TSTP Solution File: GRP256-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP256-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 0.35s 0.55s
% Output : Refutation 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP256-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 07:09:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.35/0.55
% 0.35/0.55 SPASS V 3.9
% 0.35/0.55 SPASS beiseite: Proof found.
% 0.35/0.55 % SZS status Theorem
% 0.35/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.55 SPASS derived 1648 clauses, backtracked 504 clauses, performed 12 splits and kept 897 clauses.
% 0.35/0.55 SPASS allocated 64449 KBytes.
% 0.35/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.35/0.55 0:00:00.03 for the input.
% 0.35/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.35/0.55 0:00:00.01 for inferences.
% 0.35/0.55 0:00:00.00 for the backtracking.
% 0.35/0.55 0:00:00.13 for the reduction.
% 0.35/0.55
% 0.35/0.55
% 0.35/0.55 Here is a proof with depth 7, length 396 :
% 0.35/0.55 % SZS output start Refutation
% 0.35/0.55 1[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.35/0.55 2[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.35/0.55 5[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.35/0.55 6[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.35/0.55 7[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.35/0.55 8[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.55 9[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c10).
% 0.35/0.55 10[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.35/0.55 11[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c10).
% 0.35/0.55 12[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 13[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 14[0:Inp] || -> equal(inverse(sk_c6),sk_c9)** equal(inverse(sk_c1),sk_c10).
% 0.35/0.55 16[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.35/0.55 19[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.35/0.55 20[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.35/0.55 21[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.35/0.55 22[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.55 23[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c9)**.
% 0.35/0.55 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.35/0.55 26[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 27[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 28[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.35/0.55 29[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.55 30[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c3),sk_c8)**.
% 0.35/0.55 31[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.35/0.55 32[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c8)**.
% 0.35/0.55 33[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 34[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 35[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c3),sk_c8)**.
% 0.35/0.55 36[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.35/0.55 37[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.35/0.55 39[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.35/0.55 40[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.35/0.55 41[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.35/0.55 42[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.35/0.55 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_c9,z),sk_c8)** equal(multiply(x1,sk_c9),z)* equal(inverse(x1),sk_c9) -> .
% 0.35/0.55 44[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.35/0.55 45[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.35/0.55 46[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.35/0.55 47[0:Con:43.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(inverse(y),sk_c10) equal(multiply(u,sk_c9),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_c9,z),sk_c8)** -> .
% 0.35/0.55 48[1:Spt:47.3,47.8] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.35/0.55 49[2:Spt:35.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.35/0.55 51[3:Spt:25.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.35/0.55 53[4:Spt:14.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.35/0.55 55[5:Spt:37.1] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.35/0.55 57[5:SpL:55.0,48.1] || equal(inverse(sk_c3),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.35/0.55 58[5:Obv:57.1] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.35/0.55 59[5:Rew:49.0,58.0] || equal(sk_c8,sk_c9)** -> .
% 0.35/0.55 60[6:Spt:16.1] || -> equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.35/0.55 62[6:SpL:60.0,48.1] || equal(inverse(sk_c2),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.35/0.55 63[6:Obv:62.1] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.35/0.55 64[6:Rew:51.0,63.0] || equal(sk_c9,sk_c9)* -> .
% 0.35/0.55 65[6:Obv:64.0] || -> .
% 0.35/0.55 66[6:Spt:65.0,16.1,60.0] || equal(multiply(sk_c2,sk_c9),sk_c8)** -> .
% 0.35/0.55 67[6:Spt:65.0,16.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.55 68[6:MRR:21.1,66.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.55 70[6:MRR:20.1,66.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 71[6:MRR:19.1,66.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 87[2:SpR:49.0,45.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.35/0.55 88[3:SpR:51.0,45.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.35/0.55 89[4:SpR:53.0,45.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.35/0.55 93[1:SpL:45.0,48.1] || equal(inverse(inverse(sk_c9)),sk_c9)** equal(identity,sk_c8) -> .
% 0.35/0.55 106[0:SpR:45.0,46.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.35/0.55 113[0:Rew:44.0,106.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.35/0.55 128[0:SpR:113.0,113.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.35/0.55 131[6:SpR:70.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.55 133[3:SpR:88.0,113.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.35/0.55 139[0:SpR:45.0,113.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.35/0.55 140[2:SpR:87.0,113.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.35/0.55 142[4:SpR:89.0,113.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.35/0.55 152[6:Rew:71.0,131.0,68.0,131.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.55 153[6:MRR:152.0,59.0] || -> .
