TSTP Solution File: GRP257-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP257-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:46:33 EDT 2022
% Result : Unsatisfiable 0.36s 0.54s
% Output : Refutation 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP257-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 19:39:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.36/0.54
% 0.36/0.54 SPASS V 3.9
% 0.36/0.54 SPASS beiseite: Proof found.
% 0.36/0.54 % SZS status Theorem
% 0.36/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/0.54 SPASS derived 1667 clauses, backtracked 400 clauses, performed 11 splits and kept 806 clauses.
% 0.36/0.54 SPASS allocated 64437 KBytes.
% 0.36/0.54 SPASS spent 0:00:00.20 on the problem.
% 0.36/0.54 0:00:00.03 for the input.
% 0.36/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.54 0:00:00.01 for inferences.
% 0.36/0.54 0:00:00.00 for the backtracking.
% 0.36/0.54 0:00:00.13 for the reduction.
% 0.36/0.54
% 0.36/0.54
% 0.36/0.54 Here is a proof with depth 7, length 350 :
% 0.36/0.54 % SZS output start Refutation
% 0.36/0.54 2[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.36/0.54 5[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.36/0.54 6[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.36/0.54 7[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.36/0.54 8[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.36/0.54 9[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c10).
% 0.36/0.54 10[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.36/0.54 11[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c10).
% 0.36/0.54 12[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.36/0.54 13[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.36/0.54 14[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c1),sk_c10).
% 0.36/0.54 15[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.36/0.54 16[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.36/0.54 19[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.36/0.54 20[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.36/0.54 21[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.36/0.54 22[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.36/0.54 23[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c9)**.
% 0.36/0.54 24[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.36/0.54 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.36/0.54 26[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.36/0.54 27[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.36/0.54 28[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.36/0.54 29[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.36/0.54 30[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c3),sk_c8)**.
% 0.36/0.54 31[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.36/0.54 32[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.36/0.54 33[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.36/0.54 34[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.36/0.54 35[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.36/0.54 37[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.36/0.54 38[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.36/0.54 39[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.36/0.54 40[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.36/0.54 41[0:Inp] || -> equal(multiply(sk_c6,sk_c8),sk_c7) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.36/0.54 42[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.36/0.54 43[0:Inp] || equal(multiply(u,sk_c10),sk_c9)** equal(inverse(u),sk_c10) equal(multiply(v,sk_c9),sk_c8)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(inverse(x),sk_c10) equal(multiply(y,sk_c8),sk_c9)** equal(inverse(y),sk_c8) equal(multiply(sk_c8,z),sk_c9)** equal(multiply(x1,sk_c8),z)* equal(inverse(x1),sk_c8) -> .
% 0.36/0.54 44[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.36/0.54 45[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.36/0.54 46[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.36/0.54 47[0:Con:43.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(inverse(y),sk_c10) equal(multiply(u,sk_c8),z)*+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(y,sk_c10),sk_c9)** equal(multiply(sk_c8,z),sk_c9)** -> .
% 0.36/0.54 48[1:Spt:47.2,47.7] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.36/0.54 49[2:Spt:30.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.36/0.54 55[3:Spt:37.1] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.36/0.54 57[3:SpL:55.0,48.1] || equal(inverse(sk_c3),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.36/0.54 58[3:Obv:57.1] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.36/0.54 59[3:Rew:49.0,58.0] || equal(sk_c8,sk_c8)* -> .
% 0.36/0.54 60[3:Obv:59.0] || -> .
% 0.36/0.54 61[3:Spt:60.0,37.1,55.0] || equal(multiply(sk_c3,sk_c9),sk_c8)** -> .
% 0.36/0.54 62[3:Spt:60.0,37.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.36/0.54 63[3:MRR:42.1,61.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.36/0.54 64[3:MRR:39.1,61.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.36/0.54 65[3:MRR:41.1,61.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.36/0.54 66[3:MRR:40.1,61.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.36/0.54 67[3:MRR:38.1,61.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.36/0.54 77[1:SpL:44.0,48.1] || equal(inverse(identity),sk_c8)** equal(sk_c8,sk_c9) -> .
