TSTP Solution File: GRP283-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP283-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:46:40 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP283-1 : TPTP v8.1.0. Released v2.5.0.
% 0.00/0.08 % Command : run_spass %d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 600
% 0.08/0.27 % DateTime : Mon Jun 13 06:25:41 EDT 2022
% 0.08/0.27 % CPUTime :
% 0.12/0.36
% 0.12/0.36 SPASS V 3.9
% 0.12/0.36 SPASS beiseite: Proof found.
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 SPASS derived 607 clauses, backtracked 399 clauses, performed 13 splits and kept 662 clauses.
% 0.12/0.36 SPASS allocated 63567 KBytes.
% 0.12/0.36 SPASS spent 0:00:00.08 on the problem.
% 0.12/0.36 0:00:00.03 for the input.
% 0.12/0.36 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.36 0:00:00.00 for inferences.
% 0.12/0.36 0:00:00.00 for the backtracking.
% 0.12/0.36 0:00:00.03 for the reduction.
% 0.12/0.36
% 0.12/0.36
% 0.12/0.36 Here is a proof with depth 5, length 328 :
% 0.12/0.36 % SZS output start Refutation
% 0.12/0.36 1[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.12/0.36 2[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c7),sk_c6).
% 0.12/0.36 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 7[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.12/0.36 8[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.12/0.36 11[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.12/0.36 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.12/0.36 14[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(inverse(sk_c1),sk_c8)**.
% 0.12/0.36 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.12/0.36 19[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.12/0.36 20[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.12/0.36 22[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.12/0.36 23[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.12/0.36 24[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.12/0.36 25[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 26[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 28[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 29[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 30[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 31[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.12/0.36 32[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 34[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 35[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.12/0.36 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 37[0:Inp] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(inverse(sk_c7),sk_c6) equal(multiply(w,sk_c8),y)*+ equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c7)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.12/0.36 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.12/0.36 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.12/0.36 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.12/0.36 41[1:Spt:37.2,37.5,37.9] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)* equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.12/0.36 43[2:Spt:2.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.12/0.36 45[3:Spt:1.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.12/0.36 47[4:Spt:6.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.12/0.36 49[5:Spt:4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.12/0.36 52[1:SpL:38.0,41.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.12/0.36 53[6:Spt:5.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.12/0.36 61[2:SpR:43.0,39.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.12/0.36 62[4:SpR:47.0,39.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.12/0.36 63[5:SpR:49.0,39.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.12/0.36 64[1:SpL:39.0,41.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.12/0.36 70[4:SpR:62.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.12/0.36 71[3:SpR:45.0,40.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.12/0.36 73[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.12/0.36 75[2:SpR:61.0,40.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.12/0.36 77[4:Rew:38.0,70.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.12/0.36 78[2:Rew:38.0,75.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.12/0.36 79[0:Rew:38.0,73.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.12/0.36 86[6:SpR:53.0,77.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.12/0.36 92[3:SpR:45.0,78.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.12/0.36 93[5:SpR:63.0,78.0] || -> equal(multiply(sk_c6,identity),sk_c4)**.
% 0.12/0.36 96[0:SpR:79.0,79.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.12/0.36 99[4:SpR:62.0,79.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.12/0.36 101[6:SpR:86.0,79.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.12/0.36 105[0:SpR:39.0,79.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.12/0.36 107[2:SpR:61.0,79.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c7)**.
% 0.12/0.36 114[6:Rew:39.0,101.0] || -> equal(identity,sk_c6)**.
% 0.12/0.36 115[6:Rew:114.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.12/0.36 117[6:Rew:114.0,61.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.12/0.36 118[6:Rew:114.0,62.0] || -> equal(multiply(sk_c8,sk_c5),sk_c6)**.
% 0.12/0.36 121[6:Rew:114.0,64.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c6,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.12/0.36 125[6:Rew:115.0,92.0] || -> equal(sk_c6,sk_c8)**.
% 0.12/0.36 135[6:Rew:125.0,115.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.12/0.36 136[6:Rew:125.0,117.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.12/0.36 137[6:Rew:125.0,118.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.12/0.36 148[6:Rew:135.0,137.0] || -> equal(sk_c5,sk_c8)**.
