TSTP Solution File: GRP322-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP322-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:46:51 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP322-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 16:54:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 1044 clauses, backtracked 499 clauses, performed 14 splits and kept 929 clauses.
% 0.19/0.48 SPASS allocated 63693 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.48 0:00:00.03 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.07 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 4, length 425 :
% 0.19/0.48 % SZS output start Refutation
% 0.19/0.48 1[0:Inp] || -> equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.19/0.48 2[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.19/0.48 3[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 4[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.19/0.48 5[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6)** equal(multiply(sk_c8,sk_c9),sk_c7).
% 0.19/0.48 6[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 8[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 9[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 10[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 11[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 12[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.48 15[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 16[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.19/0.48 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.19/0.48 18[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 19[0:Inp] || -> equal(multiply(sk_c9,sk_c8),sk_c7) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 21[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 22[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c8) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 23[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6)** equal(multiply(sk_c9,sk_c3),sk_c8).
% 0.19/0.48 24[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 25[0:Inp] || -> equal(multiply(sk_c9,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 27[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 28[0:Inp] || -> equal(multiply(sk_c9,sk_c6),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 29[0:Inp] || -> equal(multiply(sk_c5,sk_c9),sk_c6) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 30[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 31[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.19/0.48 33[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 34[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.19/0.48 35[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.19/0.48 36[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 37[0:Inp] || equal(multiply(sk_c8,sk_c9),sk_c7) equal(multiply(u,sk_c8),sk_c9)** equal(inverse(u),sk_c8) equal(multiply(sk_c9,v),sk_c8)** equal(multiply(w,sk_c9),v)* equal(inverse(w),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(x,sk_c9),sk_c8)** equal(inverse(x),sk_c9) equal(multiply(sk_c9,y),sk_c8)** equal(multiply(z,sk_c9),y)* equal(inverse(z),sk_c9) -> .
% 0.19/0.48 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.48 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.48 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.48 41[0:Con:37.9] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(multiply(v,sk_c9),x)*+ equal(multiply(u,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.19/0.48 42[1:Spt:41.1,41.3,41.6] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),v)*+ equal(multiply(sk_c9,v),sk_c8)** -> .
% 0.19/0.48 44[2:Spt:1.0] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.19/0.48 46[3:Spt:6.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.19/0.48 48[4:Spt:3.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.48 50[5:Spt:5.0] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.19/0.48 56[1:SpL:38.0,42.1] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c9,u),sk_c8)** -> .
% 0.19/0.48 57[6:Spt:4.0] || -> equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.19/0.48 59[7:Spt:2.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.48 65[3:SpR:46.0,39.0] || -> equal(multiply(sk_c9,sk_c5),identity)**.
% 0.19/0.48 66[4:SpR:48.0,39.0] || -> equal(multiply(sk_c9,sk_c4),identity)**.
% 0.19/0.48 67[1:SpL:39.0,42.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c9,u),sk_c8)** -> .
% 0.19/0.48 76[3:SpR:65.0,40.0] || -> equal(multiply(sk_c9,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.19/0.48 79[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.48 81[3:Rew:38.0,76.0] || -> equal(multiply(sk_c9,multiply(sk_c5,u)),u)**.
% 0.19/0.48 83[0:Rew:38.0,79.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.48 87[5:SpR:50.0,81.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.19/0.48 88[6:Rew:57.0,87.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 90[6:Rew:88.0,44.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.48 91[6:Rew:88.0,46.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.48 92[6:Rew:88.0,48.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 93[6:Rew:88.0,50.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.48 94[6:Rew:88.0,57.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.48 95[7:Rew:88.0,59.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.19/0.48 96[6:Rew:88.0,65.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.48 97[6:Rew:88.0,66.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.48 100[6:Rew:88.0,67.2] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 114[6:Rew:88.0,100.0] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 134[0:SpR:83.0,83.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.48 137[0:SpR:39.0,83.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.48 139[6:SpR:90.0,83.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.48 141[7:SpR:95.0,83.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c8)**.
