TSTP Solution File: GRP231-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP231-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 11:46:26 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP231-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 05:16:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 945 clauses, backtracked 390 clauses, performed 12 splits and kept 681 clauses.
% 0.19/0.47 SPASS allocated 63713 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.01 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 4, length 364 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.47 2[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.47 3[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.47 4[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.47 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.47 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 8[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c2),sk_c8).
% 0.19/0.47 9[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 11[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 12[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.47 13[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.47 14[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.47 15[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 18[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.19/0.47 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 22[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.47 23[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.47 24[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.47 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 26[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 27[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 28[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c3,sk_c7),sk_c8).
% 0.19/0.47 29[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 30[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 31[0:Inp] || equal(inverse(sk_c8),sk_c7) equal(multiply(u,v),sk_c8)** equal(inverse(u),v) equal(multiply(v,sk_c7),sk_c8)** equal(inverse(w),sk_c8) equal(multiply(w,sk_c7),sk_c8)** equal(inverse(x),sk_c8) equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(z,sk_c8),y)* equal(inverse(z),sk_c8) -> .
% 0.19/0.47 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 35[0:Con:31.6] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),y)* equal(multiply(x,sk_c7),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** -> .
% 0.19/0.47 36[1:Spt:35.0,35.4,35.7] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.19/0.47 37[2:Spt:5.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.47 39[3:Spt:1.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 41[4:Spt:4.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.47 47[1:SpL:32.0,36.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 48[5:Spt:3.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.47 50[5:SpL:48.0,36.1] || equal(inverse(sk_c8),sk_c6) equal(sk_c8,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.19/0.47 51[6:Spt:2.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.47 57[2:SpR:37.0,33.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.47 58[3:SpR:39.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.47 61[2:SpL:57.0,36.1] || equal(inverse(sk_c8),sk_c5) equal(sk_c8,identity) equal(multiply(sk_c5,sk_c7),sk_c8)** -> .
% 0.19/0.47 63[3:SpL:58.0,36.1] || equal(inverse(sk_c8),sk_c4) equal(sk_c8,identity) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.19/0.47 71[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 73[2:SpR:57.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.19/0.47 76[2:Rew:32.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.19/0.47 78[0:Rew:32.0,71.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 82[4:SpR:41.0,76.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.47 84[5:Rew:48.0,82.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 87[5:Rew:84.0,39.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.47 88[5:Rew:84.0,41.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 89[5:Rew:84.0,48.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 90[6:Rew:84.0,51.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.47 91[5:Rew:84.0,57.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.19/0.47 92[5:Rew:84.0,58.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.47 94[5:Rew:84.0,50.0] || equal(inverse(sk_c7),sk_c6) equal(sk_c8,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.19/0.47 95[5:Rew:84.0,61.0] || equal(inverse(sk_c7),sk_c5) equal(sk_c8,identity) equal(multiply(sk_c5,sk_c7),sk_c8)** -> .
% 0.19/0.47 112[5:Rew:84.0,94.2,84.0,94.1] || equal(inverse(sk_c7),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.19/0.47 113[5:Obv:112.1] || equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.19/0.47 114[5:Rew:88.0,95.2,84.0,95.2,84.0,95.1] || equal(inverse(sk_c7),sk_c5)** equal(identity,sk_c7) equal(sk_c6,sk_c7) -> .
% 0.19/0.47 139[0:SpR:78.0,78.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 141[0:SpR:32.0,78.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.19/0.47 142[0:SpR:33.0,78.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 146[5:SpR:89.0,78.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 147[5:SpR:91.0,78.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.19/0.47 148[5:SpR:92.0,78.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.19/0.47 154[5:Rew:33.0,146.0] || -> equal(identity,sk_c6)**.
% 0.19/0.47 155[5:Rew:154.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 160[5:Rew:154.0,114.1] || equal(inverse(sk_c7),sk_c5)** equal(sk_c6,sk_c7) equal(sk_c6,sk_c7) -> .
% 0.19/0.47 163[5:Rew:154.0,141.0] || -> equal(multiply(inverse(sk_c6),u),u)**.
% 0.19/0.47 166[5:Rew:155.0,113.1] || equal(inverse(sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.47 167[5:Rew:154.0,147.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.47 168[5:Rew:167.0,148.0,154.0,148.0] || -> equal(sk_c5,sk_c4)**.
% 0.19/0.47 170[5:Rew:168.0,88.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.19/0.47 174[5:Rew:168.0,167.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c4)**.
% 0.19/0.47 175[6:Rew:90.0,170.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 184[6:Rew:175.0,163.0] || -> equal(multiply(inverse(sk_c7),u),u)**.
