TSTP Solution File: GRP221-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP221-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:46:23 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP221-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.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 01:11:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 1285 clauses, backtracked 595 clauses, performed 14 splits and kept 1092 clauses.
% 0.20/0.50 SPASS allocated 63910 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.50 0:00:00.03 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.08 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 5, length 563 :
% 0.20/0.50 % SZS output start Refutation
% 0.20/0.50 1[0:Inp] || -> equal(inverse(sk_c10),sk_c9)** equal(inverse(sk_c1),sk_c10).
% 0.20/0.50 3[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 4[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.50 7[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 8[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 10[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c9),sk_c10).
% 0.20/0.50 12[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 13[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 14[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 15[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 17[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 18[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 19[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 20[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 21[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 22[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.50 23[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.20/0.50 24[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 25[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 26[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 27[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 29[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c8) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 30[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 31[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 32[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 33[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c5),sk_c9).
% 0.20/0.50 34[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 35[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c8)** equal(multiply(sk_c10,sk_c5),sk_c9).
% 0.20/0.50 36[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 37[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 38[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 39[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 40[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 41[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c8) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 42[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 43[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 44[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 45[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 46[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.50 47[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.20/0.50 48[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 49[0:Inp] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(v,w),sk_c9)** equal(inverse(v),w) equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c10,x),sk_c9)** equal(multiply(y,sk_c10),x)* equal(inverse(y),sk_c10) equal(inverse(sk_c10),sk_c9) equal(inverse(z),sk_c10) equal(multiply(z,sk_c9),sk_c10)** equal(multiply(sk_c10,x1),sk_c9)** equal(multiply(x2,sk_c10),x1)* equal(inverse(x2),sk_c10) -> .
% 0.20/0.50 50[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.50 51[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.50 52[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.50 53[0:Con:49.9] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(u,v),sk_c9)**+ equal(multiply(w,sk_c10),y)* equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,y),sk_c9)** -> .
% 0.20/0.50 54[1:Spt:53.0,53.4,53.6] || equal(inverse(u),v) equal(multiply(u,v),sk_c9)**+ equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.20/0.50 55[2:Spt:19.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.20/0.50 57[3:Spt:24.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.20/0.50 59[4:Spt:20.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.20/0.50 61[5:Spt:23.1] || -> equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.20/0.50 67[1:SpL:50.0,54.1] || equal(inverse(identity),u) equal(u,sk_c9) equal(multiply(u,sk_c10),sk_c9)** -> .
% 0.20/0.50 68[6:Spt:22.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.50 73[7:Spt:21.1] || -> equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 79[2:SpR:55.0,51.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.20/0.50 80[3:SpR:57.0,51.0] || -> equal(multiply(sk_c10,sk_c7),identity)**.
% 0.20/0.50 81[4:SpR:59.0,51.0] || -> equal(multiply(sk_c10,sk_c6),identity)**.
% 0.20/0.50 85[2:SpL:79.0,54.1] || equal(inverse(sk_c9),sk_c10) equal(identity,sk_c9) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.20/0.50 87[3:SpL:80.0,54.1] || equal(inverse(sk_c10),sk_c7) equal(identity,sk_c9) equal(multiply(sk_c7,sk_c10),sk_c9)** -> .
% 0.20/0.50 92[2:SpR:79.0,52.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),multiply(identity,u))**.
% 0.20/0.50 94[0:SpR:51.0,52.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.50 95[6:SpR:68.0,52.0] || -> equal(multiply(sk_c10,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.20/0.50 99[2:Rew:50.0,92.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.20/0.50 101[0:Rew:50.0,94.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.50 105[4:SpL:81.0,54.1] || equal(inverse(sk_c10),sk_c6) equal(identity,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.20/0.50 107[4:Rew:55.0,105.0] || equal(sk_c6,sk_c9) equal(identity,sk_c9) equal(multiply(sk_c6,sk_c10),sk_c9)** -> .
% 0.20/0.50 110[6:SpR:68.0,99.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.50 111[3:SpR:80.0,99.0] || -> equal(multiply(sk_c9,identity),sk_c7)**.
% 0.20/0.50 112[4:SpR:81.0,99.0] || -> equal(multiply(sk_c9,identity),sk_c6)**.
% 0.20/0.50 114[4:Rew:111.0,112.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.50 116[5:Rew:114.0,61.0] || -> equal(multiply(sk_c6,sk_c10),sk_c8)**.
% 0.20/0.50 121[4:Rew:114.0,111.0] || -> equal(multiply(sk_c9,identity),sk_c6)**.
% 0.20/0.50 133[4:SpR:121.0,52.0] || -> equal(multiply(sk_c9,multiply(identity,u)),multiply(sk_c6,u))**.
% 0.20/0.50 136[4:Rew:50.0,133.0] || -> equal(multiply(sk_c6,u),multiply(sk_c9,u))**.
% 0.20/0.50 137[7:Rew:136.0,73.0] || -> equal(multiply(sk_c9,sk_c9),sk_c10)**.
% 0.20/0.50 138[5:Rew:136.0,116.0] || -> equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.20/0.50 142[7:Rew:110.0,137.0] || -> equal(sk_c8,sk_c10)**.
% 0.20/0.50 143[7:Rew:142.0,68.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.20/0.50 151[5:Rew:79.0,138.0] || -> equal(identity,sk_c8)**.
% 0.20/0.50 152[7:Rew:142.0,151.0] || -> equal(identity,sk_c10)**.
