TSTP Solution File: GRP215-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP215-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:46:22 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
% 0.08/0.13 % Problem : GRP215-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 10:42:50 EDT 2022
% 0.14/0.36 % 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 856 clauses, backtracked 234 clauses, performed 10 splits and kept 587 clauses.
% 0.21/0.49 SPASS allocated 63666 KBytes.
% 0.21/0.49 SPASS spent 0:00:00.12 on the problem.
% 0.21/0.49 0:00:00.03 for the input.
% 0.21/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.49 0:00:00.01 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 5, length 364 :
% 0.21/0.49 % SZS output start Refutation
% 0.21/0.49 1[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.49 2[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.21/0.49 3[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.21/0.49 4[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.21/0.49 5[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.49 6[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.21/0.49 7[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.49 8[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.49 9[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.21/0.49 10[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.21/0.49 11[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.49 12[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.49 13[0:Inp] || -> equal(multiply(sk_c7,sk_c5),sk_c6)** equal(multiply(sk_c2,sk_c6),sk_c7).
% 0.21/0.49 14[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.49 15[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.49 16[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 17[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.49 18[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.49 19[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.21/0.49 20[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 21[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c7),y)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c7)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c7,y),sk_c6)** -> .
% 0.21/0.49 22[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.49 23[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.49 24[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.49 25[1:Spt:21.1,21.5] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.21/0.49 26[2:Spt:20.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 28[3:Spt:10.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.49 31[1:SpL:22.0,25.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c6) -> .
% 0.21/0.49 32[4:Spt:15.1] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.49 34[4:SpL:32.0,25.1] || equal(inverse(sk_c2),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.21/0.49 35[4:Obv:34.1] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.21/0.49 36[4:Rew:26.0,35.0] || equal(sk_c7,sk_c6)** -> .
% 0.21/0.49 37[5:Spt:5.1] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.49 40[2:SpR:26.0,23.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.21/0.49 41[3:SpR:28.0,23.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.21/0.49 46[4:SpR:32.0,24.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.21/0.49 48[0:SpR:23.0,24.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.49 49[5:SpR:37.0,24.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.21/0.49 50[2:SpR:40.0,24.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.21/0.49 52[2:Rew:22.0,50.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.21/0.49 53[0:Rew:22.0,48.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.49 60[4:SpR:32.0,52.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.21/0.49 69[0:SpR:53.0,53.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.49 73[0:SpR:23.0,53.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.49 75[2:SpR:40.0,53.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c2)**.
% 0.21/0.49 76[2:SpR:52.0,53.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c2,u))**.
% 0.21/0.49 77[4:SpR:60.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.21/0.49 79[3:SpR:41.0,53.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.21/0.49 85[4:Rew:23.0,77.0] || -> equal(sk_c7,identity)**.
% 0.21/0.49 87[4:Rew:85.0,28.0] || -> equal(inverse(sk_c1),identity)**.
% 0.21/0.49 88[4:Rew:85.0,32.0] || -> equal(multiply(sk_c2,sk_c6),identity)**.
% 0.21/0.49 90[4:Rew:85.0,36.0] || equal(identity,sk_c6)** -> .
% 0.21/0.49 91[4:Rew:85.0,41.0] || -> equal(multiply(identity,sk_c1),identity)**.
% 0.21/0.49 95[4:Rew:85.0,46.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.21/0.49 96[5:Rew:85.0,49.0] || -> equal(multiply(sk_c1,multiply(identity,u)),multiply(sk_c6,u))**.
% 0.21/0.49 100[4:Rew:22.0,91.0] || -> equal(identity,sk_c1)**.
% 0.21/0.49 101[4:Rew:100.0,22.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 103[4:Rew:100.0,40.0] || -> equal(multiply(sk_c6,sk_c2),sk_c1)**.
% 0.21/0.49 106[4:Rew:100.0,85.0] || -> equal(sk_c7,sk_c1)**.
% 0.21/0.49 107[4:Rew:100.0,87.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.49 108[4:Rew:100.0,90.0] || equal(sk_c6,sk_c1)** -> .
