TSTP Solution File: GRP227-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP227-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:46:25 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP227-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 06:50:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 982 clauses, backtracked 423 clauses, performed 12 splits and kept 790 clauses.
% 0.20/0.49 SPASS allocated 63778 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.49 0:00:00.03 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.07 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 4, length 401 :
% 0.20/0.49 % SZS output start Refutation
% 0.20/0.49 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c1),sk_c8).
% 0.20/0.49 2[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.49 3[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.20/0.49 4[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.49 5[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c1),sk_c8).
% 0.20/0.49 6[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 7[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 8[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.20/0.49 9[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 10[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.20/0.49 11[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 12[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.20/0.49 13[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.49 14[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.20/0.49 15[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.49 16[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.20/0.49 17[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.49 18[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.20/0.49 19[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 20[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 22[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 23[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 24[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 25[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 26[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.49 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 28[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.49 29[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 30[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 31[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(inverse(y),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,v),sk_c7)**+ equal(multiply(x,sk_c8),z)* equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(y,sk_c7),sk_c8)** equal(multiply(sk_c8,z),sk_c7)** -> .
% 0.20/0.49 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.49 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.49 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.49 35[1:Spt:31.0,31.5,31.7] || equal(inverse(u),v) equal(multiply(u,v),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.20/0.49 36[2:Spt:25.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 38[3:Spt:1.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 40[4:Spt:19.1] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 46[1:SpL:32.0,35.1] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.49 47[5:Spt:13.1] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.49 51[6:Spt:7.1] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 57[2:SpR:36.0,33.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.20/0.49 58[3:SpR:38.0,33.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.20/0.49 67[4:SpR:40.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),multiply(sk_c3,u))**.
% 0.20/0.49 69[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.49 71[2:SpR:57.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.20/0.49 72[3:SpR:58.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.20/0.49 75[2:Rew:32.0,71.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.20/0.49 76[3:Rew:32.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 77[0:Rew:32.0,69.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.49 81[4:SpR:40.0,75.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.20/0.49 82[2:SpL:75.0,35.1] || equal(multiply(sk_c2,u),inverse(sk_c8)) equal(u,sk_c7) equal(multiply(multiply(sk_c2,u),sk_c8),sk_c7)** -> .
% 0.20/0.49 83[5:Rew:47.0,81.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 85[5:Rew:83.0,47.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.20/0.49 86[6:Rew:83.0,51.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.49 107[2:Rew:34.0,82.2] || equal(multiply(sk_c2,u),inverse(sk_c8)) equal(u,sk_c7) equal(multiply(sk_c2,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.49 108[5:Rew:83.0,107.2,83.0,107.1] || equal(multiply(sk_c2,u),inverse(sk_c8)) equal(u,sk_c8) equal(multiply(sk_c2,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.49 116[0:SpR:77.0,77.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.49 120[0:SpR:32.0,77.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.20/0.49 121[0:SpR:33.0,77.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.49 122[2:SpR:57.0,77.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.20/0.49 123[3:SpR:58.0,77.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.20/0.49 125[5:SpR:85.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.20/0.49 132[3:Rew:122.0,123.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.49 134[4:Rew:132.0,40.0] || -> equal(multiply(sk_c1,sk_c8),sk_c3)**.
% 0.20/0.49 137[4:Rew:132.0,67.0] || -> equal(multiply(sk_c1,multiply(sk_c8,u)),multiply(sk_c3,u))**.
% 0.20/0.49 139[5:Rew:132.0,108.0] || equal(multiply(sk_c1,u),inverse(sk_c8)) equal(u,sk_c8) equal(multiply(sk_c2,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.49 140[3:Rew:132.0,122.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.20/0.49 141[6:Rew:86.0,134.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 146[5:Rew:33.0,125.0] || -> equal(identity,sk_c3)**.
% 0.20/0.49 147[6:Rew:141.0,146.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 149[6:Rew:147.0,33.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.49 154[6:Rew:147.0,120.0] || -> equal(multiply(inverse(sk_c8),u),u)**.
% 0.20/0.49 156[6:Rew:147.0,140.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c1)**.
% 0.20/0.49 157[6:Rew:149.0,156.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.49 158[6:Rew:157.0,38.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.49 167[6:Rew:157.0,147.0] || -> equal(identity,sk_c1)**.