% 0.20/0.50 153[7:Rew:152.0,50.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 159[7:Rew:152.0,85.1] || equal(inverse(sk_c9),sk_c10) equal(sk_c9,sk_c10) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.20/0.50 164[7:Rew:153.0,143.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 166[7:Rew:164.0,55.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 197[7:Rew:153.0,159.2,164.0,159.2,164.0,159.1,166.0,159.0,164.0,159.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.20/0.50 198[7:Obv:197.2] || -> .
% 0.20/0.50 205[7:Spt:198.0,21.1,73.0] || equal(multiply(sk_c6,sk_c9),sk_c10)** -> .
% 0.20/0.50 206[7:Spt:198.0,21.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 207[5:Rew:151.0,121.0] || -> equal(multiply(sk_c9,sk_c8),sk_c6)**.
% 0.20/0.50 210[5:Rew:151.0,50.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.50 211[5:Rew:151.0,51.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.50 212[7:Rew:136.0,205.0] || equal(multiply(sk_c9,sk_c9),sk_c10)** -> .
% 0.20/0.50 213[7:Rew:110.0,212.0] || equal(sk_c8,sk_c10)** -> .
% 0.20/0.50 214[6:Rew:110.0,45.1,136.0,45.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c8,sk_c10).
% 0.20/0.50 215[7:MRR:214.1,213.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 216[6:Rew:110.0,3.1,136.0,3.1] || -> equal(inverse(sk_c1),sk_c10)** equal(sk_c8,sk_c10).
% 0.20/0.50 217[7:MRR:216.1,213.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.50 219[6:Rew:210.0,95.0] || -> equal(multiply(sk_c9,u),multiply(sk_c10,u))**.
% 0.20/0.50 224[6:Rew:219.0,207.0] || -> equal(multiply(sk_c10,sk_c8),sk_c6)**.
% 0.20/0.50 225[6:Rew:219.0,138.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.20/0.50 226[6:Rew:219.0,110.0] || -> equal(multiply(sk_c10,sk_c9),sk_c8)**.
% 0.20/0.50 227[6:Rew:68.0,224.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.50 234[6:Rew:226.0,39.0,219.0,39.0,227.0,39.0] || -> equal(sk_c8,sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 235[7:MRR:234.0,213.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 236[6:Rew:226.0,33.0,219.0,33.0,227.0,33.0] || -> equal(sk_c8,sk_c10) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 237[7:MRR:236.0,213.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 238[6:Rew:226.0,27.0,219.0,27.0,227.0,27.0] || -> equal(sk_c8,sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 239[7:MRR:238.0,213.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 240[6:Rew:226.0,15.0,219.0,15.0,227.0,15.0] || -> equal(sk_c8,sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 241[7:MRR:240.0,213.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 275[7:SpR:239.0,52.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.20/0.50 277[7:Rew:219.0,275.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 288[7:SpR:206.0,211.0] || -> equal(multiply(sk_c3,sk_c2),sk_c8)**.
% 0.20/0.50 291[7:SpR:217.0,211.0] || -> equal(multiply(sk_c10,sk_c1),sk_c8)**.
% 0.20/0.50 308[0:SpR:101.0,101.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.50 311[7:SpR:235.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 318[7:SpR:291.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c8),sk_c1)**.
% 0.20/0.50 319[7:SpR:241.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c3)**.
% 0.20/0.50 322[5:SpR:211.0,101.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.20/0.50 324[7:SpR:288.0,101.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c2)**.
% 0.20/0.50 325[7:SpR:206.0,101.0] || -> equal(multiply(sk_c3,multiply(sk_c2,u)),u)**.
% 0.20/0.50 326[2:SpR:55.0,101.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),u)**.
% 0.20/0.50 330[7:Rew:237.0,311.0,215.0,311.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 333[7:Rew:330.0,55.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 336[7:Rew:330.0,68.0] || -> equal(multiply(sk_c10,sk_c8),sk_c10)**.
% 0.20/0.50 339[7:Rew:330.0,239.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.50 362[7:Rew:336.0,318.0,333.0,318.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.50 363[7:Rew:362.0,213.0] || equal(sk_c8,sk_c1)** -> .
% 0.20/0.50 364[7:Rew:362.0,217.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 365[7:Rew:362.0,225.0] || -> equal(multiply(sk_c1,sk_c1),sk_c8)**.
% 0.20/0.50 367[7:Rew:362.0,277.0] || -> equal(multiply(sk_c3,multiply(sk_c1,u)),multiply(sk_c1,u))**.
% 0.20/0.50 372[7:Rew:362.0,330.0] || -> equal(sk_c9,sk_c1)**.
% 0.20/0.50 376[7:Rew:362.0,336.0] || -> equal(multiply(sk_c1,sk_c8),sk_c1)**.
% 0.20/0.50 377[7:Rew:362.0,339.0] || -> equal(multiply(sk_c3,sk_c1),sk_c1)**.
% 0.20/0.50 384[7:Rew:206.0,319.0] || -> equal(multiply(sk_c3,sk_c9),sk_c3)**.
% 0.20/0.50 385[7:Rew:377.0,384.0,372.0,384.0] || -> equal(sk_c3,sk_c1)**.
% 0.20/0.50 395[7:Rew:376.0,324.0,364.0,324.0,385.0,324.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.50 403[7:Rew:385.0,325.0,395.0,325.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),u)**.
% 0.20/0.50 411[5:Rew:308.0,322.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.50 415[7:Rew:403.0,367.0,385.0,367.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.50 417[7:Rew:415.0,365.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.50 418[7:MRR:417.0,363.0] || -> .
% 0.20/0.50 426[6:Spt:418.0,22.1,68.0] || equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.20/0.50 427[6:Spt:418.0,22.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 432[6:Rew:411.0,426.0] || equal(sk_c9,sk_c10)** -> .