% 0.21/0.49 109[4:Rew:100.0,88.0] || -> equal(multiply(sk_c2,sk_c6),sk_c1)**.
% 0.21/0.49 119[4:Rew:100.0,73.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.21/0.49 124[4:Rew:69.0,119.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.21/0.49 125[4:Rew:101.0,95.0,100.0,95.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.21/0.49 126[5:Rew:101.0,96.0,101.0,96.0,100.0,96.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 129[5:Rew:126.0,103.0] || -> equal(sk_c2,sk_c1)**.
% 0.21/0.49 131[5:Rew:129.0,109.0] || -> equal(multiply(sk_c1,sk_c6),sk_c1)**.
% 0.21/0.49 137[5:Rew:101.0,131.0] || -> equal(sk_c6,sk_c1)**.
% 0.21/0.49 138[5:MRR:137.0,108.0] || -> .
% 0.21/0.49 146[5:Spt:138.0,5.1,37.0] || equal(multiply(sk_c1,sk_c7),sk_c6)** -> .
% 0.21/0.49 147[5:Spt:138.0,5.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.49 148[5:Rew:106.0,147.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.21/0.49 153[4:Rew:106.0,4.1,101.0,4.1,124.0,4.0,106.0,4.0] || -> equal(sk_c4,sk_c5)** equal(sk_c6,sk_c1).
% 0.21/0.49 154[4:MRR:153.1,108.0] || -> equal(sk_c4,sk_c5)**.
% 0.21/0.49 155[5:Rew:154.0,148.0] || -> equal(inverse(sk_c5),sk_c1)**.
% 0.21/0.49 156[4:Rew:106.0,3.1,101.0,3.1,101.0,3.0,106.0,3.0] || -> equal(sk_c5,sk_c6)** equal(sk_c6,sk_c1).
% 0.21/0.49 157[4:MRR:156.1,108.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 159[5:Rew:157.0,155.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.21/0.49 161[5:Rew:159.0,76.0] || -> equal(multiply(sk_c2,u),multiply(sk_c1,u))**.
% 0.21/0.49 164[5:Rew:101.0,161.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.21/0.49 165[5:Rew:164.0,125.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 169[5:Rew:165.0,103.0] || -> equal(sk_c2,sk_c1)**.
% 0.21/0.49 170[5:Rew:169.0,26.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.49 172[5:Rew:107.0,170.0] || -> equal(sk_c6,sk_c1)**.
% 0.21/0.49 173[5:MRR:172.0,108.0] || -> .
% 0.21/0.49 176[4:Spt:173.0,15.1,32.0] || equal(multiply(sk_c2,sk_c6),sk_c7)** -> .
% 0.21/0.49 177[4:Spt:173.0,15.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.49 178[0:Rew:69.0,73.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.49 179[3:Rew:178.0,79.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.21/0.49 180[2:Rew:178.0,75.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.21/0.49 183[4:MRR:11.1,176.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.49 184[4:MRR:14.1,176.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.21/0.49 185[4:MRR:13.1,176.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.49 186[4:MRR:12.1,176.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.49 196[2:SpR:180.0,53.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.21/0.49 211[4:SpR:184.0,53.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.21/0.49 213[4:Rew:177.0,211.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.49 214[4:Rew:185.0,213.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.49 217[4:Rew:214.0,179.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.21/0.49 218[4:Rew:214.0,183.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.49 221[4:Rew:214.0,176.0] || equal(multiply(sk_c2,sk_c6),sk_c6)** -> .
% 0.21/0.49 225[4:Rew:214.0,185.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.49 226[4:Rew:214.0,186.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.21/0.49 232[4:Rew:180.0,217.0] || -> equal(sk_c2,sk_c1)**.
% 0.21/0.49 234[4:Rew:232.0,180.0] || -> equal(inverse(sk_c6),sk_c1)**.
% 0.21/0.49 238[4:Rew:232.0,221.0] || equal(multiply(sk_c1,sk_c6),sk_c6)** -> .
