TSTP Solution File: GRP320-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP320-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:46:50 EDT 2022
% Result : Unsatisfiable 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP320-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 21:06:33 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.50
% 0.22/0.50 SPASS V 3.9
% 0.22/0.50 SPASS beiseite: Proof found.
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.50 SPASS derived 909 clauses, backtracked 369 clauses, performed 11 splits and kept 797 clauses.
% 0.22/0.50 SPASS allocated 63672 KBytes.
% 0.22/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.22/0.50 0:00:00.04 for the input.
% 0.22/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.50 0:00:00.00 for inferences.
% 0.22/0.50 0:00:00.00 for the backtracking.
% 0.22/0.50 0:00:00.06 for the reduction.
% 0.22/0.50
% 0.22/0.50
% 0.22/0.50 Here is a proof with depth 5, length 407 :
% 0.22/0.50 % SZS output start Refutation
% 0.22/0.50 1[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 3[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 4[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 5[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.50 6[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.50 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.50 8[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.50 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.50 10[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.50 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.22/0.50 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.50 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.50 14[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.50 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.22/0.50 16[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.22/0.50 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.50 18[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.22/0.50 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.50 20[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.22/0.50 21[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.50 22[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.50 23[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.50 24[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.50 25[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.50 26[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.22/0.50 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.50 28[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.50 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.50 30[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.22/0.50 31[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(w,sk_c8),y)*+ equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.50 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.22/0.50 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.22/0.50 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.22/0.50 35[1:Spt:31.2,31.4,31.8] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)* equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.22/0.50 37[2:Spt:5.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.22/0.50 40[3:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.22/0.50 42[4:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.22/0.50 45[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.22/0.50 46[5:Spt:3.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.50 48[6:Spt:1.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.22/0.50 54[3:SpR:40.0,33.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.22/0.50 55[4:SpR:42.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.22/0.50 56[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.22/0.50 63[4:SpR:55.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.22/0.50 65[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.22/0.50 67[3:SpR:54.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.22/0.50 69[4:Rew:32.0,63.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.22/0.50 70[3:Rew:32.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.22/0.50 71[0:Rew:32.0,65.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.22/0.50 75[6:SpR:48.0,69.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.22/0.50 81[5:SpR:46.0,70.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.22/0.50 86[0:SpR:71.0,71.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.22/0.50 88[2:SpR:37.0,71.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.22/0.51 90[4:SpR:55.0,71.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.22/0.51 92[6:SpR:75.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.22/0.51 94[0:SpR:33.0,71.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.22/0.51 96[3:SpR:54.0,71.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.22/0.51 98[5:SpR:81.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.22/0.51 103[6:Rew:33.0,92.0] || -> equal(sk_c7,identity)**.
% 0.22/0.51 105[6:Rew:103.0,37.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.22/0.51 106[6:Rew:103.0,40.0] || -> equal(inverse(sk_c5),identity)**.
% 0.22/0.51 109[6:Rew:103.0,54.0] || -> equal(multiply(identity,sk_c5),identity)**.
% 0.22/0.51 112[6:Rew:103.0,81.0] || -> equal(multiply(identity,sk_c6),identity)**.
% 0.22/0.51 114[6:Rew:103.0,56.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),identity)** -> .
% 0.22/0.51 124[6:Rew:32.0,109.0] || -> equal(identity,sk_c5)**.
% 0.22/0.51 125[6:Rew:124.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.22/0.51 130[6:Rew:124.0,106.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.22/0.51 131[6:Rew:124.0,105.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.22/0.51 135[6:Rew:124.0,112.0] || -> equal(multiply(sk_c5,sk_c6),sk_c5)**.
% 0.22/0.51 136[6:Rew:125.0,135.0] || -> equal(sk_c5,sk_c6)**.
% 0.22/0.51 137[6:Rew:136.0,124.0] || -> equal(identity,sk_c6)**.
% 0.22/0.51 139[6:Rew:136.0,130.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.22/0.51 141[6:Rew:136.0,125.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.51 143[6:Rew:136.0,131.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.22/0.51 146[6:Rew:141.0,143.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 148[6:Rew:146.0,137.0] || -> equal(identity,sk_c8)**.
% 0.22/0.51 150[6:Rew:146.0,139.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.51 154[6:Rew:146.0,141.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.51 187[6:Rew:154.0,114.2,148.0,114.2,148.0,114.1,150.0,114.0,150.0,114.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.22/0.51 188[6:Obv:187.1] || equal(u,sk_c8)* -> .
