TSTP Solution File: GRP270-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP270-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 11:46:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP270-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.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 13:11:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 760 clauses, backtracked 339 clauses, performed 12 splits and kept 650 clauses.
% 0.19/0.47 SPASS allocated 63597 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 5, length 339 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 6[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.19/0.47 8[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6)** equal(inverse(sk_c1),sk_c7).
% 0.19/0.47 10[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 11[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.47 12[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 13[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.47 14[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 15[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.47 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 21[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 23[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 25[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 26[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c5)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) -> .
% 0.19/0.47 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 30[1:Spt:26.2,26.6] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c5)** -> .
% 0.19/0.47 31[2:Spt:11.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 33[2:SpL:31.0,30.1] || equal(inverse(sk_c6),sk_c7)** equal(sk_c5,sk_c5) -> .
% 0.19/0.47 34[2:Obv:33.1] || equal(inverse(sk_c6),sk_c7)** -> .
% 0.19/0.47 35[3:Spt:14.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.47 37[4:Spt:12.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 39[5:Spt:15.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 41[6:Spt:13.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 44[1:SpL:27.0,30.1] || equal(inverse(identity),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.19/0.47 46[3:SpR:35.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.47 47[4:SpR:37.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.47 56[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 57[3:SpR:46.0,29.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.47 59[3:Rew:27.0,57.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.47 60[0:Rew:27.0,56.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 62[4:SpR:47.0,29.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.19/0.47 64[4:Rew:27.0,62.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.47 67[5:SpR:39.0,59.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.47 73[6:SpR:41.0,64.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 76[0:SpR:60.0,60.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 78[2:SpR:31.0,60.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.47 81[0:SpR:27.0,60.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.19/0.47 82[0:SpR:28.0,60.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 83[3:SpR:46.0,60.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.47 85[5:SpR:67.0,60.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.47 87[4:SpR:47.0,60.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.47 93[5:Rew:78.0,85.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 94[5:Rew:93.0,31.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 95[5:Rew:93.0,35.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.47 96[5:Rew:93.0,34.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.47 99[5:Rew:93.0,46.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.47 106[6:Rew:93.0,73.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 107[5:Rew:93.0,78.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.19/0.47 109[6:Rew:94.0,106.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 116[6:Rew:109.0,107.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.47 117[6:Rew:28.0,116.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 118[6:Rew:117.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 122[6:Rew:117.0,99.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.19/0.47 129[6:Rew:118.0,122.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 130[6:Rew:129.0,95.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 132[6:MRR:130.0,96.0] || -> .
% 0.19/0.47 154[6:Spt:132.0,13.0,41.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.47 155[6:Spt:132.0,13.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 156[6:Rew:93.0,155.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.19/0.47 161[6:Rew:93.0,154.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.19/0.47 162[0:Rew:76.0,82.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 163[4:Rew:162.0,87.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.47 172[5:Rew:93.0,8.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 173[6:MRR:172.1,161.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 177[5:Rew:93.0,3.1,93.0,3.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c7).
% 0.19/0.47 178[6:MRR:177.0,161.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 205[6:SpR:156.0,60.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.19/0.47 207[6:Rew:163.0,205.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.47 208[6:Rew:207.0,161.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.47 214[6:SpR:178.0,60.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 216[6:Rew:94.0,214.0,173.0,214.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 217[6:MRR:216.0,208.0] || -> .
% 0.19/0.47 218[5:Spt:217.0,15.0,39.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.47 219[5:Spt:217.0,15.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 220[3:Rew:162.0,83.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.47 222[3:Rew:220.0,78.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.47 223[5:Rew:222.0,218.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.47 225[3:Rew:222.0,25.1] || -> equal(inverse(sk_c2),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 226[5:MRR:225.1,223.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 229[3:Rew:222.0,20.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 230[5:MRR:229.0,223.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 239[3:SpR:220.0,60.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.19/0.47 254[3:SpR:222.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 259[5:SpR:230.0,60.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.19/0.47 261[5:Rew:219.0,259.0,226.0,259.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 262[5:MRR:261.0,223.0] || -> .
