TSTP Solution File: GRP230-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP230-1 : 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 11:46:26 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP230-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.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 07:18:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 932 clauses, backtracked 274 clauses, performed 9 splits and kept 729 clauses.
% 0.19/0.49 SPASS allocated 63778 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.03 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.07 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 5, length 358 :
% 0.19/0.49 % SZS output start Refutation
% 0.19/0.49 1[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.19/0.49 2[0:Inp] || -> equal(inverse(sk_c3),sk_c4)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.49 3[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 4[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 5[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.49 7[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c8)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.19/0.49 8[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.49 9[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.19/0.49 10[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.19/0.49 11[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.19/0.49 12[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.49 13[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 14[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 15[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 16[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c7),sk_c8).
% 0.19/0.49 17[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 18[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 19[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.19/0.49 20[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.49 21[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 22[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 23[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 24[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.49 25[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(inverse(y),sk_c8) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),z)* equal(multiply(v,sk_c7),sk_c8)** equal(multiply(x,sk_c7),sk_c8)** equal(multiply(y,sk_c7),sk_c8)** equal(multiply(sk_c8,z),sk_c7)** -> .
% 0.19/0.49 26[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.49 27[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.49 28[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.49 29[1:Spt:25.0,25.4,25.6] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.19/0.49 30[2:Spt:24.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.49 32[3:Spt:2.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 35[1:SpL:26.0,29.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.49 36[4:Spt:14.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 47[2:SpR:30.0,27.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.19/0.49 48[3:SpR:32.0,27.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.19/0.49 51[2:SpL:47.0,29.1] || equal(inverse(sk_c7),sk_c2) equal(sk_c8,identity) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 52[4:Rew:36.0,51.2] || equal(inverse(sk_c7),sk_c2)** equal(sk_c8,identity) equal(sk_c8,sk_c8) -> .
% 0.19/0.49 53[4:Obv:52.2] || equal(inverse(sk_c7),sk_c2)** equal(sk_c8,identity) -> .
% 0.19/0.49 59[0:SpR:27.0,28.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.49 60[2:SpR:47.0,28.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.49 62[2:Rew:26.0,60.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.19/0.49 63[0:Rew:26.0,59.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.49 73[4:SpR:36.0,62.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.49 87[0:SpR:63.0,63.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.49 92[0:SpR:27.0,63.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.49 93[2:SpR:47.0,63.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c2)**.
% 0.19/0.49 95[4:SpR:73.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.49 97[3:SpR:48.0,63.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.19/0.49 104[4:Rew:27.0,95.0] || -> equal(sk_c8,identity)**.
% 0.19/0.49 110[4:Rew:104.0,48.0] || -> equal(multiply(identity,sk_c1),identity)**.
% 0.19/0.49 118[4:Rew:104.0,53.1] || equal(inverse(sk_c7),sk_c2)** equal(identity,identity) -> .
% 0.19/0.49 125[4:Rew:26.0,110.0] || -> equal(identity,sk_c1)**.
% 0.19/0.49 130[4:Rew:125.0,93.0] || -> equal(multiply(inverse(sk_c7),sk_c1),sk_c2)**.
% 0.19/0.49 150[4:Rew:125.0,92.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.19/0.49 157[4:Rew:87.0,150.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.49 161[4:Obv:118.1] || equal(inverse(sk_c7),sk_c2)** -> .
% 0.19/0.49 188[4:Rew:157.0,130.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.49 189[4:MRR:188.0,161.0] || -> .
% 0.19/0.49 234[4:Spt:189.0,14.1,36.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 235[4:Spt:189.0,14.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.19/0.49 236[0:Rew:87.0,92.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.49 237[3:Rew:236.0,97.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.19/0.49 238[2:Rew:236.0,93.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.49 241[4:MRR:18.1,234.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 242[4:MRR:17.1,234.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 243[4:MRR:16.1,234.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 244[4:MRR:15.1,234.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 245[4:MRR:13.1,234.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.19/0.49 259[2:SpR:238.0,63.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),u)**.
% 0.19/0.49 274[4:SpR:242.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 276[4:Rew:241.0,274.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 277[4:Rew:243.0,276.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 279[4:Rew:277.0,237.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.49 283[4:Rew:277.0,234.0] || equal(multiply(sk_c2,sk_c7),sk_c7)** -> .