% 0.35/0.55 182[0:Rew:128.0,139.0] || -> equal(multiply(u,identity),u)**.
% 0.35/0.55 184[4:Rew:182.0,142.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.35/0.55 186[5:Spt:153.0,37.1,55.0] || equal(multiply(sk_c3,sk_c9),sk_c8)** -> .
% 0.35/0.55 187[5:Spt:153.0,37.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.55 188[3:Rew:182.0,133.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.35/0.55 189[3:Rew:188.0,93.0] || equal(inverse(sk_c2),sk_c9)** equal(identity,sk_c8) -> .
% 0.35/0.55 190[2:Rew:182.0,140.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.35/0.55 192[5:MRR:42.1,186.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.55 193[5:MRR:39.1,186.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.35/0.55 194[3:Rew:51.0,189.0] || equal(sk_c9,sk_c9) equal(identity,sk_c8)** -> .
% 0.35/0.55 195[3:Obv:194.0] || equal(identity,sk_c8)** -> .
% 0.35/0.55 196[5:MRR:41.1,186.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 197[5:MRR:40.1,186.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 199[5:MRR:36.1,186.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.55 200[5:SpR:187.0,45.0] || -> equal(multiply(sk_c10,sk_c4),identity)**.
% 0.35/0.55 204[4:SpR:184.0,113.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),u)**.
% 0.35/0.55 212[3:SpR:188.0,45.0] || -> equal(multiply(sk_c2,sk_c9),identity)**.
% 0.35/0.55 215[5:SpR:192.0,45.0] || -> equal(multiply(sk_c9,sk_c6),identity)**.
% 0.35/0.55 218[2:SpR:190.0,45.0] || -> equal(multiply(sk_c3,sk_c8),identity)**.
% 0.35/0.55 221[5:SpR:193.0,45.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.35/0.55 222[5:SpR:193.0,113.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.35/0.55 231[5:SpR:196.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.55 232[5:SpL:196.0,48.1] || equal(inverse(sk_c6),sk_c9)** equal(sk_c7,sk_c8) -> .
% 0.35/0.55 233[5:Rew:192.0,231.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.55 234[5:Rew:197.0,233.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.55 249[5:Rew:234.0,221.0] || -> equal(multiply(sk_c9,sk_c5),identity)**.
% 0.35/0.55 250[5:Rew:234.0,222.0] || -> equal(multiply(sk_c9,multiply(sk_c5,u)),u)**.
% 0.35/0.55 258[5:Rew:192.0,232.0] || equal(sk_c9,sk_c9) equal(sk_c7,sk_c8)** -> .
% 0.35/0.55 259[5:Obv:258.0] || equal(sk_c7,sk_c8)** -> .
% 0.35/0.55 260[5:Rew:234.0,259.0] || equal(sk_c7,sk_c9)** -> .
% 0.35/0.55 267[5:SpR:199.0,46.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.35/0.55 273[5:SpR:200.0,113.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c4)**.
% 0.35/0.55 274[5:Rew:184.0,273.0] || -> equal(multiply(sk_c1,identity),sk_c4)**.
% 0.35/0.55 275[5:Rew:182.0,274.0] || -> equal(sk_c4,sk_c1)**.
% 0.35/0.55 280[5:Rew:275.0,267.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.35/0.55 285[5:Rew:204.0,280.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.35/0.55 286[5:Rew:285.0,88.0] || -> equal(identity,sk_c2)**.
% 0.35/0.55 287[5:Rew:285.0,249.0] || -> equal(identity,sk_c5)**.
% 0.35/0.55 289[5:Rew:285.0,250.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.35/0.55 291[5:Rew:285.0,215.0] || -> equal(identity,sk_c6)**.
% 0.35/0.55 304[5:Rew:286.0,287.0] || -> equal(sk_c2,sk_c5)**.
% 0.35/0.55 308[5:Rew:304.0,286.0] || -> equal(identity,sk_c5)**.
% 0.35/0.55 310[5:Rew:291.0,308.0] || -> equal(sk_c6,sk_c5)**.
% 0.35/0.55 312[5:Rew:310.0,196.0] || -> equal(multiply(sk_c5,sk_c9),sk_c7)**.
% 0.35/0.55 327[5:Rew:289.0,312.0] || -> equal(sk_c7,sk_c9)**.
