TSTP Solution File: GRP287-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP287-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:46:41 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP287-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 13:52:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 946 clauses, backtracked 402 clauses, performed 13 splits and kept 796 clauses.
% 0.20/0.49 SPASS allocated 63704 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.00 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.07 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 5, length 436 :
% 0.20/0.49 % SZS output start Refutation
% 0.20/0.49 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.49 2[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.49 3[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.20/0.49 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.20/0.49 7[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 8[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 10[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.49 12[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.49 13[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 14[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.49 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c2,sk_c6),sk_c5).
% 0.20/0.49 18[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 21[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.49 23[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 25[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.49 26[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.49 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.49 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.49 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.49 30[1:Spt:26.2,26.6] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.20/0.49 31[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.49 33[3:Spt:4.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.49 35[4:Spt:3.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 38[1:SpL:27.0,30.1] || equal(inverse(identity),sk_c6)** equal(sk_c6,sk_c5) -> .
% 0.20/0.49 39[5:Spt:5.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.49 41[6:Spt:2.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.49 43[6:SpL:41.0,30.1] || equal(inverse(sk_c3),sk_c6)** equal(sk_c5,sk_c7) -> .
% 0.20/0.49 44[6:Rew:35.0,43.0] || equal(sk_c6,sk_c6)* equal(sk_c5,sk_c7) -> .
% 0.20/0.49 45[6:Obv:44.0] || equal(sk_c5,sk_c7)** -> .
% 0.20/0.49 47[3:SpR:33.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.49 48[4:SpR:35.0,28.0] || -> equal(multiply(sk_c6,sk_c3),identity)**.
% 0.20/0.49 49[1:SpL:28.0,30.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c5) -> .
% 0.20/0.49 53[6:SpR:41.0,29.0] || -> equal(multiply(sk_c3,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.49 55[3:SpR:47.0,29.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.20/0.49 57[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.49 58[5:SpR:39.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.20/0.49 60[3:Rew:27.0,55.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.20/0.49 61[0:Rew:27.0,57.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.49 68[5:SpR:39.0,60.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.49 75[0:SpR:61.0,61.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.49 77[6:SpR:41.0,61.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.49 78[2:SpR:31.0,61.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.49 79[3:SpR:47.0,61.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.20/0.49 80[4:SpR:48.0,61.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c3)**.
% 0.20/0.49 82[5:SpR:68.0,61.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.49 83[0:SpR:27.0,61.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.20/0.49 84[0:SpR:28.0,61.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.49 89[6:Rew:31.0,77.0,35.0,77.0] || -> equal(sk_c6,sk_c5)**.
% 0.20/0.49 95[6:Rew:89.0,41.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.20/0.49 97[6:Rew:89.0,48.0] || -> equal(multiply(sk_c5,sk_c3),identity)**.
% 0.20/0.49 103[6:Rew:89.0,53.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.49 104[6:Rew:89.0,58.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c5,u))**.
% 0.20/0.49 109[6:Rew:89.0,78.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.20/0.49 110[6:Rew:28.0,109.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 111[6:Rew:110.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 114[6:Rew:110.0,97.0] || -> equal(multiply(sk_c5,sk_c3),sk_c7)**.
% 0.20/0.49 115[6:Rew:89.0,79.0,110.0,79.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c4)**.
% 0.20/0.49 116[6:Rew:115.0,80.0,89.0,80.0,110.0,80.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 137[6:Rew:111.0,103.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),u)**.
% 0.20/0.49 138[6:Rew:137.0,104.0,116.0,104.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.49 141[6:Rew:138.0,114.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.49 143[6:Rew:141.0,95.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.20/0.49 149[6:Rew:111.0,143.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 150[6:MRR:149.0,45.0] || -> .
% 0.20/0.49 157[6:Spt:150.0,2.0,41.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.20/0.49 158[6:Spt:150.0,2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 159[4:Rew:79.0,80.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 163[4:Rew:159.0,79.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c3)**.