% 0.19/0.48 142[6:SpR:94.0,83.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.48 143[6:SpR:96.0,83.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.19/0.48 147[7:Rew:90.0,141.0,92.0,141.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.48 150[7:Rew:147.0,139.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.48 151[6:Rew:39.0,142.0] || -> equal(identity,sk_c6)**.
% 0.19/0.48 152[6:Rew:151.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.48 153[6:Rew:151.0,39.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.48 154[6:Rew:151.0,96.0] || -> equal(multiply(sk_c8,sk_c5),sk_c6)**.
% 0.19/0.48 155[6:Rew:151.0,97.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.19/0.48 156[6:Rew:151.0,114.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c6,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 160[6:Rew:151.0,143.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c5)**.
% 0.19/0.48 161[7:Rew:153.0,150.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.48 166[7:Rew:161.0,152.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.48 167[7:Rew:161.0,154.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.19/0.48 178[7:Rew:166.0,167.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.48 179[7:Rew:178.0,91.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.48 202[7:Rew:166.0,156.2,161.0,156.1,179.0,156.0,179.0,156.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.19/0.48 203[7:Obv:202.1] || equal(u,sk_c8)* -> .
% 0.19/0.48 204[7:UnC:203.0,88.0] || -> .
% 0.19/0.48 206[7:Spt:204.0,2.0,59.0] || equal(multiply(sk_c4,sk_c9),sk_c8)** -> .
% 0.19/0.48 207[7:Spt:204.0,2.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 209[7:Rew:88.0,206.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.19/0.48 210[6:Rew:134.0,137.0,151.0,137.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.48 211[6:Rew:210.0,160.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.19/0.48 212[6:Rew:211.0,139.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.19/0.48 215[6:Rew:88.0,14.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.19/0.48 216[7:MRR:215.1,209.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 221[6:Rew:88.0,8.1,88.0,8.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.48 222[7:MRR:221.0,209.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.48 245[6:SpR:155.0,83.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c4)**.
% 0.19/0.48 247[6:Rew:211.0,245.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.19/0.48 248[6:Rew:210.0,247.0] || -> equal(sk_c5,sk_c4)**.
% 0.19/0.48 251[6:Rew:248.0,93.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.19/0.48 254[6:Rew:248.0,212.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.48 256[7:Rew:251.0,209.0] || equal(sk_c6,sk_c8)** -> .
% 0.19/0.48 276[7:SpR:222.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.19/0.48 278[7:Rew:90.0,276.0,216.0,276.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.48 281[7:Rew:278.0,254.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.19/0.48 282[7:Rew:251.0,281.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.48 283[7:MRR:282.0,256.0] || -> .
% 0.19/0.48 284[6:Spt:283.0,4.0,57.0] || equal(multiply(sk_c9,sk_c6),sk_c8)** -> .
% 0.19/0.48 285[6:Spt:283.0,4.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 286[6:Rew:87.0,284.0] || equal(sk_c9,sk_c8)** -> .
% 0.19/0.48 287[0:Rew:134.0,137.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.48 288[5:Rew:87.0,34.1] || -> equal(inverse(sk_c2),sk_c9)** equal(sk_c9,sk_c8).
% 0.19/0.48 289[6:MRR:288.1,286.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 292[5:Rew:87.0,28.0] || -> equal(sk_c9,sk_c8) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 293[6:MRR:292.0,286.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 294[5:Rew:87.0,22.0] || -> equal(sk_c9,sk_c8) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 295[6:MRR:294.0,286.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 331[2:SpR:44.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.19/0.48 334[6:SpR:293.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.48 336[6:Rew:289.0,334.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.48 337[6:Rew:295.0,336.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 338[6:MRR:337.0,286.0] || -> .
