MRR:22.0,373.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.46 379[2:MRR:21.0,373.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.18/0.46 380[2:SpR:374.0,57.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.18/0.46 387[2:SpR:377.0,57.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.18/0.46 389[2:Rew:375.0,387.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.18/0.46 390[2:Rew:378.0,389.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.46 391[2:Rew:390.0,374.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.18/0.46 394[2:Rew:390.0,378.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.18/0.46 395[2:Rew:390.0,379.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.18/0.46 396[2:Rew:390.0,46.0] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c7) -> .
% 0.18/0.46 399[2:Rew:390.0,380.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.18/0.46 401[2:Rew:391.0,396.0,391.0,396.0] || equal(sk_c7,sk_c7) equal(identity,sk_c7)** -> .
% 0.18/0.46 402[2:Obv:401.0] || equal(identity,sk_c7)** -> .
% 0.18/0.46 406[2:SpR:394.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.18/0.46 407[2:SpR:394.0,57.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.18/0.46 409[2:Rew:391.0,407.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.18/0.46 411[2:SpR:395.0,57.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.18/0.46 413[2:Rew:376.0,411.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.18/0.46 414[2:Rew:409.0,413.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.46 418[2:Rew:414.0,406.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.18/0.46 420[2:Rew:399.0,418.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.46 438[0:SpR:27.0,57.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.46 441[2:SpR:375.0,27.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.18/0.46 442[2:SpR:376.0,27.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.18/0.46 443[2:SpR:391.0,27.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.18/0.46 446[2:Rew:420.0,441.0] || -> equal(identity,sk_c4)**.
% 0.18/0.46 447[2:Rew:446.0,402.0] || equal(sk_c4,sk_c7)** -> .
% 0.18/0.46 454[2:Rew:420.0,442.0,446.0,442.0] || -> equal(sk_c4,sk_c3)**.
% 0.18/0.46 457[2:Rew:454.0,446.0] || -> equal(identity,sk_c3)**.
% 0.18/0.46 458[2:Rew:454.0,447.0] || equal(sk_c3,sk_c7)** -> .
% 0.18/0.46 459[2:Rew:420.0,443.0,457.0,443.0] || -> equal(sk_c3,sk_c7)**.
% 0.18/0.46 460[2:MRR:459.0,458.0] || -> .
% 0.18/0.46 469[1:Spt:460.0,25.0,25.2,25.3,25.4,25.5,25.7,25.8,25.9] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c7),x)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,x),sk_c6)** -> .
% 0.18/0.46 470[0:Rew:185.0,438.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.46 473[1:EqR:469.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.18/0.46 475[2:Spt:7.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.18/0.46 478[2:Rew:475.0,473.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(sk_c6,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.18/0.46 479[2:Obv:478.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.18/0.46 482[2:SpR:475.0,57.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.18/0.46 484[3:Spt:24.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.18/0.46 487[4:Spt:12.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.46 504[0:SpR:470.0,57.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.18/0.46 507[2:SpR:475.0,470.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.46 508[3:SpR:484.0,470.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.18/0.46 509[4:SpR:487.0,470.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.18/0.46 511[3:Rew:507.0,508.0] || -> equal(sk_c2,sk_c7)**.
% 0.18/0.46 512[3:Rew:511.0,484.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.18/0.46 513[3:Rew:511.0,15.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c7).
% 0.18/0.46 514[3:Rew:511.0,16.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c7).
% 0.18/0.46 515[3:Rew:511.0,17.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c7).
% 0.18/0.46 516[3:Rew:511.0,14.1] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.46 517[3:Rew:511.0,18.1] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.46 519[4:Rew:475.0,509.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.46 521[4:Rew:519.0,3.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c1).
% 0.18/0.46 522[4:Rew:519.0,4.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c1).
% 0.18/0.47 523[4:Rew:519.0,5.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(multiply(sk_c1,sk_c7),sk_c1).