% 0.20/0.49 164[5:Rew:78.0,82.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 165[5:Rew:164.0,35.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.49 168[5:Rew:164.0,68.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.49 169[5:Rew:164.0,48.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.20/0.49 174[6:Rew:164.0,157.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.20/0.49 175[5:Rew:164.0,163.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.20/0.49 178[0:Rew:75.0,84.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.49 179[5:Rew:178.0,175.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.20/0.49 187[5:Rew:164.0,12.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.49 188[6:MRR:187.1,174.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 191[5:Rew:159.0,58.0,164.0,58.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.49 192[5:Rew:164.0,38.1,164.0,38.0] || equal(inverse(identity),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.20/0.49 195[5:Rew:164.0,7.1,164.0,7.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.49 196[6:MRR:195.0,174.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.49 205[5:SpR:179.0,61.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.20/0.49 229[6:SpR:196.0,61.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.20/0.49 231[6:Rew:168.0,229.0,188.0,229.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 237[6:Rew:231.0,191.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.20/0.49 239[6:Rew:231.0,192.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.49 244[6:Rew:205.0,237.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 245[6:Rew:244.0,169.0] || -> equal(identity,sk_c3)**.
% 0.20/0.49 260[6:Obv:239.1] || equal(inverse(identity),sk_c7)** -> .
% 0.20/0.49 261[6:Rew:245.0,260.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.49 262[6:Rew:165.0,261.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 263[6:Obv:262.0] || -> .
% 0.20/0.49 264[5:Spt:263.0,5.0,39.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.20/0.49 265[5:Spt:263.0,5.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 266[4:Rew:178.0,163.0] || -> equal(inverse(sk_c6),sk_c3)**.
% 0.20/0.49 267[4:Rew:266.0,78.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.20/0.49 268[5:Rew:159.0,264.0] || equal(multiply(sk_c3,sk_c5),sk_c6)** -> .
% 0.20/0.49 269[5:Rew:267.0,268.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.49 274[4:Rew:159.0,25.1] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.20/0.49 275[4:Rew:267.0,274.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.20/0.49 276[5:MRR:275.1,269.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 277[4:Rew:159.0,15.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.20/0.49 278[4:Rew:267.0,277.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.20/0.49 279[5:MRR:278.1,269.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 280[4:Rew:159.0,20.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 281[4:Rew:267.0,280.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 282[5:MRR:281.0,269.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 283[4:Rew:159.0,10.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 284[4:Rew:267.0,283.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 285[5:MRR:284.0,269.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 286[4:Rew:35.0,49.0,266.0,49.0] || equal(sk_c6,sk_c6)* equal(identity,sk_c5) -> .
% 0.20/0.49 287[4:Obv:286.0] || equal(identity,sk_c5)** -> .
% 0.20/0.49 289[5:SpR:265.0,61.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.20/0.49 295[5:SpR:276.0,61.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.20/0.49 297[5:SpR:279.0,61.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.20/0.49 317[5:SpR:285.0,61.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.49 319[5:Rew:265.0,317.0,279.0,317.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 321[5:Rew:319.0,287.0] || equal(identity,sk_c7)** -> .
% 0.20/0.49 322[5:Rew:319.0,282.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 332[5:Rew:319.0,289.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 336[5:Rew:28.0,332.0] || -> equal(sk_c6,identity)**.
% 0.20/0.49 339[5:Rew:336.0,266.0] || -> equal(inverse(identity),sk_c3)**.
% 0.20/0.49 341[5:Rew:336.0,48.0] || -> equal(multiply(identity,sk_c3),identity)**.
% 0.20/0.49 342[5:Rew:336.0,285.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.20/0.49 345[5:Rew:336.0,295.0] || -> equal(multiply(identity,multiply(sk_c2,u)),u)**.
% 0.20/0.49 347[5:Rew:336.0,322.0] || -> equal(multiply(sk_c2,identity),sk_c7)**.