% 0.20/0.50 436[5:Rew:411.0,46.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c9,sk_c10).
% 0.20/0.50 437[6:MRR:436.1,432.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 446[5:Rew:411.0,40.0] || -> equal(sk_c9,sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 447[6:MRR:446.0,432.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 448[5:Rew:411.0,34.0] || -> equal(sk_c9,sk_c10) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 449[6:MRR:448.0,432.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 486[6:SpR:447.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 488[6:Rew:437.0,486.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 489[6:Rew:449.0,488.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 490[6:MRR:489.0,432.0] || -> .
% 0.20/0.50 491[5:Spt:490.0,23.1,61.0] || equal(multiply(sk_c7,sk_c10),sk_c8)** -> .
% 0.20/0.50 492[5:Spt:490.0,23.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 493[5:Rew:114.0,491.0] || equal(multiply(sk_c6,sk_c10),sk_c8)** -> .
% 0.20/0.50 494[5:Rew:136.0,493.0] || equal(multiply(sk_c9,sk_c10),sk_c8)** -> .
% 0.20/0.50 495[5:Rew:79.0,494.0] || equal(identity,sk_c8)** -> .
% 0.20/0.50 496[4:Rew:79.0,47.1,136.0,47.1,114.0,47.1] || -> equal(inverse(sk_c4),sk_c10)** equal(identity,sk_c8).
% 0.20/0.50 497[5:MRR:496.1,495.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 500[4:Rew:79.0,41.0,136.0,41.0,114.0,41.0] || -> equal(identity,sk_c8) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 501[5:MRR:500.0,495.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 502[4:Rew:79.0,35.0,136.0,35.0,114.0,35.0] || -> equal(identity,sk_c8) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 503[5:MRR:502.0,495.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 504[4:Rew:79.0,29.0,136.0,29.0,114.0,29.0] || -> equal(identity,sk_c8) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 505[5:MRR:504.0,495.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 506[4:Rew:79.0,17.0,136.0,17.0,114.0,17.0] || -> equal(identity,sk_c8) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 507[5:MRR:506.0,495.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 510[4:Rew:79.0,107.2,136.0,107.2] || equal(sk_c6,sk_c9) equal(identity,sk_c9)** equal(identity,sk_c9)** -> .
% 0.20/0.50 511[4:Obv:510.1] || equal(sk_c6,sk_c9) equal(identity,sk_c9)** -> .
% 0.20/0.50 512[3:Rew:55.0,87.0] || equal(sk_c7,sk_c9) equal(identity,sk_c9) equal(multiply(sk_c7,sk_c10),sk_c9)** -> .
% 0.20/0.50 536[2:SpR:79.0,101.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c10)**.
% 0.20/0.50 539[5:SpR:501.0,52.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),multiply(sk_c5,u))**.
% 0.20/0.50 540[5:SpR:501.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 542[5:Rew:497.0,540.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 543[5:Rew:503.0,542.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 544[5:Rew:543.0,55.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 545[5:Rew:543.0,121.0] || -> equal(multiply(sk_c10,identity),sk_c6)**.
% 0.20/0.50 546[5:Rew:543.0,79.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.20/0.50 547[5:Rew:543.0,326.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),u)**.
% 0.20/0.50 552[5:Rew:543.0,503.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 553[5:Rew:543.0,505.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.50 554[5:Rew:543.0,507.0] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.20/0.50 557[5:Rew:543.0,511.0] || equal(sk_c6,sk_c10) equal(identity,sk_c9)** -> .
% 0.20/0.50 563[5:Rew:543.0,536.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c10)**.
% 0.20/0.50 565[5:Rew:545.0,563.0,544.0,563.0] || -> equal(sk_c6,sk_c10)**.
% 0.20/0.50 571[5:Rew:543.0,557.1,565.0,557.0] || equal(sk_c10,sk_c10) equal(identity,sk_c10)** -> .
% 0.20/0.50 572[5:Obv:571.0] || equal(identity,sk_c10)** -> .
% 0.20/0.50 580[5:SpR:552.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c5)**.
% 0.20/0.50 582[5:Rew:546.0,580.0,544.0,580.0] || -> equal(identity,sk_c5)**.
% 0.20/0.50 584[5:Rew:582.0,50.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.50 588[5:Rew:582.0,572.0] || equal(sk_c5,sk_c10)** -> .
% 0.20/0.50 590[5:Rew:584.0,539.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),u)**.
% 0.20/0.50 598[5:SpR:553.0,52.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 602[5:SpR:554.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c3)**.
% 0.20/0.50 604[5:Rew:553.0,602.0,492.0,602.0] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.50 610[5:Rew:604.0,598.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 617[5:Rew:547.0,610.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 622[5:Rew:617.0,590.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.50 629[5:Rew:622.0,501.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.50 630[5:MRR:629.0,588.0] || -> .
% 0.20/0.50 633[4:Spt:630.0,20.0,59.0] || equal(inverse(sk_c6),sk_c10)** -> .
% 0.20/0.50 634[4:Spt:630.0,20.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 635[4:MRR:44.0,633.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 637[4:MRR:38.0,633.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 638[4:MRR:32.0,633.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 639[4:MRR:26.0,633.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 640[4:MRR:14.0,633.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 662[3:SpR:111.0,52.0] || -> equal(multiply(sk_c9,multiply(identity,u)),multiply(sk_c7,u))**.
% 0.20/0.50 665[3:Rew:50.0,662.0] || -> equal(multiply(sk_c7,u),multiply(sk_c9,u))**.
