TSTP Solution File: GRP289-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP289-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:46:42 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP289-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 14:10:08 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 763 clauses, backtracked 360 clauses, performed 12 splits and kept 692 clauses.
% 0.21/0.48 SPASS allocated 63582 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.21/0.48 0:00:00.03 for the input.
% 0.21/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.00 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.06 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 5, length 349 :
% 0.21/0.48 % SZS output start Refutation
% 0.21/0.48 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.48 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.48 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.21/0.48 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 8[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 10[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.48 12[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.48 14[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.48 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 21[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.48 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 25[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.48 26[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.48 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.48 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.48 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.48 30[1:Spt:26.2,26.6] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c5)** -> .
% 0.21/0.48 31[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.48 33[3:Spt:4.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.48 35[4:Spt:2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.48 38[1:SpL:27.0,30.1] || equal(inverse(identity),sk_c6)** equal(sk_c5,sk_c6) -> .
% 0.21/0.48 39[5:Spt:5.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.48 41[6:Spt:3.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.21/0.48 43[6:SpL:41.0,30.1] || equal(inverse(sk_c3),sk_c6)** equal(sk_c5,sk_c7) -> .
% 0.21/0.48 44[6:Rew:35.0,43.0] || equal(sk_c6,sk_c7) equal(sk_c5,sk_c7)** -> .
% 0.21/0.48 46[3:SpR:33.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.21/0.48 47[4:SpR:35.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.21/0.48 48[1:SpL:28.0,30.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c5) -> .
% 0.21/0.48 55[3:SpR:46.0,29.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.21/0.48 57[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.48 58[5:SpR:39.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.21/0.48 59[4:SpR:47.0,29.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.21/0.48 61[3:Rew:27.0,55.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.21/0.48 62[4:Rew:27.0,59.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.21/0.48 63[0:Rew:27.0,57.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.48 67[5:SpR:39.0,61.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.48 75[6:SpR:41.0,62.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.48 78[0:SpR:63.0,63.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.48 81[2:SpR:31.0,63.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.21/0.48 82[3:SpR:46.0,63.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.21/0.48 84[5:SpR:67.0,63.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.21/0.48 86[0:SpR:28.0,63.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.48 88[4:SpR:47.0,63.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.21/0.48 94[5:Rew:81.0,84.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 96[5:Rew:94.0,31.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.48 104[5:Rew:94.0,38.0] || equal(inverse(identity),sk_c7)** equal(sk_c5,sk_c6) -> .
% 0.21/0.48 105[6:Rew:94.0,44.0] || equal(sk_c7,sk_c7) equal(sk_c5,sk_c7)** -> .
% 0.21/0.48 107[5:Rew:94.0,82.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.21/0.48 110[5:Rew:94.0,58.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.21/0.48 114[6:Rew:94.0,75.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.48 115[6:Rew:96.0,114.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 145[6:Obv:105.0] || equal(sk_c5,sk_c7)** -> .
% 0.21/0.48 146[6:Rew:115.0,145.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 147[6:Obv:146.0] || -> .
% 0.21/0.48 160[6:Spt:147.0,3.0,41.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.21/0.48 161[6:Spt:147.0,3.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 164[5:Rew:88.0,107.0] || -> equal(sk_c4,sk_c3)**.
% 0.21/0.48 168[6:Rew:94.0,160.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.21/0.48 169[0:Rew:78.0,86.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.48 170[4:Rew:169.0,88.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.21/0.48 179[5:Rew:94.0,13.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.48 180[6:MRR:179.1,168.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 181[5:Rew:94.0,104.1] || equal(inverse(identity),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.21/0.48 182[5:Rew:164.0,110.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.21/0.48 185[5:Rew:94.0,8.1,94.0,8.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.48 186[6:MRR:185.0,168.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.48 195[4:SpR:170.0,63.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.21/0.48 219[6:SpR:186.0,63.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.48 221[6:Rew:96.0,219.0,180.0,219.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 226[6:Rew:221.0,181.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.21/0.48 227[6:Rew:221.0,182.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.21/0.48 234[6:Obv:226.1] || equal(inverse(identity),sk_c7)** -> .