% 0.12/0.36 149[6:Rew:135.0,136.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 152[6:Rew:148.0,47.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.12/0.36 186[6:Rew:135.0,121.2,149.0,121.2,125.0,121.1,152.0,121.0,152.0,121.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.12/0.36 187[6:Obv:186.1] || equal(u,sk_c8)* -> .
% 0.12/0.36 188[6:UnC:187.0,79.0] || -> .
% 0.12/0.36 190[6:Spt:188.0,5.0,53.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.12/0.36 191[6:Spt:188.0,5.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 194[0:Rew:96.0,105.0] || -> equal(multiply(u,identity),u)**.
% 0.12/0.36 195[5:Rew:194.0,93.0] || -> equal(sk_c4,sk_c6)**.
% 0.12/0.36 196[2:Rew:194.0,107.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.12/0.36 197[4:Rew:194.0,99.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.12/0.36 199[5:Rew:195.0,63.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.12/0.36 201[5:Rew:45.0,199.0] || -> equal(identity,sk_c8)**.
% 0.12/0.36 202[5:Rew:201.0,62.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.12/0.36 204[5:Rew:201.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.12/0.36 207[5:Rew:201.0,194.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.12/0.36 208[5:Rew:204.0,202.0] || -> equal(sk_c5,sk_c8)**.
% 0.12/0.36 210[6:Rew:204.0,191.0] || -> equal(sk_c6,sk_c7)**.
% 0.12/0.36 212[6:Rew:208.0,190.0] || equal(multiply(sk_c8,sk_c8),sk_c6)** -> .
% 0.12/0.36 214[6:Rew:210.0,43.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.12/0.36 223[6:Rew:204.0,212.0,210.0,212.0] || equal(sk_c7,sk_c8)** -> .
% 0.12/0.36 234[6:Rew:208.0,17.1,207.0,17.1,210.0,17.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c8).
% 0.12/0.36 235[6:MRR:234.1,223.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.12/0.36 250[6:Rew:207.0,11.1,208.0,11.0,207.0,11.0,210.0,11.0] || -> equal(sk_c7,sk_c8) equal(sk_c1,sk_c7)**.
% 0.12/0.36 251[6:MRR:250.0,223.0] || -> equal(sk_c1,sk_c7)**.
% 0.12/0.36 252[6:Rew:251.0,235.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.12/0.36 253[6:Rew:214.0,252.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 254[6:MRR:253.0,223.0] || -> .
% 0.12/0.36 262[5:Spt:254.0,4.0,49.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.12/0.36 263[5:Spt:254.0,4.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 265[5:MRR:34.0,262.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 268[5:MRR:28.0,262.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 269[5:MRR:22.0,262.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.12/0.36 277[2:SpR:196.0,79.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.12/0.36 279[3:Rew:71.0,277.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.12/0.36 280[5:Rew:279.0,263.0] || -> equal(sk_c6,sk_c7)**.
% 0.12/0.36 283[5:Rew:279.0,269.0] || -> equal(sk_c3,sk_c7)**.
% 0.12/0.36 286[3:Rew:279.0,52.2] || equal(inverse(identity),sk_c8)** equal(sk_c8,u) equal(u,sk_c7)* -> .
% 0.12/0.36 290[4:Rew:279.0,62.0] || -> equal(identity,sk_c5)**.
% 0.12/0.36 291[5:Rew:280.0,196.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.12/0.36 293[5:Rew:280.0,45.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.12/0.36 295[5:Rew:280.0,61.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.12/0.36 298[5:Rew:283.0,268.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.12/0.36 299[4:Rew:290.0,194.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.12/0.36 303[5:Rew:293.0,295.0,290.0,295.0] || -> equal(sk_c5,sk_c8)**.
% 0.12/0.36 304[5:Rew:303.0,197.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.12/0.36 306[5:Rew:303.0,290.0] || -> equal(identity,sk_c8)**.
% 0.12/0.36 309[5:Rew:303.0,299.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.12/0.36 310[5:Rew:309.0,298.0] || -> equal(sk_c2,sk_c7)**.