% 0.20/0.50 666[3:Rew:665.0,512.2] || equal(sk_c7,sk_c9) equal(identity,sk_c9) equal(multiply(sk_c9,sk_c10),sk_c9)** -> .
% 0.20/0.50 668[3:Rew:79.0,666.2] || equal(sk_c7,sk_c9) equal(identity,sk_c9)** equal(identity,sk_c9)** -> .
% 0.20/0.50 669[3:Obv:668.1] || equal(sk_c7,sk_c9) equal(identity,sk_c9)** -> .
% 0.20/0.50 670[4:SpR:637.0,52.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),multiply(sk_c5,u))**.
% 0.20/0.50 671[4:SpR:637.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 673[4:Rew:635.0,671.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 674[4:Rew:638.0,673.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 675[4:Rew:674.0,55.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 676[4:Rew:674.0,79.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.20/0.50 677[4:Rew:674.0,111.0] || -> equal(multiply(sk_c10,identity),sk_c7)**.
% 0.20/0.50 678[4:Rew:674.0,536.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c10)**.
% 0.20/0.50 682[4:Rew:674.0,326.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),u)**.
% 0.20/0.50 683[4:Rew:674.0,638.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 684[4:Rew:674.0,639.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.50 685[4:Rew:674.0,640.0] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.20/0.50 687[4:Rew:674.0,669.1] || equal(sk_c7,sk_c9) equal(identity,sk_c10)** -> .
% 0.20/0.50 694[4:Rew:677.0,678.0,675.0,678.0] || -> equal(sk_c7,sk_c10)**.
% 0.20/0.50 700[4:Rew:694.0,687.0,674.0,687.0] || equal(sk_c10,sk_c10) equal(identity,sk_c10)** -> .
% 0.20/0.50 701[4:Obv:700.0] || equal(identity,sk_c10)** -> .
% 0.20/0.50 710[4:SpR:683.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c5)**.
% 0.20/0.50 712[4:Rew:676.0,710.0,675.0,710.0] || -> equal(identity,sk_c5)**.
% 0.20/0.50 713[4:Rew:712.0,50.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.50 717[4:Rew:712.0,701.0] || equal(sk_c5,sk_c10)** -> .
% 0.20/0.50 719[4:Rew:713.0,670.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),u)**.
% 0.20/0.50 725[4:SpR:684.0,52.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 729[4:SpR:685.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c3)**.
% 0.20/0.50 731[4:Rew:684.0,729.0,634.0,729.0] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.50 737[4:Rew:731.0,725.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 744[4:Rew:682.0,737.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 749[4:Rew:744.0,719.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.50 756[4:Rew:749.0,637.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.50 757[4:MRR:756.0,717.0] || -> .
% 0.20/0.50 760[3:Spt:757.0,24.0,57.0] || equal(inverse(sk_c7),sk_c10)** -> .
% 0.20/0.50 761[3:Spt:757.0,24.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 762[3:MRR:48.0,760.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 764[3:MRR:42.0,760.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 765[3:MRR:36.0,760.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 766[3:MRR:30.0,760.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 767[3:MRR:18.0,760.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 781[3:SpR:764.0,52.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),multiply(sk_c5,u))**.
% 0.20/0.50 782[3:SpR:764.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 784[3:Rew:762.0,782.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 785[3:Rew:765.0,784.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 786[3:Rew:785.0,55.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 787[3:Rew:785.0,79.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.20/0.50 789[3:Rew:785.0,85.0] || equal(inverse(sk_c10),sk_c10) equal(identity,sk_c9) equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.20/0.50 791[3:Rew:785.0,326.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),u)**.
% 0.20/0.50 792[3:Rew:785.0,765.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 793[3:Rew:785.0,766.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.50 794[3:Rew:785.0,767.0] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.20/0.50 801[3:Rew:787.0,789.2,785.0,789.2,785.0,789.1,786.0,789.0] || equal(sk_c10,sk_c10) equal(identity,sk_c10)** equal(identity,sk_c10)** -> .
% 0.20/0.50 802[3:Obv:801.1] || equal(identity,sk_c10)** -> .
% 0.20/0.50 812[3:SpR:792.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c5)**.
% 0.20/0.50 814[3:Rew:786.0,812.0] || -> equal(multiply(sk_c10,sk_c10),sk_c5)**.
% 0.20/0.50 815[3:Rew:787.0,814.0] || -> equal(identity,sk_c5)**.
% 0.20/0.50 816[3:Rew:815.0,50.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.50 820[3:Rew:815.0,802.0] || equal(sk_c5,sk_c10)** -> .
% 0.20/0.50 822[3:Rew:816.0,781.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),u)**.
% 0.20/0.50 825[3:SpR:793.0,52.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 829[3:SpR:794.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c3)**.
% 0.20/0.50 831[3:Rew:793.0,829.0,761.0,829.0] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.50 837[3:Rew:831.0,825.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 844[3:Rew:791.0,837.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 849[3:Rew:844.0,822.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.50 856[3:Rew:849.0,764.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.50 857[3:MRR:856.0,820.0] || -> .
% 0.20/0.50 860[2:Spt:857.0,19.0,55.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.20/0.50 861[2:Spt:857.0,19.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 862[2:MRR:43.0,860.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 863[2:MRR:1.0,860.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.50 864[2:MRR:37.0,860.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 865[2:MRR:31.0,860.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 866[2:MRR:25.0,860.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 867[2:MRR:13.0,860.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 876[2:SpR:864.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 878[2:Rew:862.0,876.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 879[2:Rew:865.0,878.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 881[2:Rew:879.0,865.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 882[2:Rew:879.0,866.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.50 883[2:Rew:879.0,867.0] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.20/0.50 885[2:Rew:879.0,67.1] || equal(inverse(identity),u) equal(u,sk_c10) equal(multiply(u,sk_c10),sk_c9)** -> .