% 0.20/0.49 170[6:Rew:158.0,154.0,157.0,154.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 173[6:Rew:167.0,121.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.20/0.49 179[6:Rew:116.0,173.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.49 196[6:Rew:170.0,139.2,132.0,139.2,179.0,139.2,157.0,139.2,157.0,139.1,170.0,139.0,158.0,139.0,157.0,139.0] || equal(u,sk_c1)* equal(u,sk_c1)* equal(u,sk_c1)* -> .
% 0.20/0.49 197[6:Obv:196.1] || equal(u,sk_c1)* -> .
% 0.20/0.49 198[6:UnC:197.0,77.0] || -> .
% 0.20/0.49 200[6:Spt:198.0,7.1,51.0] || equal(multiply(sk_c1,sk_c7),sk_c8)** -> .
% 0.20/0.49 201[6:Spt:198.0,7.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 202[6:Rew:83.0,201.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.49 208[6:Rew:85.0,140.0,202.0,140.0,146.0,140.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.49 209[6:Rew:208.0,83.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.49 212[6:Rew:208.0,134.0] || -> equal(multiply(sk_c1,sk_c1),sk_c3)**.
% 0.20/0.49 216[6:Rew:212.0,200.0,209.0,200.0,208.0,200.0] || equal(sk_c3,sk_c1)** -> .
% 0.20/0.49 217[6:Rew:208.0,76.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),u)**.
% 0.20/0.49 223[6:Rew:212.0,11.1,209.0,11.1,208.0,11.1] || -> equal(inverse(sk_c5),sk_c6)** equal(sk_c3,sk_c1).
% 0.20/0.49 224[6:MRR:223.1,216.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 229[6:Rew:212.0,12.1,209.0,12.1,208.0,12.1,208.0,12.0,209.0,12.0] || -> equal(multiply(sk_c6,sk_c1),sk_c1)** equal(sk_c3,sk_c1).
% 0.20/0.49 230[6:MRR:229.1,216.0] || -> equal(multiply(sk_c6,sk_c1),sk_c1)**.
% 0.20/0.49 231[6:Rew:212.0,10.1,209.0,10.1,208.0,10.1,209.0,10.0] || -> equal(multiply(sk_c5,sk_c6),sk_c1)** equal(sk_c3,sk_c1).
% 0.20/0.49 232[6:MRR:231.1,216.0] || -> equal(multiply(sk_c5,sk_c6),sk_c1)**.
% 0.20/0.49 263[6:SpR:230.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),multiply(sk_c1,u))**.
% 0.20/0.49 267[6:SpR:232.0,77.0] || -> equal(multiply(inverse(sk_c5),sk_c1),sk_c6)**.
% 0.20/0.49 269[6:Rew:230.0,267.0,224.0,267.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.49 275[6:Rew:269.0,263.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),multiply(sk_c1,u))**.
% 0.20/0.49 281[6:Rew:217.0,275.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 282[6:Rew:281.0,212.0] || -> equal(sk_c3,sk_c1)**.
% 0.20/0.49 288[6:MRR:282.0,216.0] || -> .
% 0.20/0.49 291[5:Spt:288.0,13.1,47.0] || equal(multiply(sk_c8,sk_c3),sk_c7)** -> .
% 0.20/0.49 292[5:Spt:288.0,13.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 293[5:Rew:292.0,140.0] || -> equal(multiply(sk_c7,identity),sk_c1)**.
% 0.20/0.49 296[5:Rew:81.0,291.0] || equal(sk_c7,sk_c8)** -> .
% 0.20/0.49 298[0:Rew:116.0,121.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.49 299[5:Rew:298.0,293.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.49 300[5:Rew:299.0,292.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.20/0.49 301[5:Rew:299.0,296.0] || equal(sk_c8,sk_c1)** -> .
% 0.20/0.49 309[5:Rew:81.0,15.1,299.0,15.1] || -> equal(inverse(sk_c4),sk_c8)** equal(sk_c8,sk_c1).
% 0.20/0.49 310[5:MRR:309.1,301.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 318[5:Rew:81.0,14.1,299.0,14.1,299.0,14.0] || -> equal(multiply(sk_c4,sk_c8),sk_c1)** equal(sk_c8,sk_c1).