% 0.35/0.55 328[5:MRR:327.0,260.0] || -> .
% 0.35/0.55 333[4:Spt:328.0,14.1,53.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.35/0.55 334[4:Spt:328.0,14.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.55 336[4:MRR:9.1,333.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.55 337[4:MRR:13.0,333.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 338[4:MRR:12.0,333.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 340[4:MRR:8.0,333.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.55 376[4:SpR:337.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.55 378[4:Rew:334.0,376.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.55 379[4:Rew:338.0,378.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.55 380[4:Rew:379.0,195.0] || equal(identity,sk_c9)** -> .
% 0.35/0.55 389[4:Rew:379.0,338.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.55 406[4:SpR:340.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.35/0.55 408[4:Rew:336.0,406.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.35/0.55 410[4:SpR:389.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.35/0.55 412[4:Rew:212.0,410.0,188.0,410.0] || -> equal(identity,sk_c7)**.
% 0.35/0.55 415[4:Rew:412.0,380.0] || equal(sk_c7,sk_c9)** -> .
% 0.35/0.55 418[4:Rew:412.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.35/0.55 432[4:SpR:408.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.35/0.55 434[4:Rew:418.0,432.0] || -> equal(sk_c7,sk_c9)**.
% 0.35/0.55 435[4:MRR:434.0,415.0] || -> .
% 0.35/0.55 436[3:Spt:435.0,25.1,51.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.35/0.55 437[3:Spt:435.0,25.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.35/0.55 438[3:MRR:28.1,436.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.55 439[3:MRR:23.1,436.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.55 440[3:MRR:27.0,436.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 441[3:MRR:26.0,436.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 443[3:MRR:22.0,436.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.55 465[3:SpR:440.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.55 467[3:Rew:438.0,465.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.55 468[3:Rew:441.0,467.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.55 470[3:Rew:468.0,49.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.35/0.55 471[3:Rew:468.0,190.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.35/0.55 473[3:Rew:468.0,218.0] || -> equal(multiply(sk_c3,sk_c9),identity)**.
% 0.35/0.55 477[3:Rew:468.0,441.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.55 479[3:Rew:468.0,93.1] || equal(inverse(inverse(sk_c9)),sk_c9)** equal(identity,sk_c9) -> .
% 0.35/0.55 484[3:Rew:470.0,479.0,471.0,479.0] || equal(sk_c9,sk_c9) equal(identity,sk_c9)** -> .
% 0.35/0.55 485[3:Obv:484.0] || equal(identity,sk_c9)** -> .
% 0.35/0.55 487[3:SpR:443.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.35/0.55 489[3:Rew:439.0,487.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.35/0.55 498[3:SpR:477.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.35/0.55 500[3:Rew:471.0,498.0] || -> equal(multiply(sk_c3,sk_c9),sk_c7)**.
% 0.35/0.55 501[3:Rew:473.0,500.0] || -> equal(identity,sk_c7)**.
% 0.35/0.55 506[3:Rew:501.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.35/0.55 509[3:Rew:501.0,485.0] || equal(sk_c7,sk_c9)** -> .
% 0.35/0.55 518[3:SpR:489.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.35/0.55 520[3:Rew:506.0,518.0] || -> equal(sk_c7,sk_c9)**.
% 0.35/0.55 521[3:MRR:520.0,509.0] || -> .
% 0.35/0.55 522[2:Spt:521.0,35.1,49.0] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.35/0.55 523[2:Spt:521.0,35.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.55 524[2:MRR:32.1,522.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.35/0.55 525[2:MRR:30.1,522.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.55 526[2:MRR:34.0,522.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 527[2:MRR:33.0,522.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 528[2:MRR:31.0,522.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.35/0.55 529[2:MRR:29.0,522.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.55 537[2:SpR:526.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.55 539[2:Rew:523.0,537.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.55 540[2:Rew:527.0,539.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.55 541[2:Rew:540.0,524.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.35/0.55 544[2:Rew:540.0,527.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.55 545[2:Rew:540.0,528.0] || -> equal(multiply(sk_c5,sk_c9),sk_c9)**.
% 0.35/0.55 546[2:Rew:540.0,93.1] || equal(inverse(inverse(sk_c9)),sk_c9)** equal(identity,sk_c9) -> .
% 0.35/0.55 555[2:SpR:529.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.35/0.55 557[2:Rew:525.0,555.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.35/0.55 559[2:SpR:544.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.35/0.55 561[2:Rew:45.0,559.0] || -> equal(identity,sk_c7)**.
