TSTP Solution File: GRP324-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP324-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:46:51 EDT 2022
% Result : Unsatisfiable 0.22s 0.52s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : GRP324-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.15 % Command : run_spass %d %s
% 0.14/0.37 % Computer : n005.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Tue Jun 14 02:52:24 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.22/0.52
% 0.22/0.52 SPASS V 3.9
% 0.22/0.52 SPASS beiseite: Proof found.
% 0.22/0.52 % SZS status Theorem
% 0.22/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.52 SPASS derived 1096 clauses, backtracked 439 clauses, performed 13 splits and kept 809 clauses.
% 0.22/0.52 SPASS allocated 63774 KBytes.
% 0.22/0.52 SPASS spent 0:00:00.14 on the problem.
% 0.22/0.52 0:00:00.04 for the input.
% 0.22/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.52 0:00:00.01 for inferences.
% 0.22/0.52 0:00:00.00 for the backtracking.
% 0.22/0.52 0:00:00.07 for the reduction.
% 0.22/0.52
% 0.22/0.52
% 0.22/0.52 Here is a proof with depth 4, length 393 :
% 0.22/0.52 % SZS output start Refutation
% 0.22/0.52 1[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.22/0.52 2[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.22/0.52 3[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 4[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 5[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.22/0.52 6[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 7[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 9[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 10[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 11[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 12[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.22/0.52 15[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 16[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 17[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.52 18[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 19[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 20[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.22/0.52 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 22[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 23[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.22/0.52 24[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 25[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 26[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 28[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 29[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 30[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 31[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.22/0.52 32[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.22/0.52 33[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 34[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 35[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.52 36[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 37[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(inverse(sk_c8),sk_c6) equal(multiply(w,sk_c8),y)*+ equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.52 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.22/0.52 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.22/0.52 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.22/0.52 41[1:Spt:37.0,37.6] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.22/0.52 42[2:Spt:4.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.22/0.52 44[3:Spt:1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.22/0.52 46[3:SpL:44.0,41.1] || equal(inverse(sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.22/0.52 47[3:Obv:46.1] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.22/0.52 48[3:Rew:42.0,47.0] || equal(sk_c6,sk_c7)** -> .
% 0.22/0.52 49[4:Spt:6.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.22/0.52 53[5:Spt:5.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.52 55[5:SpL:53.0,41.1] || equal(inverse(sk_c5),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.22/0.52 56[5:Obv:55.1] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.22/0.52 57[5:Rew:49.0,56.0] || equal(sk_c7,sk_c7)* -> .
% 0.22/0.52 58[5:Obv:57.0] || -> .
% 0.22/0.52 59[5:Spt:58.0,5.0,53.0] || equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.22/0.52 60[5:Spt:58.0,5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 62[5:MRR:17.1,59.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 65[5:MRR:11.0,59.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 78[2:SpR:42.0,39.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.22/0.52 82[5:SpR:62.0,39.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.22/0.52 94[2:SpR:78.0,40.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.22/0.52 99[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.22/0.52 102[2:Rew:38.0,94.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.22/0.52 106[0:Rew:38.0,99.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.22/0.52 109[5:SpR:82.0,40.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.22/0.52 110[5:Rew:38.0,109.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.22/0.52 113[3:SpR:44.0,102.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.22/0.52 205[5:SpR:65.0,110.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.22/0.52 206[5:Rew:60.0,205.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 207[5:MRR:206.0,48.0] || -> .
% 0.22/0.52 209[4:Spt:207.0,6.0,49.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.22/0.52 210[4:Spt:207.0,6.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 211[4:MRR:36.0,209.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 212[4:MRR:18.0,209.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 213[4:MRR:30.0,209.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 214[4:MRR:24.0,209.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 215[4:MRR:12.0,209.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 243[4:SpR:211.0,39.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.22/0.52 244[4:SpR:212.0,39.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.22/0.52 254[0:SpR:106.0,106.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.22/0.52 262[4:SpR:213.0,106.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.52 263[4:SpR:214.0,106.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.22/0.52 264[4:SpR:243.0,106.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.22/0.52 265[0:SpR:38.0,106.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.22/0.52 266[0:SpR:39.0,106.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.22/0.52 267[4:SpR:244.0,106.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.22/0.52 274[4:Rew:214.0,262.0,211.0,262.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 275[4:Rew:274.0,42.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.22/0.52 278[4:Rew:274.0,78.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.22/0.52 280[4:Rew:274.0,213.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.22/0.52 282[4:Rew:274.0,215.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.52 295[4:Rew:278.0,263.0,275.0,263.0,274.0,263.0] || -> equal(identity,sk_c3)**.
% 0.22/0.52 301[4:Rew:275.0,264.0,274.0,264.0,295.0,264.0] || -> equal(multiply(sk_c6,sk_c3),sk_c2)**.