% 0.19/0.47 185[6:Rew:184.0,174.0,175.0,174.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 186[6:Rew:185.0,87.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 190[6:Rew:185.0,168.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 205[5:Obv:166.1] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.19/0.47 211[5:Obv:160.1] || equal(inverse(sk_c7),sk_c5)** equal(sk_c6,sk_c7) -> .
% 0.19/0.47 212[6:Rew:175.0,211.1,186.0,211.0,190.0,211.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 213[6:Obv:212.1] || -> .
% 0.19/0.47 219[6:Spt:213.0,2.1,51.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.19/0.47 220[6:Spt:213.0,2.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.47 221[6:Rew:84.0,220.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 222[6:Rew:221.0,205.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.47 223[6:Rew:89.0,174.0,221.0,174.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 226[6:Rew:223.0,170.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 236[5:Rew:84.0,22.1,84.0,22.0] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.47 237[6:Rew:226.0,236.1,223.0,236.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 238[6:MRR:237.1,222.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 244[5:Rew:84.0,27.1,84.0,27.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 245[6:Rew:226.0,244.0,223.0,244.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 246[6:MRR:245.0,222.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 273[6:SpR:246.0,78.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.19/0.47 275[6:Rew:226.0,273.0,238.0,273.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 276[6:MRR:275.0,222.0] || -> .
% 0.19/0.47 277[5:Spt:276.0,3.1,48.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.19/0.47 278[5:Spt:276.0,3.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.47 279[5:Rew:82.0,277.0] || equal(sk_c8,sk_c7)** -> .
% 0.19/0.47 280[0:Rew:139.0,142.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 281[4:Rew:82.0,23.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c8,sk_c7).
% 0.19/0.47 282[5:MRR:281.1,279.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 283[4:Rew:82.0,13.1] || -> equal(inverse(sk_c1),sk_c2)** equal(sk_c8,sk_c7).
% 0.19/0.47 284[5:MRR:283.1,279.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 285[4:Rew:82.0,28.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 286[5:MRR:285.0,279.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 289[4:Rew:82.0,8.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 290[5:MRR:289.0,279.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 292[5:Rew:278.0,63.0] || equal(sk_c4,sk_c7) equal(sk_c8,identity) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.19/0.47 308[5:SpR:286.0,78.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.47 310[5:Rew:282.0,308.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.47 316[3:SpR:58.0,78.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.19/0.47 318[5:Rew:278.0,316.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.19/0.47 319[5:Rew:280.0,318.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 323[5:Rew:319.0,292.0] || equal(sk_c7,sk_c7) equal(sk_c8,identity) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.19/0.47 326[5:Obv:323.0] || equal(sk_c8,identity) equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.19/0.47 327[5:Rew:319.0,326.1] || equal(sk_c8,identity) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.47 335[2:SpR:57.0,78.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.19/0.47 354[5:SpR:290.0,78.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.19/0.47 356[5:Rew:284.0,354.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.19/0.47 358[5:SpR:310.0,78.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.47 360[5:Rew:278.0,358.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.47 361[5:Rew:360.0,327.1] || equal(sk_c8,identity) equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 362[5:Obv:361.1] || equal(sk_c8,identity)** -> .
% 0.19/0.47 377[5:SpR:356.0,78.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.19/0.47 379[5:Rew:33.0,377.0] || -> equal(sk_c8,identity)**.
% 0.19/0.47 380[5:MRR:379.0,362.0] || -> .
% 0.19/0.47 381[4:Spt:380.0,4.1,41.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.19/0.47 382[4:Spt:380.0,4.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.47 383[4:Rew:280.0,316.0,382.0,316.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 386[4:Rew:280.0,335.0,382.0,335.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 389[4:Rew:386.0,381.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.19/0.47 398[4:Rew:386.0,24.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 399[4:MRR:398.1,389.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 400[4:Rew:386.0,14.1] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 401[4:MRR:400.1,389.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 405[4:Rew:386.0,29.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 406[4:MRR:405.0,389.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 409[4:Rew:386.0,9.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 410[4:MRR:409.0,389.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 411[4:Rew:383.0,63.2,382.0,63.0,383.0,63.0] || equal(sk_c7,sk_c7) equal(sk_c8,identity) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.47 412[4:Obv:411.0] || equal(sk_c8,identity) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.47 430[4:SpR:406.0,78.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.47 432[4:Rew:399.0,430.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.47 442[4:SpR:410.0,78.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.19/0.47 444[4:Rew:401.0,442.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.19/0.47 446[4:SpR:432.0,78.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.47 448[4:Rew:382.0,446.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.47 449[4:Rew:448.0,412.1] || equal(sk_c8,identity) equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 450[4:Obv:449.1] || equal(sk_c8,identity)** -> .