% 0.22/0.51 189[6:UnC:188.0,71.0] || -> .
% 0.22/0.51 192[6:Spt:189.0,1.0,48.0] || equal(multiply(sk_c4,sk_c8),sk_c7)** -> .
% 0.22/0.51 193[6:Spt:189.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 195[5:Rew:33.0,98.0] || -> equal(identity,sk_c6)**.
% 0.22/0.51 198[5:Rew:195.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.51 200[5:Rew:195.0,90.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c4)**.
% 0.22/0.51 202[5:Rew:195.0,96.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.22/0.51 203[5:Rew:198.0,37.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 206[5:Rew:203.0,46.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.51 207[6:Rew:203.0,193.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 210[6:Rew:203.0,192.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.22/0.51 211[5:Rew:200.0,202.0,203.0,202.0] || -> equal(sk_c5,sk_c4)**.
% 0.22/0.51 213[5:Rew:211.0,206.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.22/0.51 215[6:Rew:213.0,210.0] || equal(sk_c6,sk_c8)** -> .
% 0.22/0.51 224[5:Rew:213.0,11.1,203.0,11.1,203.0,11.0] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c6,sk_c8).
% 0.22/0.51 225[6:MRR:224.1,215.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 233[5:Rew:203.0,6.1,213.0,6.0,203.0,6.0] || -> equal(sk_c6,sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 234[6:MRR:233.0,215.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 290[6:SpR:234.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 292[6:Rew:207.0,290.0,225.0,290.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 293[6:MRR:292.0,215.0] || -> .
% 0.22/0.51 294[5:Spt:293.0,3.0,46.0] || equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.22/0.51 295[5:Spt:293.0,3.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 296[0:Rew:86.0,94.0] || -> equal(multiply(u,identity),u)**.
% 0.22/0.51 297[4:Rew:296.0,90.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.22/0.51 298[3:Rew:296.0,96.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.22/0.51 301[5:MRR:28.1,294.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 302[5:MRR:13.1,294.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.51 303[5:MRR:23.0,294.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.51 304[5:MRR:18.0,294.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.51 305[5:MRR:8.0,294.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 320[3:SpR:298.0,71.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.22/0.51 330[5:SpR:303.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.51 332[5:Rew:301.0,330.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 333[5:Rew:304.0,332.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 334[5:Rew:333.0,295.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 336[5:Rew:333.0,298.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.22/0.51 337[5:Rew:333.0,302.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 340[5:Rew:333.0,88.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c8)**.
% 0.22/0.51 341[5:Rew:333.0,294.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.22/0.51 345[5:Rew:333.0,304.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 346[5:Rew:333.0,305.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 355[5:Rew:297.0,336.0] || -> equal(sk_c5,sk_c4)**.
% 0.22/0.51 359[5:Rew:355.0,341.0] || equal(multiply(sk_c4,sk_c8),sk_c6)** -> .
% 0.22/0.51 372[5:SpR:345.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.22/0.51 374[5:Rew:297.0,372.0] || -> equal(multiply(sk_c4,sk_c8),sk_c3)**.
% 0.22/0.51 375[5:Rew:374.0,359.0] || equal(sk_c3,sk_c6)** -> .
% 0.22/0.51 380[5:SpR:346.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 382[5:Rew:334.0,380.0,337.0,380.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 384[5:Rew:382.0,375.0] || equal(sk_c3,sk_c8)** -> .
% 0.22/0.51 387[5:Rew:382.0,340.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.22/0.51 393[5:Rew:297.0,387.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.22/0.51 394[5:Rew:374.0,393.0] || -> equal(sk_c3,sk_c8)**.
% 0.22/0.51 395[5:MRR:394.0,384.0] || -> .
% 0.22/0.51 397[4:Spt:395.0,2.0,42.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.22/0.51 398[4:Spt:395.0,2.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 399[4:MRR:27.0,397.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 400[4:MRR:12.0,397.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.51 401[4:MRR:22.0,397.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.51 402[4:MRR:17.0,397.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.51 403[4:MRR:7.0,397.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 405[4:SpR:398.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.22/0.51 407[4:Rew:298.0,405.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.22/0.51 425[4:SpR:401.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.51 427[4:Rew:399.0,425.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 428[4:Rew:402.0,427.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 429[4:Rew:428.0,398.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 431[4:Rew:428.0,40.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.51 432[4:Rew:428.0,400.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 434[4:Rew:428.0,54.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.22/0.51 436[4:Rew:428.0,320.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.22/0.51 440[4:Rew:428.0,403.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 444[4:Rew:428.0,45.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.22/0.51 459[4:SpR:407.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.22/0.51 480[4:SpR:440.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 482[4:Rew:429.0,480.0,432.0,480.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 490[4:Rew:482.0,459.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.22/0.51 498[4:Rew:436.0,490.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.51 499[4:Rew:498.0,434.0] || -> equal(identity,sk_c5)**.