% 0.19/0.47 263[4:Spt:262.0,12.0,37.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.47 264[4:Spt:262.0,12.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 265[4:MRR:22.0,263.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 266[4:MRR:7.0,263.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 267[4:MRR:17.0,263.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 268[4:MRR:2.0,263.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 277[4:SpR:267.0,60.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.19/0.47 279[4:Rew:264.0,277.0,265.0,277.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 280[4:Rew:279.0,35.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.47 282[4:Rew:279.0,46.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.47 283[4:Rew:279.0,31.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 287[4:Rew:279.0,239.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.19/0.47 289[4:Rew:279.0,268.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 296[4:SpR:289.0,60.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 298[4:Rew:266.0,296.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 299[4:Rew:283.0,298.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 304[4:Rew:299.0,44.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.47 305[4:Rew:299.0,254.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.47 313[4:Obv:304.1] || equal(inverse(identity),sk_c7)** -> .
% 0.19/0.47 314[4:Rew:287.0,305.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 316[4:Rew:314.0,282.0] || -> equal(identity,sk_c4)**.
% 0.19/0.47 324[4:Rew:316.0,313.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.19/0.47 327[4:Rew:280.0,324.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 328[4:Obv:327.0] || -> .
% 0.19/0.47 330[3:Spt:328.0,14.0,35.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.47 331[3:Spt:328.0,14.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 332[3:MRR:24.0,330.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 334[3:MRR:19.0,330.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 337[3:SpR:331.0,60.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.47 347[3:SpR:334.0,60.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.19/0.47 349[3:Rew:331.0,347.0,332.0,347.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 352[3:Rew:349.0,34.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.47 354[3:Rew:349.0,78.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.19/0.47 357[3:Rew:349.0,337.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.19/0.47 359[3:Rew:28.0,357.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 360[3:Rew:359.0,162.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 366[3:Rew:360.0,354.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 367[3:MRR:366.0,352.0] || -> .
% 0.19/0.47 372[2:Spt:367.0,11.0,31.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.47 373[2:Spt:367.0,11.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 374[2:MRR:21.1,372.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 375[2:MRR:6.1,372.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 376[2:MRR:16.0,372.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 377[2:MRR:1.0,372.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 379[2:SpR:373.0,60.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.47 386[2:SpR:376.0,60.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c7)**.
% 0.19/0.47 388[2:Rew:373.0,386.0,374.0,386.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 390[2:Rew:388.0,372.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.19/0.47 391[2:Rew:388.0,377.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 392[2:Rew:388.0,379.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.19/0.47 394[2:Rew:28.0,392.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 397[2:Rew:394.0,28.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 405[2:SpR:391.0,60.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 407[2:Rew:375.0,405.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 408[2:Rew:407.0,390.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.47 412[2:SpR:407.0,60.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.47 414[2:Rew:397.0,412.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 415[2:MRR:414.0,408.0] || -> .
% 0.19/0.47 416[1:Spt:415.0,26.0,26.1,26.3,26.4,26.5,26.7,26.8,26.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) -> .
% 0.19/0.47 418[2:Spt:11.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 419[2:Rew:418.0,416.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.47 421[2:Obv:419.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.47 424[2:SpR:418.0,60.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.47 426[3:Spt:12.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 428[3:Rew:426.0,421.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 429[3:Obv:428.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.47 432[3:SpR:426.0,60.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.47 434[4:Spt:24.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.47 440[5:Spt:22.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 460[0:SpR:81.0,162.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.47 467[0:SpR:28.0,60.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 470[4:SpR:434.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.47 471[5:SpR:440.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.47 472[0:Rew:162.0,467.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.47 480[4:SpR:470.0,60.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.47 482[4:Rew:162.0,480.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.47 483[4:Rew:482.0,424.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.47 485[4:Rew:483.0,5.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 486[4:Rew:483.0,20.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 487[4:Rew:483.0,10.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 488[4:Rew:483.0,25.1] || -> equal(inverse(sk_c2),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 489[4:Rew:487.1,8.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 490[4:Rew:488.1,23.1] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 491[4:Rew:485.0,3.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 495[4:SpR:482.0,28.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.19/0.47 498[5:SpR:471.0,60.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.47 500[5:Rew:162.0,498.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.47 501[5:Rew:500.0,432.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.47 504[6:Spt:487.1] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 505[6:Rew:504.0,418.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 509[6:Rew:504.0,482.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.47 511[6:Rew:504.0,429.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.47 517[6:Rew:504.0,491.1] || -> equal(multiply(sk_c3,sk_c7),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c7).
% 0.19/0.47 518[6:Rew:504.0,495.0] || -> equal(multiply(sk_c4,sk_c7),identity)**.