% 0.19/0.47 452[4:SpR:444.0,78.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.19/0.47 454[4:Rew:33.0,452.0] || -> equal(sk_c8,identity)**.
% 0.19/0.47 455[4:MRR:454.0,450.0] || -> .
% 0.19/0.47 456[3:Spt:455.0,1.0,39.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.47 457[3:Spt:455.0,1.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.47 458[3:Rew:280.0,335.0,457.0,335.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 463[3:MRR:21.0,456.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 464[3:MRR:11.0,456.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 467[3:MRR:26.0,456.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 469[3:MRR:6.0,456.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 470[3:Rew:458.0,61.2,457.0,61.0,458.0,61.0] || equal(sk_c7,sk_c7) equal(sk_c8,identity) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.47 471[3:Obv:470.0] || equal(sk_c8,identity) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.47 492[3:SpR:467.0,78.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.47 494[3:Rew:463.0,492.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.47 499[3:SpR:469.0,78.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.19/0.47 501[3:Rew:464.0,499.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.19/0.47 503[3:SpR:494.0,78.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.47 505[3:Rew:457.0,503.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.47 506[3:Rew:505.0,471.1] || equal(sk_c8,identity) equal(sk_c8,sk_c8)* -> .
% 0.19/0.47 507[3:Obv:506.1] || equal(sk_c8,identity)** -> .
% 0.19/0.47 509[3:SpR:501.0,78.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.19/0.47 511[3:Rew:33.0,509.0] || -> equal(sk_c8,identity)**.
% 0.19/0.47 512[3:MRR:511.0,507.0] || -> .
% 0.19/0.47 513[2:Spt:512.0,5.0,37.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.47 514[2:Spt:512.0,5.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.47 515[2:MRR:25.0,513.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 516[2:MRR:15.0,513.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 517[2:MRR:30.0,513.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 519[2:MRR:10.0,513.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 527[2:SpR:517.0,78.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.19/0.47 529[2:Rew:515.0,527.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.47 534[2:SpR:519.0,78.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.19/0.47 536[2:Rew:516.0,534.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.19/0.47 542[2:SpR:536.0,78.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.19/0.47 544[2:Rew:33.0,542.0] || -> equal(sk_c8,identity)**.
% 0.19/0.47 545[2:Rew:544.0,514.0] || -> equal(inverse(identity),sk_c7)**.
% 0.19/0.47 551[2:Rew:544.0,529.0] || -> equal(multiply(identity,identity),sk_c7)**.
% 0.19/0.47 553[2:Rew:544.0,47.1] || equal(inverse(identity),u) equal(u,identity) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.47 566[2:Rew:32.0,551.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 569[2:Rew:566.0,280.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 570[2:Rew:566.0,544.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 571[2:Rew:566.0,545.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 595[2:Rew:569.0,553.2,570.0,553.2,566.0,553.1,571.0,553.0,566.0,553.0] || equal(sk_c7,u)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.19/0.47 596[2:Obv:595.1] || equal(u,sk_c7)* -> .
% 0.19/0.47 597[2:UnC:596.0,78.0] || -> .
% 0.19/0.47 602[1:Spt:597.0,35.1,35.2,35.3,35.5,35.6,35.8] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),w)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,w),sk_c7)** -> .
% 0.19/0.47 603[1:EqR:602.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.47 605[2:Spt:1.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.47 608[2:Rew:605.0,603.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c7,sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.47 609[2:Obv:608.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.47 612[2:SpR:605.0,78.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.47 614[3:Spt:25.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.47 617[4:Spt:21.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.47 631[0:SpR:33.0,78.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 632[0:SpR:33.0,280.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.47 634[2:SpR:605.0,33.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.19/0.47 635[3:SpR:614.0,33.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.47 636[4:SpR:617.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.47 638[0:Rew:280.0,631.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.47 646[2:SpR:634.0,78.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c8)**.
% 0.19/0.47 648[2:Rew:280.0,646.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.47 651[2:SpR:648.0,33.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.47 654[3:SpR:635.0,78.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.19/0.47 656[3:Rew:280.0,654.0,605.0,654.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 659[3:Rew:656.0,9.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 662[3:Rew:656.0,14.1] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 667[3:Rew:634.0,662.1] || -> equal(inverse(sk_c1),sk_c2)** equal(identity,sk_c6).
