TSTP Solution File: GRP244-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP244-1 : 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 11:46:30 EDT 2022
% Result : Unsatisfiable 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP244-1 : 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 01:23:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.54
% 0.20/0.54 SPASS V 3.9
% 0.20/0.54 SPASS beiseite: Proof found.
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.54 SPASS derived 1748 clauses, backtracked 552 clauses, performed 13 splits and kept 986 clauses.
% 0.20/0.54 SPASS allocated 64399 KBytes.
% 0.20/0.54 SPASS spent 0:00:00.19 on the problem.
% 0.20/0.54 0:00:00.04 for the input.
% 0.20/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.54 0:00:00.01 for inferences.
% 0.20/0.54 0:00:00.00 for the backtracking.
% 0.20/0.54 0:00:00.11 for the reduction.
% 0.20/0.54
% 0.20/0.54
% 0.20/0.54 Here is a proof with depth 5, length 376 :
% 0.20/0.54 % SZS output start Refutation
% 0.20/0.54 5[0:Inp] || -> equal(inverse(sk_c6),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.20/0.54 6[0:Inp] || -> equal(multiply(sk_c6,sk_c10),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.20/0.54 7[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.20/0.54 8[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.20/0.54 9[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.20/0.54 12[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.54 13[0:Inp] || -> equal(inverse(sk_c5),sk_c10)** equal(inverse(sk_c1),sk_c11).
% 0.20/0.54 14[0:Inp] || -> equal(inverse(sk_c6),sk_c11)** equal(inverse(sk_c1),sk_c11).
% 0.20/0.54 15[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.20/0.54 16[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 17[0:Inp] || -> equal(inverse(sk_c7),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.20/0.54 21[0:Inp] || -> equal(multiply(sk_c5,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.20/0.54 22[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.20/0.54 25[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.20/0.54 26[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.20/0.54 27[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.20/0.54 28[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c4,sk_c11),sk_c10)**.
% 0.20/0.54 30[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.54 31[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.54 32[0:Inp] || -> equal(inverse(sk_c6),sk_c11) equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.54 33[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.20/0.54 34[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 35[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.54 36[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.20/0.54 39[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.54 40[0:Inp] || -> equal(inverse(sk_c5),sk_c10) equal(inverse(sk_c3),sk_c11)**.
% 0.20/0.54 41[0:Inp] || -> equal(inverse(sk_c6),sk_c11) equal(inverse(sk_c3),sk_c11)**.
% 0.20/0.54 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.20/0.54 43[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 44[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c3),sk_c11)**.
% 0.20/0.54 45[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.20/0.54 50[0:Inp] || -> equal(inverse(sk_c6),sk_c11) equal(multiply(sk_c3,sk_c10),sk_c11)**.
% 0.20/0.54 51[0:Inp] || -> equal(multiply(sk_c6,sk_c10),sk_c11) equal(multiply(sk_c3,sk_c10),sk_c11)**.
% 0.20/0.54 55[0:Inp] || equal(multiply(u,sk_c11),sk_c10)** equal(inverse(u),sk_c11) equal(multiply(v,sk_c10),sk_c9)** equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(w,sk_c10),sk_c11)** equal(multiply(x,sk_c11),sk_c10)** equal(inverse(x),sk_c11) equal(multiply(y,sk_c10),sk_c9)** equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(multiply(z,sk_c10),sk_c11)** equal(multiply(x1,x2),sk_c10)** equal(inverse(x1),x2) equal(multiply(x2,sk_c9),sk_c10)** -> .
% 0.20/0.54 56[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.54 57[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.54 58[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.54 59[0:Con:55.6] || equal(inverse(u),v) equal(inverse(w),sk_c11) equal(inverse(x),sk_c10) equal(inverse(y),sk_c11) equal(multiply(u,v),sk_c10)**+ equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c10),sk_c11)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(y,sk_c11),sk_c10)** -> .
% 0.20/0.54 60[1:Spt:59.0,59.4,59.5] || equal(inverse(u),v) equal(multiply(u,v),sk_c10)**+ equal(multiply(v,sk_c9),sk_c10)** -> .
% 0.20/0.54 63[2:Spt:35.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.54 65[3:Spt:17.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.20/0.54 72[4:Spt:26.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.20/0.54 74[4:SpL:72.0,60.1] || equal(inverse(sk_c2),sk_c10) equal(sk_c9,sk_c10) equal(multiply(sk_c10,sk_c9),sk_c10)** -> .