% 0.22/0.52 302[4:Rew:295.0,265.0] || -> equal(multiply(inverse(sk_c3),u),u)**.
% 0.22/0.52 303[4:Rew:301.0,267.0,275.0,267.0,295.0,267.0] || -> equal(sk_c2,sk_c1)**.
% 0.22/0.52 305[4:Rew:303.0,280.0] || -> equal(multiply(sk_c1,sk_c7),sk_c3)**.
% 0.22/0.52 308[4:Rew:282.0,305.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.52 314[4:Rew:308.0,302.0] || -> equal(multiply(inverse(sk_c7),u),u)**.
% 0.22/0.52 336[4:Rew:275.0,314.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.52 337[4:Rew:336.0,113.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 338[4:MRR:337.0,48.0] || -> .
% 0.22/0.52 358[3:Spt:338.0,1.0,44.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.22/0.52 359[3:Spt:338.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 360[0:Rew:254.0,266.0] || -> equal(multiply(u,identity),u)**.
% 0.22/0.52 362[3:MRR:31.1,358.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 364[3:MRR:25.0,358.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 365[3:MRR:19.0,358.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 379[3:SpR:364.0,106.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.52 381[3:Rew:362.0,379.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.52 382[3:Rew:365.0,381.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 383[3:Rew:382.0,359.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.52 389[3:Rew:382.0,358.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.22/0.52 398[3:Rew:383.0,389.0] || equal(sk_c6,sk_c6)* -> .
% 0.22/0.52 399[3:Obv:398.0] || -> .
% 0.22/0.52 404[2:Spt:399.0,4.0,42.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.22/0.52 405[2:Spt:399.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 406[2:MRR:34.0,404.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 407[2:MRR:16.0,404.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 408[2:MRR:28.0,404.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 409[2:MRR:22.0,404.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 410[2:MRR:10.0,404.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 412[2:SpR:405.0,106.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.22/0.52 419[2:SpR:408.0,106.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.52 421[2:Rew:406.0,419.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.52 422[2:Rew:409.0,421.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 423[2:Rew:422.0,405.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.52 424[2:Rew:422.0,406.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.22/0.52 425[2:Rew:422.0,404.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.22/0.52 426[2:Rew:422.0,408.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.22/0.52 427[2:Rew:422.0,409.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.22/0.52 428[2:Rew:422.0,410.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.52 429[2:Rew:422.0,412.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.22/0.52 444[2:SpR:427.0,106.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.22/0.52 446[2:Rew:39.0,444.0] || -> equal(identity,sk_c3)**.
% 0.22/0.52 448[2:Rew:446.0,39.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.22/0.52 451[2:Rew:446.0,360.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.22/0.52 457[2:SpR:428.0,106.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.22/0.52 459[2:Rew:423.0,457.0,407.0,457.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 461[2:Rew:459.0,425.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.22/0.52 464[2:Rew:459.0,429.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.22/0.52 468[2:Rew:448.0,464.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.52 469[2:Rew:468.0,426.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.22/0.52 472[2:Rew:468.0,451.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.52 479[2:Rew:472.0,469.0] || -> equal(sk_c2,sk_c7)**.
% 0.22/0.52 481[2:Rew:479.0,424.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.52 483[2:MRR:481.0,461.0] || -> .
% 0.22/0.52 494[1:Spt:483.0,37.1,37.2,37.3,37.4,37.5,37.7,37.8,37.9,37.10,37.11] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(sk_c8),sk_c6) equal(multiply(v,sk_c8),x)*+ equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,x),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.52 495[1:EqR:494.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(sk_c8),sk_c6) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.52 497[2:Spt:4.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.22/0.52 500[2:Rew:497.0,495.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.52 501[2:Obv:500.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.52 504[2:SpR:497.0,106.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.22/0.52 506[3:Spt:1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.22/0.52 509[3:Rew:506.0,501.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(sk_c6,sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.52 510[3:Obv:509.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.52 513[3:SpR:506.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.22/0.52 514[3:SpR:506.0,106.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.22/0.52 516[3:Rew:497.0,514.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.22/0.52 517[4:Spt:3.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 520[4:Rew:517.0,510.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.22/0.52 521[4:Obv:520.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.22/0.52 525[4:SpR:517.0,106.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.22/0.52 527[5:Spt:36.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.22/0.52 533[6:Spt:33.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.22/0.52 536[7:Spt:35.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.52 538[7:SpR:536.0,106.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.22/0.52 540[7:Rew:527.0,538.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.22/0.52 541[8:Spt:32.1] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.22/0.52 543[8:SpR:541.0,106.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c8)**.
% 0.22/0.52 545[8:Rew:506.0,543.0,533.0,543.0] || -> equal(sk_c6,sk_c8)**.
% 0.22/0.52 546[8:Rew:545.0,497.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.22/0.52 548[8:Rew:545.0,517.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.22/0.52 551[8:Rew:545.0,504.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),u)**.