% 0.19/0.47 669[3:Rew:634.0,659.0] || -> equal(identity,sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 672[5:Spt:667.1] || -> equal(identity,sk_c6)**.
% 0.19/0.47 673[5:Rew:672.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 674[5:Rew:672.0,280.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.47 677[5:Rew:672.0,634.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.47 678[5:Rew:672.0,636.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.19/0.47 679[5:Rew:672.0,651.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.47 680[5:Rew:674.0,8.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 681[5:Rew:674.0,18.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.47 682[5:Rew:674.0,28.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 683[5:Rew:674.0,13.1] || -> equal(inverse(sk_c1),sk_c2)** equal(sk_c8,sk_c7).
% 0.19/0.47 684[5:Rew:674.0,23.1] || -> equal(inverse(sk_c3),sk_c8)** equal(sk_c8,sk_c7).
% 0.19/0.47 685[5:Rew:683.1,12.1] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.47 686[5:Rew:684.1,22.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.47 689[5:Rew:682.0,27.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 701[5:SpR:678.0,78.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c4)**.
% 0.19/0.47 703[5:Rew:605.0,701.0] || -> equal(multiply(sk_c7,sk_c6),sk_c4)**.
% 0.19/0.47 704[5:Rew:674.0,703.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 708[5:Rew:704.0,689.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.19/0.47 711[5:Rew:704.0,686.1] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 712[5:Rew:704.0,685.1] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 724[0:SpR:638.0,78.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.47 757[6:Spt:683.1] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 758[6:Rew:757.0,605.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 760[6:Rew:757.0,677.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 763[6:Rew:757.0,609.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.47 767[6:Rew:757.0,711.0] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 770[6:Rew:757.0,708.1] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 771[6:Rew:760.0,712.1] || -> equal(inverse(sk_c1),sk_c2)** equal(sk_c6,sk_c7).
% 0.19/0.47 772[6:Rew:760.0,767.1] || -> equal(inverse(sk_c3),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 775[6:Rew:760.0,770.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 776[6:Rew:757.0,763.3,757.0,763.2,757.0,763.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.19/0.47 790[7:Spt:771.1] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 793[7:Rew:790.0,673.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 794[7:Rew:790.0,674.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 801[7:Rew:793.0,776.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.47 803[7:Con:801.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.47 804[7:Rew:794.0,803.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 829[7:SpL:758.0,804.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 830[7:Obv:829.1] || -> .
% 0.19/0.47 831[7:Spt:830.0,771.1,790.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.47 832[7:Spt:830.0,771.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 833[7:MRR:772.1,831.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 836[7:MRR:775.0,831.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 846[7:SpR:833.0,638.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.47 848[7:Rew:758.0,846.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 850[7:Rew:848.0,836.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 851[7:Rew:760.0,850.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 852[7:MRR:851.0,831.0] || -> .
% 0.19/0.47 854[6:Spt:852.0,683.1,757.0] || equal(sk_c8,sk_c7)** -> .
% 0.19/0.47 855[6:Spt:852.0,683.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 857[6:MRR:680.0,854.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 858[6:MRR:681.0,854.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.47 861[6:SpR:855.0,638.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.19/0.47 877[6:SpR:857.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.47 881[6:SpR:861.0,78.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.47 884[6:Rew:877.0,881.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 887[6:Rew:884.0,679.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 888[6:Rew:884.0,612.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 894[6:Rew:887.0,674.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 899[6:Rew:887.0,677.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.47 904[6:Rew:894.0,858.0] || -> equal(sk_c8,sk_c2)**.
% 0.19/0.47 905[6:Rew:904.0,854.0] || equal(sk_c2,sk_c7)** -> .
% 0.19/0.47 915[6:Rew:888.0,899.0,904.0,899.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.47 916[6:MRR:915.0,905.0] || -> .
% 0.19/0.47 923[5:Spt:916.0,667.1,672.0] || equal(identity,sk_c6)** -> .
% 0.19/0.47 924[5:Spt:916.0,667.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 926[5:MRR:669.0,923.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 930[5:SpR:924.0,638.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.19/0.47 959[5:SpR:926.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.47 963[5:SpR:930.0,78.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.47 966[5:Rew:959.0,963.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 971[5:Rew:966.0,609.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.47 973[5:Rew:966.0,651.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 974[5:Rew:973.0,632.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 977[5:Rew:973.0,280.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 980[5:Rew:648.0,974.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 981[5:Rew:980.0,605.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 999[5:Rew:977.0,971.3,980.0,971.3,977.0,971.2,980.0,971.2,980.0,971.1,980.0,971.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(u,sk_c7) -> .
