TSTP Solution File: GRP367-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP367-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:47:03 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP367-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 02:05:42 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 744 clauses, backtracked 380 clauses, performed 11 splits and kept 734 clauses.
% 0.20/0.48 SPASS allocated 63615 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.06 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 5, length 362 :
% 0.20/0.48 % SZS output start Refutation
% 0.20/0.48 1[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.20/0.48 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 3[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.20/0.48 4[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.20/0.48 6[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c2),sk_c7).
% 0.20/0.48 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 8[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c2),sk_c7).
% 0.20/0.48 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 10[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c2),sk_c7).
% 0.20/0.48 11[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 13[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 14[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 15[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 16[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 18[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 20[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.48 21[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 22[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 23[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 24[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 25[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 26[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 28[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 30[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.48 31[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c8) equal(multiply(x,sk_c8),y)*+ equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7) -> .
% 0.20/0.48 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.48 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.48 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.48 35[1:Spt:31.3,31.4,31.8] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.20/0.48 37[2:Spt:1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 40[3:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 42[4:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 45[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.48 46[5:Spt:5.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.48 48[6:Spt:3.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 51[3:SpR:40.0,33.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.20/0.48 52[4:SpR:42.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.48 53[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.48 59[4:SpR:52.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.20/0.48 61[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.48 62[5:SpR:46.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.48 64[3:SpR:51.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.20/0.48 66[4:Rew:32.0,59.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.48 67[3:Rew:32.0,64.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.20/0.48 68[0:Rew:32.0,61.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.48 72[6:SpR:48.0,66.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.48 79[5:SpR:46.0,67.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.48 84[0:SpR:68.0,68.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.48 86[2:SpR:37.0,68.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.20/0.48 87[4:SpR:52.0,68.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.20/0.48 91[0:SpR:33.0,68.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.48 94[3:SpR:51.0,68.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.20/0.48 96[5:SpR:79.0,68.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.48 102[5:Rew:86.0,96.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 104[5:Rew:102.0,37.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.48 109[6:Rew:102.0,72.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.48 114[5:Rew:102.0,86.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.20/0.48 115[5:Rew:102.0,94.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.20/0.48 117[5:Rew:102.0,53.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.20/0.48 118[5:Rew:102.0,45.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.20/0.48 120[5:Rew:102.0,62.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.48 126[6:Rew:104.0,109.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 127[6:Rew:126.0,42.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 128[6:Rew:126.0,52.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.48 138[6:Rew:126.0,114.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.20/0.48 139[6:Rew:33.0,138.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 140[6:Rew:139.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 143[6:Rew:139.0,128.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.20/0.48 145[6:Rew:140.0,143.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 146[6:Rew:145.0,127.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 179[6:Rew:140.0,117.2,126.0,117.2,139.0,117.1,146.0,117.0,146.0,117.0,126.0,117.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.48 180[6:Obv:179.1] || equal(u,sk_c6)* -> .
% 0.20/0.48 181[6:UnC:180.0,68.0] || -> .
% 0.20/0.48 184[6:Spt:181.0,3.0,48.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.48 185[6:Spt:181.0,3.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 186[6:Rew:102.0,185.0] || -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.20/0.48 187[5:Rew:87.0,115.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.48 191[6:Rew:102.0,184.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.20/0.48 192[0:Rew:84.0,91.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.48 193[4:Rew:192.0,87.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.20/0.48 199[5:Rew:102.0,28.1] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.20/0.48 200[6:MRR:199.1,191.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 203[5:Rew:187.0,120.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.48 204[5:Rew:102.0,23.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 205[6:MRR:204.0,191.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 217[4:SpR:193.0,68.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.20/0.48 236[6:SpR:205.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.48 238[6:Rew:186.0,236.0,200.0,236.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 240[6:Rew:238.0,42.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 243[6:Rew:238.0,52.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.48 250[6:Rew:238.0,203.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.20/0.48 251[6:Rew:238.0,217.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.20/0.48 260[6:Rew:238.0,118.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.20/0.48 268[6:Rew:251.0,250.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 272[6:Rew:268.0,243.0] || -> equal(identity,sk_c4)**.
% 0.20/0.48 287[6:Rew:268.0,260.2,238.0,260.1,240.0,260.0,272.0,260.0,238.0,260.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.48 288[6:Obv:287.1] || equal(u,sk_c6)* -> .
% 0.20/0.48 289[6:UnC:288.0,200.0] || -> .
% 0.20/0.48 292[5:Spt:289.0,5.0,46.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.48 293[5:Spt:289.0,5.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 294[3:Rew:192.0,94.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.48 295[3:Rew:294.0,86.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.20/0.48 296[5:Rew:295.0,292.0] || equal(sk_c7,sk_c8)** -> .