% 0.20/0.54 75[4:Rew:63.0,74.0] || equal(sk_c10,sk_c10) equal(sk_c9,sk_c10) equal(multiply(sk_c10,sk_c9),sk_c10)** -> .
% 0.20/0.54 76[4:Obv:75.0] || equal(sk_c9,sk_c10) equal(multiply(sk_c10,sk_c9),sk_c10)** -> .
% 0.20/0.54 78[1:SpL:56.0,60.1] || equal(inverse(identity),u) equal(u,sk_c10) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.20/0.54 79[5:Spt:8.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.20/0.54 87[2:SpR:63.0,57.0] || -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.20/0.54 97[0:SpR:57.0,58.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.54 102[0:Rew:56.0,97.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.54 123[0:SpR:102.0,102.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.54 126[4:SpR:72.0,102.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c10)**.
% 0.20/0.54 128[0:SpR:57.0,102.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.54 129[5:SpR:79.0,102.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c11)**.
% 0.20/0.54 135[2:SpR:87.0,102.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c2)**.
% 0.20/0.54 141[4:Rew:63.0,126.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.54 142[4:Rew:141.0,76.1] || equal(sk_c9,sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.20/0.54 144[5:Rew:65.0,129.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.20/0.54 158[4:Obv:142.1] || equal(sk_c9,sk_c10)** -> .
% 0.20/0.54 160[0:Rew:123.0,128.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.54 161[2:Rew:160.0,135.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.20/0.54 169[2:SpR:161.0,57.0] || -> equal(multiply(sk_c2,sk_c10),identity)**.
% 0.20/0.54 172[4:Rew:72.0,169.0] || -> equal(identity,sk_c9)**.
% 0.20/0.54 174[4:Rew:172.0,57.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.20/0.54 182[4:Rew:172.0,160.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.54 196[5:SpR:144.0,102.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.20/0.54 198[5:Rew:174.0,196.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.54 199[5:MRR:198.0,158.0] || -> .
% 0.20/0.54 200[5:Spt:199.0,8.1,79.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.20/0.54 201[5:Spt:199.0,8.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.54 205[4:Rew:182.0,9.0] || -> equal(sk_c8,sk_c10) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.20/0.54 206[5:MRR:205.1,200.0] || -> equal(sk_c8,sk_c10)**.
% 0.20/0.54 207[5:Rew:206.0,201.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.20/0.54 208[5:Rew:206.0,7.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.20/0.54 209[5:MRR:208.1,200.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)**.
% 0.20/0.54 233[5:SpR:209.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c10)**.
% 0.20/0.54 235[5:Rew:207.0,233.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.20/0.54 255[5:SpR:235.0,102.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c10)**.
% 0.20/0.54 257[5:Rew:72.0,255.0,161.0,255.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.54 258[5:MRR:257.0,158.0] || -> .
% 0.20/0.54 259[4:Spt:258.0,26.1,72.0] || equal(multiply(sk_c2,sk_c10),sk_c9)** -> .
% 0.20/0.54 260[4:Spt:258.0,26.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.54 261[4:Rew:169.0,259.0] || equal(identity,sk_c9)** -> .
% 0.20/0.54 264[2:Rew:169.0,22.1] || -> equal(inverse(sk_c5),sk_c10)** equal(identity,sk_c9).
% 0.20/0.54 265[4:MRR:264.1,261.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.20/0.54 268[2:Rew:169.0,27.1] || -> equal(multiply(sk_c8,sk_c9),sk_c10)** equal(identity,sk_c9).
% 0.20/0.54 269[4:MRR:268.1,261.0] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.20/0.54 270[2:Rew:169.0,25.1] || -> equal(multiply(sk_c7,sk_c8),sk_c10)** equal(identity,sk_c9).
% 0.20/0.54 271[4:MRR:270.1,261.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 274[2:Rew:169.0,21.1] || -> equal(multiply(sk_c5,sk_c10),sk_c9)** equal(identity,sk_c9).
% 0.20/0.54 275[4:MRR:274.1,261.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.54 278[4:SpR:260.0,102.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),u)**.
% 0.20/0.54 282[4:SpR:265.0,102.0] || -> equal(multiply(sk_c10,multiply(sk_c5,u)),u)**.
% 0.20/0.54 301[4:SpR:269.0,58.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.20/0.54 302[4:SpR:269.0,102.0] || -> equal(multiply(inverse(sk_c8),sk_c10),sk_c9)**.