% 0.20/0.50 889[2:Rew:879.0,885.2] || equal(inverse(identity),u) equal(u,sk_c10) equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.20/0.50 895[2:SpR:881.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c5)**.
% 0.20/0.50 897[2:Rew:51.0,895.0] || -> equal(identity,sk_c5)**.
% 0.20/0.50 898[2:Rew:897.0,50.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.50 899[2:Rew:897.0,51.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.50 900[2:Rew:897.0,889.0] || equal(inverse(sk_c5),u) equal(u,sk_c10) equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.20/0.50 906[2:SpR:882.0,101.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c10)**.
% 0.20/0.50 909[2:SpR:883.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c3)**.
% 0.20/0.50 911[2:Rew:882.0,909.0,861.0,909.0] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.50 916[2:Rew:911.0,906.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c10)**.
% 0.20/0.50 918[2:Rew:899.0,916.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.50 922[2:Rew:918.0,898.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 923[2:Rew:918.0,899.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.20/0.50 924[2:Rew:918.0,900.0] || equal(inverse(sk_c10),u) equal(u,sk_c10) equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.20/0.50 942[2:SpR:923.0,101.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.20/0.50 945[2:SpR:863.0,923.0] || -> equal(multiply(sk_c10,sk_c1),sk_c10)**.
% 0.20/0.50 951[2:Rew:922.0,945.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.50 952[2:Rew:951.0,863.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 963[2:Rew:951.0,924.0] || equal(inverse(sk_c1),u) equal(u,sk_c10) equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.20/0.50 974[2:Rew:308.0,942.0,951.0,942.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.50 978[2:Rew:974.0,963.2,951.0,963.2,951.0,963.1,952.0,963.0] || equal(sk_c1,u)* equal(u,sk_c1)* equal(u,sk_c1)* -> .
% 0.20/0.50 979[2:Obv:978.1] || equal(u,sk_c1)* -> .
% 0.20/0.50 980[2:UnC:979.0,101.0] || -> .
% 0.20/0.50 983[1:Spt:980.0,53.1,53.2,53.3,53.5,53.7,53.8] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(u,sk_c10),w)*+ equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,w),sk_c9)** -> .
% 0.20/0.50 984[1:EqR:983.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.20/0.50 986[2:Spt:43.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.20/0.50 989[2:Rew:986.0,984.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(sk_c9,sk_c9) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.20/0.50 990[2:Obv:989.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.20/0.50 995[3:Spt:20.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.20/0.50 998[4:Spt:24.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.20/0.50 1001[5:Spt:21.1] || -> equal(multiply(sk_c6,sk_c9),sk_c10)**.
% 0.20/0.50 1003[5:SpR:1001.0,101.0] || -> equal(multiply(inverse(sk_c6),sk_c10),sk_c9)**.
% 0.20/0.50 1005[5:Rew:995.0,1003.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.20/0.50 1006[6:Spt:22.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.50 1008[6:SpR:1006.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c8)**.
% 0.20/0.50 1010[6:Rew:986.0,1008.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.50 1011[5:SpR:1005.0,52.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.20/0.50 1012[5:SpR:1005.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c10)**.
% 0.20/0.50 1014[5:Rew:986.0,1012.0] || -> equal(multiply(sk_c9,sk_c9),sk_c10)**.
% 0.20/0.50 1015[6:Rew:1010.0,1014.0] || -> equal(sk_c8,sk_c10)**.
% 0.20/0.50 1020[6:Rew:1015.0,35.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)** equal(multiply(sk_c10,sk_c5),sk_c9).
% 0.20/0.50 1021[6:Rew:1015.0,41.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1024[6:Rew:1015.0,47.1] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c7,sk_c10),sk_c10)**.
% 0.20/0.50 1035[0:SpR:51.0,101.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.50 1037[2:SpR:986.0,51.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.20/0.50 1038[3:SpR:995.0,51.0] || -> equal(multiply(sk_c10,sk_c6),identity)**.
% 0.20/0.50 1039[4:SpR:998.0,51.0] || -> equal(multiply(sk_c10,sk_c7),identity)**.
% 0.20/0.50 1040[0:Rew:308.0,1035.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.50 1043[2:SpR:1037.0,101.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c10)**.
% 0.20/0.50 1045[2:Rew:1040.0,1043.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.20/0.50 1048[2:SpR:1045.0,101.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.20/0.50 1049[2:SpR:1045.0,51.0] || -> equal(multiply(sk_c10,sk_c9),identity)**.
% 0.20/0.50 1052[3:SpR:1038.0,101.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c6)**.
% 0.20/0.50 1054[3:Rew:986.0,1052.0] || -> equal(multiply(sk_c9,identity),sk_c6)**.
% 0.20/0.50 1055[3:Rew:1040.0,1054.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.50 1069[4:SpR:1039.0,101.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c7)**.
% 0.20/0.50 1071[4:Rew:986.0,1069.0] || -> equal(multiply(sk_c9,identity),sk_c7)**.
% 0.20/0.50 1072[4:Rew:1040.0,1071.0] || -> equal(sk_c7,sk_c9)**.
% 0.20/0.50 1076[6:Rew:1072.0,1021.0] || -> equal(multiply(sk_c9,sk_c10),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1077[6:Rew:1072.0,1020.0] || -> equal(multiply(sk_c9,sk_c10),sk_c10)** equal(multiply(sk_c10,sk_c5),sk_c9).