% 0.21/0.49 266[4:SpR:225.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.21/0.49 268[4:Rew:234.0,266.0] || -> equal(multiply(sk_c1,sk_c6),sk_c5)**.
% 0.21/0.49 269[4:Rew:268.0,238.0] || equal(sk_c5,sk_c6)** -> .
% 0.21/0.49 271[4:SpR:226.0,53.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c6)**.
% 0.21/0.49 273[4:Rew:218.0,271.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 282[4:SpR:273.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.21/0.49 284[4:Rew:268.0,282.0,234.0,282.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 285[4:MRR:284.0,269.0] || -> .
% 0.21/0.49 286[3:Spt:285.0,10.1,28.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.21/0.49 287[3:Spt:285.0,10.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.49 288[3:MRR:6.1,286.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.49 289[3:MRR:9.0,286.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.21/0.49 290[3:MRR:8.0,286.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.49 291[3:MRR:7.0,286.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.49 306[3:SpR:289.0,53.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.21/0.49 308[3:Rew:287.0,306.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.49 309[3:Rew:290.0,308.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.49 311[3:Rew:309.0,288.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.49 314[3:Rew:309.0,31.1] || equal(inverse(identity),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.21/0.49 316[3:Rew:309.0,290.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.49 317[3:Rew:309.0,291.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.21/0.49 325[3:Obv:314.1] || equal(inverse(identity),sk_c7)** -> .
% 0.21/0.49 326[3:Rew:309.0,325.0] || equal(inverse(identity),sk_c6)** -> .
% 0.21/0.49 339[3:SpR:316.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.21/0.49 341[3:Rew:180.0,339.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.49 343[3:SpR:317.0,53.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c6)**.
% 0.21/0.49 345[3:Rew:311.0,343.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 346[3:SpR:341.0,24.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.21/0.49 350[3:Rew:196.0,346.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.49 357[3:SpR:345.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.21/0.49 359[3:Rew:341.0,357.0,180.0,357.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 363[3:Rew:359.0,350.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 364[3:Rew:363.0,40.0] || -> equal(identity,sk_c2)**.
% 0.21/0.49 372[3:Rew:364.0,326.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.21/0.49 377[3:Rew:26.0,372.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.49 378[3:Obv:377.0] || -> .
% 0.21/0.49 380[2:Spt:378.0,20.1,26.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.21/0.49 381[2:Spt:378.0,20.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.49 382[2:MRR:16.1,380.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.49 383[2:MRR:19.0,380.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.21/0.49 384[2:MRR:18.0,380.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.49 385[2:MRR:17.0,380.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.49 391[2:SpR:383.0,53.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.21/0.49 393[2:Rew:381.0,391.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.49 394[2:Rew:384.0,393.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.49 395[2:Rew:394.0,381.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.49 396[2:Rew:394.0,382.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.49 397[2:Rew:394.0,383.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.21/0.49 398[2:Rew:394.0,31.0] || equal(inverse(identity),sk_c6)** equal(sk_c7,sk_c6) -> .
% 0.21/0.49 399[2:Rew:394.0,384.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.49 400[2:Rew:394.0,385.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.21/0.49 407[2:Rew:394.0,398.1] || equal(inverse(identity),sk_c6)** equal(sk_c6,sk_c6) -> .
% 0.21/0.49 408[2:Obv:407.1] || equal(inverse(identity),sk_c6)** -> .
% 0.21/0.49 422[2:SpR:399.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.21/0.49 424[2:Rew:23.0,422.0] || -> equal(identity,sk_c5)**.
% 0.21/0.49 426[2:Rew:424.0,178.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.49 428[2:Rew:424.0,408.0] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.21/0.49 429[2:Rew:424.0,23.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.21/0.49 434[2:SpR:400.0,53.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c6)**.
% 0.21/0.49 436[2:Rew:396.0,434.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 439[2:SpR:436.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.21/0.49 441[2:Rew:429.0,439.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 442[2:Rew:441.0,397.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.21/0.49 444[2:Rew:441.0,428.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.21/0.49 446[2:Rew:441.0,426.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.49 455[2:Rew:446.0,442.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.49 459[2:Rew:455.0,395.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.49 461[2:MRR:459.0,444.0] || -> .