% 0.35/0.55 563[2:Rew:561.0,182.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.35/0.55 564[2:Rew:561.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.35/0.55 567[2:Rew:561.0,546.1] || equal(inverse(inverse(sk_c9)),sk_c9)** equal(sk_c7,sk_c9) -> .
% 0.35/0.55 576[2:SpR:557.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.35/0.55 578[2:Rew:564.0,576.0] || -> equal(sk_c7,sk_c9)**.
% 0.35/0.55 582[2:Rew:578.0,563.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.35/0.55 586[2:Rew:578.0,567.1] || equal(inverse(inverse(sk_c9)),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.35/0.55 592[2:Rew:582.0,545.0] || -> equal(sk_c5,sk_c9)**.
% 0.35/0.55 596[2:Rew:592.0,541.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.35/0.55 606[2:Obv:586.1] || equal(inverse(inverse(sk_c9)),sk_c9)** -> .
% 0.35/0.55 607[2:Rew:596.0,606.0,596.0,606.0] || equal(sk_c9,sk_c9)* -> .
% 0.35/0.55 608[2:Obv:607.0] || -> .
% 0.35/0.55 609[1:Spt:608.0,47.0,47.1,47.2,47.4,47.5,47.6,47.7,47.9,47.10] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c10) equal(multiply(u,sk_c9),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_c9,y),sk_c8)** -> .
% 0.35/0.55 610[1:EqR:609.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) 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_c9,multiply(u,sk_c9)),sk_c8)** -> .
% 0.35/0.55 612[2:Spt:28.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.35/0.55 615[3:Spt:14.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.35/0.55 616[3:SpR:615.0,113.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.35/0.55 618[4:Spt:32.1] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.35/0.55 621[5:Spt:2.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.35/0.55 623[5:SpR:621.0,113.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c10)**.
% 0.35/0.55 625[5:Rew:615.0,623.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.35/0.55 626[6:Spt:16.1] || -> equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.35/0.55 628[6:SpR:626.0,113.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c9)**.
% 0.35/0.55 630[6:SpL:626.0,609.4] || equal(inverse(sk_c2),sk_c9) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c10) equal(sk_c8,x) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.35/0.55 631[6:Rew:612.0,628.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.35/0.55 632[6:Rew:612.0,630.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c10) equal(sk_c8,x) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.35/0.55 633[6:Obv:632.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c10) equal(sk_c8,x) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.35/0.55 635[5:SpR:625.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.35/0.55 638[5:Rew:45.0,635.0] || -> equal(identity,sk_c9)**.
% 0.35/0.55 639[5:Rew:638.0,182.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.35/0.55 640[5:Rew:638.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.35/0.55 642[5:Rew:638.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.35/0.55 643[6:Rew:639.0,626.0] || -> equal(sk_c2,sk_c8)**.
% 0.35/0.55 646[6:Rew:639.0,633.5] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8)** equal(inverse(w),sk_c10) equal(sk_c8,x) equal(multiply(u,sk_c8),sk_c9)** equal(v,sk_c8) equal(multiply(w,sk_c10),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.35/0.55 655[6:Rew:643.0,612.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.35/0.55 658[6:Rew:640.0,631.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.55 663[6:Rew:658.0,655.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.35/0.55 680[6:Rew:640.0,646.7,658.0,646.7,658.0,646.5,639.0,646.4,658.0,646.4,658.0,646.3,658.0,646.1,658.0,646.0] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(sk_c9,x)* equal(u,sk_c9) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** equal(x,sk_c9)* -> .
% 0.35/0.55 681[6:Obv:680.3] || 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)** equal(x,sk_c9)* -> .
% 0.35/0.55 682[6:Con:681.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c9)**+ -> .
% 0.35/0.55 716[5:SpR:642.0,113.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.35/0.55 717[5:SpR:642.0,639.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.35/0.55 721[5:Rew:639.0,716.0] || -> equal(inverse(inverse(u)),u)**.
% 0.35/0.55 733[5:SpR:721.0,642.0] || -> equal(multiply(u,inverse(u)),sk_c9)**.
% 0.35/0.55 1010[6:SpL:621.0,682.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.35/0.55 1013[6:Obv:1010.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) -> .