% 0.20/0.50 1081[6:Rew:1072.0,1024.1] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c9,sk_c10),sk_c10)**.
% 0.20/0.50 1085[6:Rew:1037.0,1081.1] || -> equal(inverse(sk_c4),sk_c10)** equal(identity,sk_c10).
% 0.20/0.50 1087[6:Rew:1037.0,1076.0] || -> equal(identity,sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1088[6:Rew:1037.0,1077.0] || -> equal(identity,sk_c10) equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 1103[7:Spt:1085.1] || -> equal(identity,sk_c10)**.
% 0.20/0.50 1104[7:Rew:1103.0,50.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 1110[7:Rew:1103.0,1040.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.50 1111[7:Rew:1104.0,1005.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 1118[7:Rew:1104.0,990.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c9),sk_c10)** equal(multiply(u,sk_c10),sk_c9)** -> .
% 0.20/0.50 1119[7:Rew:1111.0,986.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 1131[7:Rew:1110.0,1118.3,1111.0,1118.3,1110.0,1118.2,1111.0,1118.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(v,sk_c10) equal(u,sk_c10) -> .
% 0.20/0.50 1132[7:Con:1131.0] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.20/0.50 1214[7:SpL:1119.0,1132.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.20/0.50 1216[7:Obv:1214.1] || -> .
% 0.20/0.50 1217[7:Spt:1216.0,1085.1,1103.0] || equal(identity,sk_c10)** -> .
% 0.20/0.50 1218[7:Spt:1216.0,1085.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 1220[7:MRR:1087.0,1217.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1221[7:MRR:1088.0,1217.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 1252[7:SpR:1220.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 1254[7:Rew:1218.0,1252.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 1255[7:Rew:1221.0,1254.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 1260[7:Rew:1255.0,1049.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.20/0.50 1264[7:Rew:1255.0,1048.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),u)**.
% 0.20/0.50 1265[7:Rew:1255.0,1011.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 1279[7:Rew:1264.0,1265.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 1283[7:Rew:1279.0,1260.0] || -> equal(identity,sk_c10)**.
% 0.20/0.50 1287[7:MRR:1283.0,1217.0] || -> .
% 0.20/0.50 1291[6:Spt:1287.0,22.1,1006.0] || equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.20/0.50 1292[6:Spt:1287.0,22.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 1294[6:MRR:46.1,1291.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 1295[6:MRR:4.1,1291.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.50 1296[6:MRR:40.0,1291.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1297[6:MRR:34.0,1291.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 1300[6:MRR:10.0,1291.0] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 1311[6:SpR:1295.0,101.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.20/0.50 1328[6:SpR:1296.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 1330[6:Rew:1294.0,1328.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 1331[6:Rew:1297.0,1330.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 1336[6:Rew:1331.0,1037.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.20/0.50 1338[6:Rew:1331.0,1005.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.20/0.50 1348[6:Rew:1331.0,1300.0] || -> equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.20/0.50 1350[6:Rew:1331.0,990.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c10),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.20/0.50 1352[6:Rew:1336.0,1338.0] || -> equal(identity,sk_c10)**.
% 0.20/0.50 1353[6:Rew:1352.0,50.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 1354[6:Rew:1352.0,1040.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.50 1359[6:Rew:1353.0,1311.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.50 1362[6:Rew:1354.0,1348.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.50 1365[6:Rew:1362.0,1295.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 1366[6:Rew:1362.0,1331.0] || -> equal(sk_c9,sk_c1)**.
% 0.20/0.50 1374[6:Rew:1362.0,1354.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.50 1391[6:Rew:1374.0,1350.3,1359.0,1350.3,1362.0,1350.3,1366.0,1350.3,1374.0,1350.2,1362.0,1350.2,1362.0,1350.1,1362.0,1350.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(v,sk_c1) equal(u,sk_c1) -> .
% 0.20/0.50 1392[6:Con:1391.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.50 1466[6:SpL:1365.0,1392.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.50 1468[6:Obv:1466.1] || -> .
% 0.20/0.50 1469[5:Spt:1468.0,21.1,1001.0] || equal(multiply(sk_c6,sk_c9),sk_c10)** -> .
% 0.20/0.50 1470[5:Spt:1468.0,21.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 1471[5:Rew:1055.0,1469.0] || equal(multiply(sk_c9,sk_c9),sk_c10)** -> .
% 0.20/0.50 1474[3:Rew:1055.0,45.1] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c9,sk_c9),sk_c10)**.
% 0.20/0.50 1475[5:MRR:1474.1,1471.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 1483[3:Rew:1055.0,39.0] || -> equal(multiply(sk_c9,sk_c9),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1484[5:MRR:1483.0,1471.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1485[3:Rew:1055.0,33.0] || -> equal(multiply(sk_c9,sk_c9),sk_c10)** equal(multiply(sk_c10,sk_c5),sk_c9).
% 0.20/0.50 1486[5:MRR:1485.0,1471.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 1487[3:Rew:1055.0,27.0] || -> equal(multiply(sk_c9,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 1488[5:MRR:1487.0,1471.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 1489[3:Rew:1055.0,15.0] || -> equal(multiply(sk_c9,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 1490[5:MRR:1489.0,1471.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 1515[5:SpR:1484.0,52.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),multiply(sk_c5,u))**.
% 0.20/0.50 1516[5:SpR:1484.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 1518[5:Rew:1475.0,1516.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 1519[5:Rew:1486.0,1518.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 1522[5:Rew:1519.0,1045.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 1524[5:Rew:1519.0,1049.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.20/0.50 1526[5:Rew:1519.0,1471.0] || equal(multiply(sk_c10,sk_c10),sk_c10)** -> .