% 0.20/0.54 305[4:SpR:271.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.20/0.54 307[4:Rew:260.0,305.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.20/0.54 326[4:SpR:307.0,102.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.20/0.54 328[4:Rew:57.0,326.0] || -> equal(identity,sk_c10)**.
% 0.20/0.54 329[4:Rew:328.0,261.0] || equal(sk_c9,sk_c10)** -> .
% 0.20/0.54 332[4:Rew:328.0,87.0] || -> equal(multiply(sk_c10,sk_c2),sk_c10)**.
% 0.20/0.54 333[4:Rew:328.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.54 334[4:Rew:328.0,160.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.54 342[4:Rew:333.0,282.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.54 344[4:Rew:333.0,332.0] || -> equal(sk_c2,sk_c10)**.
% 0.20/0.54 348[4:Rew:333.0,301.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),u)**.
% 0.20/0.54 354[4:Rew:344.0,63.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.54 357[4:Rew:334.0,275.0] || -> equal(sk_c9,sk_c5)**.
% 0.20/0.54 360[4:Rew:334.0,302.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.20/0.54 367[4:Rew:357.0,329.0] || equal(sk_c5,sk_c10)** -> .
% 0.20/0.54 380[4:Rew:357.0,360.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.20/0.54 387[4:Rew:342.0,348.0,357.0,348.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.54 389[4:Rew:387.0,278.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.54 391[4:Rew:389.0,271.0] || -> equal(sk_c8,sk_c10)**.
% 0.20/0.54 393[4:Rew:391.0,380.0] || -> equal(inverse(sk_c10),sk_c5)**.
% 0.20/0.54 395[4:Rew:354.0,393.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.54 396[4:MRR:395.0,367.0] || -> .
% 0.20/0.54 416[3:Spt:396.0,17.1,65.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.20/0.54 417[3:Spt:396.0,17.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.54 420[3:MRR:13.1,416.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.20/0.54 424[3:MRR:16.0,416.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 426[3:MRR:12.0,416.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.54 466[3:SpR:424.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.20/0.54 468[3:Rew:417.0,466.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.20/0.54 474[3:SpR:426.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c10)**.
% 0.20/0.54 476[3:Rew:420.0,474.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.54 482[3:SpR:468.0,102.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.20/0.54 484[3:Rew:57.0,482.0] || -> equal(identity,sk_c10)**.
% 0.20/0.54 485[3:Rew:484.0,87.0] || -> equal(multiply(sk_c10,sk_c2),sk_c10)**.
% 0.20/0.54 488[3:Rew:484.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.54 489[3:Rew:484.0,160.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.54 491[3:Rew:484.0,78.0] || equal(inverse(sk_c10),u) equal(u,sk_c10) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.20/0.54 496[3:Rew:488.0,485.0] || -> equal(sk_c2,sk_c10)**.
% 0.20/0.54 497[3:Rew:488.0,476.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.54 506[3:Rew:496.0,161.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.54 546[3:Rew:489.0,491.2,497.0,491.2,506.0,491.0] || equal(sk_c10,u)* equal(u,sk_c10)* equal(u,sk_c10)* -> .
% 0.20/0.54 547[3:Obv:546.1] || equal(u,sk_c10)* -> .
% 0.20/0.54 548[3:UnC:547.0,420.0] || -> .
% 0.20/0.54 555[2:Spt:548.0,35.1,63.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.20/0.54 556[2:Spt:548.0,35.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.54 558[2:MRR:31.1,555.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.20/0.54 561[2:MRR:34.0,555.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 563[2:MRR:30.0,555.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.54 564[2:MRR:28.0,555.0] || -> equal(multiply(sk_c4,sk_c11),sk_c10)**.
% 0.20/0.54 586[2:SpR:561.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.20/0.54 588[2:Rew:556.0,586.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.20/0.54 594[2:SpR:563.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c10)**.
% 0.20/0.54 596[2:Rew:558.0,594.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.54 602[2:SpR:588.0,102.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.20/0.54 604[2:Rew:57.0,602.0] || -> equal(identity,sk_c10)**.
% 0.20/0.54 606[2:Rew:604.0,160.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.54 607[2:Rew:604.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.54 610[2:Rew:604.0,78.0] || equal(inverse(sk_c10),u) equal(u,sk_c10) equal(multiply(u,sk_c9),sk_c10)** -> .