% 0.19/0.49 285[4:Rew:277.0,243.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 286[4:Rew:277.0,244.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 287[4:Rew:277.0,245.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.19/0.49 298[4:Rew:238.0,279.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.49 300[4:Rew:298.0,238.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.49 304[4:Rew:298.0,283.0] || equal(multiply(sk_c1,sk_c7),sk_c7)** -> .
% 0.19/0.49 332[4:SpR:285.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 334[4:Rew:300.0,332.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.49 335[4:Rew:334.0,304.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.49 337[4:SpR:286.0,63.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 340[4:SpR:287.0,63.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.19/0.49 342[4:Rew:286.0,340.0,235.0,340.0] || -> equal(sk_c7,sk_c4)**.
% 0.19/0.49 346[4:Rew:342.0,300.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.19/0.49 350[4:Rew:342.0,335.0] || equal(sk_c6,sk_c4)** -> .
% 0.19/0.49 364[4:Rew:342.0,334.0] || -> equal(multiply(sk_c1,sk_c4),sk_c6)**.
% 0.19/0.49 366[4:Rew:342.0,337.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c4)**.
% 0.19/0.49 367[4:Rew:364.0,366.0,346.0,366.0] || -> equal(sk_c6,sk_c4)**.
% 0.19/0.49 368[4:MRR:367.0,350.0] || -> .
% 0.19/0.49 376[3:Spt:368.0,2.1,32.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.49 377[3:Spt:368.0,2.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.19/0.49 378[3:MRR:6.1,376.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 379[3:MRR:5.0,376.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 380[3:MRR:4.0,376.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 381[3:MRR:3.0,376.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 382[3:MRR:1.0,376.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.19/0.49 383[2:Rew:238.0,51.0] || equal(sk_c2,sk_c2) equal(sk_c8,identity) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 384[2:Obv:383.0] || equal(sk_c8,identity) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 399[3:SpR:379.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 401[3:Rew:378.0,399.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 402[3:Rew:380.0,401.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 406[3:Rew:402.0,380.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 407[3:Rew:402.0,381.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 408[3:Rew:402.0,382.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.19/0.49 410[3:Rew:402.0,384.0] || equal(identity,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 418[3:Rew:402.0,410.1] || equal(identity,sk_c7) equal(multiply(sk_c2,sk_c7),sk_c7)** -> .
% 0.19/0.49 433[3:SpR:406.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 435[3:Rew:238.0,433.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.19/0.49 436[3:Rew:435.0,418.1] || equal(identity,sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.49 438[3:SpR:407.0,63.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 440[3:SpR:408.0,28.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),multiply(sk_c7,u))**.
% 0.19/0.49 441[3:SpR:408.0,63.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.19/0.49 443[3:Rew:407.0,441.0,377.0,441.0] || -> equal(sk_c7,sk_c4)**.
% 0.19/0.49 444[3:Rew:443.0,238.0] || -> equal(inverse(sk_c4),sk_c2)**.
% 0.19/0.49 446[3:Rew:443.0,47.0] || -> equal(multiply(sk_c4,sk_c2),identity)**.
% 0.19/0.49 454[3:Rew:443.0,259.0] || -> equal(multiply(sk_c2,multiply(sk_c4,u)),u)**.
% 0.19/0.49 459[3:Rew:443.0,436.0] || equal(identity,sk_c4)** equal(sk_c6,sk_c7) -> .
% 0.19/0.49 466[3:Rew:443.0,435.0] || -> equal(multiply(sk_c2,sk_c4),sk_c6)**.
% 0.19/0.49 468[3:Rew:443.0,438.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c4)**.
% 0.19/0.49 469[3:Rew:466.0,468.0,444.0,468.0] || -> equal(sk_c6,sk_c4)**.
% 0.19/0.49 472[3:Rew:469.0,466.0] || -> equal(multiply(sk_c2,sk_c4),sk_c4)**.
% 0.19/0.49 473[3:Rew:469.0,459.1,443.0,459.1] || equal(identity,sk_c4)** equal(sk_c4,sk_c4) -> .
% 0.19/0.49 474[3:Obv:473.1] || equal(identity,sk_c4)** -> .
% 0.19/0.49 475[3:Rew:443.0,440.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),multiply(sk_c4,u))**.