% 0.21/0.48 235[6:Rew:195.0,227.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.48 236[6:Rew:235.0,47.0] || -> equal(identity,sk_c3)**.
% 0.21/0.48 245[6:Rew:236.0,234.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.21/0.48 251[6:Rew:35.0,245.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 252[6:Obv:251.0] || -> .
% 0.21/0.48 254[5:Spt:252.0,5.0,39.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.21/0.48 255[5:Spt:252.0,5.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 256[3:Rew:169.0,82.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.21/0.48 257[3:Rew:256.0,81.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.21/0.48 258[5:Rew:257.0,254.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.48 260[3:Rew:257.0,25.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.21/0.48 261[5:MRR:260.1,258.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 262[3:Rew:257.0,15.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.21/0.48 263[5:MRR:262.1,258.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 264[3:Rew:257.0,20.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 265[5:MRR:264.0,258.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 266[3:Rew:257.0,10.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 267[5:MRR:266.0,258.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 276[3:SpR:256.0,63.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.21/0.48 283[5:SpR:265.0,63.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.21/0.48 285[5:Rew:261.0,283.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.48 300[3:SpR:257.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.21/0.48 305[5:SpR:267.0,63.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.21/0.48 307[5:Rew:255.0,305.0,263.0,305.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 311[5:Rew:307.0,31.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.21/0.48 321[5:Rew:307.0,285.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.21/0.48 322[5:Rew:311.0,321.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 323[5:MRR:322.0,258.0] || -> .
% 0.21/0.48 324[4:Spt:323.0,2.0,35.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.21/0.48 325[4:Spt:323.0,2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 326[4:MRR:22.0,324.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 327[4:MRR:12.0,324.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 328[4:MRR:17.0,324.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 329[4:MRR:7.0,324.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 346[4:SpR:328.0,63.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.21/0.48 348[4:Rew:326.0,346.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.48 350[4:SpR:329.0,63.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.21/0.48 352[4:Rew:325.0,350.0,327.0,350.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 356[4:Rew:352.0,31.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.21/0.48 358[4:Rew:352.0,38.1] || equal(inverse(identity),sk_c6)** equal(sk_c6,sk_c7) -> .
% 0.21/0.48 359[4:Rew:352.0,300.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.21/0.48 366[4:Rew:352.0,348.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.21/0.48 367[4:Rew:356.0,366.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 368[4:Rew:367.0,33.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.48 370[4:Rew:367.0,46.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.21/0.48 374[4:Rew:367.0,276.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.21/0.48 381[4:Rew:367.0,358.1,367.0,358.0] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.21/0.48 382[4:Obv:381.1] || equal(inverse(identity),sk_c7)** -> .
% 0.21/0.48 383[4:Rew:374.0,359.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.48 384[4:Rew:383.0,370.0] || -> equal(identity,sk_c4)**.
% 0.21/0.48 393[4:Rew:384.0,382.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.21/0.48 396[4:Rew:368.0,393.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 397[4:Obv:396.0] || -> .
% 0.21/0.48 404[3:Spt:397.0,4.0,33.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.21/0.48 405[3:Spt:397.0,4.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 406[3:MRR:24.0,404.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 407[3:MRR:14.0,404.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 408[3:MRR:19.0,404.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 409[3:MRR:9.0,404.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 421[3:SpR:408.0,63.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.21/0.48 423[3:Rew:406.0,421.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.48 425[3:SpR:409.0,63.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.21/0.48 427[3:Rew:405.0,425.0,407.0,425.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 429[3:Rew:427.0,31.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.21/0.48 430[3:Rew:427.0,408.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.48 431[3:Rew:427.0,81.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c7)**.