% 0.20/0.54 613[2:Rew:606.0,563.0] || -> equal(sk_c9,sk_c5)**.
% 0.20/0.54 623[2:Rew:613.0,596.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.54 637[2:Rew:607.0,623.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.54 638[2:Rew:637.0,558.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.54 639[2:Rew:637.0,613.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.54 659[2:Rew:606.0,610.2,639.0,610.2,638.0,610.0] || equal(sk_c10,u)* equal(u,sk_c10)* equal(u,sk_c10)* -> .
% 0.20/0.54 660[2:Obv:659.1] || equal(u,sk_c10)* -> .
% 0.20/0.54 661[2:UnC:660.0,564.0] || -> .
% 0.20/0.54 668[1:Spt:661.0,59.1,59.2,59.3,59.6,59.7,59.8] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c11)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.20/0.54 670[2:Spt:17.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.20/0.54 673[3:Spt:32.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.54 676[4:Spt:41.1] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.20/0.54 679[5:Spt:8.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.20/0.54 681[5:SpR:679.0,102.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c11)**.
% 0.20/0.54 683[5:Rew:670.0,681.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.20/0.54 684[6:Spt:26.1] || -> equal(multiply(sk_c2,sk_c10),sk_c9)**.
% 0.20/0.54 686[6:SpR:684.0,102.0] || -> equal(multiply(inverse(sk_c2),sk_c9),sk_c10)**.
% 0.20/0.54 689[6:Rew:673.0,686.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.54 691[7:Spt:50.1] || -> equal(multiply(sk_c3,sk_c10),sk_c11)**.
% 0.20/0.54 695[7:SpL:691.0,668.3] || equal(inverse(sk_c3),sk_c11) equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(sk_c11,sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.20/0.54 697[7:Obv:695.3] || equal(inverse(sk_c3),sk_c11) equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.20/0.54 698[7:Rew:676.0,697.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.20/0.54 699[7:Obv:698.0] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.20/0.54 701[5:SpR:683.0,102.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.20/0.54 703[5:Rew:57.0,701.0] || -> equal(identity,sk_c10)**.
% 0.20/0.54 704[5:Rew:703.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.54 705[5:Rew:703.0,160.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.54 707[5:Rew:703.0,57.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.20/0.54 708[6:Rew:704.0,689.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.54 714[7:Rew:708.0,699.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.20/0.54 715[7:Rew:705.0,691.0] || -> equal(sk_c3,sk_c11)**.
% 0.20/0.54 716[7:Rew:715.0,676.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.20/0.54 721[7:Rew:705.0,714.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(u,sk_c10) equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.20/0.54 743[5:SpR:707.0,102.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.20/0.54 744[5:SpR:707.0,705.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.54 746[5:SpR:670.0,707.0] || -> equal(multiply(sk_c11,sk_c1),sk_c10)**.
% 0.20/0.54 747[5:SpR:673.0,707.0] || -> equal(multiply(sk_c10,sk_c2),sk_c10)**.
% 0.20/0.54 750[5:Rew:704.0,747.0] || -> equal(sk_c2,sk_c10)**.
% 0.20/0.54 753[5:Rew:705.0,743.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.54 762[5:SpR:746.0,102.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c1)**.
% 0.20/0.54 764[7:Rew:705.0,762.0,716.0,762.0] || -> equal(sk_c11,sk_c1)**.
% 0.20/0.54 765[7:Rew:764.0,670.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.54 766[7:Rew:764.0,679.0] || -> equal(multiply(sk_c1,sk_c1),sk_c10)**.
% 0.20/0.54 774[7:Rew:764.0,721.1] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c1) equal(u,sk_c10) equal(multiply(v,sk_c11),sk_c10)** -> .
% 0.20/0.54 777[7:Rew:764.0,774.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c1) equal(u,sk_c10) equal(multiply(v,sk_c1),sk_c10)**+ -> .
% 0.20/0.54 789[5:SpR:753.0,707.0] || -> equal(multiply(u,inverse(u)),sk_c10)**.
% 0.20/0.54 1115[7:SpL:766.0,777.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c10) equal(sk_c10,sk_c10) -> .
% 0.20/0.54 1118[7:Obv:1115.3] || equal(inverse(u),sk_c10)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c10) -> .
% 0.20/0.54 1119[7:Rew:765.0,1118.1] || equal(inverse(u),sk_c10)** equal(sk_c1,sk_c1) equal(u,sk_c10) -> .