% 0.19/0.49 512[3:SpR:472.0,28.0] || -> equal(multiply(sk_c2,multiply(sk_c4,u)),multiply(sk_c4,u))**.
% 0.19/0.49 516[3:Rew:454.0,512.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.49 517[3:Rew:516.0,446.0] || -> equal(identity,sk_c2)**.
% 0.19/0.49 521[3:Rew:516.0,475.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.49 524[3:Rew:517.0,474.0] || equal(sk_c2,sk_c4)** -> .
% 0.19/0.49 526[3:Rew:517.0,27.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.49 543[3:SpR:377.0,526.0] || -> equal(multiply(sk_c4,sk_c3),sk_c2)**.
% 0.19/0.49 545[3:SpR:444.0,526.0] || -> equal(multiply(sk_c2,sk_c4),sk_c2)**.
% 0.19/0.49 547[3:Rew:516.0,543.0] || -> equal(sk_c2,sk_c3)**.
% 0.19/0.49 551[3:Rew:547.0,524.0] || equal(sk_c4,sk_c3)** -> .
% 0.19/0.49 559[3:Rew:521.0,545.0,547.0,545.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.49 560[3:MRR:559.0,551.0] || -> .
% 0.19/0.49 566[2:Spt:560.0,24.1,30.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.19/0.49 567[2:Spt:560.0,24.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 568[2:MRR:20.1,566.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.19/0.49 569[2:MRR:23.0,566.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 570[2:MRR:22.0,566.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 571[2:MRR:21.0,566.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 572[2:MRR:19.0,566.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.19/0.49 578[2:SpR:569.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 580[2:Rew:567.0,578.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 581[2:Rew:570.0,580.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 584[2:Rew:581.0,570.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 585[2:Rew:581.0,571.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 586[2:Rew:581.0,572.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.19/0.49 587[2:Rew:581.0,35.1] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.49 594[2:Rew:581.0,587.2] || equal(inverse(identity),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 607[2:SpR:584.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 609[2:Rew:27.0,607.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 611[2:Rew:609.0,236.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.49 613[2:Rew:609.0,594.0] || equal(inverse(sk_c6),u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 614[2:Rew:609.0,27.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.49 620[2:SpR:585.0,63.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 623[2:SpR:586.0,63.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.19/0.49 625[2:Rew:585.0,623.0,568.0,623.0] || -> equal(sk_c7,sk_c4)**.
% 0.19/0.49 631[2:Rew:625.0,586.0] || -> equal(multiply(sk_c3,sk_c4),sk_c4)**.
% 0.19/0.49 638[2:Rew:625.0,613.1] || equal(inverse(sk_c6),u) equal(u,sk_c4) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 640[2:Rew:625.0,620.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c4)**.
% 0.19/0.49 641[2:Rew:614.0,640.0] || -> equal(sk_c6,sk_c4)**.
% 0.19/0.49 644[2:Rew:641.0,611.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.49 649[2:Rew:644.0,631.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.49 650[2:Rew:649.0,568.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.19/0.49 651[2:Rew:649.0,625.0] || -> equal(sk_c7,sk_c3)**.
% 0.19/0.49 655[2:Rew:649.0,641.0] || -> equal(sk_c6,sk_c3)**.
% 0.19/0.49 658[2:Rew:649.0,644.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.49 668[2:Rew:658.0,638.2,651.0,638.2,649.0,638.1,650.0,638.0,655.0,638.0] || equal(sk_c3,u)* equal(u,sk_c3)* equal(u,sk_c3)* -> .
% 0.19/0.49 669[2:Obv:668.1] || equal(u,sk_c3)* -> .
% 0.19/0.49 670[2:UnC:669.0,63.0] || -> .
% 0.19/0.49 676[1:Spt:670.0,25.1,25.2,25.3,25.5,25.7,25.8,25.9] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),x)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,x),sk_c7)** -> .
% 0.19/0.49 677[1:EqR:676.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.49 679[2:Spt:6.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 680[2:SpR:679.0,63.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.19/0.49 682[3:Spt:20.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.49 683[3:SpR:682.0,63.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.19/0.49 685[4:Spt:8.1] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.49 687[4:SpR:685.0,63.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.19/0.49 689[4:Rew:679.0,687.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.49 691[4:SpR:689.0,63.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.49 694[5:Spt:18.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.49 696[5:SpR:694.0,63.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c7)**.