% 0.21/0.48 436[3:Rew:427.0,48.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c7) -> .
% 0.21/0.48 440[3:Rew:427.0,423.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.21/0.48 441[3:Rew:429.0,440.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 442[3:Rew:441.0,406.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.21/0.48 448[3:Rew:441.0,430.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.21/0.48 449[3:Rew:28.0,431.0,441.0,431.0] || -> equal(identity,sk_c7)**.
% 0.21/0.48 451[3:Rew:449.0,169.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 455[3:Rew:451.0,448.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.48 457[3:Rew:455.0,442.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 469[3:Rew:449.0,436.1,457.0,436.0,457.0,436.0,441.0,436.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 470[3:Obv:469.1] || -> .
% 0.21/0.48 473[2:Spt:470.0,1.0,31.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.21/0.48 474[2:Spt:470.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 475[2:MRR:21.1,473.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 476[2:MRR:11.1,473.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 477[2:MRR:16.0,473.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 478[2:MRR:6.0,473.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 480[2:SpR:474.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.21/0.48 482[2:SpR:475.0,63.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.21/0.48 484[2:SpR:476.0,63.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.21/0.48 487[2:SpR:477.0,63.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.21/0.48 489[2:Rew:475.0,487.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.48 491[2:SpR:478.0,63.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.21/0.48 493[2:Rew:474.0,491.0,476.0,491.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 495[2:Rew:493.0,477.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.48 496[2:Rew:493.0,473.0] || equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.21/0.48 501[2:Rew:493.0,480.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.21/0.48 504[2:Rew:493.0,489.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.21/0.48 505[2:Rew:504.0,496.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.48 506[2:Rew:28.0,501.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 507[2:Rew:506.0,169.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 508[2:Rew:506.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.48 511[2:Rew:507.0,495.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.48 513[2:Rew:511.0,482.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.21/0.48 516[2:Rew:508.0,513.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.48 517[2:Rew:516.0,484.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.48 518[2:Rew:517.0,478.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 519[2:MRR:518.0,505.0] || -> .
% 0.21/0.48 526[1:Spt:519.0,26.0,26.1,26.3,26.4,26.5,26.7,26.8,26.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c6),sk_c5) -> .
% 0.21/0.48 528[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.21/0.48 529[2:Rew:528.0,526.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.21/0.48 531[2:Obv:529.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.21/0.48 534[2:SpR:528.0,63.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.21/0.48 536[3:Spt:2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.48 538[3:Rew:536.0,531.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.21/0.48 539[3:Obv:538.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 542[3:SpR:536.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c6)**.
% 0.21/0.48 544[4:Spt:24.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.48 550[5:Spt:22.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.48 554[0:SpR:28.0,63.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.48 556[4:SpR:544.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.21/0.48 557[5:SpR:550.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.21/0.48 558[0:Rew:169.0,554.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.48 562[4:SpR:556.0,63.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.21/0.48 564[4:Rew:169.0,562.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.21/0.48 565[4:Rew:564.0,534.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.21/0.48 566[4:Rew:565.0,10.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 567[4:Rew:565.0,20.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 568[4:Rew:565.0,15.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.21/0.48 569[4:Rew:565.0,25.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.21/0.48 570[4:Rew:568.1,13.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.48 572[4:Rew:566.0,8.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 576[4:SpR:564.0,28.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.21/0.48 579[5:SpR:557.0,63.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.21/0.48 581[5:Rew:169.0,579.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.21/0.48 585[5:SpR:581.0,28.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.21/0.48 588[5:Rew:585.0,572.0] || -> equal(identity,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 590[5:Rew:585.0,570.1] || -> equal(inverse(sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.21/0.48 591[6:Spt:568.1] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 592[6:Rew:591.0,528.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.48 598[6:Rew:591.0,539.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 604[6:Rew:591.0,588.1] || -> equal(identity,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.48 615[6:Rew:591.0,598.5,591.0,598.4,591.0,598.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.21/0.48 616[6:Con:615.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.21/0.48 634[7:Spt:590.1] || -> equal(identity,sk_c7)**.