% 0.20/0.49 319[5:MRR:318.1,301.0] || -> equal(multiply(sk_c4,sk_c8),sk_c1)**.
% 0.20/0.49 329[3:Rew:132.0,107.2,132.0,107.0] || equal(multiply(sk_c1,u),inverse(sk_c8)) equal(u,sk_c7) equal(multiply(sk_c1,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.49 330[5:Rew:299.0,329.2,299.0,329.1,300.0,329.0] || equal(multiply(sk_c1,u),sk_c1) equal(u,sk_c1) equal(multiply(sk_c1,multiply(u,sk_c8)),sk_c1)** -> .
% 0.20/0.49 337[5:SpR:300.0,77.0] || -> equal(multiply(sk_c1,multiply(sk_c8,u)),u)**.
% 0.20/0.49 339[5:Rew:137.0,337.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.49 340[5:Rew:339.0,137.0] || -> equal(multiply(sk_c1,multiply(sk_c8,u)),u)**.
% 0.20/0.49 368[5:SpR:319.0,77.0] || -> equal(multiply(inverse(sk_c4),sk_c1),sk_c8)**.
% 0.20/0.49 370[5:Rew:58.0,368.0,310.0,368.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 372[5:Rew:370.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 376[5:Rew:370.0,298.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 382[5:Rew:372.0,340.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 393[5:Rew:376.0,330.2] || equal(multiply(sk_c1,u),sk_c1)** equal(u,sk_c1) equal(multiply(sk_c1,u),sk_c1)** -> .
% 0.20/0.49 411[5:Obv:393.0] || equal(u,sk_c1) equal(multiply(sk_c1,u),sk_c1)** -> .
% 0.20/0.49 412[5:Rew:382.0,411.1] || equal(u,sk_c1)* equal(u,sk_c1)* -> .
% 0.20/0.49 413[5:Obv:412.0] || equal(u,sk_c1)* -> .
% 0.20/0.49 414[5:UnC:413.0,300.0] || -> .
% 0.20/0.49 415[4:Spt:414.0,19.1,40.0] || equal(multiply(sk_c2,sk_c8),sk_c3)** -> .
% 0.20/0.49 416[4:Spt:414.0,19.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 417[4:Rew:298.0,140.0,416.0,140.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.49 418[4:Rew:417.0,416.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.20/0.49 420[4:Rew:132.0,415.0] || equal(multiply(sk_c1,sk_c8),sk_c3)** -> .
% 0.20/0.49 432[3:Rew:132.0,21.1] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c3)**.
% 0.20/0.49 433[4:MRR:432.1,420.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 446[3:Rew:132.0,20.1] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c3).
% 0.20/0.49 447[4:Rew:417.0,446.0] || -> equal(multiply(sk_c4,sk_c8),sk_c1)** equal(multiply(sk_c1,sk_c8),sk_c3).
% 0.20/0.49 448[4:MRR:447.1,420.0] || -> equal(multiply(sk_c4,sk_c8),sk_c1)**.
% 0.20/0.49 457[4:Rew:417.0,329.2,417.0,329.1,418.0,329.0] || equal(multiply(sk_c1,u),sk_c1) equal(u,sk_c1) equal(multiply(sk_c1,multiply(u,sk_c8)),sk_c1)** -> .
% 0.20/0.49 467[4:SpR:418.0,77.0] || -> equal(multiply(sk_c1,multiply(sk_c8,u)),u)**.
% 0.20/0.49 484[4:SpR:448.0,77.0] || -> equal(multiply(inverse(sk_c4),sk_c1),sk_c8)**.
% 0.20/0.49 486[4:Rew:58.0,484.0,433.0,484.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 488[4:Rew:486.0,298.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 489[4:Rew:486.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 499[4:Rew:488.0,457.2] || equal(multiply(sk_c1,u),sk_c1)** equal(u,sk_c1) equal(multiply(sk_c1,u),sk_c1)** -> .
% 0.20/0.49 511[4:Rew:489.0,467.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 535[4:Obv:499.0] || equal(u,sk_c1) equal(multiply(sk_c1,u),sk_c1)** -> .
% 0.20/0.49 536[4:Rew:511.0,535.1] || equal(u,sk_c1)* equal(u,sk_c1)* -> .