% 0.12/0.36 312[5:Rew:310.0,265.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.12/0.36 314[5:Rew:291.0,312.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 333[5:Rew:314.0,286.2,304.0,286.0,306.0,286.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.12/0.36 334[5:Obv:333.1] || equal(u,sk_c8)* -> .
% 0.12/0.36 335[5:UnC:334.0,79.0] || -> .
% 0.12/0.36 338[4:Spt:335.0,6.0,47.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.12/0.36 339[4:Spt:335.0,6.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 340[4:Rew:279.0,339.0] || -> equal(sk_c6,sk_c7)**.
% 0.12/0.36 341[4:Rew:340.0,196.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.12/0.36 343[4:Rew:340.0,61.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.12/0.36 345[4:Rew:340.0,45.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.12/0.36 346[4:Rew:343.0,345.0] || -> equal(identity,sk_c8)**.
% 0.12/0.36 348[4:Rew:346.0,194.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.12/0.36 354[4:MRR:36.0,338.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 361[4:Rew:348.0,30.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c2,sk_c3).
% 0.12/0.36 362[4:MRR:361.0,338.0] || -> equal(sk_c2,sk_c3)**.
% 0.12/0.36 363[4:Rew:362.0,354.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.12/0.36 365[3:Rew:279.0,24.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c3,sk_c7).
% 0.12/0.36 366[4:MRR:365.0,338.0] || -> equal(sk_c3,sk_c7)**.
% 0.12/0.36 368[4:Rew:366.0,363.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.12/0.36 369[4:Rew:341.0,368.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 371[4:Rew:369.0,341.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.12/0.36 396[4:Rew:279.0,64.2,369.0,64.2,346.0,64.1,371.0,64.0,371.0,64.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.12/0.36 397[4:Obv:396.1] || equal(u,sk_c8)* -> .
% 0.12/0.36 398[4:UnC:397.0,79.0] || -> .
% 0.12/0.36 400[3:Spt:398.0,1.0,45.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.12/0.36 401[3:Spt:398.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 402[3:MRR:31.1,400.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 403[3:MRR:13.1,400.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.12/0.36 404[3:MRR:25.0,400.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 405[3:MRR:19.0,400.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.12/0.36 406[3:MRR:7.0,400.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.12/0.36 424[3:SpR:404.0,79.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.12/0.36 426[3:Rew:402.0,424.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.12/0.36 427[3:Rew:405.0,426.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 428[3:Rew:427.0,401.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.12/0.36 429[3:Rew:427.0,43.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.12/0.36 431[3:Rew:427.0,61.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.12/0.36 436[3:Rew:427.0,405.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.12/0.36 437[3:Rew:427.0,406.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.12/0.36 440[3:Rew:427.0,52.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.12/0.36 451[3:SpR:436.0,79.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.12/0.36 453[3:Rew:429.0,451.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.12/0.36 454[3:Rew:431.0,453.0] || -> equal(identity,sk_c3)**.
% 0.12/0.36 456[3:Rew:454.0,38.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.12/0.36 459[3:Rew:454.0,440.0] || equal(inverse(sk_c3),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.12/0.36 460[3:Rew:454.0,431.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.12/0.36 472[3:SpR:437.0,79.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.12/0.36 474[3:Rew:428.0,472.0,403.0,472.0] || -> equal(sk_c6,sk_c8)**.
% 0.12/0.36 475[3:Rew:474.0,429.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.12/0.36 477[3:Rew:474.0,428.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.12/0.36 483[3:Rew:474.0,460.0] || -> equal(multiply(sk_c8,sk_c8),sk_c3)**.
% 0.12/0.36 484[3:Rew:477.0,483.0] || -> equal(sk_c3,sk_c8)**.
% 0.12/0.36 488[3:Rew:484.0,456.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.12/0.36 491[3:Rew:484.0,459.0] || equal(inverse(sk_c8),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.12/0.36 516[3:Rew:488.0,491.2,475.0,491.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.12/0.36 517[3:Obv:516.1] || equal(u,sk_c8)* -> .
% 0.12/0.36 518[3:UnC:517.0,427.0] || -> .