% 0.20/0.54 1120[7:Obv:1119.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.20/0.54 1122[7:SpL:744.0,1120.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.20/0.54 1125[7:Obv:1122.1] || -> .
% 0.20/0.54 1127[7:Spt:1125.0,50.1,691.0] || equal(multiply(sk_c3,sk_c10),sk_c11)** -> .
% 0.20/0.54 1128[7:Spt:1125.0,50.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.20/0.54 1129[5:Rew:705.0,762.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.20/0.54 1130[7:Rew:705.0,1127.0] || equal(sk_c3,sk_c11)** -> .
% 0.20/0.54 1146[5:Rew:705.0,51.1,705.0,51.0] || -> equal(sk_c6,sk_c11) equal(sk_c3,sk_c11)**.
% 0.20/0.54 1147[7:MRR:1146.1,1130.0] || -> equal(sk_c6,sk_c11)**.
% 0.20/0.54 1148[7:Rew:1147.0,1128.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.20/0.54 1149[7:Rew:1129.0,1148.0] || -> equal(sk_c11,sk_c1)**.
% 0.20/0.54 1150[7:Rew:1149.0,676.0] || -> equal(inverse(sk_c3),sk_c1)**.
% 0.20/0.54 1151[7:Rew:1149.0,670.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.54 1155[7:Rew:1149.0,1130.0] || equal(sk_c3,sk_c1)** -> .
% 0.20/0.54 1182[7:SpR:1150.0,753.0] || -> equal(inverse(sk_c1),sk_c3)**.
% 0.20/0.54 1188[7:Rew:1151.0,1182.0] || -> equal(sk_c3,sk_c1)**.
% 0.20/0.54 1189[7:MRR:1188.0,1155.0] || -> .
% 0.20/0.54 1190[6:Spt:1189.0,26.1,684.0] || equal(multiply(sk_c2,sk_c10),sk_c9)** -> .
% 0.20/0.54 1191[6:Spt:1189.0,26.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.54 1192[6:Rew:704.0,1190.0,750.0,1190.0] || equal(sk_c9,sk_c10)** -> .
% 0.20/0.54 1202[5:Rew:750.0,22.1,705.0,22.1] || -> equal(inverse(sk_c5),sk_c10)** equal(sk_c9,sk_c10).
% 0.20/0.54 1203[6:MRR:1202.1,1192.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.20/0.54 1237[5:Rew:750.0,21.1,705.0,21.1,705.0,21.0] || -> equal(sk_c9,sk_c5)** equal(sk_c9,sk_c10).
% 0.20/0.54 1238[6:MRR:1237.1,1192.0] || -> equal(sk_c9,sk_c5)**.
% 0.20/0.54 1239[6:Rew:1238.0,1192.0] || equal(sk_c5,sk_c10)** -> .
% 0.20/0.54 1262[6:SpR:1203.0,789.0] || -> equal(multiply(sk_c5,sk_c10),sk_c10)**.
% 0.20/0.54 1271[6:Rew:705.0,1262.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.54 1272[6:MRR:1271.0,1239.0] || -> .
% 0.20/0.54 1278[5:Spt:1272.0,8.1,679.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.20/0.54 1279[5:Spt:1272.0,8.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.54 1280[5:MRR:5.1,1278.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.20/0.54 1285[5:MRR:7.1,1278.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 1286[5:MRR:6.1,1278.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.20/0.54 1315[5:SpR:1285.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.20/0.54 1317[5:Rew:1279.0,1315.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.20/0.54 1319[5:SpR:1286.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c11),sk_c10)**.
% 0.20/0.54 1321[5:Rew:1280.0,1319.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.20/0.54 1331[5:SpR:1317.0,102.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.20/0.54 1333[5:Rew:57.0,1331.0] || -> equal(identity,sk_c10)**.
% 0.20/0.54 1334[5:Rew:1333.0,160.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.54 1336[5:Rew:1333.0,57.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.20/0.54 1339[5:Rew:1334.0,1286.0] || -> equal(sk_c6,sk_c11)**.
% 0.20/0.54 1347[5:Rew:1339.0,1280.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.20/0.54 1419[5:SpR:670.0,1336.0] || -> equal(multiply(sk_c11,sk_c1),sk_c10)**.
% 0.20/0.54 1449[5:SpR:1419.0,102.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c1)**.
% 0.20/0.54 1451[5:Rew:1334.0,1449.0,1347.0,1449.0] || -> equal(sk_c11,sk_c1)**.