% 0.20/0.49 537[4:Obv:536.0] || equal(u,sk_c1)* -> .
% 0.20/0.49 538[4:UnC:537.0,417.0] || -> .
% 0.20/0.49 539[3:Spt:538.0,1.1,38.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.20/0.49 540[3:Spt:538.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 541[3:Rew:298.0,122.0,540.0,122.0] || -> equal(sk_c2,sk_c7)**.
% 0.20/0.49 543[3:Rew:541.0,57.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.20/0.49 548[3:MRR:3.1,539.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 551[3:MRR:2.0,539.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.49 554[3:Rew:541.0,107.2,541.0,107.0,540.0,107.0] || equal(multiply(sk_c7,u),sk_c7) equal(u,sk_c7) equal(multiply(sk_c7,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.49 579[3:SpR:551.0,77.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c8)**.
% 0.20/0.49 581[3:Rew:543.0,579.0,548.0,579.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 582[3:Rew:581.0,543.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.49 583[3:Rew:581.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 584[3:Rew:581.0,298.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 590[3:Rew:583.0,582.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 602[3:Rew:590.0,554.1] || equal(multiply(sk_c7,u),sk_c7) equal(u,sk_c8) equal(multiply(sk_c7,multiply(u,sk_c8)),sk_c7)** -> .
% 0.20/0.49 628[3:Rew:584.0,602.2,583.0,602.2,590.0,602.2,583.0,602.0,590.0,602.0] || equal(u,sk_c8)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.20/0.49 629[3:Obv:628.1] || equal(u,sk_c8)* -> .
% 0.20/0.49 630[3:UnC:629.0,548.0] || -> .
% 0.20/0.49 632[2:Spt:630.0,25.1,36.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.20/0.49 633[2:Spt:630.0,25.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 634[2:MRR:29.1,632.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 635[2:MRR:27.1,632.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 637[2:MRR:28.0,632.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.49 638[2:MRR:26.0,632.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.49 639[2:SpR:633.0,77.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.20/0.49 643[2:SpR:635.0,77.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.49 649[2:SpR:637.0,77.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.20/0.49 651[2:Rew:634.0,649.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 657[2:SpR:651.0,77.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.49 659[2:Rew:33.0,657.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 660[2:Rew:659.0,298.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 661[2:Rew:659.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 663[2:Rew:659.0,46.0] || equal(inverse(sk_c7),u) equal(u,sk_c7) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.20/0.49 670[2:Rew:661.0,639.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 671[2:Rew:670.0,643.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.49 672[2:Rew:671.0,638.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 673[2:Rew:672.0,633.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.49 679[2:Rew:672.0,660.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 695[2:Rew:679.0,663.2,672.0,663.2,672.0,663.1,673.0,663.0,672.0,663.0] || equal(sk_c8,u)* equal(u,sk_c8)* equal(u,sk_c8)* -> .
% 0.20/0.49 696[2:Obv:695.1] || equal(u,sk_c8)* -> .
% 0.20/0.49 697[2:UnC:696.0,635.0] || -> .
% 0.20/0.49 702[1:Spt:697.0,31.1,31.2,31.3,31.4,31.6,31.8,31.9,31.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c8),x)*+ equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,x),sk_c7)** -> .
% 0.20/0.49 703[1:EqR:702.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.20/0.49 705[2:Spt:1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.20/0.49 708[2:Rew:705.0,703.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(sk_c7,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.20/0.49 709[2:Obv:708.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.20/0.49 712[2:SpR:705.0,77.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.20/0.49 714[3:Spt:29.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 715[3:SpR:714.0,77.0] || -> equal(multiply(sk_c6,multiply(sk_c5,u)),u)**.