% 0.18/0.47 524[4:Rew:519.0,2.1] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c1)**.
% 0.18/0.47 525[4:Rew:519.0,6.1] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c1)**.
% 0.18/0.47 527[4:Rew:519.0,479.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c1) equal(inverse(w),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.18/0.47 531[4:Rew:519.0,512.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.18/0.47 533[4:Rew:519.0,516.1] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.18/0.47 534[4:Rew:519.0,517.1] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.18/0.47 535[4:Rew:519.0,513.1,519.0,513.0] || -> equal(multiply(sk_c3,sk_c1),sk_c7)** equal(multiply(sk_c7,sk_c1),sk_c7).
% 0.18/0.47 536[4:Rew:519.0,514.1,519.0,514.0] || -> equal(multiply(sk_c7,sk_c5),sk_c1)** equal(multiply(sk_c7,sk_c1),sk_c7).
% 0.18/0.47 537[4:Rew:519.0,515.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c1),sk_c7).
% 0.18/0.47 538[4:Rew:519.0,521.0] || -> equal(multiply(sk_c3,sk_c1),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c1).
% 0.18/0.47 539[4:Rew:519.0,522.0] || -> equal(multiply(sk_c7,sk_c5),sk_c1)** equal(multiply(sk_c1,sk_c7),sk_c1).
% 0.18/0.47 540[4:Rew:519.0,527.5,519.0,527.4,519.0,527.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c1) equal(inverse(w),sk_c7) equal(multiply(v,sk_c1),sk_c7)** equal(multiply(w,sk_c7),sk_c1)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c1)** -> .
% 0.18/0.47 547[4:SpR:487.0,27.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.18/0.47 550[4:Rew:547.0,537.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(identity,sk_c7).
% 0.18/0.47 551[4:Rew:547.0,536.1] || -> equal(multiply(sk_c7,sk_c5),sk_c1)** equal(identity,sk_c7).
% 0.18/0.47 552[4:Rew:547.0,535.1] || -> equal(multiply(sk_c3,sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.18/0.47 553[4:Rew:547.0,534.1] || -> equal(inverse(sk_c4),sk_c7)** equal(identity,sk_c7).
% 0.18/0.47 554[4:Rew:547.0,533.1] || -> equal(inverse(sk_c3),sk_c7)** equal(identity,sk_c7).
% 0.18/0.47 561[4:SpR:531.0,27.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.18/0.47 563[4:Rew:561.0,523.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(identity,sk_c1).
% 0.18/0.47 564[4:Rew:561.0,539.1] || -> equal(multiply(sk_c7,sk_c5),sk_c1)** equal(identity,sk_c1).
% 0.18/0.47 565[4:Rew:561.0,538.1] || -> equal(multiply(sk_c3,sk_c1),sk_c7)** equal(identity,sk_c1).
% 0.18/0.47 566[4:Rew:561.0,525.1] || -> equal(inverse(sk_c4),sk_c7)** equal(identity,sk_c1).
% 0.18/0.47 567[4:Rew:561.0,524.1] || -> equal(inverse(sk_c3),sk_c7)** equal(identity,sk_c1).
% 0.18/0.47 568[4:Rew:553.1,566.1] || -> equal(inverse(sk_c4),sk_c7)** equal(sk_c7,sk_c1).
% 0.18/0.47 569[4:Rew:568.1,553.1] || -> equal(inverse(sk_c4),sk_c7)** equal(identity,sk_c1).
% 0.18/0.47 570[4:Rew:554.1,567.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c7,sk_c1).
% 0.18/0.47 571[4:Rew:570.1,554.1] || -> equal(inverse(sk_c3),sk_c7)** equal(identity,sk_c1).
% 0.18/0.47 572[4:Rew:550.1,563.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(sk_c7,sk_c1).
% 0.18/0.47 573[4:Rew:572.1,550.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(identity,sk_c1).
