TSTP Solution File: GRP259-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP259-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:46:34 EDT 2022
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP259-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 : Tue Jun 14 06:59:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 828 clauses, backtracked 410 clauses, performed 11 splits and kept 797 clauses.
% 0.18/0.47 SPASS allocated 63655 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.47 0:00:00.04 for the input.
% 0.18/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.00 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.06 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 5, length 338 :
% 0.18/0.47 % SZS output start Refutation
% 0.18/0.47 1[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.18/0.47 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 3[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.18/0.47 4[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.18/0.47 6[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.18/0.47 8[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7)** equal(inverse(sk_c1),sk_c8).
% 0.18/0.47 10[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 21[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 22[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 23[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.18/0.47 24[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 25[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.18/0.47 26[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 28[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 30[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 31[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 32[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 33[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 34[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 35[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 36[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(inverse(y),sk_c8) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(y,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.47 37[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.47 38[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.47 39[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.47 40[1:Spt:36.4,36.9] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.18/0.47 41[2:Spt:21.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 44[3:Spt:24.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 46[4:Spt:22.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.47 48[5:Spt:25.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 51[1:SpL:37.0,40.1] || equal(inverse(identity),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.18/0.47 52[6:Spt:23.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 55[3:SpR:44.0,38.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.18/0.47 56[4:SpR:46.0,38.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.18/0.47 57[1:SpL:38.0,40.1] || equal(inverse(inverse(sk_c8)),sk_c8)** equal(identity,sk_c7) -> .
% 0.18/0.47 63[5:SpR:48.0,39.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.18/0.47 65[0:SpR:38.0,39.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.47 67[3:SpR:55.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.18/0.47 68[4:SpR:56.0,39.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.18/0.47 70[3:Rew:37.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.18/0.47 71[4:Rew:37.0,68.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.18/0.47 72[0:Rew:37.0,65.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.47 76[5:SpR:48.0,70.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 82[6:SpR:52.0,71.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 86[6:SpL:82.0,40.1] || equal(inverse(sk_c8),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.47 87[6:Obv:86.1] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.18/0.47 89[0:SpR:72.0,72.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.47 91[2:SpR:41.0,72.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.18/0.47 94[0:SpR:38.0,72.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.47 96[3:SpR:55.0,72.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.18/0.47 98[5:SpR:76.0,72.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.47 99[4:SpR:56.0,72.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.18/0.47 101[6:SpR:82.0,72.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.18/0.47 107[5:Rew:91.0,98.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 110[5:Rew:107.0,44.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.18/0.47 113[5:Rew:107.0,55.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.18/0.47 119[5:Rew:107.0,96.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.18/0.47 120[5:Rew:107.0,51.1] || equal(inverse(identity),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.18/0.47 123[5:Rew:107.0,63.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 131[6:Rew:107.0,101.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.18/0.47 132[6:Rew:38.0,131.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 133[6:Rew:132.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 137[6:Rew:132.0,113.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.18/0.47 144[6:Rew:133.0,137.0] || -> equal(sk_c5,sk_c8)**.
% 0.18/0.47 145[6:Rew:144.0,110.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 147[6:MRR:145.0,87.0] || -> .
% 0.18/0.47 159[5:Obv:120.1] || equal(inverse(identity),sk_c8)** -> .
% 0.18/0.47 170[6:Spt:147.0,23.0,52.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.18/0.47 171[6:Spt:147.0,23.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 172[6:Rew:107.0,171.0] || -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.18/0.47 173[5:Rew:99.0,119.0] || -> equal(sk_c5,sk_c4)**.
% 0.18/0.47 177[6:Rew:107.0,170.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.18/0.47 178[0:Rew:89.0,94.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.47 179[4:Rew:178.0,99.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.18/0.47 185[5:Rew:107.0,33.1] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.18/0.47 186[6:MRR:185.1,177.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 193[5:Rew:173.0,123.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 194[5:Rew:107.0,28.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 195[6:MRR:194.0,177.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 206[4:SpR:179.0,72.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.18/0.47 219[6:SpR:195.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.47 221[6:Rew:186.0,219.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.18/0.47 222[6:Rew:172.0,221.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 230[6:Rew:222.0,193.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.18/0.47 236[6:Rew:206.0,230.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 243[6:Rew:236.0,56.0] || -> equal(identity,sk_c4)**.
