TSTP Solution File: GRP290-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP290-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:46:42 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP290-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 07:30:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.49
% 0.21/0.49 SPASS V 3.9
% 0.21/0.49 SPASS beiseite: Proof found.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 SPASS derived 843 clauses, backtracked 335 clauses, performed 12 splits and kept 713 clauses.
% 0.21/0.49 SPASS allocated 63636 KBytes.
% 0.21/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.49 0:00:00.04 for the input.
% 0.21/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.49 0:00:00.00 for inferences.
% 0.21/0.49 0:00:00.00 for the backtracking.
% 0.21/0.49 0:00:00.06 for the reduction.
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 Here is a proof with depth 4, length 364 :
% 0.21/0.49 % SZS output start Refutation
% 0.21/0.49 1[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.21/0.49 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.21/0.49 6[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.21/0.49 7[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 8[0:Inp] || -> equal(multiply(sk_c8,sk_c4),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 9[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 10[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 11[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 12[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.49 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 15[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 16[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.49 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 18[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.49 19[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 20[0:Inp] || -> equal(multiply(sk_c8,sk_c4),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 21[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c4) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 22[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 23[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 24[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 25[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.49 26[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 27[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 28[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.49 29[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 30[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.49 31[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(v,sk_c8),y)*+ equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.21/0.49 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.49 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.49 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.49 35[1:Spt:31.3,31.7] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.21/0.49 38[2:Spt:25.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.49 40[3:Spt:13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.49 43[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.21/0.49 44[4:Spt:19.1] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 46[5:Spt:7.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 48[5:SpL:46.0,35.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.21/0.49 49[5:Obv:48.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.21/0.49 50[5:Rew:40.0,49.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 51[5:Obv:50.0] || -> .
% 0.21/0.49 52[5:Spt:51.0,7.1,46.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.21/0.49 53[5:Spt:51.0,7.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.49 54[5:MRR:12.1,52.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 55[5:MRR:10.1,52.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 56[5:MRR:11.1,52.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 57[5:MRR:9.1,52.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 58[5:MRR:8.1,52.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 66[5:SpL:57.0,35.1] || equal(inverse(sk_c3),sk_c8)** equal(sk_c4,sk_c7) -> .
% 0.21/0.49 67[5:Rew:55.0,66.0] || equal(sk_c8,sk_c8) equal(sk_c4,sk_c7)** -> .
% 0.21/0.49 68[5:Obv:67.0] || equal(sk_c4,sk_c7)** -> .
% 0.21/0.49 71[2:SpR:38.0,33.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.21/0.49 72[3:SpR:40.0,33.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.21/0.49 73[5:SpR:54.0,33.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.21/0.49 74[5:SpR:55.0,33.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.21/0.49 75[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c8)),sk_c8)** equal(identity,sk_c7) -> .
% 0.21/0.49 83[5:SpR:57.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),multiply(sk_c4,u))**.
% 0.21/0.49 85[4:SpR:44.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.21/0.49 87[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.49 91[5:SpR:74.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.21/0.49 93[5:SpR:73.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.21/0.49 96[5:Rew:32.0,91.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.21/0.49 98[5:Rew:32.0,93.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.21/0.49 99[0:Rew:32.0,87.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.49 106[5:SpR:57.0,96.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.21/0.49 107[5:Rew:58.0,106.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 112[5:Rew:107.0,53.0] || -> equal(multiply(sk_c6,sk_c8),sk_c8)**.
% 0.21/0.49 113[5:Rew:107.0,68.0] || equal(sk_c4,sk_c8)** -> .
% 0.21/0.49 114[5:Rew:107.0,58.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.21/0.49 116[5:Rew:107.0,71.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.21/0.49 121[5:Rew:107.0,85.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.21/0.49 143[5:SpR:56.0,98.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.21/0.49 144[5:Rew:112.0,143.0] || -> equal(sk_c6,sk_c8)**.