% 0.22/0.51 504[4:Rew:498.0,444.2] || equal(inverse(identity),sk_c8)** equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.22/0.51 516[4:Obv:504.1] || equal(inverse(identity),sk_c8)** equal(u,sk_c8)* -> .
% 0.22/0.51 517[4:Con:516.1] || equal(inverse(identity),sk_c8)** -> .
% 0.22/0.51 518[4:Rew:499.0,517.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.22/0.51 519[4:Rew:431.0,518.0] || equal(sk_c8,sk_c8)* -> .
% 0.22/0.51 520[4:Obv:519.0] || -> .
% 0.22/0.51 525[3:Spt:520.0,4.0,40.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.22/0.51 526[3:Spt:520.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 527[3:MRR:29.0,525.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 528[3:MRR:14.0,525.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.51 529[3:MRR:24.0,525.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.51 530[3:MRR:19.0,525.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.51 531[3:MRR:9.0,525.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 543[3:SpR:529.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.51 545[3:Rew:527.0,543.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 546[3:Rew:530.0,545.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 547[3:Rew:546.0,526.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 548[3:Rew:546.0,528.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 551[3:Rew:546.0,88.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c8)**.
% 0.22/0.51 553[3:Rew:546.0,530.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 554[3:Rew:546.0,531.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 556[3:Rew:546.0,56.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.22/0.51 575[3:SpR:553.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.22/0.51 577[3:Rew:33.0,575.0] || -> equal(identity,sk_c3)**.
% 0.22/0.51 578[3:Rew:577.0,296.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.22/0.51 579[3:Rew:577.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.22/0.51 580[3:Rew:577.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.22/0.51 583[3:Rew:577.0,556.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c3,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.22/0.51 588[3:SpR:554.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 590[3:Rew:547.0,588.0,548.0,588.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 593[3:Rew:590.0,551.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.22/0.51 598[3:Rew:580.0,593.0] || -> equal(sk_c3,sk_c8)**.
% 0.22/0.51 601[3:Rew:598.0,578.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.51 602[3:Rew:598.0,579.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.51 606[3:Rew:598.0,583.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.22/0.51 607[3:Rew:601.0,554.0] || -> equal(sk_c1,sk_c8)**.
% 0.22/0.51 612[3:Rew:607.0,548.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.51 631[3:Rew:602.0,606.2,612.0,606.0,612.0,606.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.22/0.51 632[3:Obv:631.1] || equal(u,sk_c8)* -> .
% 0.22/0.51 633[3:UnC:632.0,546.0] || -> .
% 0.22/0.51 635[2:Spt:633.0,5.0,37.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.22/0.51 636[2:Spt:633.0,5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 637[2:MRR:30.1,635.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 638[2:MRR:15.1,635.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.51 639[2:MRR:25.0,635.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.51 640[2:MRR:20.0,635.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.51 641[2:MRR:10.0,635.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 643[2:SpR:636.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.22/0.51 650[2:SpR:639.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.51 652[2:Rew:637.0,650.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 653[2:Rew:640.0,652.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 654[2:Rew:653.0,636.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 655[2:Rew:653.0,638.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 657[2:Rew:653.0,640.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 658[2:Rew:653.0,641.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 660[2:Rew:653.0,56.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.22/0.51 664[2:Rew:653.0,643.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.22/0.51 671[2:SpR:657.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.22/0.51 673[2:Rew:33.0,671.0] || -> equal(identity,sk_c3)**.
% 0.22/0.51 674[2:Rew:673.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.22/0.51 675[2:Rew:673.0,296.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.22/0.51 678[2:Rew:673.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.22/0.51 679[2:Rew:673.0,660.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c3,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.22/0.51 687[2:SpR:658.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 689[2:Rew:654.0,687.0,655.0,687.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 692[2:Rew:689.0,664.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.22/0.51 696[2:Rew:678.0,692.0] || -> equal(sk_c3,sk_c8)**.