% 0.18/0.47 246[6:Rew:243.0,159.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.18/0.47 253[6:Rew:46.0,246.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 254[6:Obv:253.0] || -> .
% 0.18/0.47 256[5:Spt:254.0,25.0,48.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.18/0.47 257[5:Spt:254.0,25.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 258[3:Rew:178.0,96.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.18/0.47 259[3:Rew:258.0,91.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.18/0.47 260[5:Rew:259.0,256.0] || equal(sk_c7,sk_c8)** -> .
% 0.18/0.47 262[3:Rew:259.0,35.1] || -> equal(inverse(sk_c3),sk_c6)** equal(sk_c7,sk_c8).
% 0.18/0.47 263[5:MRR:262.1,260.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 266[3:Rew:259.0,10.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c8).
% 0.18/0.47 267[5:MRR:266.1,260.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 269[3:Rew:259.0,30.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 270[5:MRR:269.0,260.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 273[3:Rew:259.0,5.0] || -> equal(sk_c7,sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 274[5:MRR:273.0,260.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 282[3:SpR:258.0,72.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.18/0.47 288[5:SpR:267.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.18/0.47 301[5:SpR:270.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.47 303[5:Rew:257.0,301.0,263.0,301.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 308[5:Rew:303.0,259.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.18/0.47 321[5:SpR:274.0,39.0] || -> equal(multiply(sk_c1,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.18/0.47 333[5:SpR:308.0,39.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.18/0.47 337[5:Rew:282.0,333.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 338[5:Rew:337.0,56.0] || -> equal(identity,sk_c4)**.
% 0.18/0.47 340[5:Rew:337.0,206.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.18/0.47 343[5:Rew:337.0,321.0] || -> equal(multiply(sk_c7,u),multiply(sk_c1,u))**.
% 0.18/0.47 344[5:Rew:337.0,288.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 347[5:Rew:338.0,55.0] || -> equal(multiply(sk_c7,sk_c5),sk_c4)**.
% 0.18/0.47 356[5:Rew:344.0,343.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.47 358[5:Rew:356.0,347.0] || -> equal(sk_c5,sk_c4)**.
% 0.18/0.47 368[5:Rew:358.0,308.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 375[5:Rew:340.0,368.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 376[5:MRR:375.0,260.0] || -> .
% 0.18/0.47 377[4:Spt:376.0,22.0,46.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.18/0.47 378[4:Spt:376.0,22.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 379[4:MRR:32.0,377.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 381[4:MRR:7.0,377.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 382[4:MRR:27.0,377.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 384[4:MRR:2.0,377.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 396[4:SpR:381.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.18/0.47 398[3:SpR:259.0,39.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.18/0.47 412[4:SpR:382.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.47 414[4:Rew:378.0,412.0,379.0,412.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 422[4:Rew:414.0,398.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.18/0.47 430[4:Rew:282.0,422.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 433[4:Rew:430.0,396.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 434[4:Rew:433.0,384.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 436[4:Rew:434.0,44.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.18/0.47 438[4:Rew:434.0,55.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.18/0.47 441[4:Rew:434.0,51.1] || equal(inverse(identity),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.18/0.47 453[4:Rew:430.0,438.0] || -> equal(identity,sk_c5)**.
% 0.18/0.47 465[4:Obv:441.1] || equal(inverse(identity),sk_c8)** -> .
% 0.18/0.47 466[4:Rew:436.0,465.0,453.0,465.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 467[4:Obv:466.0] || -> .
% 0.18/0.47 470[3:Spt:467.0,24.0,44.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.18/0.47 471[3:Spt:467.0,24.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 472[3:MRR:34.0,470.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 474[3:MRR:9.0,470.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 475[3:MRR:29.0,470.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 477[3:MRR:4.0,470.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 479[3:SpR:471.0,72.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.18/0.47 491[3:SpR:475.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.47 493[3:Rew:471.0,491.0,472.0,491.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 498[3:Rew:493.0,91.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.47 502[3:Rew:493.0,479.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.47 505[3:Rew:38.0,498.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 506[3:Rew:505.0,178.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 507[3:Rew:505.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 511[3:Rew:505.0,57.1] || equal(inverse(inverse(sk_c8)),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.18/0.47 514[3:Rew:506.0,477.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.47 523[3:Rew:514.0,502.0] || -> equal(multiply(inverse(sk_c1),sk_c1),sk_c8)**.