% 0.21/0.49 148[5:Rew:144.0,73.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.49 155[5:Rew:144.0,121.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.21/0.49 180[0:SpR:99.0,99.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.49 186[0:SpR:33.0,99.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.49 187[3:SpR:72.0,99.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.21/0.49 188[5:SpR:74.0,99.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.21/0.49 193[5:SpR:114.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c4)**.
% 0.21/0.49 194[5:SpR:116.0,99.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.21/0.49 195[5:SpR:148.0,99.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.21/0.49 205[5:Rew:187.0,188.0] || -> equal(sk_c1,sk_c3)**.
% 0.21/0.49 210[5:Rew:205.0,187.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.21/0.49 211[5:Rew:33.0,193.0] || -> equal(identity,sk_c4)**.
% 0.21/0.49 212[5:Rew:211.0,32.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.21/0.49 214[5:Rew:211.0,74.0] || -> equal(multiply(sk_c8,sk_c3),sk_c4)**.
% 0.21/0.49 220[5:Rew:212.0,83.0] || -> equal(multiply(sk_c3,multiply(sk_c8,u)),u)**.
% 0.21/0.49 222[5:Rew:211.0,194.0] || -> equal(multiply(inverse(sk_c8),sk_c4),sk_c2)**.
% 0.21/0.49 223[5:Rew:222.0,195.0,211.0,195.0] || -> equal(sk_c2,sk_c5)**.
% 0.21/0.49 227[5:Rew:223.0,155.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.21/0.49 229[5:Rew:223.0,222.0] || -> equal(multiply(inverse(sk_c8),sk_c4),sk_c5)**.
% 0.21/0.49 231[5:Rew:211.0,210.0] || -> equal(multiply(inverse(sk_c8),sk_c4),sk_c3)**.
% 0.21/0.49 234[5:Rew:231.0,229.0] || -> equal(sk_c5,sk_c3)**.
% 0.21/0.49 253[5:Rew:220.0,227.0,234.0,227.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 255[5:Rew:253.0,214.0] || -> equal(sk_c3,sk_c4)**.
% 0.21/0.49 258[5:Rew:255.0,57.0] || -> equal(multiply(sk_c4,sk_c8),sk_c4)**.
% 0.21/0.49 266[5:Rew:212.0,258.0] || -> equal(sk_c4,sk_c8)**.
% 0.21/0.49 267[5:MRR:266.0,113.0] || -> .
% 0.21/0.49 271[4:Spt:267.0,19.1,44.0] || equal(multiply(sk_c2,sk_c7),sk_c6)** -> .
% 0.21/0.49 272[4:Spt:267.0,19.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.49 273[0:Rew:180.0,186.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.49 274[3:Rew:273.0,187.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.21/0.49 276[4:MRR:24.1,271.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 277[4:MRR:22.1,271.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 278[3:Rew:40.0,75.0,274.0,75.0] || equal(sk_c8,sk_c8) equal(identity,sk_c7)** -> .
% 0.21/0.49 279[3:Obv:278.0] || equal(identity,sk_c7)** -> .
% 0.21/0.49 280[4:MRR:23.1,271.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 281[4:MRR:21.1,271.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 282[4:MRR:20.1,271.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 284[4:SpR:272.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.21/0.49 294[4:SpR:277.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.21/0.49 297[4:SpR:280.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.21/0.49 299[4:Rew:272.0,297.0,276.0,297.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 306[4:Rew:299.0,284.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.49 309[4:Rew:33.0,306.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 310[4:Rew:309.0,279.0] || equal(sk_c7,sk_c8)** -> .
% 0.21/0.49 313[4:Rew:309.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 318[4:Rew:313.0,294.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.49 321[4:Rew:313.0,282.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.49 325[4:Rew:321.0,281.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.21/0.49 330[4:Rew:318.0,325.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 331[4:MRR:330.0,310.0] || -> .