% 0.19/0.48 339[5:Spt:338.0,5.0,50.0] || equal(multiply(sk_c5,sk_c9),sk_c6)** -> .
% 0.19/0.48 340[5:Spt:338.0,5.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 341[5:MRR:35.1,339.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 342[5:MRR:17.1,339.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 343[5:MRR:29.0,339.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 344[5:MRR:23.0,339.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 345[5:MRR:11.0,339.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 354[3:SpR:65.0,83.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c5)**.
% 0.19/0.48 356[3:Rew:287.0,354.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.19/0.48 357[3:Rew:356.0,331.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.19/0.48 362[3:SpR:356.0,83.0] || -> equal(multiply(sk_c5,multiply(sk_c9,u)),u)**.
% 0.19/0.48 365[5:SpR:343.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.48 367[5:Rew:341.0,365.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.48 368[5:Rew:344.0,367.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 369[5:Rew:368.0,48.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 371[5:Rew:368.0,44.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.48 375[5:Rew:368.0,356.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.19/0.48 383[5:Rew:368.0,66.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.48 386[5:Rew:368.0,345.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.48 387[5:Rew:368.0,56.0] || equal(inverse(identity),sk_c8) equal(sk_c9,u) equal(multiply(sk_c9,u),sk_c8)** -> .
% 0.19/0.48 390[5:Rew:368.0,362.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.19/0.48 396[5:Rew:368.0,387.2,368.0,387.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 412[3:SpR:357.0,40.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.19/0.48 431[5:SpR:383.0,83.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.19/0.48 433[5:Rew:375.0,431.0] || -> equal(multiply(sk_c5,identity),sk_c4)**.
% 0.19/0.48 434[5:Rew:287.0,433.0] || -> equal(sk_c5,sk_c4)**.
% 0.19/0.48 440[5:Rew:434.0,390.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.19/0.48 441[5:Rew:434.0,412.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.19/0.48 448[5:SpR:386.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.19/0.48 450[5:Rew:371.0,448.0,342.0,448.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.48 453[5:Rew:450.0,441.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.19/0.48 462[5:Rew:440.0,453.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.48 463[5:Rew:462.0,383.0] || -> equal(identity,sk_c4)**.
% 0.19/0.48 466[5:Rew:462.0,396.2] || equal(inverse(identity),sk_c8)** equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.19/0.48 480[5:Obv:466.1] || equal(inverse(identity),sk_c8)** equal(u,sk_c8)* -> .
% 0.19/0.48 481[5:Con:480.1] || equal(inverse(identity),sk_c8)** -> .
% 0.19/0.48 482[5:Rew:463.0,481.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.48 483[5:Rew:369.0,482.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.48 484[5:Obv:483.0] || -> .
% 0.19/0.48 485[4:Spt:484.0,3.0,48.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.19/0.48 486[4:Spt:484.0,3.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 488[4:MRR:33.0,485.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 489[4:MRR:15.0,485.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 490[4:MRR:27.0,485.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 491[4:MRR:21.0,485.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 492[4:MRR:9.0,485.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 518[4:SpR:490.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.48 520[4:Rew:488.0,518.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.48 521[4:Rew:491.0,520.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 522[4:Rew:521.0,486.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.48 524[4:Rew:521.0,46.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.48 527[4:Rew:521.0,65.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.48 530[4:Rew:521.0,362.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.19/0.48 531[4:Rew:521.0,56.2] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 537[4:Rew:521.0,492.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.48 546[4:Rew:521.0,531.1,521.0,531.0] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 574[4:SpR:537.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.19/0.48 576[4:Rew:522.0,574.0,489.0,574.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.48 579[4:Rew:576.0,412.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.19/0.48 587[4:Rew:530.0,579.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.48 588[4:Rew:587.0,527.0] || -> equal(identity,sk_c5)**.