% 0.20/0.49 349[5:Rew:339.0,83.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.49 350[5:Rew:27.0,341.0] || -> equal(identity,sk_c3)**.
% 0.20/0.49 351[5:Rew:350.0,178.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.20/0.49 354[5:Rew:350.0,321.0] || equal(sk_c3,sk_c7)** -> .
% 0.20/0.49 359[5:Rew:350.0,342.0] || -> equal(multiply(sk_c1,sk_c7),sk_c3)**.
% 0.20/0.49 361[5:Rew:350.0,347.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.49 363[5:Rew:351.0,361.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.49 367[5:Rew:349.0,345.0,350.0,345.0,363.0,345.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 368[5:Rew:367.0,297.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 369[5:Rew:368.0,359.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.49 370[5:MRR:369.0,354.0] || -> .
% 0.20/0.49 379[4:Spt:370.0,3.0,35.0] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.20/0.49 380[4:Spt:370.0,3.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 381[3:Rew:178.0,79.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.49 382[3:Rew:381.0,78.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.20/0.49 384[4:MRR:23.0,379.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 385[4:MRR:13.0,379.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 387[4:MRR:18.0,379.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 388[4:MRR:8.0,379.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 398[3:SpR:381.0,61.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.20/0.49 411[3:SpR:382.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.49 416[4:SpR:387.0,61.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.49 418[4:Rew:384.0,416.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.20/0.49 420[4:SpR:388.0,61.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.49 422[4:Rew:380.0,420.0,385.0,420.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 425[4:Rew:422.0,31.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.20/0.49 428[4:Rew:422.0,38.1] || equal(inverse(identity),sk_c6)** equal(sk_c6,sk_c7) -> .
% 0.20/0.49 431[4:Rew:422.0,411.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.20/0.49 436[4:Rew:422.0,418.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 437[4:Rew:425.0,436.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 439[4:Rew:437.0,33.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 442[4:Rew:437.0,47.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.49 445[4:Rew:437.0,398.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.20/0.49 452[4:Rew:437.0,428.1,437.0,428.0] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.49 453[4:Obv:452.1] || equal(inverse(identity),sk_c7)** -> .
% 0.20/0.49 456[4:Rew:445.0,431.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 457[4:Rew:456.0,442.0] || -> equal(identity,sk_c4)**.
% 0.20/0.49 466[4:Rew:457.0,453.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.20/0.49 469[4:Rew:439.0,466.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 470[4:Obv:469.0] || -> .
% 0.20/0.49 475[3:Spt:470.0,4.0,33.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.49 476[3:Spt:470.0,4.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 477[3:MRR:24.0,475.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 478[3:MRR:14.0,475.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 479[3:MRR:19.0,475.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 480[3:MRR:9.0,475.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 492[3:SpR:479.0,61.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.49 494[3:Rew:477.0,492.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.20/0.49 496[3:SpR:480.0,61.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.49 498[3:Rew:476.0,496.0,478.0,496.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 500[3:Rew:498.0,31.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.20/0.49 501[3:Rew:498.0,479.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 502[3:Rew:498.0,78.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c7)**.
% 0.20/0.49 507[3:Rew:498.0,49.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c7) -> .
% 0.20/0.49 511[3:Rew:498.0,494.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 512[3:Rew:500.0,511.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 513[3:Rew:512.0,477.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 519[3:Rew:512.0,501.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.20/0.49 520[3:Rew:28.0,502.0,512.0,502.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 521[3:Rew:520.0,178.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 525[3:Rew:521.0,519.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.49 527[3:Rew:525.0,513.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 540[3:Rew:520.0,507.1,527.0,507.0,527.0,507.0,512.0,507.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 541[3:Obv:540.1] || -> .