% 0.21/0.49 335[3:Spt:331.0,13.0,40.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.21/0.49 336[3:Spt:331.0,13.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.49 337[3:MRR:18.1,335.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 338[3:MRR:16.1,335.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 339[3:MRR:17.0,335.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 340[3:MRR:15.0,335.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 341[3:MRR:14.0,335.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 343[3:SpR:336.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.21/0.49 353[2:SpR:71.0,99.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c2)**.
% 0.21/0.49 355[2:Rew:273.0,353.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.21/0.49 357[2:SpR:355.0,99.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),u)**.
% 0.21/0.49 360[3:SpR:339.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.21/0.49 362[3:Rew:336.0,360.0,337.0,360.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 368[3:Rew:362.0,343.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.49 372[3:Rew:355.0,368.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.21/0.49 378[3:SpR:340.0,99.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c8)**.
% 0.21/0.49 380[3:Rew:338.0,378.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.21/0.49 381[3:Rew:341.0,380.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 382[3:Rew:381.0,38.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 383[3:Rew:381.0,71.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.21/0.49 388[3:Rew:381.0,357.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),u)**.
% 0.21/0.49 391[3:Rew:381.0,43.1] || equal(inverse(identity),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.21/0.49 399[3:Rew:381.0,372.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.21/0.49 404[3:Obv:391.1] || equal(inverse(identity),sk_c8)** -> .
% 0.21/0.49 438[3:SpR:399.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.21/0.49 442[3:Rew:388.0,438.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 443[3:Rew:442.0,383.0] || -> equal(identity,sk_c2)**.
% 0.21/0.49 454[3:Rew:443.0,404.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.21/0.49 456[3:Rew:382.0,454.0] || equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 457[3:Obv:456.0] || -> .
% 0.21/0.49 459[2:Spt:457.0,25.0,38.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.21/0.49 460[2:Spt:457.0,25.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.49 461[2:MRR:30.1,459.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 462[2:MRR:28.1,459.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 463[2:MRR:29.0,459.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 464[2:MRR:27.0,459.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 465[2:MRR:26.0,459.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 467[2:SpR:460.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.21/0.49 471[2:SpR:462.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.21/0.49 477[2:SpR:463.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.21/0.49 479[2:Rew:460.0,477.0,461.0,477.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 481[2:Rew:479.0,461.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.21/0.49 483[2:Rew:479.0,463.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.21/0.49 486[2:Rew:479.0,467.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.49 489[2:Rew:33.0,486.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 490[2:Rew:489.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 491[2:Rew:489.0,273.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 495[2:Rew:489.0,75.1] || equal(inverse(inverse(sk_c8)),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.21/0.49 496[2:Rew:490.0,465.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.49 497[2:Rew:490.0,471.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.49 498[2:Rew:496.0,464.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.21/0.49 501[2:Rew:497.0,498.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 504[2:Rew:501.0,481.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.49 505[2:Rew:501.0,483.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.21/0.49 508[2:Rew:491.0,505.0] || -> equal(sk_c5,sk_c8)**.
% 0.21/0.49 509[2:Rew:508.0,504.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 517[2:Rew:501.0,495.1,509.0,495.0,509.0,495.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 518[2:Obv:517.1] || -> .
% 0.21/0.49 520[1:Spt:518.0,31.0,31.1,31.2,31.4,31.5,31.6,31.8,31.9,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(v,sk_c8),x)*+ equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,x),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.21/0.49 521[1:EqR:520.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.21/0.49 523[2:Spt:1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.21/0.49 526[2:Rew:523.0,521.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7) equal(sk_c6,sk_c6) -> .
% 0.21/0.49 527[2:Obv:526.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7) -> .