% 0.12/0.36 521[2:Spt:518.0,2.0,43.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.12/0.36 522[2:Spt:518.0,2.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 523[2:MRR:32.0,521.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 524[2:MRR:14.0,521.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.12/0.36 525[2:MRR:26.0,521.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 526[2:MRR:20.0,521.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.12/0.36 527[2:MRR:8.0,521.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.12/0.36 529[2:SpR:522.0,79.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.12/0.36 536[2:SpR:525.0,79.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.12/0.36 538[2:Rew:523.0,536.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.12/0.36 539[2:Rew:526.0,538.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 540[2:Rew:539.0,522.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.12/0.36 541[2:Rew:539.0,521.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.12/0.36 542[2:Rew:539.0,526.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.12/0.36 543[2:Rew:539.0,527.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.12/0.36 549[2:Rew:539.0,529.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.12/0.36 556[2:SpR:542.0,79.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.12/0.36 558[2:Rew:39.0,556.0] || -> equal(identity,sk_c3)**.
% 0.12/0.36 560[2:Rew:558.0,194.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.12/0.36 563[2:Rew:558.0,39.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.12/0.36 569[2:SpR:543.0,79.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.12/0.36 571[2:Rew:540.0,569.0,524.0,569.0] || -> equal(sk_c6,sk_c8)**.
% 0.12/0.36 572[2:Rew:571.0,541.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.12/0.36 574[2:Rew:571.0,549.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.12/0.36 576[2:Rew:563.0,574.0] || -> equal(sk_c3,sk_c8)**.
% 0.12/0.36 577[2:Rew:576.0,525.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.12/0.36 580[2:Rew:576.0,560.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.12/0.36 592[2:Rew:580.0,577.0] || -> equal(sk_c2,sk_c8)**.
% 0.12/0.36 594[2:Rew:592.0,523.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.12/0.36 596[2:MRR:594.0,572.0] || -> .
% 0.12/0.36 607[1:Spt:596.0,37.0,37.1,37.3,37.4,37.6,37.7,37.8,37.10,37.11] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.12/0.36 609[2:Spt:2.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.12/0.36 610[2:Rew:609.0,607.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(sk_c6,sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.12/0.36 612[2:Obv:610.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6) -> .
% 0.12/0.36 616[3:Spt:1.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.12/0.36 618[3:Rew:616.0,612.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c8,sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.12/0.36 619[3:Obv:618.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.12/0.36 622[3:SpR:616.0,79.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c6)**.
% 0.12/0.36 624[3:Rew:609.0,622.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.12/0.36 625[4:Spt:6.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.12/0.36 626[4:SpR:625.0,79.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.12/0.36 635[3:SpR:624.0,79.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.12/0.36 637[3:Rew:39.0,635.0] || -> equal(identity,sk_c8)**.
% 0.12/0.36 638[3:Rew:637.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.12/0.36 639[3:Rew:637.0,194.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.12/0.36 640[3:Rew:637.0,39.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.12/0.36 642[3:Rew:638.0,23.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(sk_c3,sk_c7).
% 0.12/0.36 645[3:Rew:638.0,619.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.12/0.36 646[3:Rew:638.0,5.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(sk_c6,sk_c7).
% 0.12/0.36 649[4:Rew:638.0,626.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.12/0.36 652[3:Rew:639.0,29.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(sk_c2,sk_c3).
% 0.12/0.36 655[3:Rew:639.0,35.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c5,sk_c6).
% 0.12/0.36 656[4:Rew:649.0,642.0] || -> equal(sk_c6,sk_c8) equal(sk_c3,sk_c7)**.
% 0.12/0.36 657[4:Rew:649.0,646.0] || -> equal(sk_c6,sk_c8) equal(sk_c6,sk_c7)**.
% 0.12/0.36 660[4:Rew:649.0,652.0] || -> equal(sk_c6,sk_c8) equal(sk_c2,sk_c3)**.
% 0.12/0.36 671[3:Rew:639.0,645.5,639.0,645.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c8)** equal(u,sk_c6) equal(multiply(v,sk_c7),sk_c8)** equal(w,sk_c7) equal(sk_c6,sk_c7) -> .
% 0.12/0.36 684[5:Spt:656.0] || -> equal(sk_c6,sk_c8)**.