% 0.19/0.47 519[6:Rew:504.0,501.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.47 520[6:Rew:500.0,509.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.47 521[6:Rew:520.0,483.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.19/0.47 525[6:Rew:520.0,518.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.19/0.47 527[6:Rew:525.0,490.1] || -> equal(inverse(sk_c2),sk_c7)** equal(identity,sk_c7).
% 0.19/0.47 528[6:Rew:525.0,489.1] || -> equal(inverse(sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.19/0.47 529[6:Rew:525.0,519.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 531[6:Rew:529.0,162.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 536[6:Rew:531.0,521.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 537[6:Rew:536.0,440.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 545[6:Rew:529.0,527.1] || -> equal(inverse(sk_c2),sk_c7)** equal(sk_c5,sk_c7).
% 0.19/0.47 546[6:Rew:529.0,528.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c5,sk_c7).
% 0.19/0.47 552[6:Rew:505.0,517.0,536.0,517.0] || -> equal(sk_c5,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 553[6:Rew:504.0,511.5,504.0,511.4,531.0,511.3,504.0,511.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.47 554[6:Con:553.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.47 605[7:Spt:545.1] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 610[7:Rew:605.0,531.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 615[7:Rew:610.0,554.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.19/0.47 616[7:Con:615.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 663[7:SpL:537.0,616.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 665[7:Obv:663.1] || -> .
% 0.19/0.47 666[7:Spt:665.0,545.1,605.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.47 667[7:Spt:665.0,545.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 668[7:MRR:546.1,666.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 670[7:MRR:552.0,666.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 689[7:SpR:668.0,472.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 692[7:Rew:537.0,689.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 697[7:Rew:692.0,666.0] || equal(sk_c5,sk_c1)** -> .
% 0.19/0.47 700[7:Rew:692.0,505.0] || -> equal(multiply(sk_c1,sk_c1),sk_c5)**.
% 0.19/0.47 702[7:Rew:692.0,670.0] || -> equal(multiply(sk_c1,sk_c1),sk_c1)**.
% 0.19/0.47 704[7:Rew:700.0,702.0] || -> equal(sk_c5,sk_c1)**.
% 0.19/0.47 705[7:MRR:704.0,697.0] || -> .
% 0.19/0.47 709[6:Spt:705.0,487.1,504.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.47 710[6:Spt:705.0,487.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 711[6:MRR:488.1,709.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 712[6:MRR:485.0,709.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 713[6:MRR:486.0,709.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 715[6:SpR:710.0,472.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 718[6:Rew:500.0,715.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.47 720[6:Rew:718.0,500.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 741[6:SpR:711.0,472.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.47 744[6:Rew:720.0,741.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.47 746[6:Rew:744.0,713.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.19/0.47 747[6:Rew:712.0,746.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 750[6:Rew:747.0,483.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.19/0.47 758[6:Rew:495.0,750.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 759[6:Rew:758.0,460.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 763[6:Rew:758.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 766[6:Rew:720.0,759.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 768[6:Rew:766.0,709.0] || equal(sk_c6,sk_c1)** -> .
% 0.19/0.47 769[6:Rew:766.0,712.0] || -> equal(multiply(sk_c1,sk_c1),sk_c6)**.
% 0.19/0.47 779[6:Rew:766.0,763.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.47 780[6:Rew:779.0,769.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 781[6:MRR:780.0,768.0] || -> .
% 0.19/0.47 792[5:Spt:781.0,22.0,440.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.47 793[5:Spt:781.0,22.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 794[5:MRR:7.0,792.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 795[5:MRR:17.0,792.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 796[5:MRR:2.0,792.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 798[5:SpR:793.0,472.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.47 810[5:SpR:794.0,472.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 813[5:Rew:798.0,810.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.47 815[5:Rew:813.0,795.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.19/0.47 816[5:Rew:813.0,798.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 821[5:Rew:796.0,815.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 822[5:Rew:821.0,483.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.19/0.47 828[5:Rew:821.0,429.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.47 831[5:Rew:495.0,822.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 832[5:Rew:831.0,460.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 833[5:Rew:831.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 834[5:Rew:831.0,162.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 838[5:Rew:816.0,832.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 839[5:Rew:838.0,794.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 841[5:Rew:838.0,796.0] || -> equal(multiply(sk_c1,sk_c1),sk_c6)**.