% 0.20/0.54 1455[5:Rew:1451.0,1321.0] || -> equal(multiply(sk_c1,sk_c1),sk_c10)**.
% 0.20/0.54 1456[5:Rew:1451.0,1278.0] || equal(multiply(sk_c1,sk_c1),sk_c10)** -> .
% 0.20/0.54 1463[5:Rew:1455.0,1456.0] || equal(sk_c10,sk_c10)* -> .
% 0.20/0.54 1464[5:Obv:1463.0] || -> .
% 0.20/0.54 1468[4:Spt:1464.0,41.1,676.0] || equal(inverse(sk_c3),sk_c11)** -> .
% 0.20/0.54 1469[4:Spt:1464.0,41.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.20/0.54 1470[4:MRR:40.1,1468.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.20/0.54 1472[4:MRR:44.1,1468.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.54 1473[4:MRR:45.0,1468.0] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.20/0.54 1474[4:MRR:43.0,1468.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 1475[4:MRR:42.0,1468.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.20/0.54 1476[4:MRR:39.0,1468.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.54 1494[4:SpR:1474.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.20/0.54 1496[4:Rew:1472.0,1494.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.20/0.54 1498[4:SpR:1475.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c11),sk_c10)**.
% 0.20/0.54 1500[4:Rew:1469.0,1498.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.20/0.54 1502[4:SpR:1476.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c10)**.
% 0.20/0.54 1504[4:Rew:1470.0,1502.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.54 1513[4:SpR:1496.0,102.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.20/0.54 1515[4:Rew:57.0,1513.0] || -> equal(identity,sk_c10)**.
% 0.20/0.54 1516[4:Rew:1515.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.54 1517[4:Rew:1515.0,160.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.54 1519[4:Rew:1515.0,57.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.20/0.54 1520[4:Rew:1516.0,1504.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.54 1528[4:Rew:1520.0,1473.0] || -> equal(multiply(sk_c8,sk_c10),sk_c10)**.
% 0.20/0.54 1530[4:Rew:1520.0,668.4] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c11)** equal(multiply(v,sk_c10),sk_c10)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.20/0.54 1533[4:Rew:1517.0,1475.0] || -> equal(sk_c6,sk_c11)**.
% 0.20/0.54 1534[4:Rew:1533.0,1469.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.20/0.54 1536[4:Rew:1517.0,1528.0] || -> equal(sk_c8,sk_c10)**.
% 0.20/0.54 1537[4:Rew:1536.0,1472.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.20/0.54 1538[4:Rew:1536.0,1474.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)**.
% 0.20/0.54 1540[4:Rew:1517.0,1538.0] || -> equal(sk_c7,sk_c10)**.
% 0.20/0.54 1541[4:Rew:1540.0,1537.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.54 1550[4:Rew:1517.0,1530.4,1517.0,1530.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c11) equal(u,sk_c11) equal(v,sk_c10) equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.20/0.54 1601[4:SpR:670.0,1519.0] || -> equal(multiply(sk_c11,sk_c1),sk_c10)**.
% 0.20/0.54 1610[4:SpR:1601.0,102.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c1)**.
% 0.20/0.54 1612[4:Rew:1517.0,1610.0,1534.0,1610.0] || -> equal(sk_c11,sk_c1)**.
% 0.20/0.54 1613[4:Rew:1612.0,670.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.54 1619[4:Rew:1612.0,1500.0] || -> equal(multiply(sk_c1,sk_c1),sk_c10)**.
% 0.20/0.54 1625[4:Rew:1612.0,1550.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c11) equal(u,sk_c11) equal(v,sk_c10) equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.20/0.54 1629[4:Rew:1612.0,1625.5,1612.0,1625.3,1612.0,1625.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c1) equal(u,sk_c1) equal(v,sk_c10) equal(multiply(w,sk_c1),sk_c10)**+ -> .
% 0.20/0.54 1688[4:SpL:1619.0,1629.5] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(v,sk_c10) equal(sk_c10,sk_c10) -> .
% 0.20/0.54 1689[4:Obv:1688.5] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(v,sk_c10) -> .
% 0.20/0.54 1690[4:Rew:1613.0,1689.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(sk_c1,sk_c1) equal(u,sk_c1) equal(v,sk_c10) -> .
% 0.20/0.54 1691[4:Obv:1690.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c10)** equal(u,sk_c1) equal(v,sk_c10) -> .