% 0.12/0.36 685[5:Rew:684.0,609.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.12/0.36 686[5:Rew:684.0,616.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.12/0.36 691[5:Rew:684.0,671.6] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c8)** equal(u,sk_c6) equal(multiply(v,sk_c7),sk_c8)** equal(w,sk_c7) equal(sk_c7,sk_c8) -> .
% 0.12/0.36 692[5:Rew:639.0,686.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 698[5:Rew:692.0,685.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.12/0.36 705[5:Rew:692.0,691.6,692.0,691.5,692.0,691.4,684.0,691.3,692.0,691.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(w,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.12/0.36 706[5:Obv:705.6] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(w,sk_c8) -> .
% 0.12/0.36 707[5:Con:706.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.12/0.36 708[5:Rew:639.0,707.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.12/0.36 709[5:Con:708.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.12/0.36 720[4:SpR:649.0,639.0] || -> equal(sk_c5,sk_c8)**.
% 0.12/0.36 729[3:SpR:640.0,639.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.12/0.36 754[5:SpL:698.0,709.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.12/0.36 756[5:Obv:754.1] || -> .
% 0.12/0.36 757[5:Spt:756.0,656.0,684.0] || equal(sk_c6,sk_c8)** -> .
% 0.12/0.36 758[5:Spt:756.0,656.1] || -> equal(sk_c3,sk_c7)**.
% 0.12/0.36 759[5:MRR:657.0,757.0] || -> equal(sk_c6,sk_c7)**.
% 0.12/0.36 760[5:Rew:759.0,609.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.12/0.36 761[5:Rew:759.0,757.0] || equal(sk_c7,sk_c8)** -> .
% 0.12/0.36 765[5:Rew:758.0,660.1,759.0,660.0] || -> equal(sk_c7,sk_c8) equal(sk_c2,sk_c7)**.
% 0.12/0.36 766[5:MRR:765.0,761.0] || -> equal(sk_c2,sk_c7)**.
% 0.12/0.36 775[4:Rew:720.0,655.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c6,sk_c8).
% 0.12/0.36 776[5:Rew:759.0,775.1,760.0,775.0,766.0,775.0] || -> equal(sk_c7,sk_c8)** equal(sk_c7,sk_c8)**.
% 0.12/0.36 777[5:Obv:776.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 778[5:MRR:777.0,761.0] || -> .
% 0.12/0.36 786[4:Spt:778.0,6.0,625.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.12/0.36 787[4:Spt:778.0,6.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 788[4:Rew:638.0,787.0] || -> equal(sk_c6,sk_c7)**.
% 0.12/0.36 789[4:Rew:788.0,609.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.12/0.36 793[4:Rew:788.0,655.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c5,sk_c7).
% 0.12/0.36 797[4:Rew:789.0,36.0,793.1,36.0] || -> equal(sk_c7,sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 803[3:Rew:639.0,642.0] || -> equal(sk_c5,sk_c6) equal(sk_c3,sk_c7)**.
% 0.12/0.36 804[4:Rew:788.0,803.0] || -> equal(sk_c5,sk_c7) equal(sk_c3,sk_c7)**.
% 0.12/0.36 814[3:Rew:639.0,30.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c2,sk_c3).
% 0.12/0.36 815[4:MRR:814.0,786.0] || -> equal(sk_c2,sk_c3)**.
% 0.12/0.36 819[4:Rew:815.0,797.1] || -> equal(sk_c7,sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.12/0.36 822[3:Rew:638.0,24.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c3,sk_c7).
% 0.12/0.36 823[4:Rew:789.0,822.0,804.0,822.0] || -> equal(sk_c7,sk_c8) equal(sk_c3,sk_c7)**.
% 0.12/0.36 826[4:Rew:823.1,819.1] || -> equal(sk_c7,sk_c8) equal(inverse(sk_c7),sk_c8)**.
% 0.12/0.36 829[4:Rew:789.0,826.1] || -> equal(sk_c7,sk_c8)** equal(sk_c7,sk_c8)**.
% 0.12/0.36 830[4:Obv:829.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 831[4:Rew:830.0,788.0] || -> equal(sk_c6,sk_c8)**.