% 0.19/0.48 596[4:Rew:587.0,546.2] || equal(inverse(identity),sk_c8)** equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.19/0.48 605[4:Obv:596.1] || equal(inverse(identity),sk_c8)** equal(u,sk_c8)* -> .
% 0.19/0.48 606[4:Con:605.1] || equal(inverse(identity),sk_c8)** -> .
% 0.19/0.48 607[4:Rew:588.0,606.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.48 608[4:Rew:524.0,607.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.48 609[4:Obv:608.0] || -> .
% 0.19/0.48 610[3:Spt:609.0,6.0,46.0] || equal(inverse(sk_c5),sk_c9)** -> .
% 0.19/0.48 611[3:Spt:609.0,6.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 612[3:MRR:36.0,610.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 613[3:MRR:18.0,610.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 614[3:MRR:30.0,610.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 615[3:MRR:24.0,610.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 616[3:MRR:12.0,610.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 628[3:SpR:614.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.48 630[3:Rew:612.0,628.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.48 631[3:Rew:615.0,630.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 632[3:Rew:631.0,611.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.48 637[3:Rew:631.0,331.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.48 639[3:Rew:631.0,615.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.48 640[3:Rew:631.0,616.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.48 644[3:Rew:631.0,67.2] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 652[3:Rew:631.0,644.0] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 666[3:SpR:639.0,83.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.19/0.48 668[3:Rew:39.0,666.0] || -> equal(identity,sk_c3)**.
% 0.19/0.48 669[3:Rew:668.0,287.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.48 670[3:Rew:668.0,38.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.48 673[3:Rew:668.0,39.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.48 674[3:Rew:668.0,652.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c3,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 679[3:SpR:640.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.19/0.48 681[3:Rew:632.0,679.0,613.0,679.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.48 683[3:Rew:681.0,637.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.48 685[3:Rew:673.0,683.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.48 688[3:Rew:685.0,669.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.48 689[3:Rew:685.0,670.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.48 693[3:Rew:685.0,674.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.19/0.48 694[3:Rew:688.0,640.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.48 699[3:Rew:694.0,613.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.48 714[3:Rew:689.0,693.2,699.0,693.0,699.0,693.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.19/0.48 715[3:Obv:714.1] || equal(u,sk_c8)* -> .
% 0.19/0.48 716[3:UnC:715.0,631.0] || -> .
% 0.19/0.48 718[2:Spt:716.0,1.0,44.0] || equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.19/0.48 719[2:Spt:716.0,1.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 720[2:MRR:31.1,718.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 722[2:MRR:25.0,718.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 723[2:MRR:19.0,718.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 733[2:SpR:722.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.48 735[2:Rew:720.0,733.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.48 736[2:Rew:723.0,735.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 737[2:Rew:736.0,719.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.48 740[2:Rew:736.0,718.0] || equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.19/0.48 751[2:Rew:737.0,740.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 752[2:Obv:751.0] || -> .
% 0.19/0.48 759[1:Spt:752.0,41.0,41.2,41.4,41.5,41.7,41.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)**+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.19/0.48 761[2:Spt:1.0] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.19/0.48 762[2:Rew:761.0,759.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(sk_c7,sk_c7) equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.19/0.48 764[2:Obv:762.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.19/0.48 767[2:SpR:761.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.19/0.48 769[3:Spt:3.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.48 771[3:Rew:769.0,764.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** equal(sk_c7,sk_c7) -> .
% 0.19/0.48 772[3:Obv:771.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.19/0.48 775[3:SpR:769.0,83.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.19/0.48 777[4:Spt:36.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.19/0.48 780[5:Spt:33.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.48 786[6:Spt:35.1] || -> equal(multiply(sk_c5,sk_c9),sk_c6)**.
% 0.19/0.48 788[6:SpR:786.0,83.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c9)**.