% 0.19/0.47 846[5:Rew:838.0,833.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.47 847[5:Rew:838.0,834.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.47 850[5:Rew:846.0,841.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 873[5:Rew:847.0,828.5,838.0,828.5,850.0,828.5,847.0,828.4,850.0,828.4,838.0,828.4,847.0,828.3,850.0,828.3,838.0,828.2,838.0,828.1,850.0,828.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) -> .
% 0.19/0.47 874[5:Con:873.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.47 923[5:SpL:839.0,874.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 924[5:Obv:923.1] || -> .
% 0.19/0.47 925[4:Spt:924.0,24.0,434.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.47 926[4:Spt:924.0,24.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 927[4:MRR:9.0,925.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 928[4:MRR:19.0,925.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 929[4:MRR:4.0,925.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 931[4:SpR:926.0,472.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.47 943[4:SpR:927.0,472.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 946[4:Rew:931.0,943.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.47 948[4:Rew:946.0,928.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.19/0.47 949[4:Rew:946.0,931.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 954[4:Rew:929.0,948.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 957[4:Rew:954.0,424.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.47 961[4:Rew:954.0,429.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.47 964[4:Rew:28.0,957.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 965[4:Rew:964.0,460.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 966[4:Rew:964.0,162.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 967[4:Rew:964.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 969[4:Rew:949.0,965.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 970[4:Rew:969.0,927.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 971[4:Rew:969.0,929.0] || -> equal(multiply(sk_c1,sk_c1),sk_c6)**.
% 0.19/0.47 976[4:Rew:969.0,966.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.47 977[4:Rew:969.0,967.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.47 978[4:Rew:977.0,971.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 991[4:Rew:976.0,961.5,969.0,961.5,978.0,961.5,976.0,961.4,978.0,961.4,969.0,961.4,976.0,961.3,978.0,961.3,969.0,961.2,969.0,961.1,978.0,961.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) -> .
% 0.19/0.47 992[4:Con:991.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.47 1040[4:SpL:970.0,992.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 1041[4:Obv:1040.1] || -> .
% 0.19/0.47 1042[3:Spt:1041.0,12.1,426.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.47 1043[3:Spt:1041.0,12.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 1044[3:MRR:14.1,1042.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.47 1045[3:MRR:13.1,1042.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 1046[3:MRR:15.1,1042.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 1052[3:SpR:1044.0,472.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.47 1055[3:Rew:1052.0,424.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.47 1057[3:Rew:1046.0,1055.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1059[3:Rew:1057.0,418.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 1060[3:Rew:1057.0,1042.0] || equal(multiply(sk_c7,sk_c5),sk_c7)** -> .
% 0.19/0.47 1062[3:Rew:1057.0,1045.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 1084[3:SpR:1062.0,60.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.19/0.47 1086[3:Rew:1043.0,1084.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 1087[3:Rew:1059.0,1086.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 1088[3:Rew:1087.0,1059.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 1090[3:Rew:1087.0,1060.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.19/0.47 1093[3:Rew:1088.0,1090.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 1094[3:Obv:1093.0] || -> .
% 0.19/0.47 1098[2:Spt:1094.0,11.0,418.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.47 1099[2:Spt:1094.0,11.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 1100[2:MRR:21.1,1098.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 1101[2:MRR:6.1,1098.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 1102[2:MRR:16.0,1098.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.47 1103[2:MRR:1.0,1098.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 1108[2:SpR:1100.0,472.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.47 1113[2:SpR:1101.0,472.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 1116[2:Rew:1108.0,1113.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.47 1118[2:Rew:1116.0,1102.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.19/0.47 1123[2:Rew:1103.0,1118.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 1124[2:Rew:1123.0,1099.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.19/0.47 1125[2:Rew:1123.0,1098.0] || equal(multiply(sk_c6,sk_c7),sk_c6)** -> .
% 0.19/0.47 1131[2:SpR:1103.0,60.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 1133[2:Rew:1101.0,1131.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 1134[2:Rew:1124.0,1133.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1138[2:Rew:1134.0,1124.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 1139[2:Rew:1134.0,1125.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.19/0.47 1141[2:Rew:1138.0,1139.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 1142[2:Obv:1141.0] || -> .
% 0.19/0.47 % SZS output end Refutation
% 0.19/0.47 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_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 left_identity left_inverse associativity
% 0.19/0.47
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