% 0.20/0.50 1527[5:Rew:1519.0,1048.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),u)**.
% 0.20/0.50 1529[5:Rew:1519.0,1486.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 1530[5:Rew:1519.0,1488.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.50 1531[5:Rew:1519.0,1490.0] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.20/0.50 1536[5:Rew:1524.0,1526.0] || equal(identity,sk_c10)** -> .
% 0.20/0.50 1546[5:SpR:1529.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c5)**.
% 0.20/0.50 1548[5:Rew:1522.0,1546.0] || -> equal(multiply(sk_c10,sk_c10),sk_c5)**.
% 0.20/0.50 1549[5:Rew:1524.0,1548.0] || -> equal(identity,sk_c5)**.
% 0.20/0.50 1550[5:Rew:1549.0,1536.0] || equal(sk_c5,sk_c10)** -> .
% 0.20/0.50 1552[5:Rew:1549.0,50.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.50 1556[5:Rew:1552.0,1515.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),u)**.
% 0.20/0.50 1559[5:SpR:1530.0,52.0] || -> equal(multiply(sk_c3,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 1563[5:SpR:1531.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c3)**.
% 0.20/0.50 1565[5:Rew:1530.0,1563.0,1470.0,1563.0] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.50 1571[5:Rew:1565.0,1559.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.20/0.50 1578[5:Rew:1527.0,1571.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 1581[5:Rew:1578.0,1556.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.50 1590[5:Rew:1581.0,1484.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.50 1591[5:MRR:1590.0,1550.0] || -> .
% 0.20/0.50 1593[4:Spt:1591.0,24.0,998.0] || equal(inverse(sk_c7),sk_c10)** -> .
% 0.20/0.50 1594[4:Spt:1591.0,24.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 1595[4:MRR:48.0,1593.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 1597[4:MRR:42.0,1593.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1598[4:MRR:36.0,1593.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 1599[4:MRR:30.0,1593.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 1600[4:MRR:18.0,1593.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 1601[4:MRR:12.0,1593.0] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 1624[4:SpR:1597.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 1626[4:Rew:1595.0,1624.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 1627[4:Rew:1598.0,1626.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 1629[4:Rew:1627.0,986.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 1631[4:Rew:1627.0,1037.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.20/0.50 1635[4:Rew:1627.0,1598.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 1636[4:Rew:1627.0,1599.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.50 1637[4:Rew:1627.0,1600.0] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.20/0.50 1638[4:Rew:1627.0,1601.0] || -> equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.20/0.50 1640[4:Rew:1627.0,990.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c10),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.20/0.50 1642[4:Rew:1627.0,1640.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c10),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c10)** -> .
% 0.20/0.50 1647[4:SpR:1635.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c5)**.
% 0.20/0.50 1649[4:Rew:1631.0,1647.0,1629.0,1647.0] || -> equal(identity,sk_c5)**.
% 0.20/0.50 1650[4:Rew:1649.0,50.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.50 1651[4:Rew:1649.0,1040.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.50 1654[4:Rew:1649.0,1631.0] || -> equal(multiply(sk_c10,sk_c10),sk_c5)**.
% 0.20/0.50 1665[4:SpR:1637.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c3)**.
% 0.20/0.50 1667[4:Rew:1636.0,1665.0,1594.0,1665.0] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.50 1669[4:Rew:1667.0,1636.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.20/0.50 1674[4:Rew:1654.0,1669.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.50 1675[4:Rew:1674.0,1597.0] || -> equal(multiply(sk_c4,sk_c10),sk_c10)**.
% 0.20/0.50 1677[4:Rew:1674.0,1650.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 1678[4:Rew:1674.0,1651.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.50 1686[4:Rew:1677.0,1642.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c10),sk_c10)** equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.20/0.50 1689[4:Rew:1678.0,1675.0] || -> equal(sk_c4,sk_c10)**.
% 0.20/0.50 1691[4:Rew:1678.0,1638.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.50 1692[4:Rew:1689.0,1595.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 1703[4:Rew:1691.0,1678.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.50 1706[4:Rew:1691.0,1692.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 1718[4:Con:1686.0] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c10),sk_c10)** -> .
% 0.20/0.50 1719[4:Rew:1703.0,1718.1,1691.0,1718.1,1691.0,1718.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.50 1757[4:SpL:1706.0,1719.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.50 1759[4:Obv:1757.1] || -> .
% 0.20/0.50 1760[3:Spt:1759.0,20.0,995.0] || equal(inverse(sk_c6),sk_c10)** -> .
% 0.20/0.50 1761[3:Spt:1759.0,20.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 1762[3:MRR:44.0,1760.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.50 1764[3:MRR:38.0,1760.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.50 1765[3:MRR:32.0,1760.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.50 1766[3:MRR:26.0,1760.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.50 1767[3:MRR:14.0,1760.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.50 1768[3:MRR:8.0,1760.0] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.50 1790[3:SpR:1764.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.50 1792[3:Rew:1762.0,1790.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 1793[3:Rew:1765.0,1792.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.50 1794[3:Rew:1793.0,1045.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 1796[3:Rew:1793.0,1049.0] || -> equal(multiply(sk_c10,sk_c10),identity)**.
% 0.20/0.50 1800[3:Rew:1793.0,1765.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.50 1801[3:Rew:1793.0,1766.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.50 1802[3:Rew:1793.0,1767.0] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.20/0.50 1803[3:Rew:1793.0,1768.0] || -> equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.20/0.50 1805[3:Rew:1793.0,990.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c10),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.20/0.50 1807[3:Rew:1793.0,1805.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c10),sk_c10)** equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c10)** -> .