% 0.18/0.47 524[3:Rew:474.0,523.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.18/0.47 525[3:Rew:507.0,524.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.47 526[3:Rew:525.0,474.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.47 548[3:Rew:514.0,511.1,525.0,511.1,526.0,511.0,526.0,511.0,525.0,511.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.47 549[3:Obv:548.1] || -> .
% 0.18/0.47 551[2:Spt:549.0,21.0,41.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.18/0.47 552[2:Spt:549.0,21.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 553[2:MRR:31.1,551.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 555[2:MRR:6.1,551.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 556[2:MRR:26.0,551.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 558[2:MRR:1.0,551.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 560[2:SpR:552.0,72.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.18/0.47 562[2:SpR:553.0,72.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.18/0.47 566[2:SpR:555.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.18/0.47 569[2:SpR:556.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.47 571[2:Rew:552.0,569.0,553.0,569.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 574[2:Rew:571.0,556.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.18/0.47 577[2:Rew:571.0,560.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.47 579[2:Rew:571.0,562.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.18/0.47 582[2:Rew:38.0,577.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 583[2:Rew:582.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 584[2:Rew:582.0,178.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 588[2:Rew:582.0,57.1] || equal(inverse(inverse(sk_c8)),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.18/0.47 589[2:Rew:583.0,566.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 592[2:Rew:584.0,558.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.47 597[2:Rew:592.0,574.0] || -> equal(multiply(sk_c3,sk_c1),sk_c8)**.
% 0.18/0.47 599[2:Rew:589.0,579.0,592.0,579.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.18/0.47 600[2:Rew:599.0,597.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.47 601[2:Rew:600.0,555.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.47 616[2:Rew:592.0,588.1,600.0,588.1,601.0,588.0,601.0,588.0,600.0,588.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.47 617[2:Obv:616.1] || -> .
% 0.18/0.47 619[1:Spt:617.0,36.0,36.1,36.2,36.3,36.5,36.6,36.7,36.8,36.10,36.11] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.47 621[2:Spt:21.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.18/0.47 622[2:Rew:621.0,619.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** equal(sk_c6,sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.47 624[2:Obv:622.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.47 627[2:SpR:621.0,72.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.18/0.47 629[3:Spt:22.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.47 630[3:SpR:629.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.18/0.47 632[4:Spt:24.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.18/0.47 635[5:Spt:23.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.47 637[5:SpR:635.0,72.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.18/0.47 639[5:Rew:629.0,637.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.18/0.47 640[6:Spt:25.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.18/0.47 642[6:SpR:640.0,72.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.18/0.47 644[6:Rew:632.0,642.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.18/0.47 649[6:SpR:644.0,72.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.18/0.47 651[6:Rew:627.0,649.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 652[6:Rew:651.0,621.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.18/0.47 653[6:Rew:651.0,632.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.18/0.47 655[6:Rew:651.0,640.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.18/0.47 656[6:Rew:651.0,639.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.18/0.47 659[6:Rew:651.0,624.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c8)** -> .
% 0.18/0.47 660[6:Rew:651.0,627.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.18/0.47 667[6:Rew:652.0,656.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.47 669[6:Rew:667.0,655.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.18/0.47 671[6:Rew:38.0,660.0,667.0,660.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 672[6:Rew:671.0,178.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 676[6:Rew:672.0,669.0] || -> equal(sk_c5,sk_c8)**.
% 0.18/0.47 678[6:Rew:676.0,653.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.47 689[6:Rew:667.0,659.8,672.0,659.8,672.0,659.7,651.0,659.7,667.0,659.7,672.0,659.6,667.0,659.6,672.0,659.5,651.0,659.5,672.0,659.4,667.0,659.4,651.0,659.4,651.0,659.3,667.0,659.2,651.0,659.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(inverse(x),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) equal(x,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.18/0.47 690[6:Obv:689.8] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(inverse(x),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) equal(x,sk_c8) -> .