% 0.20/0.49 544[2:Spt:541.0,1.0,31.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.49 545[2:Spt:541.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 546[2:MRR:21.1,544.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 547[2:MRR:11.1,544.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 548[2:MRR:16.0,544.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 549[2:MRR:6.0,544.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 551[2:SpR:545.0,61.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.20/0.49 553[2:SpR:546.0,61.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.20/0.49 555[2:SpR:547.0,61.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.20/0.49 558[2:SpR:548.0,61.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.49 560[2:Rew:546.0,558.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.20/0.49 562[2:SpR:549.0,61.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.49 564[2:Rew:545.0,562.0,547.0,562.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 566[2:Rew:564.0,548.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.20/0.49 567[2:Rew:564.0,544.0] || equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.20/0.49 572[2:Rew:564.0,551.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 575[2:Rew:564.0,560.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 576[2:Rew:575.0,567.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.49 577[2:Rew:28.0,572.0] || -> equal(sk_c6,identity)**.
% 0.20/0.49 579[2:Rew:577.0,549.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.20/0.49 580[2:Rew:577.0,553.0] || -> equal(multiply(identity,multiply(sk_c2,u)),u)**.
% 0.20/0.49 582[2:Rew:577.0,566.0] || -> equal(multiply(sk_c2,identity),sk_c7)**.
% 0.20/0.49 584[2:Rew:577.0,576.0] || equal(identity,sk_c7)** -> .
% 0.20/0.49 585[2:Rew:178.0,582.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.49 589[2:Rew:27.0,580.0,585.0,580.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 590[2:Rew:589.0,555.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 591[2:Rew:590.0,579.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 592[2:MRR:591.0,584.0] || -> .
% 0.20/0.49 599[1:Spt:592.0,26.0,26.1,26.3,26.4,26.5,26.7,26.8,26.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.20/0.49 601[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.49 602[2:Rew:601.0,599.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.49 604[2:Obv:602.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.49 607[2:SpR:601.0,61.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.49 609[3:Spt:3.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 611[3:Rew:609.0,604.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.20/0.49 612[3:Obv:611.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.20/0.49 615[3:SpR:609.0,61.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.20/0.49 617[4:Spt:24.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.49 623[5:Spt:23.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 633[2:SpR:607.0,29.0] || -> equal(multiply(inverse(sk_c6),multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.49 637[3:SpR:615.0,29.0] || -> equal(multiply(inverse(sk_c7),multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.20/0.49 642[0:SpR:28.0,61.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.49 643[0:SpR:28.0,178.0] || -> equal(inverse(identity),identity)**.
% 0.20/0.49 645[4:SpR:617.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.49 646[5:SpR:623.0,28.0] || -> equal(multiply(sk_c6,sk_c3),identity)**.
% 0.20/0.49 648[0:Rew:178.0,642.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.49 656[4:SpR:645.0,61.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.20/0.49 658[4:Rew:178.0,656.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.49 659[4:Rew:658.0,607.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.20/0.49 661[4:Rew:659.0,10.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 662[4:Rew:659.0,20.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 663[4:Rew:659.0,15.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.20/0.49 664[4:Rew:659.0,25.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.20/0.49 665[4:Rew:663.1,12.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.49 667[4:Rew:661.0,7.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 671[4:SpR:658.0,28.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.20/0.49 674[5:SpR:646.0,61.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c3)**.
% 0.20/0.49 676[5:Rew:178.0,674.0,658.0,674.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 679[5:Rew:676.0,658.0] || -> equal(inverse(sk_c6),sk_c3)**.
% 0.20/0.49 681[5:Rew:676.0,659.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.20/0.49 683[5:Rew:676.0,671.0] || -> equal(multiply(sk_c3,sk_c6),identity)**.