% 0.18/0.47 574[4:Rew:551.1,564.1] || -> equal(multiply(sk_c7,sk_c5),sk_c1)** equal(sk_c7,sk_c1).
% 0.18/0.47 576[4:Rew:552.1,565.1] || -> equal(multiply(sk_c3,sk_c1),sk_c7)** equal(sk_c7,sk_c1).
% 0.18/0.47 577[4:Rew:576.1,552.1] || -> equal(multiply(sk_c3,sk_c1),sk_c7)** equal(identity,sk_c1).
% 0.18/0.47 583[5:Spt:568.1] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.47 584[5:Rew:583.0,487.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.47 587[5:Rew:583.0,547.0] || -> equal(multiply(sk_c1,sk_c1),identity)**.
% 0.18/0.47 591[5:Rew:583.0,540.0] || equal(inverse(u),sk_c1) equal(inverse(v),sk_c1) equal(inverse(w),sk_c7) equal(multiply(v,sk_c1),sk_c7)** equal(multiply(w,sk_c7),sk_c1)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c1)** -> .
% 0.18/0.47 594[5:Rew:583.0,569.0] || -> equal(inverse(sk_c4),sk_c1)** equal(identity,sk_c1).
% 0.18/0.47 595[5:Rew:583.0,571.0] || -> equal(inverse(sk_c3),sk_c1)** equal(identity,sk_c1).
% 0.18/0.47 596[5:Rew:583.0,573.0] || -> equal(multiply(sk_c4,sk_c1),sk_c5)** equal(identity,sk_c1).
% 0.18/0.47 598[5:Rew:583.0,577.0] || -> equal(multiply(sk_c3,sk_c1),sk_c1)** equal(identity,sk_c1).
% 0.18/0.47 599[5:Rew:583.0,591.5,583.0,591.4,583.0,591.3,583.0,591.2] || equal(inverse(u),sk_c1) equal(inverse(v),sk_c1) equal(inverse(w),sk_c1) equal(multiply(v,sk_c1),sk_c1)** equal(multiply(w,sk_c1),sk_c1)** equal(multiply(sk_c1,multiply(u,sk_c1)),sk_c1)** -> .
% 0.18/0.47 600[5:Con:599.2] || equal(inverse(u),sk_c1) equal(inverse(v),sk_c1) equal(multiply(v,sk_c1),sk_c1)** equal(multiply(sk_c1,multiply(u,sk_c1)),sk_c1)** -> .
% 0.18/0.47 625[6:Spt:594.1] || -> equal(identity,sk_c1)**.
% 0.18/0.47 627[6:Rew:625.0,185.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.47 628[6:Rew:625.0,26.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 634[6:Rew:627.0,600.3] || equal(inverse(u),sk_c1) equal(inverse(v),sk_c1) equal(multiply(v,sk_c1),sk_c1)** equal(multiply(sk_c1,u),sk_c1)** -> .
% 0.18/0.47 637[6:Rew:628.0,634.3,627.0,634.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(v,sk_c1) equal(u,sk_c1) -> .
% 0.18/0.47 638[6:Con:637.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.18/0.47 669[6:SpL:584.0,638.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.47 670[6:Obv:669.1] || -> .
% 0.18/0.47 671[6:Spt:670.0,594.1,625.0] || equal(identity,sk_c1)** -> .
% 0.18/0.47 672[6:Spt:670.0,594.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.18/0.47 673[6:MRR:595.1,671.0] || -> equal(inverse(sk_c3),sk_c1)**.
% 0.18/0.47 674[6:MRR:596.1,671.0] || -> equal(multiply(sk_c4,sk_c1),sk_c5)**.
% 0.18/0.47 676[6:MRR:598.1,671.0] || -> equal(multiply(sk_c3,sk_c1),sk_c1)**.
% 0.18/0.47 678[6:SpR:672.0,470.0] || -> equal(inverse(sk_c1),sk_c4)**.
% 0.18/0.47 680[6:Rew:584.0,678.0] || -> equal(sk_c4,sk_c1)**.