% 0.21/0.48 635[7:Rew:634.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.48 637[7:Rew:634.0,557.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.48 639[7:Rew:634.0,169.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 641[7:Rew:635.0,592.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 647[7:Rew:641.0,616.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.21/0.48 649[7:Rew:635.0,637.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.48 650[7:Rew:649.0,550.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 660[7:Con:647.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.21/0.48 661[7:Rew:639.0,660.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 675[0:SpR:558.0,63.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.21/0.48 702[7:SpL:650.0,661.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 704[7:Obv:702.1] || -> .
% 0.21/0.48 705[7:Spt:704.0,590.1,634.0] || equal(identity,sk_c7)** -> .
% 0.21/0.48 706[7:Spt:704.0,590.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 708[7:MRR:604.0,705.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.48 711[7:SpR:706.0,558.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.21/0.48 713[7:Rew:581.0,711.0] || -> equal(sk_c1,sk_c3)**.
% 0.21/0.48 715[7:Rew:713.0,708.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.48 716[7:Rew:585.0,715.0] || -> equal(identity,sk_c7)**.
% 0.21/0.48 717[7:MRR:716.0,705.0] || -> .
% 0.21/0.48 719[6:Spt:717.0,568.1,591.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.48 720[6:Spt:717.0,568.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 721[6:MRR:569.1,719.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 722[6:MRR:566.0,719.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 723[6:MRR:567.0,719.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 725[6:SpR:720.0,558.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.21/0.48 727[6:Rew:581.0,725.0] || -> equal(sk_c1,sk_c3)**.
% 0.21/0.48 729[6:Rew:727.0,722.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.48 730[6:Rew:585.0,729.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 732[6:Rew:730.0,557.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.21/0.48 733[6:Rew:730.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.48 734[6:Rew:730.0,169.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 743[6:Rew:733.0,528.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 747[6:Rew:743.0,723.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.21/0.48 757[6:Rew:734.0,747.0] || -> equal(sk_c2,sk_c7)**.
% 0.21/0.48 758[6:Rew:757.0,721.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.21/0.48 759[6:Rew:581.0,758.0] || -> equal(sk_c3,sk_c6)**.
% 0.21/0.48 766[6:Rew:759.0,732.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.21/0.48 771[6:Rew:734.0,766.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 772[6:MRR:771.0,719.0] || -> .
% 0.21/0.48 781[5:Spt:772.0,22.0,550.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.21/0.48 782[5:Spt:772.0,22.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 783[5:MRR:12.0,781.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 784[5:MRR:17.0,781.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 785[5:MRR:7.0,781.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 787[5:SpR:782.0,558.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.21/0.48 789[5:Rew:564.0,787.0] || -> equal(sk_c2,sk_c4)**.
% 0.21/0.48 791[5:Rew:789.0,784.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.21/0.48 792[5:Rew:576.0,791.0] || -> equal(identity,sk_c5)**.
% 0.21/0.48 795[5:Rew:792.0,169.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.21/0.48 800[5:Rew:795.0,542.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.21/0.48 802[5:Rew:795.0,539.3] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(u,sk_c6) equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 817[5:SpR:783.0,558.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.21/0.48 819[5:Rew:800.0,817.0] || -> equal(sk_c1,sk_c6)**.
% 0.21/0.48 821[5:Rew:819.0,785.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.21/0.48 822[5:Rew:528.0,821.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.48 825[5:Rew:822.0,536.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.21/0.48 826[5:Rew:822.0,795.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 830[5:Rew:826.0,825.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 831[5:Rew:826.0,802.4] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7) equal(u,sk_c6) equal(v,sk_c7) equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 832[5:Rew:830.0,800.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 840[5:Rew:830.0,826.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 847[5:Rew:840.0,831.5,830.0,831.5,830.0,831.3,830.0,831.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.21/0.48 848[5:Con:847.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 885[5:SpL:832.0,848.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 886[5:Obv:885.1] || -> .