% 0.20/0.49 717[4:Spt:27.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.49 718[4:SpR:717.0,77.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.49 720[5:Spt:30.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 721[5:SpR:720.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.20/0.49 727[6:Spt:28.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.49 729[6:SpR:727.0,77.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.20/0.49 731[6:Rew:714.0,729.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 732[7:Spt:26.1] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.49 738[6:SpR:731.0,77.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.49 740[6:Rew:33.0,738.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 741[6:Rew:740.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.49 742[6:Rew:740.0,298.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 748[6:Rew:741.0,712.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 752[6:Rew:742.0,709.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8)** equal(multiply(u,sk_c8),sk_c7)** equal(w,sk_c8) equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.20/0.49 753[6:Rew:748.0,718.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.49 754[7:Rew:753.0,732.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 755[7:Rew:754.0,705.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.49 760[7:Rew:754.0,742.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 775[7:Rew:760.0,752.5,748.0,752.5,754.0,752.5,760.0,752.3,754.0,752.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(w,sk_c8) equal(v,sk_c8) -> .
% 0.20/0.49 776[7:Con:775.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.49 813[7:SpL:755.0,776.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.49 815[7:Obv:813.1] || -> .
% 0.20/0.49 816[7:Spt:815.0,26.1,732.0] || equal(multiply(sk_c4,sk_c8),sk_c7)** -> .
% 0.20/0.49 817[7:Spt:815.0,26.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 819[7:Rew:753.0,816.0] || equal(sk_c7,sk_c8)** -> .
% 0.20/0.49 830[6:Rew:753.0,2.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c8).
% 0.20/0.49 831[7:MRR:830.1,819.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 833[6:Rew:742.0,8.1,753.0,8.0] || -> equal(sk_c7,sk_c8)** equal(sk_c8,sk_c1).
% 0.20/0.49 834[7:MRR:833.0,819.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.49 836[7:Rew:834.0,705.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.49 839[7:Rew:834.0,819.0] || equal(sk_c7,sk_c1)** -> .
% 0.20/0.49 841[7:Rew:834.0,831.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.49 842[7:Rew:836.0,841.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.49 843[7:MRR:842.0,839.0] || -> .
% 0.20/0.49 852[6:Spt:843.0,28.1,727.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.49 853[6:Spt:843.0,28.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 854[6:MRR:4.1,852.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 855[6:MRR:10.0,852.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 856[6:MRR:16.0,852.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.49 857[6:MRR:22.0,852.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 869[6:SpR:855.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.49 871[6:Rew:854.0,869.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.49 875[6:SpR:856.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.20/0.49 876[6:SpR:856.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.20/0.49 878[6:Rew:705.0,876.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.20/0.49 880[6:SpR:857.0,77.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.20/0.49 882[6:Rew:856.0,880.0,853.0,880.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 883[6:Rew:882.0,705.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.49 888[6:Rew:882.0,852.0] || equal(multiply(sk_c5,sk_c6),sk_c8)** -> .
% 0.20/0.49 889[6:Rew:882.0,712.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.20/0.49 890[6:Rew:882.0,721.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(sk_c8,u))**.
% 0.20/0.49 892[6:Rew:882.0,875.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c8,u))**.
% 0.20/0.49 896[6:Rew:882.0,871.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.49 897[6:Rew:882.0,878.0] || -> equal(multiply(sk_c8,sk_c8),sk_c3)**.
% 0.20/0.49 898[6:Rew:896.0,897.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 902[6:Rew:889.0,892.0,898.0,892.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 908[6:Rew:902.0,890.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 910[6:Rew:908.0,715.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.49 911[6:Rew:910.0,888.0] || equal(sk_c6,sk_c8)** -> .
% 0.20/0.49 931[0:SpR:33.0,298.0] || -> equal(inverse(identity),identity)**.
% 0.20/0.49 933[6:SpR:853.0,33.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.20/0.49 934[4:SpR:717.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.49 935[3:SpR:714.0,33.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.20/0.49 939[6:Rew:902.0,933.0] || -> equal(identity,sk_c2)**.
% 0.20/0.49 943[6:Rew:939.0,931.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.20/0.49 944[6:Rew:853.0,943.0] || -> equal(sk_c2,sk_c8)**.
% 0.20/0.49 947[6:Rew:944.0,939.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 951[6:Rew:908.0,935.0,947.0,935.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.49 952[6:Rew:951.0,714.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.20/0.49 954[6:Rew:883.0,952.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 955[6:MRR:954.0,911.0] || -> .