% 0.35/0.55 1014[6:Rew:615.0,1013.1] || equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.35/0.55 1015[6:Obv:1014.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.35/0.55 1072[6:SpL:663.0,1015.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.35/0.55 1077[6:Obv:1072.1] || -> .
% 0.35/0.55 1078[6:Spt:1077.0,16.1,626.0] || equal(multiply(sk_c2,sk_c9),sk_c8)** -> .
% 0.35/0.55 1079[6:Spt:1077.0,16.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.55 1088[6:Rew:639.0,1078.0] || equal(sk_c2,sk_c8)** -> .
% 0.35/0.55 1112[5:Rew:639.0,21.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c2,sk_c8).
% 0.35/0.55 1113[6:MRR:1112.1,1088.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.55 1122[5:Rew:639.0,20.1,639.0,20.0] || -> equal(sk_c6,sk_c7) equal(sk_c2,sk_c8)**.
% 0.35/0.55 1123[6:MRR:1122.1,1088.0] || -> equal(sk_c6,sk_c7)**.
% 0.35/0.55 1125[6:Rew:1123.0,1113.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.35/0.55 1126[5:Rew:639.0,19.1,640.0,19.0] || -> equal(sk_c7,sk_c8) equal(sk_c2,sk_c8)**.
% 0.35/0.55 1127[6:MRR:1126.1,1088.0] || -> equal(sk_c7,sk_c8)**.
% 0.35/0.55 1129[6:Rew:1127.0,1125.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.35/0.55 1171[5:SpR:612.0,721.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.35/0.55 1177[5:Rew:717.0,1171.0] || -> equal(sk_c2,sk_c9)**.
% 0.35/0.55 1179[6:Rew:1177.0,1088.0] || equal(sk_c8,sk_c9)** -> .
% 0.35/0.55 1196[5:SpR:618.0,721.0] || -> equal(inverse(sk_c8),sk_c3)**.
% 0.35/0.55 1197[5:SpR:618.0,733.0] || -> equal(multiply(sk_c3,sk_c8),sk_c9)**.
% 0.35/0.55 1202[6:Rew:1129.0,1196.0] || -> equal(sk_c3,sk_c9)**.
% 0.35/0.55 1210[6:Rew:1202.0,1197.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.35/0.55 1211[6:Rew:640.0,1210.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.55 1212[6:MRR:1211.0,1179.0] || -> .
% 0.35/0.55 1221[5:Spt:1212.0,2.1,621.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.35/0.55 1222[5:Spt:1212.0,2.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.55 1223[5:MRR:7.1,1221.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.55 1226[5:MRR:6.1,1221.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.55 1227[5:MRR:5.1,1221.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.55 1229[5:MRR:1.1,1221.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.55 1249[5:SpR:1226.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.55 1251[5:Rew:1223.0,1249.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.56 1252[5:Rew:1227.0,1251.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.56 1256[5:Rew:1252.0,1227.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.56 1274[5:SpR:1229.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.35/0.56 1276[5:Rew:1222.0,1274.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.35/0.56 1278[5:SpR:1256.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.35/0.56 1280[5:Rew:45.0,1278.0] || -> equal(identity,sk_c7)**.
% 0.35/0.56 1282[5:Rew:1280.0,182.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.35/0.56 1283[5:Rew:1280.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.35/0.56 1293[5:SpR:1276.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.35/0.56 1295[5:Rew:1283.0,1293.0] || -> equal(sk_c7,sk_c9)**.
% 0.35/0.56 1299[5:Rew:1295.0,1282.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.35/0.56 1300[5:Rew:1295.0,1283.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.35/0.56 1341[5:SpR:1299.0,616.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.35/0.56 1348[5:SpR:1341.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.35/0.56 1350[5:Rew:1299.0,1348.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.35/0.56 1373[5:SpR:1350.0,1300.0] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.35/0.56 1377[5:MRR:1373.0,1221.0] || -> .
% 0.35/0.56 1381[4:Spt:1377.0,32.1,618.0] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.35/0.56 1382[4:Spt:1377.0,32.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.35/0.56 1383[4:MRR:30.1,1381.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.56 1384[4:MRR:35.1,1381.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.56 1385[4:MRR:34.0,1381.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.56 1386[4:MRR:33.0,1381.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.56 1387[4:MRR:31.0,1381.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.35/0.56 1388[4:MRR:29.0,1381.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.56 1398[4:SpR:1385.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.56 1400[4:Rew:1384.0,1398.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.56 1401[4:Rew:1386.0,1400.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.56 1402[4:Rew:1401.0,1382.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.35/0.56 1404[4:Rew:1401.0,1386.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.56 1405[4:Rew:1401.0,1387.0] || -> equal(multiply(sk_c5,sk_c9),sk_c9)**.