% 0.18/0.47 691[6:Con:690.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.47 727[6:SpL:678.0,691.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.47 729[6:Obv:727.1] || -> .
% 0.18/0.47 730[6:Spt:729.0,25.0,640.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.18/0.47 731[6:Spt:729.0,25.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 732[6:MRR:35.1,730.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 734[6:MRR:10.1,730.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 735[6:MRR:30.0,730.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 753[6:SpR:734.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.18/0.47 766[6:SpR:735.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.47 768[6:Rew:731.0,766.0,732.0,766.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 773[6:Rew:768.0,627.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.47 774[6:Rew:768.0,730.0] || equal(multiply(sk_c5,sk_c7),sk_c7)** -> .
% 0.18/0.47 782[6:Rew:38.0,773.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 783[6:Rew:782.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 784[6:Rew:782.0,178.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 786[6:Rew:782.0,38.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.47 787[6:Rew:783.0,639.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.47 788[6:Rew:783.0,753.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.18/0.47 792[6:Rew:787.0,632.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.18/0.47 808[6:Rew:784.0,774.0,787.0,774.0] || equal(sk_c5,sk_c8)** -> .
% 0.18/0.47 850[6:SpR:734.0,786.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.18/0.47 852[6:SpR:792.0,786.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.18/0.47 856[6:Rew:783.0,850.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.47 865[6:Rew:856.0,808.0] || equal(sk_c5,sk_c1)** -> .
% 0.18/0.47 872[6:Rew:788.0,852.0,856.0,852.0] || -> equal(sk_c5,sk_c1)**.
% 0.18/0.47 873[6:MRR:872.0,865.0] || -> .
% 0.18/0.47 879[5:Spt:873.0,23.0,635.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.18/0.47 880[5:Spt:873.0,23.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 881[5:MRR:33.1,879.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 883[5:MRR:8.1,879.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 884[5:MRR:28.0,879.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 886[5:MRR:3.0,879.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 892[5:SpR:880.0,72.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.18/0.47 908[5:SpR:884.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.47 910[5:Rew:880.0,908.0,881.0,908.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 915[5:Rew:910.0,627.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.47 920[5:Rew:910.0,892.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.47 923[5:Rew:38.0,915.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 924[5:Rew:923.0,178.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 925[5:Rew:923.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 928[5:Rew:924.0,886.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.47 931[5:Rew:928.0,879.0] || equal(multiply(sk_c4,sk_c1),sk_c8)** -> .
% 0.18/0.47 939[5:Rew:925.0,630.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.18/0.47 940[5:Rew:928.0,920.0] || -> equal(multiply(inverse(sk_c1),sk_c1),sk_c8)**.
% 0.18/0.47 941[5:Rew:883.0,940.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.18/0.47 942[5:Rew:925.0,941.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.47 955[5:Rew:939.0,931.0,942.0,931.0] || equal(sk_c1,sk_c1)* -> .
% 0.18/0.47 956[5:Obv:955.0] || -> .
% 0.18/0.47 967[4:Spt:956.0,24.0,632.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.18/0.47 968[4:Spt:956.0,24.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 969[4:MRR:34.0,967.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 971[4:MRR:9.0,967.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 972[4:MRR:29.0,967.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 974[4:MRR:4.0,967.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 975[4:Rew:968.0,624.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.18/0.47 976[4:Obv:975.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** -> .
% 0.18/0.47 980[4:SpR:968.0,72.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.18/0.47 994[4:SpR:972.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.47 996[4:Rew:968.0,994.0,969.0,994.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.47 1001[4:Rew:996.0,627.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.47 1004[4:Rew:996.0,976.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** -> .
% 0.18/0.47 1006[4:Rew:996.0,980.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.47 1009[4:Rew:38.0,1001.0] || -> equal(identity,sk_c8)**.
% 0.18/0.47 1010[4:Rew:1009.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.47 1011[4:Rew:1009.0,178.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.47 1016[4:Rew:1011.0,974.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.47 1020[4:Rew:1016.0,996.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.47 1024[4:Rew:1016.0,1006.0] || -> equal(multiply(inverse(sk_c1),sk_c1),sk_c8)**.