% 0.18/0.47 682[6:Rew:680.0,674.0] || -> equal(multiply(sk_c1,sk_c1),sk_c5)**.
% 0.18/0.47 683[6:Rew:587.0,682.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 685[6:Rew:683.0,671.0] || equal(sk_c5,sk_c1)** -> .
% 0.18/0.47 686[6:Rew:683.0,587.0] || -> equal(multiply(sk_c1,sk_c1),sk_c5)**.
% 0.18/0.47 696[6:SpR:673.0,470.0] || -> equal(inverse(sk_c1),sk_c3)**.
% 0.18/0.47 698[6:Rew:584.0,696.0] || -> equal(sk_c3,sk_c1)**.
% 0.18/0.47 700[6:Rew:698.0,676.0] || -> equal(multiply(sk_c1,sk_c1),sk_c1)**.
% 0.18/0.47 701[6:Rew:686.0,700.0] || -> equal(sk_c5,sk_c1)**.
% 0.18/0.47 702[6:MRR:701.0,685.0] || -> .
% 0.18/0.47 704[5:Spt:702.0,568.1,583.0] || equal(sk_c7,sk_c1)** -> .
% 0.18/0.47 705[5:Spt:702.0,568.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.47 707[5:MRR:572.1,704.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.47 708[5:MRR:574.1,704.0] || -> equal(multiply(sk_c7,sk_c5),sk_c1)**.
% 0.18/0.47 711[5:SpR:705.0,470.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.18/0.47 713[5:Rew:531.0,711.0] || -> equal(sk_c4,sk_c1)**.
% 0.18/0.47 715[5:Rew:713.0,707.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.18/0.47 716[5:Rew:561.0,715.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 718[5:Rew:716.0,185.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.18/0.47 725[5:Rew:718.0,708.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.47 726[5:MRR:725.0,704.0] || -> .
% 0.18/0.47 728[4:Spt:726.0,12.1,487.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.18/0.47 729[4:Spt:726.0,12.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.47 730[4:MRR:8.1,728.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.18/0.47 731[4:MRR:11.0,728.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.47 732[4:MRR:10.0,728.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.47 733[4:MRR:9.0,728.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.18/0.47 735[4:SpR:729.0,470.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.18/0.47 737[4:Rew:475.0,735.0] || -> equal(sk_c4,sk_c6)**.
% 0.18/0.47 739[4:Rew:737.0,731.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.47 743[4:SpR:730.0,470.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.18/0.47 745[4:Rew:475.0,743.0] || -> equal(sk_c3,sk_c6)**.
% 0.18/0.47 747[4:Rew:745.0,733.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.18/0.47 758[2:SpR:507.0,57.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.18/0.47 762[4:SpR:732.0,57.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.18/0.47 764[4:Rew:475.0,762.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.18/0.47 765[4:Rew:747.0,764.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.47 766[4:Rew:765.0,732.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 767[4:Rew:765.0,739.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.18/0.47 778[4:SpR:767.0,28.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.18/0.47 779[4:SpR:767.0,57.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c7)**.
% 0.18/0.47 781[4:Rew:766.0,779.0,507.0,779.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 784[4:Rew:781.0,475.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.18/0.47 789[4:Rew:781.0,482.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.18/0.47 791[4:Rew:781.0,479.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.18/0.47 796[4:Rew:789.0,778.0,781.0,778.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 798[4:Rew:796.0,791.5,781.0,791.5,781.0,791.4,781.0,791.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.18/0.47 799[4:Con:798.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.18/0.47 824[4:SpR:796.0,185.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 828[4:Rew:824.0,185.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.47 832[4:Rew:828.0,799.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.18/0.47 876[4:SpL:784.0,832.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.18/0.47 877[4:Obv:876.1] || -> .