% 0.35/0.56 1407[4:Rew:1401.0,610.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) 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_c9,multiply(u,sk_c9)),sk_c8)** -> .
% 0.35/0.56 1410[4:Rew:1401.0,1407.7,1401.0,1407.5,1401.0,1407.4,1401.0,1407.2] || 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)** -> .
% 0.35/0.56 1411[4:Con:1410.2] || 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)** -> .
% 0.35/0.56 1420[4:SpR:1388.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.35/0.56 1422[4:Rew:1383.0,1420.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.35/0.56 1424[4:SpR:1404.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.35/0.56 1426[4:Rew:45.0,1424.0] || -> equal(identity,sk_c7)**.
% 0.35/0.56 1427[4:Rew:1426.0,182.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.35/0.56 1428[4:Rew:1426.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.35/0.56 1430[4:Rew:1426.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.35/0.56 1439[4:SpR:1422.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.35/0.56 1441[4:Rew:1430.0,1439.0] || -> equal(sk_c7,sk_c9)**.
% 0.35/0.56 1444[4:Rew:1441.0,1427.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.35/0.56 1445[4:Rew:1441.0,1428.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.35/0.56 1447[4:Rew:1441.0,1430.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.35/0.56 1448[4:Rew:1444.0,1405.0] || -> equal(sk_c5,sk_c9)**.
% 0.35/0.56 1452[4:Rew:1444.0,1411.3] || 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(multiply(sk_c9,multiply(u,sk_c9)),sk_c9)** -> .
% 0.35/0.56 1453[4:Rew:1448.0,1402.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.35/0.56 1466[4:Rew:1444.0,1452.5,1445.0,1452.5] || 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) -> .
% 0.35/0.56 1467[4:Con:1466.0] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c9)**+ -> .
% 0.35/0.56 1479[4:SpR:1444.0,616.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.35/0.56 1490[4:SpR:1479.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.35/0.56 1492[4:Rew:1444.0,1490.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.35/0.56 1514[4:SpR:1492.0,1447.0] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.35/0.56 1699[4:SpL:1514.0,1467.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.35/0.56 1702[4:Obv:1699.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c1),sk_c10)** equal(u,sk_c9) -> .
% 0.35/0.56 1703[4:Rew:615.0,1702.1] || equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.35/0.56 1704[4:Obv:1703.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.35/0.56 1862[4:SpL:1453.0,1704.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.35/0.56 1867[4:Obv:1862.1] || -> .
% 0.35/0.56 1868[3:Spt:1867.0,14.1,615.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.35/0.56 1869[3:Spt:1867.0,14.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.56 1870[3:MRR:11.1,1868.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.35/0.56 1871[3:MRR:9.1,1868.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.56 1873[3:MRR:13.0,1868.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.56 1874[3:MRR:12.0,1868.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.56 1875[3:MRR:10.0,1868.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.35/0.56 1876[3:MRR:8.0,1868.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.56 1887[3:SpR:1873.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.56 1889[3:Rew:1869.0,1887.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.56 1890[3:Rew:1874.0,1889.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.56 1891[3:Rew:1890.0,1870.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.35/0.56 1892[3:Rew:1890.0,1874.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.56 1893[3:Rew:1890.0,1875.0] || -> equal(multiply(sk_c5,sk_c9),sk_c9)**.
% 0.35/0.56 1895[3:Rew:1890.0,610.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) 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_c9,multiply(u,sk_c9)),sk_c8)** -> .
% 0.35/0.56 1898[3:Rew:1890.0,1895.7,1890.0,1895.5,1890.0,1895.4,1890.0,1895.2] || 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)** -> .
% 0.35/0.56 1899[3:Con:1898.2] || 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)** -> .
% 0.35/0.56 1908[3:SpR:1876.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.35/0.56 1910[3:Rew:1871.0,1908.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.35/0.56 1912[3:SpR:1892.0,113.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.35/0.56 1914[3:Rew:45.0,1912.0] || -> equal(identity,sk_c7)**.