% 0.36/0.54 79[2:SpR:49.0,45.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.36/0.54 83[3:SpR:63.0,45.0] || -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.36/0.54 84[3:SpR:64.0,45.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.36/0.54 88[3:SpR:65.0,46.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.36/0.54 89[3:SpR:67.0,46.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.36/0.54 93[0:SpR:45.0,46.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.36/0.54 95[0:Rew:44.0,93.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.36/0.54 125[0:SpR:95.0,95.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.36/0.54 127[3:SpR:65.0,95.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.36/0.54 129[3:SpR:66.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c9),sk_c7)**.
% 0.36/0.54 130[2:SpR:79.0,95.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.36/0.54 131[3:SpR:83.0,95.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c6)**.
% 0.36/0.54 132[3:SpR:84.0,95.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.36/0.54 136[0:SpR:45.0,95.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.36/0.54 137[0:SpR:46.0,95.0] || -> equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(v,w))),w)**.
% 0.36/0.54 149[3:Rew:66.0,127.0,63.0,127.0] || -> equal(sk_c8,sk_c9)**.
% 0.36/0.54 153[3:Rew:149.0,64.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.36/0.54 160[3:Rew:149.0,84.0] || -> equal(multiply(sk_c9,sk_c5),identity)**.
% 0.36/0.54 162[3:Rew:149.0,77.0] || equal(inverse(identity),sk_c9)** equal(sk_c8,sk_c9) -> .
% 0.36/0.54 164[3:Rew:149.0,88.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c7,u))**.
% 0.36/0.54 165[3:Rew:149.0,89.0] || -> equal(multiply(sk_c5,multiply(sk_c9,u)),multiply(sk_c9,u))**.
% 0.36/0.54 171[3:Rew:149.0,129.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.36/0.54 172[3:Rew:45.0,171.0] || -> equal(identity,sk_c7)**.
% 0.36/0.54 173[3:Rew:172.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.36/0.54 180[3:Rew:172.0,160.0] || -> equal(multiply(sk_c9,sk_c5),sk_c7)**.
% 0.36/0.54 181[3:Rew:149.0,130.0,172.0,130.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c3)**.
% 0.36/0.54 182[3:Rew:181.0,131.0,149.0,131.0,172.0,131.0] || -> equal(sk_c3,sk_c6)**.
% 0.36/0.54 185[3:Rew:182.0,181.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c6)**.
% 0.36/0.54 186[3:Rew:149.0,132.0,172.0,132.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c5)**.
% 0.36/0.54 201[3:Rew:186.0,185.0] || -> equal(sk_c6,sk_c5)**.
% 0.36/0.54 221[3:Rew:149.0,162.1,172.0,162.0] || equal(inverse(sk_c7),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.36/0.54 222[3:Obv:221.1] || equal(inverse(sk_c7),sk_c9)** -> .
% 0.36/0.54 223[3:Rew:201.0,164.0,173.0,164.0] || -> equal(multiply(sk_c5,multiply(sk_c9,u)),u)**.
% 0.36/0.54 224[3:Rew:223.0,165.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.36/0.54 227[3:Rew:224.0,180.0] || -> equal(sk_c7,sk_c5)**.
% 0.36/0.54 232[3:Rew:227.0,222.0] || equal(inverse(sk_c5),sk_c9)** -> .
% 0.36/0.54 237[3:Rew:153.0,232.0] || equal(sk_c9,sk_c9)* -> .
% 0.36/0.54 238[3:Obv:237.0] || -> .
% 0.36/0.54 246[2:Spt:238.0,30.1,49.0] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.36/0.54 247[2:Spt:238.0,30.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.36/0.54 248[0:Rew:125.0,136.0] || -> equal(multiply(u,identity),u)**.