% 0.20/0.49 686[6:Spt:663.1] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 687[6:Rew:686.0,601.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.49 689[6:Rew:686.0,623.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.49 693[6:Rew:686.0,612.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.20/0.49 700[6:Rew:686.0,667.1] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.49 702[6:Rew:686.0,679.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.20/0.49 703[6:Rew:686.0,683.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.20/0.49 704[6:Rew:703.0,665.1] || -> equal(inverse(sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.20/0.49 708[6:Rew:703.0,700.0] || -> equal(identity,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.49 710[6:Rew:686.0,693.5,686.0,693.4,686.0,693.3,686.0,693.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.20/0.49 711[6:Con:710.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.20/0.49 726[7:Spt:704.1] || -> equal(identity,sk_c7)**.
% 0.20/0.49 727[7:Rew:726.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 728[7:Rew:726.0,178.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 730[7:Rew:726.0,643.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 733[7:Rew:702.0,730.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.49 735[7:Rew:733.0,689.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 741[7:Rew:727.0,687.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 743[7:Rew:741.0,711.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.20/0.49 752[7:Con:743.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.20/0.49 753[7:Rew:728.0,752.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.49 767[0:SpR:648.0,61.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.20/0.49 794[7:SpL:735.0,753.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 796[7:Obv:794.1] || -> .
% 0.20/0.49 797[7:Spt:796.0,704.1,726.0] || equal(identity,sk_c7)** -> .
% 0.20/0.49 798[7:Spt:796.0,704.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 800[7:MRR:708.0,797.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.49 803[7:SpR:798.0,648.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.49 805[7:Rew:702.0,803.0] || -> equal(sk_c1,sk_c3)**.
% 0.20/0.49 807[7:Rew:805.0,800.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.49 808[7:Rew:703.0,807.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 809[7:MRR:808.0,797.0] || -> .
% 0.20/0.49 811[6:Spt:809.0,663.1,686.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.49 812[6:Spt:809.0,663.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 814[6:MRR:664.1,811.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 815[6:MRR:661.0,811.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 816[6:MRR:662.0,811.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 818[6:SpR:812.0,648.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.49 820[6:Rew:818.0,615.0] || -> equal(multiply(sk_c1,sk_c5),sk_c6)**.
% 0.20/0.49 834[6:SpR:814.0,648.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.20/0.49 836[6:Rew:679.0,834.0] || -> equal(sk_c2,sk_c3)**.
% 0.20/0.49 838[6:Rew:836.0,816.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.20/0.49 839[6:Rew:683.0,838.0] || -> equal(identity,sk_c5)**.
% 0.20/0.49 840[6:Rew:839.0,643.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.20/0.49 841[6:Rew:839.0,178.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.49 844[6:Rew:839.0,646.0] || -> equal(multiply(sk_c6,sk_c3),sk_c5)**.
% 0.20/0.49 846[6:Rew:841.0,820.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.49 847[6:Rew:841.0,681.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.49 852[6:Rew:846.0,811.0] || equal(sk_c1,sk_c7)** -> .
% 0.20/0.49 859[6:Rew:846.0,815.0] || -> equal(multiply(sk_c1,sk_c7),sk_c1)**.
% 0.20/0.49 866[6:Rew:846.0,844.0,847.0,844.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.20/0.49 868[6:Rew:866.0,859.0] || -> equal(sk_c1,sk_c5)**.
% 0.20/0.49 869[6:Rew:868.0,812.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.49 873[6:Rew:868.0,852.0] || equal(sk_c5,sk_c7)** -> .
% 0.20/0.49 876[6:Rew:840.0,869.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 884[6:Rew:876.0,873.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 885[6:Obv:884.0] || -> .
% 0.20/0.49 901[5:Spt:885.0,23.0,623.0] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.20/0.49 902[5:Spt:885.0,23.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 903[4:Rew:663.1,13.0] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 904[4:Rew:662.0,18.0] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 905[4:Rew:661.0,8.0] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 907[5:SpR:902.0,648.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.20/0.49 909[5:Rew:658.0,907.0] || -> equal(sk_c2,sk_c4)**.
% 0.20/0.49 912[5:Rew:909.0,904.1] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.20/0.49 913[5:Rew:909.0,662.1] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.20/0.49 915[5:Rew:671.0,913.1] || -> equal(sk_c6,sk_c7)** equal(identity,sk_c5).