% 0.21/0.49 467[1:Spt:461.0,21.0,21.2,21.3,21.4,21.6,21.7,21.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),x)*+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,x),sk_c6)** -> .
% 0.21/0.49 468[1:EqR:467.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.21/0.49 470[2:Spt:10.1] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.49 471[2:SpR:470.0,53.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.21/0.49 473[3:Spt:16.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 474[3:SpR:473.0,53.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.21/0.49 476[4:Spt:5.1] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.49 478[4:SpR:476.0,53.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.21/0.49 480[4:SpL:476.0,467.3] || equal(inverse(sk_c1),sk_c7) equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(sk_c6,w) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c7,w),sk_c6)** -> .
% 0.21/0.49 481[4:Rew:470.0,478.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.49 482[4:Rew:470.0,480.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(sk_c6,w) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c7,w),sk_c6)** -> .
% 0.21/0.49 483[4:Obv:482.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(sk_c6,w) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c7,w),sk_c6)** -> .
% 0.21/0.49 485[4:SpR:481.0,53.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.21/0.49 487[4:Rew:23.0,485.0] || -> equal(identity,sk_c6)**.
% 0.21/0.49 488[4:Rew:487.0,178.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.49 489[4:Rew:487.0,22.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 490[4:Rew:487.0,23.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.21/0.49 493[4:Rew:488.0,483.3] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c7) equal(sk_c6,w) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c7,w),sk_c6)** -> .
% 0.21/0.49 496[4:Rew:488.0,12.0] || -> equal(sk_c7,sk_c3) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.49 497[4:Rew:488.0,13.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)** equal(sk_c7,sk_c2).
% 0.21/0.49 498[4:Rew:488.0,14.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(sk_c7,sk_c2).
% 0.21/0.49 499[4:Rew:488.0,15.1] || -> equal(inverse(sk_c4),sk_c7)** equal(sk_c7,sk_c2).
% 0.21/0.49 500[4:Rew:488.0,11.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c7,sk_c2).
% 0.21/0.49 502[4:Rew:489.0,474.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.21/0.49 503[4:Rew:502.0,496.1] || -> equal(sk_c7,sk_c3)** equal(sk_c7,sk_c6).
% 0.21/0.49 518[4:SpR:502.0,488.0] || -> equal(sk_c2,sk_c6)**.
% 0.21/0.49 520[4:Rew:518.0,473.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.49 522[4:Rew:518.0,498.1] || -> equal(multiply(sk_c4,sk_c7),sk_c5)** equal(sk_c7,sk_c6).
% 0.21/0.49 523[4:Rew:518.0,497.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)** equal(sk_c7,sk_c6).
% 0.21/0.49 524[4:Rew:518.0,500.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c7,sk_c6).
% 0.21/0.49 525[4:Rew:518.0,499.1] || -> equal(inverse(sk_c4),sk_c7)** equal(sk_c7,sk_c6).
% 0.21/0.49 528[4:Rew:503.0,524.0] || -> equal(inverse(sk_c3),sk_c3)** equal(sk_c7,sk_c6).
% 0.21/0.49 529[4:Rew:503.0,525.0] || -> equal(inverse(sk_c4),sk_c3)** equal(sk_c7,sk_c6).
% 0.21/0.49 530[4:Rew:503.0,522.0] || -> equal(multiply(sk_c4,sk_c3),sk_c5)** equal(sk_c7,sk_c6).
% 0.21/0.49 531[4:Rew:503.0,523.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6)** equal(sk_c7,sk_c6).
% 0.21/0.49 534[5:Spt:503.0] || -> equal(sk_c7,sk_c3)**.
% 0.21/0.49 535[5:Rew:534.0,470.0] || -> equal(inverse(sk_c1),sk_c3)**.
% 0.21/0.49 536[5:Rew:534.0,476.0] || -> equal(multiply(sk_c1,sk_c3),sk_c6)**.