% 0.22/0.51 699[2:Rew:696.0,674.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.51 700[2:Rew:696.0,675.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.51 704[2:Rew:696.0,679.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c8)** -> .
% 0.22/0.51 711[2:Rew:700.0,658.0] || -> equal(sk_c1,sk_c8)**.
% 0.22/0.51 713[2:Rew:711.0,655.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.51 725[2:Rew:699.0,704.2,713.0,704.0,713.0,704.0] || equal(sk_c8,sk_c8)* equal(sk_c8,u)* equal(u,sk_c8)* -> .
% 0.22/0.51 726[2:Obv:725.1] || equal(u,sk_c8)* -> .
% 0.22/0.51 727[2:UnC:726.0,653.0] || -> .
% 0.22/0.51 729[1:Spt:727.0,31.0,31.1,31.3,31.5,31.6,31.7,31.9,31.10] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)**+ equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.51 731[2:Spt:5.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.22/0.51 732[2:Rew:731.0,729.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(sk_c7,sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.51 734[2:Obv:732.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.51 737[2:SpR:731.0,71.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.22/0.51 739[3:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.22/0.51 742[4:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.22/0.51 743[4:SpR:742.0,71.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.22/0.51 745[5:Spt:1.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.22/0.51 747[5:SpR:745.0,71.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c8)**.
% 0.22/0.51 749[5:Rew:739.0,747.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.22/0.51 751[5:SpR:749.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.22/0.51 753[5:Rew:33.0,751.0] || -> equal(sk_c7,identity)**.
% 0.22/0.51 754[5:Rew:753.0,731.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.22/0.51 758[5:Rew:753.0,13.0] || -> equal(inverse(sk_c1),identity) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.51 760[5:Rew:753.0,734.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(identity,sk_c8),sk_c6)** -> .
% 0.22/0.51 761[5:Rew:753.0,3.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(identity,sk_c8),sk_c6)**.
% 0.22/0.51 762[5:Rew:753.0,8.0] || -> equal(multiply(sk_c5,identity),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 766[5:Rew:753.0,737.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c8)**.
% 0.22/0.51 769[5:Rew:753.0,743.0] || -> equal(multiply(identity,multiply(sk_c5,u)),u)**.
% 0.22/0.51 770[5:Rew:296.0,766.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.22/0.51 771[5:Rew:32.0,769.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.22/0.51 773[5:Rew:753.0,758.1,771.0,758.1] || -> equal(inverse(sk_c1),identity)** equal(identity,sk_c6).
% 0.22/0.51 777[5:Rew:32.0,761.1,753.0,761.0,771.0,761.0] || -> equal(identity,sk_c6)** equal(sk_c6,sk_c8).
% 0.22/0.51 778[5:Rew:296.0,762.1,753.0,762.1,771.0,762.0] || -> equal(identity,sk_c6)** equal(sk_c1,sk_c8).
% 0.22/0.51 779[5:Rew:778.1,773.0] || -> equal(inverse(sk_c8),identity)** equal(identity,sk_c6).
% 0.22/0.51 782[5:Rew:32.0,760.6,296.0,760.5,753.0,760.5,753.0,760.4,296.0,760.3,753.0,760.3,753.0,760.2,753.0,760.0] || equal(inverse(u),identity)** equal(inverse(v),sk_c8) equal(inverse(w),identity)** equal(u,sk_c6) equal(multiply(v,sk_c8),identity)** equal(w,sk_c8) equal(sk_c6,sk_c8) -> .
% 0.22/0.51 798[6:Spt:777.0] || -> equal(identity,sk_c6)**.
% 0.22/0.51 799[6:Rew:798.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.51 802[6:Rew:798.0,754.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.22/0.51 803[6:Rew:798.0,296.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.22/0.51 807[6:Rew:798.0,782.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c8) equal(inverse(w),identity)** equal(u,sk_c6) equal(multiply(v,sk_c8),identity)** equal(w,sk_c8) equal(sk_c6,sk_c8) -> .
% 0.22/0.51 810[6:Rew:799.0,802.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 811[6:Rew:810.0,770.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.51 812[6:Rew:810.0,798.0] || -> equal(identity,sk_c8)**.
% 0.22/0.51 816[6:Rew:810.0,803.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.51 825[6:Rew:810.0,807.6,816.0,807.4,812.0,807.4,810.0,807.3,812.0,807.2,810.0,807.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.22/0.51 826[6:Obv:825.6] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.22/0.51 827[6:Con:826.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.22/0.51 857[6:SpL:811.0,827.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.22/0.51 858[6:Obv:857.1] || -> .