% 0.20/0.49 916[5:Rew:671.0,912.1] || -> equal(inverse(sk_c3),sk_c7)** equal(identity,sk_c5).
% 0.20/0.49 965[6:Spt:915.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 966[6:Rew:965.0,658.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.49 967[6:Rew:965.0,901.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.49 969[6:Rew:965.0,601.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.49 979[6:Rew:965.0,905.1] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.49 981[6:Rew:965.0,612.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.20/0.49 983[6:MRR:903.0,967.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 984[6:MRR:916.0,967.0] || -> equal(identity,sk_c5)**.
% 0.20/0.49 987[6:Rew:984.0,178.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.49 992[6:Rew:987.0,659.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.49 994[6:Rew:992.0,966.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 1003[6:MRR:979.0,967.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.49 1006[6:Rew:965.0,981.5,965.0,981.4,987.0,981.3,965.0,981.3,965.0,981.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.20/0.49 1007[6:Con:1006.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.20/0.49 1015[6:SpR:983.0,648.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.49 1017[6:Rew:994.0,1015.0] || -> equal(sk_c1,sk_c7)**.
% 0.20/0.49 1019[6:Rew:1017.0,1003.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.49 1020[6:Rew:969.0,1019.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 1025[6:Rew:1020.0,987.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 1028[6:Rew:1025.0,1007.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.20/0.49 1030[6:Con:1028.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.49 1083[6:SpL:994.0,1030.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 1084[6:Obv:1083.1] || -> .
% 0.20/0.49 1085[6:Spt:1084.0,915.0,965.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.49 1086[6:Spt:1084.0,915.1] || -> equal(identity,sk_c5)**.
% 0.20/0.49 1087[6:Rew:1086.0,643.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.20/0.49 1090[6:Rew:1086.0,178.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.49 1092[6:Rew:1090.0,659.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.49 1094[6:Rew:1092.0,617.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.49 1100[6:MRR:663.1,1085.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 1103[6:MRR:661.0,1085.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 1120[6:SpR:1100.0,648.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.49 1123[6:Rew:1094.0,1120.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.49 1124[6:Rew:1123.0,1085.0] || equal(sk_c1,sk_c7)** -> .
% 0.20/0.49 1126[6:Rew:1123.0,601.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.20/0.49 1132[6:Rew:1123.0,1103.0] || -> equal(multiply(sk_c1,sk_c7),sk_c1)**.
% 0.20/0.49 1134[6:Rew:1126.0,1132.0] || -> equal(sk_c1,sk_c5)**.
% 0.20/0.49 1135[6:Rew:1134.0,1100.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.49 1137[6:Rew:1134.0,1124.0] || equal(sk_c5,sk_c7)** -> .
% 0.20/0.49 1142[6:Rew:1087.0,1135.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 1150[6:Rew:1142.0,1137.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 1151[6:Obv:1150.0] || -> .
% 0.20/0.49 1162[4:Spt:1151.0,24.0,617.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.49 1163[4:Spt:1151.0,24.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 1164[4:MRR:14.0,1162.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 1165[4:MRR:19.0,1162.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 1166[4:MRR:9.0,1162.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 1168[4:SpR:1163.0,648.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.20/0.49 1169[4:SpR:1163.0,767.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.20/0.49 1171[4:Rew:1168.0,607.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.20/0.49 1172[4:Rew:1168.0,633.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.49 1180[4:SpR:1164.0,648.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.49 1184[4:Rew:1180.0,637.0] || -> equal(multiply(sk_c1,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.20/0.49 1201[4:SpR:1165.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.49 1205[4:Rew:1169.0,1201.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.49 1208[4:Rew:1205.0,1172.0] || -> equal(multiply(sk_c2,u),multiply(sk_c7,u))**.
% 0.20/0.49 1209[4:Rew:1205.0,1184.0] || -> equal(multiply(sk_c6,u),multiply(sk_c1,u))**.