% 0.35/0.56 1915[3:Rew:1914.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.35/0.56 1916[3:Rew:1914.0,182.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.35/0.56 1917[3:Rew:1914.0,45.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.35/0.56 1927[3:SpR:1910.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.35/0.56 1929[3:Rew:1917.0,1927.0] || -> equal(sk_c7,sk_c9)**.
% 0.35/0.56 1932[3:Rew:1929.0,1915.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.35/0.56 1933[3:Rew:1929.0,1916.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.35/0.56 1941[3:Rew:1932.0,1899.5] || 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)** -> .
% 0.35/0.56 1945[3:Rew:1933.0,1893.0] || -> equal(sk_c5,sk_c9)**.
% 0.35/0.56 1947[3:Rew:1945.0,1891.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.35/0.56 1955[3:Con:1941.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.35/0.56 1956[3:Rew:1933.0,1955.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c9)**+ -> .
% 0.35/0.56 2017[0:SpR:128.0,113.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.35/0.56 2217[3:SpL:1876.0,1956.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c4),sk_c10)** equal(u,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.35/0.56 2221[3:Obv:2217.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c4),sk_c10)** equal(u,sk_c9) -> .
% 0.35/0.56 2222[3:Rew:1871.0,2221.1] || equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.35/0.56 2223[3:Obv:2222.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.35/0.56 2298[3:SpL:1947.0,2223.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.35/0.56 2303[3:Obv:2298.1] || -> .
% 0.35/0.56 2304[2:Spt:2303.0,28.1,612.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.35/0.56 2305[2:Spt:2303.0,28.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.35/0.56 2307[2:MRR:23.1,2304.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.35/0.56 2309[2:MRR:27.0,2304.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.35/0.56 2310[2:MRR:26.0,2304.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.35/0.56 2312[2:MRR:22.0,2304.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.35/0.56 2323[2:SpR:2307.0,2017.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),u)**.
% 0.35/0.56 2326[2:SpR:2309.0,113.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.35/0.56 2328[2:Rew:2305.0,2326.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.35/0.56 2329[2:Rew:2310.0,2328.0] || -> equal(sk_c8,sk_c9)**.
% 0.35/0.56 2334[2:Rew:2329.0,610.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) 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_c9,multiply(u,sk_c9)),sk_c8)** -> .
% 0.35/0.56 2339[2:Rew:2329.0,2334.7,2329.0,2334.5,2329.0,2334.4,2329.0,2334.2] || 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)** -> .
% 0.35/0.56 2340[2:Con:2339.2] || 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)** -> .
% 0.35/0.56 2349[2:SpR:2312.0,46.0] || -> equal(multiply(sk_c4,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.35/0.56 2350[2:SpR:2312.0,113.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.35/0.56 2352[2:Rew:2307.0,2350.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.35/0.56 2353[2:Rew:2323.0,2349.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.35/0.56 2360[2:Rew:2353.0,2340.5] || 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)** -> .
% 0.35/0.56 2364[2:Con:2360.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** -> .
% 0.35/0.56 2367[2:SpR:2352.0,113.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.35/0.56 2369[2:Rew:45.0,2367.0] || -> equal(identity,sk_c9)**.
% 0.35/0.56 2370[2:Rew:2369.0,182.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.35/0.56 2373[2:Rew:2369.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.35/0.56 2374[2:Rew:2370.0,2364.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10) equal(u,sk_c9) equal(multiply(v,sk_c10),sk_c9)**+ -> .
% 0.35/0.56 2381[2:SpR:2305.0,2373.0] || -> equal(multiply(sk_c9,sk_c6),sk_c9)**.
% 0.35/0.56 2384[2:Rew:2353.0,2381.0] || -> equal(sk_c6,sk_c9)**.
% 0.35/0.56 2385[2:Rew:2384.0,2305.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.35/0.56 2582[2:SpL:2312.0,2374.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c4),sk_c10)** equal(u,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.35/0.56 2584[2:Obv:2582.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c4),sk_c10)** equal(u,sk_c9) -> .
% 0.35/0.56 2585[2:Rew:2307.0,2584.1] || equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.35/0.56 2586[2:Obv:2585.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.35/0.56 2671[2:SpL:2385.0,2586.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.35/0.56 2676[2:Obv:2671.1] || -> .
% 0.35/0.56 % SZS output end Refutation
% 0.35/0.56 Formulae used in the proof : prove_this_1 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_16 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 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_36 prove_this_37 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 left_identity left_inverse associativity
% 0.35/0.56
%------------------------------------------------------------------------------