% 0.36/0.54 249[2:MRR:35.1,246.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.36/0.54 251[2:MRR:34.0,246.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.36/0.54 252[2:MRR:33.0,246.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.36/0.54 254[2:MRR:29.0,246.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.36/0.54 262[2:SpR:251.0,95.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.36/0.54 264[2:Rew:249.0,262.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.36/0.54 265[2:Rew:252.0,264.0] || -> equal(sk_c8,sk_c9)**.
% 0.36/0.54 266[2:Rew:265.0,249.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.36/0.54 269[2:Rew:265.0,251.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.36/0.54 270[2:Rew:265.0,77.0] || equal(inverse(identity),sk_c9)** equal(sk_c8,sk_c9) -> .
% 0.36/0.54 271[2:Rew:265.0,252.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.36/0.54 279[2:Rew:265.0,270.1] || equal(inverse(identity),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.36/0.54 280[2:Obv:279.1] || equal(inverse(identity),sk_c9)** -> .
% 0.36/0.54 290[2:SpR:254.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.36/0.54 292[2:Rew:247.0,290.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.36/0.54 298[2:SpR:271.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.36/0.54 300[2:Rew:45.0,298.0] || -> equal(identity,sk_c7)**.
% 0.36/0.54 302[2:Rew:300.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.36/0.54 304[2:Rew:300.0,280.0] || equal(inverse(sk_c7),sk_c9)** -> .
% 0.36/0.54 305[2:Rew:300.0,248.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.36/0.54 315[2:SpR:292.0,95.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.36/0.54 317[2:Rew:302.0,315.0] || -> equal(sk_c7,sk_c9)**.
% 0.36/0.54 318[2:Rew:317.0,269.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.36/0.54 321[2:Rew:317.0,304.0] || equal(inverse(sk_c9),sk_c9)** -> .
% 0.36/0.54 323[2:Rew:317.0,305.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.36/0.54 332[2:Rew:323.0,318.0] || -> equal(sk_c6,sk_c9)**.
% 0.36/0.54 336[2:Rew:332.0,266.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.36/0.54 338[2:MRR:336.0,321.0] || -> .
% 0.36/0.54 345[1:Spt:338.0,47.0,47.1,47.3,47.4,47.5,47.6,47.8,47.9,47.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c8),y)*+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,y),sk_c9)** -> .
% 0.36/0.54 346[1:EqR:345.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c9)** -> .
% 0.36/0.54 348[2:Spt:9.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.36/0.54 349[2:SpR:348.0,95.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.36/0.54 351[3:Spt:23.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.36/0.54 352[3:SpR:351.0,95.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.36/0.54 354[4:Spt:35.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.36/0.54 355[4:SpR:354.0,95.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.36/0.54 357[5:Spt:16.1] || -> equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.36/0.54 359[5:SpR:357.0,95.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c9)**.
% 0.36/0.54 361[5:Rew:351.0,359.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.36/0.54 362[6:Spt:2.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.36/0.54 363[6:SpR:362.0,46.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.36/0.54 371[7:Spt:42.1] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.36/0.54 373[7:SpR:371.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c9)**.
% 0.36/0.54 375[7:Rew:354.0,373.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.36/0.54 377[5:SpR:361.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.36/0.54 380[5:Rew:45.0,377.0] || -> equal(identity,sk_c8)**.
% 0.36/0.54 381[5:Rew:380.0,44.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.36/0.54 382[5:Rew:380.0,248.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.36/0.54 385[5:Rew:380.0,45.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.36/0.54 387[7:Rew:381.0,375.0] || -> equal(sk_c8,sk_c9)**.
% 0.36/0.54 391[5:Rew:381.0,355.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.36/0.54 392[5:Rew:381.0,346.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.36/0.54 394[7:Rew:387.0,357.0] || -> equal(multiply(sk_c2,sk_c9),sk_c9)**.
% 0.36/0.54 399[7:Rew:387.0,382.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.36/0.54 400[7:Rew:399.0,394.0] || -> equal(sk_c2,sk_c9)**.