% 0.19/0.48 790[6:Rew:777.0,788.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.19/0.48 791[6:Rew:790.0,10.0] || -> equal(sk_c9,sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 792[6:Rew:790.0,22.0] || -> equal(sk_c9,sk_c8) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 793[6:Rew:790.0,28.0] || -> equal(sk_c9,sk_c8) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 794[6:Rew:790.0,16.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c9,sk_c8).
% 0.19/0.48 795[6:Rew:790.0,34.1] || -> equal(inverse(sk_c2),sk_c9)** equal(sk_c9,sk_c8).
% 0.19/0.48 796[6:Rew:794.1,14.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.19/0.48 798[6:Rew:791.0,8.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 802[6:SpR:790.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c6)**.
% 0.19/0.48 804[6:Rew:39.0,802.0] || -> equal(identity,sk_c6)**.
% 0.19/0.48 805[6:Rew:804.0,38.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.48 806[6:Rew:804.0,287.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.48 807[6:Rew:804.0,39.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.48 816[6:SpR:807.0,83.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.19/0.48 818[6:SpR:777.0,807.0] || -> equal(multiply(sk_c9,sk_c5),sk_c6)**.
% 0.19/0.48 819[6:SpR:780.0,807.0] || -> equal(multiply(sk_c9,sk_c4),sk_c6)**.
% 0.19/0.48 820[6:Rew:806.0,816.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.48 824[6:SpR:818.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c6),sk_c5)**.
% 0.19/0.48 826[6:Rew:806.0,824.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.19/0.48 833[6:SpR:819.0,83.0] || -> equal(multiply(inverse(sk_c9),sk_c6),sk_c4)**.
% 0.19/0.48 835[6:Rew:826.0,833.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.19/0.48 836[6:Rew:806.0,835.0] || -> equal(sk_c5,sk_c4)**.
% 0.19/0.48 838[6:Rew:836.0,786.0] || -> equal(multiply(sk_c4,sk_c9),sk_c6)**.
% 0.19/0.48 840[6:Rew:836.0,826.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.19/0.48 846[7:Spt:794.1] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 849[7:Rew:846.0,780.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 850[7:Rew:846.0,819.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.19/0.48 852[7:Rew:846.0,772.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.19/0.48 859[7:Rew:846.0,798.1] || -> equal(multiply(sk_c4,sk_c8),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.48 862[7:Rew:846.0,840.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.48 863[7:Rew:846.0,838.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.19/0.48 864[7:Rew:863.0,796.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c6,sk_c8).
% 0.19/0.48 867[7:Rew:863.0,859.0] || -> equal(sk_c6,sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.48 870[7:Rew:846.0,852.3,846.0,852.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.48 871[7:Con:870.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.48 888[8:Spt:864.1] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.48 890[8:Rew:888.0,805.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.48 892[8:Rew:888.0,806.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.48 894[8:Rew:888.0,850.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.19/0.48 902[8:Rew:892.0,871.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.48 903[8:Rew:890.0,894.0] || -> equal(sk_c4,sk_c8)**.
% 0.19/0.48 905[8:Rew:903.0,849.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.48 945[8:SpL:905.0,902.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.48 947[8:Obv:945.1] || -> .
% 0.19/0.48 948[8:Spt:947.0,864.1,888.0] || equal(sk_c6,sk_c8)** -> .
% 0.19/0.48 949[8:Spt:947.0,864.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 951[8:MRR:867.0,948.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.48 955[8:SpR:949.0,820.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.19/0.48 957[8:Rew:862.0,955.0] || -> equal(sk_c1,sk_c4)**.
% 0.19/0.48 959[8:Rew:957.0,951.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.19/0.48 960[8:Rew:863.0,959.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.48 961[8:MRR:960.0,948.0] || -> .
% 0.19/0.48 963[7:Spt:961.0,794.1,846.0] || equal(sk_c9,sk_c8)** -> .