% 0.21/0.49 539[5:Rew:534.0,531.1] || -> equal(multiply(sk_c3,sk_c5),sk_c6)** equal(sk_c3,sk_c6).
% 0.21/0.49 540[5:Rew:534.0,530.1] || -> equal(multiply(sk_c4,sk_c3),sk_c5)** equal(sk_c3,sk_c6).
% 0.21/0.49 541[5:Rew:534.0,529.1] || -> equal(inverse(sk_c4),sk_c3)** equal(sk_c3,sk_c6).
% 0.21/0.49 542[5:Rew:534.0,528.1] || -> equal(inverse(sk_c3),sk_c3)** equal(sk_c3,sk_c6).
% 0.21/0.49 543[5:Rew:534.0,493.1] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c3) equal(sk_c6,w) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c7,w),sk_c6)** -> .
% 0.21/0.49 547[5:Rew:534.0,543.5,534.0,543.4,534.0,543.3] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c3) equal(sk_c6,w) equal(u,sk_c3) equal(multiply(v,sk_c3),sk_c6)** equal(multiply(sk_c3,w),sk_c6)** -> .
% 0.21/0.49 563[4:SpR:490.0,53.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.21/0.49 568[4:Rew:488.0,563.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.49 571[6:Spt:541.1] || -> equal(sk_c3,sk_c6)**.
% 0.21/0.49 574[6:Rew:571.0,536.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.21/0.49 577[6:Rew:571.0,547.1] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6) equal(sk_c6,w) equal(u,sk_c3) equal(multiply(v,sk_c3),sk_c6)** equal(multiply(sk_c3,w),sk_c6)** -> .
% 0.21/0.49 582[6:Rew:488.0,574.0] || -> equal(sk_c6,sk_c1)**.
% 0.21/0.49 583[6:Rew:582.0,489.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 585[6:Rew:582.0,488.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.21/0.49 587[6:Rew:582.0,520.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.49 589[6:Rew:582.0,571.0] || -> equal(sk_c3,sk_c1)**.
% 0.21/0.49 595[6:Rew:583.0,577.5,589.0,577.5,582.0,577.5,585.0,577.4,589.0,577.4,582.0,577.4,589.0,577.3,582.0,577.2,582.0,577.1,582.0,577.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(sk_c1,w)* equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1)* -> .
% 0.21/0.49 596[6:Obv:595.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1)* -> .
% 0.21/0.49 597[6:Con:596.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.21/0.49 660[6:SpL:587.0,597.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.21/0.49 662[6:Obv:660.1] || -> .
% 0.21/0.49 663[6:Spt:662.0,541.1,571.0] || equal(sk_c3,sk_c6)** -> .
% 0.21/0.49 664[6:Spt:662.0,541.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.21/0.49 665[6:MRR:542.1,663.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.21/0.49 666[6:MRR:539.1,663.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.21/0.49 667[6:MRR:540.1,663.0] || -> equal(multiply(sk_c4,sk_c3),sk_c5)**.
% 0.21/0.49 669[6:SpR:664.0,568.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.21/0.49 672[6:Rew:665.0,669.0] || -> equal(sk_c4,sk_c3)**.
% 0.21/0.49 674[6:Rew:672.0,667.0] || -> equal(multiply(sk_c3,sk_c3),sk_c5)**.
% 0.21/0.49 682[5:SpR:535.0,568.0] || -> equal(inverse(sk_c3),sk_c1)**.
% 0.21/0.49 685[6:Rew:665.0,682.0] || -> equal(sk_c3,sk_c1)**.
% 0.21/0.49 687[6:Rew:685.0,663.0] || equal(sk_c6,sk_c1)** -> .
% 0.21/0.49 690[6:Rew:685.0,536.0] || -> equal(multiply(sk_c1,sk_c1),sk_c6)**.
% 0.21/0.49 695[6:Rew:685.0,666.0] || -> equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.21/0.49 700[6:Rew:685.0,674.0] || -> equal(multiply(sk_c1,sk_c1),sk_c5)**.