% 0.19/0.49 698[5:Rew:682.0,696.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.49 700[5:SpR:698.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.19/0.49 703[5:Rew:27.0,700.0] || -> equal(sk_c8,identity)**.
% 0.19/0.49 705[5:Rew:703.0,679.0] || -> equal(inverse(sk_c1),identity)**.
% 0.19/0.49 706[5:Rew:703.0,685.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.19/0.49 707[5:Rew:703.0,689.0] || -> equal(multiply(identity,identity),sk_c7)**.
% 0.19/0.49 710[5:Rew:703.0,677.0] || equal(inverse(u),identity) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.49 718[5:Rew:26.0,707.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 719[5:Rew:718.0,236.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 720[5:Rew:718.0,26.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 723[5:Rew:718.0,703.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 724[5:Rew:718.0,705.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.49 725[5:Rew:718.0,706.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.49 731[5:Rew:719.0,725.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.49 732[5:Rew:731.0,718.0] || -> equal(identity,sk_c1)**.
% 0.19/0.49 733[5:Rew:731.0,723.0] || -> equal(sk_c8,sk_c1)**.
% 0.19/0.49 734[5:Rew:731.0,724.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.49 735[5:Rew:731.0,719.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.49 738[5:Rew:731.0,720.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.49 748[5:Rew:735.0,710.5,738.0,710.5,733.0,710.5,731.0,710.5,735.0,710.4,731.0,710.4,733.0,710.4,735.0,710.3,731.0,710.3,733.0,710.3,733.0,710.2,731.0,710.1,732.0,710.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(v,sk_c1) equal(w,sk_c1) equal(u,sk_c1) -> .
% 0.19/0.49 749[5:Con:748.0] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.49 816[5:SpL:734.0,749.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.49 818[5:Obv:816.1] || -> .
% 0.19/0.49 819[5:Spt:818.0,18.1,694.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.49 820[5:Spt:818.0,18.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 822[5:MRR:17.1,819.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 823[5:MRR:16.1,819.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 824[5:MRR:15.1,819.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 842[5:SpR:822.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 844[5:Rew:820.0,842.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 845[5:Rew:823.0,844.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 849[5:Rew:845.0,685.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.49 851[5:Rew:845.0,691.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.49 852[5:Rew:845.0,819.0] || equal(multiply(sk_c2,sk_c7),sk_c7)** -> .
% 0.19/0.49 857[5:Rew:845.0,824.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 864[5:Rew:27.0,851.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 865[5:Rew:864.0,26.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 866[5:Rew:864.0,236.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 870[5:Rew:865.0,683.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.49 872[5:Rew:866.0,857.0] || -> equal(sk_c7,sk_c4)**.
% 0.19/0.49 873[5:Rew:866.0,849.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.49 883[5:Rew:872.0,873.0] || -> equal(sk_c4,sk_c1)**.
% 0.19/0.49 886[5:Rew:883.0,872.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.49 901[5:Rew:870.0,852.0,886.0,852.0] || equal(sk_c1,sk_c1)* -> .
% 0.19/0.49 902[5:Obv:901.0] || -> .
% 0.19/0.49 919[4:Spt:902.0,8.1,685.0] || equal(multiply(sk_c1,sk_c7),sk_c8)** -> .
% 0.19/0.49 920[4:Spt:902.0,8.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.19/0.49 921[4:MRR:12.1,919.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 922[4:MRR:11.1,919.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 923[4:MRR:10.1,919.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 924[4:MRR:9.1,919.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 925[4:MRR:7.1,919.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.19/0.49 935[4:SpR:922.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 937[4:Rew:921.0,935.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 938[4:Rew:923.0,937.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 939[4:Rew:938.0,679.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.49 942[4:Rew:938.0,919.0] || equal(multiply(sk_c1,sk_c7),sk_c7)** -> .
% 0.19/0.49 944[4:Rew:938.0,923.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 945[4:Rew:938.0,924.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 946[4:Rew:938.0,925.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.19/0.49 968[4:SpR:944.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 970[4:Rew:27.0,968.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 971[4:Rew:970.0,236.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.49 972[4:Rew:970.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 973[4:Rew:970.0,27.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.49 978[4:SpR:945.0,63.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 982[4:SpR:946.0,63.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.19/0.49 984[4:Rew:945.0,982.0,920.0,982.0] || -> equal(sk_c7,sk_c4)**.