% 0.19/0.48 964[7:Spt:961.0,794.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 966[7:MRR:795.1,963.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 968[7:MRR:792.0,963.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 969[7:MRR:793.0,963.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 983[7:SpR:966.0,820.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.19/0.48 985[7:Rew:840.0,983.0] || -> equal(sk_c2,sk_c4)**.
% 0.19/0.48 987[7:Rew:985.0,969.0] || -> equal(multiply(sk_c4,sk_c9),sk_c3)**.
% 0.19/0.48 988[7:Rew:838.0,987.0] || -> equal(sk_c3,sk_c6)**.
% 0.19/0.48 989[7:Rew:988.0,968.0] || -> equal(multiply(sk_c9,sk_c6),sk_c8)**.
% 0.19/0.48 990[7:Rew:806.0,989.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 991[7:MRR:990.0,963.0] || -> .
% 0.19/0.48 993[6:Spt:991.0,35.1,786.0] || equal(multiply(sk_c5,sk_c9),sk_c6)** -> .
% 0.19/0.48 994[6:Spt:991.0,35.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.48 995[6:MRR:17.1,993.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 996[6:MRR:29.0,993.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.48 997[6:MRR:23.0,993.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.48 998[6:MRR:11.0,993.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.48 1009[6:SpR:996.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.48 1011[6:Rew:994.0,1009.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.48 1012[6:Rew:997.0,1011.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.48 1016[6:Rew:1012.0,769.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.48 1022[6:Rew:1012.0,772.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.19/0.48 1024[6:Rew:1012.0,775.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.48 1028[6:Rew:1012.0,997.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.49 1029[6:Rew:1012.0,998.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.49 1032[6:Rew:1012.0,1022.3,1012.0,1022.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.49 1033[6:Con:1032.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.49 1050[6:SpR:1028.0,83.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.19/0.49 1052[6:Rew:39.0,1050.0] || -> equal(identity,sk_c3)**.
% 0.19/0.49 1054[6:Rew:1052.0,287.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.49 1056[6:Rew:1052.0,39.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.49 1061[6:SpR:1029.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.19/0.49 1063[6:Rew:1016.0,1061.0,995.0,1061.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 1065[6:Rew:1063.0,1024.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.49 1067[6:Rew:1056.0,1065.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.49 1071[6:Rew:1067.0,1054.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.49 1079[6:Rew:1071.0,1029.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.49 1081[6:Rew:1071.0,1033.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.49 1083[6:Rew:1079.0,995.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 1138[6:SpL:1083.0,1081.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.49 1139[6:Obv:1138.1] || -> .
% 0.19/0.49 1140[5:Spt:1139.0,33.0,780.0] || equal(inverse(sk_c4),sk_c9)** -> .
% 0.19/0.49 1141[5:Spt:1139.0,33.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 1142[5:MRR:15.0,1140.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 1143[5:MRR:27.0,1140.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 1144[5:MRR:21.0,1140.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 1145[5:MRR:9.0,1140.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.49 1159[5:SpR:1143.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.49 1161[5:Rew:1141.0,1159.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 1162[5:Rew:1144.0,1161.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.49 1165[5:Rew:1162.0,769.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.49 1169[5:Rew:1162.0,767.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.49 1174[5:Rew:1162.0,1144.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.49 1175[5:Rew:1162.0,1145.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.49 1176[5:Rew:1162.0,772.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.19/0.49 1180[5:Rew:1162.0,1176.3,1162.0,1176.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.49 1181[5:Con:1180.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.49 1196[5:SpR:1174.0,83.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.19/0.49 1198[5:Rew:39.0,1196.0] || -> equal(identity,sk_c3)**.