% 0.20/0.54 1998[4:SpL:1613.0,1691.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c10)** equal(sk_c1,sk_c1) equal(u,sk_c10) -> .
% 0.20/0.54 2001[4:Obv:1998.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.20/0.54 2002[4:SpL:1541.0,2001.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.20/0.54 2005[4:Obv:2002.1] || -> .
% 0.20/0.54 2007[3:Spt:2005.0,32.1,673.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.20/0.54 2008[3:Spt:2005.0,32.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.20/0.54 2009[3:MRR:31.1,2007.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.20/0.54 2011[3:MRR:35.1,2007.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.54 2013[3:MRR:36.0,2007.0] || -> equal(multiply(sk_c8,sk_c9),sk_c10)**.
% 0.20/0.54 2014[3:MRR:34.0,2007.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.54 2015[3:MRR:33.0,2007.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.20/0.54 2016[3:MRR:30.0,2007.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.54 2040[3:SpR:2014.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.20/0.54 2042[3:Rew:2011.0,2040.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.20/0.54 2044[3:SpR:2015.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c11),sk_c10)**.
% 0.20/0.54 2046[3:Rew:2008.0,2044.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.20/0.54 2048[3:SpR:2016.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c10)**.
% 0.20/0.54 2050[3:Rew:2009.0,2048.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.54 2056[3:SpR:2042.0,102.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.20/0.55 2058[3:Rew:57.0,2056.0] || -> equal(identity,sk_c10)**.
% 0.20/0.55 2059[3:Rew:2058.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.55 2060[3:Rew:2058.0,160.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.55 2061[3:Rew:2058.0,57.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.20/0.55 2063[3:Rew:2059.0,2050.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.55 2070[3:Rew:2063.0,2013.0] || -> equal(multiply(sk_c8,sk_c10),sk_c10)**.
% 0.20/0.55 2072[3:Rew:2063.0,668.4] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c11)** equal(multiply(v,sk_c10),sk_c10)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.20/0.55 2075[3:Rew:2060.0,2015.0] || -> equal(sk_c6,sk_c11)**.
% 0.20/0.55 2076[3:Rew:2075.0,2008.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.20/0.55 2078[3:Rew:2060.0,2070.0] || -> equal(sk_c8,sk_c10)**.
% 0.20/0.55 2079[3:Rew:2078.0,2011.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.20/0.55 2080[3:Rew:2078.0,2014.0] || -> equal(multiply(sk_c7,sk_c10),sk_c10)**.
% 0.20/0.55 2082[3:Rew:2060.0,2080.0] || -> equal(sk_c7,sk_c10)**.
% 0.20/0.55 2083[3:Rew:2082.0,2079.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.55 2092[3:Rew:2060.0,2072.4,2060.0,2072.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c11) equal(u,sk_c11) equal(v,sk_c10) equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.20/0.55 2134[3:SpR:670.0,2061.0] || -> equal(multiply(sk_c11,sk_c1),sk_c10)**.
% 0.20/0.55 2142[3:SpR:2134.0,102.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c1)**.
% 0.20/0.55 2144[3:Rew:2060.0,2142.0,2076.0,2142.0] || -> equal(sk_c11,sk_c1)**.
% 0.20/0.55 2145[3:Rew:2144.0,670.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.55 2150[3:Rew:2144.0,2046.0] || -> equal(multiply(sk_c1,sk_c1),sk_c10)**.
% 0.20/0.55 2156[3:Rew:2144.0,2092.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c11) equal(u,sk_c11) equal(v,sk_c10) equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.20/0.55 2160[3:Rew:2144.0,2156.5,2144.0,2156.3,2144.0,2156.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c1) equal(u,sk_c1) equal(v,sk_c10) equal(multiply(w,sk_c1),sk_c10)**+ -> .
% 0.20/0.55 2194[3:SpL:2150.0,2160.5] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(v,sk_c10) equal(sk_c10,sk_c10) -> .
% 0.20/0.55 2195[3:Obv:2194.5] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(v,sk_c10) -> .
% 0.20/0.55 2196[3:Rew:2145.0,2195.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c10)** equal(sk_c1,sk_c1) equal(u,sk_c1) equal(v,sk_c10) -> .
% 0.20/0.55 2197[3:Obv:2196.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c10)** equal(u,sk_c1) equal(v,sk_c10) -> .