% 0.36/0.54 401[7:Rew:400.0,351.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.36/0.54 410[5:Con:392.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.36/0.54 411[7:Rew:399.0,410.4,387.0,410.4,399.0,410.3,387.0,410.3,387.0,410.0] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(u,sk_c9) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.36/0.54 412[7:Con:411.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c9)**+ -> .
% 0.36/0.54 615[6:SpR:362.0,137.0] || -> equal(multiply(inverse(sk_c9),multiply(sk_c1,multiply(sk_c10,u))),u)**.
% 0.36/0.54 748[7:SpL:362.0,412.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.36/0.54 751[7:Obv:748.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) -> .
% 0.36/0.54 752[7:Rew:348.0,751.1] || equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.36/0.54 753[7:Obv:752.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.36/0.54 810[7:SpL:401.0,753.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.36/0.54 815[7:Obv:810.1] || -> .
% 0.36/0.54 816[7:Spt:815.0,42.1,371.0] || equal(multiply(sk_c3,sk_c9),sk_c8)** -> .
% 0.36/0.54 817[7:Spt:815.0,42.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.36/0.54 819[7:Rew:391.0,816.0] || equal(sk_c8,sk_c9)** -> .
% 0.36/0.54 826[5:Rew:391.0,41.1,382.0,41.0] || -> equal(sk_c6,sk_c7)** equal(sk_c8,sk_c9).
% 0.36/0.54 827[7:MRR:826.1,819.0] || -> equal(sk_c6,sk_c7)**.
% 0.36/0.54 828[7:Rew:827.0,817.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.36/0.54 829[5:Rew:391.0,40.1,381.0,40.0] || -> equal(sk_c7,sk_c9)** equal(sk_c8,sk_c9).
% 0.36/0.54 830[7:MRR:829.1,819.0] || -> equal(sk_c7,sk_c9)**.
% 0.36/0.54 832[7:Rew:830.0,828.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.36/0.54 838[7:Rew:381.0,615.0,832.0,615.0,363.0,615.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.36/0.54 839[7:Rew:838.0,352.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.36/0.54 842[7:Rew:839.0,357.0] || -> equal(sk_c8,sk_c9)**.
% 0.36/0.54 843[7:MRR:842.0,819.0] || -> .
% 0.36/0.54 861[6:Spt:843.0,2.1,362.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.36/0.54 862[6:Spt:843.0,2.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.36/0.54 867[6:MRR:7.1,861.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.36/0.54 874[5:Rew:382.0,6.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.36/0.54 875[6:MRR:874.1,861.0] || -> equal(sk_c6,sk_c7)**.
% 0.36/0.54 876[6:Rew:875.0,867.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.36/0.54 877[5:Rew:381.0,5.0] || -> equal(sk_c7,sk_c9) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.36/0.54 878[6:MRR:877.1,861.0] || -> equal(sk_c7,sk_c9)**.
% 0.36/0.54 880[6:Rew:878.0,876.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.36/0.54 899[6:SpR:880.0,95.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),u)**.
% 0.36/0.54 901[6:Rew:381.0,899.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.36/0.54 902[6:Rew:901.0,352.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.36/0.54 904[6:Rew:902.0,357.0] || -> equal(sk_c8,sk_c9)**.
% 0.36/0.54 909[6:Rew:904.0,382.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.36/0.54 911[6:Rew:904.0,385.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.36/0.54 945[6:SpR:909.0,349.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.36/0.54 960[6:SpR:945.0,95.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.36/0.54 962[6:Rew:909.0,960.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.36/0.54 974[6:SpR:962.0,911.0] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.36/0.54 975[6:MRR:974.0,861.0] || -> .
% 0.36/0.54 979[5:Spt:975.0,16.1,357.0] || equal(multiply(sk_c2,sk_c9),sk_c8)** -> .