% 0.20/0.48 298[3:Rew:295.0,30.1] || -> equal(inverse(sk_c3),sk_c6)** equal(sk_c7,sk_c8).
% 0.20/0.48 299[5:MRR:298.1,296.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 300[3:Rew:295.0,20.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c8).
% 0.20/0.49 301[5:MRR:300.1,296.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 302[3:Rew:295.0,25.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 303[5:MRR:302.0,296.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 304[3:Rew:295.0,15.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 305[5:MRR:304.0,296.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 306[3:Rew:295.0,10.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 307[5:MRR:306.0,296.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 320[3:SpR:294.0,68.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.20/0.49 337[5:SpR:303.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 339[5:Rew:293.0,337.0,299.0,337.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 343[5:Rew:339.0,296.0] || equal(sk_c8,sk_c6)** -> .
% 0.20/0.49 348[5:Rew:339.0,307.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.49 365[5:SpR:305.0,68.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c8)**.
% 0.20/0.49 367[5:Rew:301.0,365.0] || -> equal(multiply(sk_c8,sk_c2),sk_c8)**.
% 0.20/0.49 368[5:Rew:348.0,367.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 369[5:MRR:368.0,343.0] || -> .
% 0.20/0.49 370[4:Spt:369.0,2.0,42.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.49 371[4:Spt:369.0,2.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 372[4:MRR:27.0,370.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 373[4:MRR:17.0,370.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 374[4:MRR:22.0,370.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 375[4:MRR:12.0,370.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 376[4:MRR:7.0,370.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 386[4:SpR:373.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 388[3:SpR:295.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.49 402[4:SpR:374.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 404[4:Rew:371.0,402.0,372.0,402.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 407[4:Rew:404.0,40.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 408[4:Rew:404.0,51.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.20/0.49 410[4:Rew:404.0,320.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.20/0.49 414[4:Rew:404.0,376.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.49 417[4:Rew:404.0,45.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c6)** -> .
% 0.20/0.49 423[4:Rew:388.0,410.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 424[4:Rew:423.0,414.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 425[4:Rew:423.0,386.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 427[4:Rew:424.0,375.0] || -> equal(multiply(sk_c1,sk_c8),sk_c6)**.
% 0.20/0.49 428[4:Rew:425.0,427.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 434[4:Rew:428.0,423.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 435[4:Rew:434.0,408.0] || -> equal(identity,sk_c5)**.
% 0.20/0.49 451[4:Rew:434.0,417.2,428.0,417.2,428.0,417.1,407.0,417.0,435.0,417.0,428.0,417.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.49 452[4:Obv:451.1] || equal(u,sk_c6)* -> .
% 0.20/0.49 453[4:UnC:452.0,372.0] || -> .
% 0.20/0.49 458[3:Spt:453.0,4.0,40.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.20/0.49 459[3:Spt:453.0,4.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 460[3:MRR:29.0,458.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 461[3:MRR:19.0,458.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 462[3:MRR:24.0,458.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 463[3:MRR:14.0,458.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 464[3:MRR:9.0,458.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 470[3:SpR:461.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 476[3:SpR:462.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 478[3:Rew:459.0,476.0,460.0,476.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 482[3:Rew:478.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 485[3:Rew:478.0,464.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.49 487[3:Rew:478.0,53.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c6)** -> .
% 0.20/0.49 493[3:Rew:33.0,482.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 494[3:Rew:493.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 495[3:Rew:493.0,192.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 498[3:Rew:494.0,485.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 499[3:Rew:494.0,470.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 500[3:Rew:498.0,463.0] || -> equal(multiply(sk_c1,sk_c8),sk_c6)**.
% 0.20/0.49 501[3:Rew:499.0,500.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 503[3:Rew:501.0,462.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.20/0.49 504[3:Rew:501.0,493.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 505[3:Rew:501.0,494.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 506[3:Rew:501.0,495.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 508[3:Rew:506.0,503.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.49 509[3:Rew:508.0,460.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 524[3:Rew:505.0,487.2,501.0,487.2,504.0,487.1,509.0,487.0,509.0,487.0,501.0,487.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.49 525[3:Obv:524.1] || equal(u,sk_c6)* -> .
% 0.20/0.49 526[3:UnC:525.0,68.0] || -> .
% 0.20/0.49 529[2:Spt:526.0,1.0,37.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.49 530[2:Spt:526.0,1.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 531[2:MRR:26.1,529.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 532[2:MRR:16.1,529.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 533[2:MRR:21.0,529.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 534[2:MRR:11.0,529.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 535[2:MRR:6.0,529.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 537[2:SpR:530.0,68.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.49 539[2:SpR:531.0,68.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.49 541[2:SpR:532.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 544[2:SpR:533.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 546[2:Rew:530.0,544.0,531.0,544.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 549[2:Rew:546.0,535.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.49 551[2:Rew:546.0,53.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c6)** -> .