% 0.20/0.55 2407[3:SpL:2145.0,2197.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c10)** equal(sk_c1,sk_c1) equal(u,sk_c10) -> .
% 0.20/0.55 2410[3:Obv:2407.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.20/0.55 2411[3:SpL:2083.0,2410.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.20/0.55 2414[3:Obv:2411.1] || -> .
% 0.20/0.55 2416[2:Spt:2414.0,17.1,670.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.20/0.55 2417[2:Spt:2414.0,17.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.20/0.55 2418[2:MRR:14.1,2416.0] || -> equal(inverse(sk_c6),sk_c11)**.
% 0.20/0.55 2419[2:MRR:13.1,2416.0] || -> equal(inverse(sk_c5),sk_c10)**.
% 0.20/0.55 2423[2:MRR:16.0,2416.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.20/0.55 2424[2:MRR:15.0,2416.0] || -> equal(multiply(sk_c6,sk_c10),sk_c11)**.
% 0.20/0.55 2425[2:MRR:12.0,2416.0] || -> equal(multiply(sk_c5,sk_c10),sk_c9)**.
% 0.20/0.55 2447[2:SpR:2423.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.20/0.55 2449[2:Rew:2417.0,2447.0] || -> equal(multiply(sk_c8,sk_c10),sk_c8)**.
% 0.20/0.55 2451[2:SpR:2424.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c11),sk_c10)**.
% 0.20/0.55 2453[2:Rew:2418.0,2451.0] || -> equal(multiply(sk_c11,sk_c11),sk_c10)**.
% 0.20/0.55 2455[2:SpR:2425.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c10)**.
% 0.20/0.55 2457[2:Rew:2419.0,2455.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.55 2463[2:SpR:2449.0,102.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c10)**.
% 0.20/0.55 2465[2:Rew:57.0,2463.0] || -> equal(identity,sk_c10)**.
% 0.20/0.55 2466[2:Rew:2465.0,160.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.20/0.55 2467[2:Rew:2465.0,56.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.55 2470[2:Rew:2466.0,2425.0] || -> equal(sk_c9,sk_c5)**.
% 0.20/0.55 2471[2:Rew:2466.0,2424.0] || -> equal(sk_c6,sk_c11)**.
% 0.20/0.55 2473[2:Rew:2466.0,668.4] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c10)** equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c11)** equal(v,sk_c9) equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.20/0.55 2478[2:Rew:2470.0,2457.0] || -> equal(multiply(sk_c10,sk_c5),sk_c10)**.
% 0.20/0.55 2479[2:Rew:2471.0,2418.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.20/0.55 2486[2:Rew:2467.0,2478.0] || -> equal(sk_c5,sk_c10)**.
% 0.20/0.55 2487[2:Rew:2486.0,2419.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.55 2488[2:Rew:2486.0,2470.0] || -> equal(sk_c9,sk_c10)**.
% 0.20/0.55 2506[2:Rew:2488.0,2473.4,2466.0,2473.3] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c11) equal(u,sk_c11) equal(v,sk_c10) equal(multiply(w,sk_c11),sk_c10)**+ -> .
% 0.20/0.55 2557[2:SpL:2453.0,2506.5] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c10)** equal(inverse(sk_c11),sk_c11)** equal(u,sk_c11) equal(v,sk_c10) equal(sk_c10,sk_c10) -> .
% 0.20/0.55 2563[2:Obv:2557.5] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c10)** equal(inverse(sk_c11),sk_c11)** equal(u,sk_c11) equal(v,sk_c10) -> .
% 0.20/0.55 2564[2:Rew:2479.0,2563.2] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c10)** equal(sk_c11,sk_c11) equal(u,sk_c11) equal(v,sk_c10) -> .
% 0.20/0.55 2565[2:Obv:2564.2] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c10)** equal(u,sk_c11) equal(v,sk_c10) -> .
% 0.20/0.55 2847[2:SpL:2479.0,2565.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c10)** equal(sk_c11,sk_c11) equal(u,sk_c10) -> .
% 0.20/0.55 2851[2:Obv:2847.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.20/0.55 2854[2:SpL:2487.0,2851.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.20/0.55 2858[2:Obv:2854.1] || -> .
% 0.20/0.55 % SZS output end Refutation
% 0.20/0.55 Formulae used in the proof : prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_21 prove_this_22 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_50 prove_this_51 prove_this_55 left_identity left_inverse associativity
% 0.20/0.55
%------------------------------------------------------------------------------