% 0.36/0.54 980[5:Spt:975.0,16.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.36/0.54 981[5:MRR:21.1,979.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.36/0.54 984[5:MRR:20.1,979.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.36/0.54 985[5:MRR:19.1,979.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.36/0.54 987[5:MRR:15.1,979.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.36/0.54 999[5:SpR:984.0,95.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.36/0.54 1001[5:Rew:981.0,999.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.36/0.54 1002[5:Rew:985.0,1001.0] || -> equal(sk_c8,sk_c9)**.
% 0.36/0.54 1007[5:Rew:1002.0,979.0] || equal(multiply(sk_c2,sk_c9),sk_c9)** -> .
% 0.36/0.54 1009[5:Rew:1002.0,985.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.36/0.54 1034[5:SpR:987.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.36/0.54 1036[5:Rew:980.0,1034.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.36/0.54 1042[5:SpR:1009.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.36/0.54 1044[5:Rew:45.0,1042.0] || -> equal(identity,sk_c7)**.
% 0.36/0.54 1045[5:Rew:1044.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.36/0.54 1046[5:Rew:1044.0,248.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.36/0.54 1047[5:Rew:1044.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.36/0.54 1061[5:SpR:1036.0,95.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.36/0.54 1063[5:Rew:1047.0,1061.0] || -> equal(sk_c7,sk_c9)**.
% 0.36/0.54 1066[5:Rew:1063.0,1045.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.36/0.54 1067[5:Rew:1063.0,1046.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.36/0.54 1068[5:Rew:1063.0,1047.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.36/0.54 1083[5:Rew:1067.0,1007.0] || equal(sk_c2,sk_c9)** -> .
% 0.36/0.54 1126[5:SpR:351.0,1068.0] || -> equal(multiply(sk_c9,sk_c2),sk_c9)**.
% 0.36/0.54 1129[5:Rew:1066.0,1126.0] || -> equal(sk_c2,sk_c9)**.
% 0.36/0.54 1130[5:MRR:1129.0,1083.0] || -> .
% 0.36/0.54 1137[4:Spt:1130.0,35.1,354.0] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.36/0.54 1138[4:Spt:1130.0,35.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.36/0.54 1139[4:MRR:32.1,1137.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.36/0.54 1140[4:MRR:30.1,1137.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.36/0.54 1141[4:MRR:34.0,1137.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.36/0.54 1142[4:MRR:33.0,1137.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.36/0.54 1143[4:MRR:31.0,1137.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.36/0.54 1144[4:MRR:29.0,1137.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.36/0.54 1152[4:SpR:1141.0,95.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.36/0.54 1154[4:Rew:1138.0,1152.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.36/0.54 1155[4:Rew:1142.0,1154.0] || -> equal(sk_c8,sk_c9)**.
% 0.36/0.54 1157[4:Rew:1155.0,1139.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.36/0.54 1160[4:Rew:1155.0,1142.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.36/0.54 1161[4:Rew:1155.0,1143.0] || -> equal(multiply(sk_c5,sk_c9),sk_c9)**.
% 0.36/0.54 1164[4:Rew:1155.0,346.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c9)** -> .
% 0.36/0.54 1169[4:Rew:1155.0,1164.7,1155.0,1164.5,1155.0,1164.4,1155.0,1164.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c9),sk_c9)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c9)** -> .
% 0.36/0.54 1170[4:Con:1169.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c9)** -> .
% 0.36/0.54 1183[4:SpR:1144.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.36/0.54 1185[4:Rew:1140.0,1183.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.36/0.54 1191[4:SpR:1160.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.36/0.54 1193[4:Rew:45.0,1191.0] || -> equal(identity,sk_c7)**.
% 0.36/0.54 1194[4:Rew:1193.0,248.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.36/0.54 1195[4:Rew:1193.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.36/0.54 1198[4:Rew:1193.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.36/0.54 1207[4:SpR:1185.0,95.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.36/0.54 1209[4:Rew:1198.0,1207.0] || -> equal(sk_c7,sk_c9)**.