% 0.21/0.49 702[6:Rew:690.0,700.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 703[6:Rew:702.0,695.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.21/0.49 704[6:Rew:488.0,703.0] || -> equal(sk_c6,sk_c1)**.
% 0.21/0.49 705[6:MRR:704.0,687.0] || -> .
% 0.21/0.49 712[5:Spt:705.0,503.0,534.0] || equal(sk_c7,sk_c3)** -> .
% 0.21/0.49 713[5:Spt:705.0,503.1] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.49 716[5:Rew:488.0,476.0,713.0,476.0] || -> equal(sk_c6,sk_c1)**.
% 0.21/0.49 719[5:Rew:716.0,520.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.49 720[5:Rew:716.0,488.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.21/0.49 721[5:Rew:716.0,489.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 723[5:Rew:716.0,713.0] || -> equal(sk_c7,sk_c1)**.
% 0.21/0.49 732[5:Rew:721.0,493.5,723.0,493.5,716.0,493.5,720.0,493.4,723.0,493.4,716.0,493.4,723.0,493.3,716.0,493.2,723.0,493.1,716.0,493.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(sk_c1,w)* equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1)* -> .
% 0.21/0.49 733[5:Obv:732.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1)* -> .
% 0.21/0.49 734[5:Con:733.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.21/0.49 785[5:SpL:719.0,734.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.21/0.49 786[5:Obv:785.1] || -> .
% 0.21/0.49 787[4:Spt:786.0,5.1,476.0] || equal(multiply(sk_c1,sk_c7),sk_c6)** -> .
% 0.21/0.49 788[4:Spt:786.0,5.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.49 789[4:MRR:1.1,787.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.49 790[4:MRR:4.1,787.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.21/0.49 791[4:MRR:3.1,787.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.49 792[4:MRR:2.1,787.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.49 802[4:SpR:790.0,53.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.21/0.49 804[4:Rew:788.0,802.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.49 805[4:Rew:791.0,804.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.49 808[4:Rew:805.0,789.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.49 810[4:Rew:805.0,787.0] || equal(multiply(sk_c1,sk_c6),sk_c6)** -> .
% 0.21/0.49 811[4:Rew:805.0,471.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),u)**.
% 0.21/0.49 812[4:Rew:805.0,791.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.49 813[4:Rew:805.0,792.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.21/0.49 838[4:SpR:812.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.21/0.49 840[4:Rew:23.0,838.0] || -> equal(identity,sk_c5)**.
% 0.21/0.49 841[4:Rew:840.0,22.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.49 842[4:Rew:840.0,178.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.49 844[4:Rew:840.0,23.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.21/0.49 849[4:SpR:813.0,53.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c6)**.
% 0.21/0.49 851[4:Rew:808.0,849.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 853[4:SpR:851.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.21/0.49 855[4:Rew:844.0,853.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 858[4:Rew:855.0,841.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 859[4:Rew:855.0,842.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.49 868[4:Rew:858.0,811.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 873[4:Rew:859.0,810.0] || equal(sk_c6,sk_c1)** -> .
% 0.21/0.49 905[4:SpR:868.0,859.0] || -> equal(sk_c6,sk_c1)**.
% 0.21/0.49 907[4:MRR:905.0,873.0] || -> .
% 0.21/0.49 909[3:Spt:907.0,16.1,473.0] || equal(inverse(sk_c2),sk_c6)** -> .
% 0.21/0.49 910[3:Spt:907.0,16.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.49 911[3:MRR:20.1,909.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.49 912[3:MRR:19.0,909.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.21/0.49 913[3:MRR:18.0,909.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.49 914[3:MRR:17.0,909.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.49 922[3:SpR:912.0,53.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.21/0.49 924[3:Rew:911.0,922.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.49 925[3:Rew:913.0,924.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.49 926[3:Rew:925.0,910.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.49 927[3:Rew:925.0,470.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.49 930[3:Rew:925.0,471.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),u)**.
% 0.21/0.49 931[3:Rew:925.0,913.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.49 932[3:Rew:925.0,914.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.21/0.49 934[3:Rew:925.0,468.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.21/0.49 939[3:Rew:925.0,934.5,925.0,934.4,925.0,934.3,925.0,934.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(w,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c6)** -> .