% 0.19/0.49 1199[5:Rew:1198.0,287.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.49 1201[5:Rew:1198.0,39.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.49 1207[5:SpR:1175.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.19/0.49 1209[5:Rew:1165.0,1207.0,1142.0,1207.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 1211[5:Rew:1209.0,1169.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.49 1213[5:Rew:1201.0,1211.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.49 1216[5:Rew:1213.0,1199.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.49 1220[5:Rew:1216.0,1175.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.49 1222[5:Rew:1216.0,1181.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.49 1223[5:Rew:1220.0,1142.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 1301[5:SpL:1223.0,1222.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.49 1303[5:Obv:1301.1] || -> .
% 0.19/0.49 1304[4:Spt:1303.0,36.0,777.0] || equal(inverse(sk_c5),sk_c9)** -> .
% 0.19/0.49 1305[4:Spt:1303.0,36.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 1306[4:MRR:18.0,1304.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 1307[4:MRR:30.0,1304.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 1308[4:MRR:24.0,1304.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 1309[4:MRR:12.0,1304.0] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.49 1321[4:SpR:1307.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.49 1323[4:Rew:1305.0,1321.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 1324[4:Rew:1308.0,1323.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.49 1326[4:Rew:1324.0,761.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.49 1330[4:Rew:1324.0,775.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.49 1334[4:Rew:1324.0,1308.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.49 1335[4:Rew:1324.0,1309.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.49 1336[4:Rew:1324.0,772.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.19/0.49 1340[4:Rew:1324.0,1336.3,1324.0,1336.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.19/0.49 1341[4:Con:1340.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.49 1354[4:SpR:1334.0,83.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.19/0.49 1356[4:Rew:39.0,1354.0] || -> equal(identity,sk_c3)**.
% 0.19/0.49 1358[4:Rew:1356.0,287.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.49 1360[4:Rew:1356.0,39.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.49 1365[4:SpR:1335.0,83.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.19/0.49 1367[4:Rew:1326.0,1365.0,1306.0,1365.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 1369[4:Rew:1367.0,1330.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.49 1371[4:Rew:1360.0,1369.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.49 1375[4:Rew:1371.0,1358.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.49 1381[4:Rew:1375.0,1335.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.49 1383[4:Rew:1375.0,1341.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.49 1384[4:Rew:1381.0,1306.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.49 1431[4:SpL:1384.0,1383.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.49 1433[4:Obv:1431.1] || -> .
% 0.19/0.49 1434[3:Spt:1433.0,3.1,769.0] || equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.19/0.49 1435[3:Spt:1433.0,3.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.19/0.49 1437[3:MRR:2.1,1434.0] || -> equal(multiply(sk_c4,sk_c9),sk_c8)**.
% 0.19/0.49 1448[3:SpR:1437.0,83.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c9)**.
% 0.19/0.49 1450[3:Rew:761.0,1448.0,1435.0,1448.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 1452[3:Rew:1450.0,767.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.49 1453[3:Rew:1450.0,1434.0] || equal(multiply(sk_c8,sk_c9),sk_c9)** -> .
% 0.19/0.49 1455[3:Rew:39.0,1452.0] || -> equal(identity,sk_c8)**.
% 0.19/0.49 1457[3:Rew:1455.0,38.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.49 1460[3:Rew:1457.0,1453.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.49 1461[3:Obv:1460.0] || -> .
% 0.19/0.49 1464[2:Spt:1461.0,1.0,761.0] || equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.19/0.49 1465[2:Spt:1461.0,1.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.49 1466[2:MRR:31.1,1464.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 1468[2:MRR:25.0,1464.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 1469[2:MRR:19.0,1464.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 1479[2:SpR:1468.0,83.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.49 1481[2:Rew:1466.0,1479.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 1482[2:Rew:1469.0,1481.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.49 1483[2:Rew:1482.0,1465.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.49 1486[2:Rew:1482.0,1464.0] || equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.19/0.49 1492[2:Rew:1483.0,1486.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.49 1493[2:Obv:1492.0] || -> .
% 0.19/0.49 % SZS output end Refutation
% 0.19/0.49 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_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.19/0.49
%------------------------------------------------------------------------------