% 0.36/0.54 1212[4:Rew:1209.0,1194.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.36/0.54 1213[4:Rew:1209.0,1195.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.36/0.54 1216[4:Rew:1209.0,1198.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.36/0.54 1217[4:Rew:1212.0,1161.0] || -> equal(sk_c5,sk_c9)**.
% 0.36/0.54 1220[4:Rew:1212.0,1170.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.36/0.54 1222[4:Rew:1217.0,1157.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.36/0.54 1235[4:Rew:1213.0,1220.5,1212.0,1220.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** equal(u,sk_c9) -> .
% 0.36/0.54 1236[4:Con:1235.0] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c9)**+ -> .
% 0.36/0.54 1256[4:SpR:1212.0,349.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.36/0.54 1263[4:SpR:1256.0,95.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.36/0.54 1265[4:Rew:1212.0,1263.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.36/0.54 1286[4:SpR:1265.0,1216.0] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.36/0.54 1588[4:SpL:1286.0,1236.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.36/0.54 1591[4:Obv:1588.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) -> .
% 0.36/0.54 1592[4:Rew:348.0,1591.1] || equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.36/0.54 1593[4:Obv:1592.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.36/0.54 1650[4:SpL:1222.0,1593.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.36/0.54 1655[4:Obv:1650.1] || -> .
% 0.36/0.54 1656[3:Spt:1655.0,23.1,351.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.36/0.54 1657[3:Spt:1655.0,23.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.36/0.54 1658[3:MRR:28.1,1656.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.36/0.54 1659[3:MRR:25.1,1656.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.36/0.54 1661[3:MRR:27.0,1656.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.36/0.54 1662[3:MRR:26.0,1656.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.36/0.54 1663[3:MRR:24.0,1656.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.36/0.54 1664[3:MRR:22.0,1656.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.36/0.54 1680[3:SpR:1661.0,95.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.36/0.54 1682[3:Rew:1658.0,1680.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.36/0.54 1683[3:Rew:1662.0,1682.0] || -> equal(sk_c8,sk_c9)**.
% 0.36/0.54 1685[3:Rew:1683.0,1659.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.36/0.54 1687[3:Rew:1683.0,1662.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.36/0.54 1688[3:Rew:1683.0,1663.0] || -> equal(multiply(sk_c5,sk_c9),sk_c9)**.
% 0.36/0.54 1691[3:Rew:1683.0,346.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c9)** -> .
% 0.36/0.54 1696[3:Rew:1683.0,1691.7,1683.0,1691.5,1683.0,1691.4,1683.0,1691.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c9),sk_c9)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c9)** -> .
% 0.36/0.54 1697[3:Con:1696.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c9)** -> .
% 0.36/0.54 1710[3:SpR:1664.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.36/0.54 1712[3:Rew:1657.0,1710.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.36/0.54 1718[3:SpR:1687.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.36/0.54 1720[3:Rew:45.0,1718.0] || -> equal(identity,sk_c7)**.
% 0.36/0.54 1721[3:Rew:1720.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.36/0.54 1722[3:Rew:1720.0,248.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.36/0.54 1723[3:Rew:1720.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.36/0.54 1734[3:SpR:1712.0,95.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.36/0.54 1736[3:Rew:1723.0,1734.0] || -> equal(sk_c7,sk_c9)**.
% 0.36/0.54 1739[3:Rew:1736.0,1721.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.36/0.54 1740[3:Rew:1736.0,1722.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.36/0.54 1741[3:Rew:1736.0,1723.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.36/0.54 1749[3:Rew:1739.0,1697.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.36/0.54 1752[3:Rew:1740.0,1688.0] || -> equal(sk_c5,sk_c9)**.
% 0.36/0.54 1754[3:Rew:1752.0,1685.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.36/0.54 1762[3:Con:1749.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.38/0.55 1763[3:Rew:1740.0,1762.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c9)**+ -> .