% 0.22/0.51 859[6:Spt:858.0,777.0,798.0] || equal(identity,sk_c6)** -> .
% 0.22/0.51 860[6:Spt:858.0,777.1] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 861[6:Rew:860.0,770.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.51 862[6:Rew:860.0,859.0] || equal(identity,sk_c8)** -> .
% 0.22/0.51 868[6:Rew:860.0,779.1,861.0,779.0] || -> equal(identity,sk_c8)** equal(identity,sk_c8)**.
% 0.22/0.51 869[6:Obv:868.0] || -> equal(identity,sk_c8)**.
% 0.22/0.51 870[6:MRR:869.0,862.0] || -> .
% 0.22/0.51 880[5:Spt:870.0,1.0,745.0] || equal(multiply(sk_c4,sk_c8),sk_c7)** -> .
% 0.22/0.51 881[5:Spt:870.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 882[5:MRR:26.1,880.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 883[5:MRR:11.1,880.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.51 884[5:MRR:21.0,880.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.51 885[5:MRR:16.0,880.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.51 886[5:MRR:6.0,880.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 903[5:SpR:884.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.51 905[5:Rew:882.0,903.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 906[5:Rew:885.0,905.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 907[5:Rew:906.0,881.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 909[5:Rew:906.0,883.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 911[5:Rew:906.0,737.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c8)**.
% 0.22/0.51 912[5:Rew:906.0,880.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.22/0.51 915[5:Rew:906.0,885.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 916[5:Rew:906.0,886.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 935[5:SpR:915.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.22/0.51 937[5:Rew:33.0,935.0] || -> equal(identity,sk_c3)**.
% 0.22/0.51 938[5:Rew:937.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.22/0.51 939[5:Rew:937.0,296.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.22/0.51 941[5:Rew:937.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.22/0.51 949[5:SpR:916.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 951[5:Rew:907.0,949.0,909.0,949.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 954[5:Rew:951.0,911.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.22/0.51 960[5:Rew:941.0,954.0] || -> equal(sk_c3,sk_c8)**.
% 0.22/0.51 963[5:Rew:960.0,938.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.51 964[5:Rew:960.0,939.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.51 966[5:Rew:960.0,941.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.22/0.51 974[5:Rew:964.0,912.0] || equal(sk_c4,sk_c8)** -> .
% 0.22/0.51 1020[5:SpR:739.0,966.0] || -> equal(multiply(sk_c8,sk_c4),sk_c8)**.
% 0.22/0.51 1022[5:Rew:963.0,1020.0] || -> equal(sk_c4,sk_c8)**.
% 0.22/0.51 1023[5:MRR:1022.0,974.0] || -> .
% 0.22/0.51 1027[4:Spt:1023.0,4.0,742.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.22/0.51 1028[4:Spt:1023.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 1029[4:MRR:29.0,1027.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 1030[4:MRR:14.0,1027.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.51 1031[4:MRR:24.0,1027.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.51 1032[4:MRR:19.0,1027.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.51 1033[4:MRR:9.0,1027.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 1034[4:Rew:1028.0,734.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.22/0.51 1035[4:Obv:1034.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.22/0.51 1049[4:SpR:1031.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.51 1051[4:Rew:1029.0,1049.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 1052[4:Rew:1032.0,1051.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 1053[4:Rew:1052.0,1028.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 1054[4:Rew:1052.0,1030.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 1057[4:Rew:1052.0,737.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c8)**.
% 0.22/0.51 1059[4:Rew:1052.0,1032.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 1060[4:Rew:1052.0,1033.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 1061[4:Rew:1052.0,1035.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.22/0.51 1066[4:Rew:1052.0,1061.5,1052.0,1061.4,1052.0,1061.3,1052.0,1061.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.22/0.51 1067[4:Con:1066.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.22/0.51 1080[4:SpR:1059.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.22/0.51 1082[4:Rew:33.0,1080.0] || -> equal(identity,sk_c3)**.
% 0.22/0.51 1083[4:Rew:1082.0,296.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.22/0.51 1085[4:Rew:1082.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.22/0.51 1091[4:SpR:1060.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 1093[4:Rew:1053.0,1091.0,1054.0,1091.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 1096[4:Rew:1093.0,1057.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.22/0.51 1100[4:Rew:1093.0,1067.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.22/0.51 1102[4:Rew:1085.0,1096.0] || -> equal(sk_c3,sk_c8)**.