% 0.19/0.49 988[4:Rew:984.0,939.0] || -> equal(inverse(sk_c1),sk_c4)**.
% 0.19/0.49 991[4:Rew:984.0,946.0] || -> equal(multiply(sk_c3,sk_c4),sk_c4)**.
% 0.19/0.49 993[4:Rew:984.0,942.0] || equal(multiply(sk_c1,sk_c4),sk_c4)** -> .
% 0.19/0.49 1001[4:Rew:984.0,978.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c4)**.
% 0.19/0.49 1002[4:Rew:973.0,1001.0] || -> equal(sk_c6,sk_c4)**.
% 0.19/0.49 1004[4:Rew:1002.0,971.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.49 1005[4:Rew:1002.0,972.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.49 1006[4:Rew:1002.0,973.0] || -> equal(multiply(inverse(u),u),sk_c4)**.
% 0.19/0.49 1009[4:Rew:1004.0,993.0] || equal(sk_c4,sk_c1)** -> .
% 0.19/0.49 1010[4:Rew:1004.0,991.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.49 1017[4:Rew:1010.0,988.0] || -> equal(inverse(sk_c1),sk_c3)**.
% 0.19/0.49 1021[4:Rew:1010.0,1009.0] || equal(sk_c3,sk_c1)** -> .
% 0.19/0.49 1022[4:Rew:1010.0,1005.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.49 1026[4:Rew:1010.0,1006.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.49 1071[4:SpR:1017.0,1026.0] || -> equal(multiply(sk_c3,sk_c1),sk_c3)**.
% 0.19/0.49 1075[4:Rew:1022.0,1071.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.49 1076[4:MRR:1075.0,1021.0] || -> .
% 0.19/0.49 1080[3:Spt:1076.0,20.1,682.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.19/0.49 1081[3:Spt:1076.0,20.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.19/0.49 1082[3:MRR:24.1,1080.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 1083[3:MRR:23.0,1080.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 1084[3:MRR:22.0,1080.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 1085[3:MRR:21.0,1080.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 1086[3:MRR:19.0,1080.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.19/0.49 1087[3:SpR:1081.0,63.0] || -> equal(multiply(sk_c4,multiply(sk_c3,u)),u)**.
% 0.19/0.49 1094[3:SpR:1083.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 1096[3:Rew:1082.0,1094.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 1097[3:Rew:1084.0,1096.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 1101[3:Rew:1097.0,680.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.49 1102[3:Rew:1097.0,1084.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 1103[3:Rew:1097.0,1085.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 1104[3:Rew:1097.0,1086.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.19/0.49 1106[3:Rew:1097.0,677.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.49 1110[3:Rew:1097.0,1106.5,1097.0,1106.4,1097.0,1106.3,1097.0,1106.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.19/0.49 1111[3:Con:1110.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.19/0.49 1126[3:SpR:1102.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 1128[3:Rew:27.0,1126.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 1129[3:Rew:1128.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 1130[3:Rew:1128.0,236.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.49 1132[3:Rew:1128.0,27.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.49 1136[3:SpR:1103.0,63.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 1140[3:SpR:1104.0,63.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.19/0.49 1142[3:Rew:1103.0,1140.0,1081.0,1140.0] || -> equal(sk_c7,sk_c4)**.
% 0.19/0.49 1149[3:Rew:1142.0,1104.0] || -> equal(multiply(sk_c3,sk_c4),sk_c4)**.
% 0.19/0.49 1150[3:Rew:1142.0,1101.0] || -> equal(multiply(sk_c4,multiply(sk_c1,u)),u)**.
% 0.19/0.49 1153[3:Rew:1142.0,1111.0] || equal(inverse(u),sk_c4) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.19/0.49 1157[3:Rew:1142.0,1136.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c4)**.
% 0.19/0.49 1158[3:Rew:1132.0,1157.0] || -> equal(sk_c6,sk_c4)**.
% 0.19/0.49 1160[3:Rew:1158.0,1129.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.49 1161[3:Rew:1158.0,1130.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.49 1165[3:Rew:1160.0,1087.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.49 1166[3:Rew:1161.0,1149.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.49 1167[3:Rew:1166.0,1081.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.19/0.49 1168[3:Rew:1166.0,1142.0] || -> equal(sk_c7,sk_c3)**.