% 0.18/0.47 1025[4:Rew:971.0,1024.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.18/0.47 1026[4:Rew:1010.0,1025.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.47 1028[4:Rew:1026.0,971.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.47 1031[4:Rew:1026.0,1011.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.47 1044[4:Rew:1031.0,1004.7,1016.0,1004.7,1020.0,1004.7,1031.0,1004.6,1020.0,1004.6,1026.0,1004.6,1031.0,1004.5,1016.0,1004.5,1026.0,1004.5,1031.0,1004.4,1020.0,1004.4,1016.0,1004.4,1016.0,1004.3,1016.0,1004.2,1026.0,1004.1,1016.0,1004.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(inverse(x),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) equal(x,sk_c1) -> .
% 0.18/0.47 1045[4:Con:1044.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.18/0.47 1083[4:SpL:1028.0,1045.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.47 1084[4:Obv:1083.1] || -> .
% 0.18/0.47 1085[3:Spt:1084.0,22.0,629.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.18/0.47 1086[3:Spt:1084.0,22.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.47 1087[3:MRR:32.0,1085.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.47 1089[3:MRR:7.0,1085.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.47 1090[3:MRR:27.0,1085.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.47 1092[3:MRR:2.0,1085.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.47 1093[3:Rew:1086.0,624.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.18/0.47 1094[3:Obv:1093.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** -> .
% 0.18/0.47 1098[3:SpR:1086.0,72.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.18/0.47 1110[3:SpR:1090.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.48 1112[3:Rew:1086.0,1110.0,1087.0,1110.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.48 1117[3:Rew:1112.0,627.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.48 1120[3:Rew:1112.0,1094.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(x,sk_c7),sk_c6)** -> .
% 0.18/0.48 1122[3:Rew:1112.0,1098.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.18/0.48 1125[3:Rew:38.0,1117.0] || -> equal(identity,sk_c8)**.
% 0.18/0.48 1126[3:Rew:1125.0,178.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.48 1127[3:Rew:1125.0,37.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.48 1130[3:Rew:1126.0,1092.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.48 1133[3:Rew:1130.0,1112.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.48 1138[3:Rew:1130.0,1122.0] || -> equal(multiply(inverse(sk_c1),sk_c1),sk_c8)**.
% 0.18/0.48 1139[3:Rew:1089.0,1138.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.18/0.48 1140[3:Rew:1127.0,1139.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.48 1141[3:Rew:1140.0,1089.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.48 1144[3:Rew:1140.0,1126.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.48 1158[3:Rew:1144.0,1120.7,1130.0,1120.7,1133.0,1120.7,1144.0,1120.6,1133.0,1120.6,1140.0,1120.6,1144.0,1120.5,1130.0,1120.5,1140.0,1120.5,1144.0,1120.4,1133.0,1120.4,1130.0,1120.4,1130.0,1120.3,1130.0,1120.2,1140.0,1120.1,1130.0,1120.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(inverse(x),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) equal(x,sk_c1) -> .
% 0.18/0.48 1159[3:Con:1158.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.18/0.48 1220[3:SpL:1141.0,1159.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.48 1222[3:Obv:1220.1] || -> .
% 0.18/0.48 1223[2:Spt:1222.0,21.0,621.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.18/0.48 1224[2:Spt:1222.0,21.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.48 1225[2:MRR:31.1,1223.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.18/0.48 1228[2:MRR:26.0,1223.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.18/0.48 1241[2:SpR:1228.0,72.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.18/0.48 1243[2:Rew:1224.0,1241.0,1225.0,1241.0] || -> equal(sk_c6,sk_c7)**.
% 0.18/0.48 1244[2:Rew:1243.0,1224.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.18/0.48 1247[2:Rew:1243.0,1223.0] || equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.18/0.48 1252[2:Rew:1244.0,1247.0] || equal(sk_c7,sk_c7)* -> .
% 0.18/0.48 1253[2:Obv:1252.0] || -> .
% 0.18/0.48 % SZS output end Refutation
% 0.18/0.48 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_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 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 left_identity left_inverse associativity
% 0.18/0.48
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