% 0.22/0.51 1105[4:Rew:1102.0,1083.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.51 1109[4:Rew:1105.0,1060.0] || -> equal(sk_c1,sk_c8)**.
% 0.22/0.51 1111[4:Rew:1109.0,1054.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.51 1123[4:Con:1100.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.22/0.51 1124[4:Rew:1105.0,1123.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.22/0.51 1164[4:SpL:1111.0,1124.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.22/0.51 1165[4:Obv:1164.1] || -> .
% 0.22/0.51 1166[3:Spt:1165.0,2.0,739.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.22/0.51 1167[3:Spt:1165.0,2.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 1168[3:MRR:27.0,1166.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 1169[3:MRR:12.0,1166.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.51 1170[3:MRR:22.0,1166.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.51 1171[3:MRR:17.0,1166.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.51 1172[3:MRR:7.0,1166.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 1173[3:Rew:1167.0,734.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.22/0.51 1174[3:Obv:1173.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.22/0.51 1188[3:SpR:1170.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.51 1190[3:Rew:1168.0,1188.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 1191[3:Rew:1171.0,1190.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 1192[3:Rew:1191.0,1167.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 1193[3:Rew:1191.0,1169.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 1195[3:Rew:1191.0,737.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c8)**.
% 0.22/0.51 1197[3:Rew:1191.0,1171.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 1198[3:Rew:1191.0,1172.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 1199[3:Rew:1191.0,1174.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.22/0.51 1204[3:Rew:1191.0,1199.5,1191.0,1199.4,1191.0,1199.3,1191.0,1199.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** -> .
% 0.22/0.51 1205[3:Con:1204.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.22/0.51 1218[3:SpR:1197.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.22/0.51 1220[3:Rew:33.0,1218.0] || -> equal(identity,sk_c3)**.
% 0.22/0.51 1222[3:Rew:1220.0,296.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.22/0.51 1224[3:Rew:1220.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.22/0.51 1229[3:SpR:1198.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 1231[3:Rew:1192.0,1229.0,1193.0,1229.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 1234[3:Rew:1231.0,1195.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.22/0.51 1238[3:Rew:1231.0,1205.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.22/0.51 1240[3:Rew:1224.0,1234.0] || -> equal(sk_c3,sk_c8)**.
% 0.22/0.51 1244[3:Rew:1240.0,1222.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.22/0.51 1250[3:Rew:1244.0,1198.0] || -> equal(sk_c1,sk_c8)**.
% 0.22/0.51 1252[3:Rew:1250.0,1193.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.51 1260[3:Con:1238.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.22/0.51 1261[3:Rew:1244.0,1260.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.22/0.51 1290[3:SpL:1252.0,1261.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.22/0.51 1291[3:Obv:1290.1] || -> .
% 0.22/0.51 1292[2:Spt:1291.0,5.0,731.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.22/0.51 1293[2:Spt:1291.0,5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.51 1294[2:MRR:30.1,1292.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.51 1295[2:MRR:15.1,1292.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.51 1296[2:MRR:25.0,1292.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.51 1297[2:MRR:20.0,1292.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.51 1298[2:MRR:10.0,1292.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.51 1307[2:SpR:1296.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.51 1309[2:Rew:1294.0,1307.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.51 1310[2:Rew:1297.0,1309.0] || -> equal(sk_c7,sk_c8)**.
% 0.22/0.51 1311[2:Rew:1310.0,1293.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.22/0.51 1312[2:Rew:1310.0,1295.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.51 1313[2:Rew:1310.0,1292.0] || equal(multiply(sk_c6,sk_c8),sk_c8)** -> .
% 0.22/0.51 1315[2:Rew:1310.0,1298.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.22/0.51 1336[2:SpR:1315.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.22/0.51 1338[2:Rew:1311.0,1336.0,1312.0,1336.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.51 1339[2:Rew:1338.0,1311.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.22/0.51 1340[2:Rew:1338.0,1313.0] || equal(multiply(sk_c8,sk_c8),sk_c8)** -> .
% 0.22/0.51 1343[2:Rew:1339.0,1340.0] || equal(sk_c8,sk_c8)* -> .
% 0.22/0.51 1344[2:Obv:1343.0] || -> .
% 0.22/0.51 % SZS output end Refutation
% 0.22/0.51 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 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
% 0.22/0.51
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