% 0.38/0.55 1784[3:SpR:1740.0,349.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.38/0.55 1791[3:SpR:1784.0,95.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.38/0.55 1793[3:Rew:1740.0,1791.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.38/0.55 1807[3:SpR:1793.0,1741.0] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.38/0.55 2106[3:SpL:1807.0,1763.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.38/0.55 2109[3:Obv:2106.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) -> .
% 0.38/0.55 2110[3:Rew:348.0,2109.1] || equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.38/0.55 2111[3:Obv:2110.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.38/0.55 2168[3:SpL:1754.0,2111.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.38/0.55 2173[3:Obv:2168.1] || -> .
% 0.38/0.55 2174[2:Spt:2173.0,9.1,348.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.38/0.55 2175[2:Spt:2173.0,9.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.38/0.55 2176[2:MRR:14.1,2174.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.38/0.55 2177[2:MRR:11.1,2174.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.38/0.55 2179[2:MRR:13.0,2174.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.38/0.55 2180[2:MRR:12.0,2174.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.38/0.55 2181[2:MRR:10.0,2174.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.38/0.55 2182[2:MRR:8.0,2174.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.38/0.55 2198[2:SpR:2179.0,95.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.38/0.55 2200[2:Rew:2176.0,2198.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.38/0.55 2201[2:Rew:2180.0,2200.0] || -> equal(sk_c8,sk_c9)**.
% 0.38/0.55 2203[2:Rew:2201.0,2177.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.38/0.55 2205[2:Rew:2201.0,2180.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.38/0.55 2206[2:Rew:2201.0,2181.0] || -> equal(multiply(sk_c5,sk_c9),sk_c9)**.
% 0.38/0.55 2209[2:Rew:2201.0,346.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c9)** -> .
% 0.38/0.55 2214[2:Rew:2201.0,2209.7,2201.0,2209.5,2201.0,2209.4,2201.0,2209.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c9),sk_c9)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c9)** -> .
% 0.38/0.55 2215[2:Con:2214.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c9)** -> .
% 0.38/0.55 2228[2:SpR:2182.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.38/0.55 2230[2:Rew:2175.0,2228.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.38/0.55 2236[2:SpR:2205.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.38/0.55 2238[2:Rew:45.0,2236.0] || -> equal(identity,sk_c7)**.
% 0.38/0.55 2239[2:Rew:2238.0,248.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.38/0.55 2240[2:Rew:2238.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.38/0.55 2243[2:Rew:2238.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.38/0.55 2252[2:SpR:2230.0,95.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.38/0.55 2254[2:Rew:2243.0,2252.0] || -> equal(sk_c7,sk_c9)**.
% 0.38/0.55 2257[2:Rew:2254.0,2239.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.38/0.55 2258[2:Rew:2254.0,2240.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.38/0.55 2262[2:Rew:2257.0,2206.0] || -> equal(sk_c5,sk_c9)**.
% 0.38/0.55 2265[2:Rew:2257.0,2215.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(v,sk_c9),sk_c9)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.38/0.55 2267[2:Rew:2262.0,2203.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.38/0.55 2279[2:Rew:2258.0,2265.5,2257.0,2265.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** equal(u,sk_c9) -> .
% 0.38/0.55 2280[2:Con:2279.0] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c9)**+ -> .
% 0.38/0.55 2672[2:SpL:2182.0,2280.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c4),sk_c10)** equal(u,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.38/0.55 2675[2:Obv:2672.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c4),sk_c10)** equal(u,sk_c9) -> .
% 0.38/0.55 2676[2:Rew:2175.0,2675.1] || equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.38/0.55 2677[2:Obv:2676.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.38/0.55 2734[2:SpL:2267.0,2677.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.38/0.55 2739[2:Obv:2734.1] || -> .
% 0.38/0.55 % SZS output end Refutation
% 0.38/0.55 Formulae used in the proof : prove_this_2 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_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 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_37 prove_this_38 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 left_identity left_inverse associativity
% 0.38/0.55
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