% 0.21/0.49 531[2:SpR:523.0,99.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.21/0.49 533[3:Spt:13.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.49 536[3:Rew:533.0,527.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.21/0.49 537[3:Obv:536.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.21/0.49 541[3:SpR:533.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.21/0.49 543[4:Spt:30.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.49 546[5:Spt:18.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.49 547[5:SpR:546.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.21/0.49 555[6:Spt:24.1] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 557[6:SpR:555.0,99.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.21/0.49 559[6:Rew:543.0,557.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.49 560[7:Spt:12.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 562[7:SpR:560.0,99.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.21/0.49 564[7:Rew:523.0,562.0,546.0,562.0] || -> equal(sk_c6,sk_c8)**.
% 0.21/0.49 567[7:Rew:564.0,555.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.21/0.49 568[7:Rew:564.0,531.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.21/0.49 573[7:Rew:564.0,537.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.21/0.49 576[7:Rew:564.0,559.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.21/0.49 577[7:Rew:33.0,568.0] || -> equal(identity,sk_c7)**.
% 0.21/0.49 578[7:Rew:577.0,273.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.49 579[7:Rew:577.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.49 582[7:Rew:578.0,567.0] || -> equal(sk_c2,sk_c8)**.
% 0.21/0.49 583[7:Rew:582.0,543.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.49 585[7:Rew:579.0,576.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 589[7:Rew:585.0,578.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 590[7:Rew:585.0,583.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 591[7:Rew:585.0,579.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 604[7:Rew:589.0,573.5,591.0,573.5,585.0,573.5,589.0,573.4,585.0,573.4,564.0,573.4,589.0,573.3,564.0,573.3,585.0,573.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(w,sk_c8) equal(v,sk_c8) -> .
% 0.21/0.49 605[7:Con:604.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.49 650[7:SpL:590.0,605.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 652[7:Obv:650.1] || -> .
% 0.21/0.49 653[7:Spt:652.0,12.1,560.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.21/0.49 654[7:Spt:652.0,12.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 655[7:MRR:10.1,653.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 656[7:MRR:11.1,653.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 657[7:MRR:9.1,653.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 658[7:MRR:8.1,653.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 659[7:SpR:654.0,99.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.21/0.49 665[7:SpR:655.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.21/0.49 672[7:SpR:656.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.21/0.49 674[7:Rew:654.0,672.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.21/0.49 675[7:Rew:533.0,674.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 678[7:Rew:675.0,656.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.21/0.49 682[7:Rew:675.0,541.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.49 690[7:Rew:675.0,659.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.21/0.49 691[7:Rew:33.0,682.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 692[7:Rew:691.0,273.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 693[7:Rew:691.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 696[7:Rew:692.0,657.0] || -> equal(sk_c3,sk_c4)**.
% 0.21/0.49 697[7:Rew:692.0,653.0] || equal(sk_c1,sk_c7)** -> .
% 0.21/0.49 699[7:Rew:696.0,665.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.21/0.49 700[7:Rew:693.0,658.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.49 701[7:Rew:693.0,547.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 704[7:Rew:693.0,699.0,700.0,699.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.49 705[7:Rew:704.0,690.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.49 707[7:Rew:705.0,678.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 712[7:Rew:707.0,697.0] || equal(sk_c1,sk_c8)** -> .
% 0.21/0.49 753[7:SpR:701.0,692.0] || -> equal(sk_c1,sk_c8)**.
% 0.21/0.49 755[7:MRR:753.0,712.0] || -> .
% 0.21/0.49 757[6:Spt:755.0,24.1,555.0] || equal(multiply(sk_c2,sk_c7),sk_c6)** -> .
% 0.21/0.49 758[6:Spt:755.0,24.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 759[6:MRR:22.1,757.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 760[6:MRR:23.1,757.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 761[6:MRR:21.1,757.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 762[6:MRR:20.1,757.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 767[6:SpR:759.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.21/0.49 770[6:SpR:760.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.21/0.49 772[6:Rew:758.0,770.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.21/0.49 773[6:Rew:533.0,772.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 779[6:Rew:773.0,541.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.49 780[6:Rew:773.0,757.0] || equal(multiply(sk_c2,sk_c7),sk_c7)** -> .