% 0.20/0.50 1812[3:SpR:1800.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c5)**.
% 0.20/0.50 1814[3:Rew:1796.0,1812.0,1794.0,1812.0] || -> equal(identity,sk_c5)**.
% 0.20/0.50 1815[3:Rew:1814.0,1040.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.50 1816[3:Rew:1814.0,50.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.50 1819[3:Rew:1814.0,1796.0] || -> equal(multiply(sk_c10,sk_c10),sk_c5)**.
% 0.20/0.50 1829[3:SpR:1802.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c3)**.
% 0.20/0.50 1831[3:Rew:1801.0,1829.0,1761.0,1829.0] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.50 1833[3:Rew:1831.0,1801.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.20/0.50 1838[3:Rew:1819.0,1833.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.50 1839[3:Rew:1838.0,1764.0] || -> equal(multiply(sk_c4,sk_c10),sk_c10)**.
% 0.20/0.50 1841[3:Rew:1838.0,1815.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.50 1842[3:Rew:1838.0,1816.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.50 1846[3:Rew:1841.0,1839.0] || -> equal(sk_c4,sk_c10)**.
% 0.20/0.50 1849[3:Rew:1841.0,1807.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(multiply(v,sk_c10),sk_c10)** equal(multiply(sk_c10,u),sk_c10)** -> .
% 0.20/0.50 1851[3:Rew:1841.0,1803.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.50 1852[3:Rew:1846.0,1762.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.50 1865[3:Rew:1851.0,1841.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.50 1868[3:Rew:1851.0,1852.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 1870[3:Rew:1851.0,1842.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.50 1882[3:Rew:1870.0,1849.3,1851.0,1849.3,1865.0,1849.2,1851.0,1849.2,1851.0,1849.1,1851.0,1849.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(v,sk_c1) equal(u,sk_c1) -> .
% 0.20/0.51 1883[3:Con:1882.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.51 1914[3:SpL:1868.0,1883.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.51 1915[3:Obv:1914.1] || -> .
% 0.20/0.51 1916[2:Spt:1915.0,43.0,986.0] || equal(inverse(sk_c10),sk_c9)** -> .
% 0.20/0.51 1917[2:Spt:1915.0,43.1] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.51 1919[2:MRR:19.0,1916.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 1920[2:MRR:37.0,1916.0] || -> equal(multiply(sk_c4,sk_c10),sk_c5)**.
% 0.20/0.51 1921[2:MRR:31.0,1916.0] || -> equal(multiply(sk_c10,sk_c5),sk_c9)**.
% 0.20/0.51 1922[2:MRR:25.0,1916.0] || -> equal(multiply(sk_c3,sk_c10),sk_c9)**.
% 0.20/0.51 1923[2:MRR:13.0,1916.0] || -> equal(multiply(sk_c2,sk_c3),sk_c9)**.
% 0.20/0.51 1924[2:MRR:7.0,1916.0] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.51 1932[2:SpR:1920.0,101.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c10)**.
% 0.20/0.51 1934[2:Rew:1917.0,1932.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.51 1935[2:Rew:1921.0,1934.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.51 1936[2:Rew:1935.0,1916.0] || equal(inverse(sk_c10),sk_c10)** -> .
% 0.20/0.51 1937[2:Rew:1935.0,1921.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.51 1938[2:Rew:1935.0,1922.0] || -> equal(multiply(sk_c3,sk_c10),sk_c10)**.
% 0.20/0.51 1939[2:Rew:1935.0,1923.0] || -> equal(multiply(sk_c2,sk_c3),sk_c10)**.
% 0.20/0.51 1940[2:Rew:1935.0,1924.0] || -> equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.20/0.51 1943[2:SpR:1937.0,101.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c5)**.
% 0.20/0.51 1945[2:Rew:51.0,1943.0] || -> equal(identity,sk_c5)**.
% 0.20/0.51 1947[2:Rew:1945.0,1040.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.51 1948[2:Rew:1945.0,51.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.51 1953[2:SpR:1938.0,101.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c10)**.
% 0.20/0.51 1957[2:SpR:1939.0,101.0] || -> equal(multiply(inverse(sk_c2),sk_c10),sk_c3)**.
% 0.20/0.51 1959[2:Rew:1938.0,1957.0,1919.0,1957.0] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.51 1964[2:Rew:1959.0,1953.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c10)**.
% 0.20/0.51 1966[2:Rew:1948.0,1964.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.51 1967[2:Rew:1966.0,1920.0] || -> equal(multiply(sk_c4,sk_c10),sk_c10)**.
% 0.20/0.51 1970[2:Rew:1966.0,1947.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.51 1976[2:Rew:1970.0,1967.0] || -> equal(sk_c4,sk_c10)**.
% 0.20/0.51 1978[2:Rew:1970.0,1940.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.51 1979[2:Rew:1976.0,1917.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.51 1983[2:Rew:1978.0,1936.0] || equal(inverse(sk_c1),sk_c1)** -> .
% 0.20/0.51 1991[2:Rew:1978.0,1979.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.51 1995[2:Rew:1991.0,1983.0] || equal(sk_c1,sk_c1)* -> .
% 0.20/0.51 1996[2:Obv:1995.0] || -> .
% 0.20/0.51 % SZS output end Refutation
% 0.20/0.51 Formulae used in the proof : prove_this_1 prove_this_3 prove_this_4 prove_this_7 prove_this_8 prove_this_10 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_38 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 prove_this_48 prove_this_49 left_identity left_inverse associativity
% 0.20/0.51
%------------------------------------------------------------------------------