% 0.20/0.49 555[2:Rew:546.0,537.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 559[2:Rew:33.0,555.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 560[2:Rew:559.0,192.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 561[2:Rew:559.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 564[2:Rew:560.0,534.0] || -> equal(sk_c1,sk_c2)**.
% 0.20/0.49 565[2:Rew:564.0,532.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 566[2:Rew:564.0,541.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.20/0.49 567[2:Rew:561.0,549.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 569[2:Rew:567.0,565.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.49 570[2:Rew:561.0,566.0,567.0,566.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 571[2:Rew:570.0,539.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.49 572[2:Rew:571.0,533.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 573[2:Rew:572.0,559.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 576[2:Rew:572.0,569.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 586[2:Rew:570.0,551.2,572.0,551.2,573.0,551.1,576.0,551.0,576.0,551.0,572.0,551.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.49 587[2:Obv:586.1] || equal(u,sk_c6)* -> .
% 0.20/0.49 588[2:UnC:587.0,531.0] || -> .
% 0.20/0.49 591[1:Spt:588.0,31.0,31.1,31.2,31.5,31.6,31.7,31.9,31.10] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7) -> .
% 0.20/0.49 593[2:Spt:1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.49 594[2:Rew:593.0,591.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(sk_c6,sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.49 596[2:Obv:594.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.49 599[2:SpR:593.0,68.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.20/0.49 601[3:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 602[3:SpR:601.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.49 604[4:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.49 605[4:SpR:604.0,68.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.20/0.49 607[5:Spt:3.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.49 609[5:SpR:607.0,68.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.20/0.49 611[5:Rew:601.0,609.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.49 615[6:Spt:5.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.49 617[6:SpR:615.0,68.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.20/0.49 619[6:Rew:604.0,617.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.49 621[6:SpR:619.0,68.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.49 623[6:Rew:599.0,621.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 624[6:Rew:623.0,593.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.49 626[6:Rew:623.0,607.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.20/0.49 627[6:Rew:623.0,611.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.49 631[6:Rew:623.0,596.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(sk_c6,sk_c8),sk_c8)** -> .
% 0.20/0.49 632[6:Rew:623.0,599.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.20/0.49 639[6:Rew:624.0,627.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 640[6:Rew:639.0,601.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.49 642[6:Rew:639.0,623.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 645[6:Rew:639.0,626.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.20/0.49 648[6:Rew:33.0,632.0,639.0,632.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 649[6:Rew:648.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 650[6:Rew:648.0,192.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 653[6:Rew:650.0,645.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.49 655[6:Rew:653.0,640.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 666[6:Rew:649.0,631.6,639.0,631.6,650.0,631.5,639.0,631.5,650.0,631.4,642.0,631.4,639.0,631.4,650.0,631.3,642.0,631.3,639.0,631.1,642.0,631.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) equal(sk_c6,sk_c6) -> .
% 0.20/0.49 667[6:Obv:666.6] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.20/0.49 668[6:Con:667.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.49 704[6:SpL:655.0,668.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 706[6:Obv:704.1] || -> .
% 0.20/0.49 707[6:Spt:706.0,5.0,615.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.49 708[6:Spt:706.0,5.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 709[6:MRR:30.1,707.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 711[6:MRR:25.0,707.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 730[6:SpR:711.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 732[6:Rew:708.0,730.0,709.0,730.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 735[6:Rew:732.0,611.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.49 739[6:Rew:732.0,599.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 740[6:Rew:732.0,707.0] || equal(multiply(sk_c5,sk_c6),sk_c6)** -> .
% 0.20/0.49 741[6:Rew:732.0,605.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.20/0.49 750[6:Rew:33.0,739.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 751[6:Rew:750.0,192.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 752[6:Rew:750.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 755[6:Rew:751.0,735.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 766[6:Rew:755.0,751.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 768[6:Rew:755.0,752.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 778[6:Rew:766.0,740.0] || equal(sk_c5,sk_c6)** -> .
% 0.20/0.49 782[6:Rew:768.0,741.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.49 820[6:SpR:782.0,766.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.49 822[6:MRR:820.0,778.0] || -> .
% 0.20/0.49 824[5:Spt:822.0,3.0,607.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.49 825[5:Spt:822.0,3.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 826[5:MRR:28.1,824.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 827[5:MRR:18.1,824.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 828[5:MRR:23.0,824.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 829[5:MRR:13.0,824.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 830[5:MRR:8.0,824.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 844[5:SpR:827.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 850[5:SpR:828.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 852[5:Rew:825.0,850.0,826.0,850.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 856[5:Rew:852.0,599.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 857[5:Rew:852.0,824.0] || equal(multiply(sk_c4,sk_c6),sk_c8)** -> .