% 0.20/0.49 1212[4:Rew:1208.0,1171.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.20/0.49 1214[4:Rew:1209.0,601.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.20/0.49 1218[4:Rew:1166.0,1214.0] || -> equal(sk_c6,sk_c5)**.
% 0.20/0.49 1222[4:Rew:1218.0,609.0] || -> equal(multiply(sk_c7,sk_c5),sk_c5)**.
% 0.20/0.49 1224[4:Rew:1218.0,612.0] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.20/0.49 1229[4:Rew:1212.0,1222.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 1230[4:Rew:1229.0,1205.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 1232[4:Rew:1229.0,1218.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 1250[4:Rew:1232.0,1224.5,1232.0,1224.4,1229.0,1224.3,1232.0,1224.3,1232.0,1224.1,1229.0,1224.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.20/0.49 1251[4:Con:1250.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.20/0.49 1278[4:SpR:1164.0,28.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.20/0.49 1280[4:Rew:1230.0,1278.0] || -> equal(identity,sk_c1)**.
% 0.20/0.49 1281[4:Rew:1280.0,643.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.49 1282[4:Rew:1280.0,178.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.49 1286[4:Rew:1164.0,1281.0] || -> equal(sk_c1,sk_c7)**.
% 0.20/0.49 1287[4:Rew:1286.0,1164.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.49 1293[4:Rew:1286.0,1282.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 1294[4:Rew:1293.0,1251.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.49 1346[4:SpL:1287.0,1294.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 1347[4:Obv:1346.1] || -> .
% 0.20/0.49 1348[3:Spt:1347.0,3.1,609.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.20/0.49 1349[3:Spt:1347.0,3.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 1351[3:MRR:4.1,1348.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.49 1354[3:MRR:5.1,1348.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.20/0.49 1356[3:SpR:1349.0,648.0] || -> equal(inverse(sk_c6),sk_c3)**.
% 0.20/0.49 1359[3:Rew:1356.0,607.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.20/0.49 1362[3:SpR:1351.0,648.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.49 1365[3:Rew:1356.0,1362.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.49 1367[3:Rew:1365.0,1354.0] || -> equal(multiply(sk_c3,sk_c5),sk_c6)**.
% 0.20/0.49 1368[3:Rew:1359.0,1367.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 1370[3:Rew:1368.0,601.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.20/0.49 1371[3:Rew:1368.0,1348.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.20/0.49 1377[3:Rew:1370.0,1371.0] || equal(sk_c5,sk_c5)* -> .
% 0.20/0.49 1378[3:Obv:1377.0] || -> .
% 0.20/0.49 1381[2:Spt:1378.0,1.0,601.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.49 1382[2:Spt:1378.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.20/0.49 1383[2:MRR:21.1,1381.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.49 1384[2:MRR:11.1,1381.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 1385[2:MRR:16.0,1381.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.49 1386[2:MRR:6.0,1381.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.49 1398[2:SpR:1383.0,767.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.20/0.49 1409[2:SpR:1385.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.49 1413[2:Rew:1398.0,1409.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.49 1420[2:SpR:1386.0,61.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.20/0.49 1422[2:Rew:1382.0,1420.0,1384.0,1420.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.49 1423[2:Rew:1422.0,1382.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 1425[2:Rew:1422.0,1381.0] || equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.20/0.49 1428[2:Rew:1422.0,1413.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 1429[2:Rew:1428.0,1423.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.49 1444[2:Rew:1428.0,1425.0,1429.0,1425.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.49 1445[2:Obv:1444.0] || -> .
% 0.20/0.49 % SZS output end Refutation
% 0.20/0.49 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_18 prove_this_19 prove_this_20 prove_this_21 prove_this_23 prove_this_24 prove_this_25 prove_this_26 left_identity left_inverse associativity
% 0.20/0.50
%------------------------------------------------------------------------------