% 0.20/0.49 982[5:Spt:955.0,30.1,720.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.49 983[5:Spt:955.0,30.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 985[5:MRR:6.1,982.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 987[5:MRR:12.0,982.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 988[5:MRR:18.0,982.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.49 989[5:MRR:24.0,982.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 1004[4:SpR:934.0,77.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.20/0.49 1006[4:Rew:705.0,1004.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.20/0.49 1007[4:Rew:298.0,1006.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.49 1009[4:Rew:1007.0,934.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.20/0.49 1021[5:SpR:987.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.49 1023[5:Rew:985.0,1021.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.49 1027[5:SpR:988.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.20/0.49 1029[5:Rew:705.0,1027.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.20/0.49 1031[5:SpR:989.0,77.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.20/0.49 1033[5:Rew:988.0,1031.0,983.0,1031.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 1037[5:Rew:1033.0,987.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.49 1043[5:Rew:1033.0,709.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.20/0.49 1044[5:Rew:1033.0,1009.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.20/0.49 1048[5:Rew:1033.0,1023.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.49 1049[5:Rew:1033.0,1029.0] || -> equal(multiply(sk_c8,sk_c8),sk_c3)**.
% 0.20/0.49 1050[5:Rew:1044.0,1048.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 1053[5:Rew:1050.0,298.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 1054[5:Rew:1050.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 1057[5:Rew:1053.0,989.0] || -> equal(sk_c2,sk_c3)**.
% 0.20/0.49 1058[5:Rew:1053.0,1049.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 1059[5:Rew:1053.0,1037.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.49 1060[5:Rew:1057.0,983.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 1066[5:Rew:1059.0,1033.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.49 1071[5:Rew:1059.0,1053.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.49 1072[5:Rew:1059.0,1058.0] || -> equal(sk_c3,sk_c1)**.
% 0.20/0.49 1074[5:Rew:1072.0,1060.0,1059.0,1060.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.49 1075[5:Rew:1059.0,1054.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 1086[5:Rew:1071.0,1043.5,1075.0,1043.5,1059.0,1043.5,1066.0,1043.5,1071.0,1043.4,1066.0,1043.4,1059.0,1043.4,1071.0,1043.3,1059.0,1043.3,1059.0,1043.2,1059.0,1043.1,1059.0,1043.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(w,sk_c1) equal(v,sk_c1) -> .
% 0.20/0.49 1087[5:Con:1086.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.49 1160[5:SpL:1074.0,1087.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.49 1162[5:Obv:1160.1] || -> .
% 0.20/0.49 1163[4:Spt:1162.0,27.0,717.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.49 1164[4:Spt:1162.0,27.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.49 1165[4:MRR:3.0,1163.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 1166[4:MRR:9.0,1163.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.49 1167[4:MRR:15.0,1163.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.49 1168[4:MRR:21.0,1163.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.49 1184[4:SpR:1166.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.49 1186[4:Rew:1165.0,1184.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.49 1187[4:SpR:1167.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.20/0.49 1188[4:SpR:1167.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.20/0.49 1190[4:Rew:705.0,1188.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.20/0.49 1192[4:SpR:1168.0,77.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.20/0.49 1194[4:Rew:1167.0,1192.0,1164.0,1192.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 1198[4:Rew:1194.0,712.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.20/0.49 1201[4:Rew:1194.0,709.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.20/0.49 1202[4:Rew:1194.0,1186.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.49 1204[4:Rew:1194.0,1187.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c8,u))**.
% 0.20/0.49 1205[4:Rew:1194.0,1190.0] || -> equal(multiply(sk_c8,sk_c8),sk_c3)**.
% 0.20/0.49 1206[4:Rew:1202.0,1205.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.49 1210[4:Rew:1198.0,1204.0,1206.0,1204.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.50 1216[4:Rew:1210.0,1201.5,1194.0,1201.5,1194.0,1201.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.20/0.50 1217[4:Con:1216.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.50 1237[4:SpR:1210.0,298.0] || -> equal(identity,sk_c8)**.
% 0.20/0.50 1242[4:Rew:1237.0,298.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.50 1243[4:Rew:1237.0,33.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.50 1244[4:Rew:1242.0,1217.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 1252[4:SpR:1165.0,1243.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.20/0.50 1257[4:Rew:1210.0,1252.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.50 1258[4:Rew:1257.0,1165.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 1268[4:Rew:1257.0,1244.0] || equal(inverse(u),sk_c1)** equal(u,sk_c8) -> .