% 0.21/0.49 940[3:Con:939.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c6)** -> .
% 0.21/0.49 957[3:SpR:931.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.21/0.49 959[3:Rew:23.0,957.0] || -> equal(identity,sk_c5)**.
% 0.21/0.49 960[3:Rew:959.0,178.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.49 961[3:Rew:959.0,22.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.49 962[3:Rew:959.0,23.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.21/0.49 968[3:SpR:932.0,53.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c6)**.
% 0.21/0.49 970[3:Rew:926.0,968.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 975[3:SpR:970.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.21/0.49 977[3:Rew:962.0,975.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 980[3:Rew:977.0,961.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 981[3:Rew:977.0,960.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.49 988[3:Rew:980.0,940.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.21/0.49 991[3:Rew:980.0,930.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 1001[3:Con:988.0] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.21/0.49 1002[3:Rew:981.0,1001.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.21/0.49 1025[3:SpR:991.0,981.0] || -> equal(sk_c6,sk_c1)**.
% 0.21/0.49 1029[3:Rew:1025.0,927.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.49 1038[3:Rew:1025.0,1002.0] || equal(inverse(u),sk_c1)** equal(u,sk_c6) -> .
% 0.21/0.49 1040[3:Rew:1025.0,1038.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.21/0.49 1095[3:SpL:1029.0,1040.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.21/0.49 1097[3:Obv:1095.1] || -> .
% 0.21/0.49 1098[2:Spt:1097.0,10.1,470.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.21/0.49 1099[2:Spt:1097.0,10.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.49 1100[2:MRR:6.1,1098.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.49 1101[2:MRR:9.0,1098.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.21/0.49 1102[2:MRR:8.0,1098.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.21/0.49 1103[2:MRR:7.0,1098.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.49 1109[2:SpR:1101.0,53.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c7)**.
% 0.21/0.49 1111[2:Rew:1099.0,1109.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.49 1112[2:Rew:1102.0,1111.0] || -> equal(sk_c7,sk_c6)**.
% 0.21/0.49 1114[2:Rew:1112.0,1100.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.21/0.49 1117[2:Rew:1112.0,1102.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.49 1118[2:Rew:1112.0,1103.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.21/0.49 1120[2:Rew:1112.0,468.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c6)** -> .
% 0.21/0.49 1125[2:Rew:1112.0,1120.5,1112.0,1120.4,1112.0,1120.3,1112.0,1120.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(w,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c6)** -> .
% 0.21/0.49 1126[2:Con:1125.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(sk_c6,multiply(u,sk_c6)),sk_c6)** -> .
% 0.21/0.49 1141[2:SpR:1117.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.21/0.49 1143[2:Rew:23.0,1141.0] || -> equal(identity,sk_c5)**.
% 0.21/0.49 1144[2:Rew:1143.0,22.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.49 1145[2:Rew:1143.0,178.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.49 1147[2:Rew:1143.0,23.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.21/0.49 1152[2:SpR:1118.0,53.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c6)**.
% 0.21/0.49 1154[2:Rew:1114.0,1152.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 1159[2:SpR:1154.0,53.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.21/0.49 1161[2:Rew:1147.0,1159.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 1164[2:Rew:1161.0,1144.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 1165[2:Rew:1161.0,1145.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.49 1172[2:Rew:1164.0,1126.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(v,sk_c6),sk_c6)** equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.21/0.49 1175[2:Rew:1165.0,1118.0] || -> equal(sk_c3,sk_c6)**.
% 0.21/0.49 1177[2:Rew:1175.0,1114.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.49 1184[2:Con:1172.0] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.21/0.49 1185[2:Rew:1165.0,1184.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.21/0.49 1244[2:SpL:1177.0,1185.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.21/0.49 1246[2:Obv:1244.1] || -> .
% 0.21/0.49 % SZS output end Refutation
% 0.21/0.49 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 left_identity left_inverse associativity
% 0.21/0.49
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