% 0.12/0.36 855[4:Rew:831.0,671.6,830.0,671.6,830.0,671.5,830.0,671.4,831.0,671.3,830.0,671.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(w,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.12/0.36 856[4:Obv:855.6] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(w,sk_c8) -> .
% 0.12/0.36 857[4:Con:856.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.12/0.36 858[4:Rew:639.0,857.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.12/0.36 859[4:Con:858.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.12/0.36 897[4:SpL:729.0,859.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.12/0.36 898[4:Obv:897.1] || -> .
% 0.12/0.36 899[3:Spt:898.0,1.0,616.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.12/0.36 900[3:Spt:898.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 901[3:MRR:31.1,899.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 902[3:MRR:13.1,899.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.12/0.36 903[3:MRR:25.0,899.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 904[3:MRR:19.0,899.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.12/0.36 905[3:MRR:7.0,899.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.12/0.36 916[3:SpR:903.0,79.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.12/0.36 918[3:Rew:901.0,916.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.12/0.36 919[3:Rew:904.0,918.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 920[3:Rew:919.0,900.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.12/0.36 922[3:Rew:919.0,899.0] || equal(multiply(sk_c8,sk_c6),sk_c8)** -> .
% 0.12/0.36 926[3:Rew:919.0,905.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.12/0.36 941[3:SpR:926.0,79.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.12/0.36 943[3:Rew:920.0,941.0,902.0,941.0] || -> equal(sk_c6,sk_c8)**.
% 0.12/0.36 945[3:Rew:943.0,920.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.12/0.36 946[3:Rew:943.0,922.0] || equal(multiply(sk_c8,sk_c8),sk_c8)** -> .
% 0.12/0.36 956[3:Rew:945.0,946.0] || equal(sk_c8,sk_c8)* -> .
% 0.12/0.36 957[3:Obv:956.0] || -> .
% 0.12/0.36 963[2:Spt:957.0,2.0,609.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.12/0.36 964[2:Spt:957.0,2.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.12/0.36 965[2:MRR:32.0,963.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.12/0.36 966[2:MRR:14.0,963.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.12/0.36 967[2:MRR:26.0,963.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.12/0.36 968[2:MRR:20.0,963.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.12/0.36 969[2:MRR:8.0,963.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.12/0.36 971[2:SpR:964.0,79.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.12/0.36 978[2:SpR:967.0,79.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.12/0.36 980[2:Rew:965.0,978.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.12/0.36 981[2:Rew:968.0,980.0] || -> equal(sk_c7,sk_c8)**.
% 0.12/0.36 982[2:Rew:981.0,964.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.12/0.36 983[2:Rew:981.0,963.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.12/0.36 984[2:Rew:981.0,968.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.12/0.36 985[2:Rew:981.0,969.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.12/0.36 986[2:Rew:981.0,971.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.12/0.36 993[2:SpR:984.0,79.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.12/0.36 995[2:Rew:39.0,993.0] || -> equal(identity,sk_c3)**.
% 0.12/0.36 997[2:Rew:995.0,194.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.12/0.36 999[2:Rew:995.0,39.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.12/0.36 1003[2:SpR:985.0,79.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.12/0.36 1005[2:Rew:982.0,1003.0,966.0,1003.0] || -> equal(sk_c6,sk_c8)**.
% 0.12/0.36 1007[2:Rew:1005.0,983.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.12/0.36 1008[2:Rew:1005.0,986.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.12/0.36 1010[2:Rew:999.0,1008.0] || -> equal(sk_c3,sk_c8)**.
% 0.12/0.36 1011[2:Rew:1010.0,967.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.12/0.36 1014[2:Rew:1010.0,997.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.12/0.36 1021[2:Rew:1014.0,1011.0] || -> equal(sk_c2,sk_c8)**.
% 0.12/0.36 1023[2:Rew:1021.0,965.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.12/0.36 1025[2:MRR:1023.0,1007.0] || -> .
% 0.12/0.36 % SZS output end Refutation
% 0.12/0.36 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_11 prove_this_13 prove_this_14 prove_this_17 prove_this_19 prove_this_20 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.12/0.36
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