% 0.21/0.49 787[6:Rew:33.0,779.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 788[6:Rew:787.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 789[6:Rew:787.0,273.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 791[6:Rew:787.0,33.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.21/0.49 792[6:Rew:788.0,767.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.49 793[6:Rew:788.0,762.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.49 795[6:Rew:793.0,761.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.21/0.49 796[6:Rew:792.0,795.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 797[6:Rew:796.0,543.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.49 806[6:Rew:789.0,780.0,796.0,780.0] || equal(sk_c2,sk_c8)** -> .
% 0.21/0.49 838[6:SpR:797.0,791.0] || -> equal(multiply(sk_c8,sk_c2),sk_c8)**.
% 0.21/0.49 846[6:Rew:788.0,838.0] || -> equal(sk_c2,sk_c8)**.
% 0.21/0.49 847[6:MRR:846.0,806.0] || -> .
% 0.21/0.49 851[5:Spt:847.0,18.1,546.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.21/0.49 852[5:Spt:847.0,18.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 853[5:MRR:16.1,851.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 854[5:MRR:17.0,851.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 855[5:MRR:15.0,851.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 856[5:MRR:14.0,851.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 857[5:SpR:852.0,99.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.21/0.49 861[5:SpR:853.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.21/0.49 870[5:SpR:854.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.21/0.49 872[5:Rew:533.0,870.0,852.0,870.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 876[5:Rew:872.0,854.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.21/0.49 877[5:Rew:872.0,541.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.49 883[5:Rew:872.0,537.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.21/0.49 884[5:Rew:872.0,857.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.21/0.49 885[5:Rew:33.0,877.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 886[5:Rew:885.0,273.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 887[5:Rew:885.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 890[5:Rew:886.0,855.0] || -> equal(sk_c3,sk_c4)**.
% 0.21/0.49 891[5:Rew:890.0,853.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.21/0.49 892[5:Rew:890.0,861.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.21/0.49 893[5:Rew:887.0,856.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.49 895[5:Rew:893.0,891.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.21/0.49 896[5:Rew:887.0,892.0,893.0,892.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.49 897[5:Rew:896.0,884.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.49 899[5:Rew:897.0,876.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 901[5:Rew:899.0,872.0] || -> equal(sk_c6,sk_c8)**.
% 0.21/0.49 905[5:Rew:899.0,895.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 910[5:Rew:886.0,883.5,887.0,883.5,899.0,883.5,886.0,883.4,899.0,883.4,901.0,883.4,886.0,883.3,901.0,883.3,899.0,883.2,899.0,883.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(w,sk_c8) equal(v,sk_c8) -> .
% 0.21/0.49 911[5:Con:910.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.49 999[5:SpL:905.0,911.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 1001[5:Obv:999.1] || -> .
% 0.21/0.49 1002[4:Spt:1001.0,30.1,543.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.21/0.49 1003[4:Spt:1001.0,30.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 1004[4:MRR:28.1,1002.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.21/0.49 1005[4:MRR:29.0,1002.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 1006[4:MRR:27.0,1002.0] || -> equal(multiply(sk_c3,sk_c8),sk_c4)**.
% 0.21/0.49 1007[4:MRR:26.0,1002.0] || -> equal(multiply(sk_c8,sk_c4),sk_c7)**.
% 0.21/0.49 1010[4:SpR:1004.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.21/0.49 1019[4:SpR:1005.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.21/0.49 1021[4:Rew:533.0,1019.0,1003.0,1019.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 1022[4:Rew:1021.0,1003.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.21/0.49 1025[4:Rew:1021.0,1005.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.21/0.49 1027[4:Rew:1021.0,541.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.49 1032[4:Rew:1021.0,537.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c8)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.21/0.49 1034[4:Rew:33.0,1027.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 1035[4:Rew:1034.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 1036[4:Rew:1034.0,273.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.49 1039[4:Rew:1035.0,1010.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.49 1040[4:Rew:1035.0,1007.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.49 1041[4:Rew:1040.0,1006.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.21/0.49 1042[4:Rew:1039.0,1041.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 1044[4:Rew:1042.0,1021.0] || -> equal(sk_c6,sk_c8)**.