% 0.19/0.49 1176[3:Rew:1166.0,1161.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.49 1182[3:Rew:1165.0,1150.0,1166.0,1150.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.49 1187[3:Rew:1176.0,1153.3,1165.0,1153.3,1168.0,1153.3,1176.0,1153.2,1168.0,1153.2,1168.0,1153.1,1166.0,1153.0] || equal(inverse(u),sk_c3)** equal(inverse(v),sk_c3)** equal(v,sk_c3) equal(u,sk_c3) -> .
% 0.19/0.49 1188[3:Con:1187.0] || equal(inverse(u),sk_c3)** equal(u,sk_c3) -> .
% 0.19/0.49 1216[3:SpR:1182.0,1176.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.49 1224[3:Rew:1216.0,1167.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.49 1230[3:Rew:1216.0,1188.0] || equal(inverse(u),sk_c1)** equal(u,sk_c3) -> .
% 0.19/0.49 1232[3:Rew:1216.0,1230.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.49 1288[3:SpL:1224.0,1232.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.49 1290[3:Obv:1288.1] || -> .
% 0.19/0.49 1291[2:Spt:1290.0,6.1,679.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.49 1292[2:Spt:1290.0,6.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 1293[2:MRR:2.1,1291.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.19/0.49 1294[2:MRR:5.0,1291.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 1295[2:MRR:4.0,1291.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 1296[2:MRR:3.0,1291.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 1297[2:MRR:1.0,1291.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.19/0.49 1303[2:SpR:1294.0,63.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 1305[2:Rew:1292.0,1303.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.49 1306[2:Rew:1295.0,1305.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 1310[2:Rew:1306.0,1295.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.49 1311[2:Rew:1306.0,1296.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.49 1312[2:Rew:1306.0,1297.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.19/0.49 1314[2:Rew:1306.0,677.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.19/0.49 1318[2:Rew:1306.0,1314.5,1306.0,1314.4,1306.0,1314.3,1306.0,1314.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.19/0.49 1319[2:Con:1318.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.19/0.49 1332[2:SpR:1310.0,63.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 1334[2:Rew:27.0,1332.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 1335[2:Rew:1334.0,236.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.49 1336[2:Rew:1334.0,26.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.49 1337[2:Rew:1334.0,27.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.49 1343[2:SpR:1311.0,63.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c7)**.
% 0.19/0.49 1346[2:SpR:1312.0,63.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.19/0.49 1348[2:Rew:1311.0,1346.0,1293.0,1346.0] || -> equal(sk_c7,sk_c4)**.
% 0.19/0.49 1354[2:Rew:1348.0,1312.0] || -> equal(multiply(sk_c3,sk_c4),sk_c4)**.
% 0.19/0.49 1357[2:Rew:1348.0,1319.0] || equal(inverse(u),sk_c4) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.19/0.49 1361[2:Rew:1348.0,1343.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c4)**.
% 0.19/0.49 1362[2:Rew:1337.0,1361.0] || -> equal(sk_c6,sk_c4)**.
% 0.19/0.49 1364[2:Rew:1362.0,1335.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.49 1365[2:Rew:1362.0,1336.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.49 1369[2:Rew:1364.0,1354.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.49 1370[2:Rew:1369.0,1293.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.19/0.49 1372[2:Rew:1369.0,1348.0] || -> equal(sk_c7,sk_c3)**.
% 0.19/0.49 1378[2:Rew:1369.0,1364.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.49 1379[2:Rew:1369.0,1365.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.49 1390[2:Rew:1378.0,1357.3,1379.0,1357.3,1372.0,1357.3,1378.0,1357.2,1372.0,1357.2,1372.0,1357.1,1369.0,1357.0] || equal(inverse(u),sk_c3)** equal(inverse(v),sk_c3)** equal(v,sk_c3) equal(u,sk_c3) -> .
% 0.19/0.49 1391[2:Con:1390.0] || equal(inverse(u),sk_c3)** equal(u,sk_c3) -> .
% 0.19/0.49 1421[2:SpL:1370.0,1391.0] || equal(sk_c3,sk_c3)* equal(sk_c3,sk_c3)* -> .
% 0.19/0.49 1422[2:Obv:1421.1] || -> .
% 0.19/0.49 % SZS output end Refutation
% 0.19/0.49 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_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 left_identity left_inverse associativity
% 0.19/0.49
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