% 0.20/0.50 1274[4:Rew:1257.0,1268.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.50 1328[4:SpL:1258.0,1274.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.50 1329[4:Obv:1328.1] || -> .
% 0.20/0.50 1330[3:Spt:1329.0,29.0,714.0] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.20/0.50 1331[3:Spt:1329.0,29.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.50 1332[3:MRR:5.0,1330.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.50 1333[3:MRR:11.0,1330.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 1334[3:MRR:17.0,1330.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.50 1335[3:MRR:23.0,1330.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.50 1346[3:SpR:1333.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.50 1348[3:Rew:1332.0,1346.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 1349[3:SpR:1334.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1350[3:SpR:1334.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.20/0.50 1352[3:Rew:705.0,1350.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.20/0.50 1354[3:SpR:1335.0,77.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.20/0.50 1356[3:Rew:1334.0,1354.0,1331.0,1354.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.50 1360[3:Rew:1356.0,712.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.20/0.50 1363[3:Rew:1356.0,709.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.20/0.50 1364[3:Rew:1356.0,1348.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.50 1366[3:Rew:1356.0,1349.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),multiply(sk_c8,u))**.
% 0.20/0.50 1367[3:Rew:1356.0,1352.0] || -> equal(multiply(sk_c8,sk_c8),sk_c3)**.
% 0.20/0.50 1368[3:Rew:1364.0,1367.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.50 1372[3:Rew:1360.0,1366.0,1368.0,1366.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.50 1378[3:Rew:1372.0,1363.5,1356.0,1363.5,1356.0,1363.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** -> .
% 0.20/0.50 1379[3:Con:1378.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.50 1398[3:SpR:1372.0,298.0] || -> equal(identity,sk_c8)**.
% 0.20/0.50 1402[3:Rew:1398.0,298.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.50 1403[3:Rew:1398.0,33.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.50 1404[3:Rew:1402.0,1379.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 1415[3:SpR:1332.0,1403.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.20/0.50 1420[3:Rew:1372.0,1415.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.50 1421[3:Rew:1420.0,1332.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 1429[3:Rew:1420.0,1404.0] || equal(inverse(u),sk_c1)** equal(u,sk_c8) -> .
% 0.20/0.50 1434[3:Rew:1420.0,1429.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.50 1494[3:SpL:1421.0,1434.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.50 1496[3:Obv:1494.1] || -> .
% 0.20/0.50 1497[2:Spt:1496.0,1.0,705.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.20/0.50 1498[2:Spt:1496.0,1.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.50 1499[2:MRR:25.0,1497.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.50 1500[2:MRR:7.0,1497.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 1501[2:MRR:13.0,1497.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.20/0.50 1502[2:MRR:19.0,1497.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.20/0.50 1511[2:SpR:1500.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.50 1513[2:Rew:1498.0,1511.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 1515[2:SpR:1501.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.20/0.50 1518[2:SpR:1502.0,77.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.20/0.50 1520[2:Rew:1501.0,1518.0,1499.0,1518.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.50 1521[2:Rew:1520.0,1497.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.20/0.50 1522[2:Rew:1520.0,1500.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.50 1524[2:Rew:1520.0,1513.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.50 1527[2:Rew:1520.0,1515.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c3)**.
% 0.20/0.50 1528[2:Rew:33.0,1527.0] || -> equal(identity,sk_c3)**.
% 0.20/0.50 1530[2:Rew:1528.0,298.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.20/0.50 1532[2:Rew:1528.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.20/0.50 1549[2:SpR:1524.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.20/0.50 1551[2:Rew:1532.0,1549.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.50 1556[2:Rew:1551.0,1530.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.50 1563[2:Rew:1556.0,1522.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.50 1565[2:Rew:1563.0,1498.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.50 1567[2:Rew:1563.0,1521.0] || equal(inverse(sk_c1),sk_c1)** -> .
% 0.20/0.50 1577[2:Rew:1565.0,1567.0] || equal(sk_c1,sk_c1)* -> .
% 0.20/0.50 1578[2:Obv:1577.0] || -> .
% 0.20/0.50 % SZS output end Refutation
% 0.20/0.50 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
% 0.20/0.50
%------------------------------------------------------------------------------