% 0.21/0.48 887[4:Spt:886.0,24.0,544.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.21/0.48 888[4:Spt:886.0,24.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 889[4:MRR:14.0,887.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.48 890[4:MRR:19.0,887.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.48 891[4:MRR:9.0,887.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.48 893[4:SpR:888.0,558.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.21/0.48 900[4:SpR:893.0,63.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.21/0.48 914[4:SpR:890.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.21/0.48 915[4:SpR:890.0,63.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.21/0.48 917[4:Rew:888.0,915.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.21/0.48 918[4:Rew:900.0,914.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.48 922[4:SpR:891.0,63.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.21/0.48 924[4:Rew:536.0,922.0,889.0,922.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.48 926[4:Rew:924.0,528.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.21/0.48 928[4:Rew:924.0,539.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.21/0.48 932[4:Rew:924.0,917.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.21/0.48 933[4:Rew:924.0,918.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.48 934[4:Rew:926.0,932.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.48 957[4:Rew:934.0,928.5,934.0,928.4,934.0,928.3,934.0,928.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.21/0.48 958[4:Con:957.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.21/0.48 976[0:SpR:28.0,169.0] || -> equal(inverse(identity),identity)**.
% 0.21/0.48 979[4:SpR:889.0,28.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.21/0.48 982[4:Rew:933.0,979.0] || -> equal(identity,sk_c1)**.
% 0.21/0.48 984[4:Rew:982.0,169.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.21/0.48 986[4:Rew:982.0,976.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.21/0.48 987[4:Rew:889.0,986.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.48 988[4:Rew:987.0,889.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.48 996[4:Rew:987.0,984.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.48 997[4:Rew:996.0,958.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.48 1056[4:SpL:988.0,997.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.48 1057[4:Obv:1056.1] || -> .
% 0.21/0.48 1058[3:Spt:1057.0,2.1,536.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.21/0.48 1059[3:Spt:1057.0,2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.21/0.48 1061[3:MRR:4.1,1058.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.48 1064[3:MRR:5.1,1058.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.49 1076[3:SpR:1061.0,558.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.21/0.49 1079[3:Rew:1076.0,534.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.21/0.49 1080[3:Rew:1064.0,1079.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 1082[3:Rew:1080.0,528.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.21/0.49 1083[3:Rew:1080.0,1058.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.21/0.49 1091[3:Rew:1082.0,1083.0] || equal(sk_c5,sk_c5)* -> .
% 0.21/0.49 1092[3:Obv:1091.0] || -> .
% 0.21/0.49 1095[2:Spt:1092.0,1.0,528.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.21/0.49 1096[2:Spt:1092.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.21/0.49 1097[2:MRR:21.1,1095.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 1098[2:MRR:11.1,1095.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.49 1099[2:MRR:16.0,1095.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.21/0.49 1100[2:MRR:6.0,1095.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.21/0.49 1106[2:SpR:1097.0,675.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.21/0.49 1113[2:SpR:1099.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.21/0.49 1117[2:Rew:1106.0,1113.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.49 1128[2:SpR:1100.0,63.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.21/0.49 1130[2:Rew:1096.0,1128.0,1098.0,1128.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.49 1131[2:Rew:1130.0,1096.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.49 1133[2:Rew:1130.0,1095.0] || equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.21/0.49 1136[2:Rew:1130.0,1117.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.49 1137[2:Rew:1136.0,1131.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.49 1152[2:Rew:1136.0,1133.0,1137.0,1133.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.49 1153[2:Obv:1152.0] || -> .
% 0.21/0.49 % SZS output end Refutation
% 0.21/0.49 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_24 prove_this_25 prove_this_26 left_identity left_inverse associativity
% 0.21/0.49
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