% 0.18/0.47 878[3:Spt:877.0,24.1,484.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.18/0.47 879[3:Spt:877.0,24.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.47 880[3:MRR:20.1,878.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.18/0.47 881[3:MRR:23.0,878.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.18/0.47 882[3:MRR:22.0,878.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.18/0.47 883[3:MRR:21.0,878.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.18/0.47 885[3:SpR:879.0,470.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.18/0.47 888[3:Rew:475.0,885.0] || -> equal(sk_c4,sk_c6)**.
% 0.18/0.47 890[3:Rew:888.0,881.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.18/0.47 894[3:SpR:880.0,470.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.18/0.47 897[3:Rew:475.0,894.0] || -> equal(sk_c3,sk_c6)**.
% 0.18/0.47 899[3:Rew:897.0,883.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.18/0.47 919[3:SpR:882.0,57.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.18/0.47 921[3:Rew:475.0,919.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.18/0.47 922[3:Rew:899.0,921.0] || -> equal(sk_c5,sk_c7)**.
% 0.18/0.47 923[3:Rew:922.0,882.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 924[3:Rew:922.0,890.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.18/0.47 935[3:SpR:924.0,28.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.18/0.47 936[3:SpR:924.0,57.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c7)**.
% 0.18/0.47 938[3:Rew:923.0,936.0,507.0,936.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 941[3:Rew:938.0,507.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.18/0.47 947[3:Rew:938.0,758.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.18/0.47 951[3:Rew:938.0,479.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.18/0.47 954[3:Rew:947.0,935.0,938.0,935.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 956[3:Rew:954.0,951.5,938.0,951.5,938.0,951.4,938.0,951.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.18/0.47 957[3:Con:956.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.18/0.47 988[3:SpR:954.0,185.0] || -> equal(identity,sk_c7)**.
% 0.18/0.47 991[3:Rew:988.0,185.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.18/0.47 996[3:Rew:991.0,957.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.18/0.47 1028[3:SpL:941.0,996.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.18/0.47 1029[3:Obv:1028.1] || -> .
% 0.18/0.47 1030[2:Spt:1029.0,7.0,475.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.18/0.47 1031[2:Spt:1029.0,7.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.18/0.47 1032[2:MRR:19.0,1030.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.18/0.47 1033[2:MRR:1.0,1030.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.18/0.47 1034[2:MRR:13.0,1030.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.18/0.47 1036[2:SpR:1031.0,470.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.18/0.47 1037[2:SpR:1031.0,504.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),u)**.
% 0.18/0.47 1039[2:Rew:1036.0,1030.0] || equal(sk_c6,sk_c1)** -> .
% 0.18/0.47 1040[2:SpR:1032.0,57.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.18/0.47 1041[2:SpR:1032.0,470.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.18/0.47 1042[2:SpR:1032.0,504.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.18/0.47 1058[2:SpR:1033.0,28.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.18/0.47 1062[2:Rew:1037.0,1058.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.47 1063[2:Rew:1062.0,1042.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.47 1064[2:Rew:1062.0,1040.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.47 1065[2:Rew:1063.0,1034.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 1067[2:Rew:1065.0,1039.0] || equal(sk_c7,sk_c1)** -> .
% 0.18/0.47 1068[2:Rew:1065.0,1041.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.18/0.47 1071[2:Rew:1065.0,1062.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 1072[2:Rew:1036.0,1068.0] || -> equal(sk_c2,sk_c1)**.
% 0.18/0.47 1075[2:Rew:1072.0,1064.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 1091[2:SpR:1031.0,27.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.18/0.47 1093[2:SpR:1036.0,27.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.18/0.47 1094[2:Rew:1071.0,1091.0] || -> equal(identity,sk_c1)**.
% 0.18/0.47 1104[2:Rew:1075.0,1093.0,1094.0,1093.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.47 1105[2:MRR:1104.0,1067.0] || -> .
% 0.18/0.47 % SZS output end Refutation
% 0.18/0.47 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_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 left_identity left_inverse associativity
% 0.18/0.47
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