% 0.19/0.47 1000[5:Con:999.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 1056[5:SpL:981.0,1000.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 1057[5:Obv:1056.1] || -> .
% 0.19/0.47 1058[4:Spt:1057.0,21.0,617.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.47 1059[4:Spt:1057.0,21.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.47 1060[4:MRR:11.0,1058.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.47 1063[4:MRR:6.0,1058.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.47 1076[4:SpR:1060.0,724.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.47 1110[4:SpR:1063.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.47 1114[4:Rew:1076.0,1110.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.47 1115[4:Rew:1114.0,651.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 1121[4:Rew:1114.0,609.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.47 1122[4:Rew:1115.0,632.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 1125[4:Rew:1115.0,280.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 1127[4:Rew:648.0,1122.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.47 1128[4:Rew:1127.0,648.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 1150[4:Rew:1125.0,1121.3,1127.0,1121.3,1125.0,1121.2,1127.0,1121.2,1127.0,1121.1,1127.0,1121.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(u,sk_c7) -> .
% 0.19/0.48 1151[4:Con:1150.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.48 1198[4:SpL:1128.0,1151.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 1199[4:Obv:1198.1] || -> .
% 0.19/0.48 1200[3:Spt:1199.0,25.0,614.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.48 1201[3:Spt:1199.0,25.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.19/0.48 1202[3:MRR:15.0,1200.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.48 1205[3:MRR:10.0,1200.0] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.19/0.48 1232[3:SpR:1202.0,724.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),u)**.
% 0.19/0.48 1252[3:SpR:1205.0,34.0] || -> equal(multiply(sk_c1,multiply(sk_c2,u)),multiply(sk_c8,u))**.
% 0.19/0.48 1256[3:Rew:1232.0,1252.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.48 1257[3:Rew:1256.0,651.0] || -> equal(identity,sk_c7)**.
% 0.19/0.48 1263[3:Rew:1256.0,609.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.19/0.48 1264[3:Rew:1257.0,632.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 1266[3:Rew:1257.0,280.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 1269[3:Rew:648.0,1264.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 1270[3:Rew:1269.0,605.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 1292[3:Rew:1266.0,1263.3,1269.0,1263.3,1266.0,1263.2,1269.0,1263.2,1269.0,1263.1,1269.0,1263.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(u,sk_c7) -> .
% 0.19/0.48 1293[3:Con:1292.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.48 1340[3:SpL:1270.0,1293.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 1341[3:Obv:1340.1] || -> .
% 0.19/0.48 1342[2:Spt:1341.0,1.1,605.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.48 1343[2:Spt:1341.0,1.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 1344[2:MRR:5.1,1342.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.48 1345[2:MRR:2.0,1342.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.48 1346[2:MRR:3.0,1342.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.48 1347[2:MRR:4.0,1342.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.48 1349[2:SpR:1343.0,638.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.48 1350[2:SpR:1343.0,724.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.19/0.48 1352[2:Rew:1349.0,1342.0] || equal(sk_c4,sk_c7)** -> .
% 0.19/0.48 1360[2:SpR:1344.0,638.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.19/0.48 1363[2:Rew:1349.0,1360.0] || -> equal(sk_c5,sk_c4)**.
% 0.19/0.48 1365[2:Rew:1363.0,1347.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.19/0.48 1378[2:SpR:1346.0,78.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.19/0.48 1380[2:Rew:1345.0,1378.0,1349.0,1378.0] || -> equal(sk_c8,sk_c6)**.
% 0.19/0.48 1381[2:Rew:1380.0,1343.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.48 1382[2:Rew:1380.0,1349.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.48 1384[2:Rew:1380.0,1346.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.19/0.48 1386[2:Rew:1380.0,1350.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.19/0.48 1388[2:Rew:1380.0,1365.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.19/0.48 1408[2:SpR:1388.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.19/0.48 1409[2:SpR:1388.0,78.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c6)**.
% 0.19/0.48 1411[2:Rew:1384.0,1409.0,1381.0,1409.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 1415[2:Rew:1411.0,1382.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.48 1419[2:Rew:1411.0,1386.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.19/0.48 1422[2:Rew:1419.0,1408.0,1411.0,1408.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 1456[2:SpR:1422.0,280.0] || -> equal(identity,sk_c7)**.
% 0.19/0.48 1458[2:Rew:1456.0,632.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 1463[2:Rew:1415.0,1458.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.48 1464[2:MRR:1463.0,1352.0] || -> .
% 0.19/0.48 % SZS output end Refutation
% 0.19/0.48 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_18 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.19/0.48
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