% 0.21/0.49 1045[4:Rew:1042.0,1022.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.49 1046[4:Rew:1042.0,1025.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.21/0.49 1049[4:Rew:1036.0,1046.0] || -> equal(sk_c5,sk_c8)**.
% 0.21/0.49 1050[4:Rew:1049.0,1045.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.21/0.49 1055[4:Rew:1036.0,1032.5,1035.0,1032.5,1042.0,1032.5,1036.0,1032.4,1042.0,1032.4,1044.0,1032.4,1036.0,1032.3,1044.0,1032.3,1042.0,1032.2,1042.0,1032.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(w,sk_c8) equal(v,sk_c8) -> .
% 0.21/0.49 1056[4:Con:1055.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.21/0.49 1123[4:SpL:1050.0,1056.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.21/0.49 1125[4:Obv:1123.1] || -> .
% 0.21/0.49 1126[3:Spt:1125.0,13.1,533.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.21/0.49 1127[3:Spt:1125.0,13.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.49 1128[3:MRR:25.1,1126.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.49 1129[3:MRR:7.0,1126.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.49 1130[3:MRR:19.0,1126.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.21/0.49 1131[3:SpR:1127.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.21/0.49 1133[3:SpR:1128.0,99.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.21/0.49 1139[3:SpR:1129.0,99.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.21/0.49 1141[3:Rew:523.0,1139.0,1127.0,1139.0] || -> equal(sk_c6,sk_c8)**.
% 0.21/0.49 1143[3:Rew:1141.0,531.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.21/0.49 1144[3:Rew:1141.0,1126.0] || equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.21/0.49 1146[3:Rew:1141.0,1130.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.21/0.49 1147[3:Rew:33.0,1143.0] || -> equal(identity,sk_c7)**.
% 0.21/0.49 1148[3:Rew:1147.0,273.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.49 1149[3:Rew:1147.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.49 1152[3:Rew:1148.0,1146.0] || -> equal(sk_c2,sk_c8)**.
% 0.21/0.49 1154[3:Rew:1152.0,1133.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.21/0.49 1155[3:Rew:1149.0,1154.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 1156[3:Rew:1155.0,1144.0] || equal(sk_c7,sk_c8)** -> .
% 0.21/0.49 1157[3:Rew:1155.0,1131.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 1158[3:Rew:1157.0,1129.0] || -> equal(sk_c7,sk_c8)**.
% 0.21/0.49 1159[3:MRR:1158.0,1156.0] || -> .
% 0.21/0.49 1162[2:Spt:1159.0,1.1,523.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.21/0.49 1163[2:Spt:1159.0,1.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.21/0.49 1164[2:MRR:6.1,1162.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.21/0.49 1166[2:MRR:5.1,1162.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.49 1170[2:SpR:1163.0,99.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.21/0.49 1177[2:SpR:1166.0,99.0] || -> equal(multiply(inverse(sk_c5),sk_c8),sk_c6)**.
% 0.21/0.49 1179[2:Rew:1163.0,1177.0,1164.0,1177.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 1183[2:Rew:1179.0,1162.0] || equal(multiply(sk_c8,sk_c7),sk_c7)** -> .
% 0.21/0.49 1184[2:Rew:1179.0,1170.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.49 1187[2:Rew:33.0,1184.0] || -> equal(identity,sk_c8)**.
% 0.21/0.49 1188[2:Rew:1187.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.49 1192[2:UnC:1188.0,1183.0] || -> .
% 0.21/0.49 % SZS output end Refutation
% 0.21/0.49 Formulae used in the proof : prove_this_1 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
% 0.21/0.49
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