% 0.20/0.49 860[5:Rew:852.0,830.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.49 865[5:Rew:33.0,856.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 866[5:Rew:865.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 870[5:Rew:866.0,860.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 871[5:Rew:866.0,844.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 872[5:Rew:866.0,602.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.49 873[5:Rew:870.0,829.0] || -> equal(multiply(sk_c1,sk_c8),sk_c6)**.
% 0.20/0.49 874[5:Rew:871.0,873.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 885[5:Rew:872.0,857.0,874.0,857.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 886[5:Obv:885.0] || -> .
% 0.20/0.49 898[4:Spt:886.0,4.0,604.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.20/0.49 899[4:Spt:886.0,4.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 900[4:MRR:29.0,898.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 901[4:MRR:19.0,898.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 902[4:MRR:24.0,898.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 903[4:MRR:14.0,898.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 904[4:MRR:9.0,898.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 905[4:Rew:899.0,596.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.20/0.49 906[4:Obv:905.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** -> .
% 0.20/0.49 910[4:SpR:899.0,68.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.49 922[4:SpR:902.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 924[4:Rew:899.0,922.0,900.0,922.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 928[4:Rew:924.0,599.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 930[4:Rew:924.0,904.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.49 931[4:Rew:924.0,906.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** -> .
% 0.20/0.49 933[4:Rew:924.0,910.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 935[4:Rew:33.0,928.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 936[4:Rew:935.0,192.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 937[4:Rew:935.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 940[4:Rew:936.0,903.0] || -> equal(sk_c1,sk_c2)**.
% 0.20/0.49 941[4:Rew:940.0,901.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 943[4:Rew:937.0,930.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 946[4:Rew:943.0,941.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.49 947[4:Rew:937.0,933.0,946.0,933.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 951[4:Rew:947.0,936.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 953[4:Rew:947.0,946.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 964[4:Rew:951.0,931.5,947.0,931.5,951.0,931.4,924.0,931.4,947.0,931.4,951.0,931.3,924.0,931.3,947.0,931.1] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.20/0.49 965[4:Con:964.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.49 1007[4:SpL:953.0,965.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 1008[4:Obv:1007.1] || -> .
% 0.20/0.49 1009[3:Spt:1008.0,2.0,601.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.49 1010[3:Spt:1008.0,2.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 1011[3:MRR:27.0,1009.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 1012[3:MRR:17.0,1009.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 1013[3:MRR:22.0,1009.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 1014[3:MRR:12.0,1009.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 1015[3:MRR:7.0,1009.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 1016[3:Rew:1010.0,596.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.20/0.49 1017[3:Obv:1016.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** -> .
% 0.20/0.49 1025[3:SpR:1012.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 1031[3:SpR:1013.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 1033[3:Rew:1010.0,1031.0,1011.0,1031.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 1036[3:Rew:1033.0,599.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 1038[3:Rew:1033.0,1015.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.49 1039[3:Rew:1033.0,1017.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** -> .
% 0.20/0.49 1043[3:Rew:33.0,1036.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 1044[3:Rew:1043.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 1045[3:Rew:1043.0,192.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 1048[3:Rew:1044.0,1038.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 1049[3:Rew:1044.0,1025.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 1050[3:Rew:1048.0,1014.0] || -> equal(multiply(sk_c1,sk_c8),sk_c6)**.
% 0.20/0.49 1051[3:Rew:1049.0,1050.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 1054[3:Rew:1051.0,1013.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.20/0.49 1057[3:Rew:1051.0,1045.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1059[3:Rew:1057.0,1054.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.49 1060[3:Rew:1059.0,1011.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 1068[3:Rew:1057.0,1039.5,1051.0,1039.5,1057.0,1039.4,1033.0,1039.4,1051.0,1039.4,1057.0,1039.3,1033.0,1039.3,1051.0,1039.1] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.20/0.49 1069[3:Con:1068.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.49 1115[3:SpL:1060.0,1069.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 1117[3:Obv:1115.1] || -> .
% 0.20/0.49 1118[2:Spt:1117.0,1.0,593.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.49 1119[2:Spt:1117.0,1.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 1120[2:MRR:26.1,1118.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 1122[2:MRR:21.0,1118.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 1133[2:SpR:1122.0,68.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 1135[2:Rew:1119.0,1133.0,1120.0,1133.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 1136[2:Rew:1135.0,1119.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.20/0.49 1137[2:Rew:1135.0,1118.0] || equal(multiply(sk_c6,sk_c8),sk_c6)** -> .
% 0.20/0.49 1141[2:Rew:1136.0,1137.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 1142[2:Obv:1141.0] || -> .
% 0.20/0.49 % SZS output end Refutation
% 0.20/0.49 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
% 0.20/0.49
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