% 0.22/0.52 552[8:Rew:545.0,513.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.22/0.52 558[8:Rew:545.0,540.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.22/0.52 559[8:Rew:548.0,558.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 564[8:Rew:559.0,521.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.22/0.52 567[8:Rew:559.0,546.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.52 574[8:Rew:559.0,551.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.22/0.52 576[8:Rew:574.0,552.0,559.0,552.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.52 583[8:Rew:576.0,564.5,559.0,564.5,559.0,564.4,559.0,564.3,559.0,564.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.22/0.52 584[8:Con:583.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.22/0.52 608[0:SpR:39.0,106.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.22/0.52 609[0:SpR:39.0,360.0] || -> equal(inverse(identity),identity)**.
% 0.22/0.52 611[5:SpR:527.0,39.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.22/0.52 615[8:Rew:576.0,611.0] || -> equal(identity,sk_c5)**.
% 0.22/0.52 617[8:Rew:615.0,360.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.22/0.52 619[8:Rew:615.0,609.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.22/0.52 620[8:Rew:527.0,619.0] || -> equal(sk_c5,sk_c7)**.
% 0.22/0.52 630[8:Rew:620.0,617.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.52 631[8:Rew:630.0,584.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.22/0.52 688[8:SpL:567.0,631.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.22/0.52 690[8:Obv:688.1] || -> .
% 0.22/0.52 691[8:Spt:690.0,32.1,541.0] || equal(multiply(sk_c4,sk_c8),sk_c7)** -> .
% 0.22/0.52 692[8:Spt:690.0,32.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 693[0:Rew:360.0,608.0] || -> equal(inverse(inverse(u)),u)**.
% 0.22/0.52 696[8:MRR:26.0,691.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 697[8:MRR:20.0,691.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 728[8:SpR:696.0,106.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.52 730[8:Rew:692.0,728.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.52 731[8:Rew:697.0,730.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 733[8:Rew:731.0,497.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.22/0.52 734[8:Rew:731.0,533.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.22/0.52 739[8:Rew:731.0,691.0] || equal(multiply(sk_c4,sk_c7),sk_c7)** -> .
% 0.22/0.52 774[5:SpR:611.0,106.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.22/0.52 776[8:Rew:733.0,774.0] || -> equal(multiply(sk_c6,identity),sk_c5)**.
% 0.22/0.52 777[8:Rew:360.0,776.0] || -> equal(sk_c5,sk_c6)**.
% 0.22/0.52 780[8:Rew:777.0,611.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.22/0.52 784[8:Rew:540.0,780.0] || -> equal(identity,sk_c7)**.
% 0.22/0.52 785[8:Rew:784.0,609.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.52 786[8:Rew:784.0,360.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.52 789[8:Rew:733.0,785.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 791[8:Rew:789.0,733.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.52 806[8:Rew:786.0,739.0] || equal(sk_c4,sk_c7)** -> .
% 0.22/0.52 837[0:SpR:693.0,106.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.22/0.52 840[8:SpR:734.0,693.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.22/0.52 842[8:Rew:791.0,840.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.52 843[8:MRR:842.0,806.0] || -> .
% 0.22/0.52 844[7:Spt:843.0,35.1,536.0] || equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.22/0.52 845[7:Spt:843.0,35.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 846[5:Rew:360.0,774.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.22/0.52 849[7:MRR:17.1,844.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 850[7:MRR:29.0,844.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 851[7:MRR:23.0,844.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 852[7:MRR:11.0,844.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 854[7:SpR:845.0,693.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.22/0.52 856[7:Rew:497.0,854.0] || -> equal(sk_c2,sk_c6)**.
% 0.22/0.52 857[7:Rew:856.0,845.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.22/0.52 858[7:Rew:856.0,850.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.22/0.52 871[7:SpR:849.0,693.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.22/0.52 873[7:Rew:846.0,871.0] || -> equal(sk_c1,sk_c5)**.
% 0.22/0.52 875[7:Rew:873.0,852.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.22/0.52 876[7:Rew:875.0,844.0] || equal(sk_c6,sk_c8)** -> .
% 0.22/0.52 880[2:SpR:497.0,693.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.22/0.52 904[7:SpR:851.0,106.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.22/0.52 906[7:Rew:497.0,904.0] || -> equal(multiply(sk_c6,sk_c7),sk_c3)**.
% 0.22/0.52 920[7:SpR:858.0,40.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),multiply(sk_c3,u))**.
% 0.22/0.52 921[7:SpR:858.0,106.0] || -> equal(multiply(inverse(sk_c6),sk_c3),sk_c8)**.
% 0.22/0.52 923[7:Rew:851.0,921.0,857.0,921.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 924[7:Rew:923.0,497.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.22/0.52 925[7:Rew:923.0,876.0] || equal(sk_c6,sk_c7)** -> .
% 0.22/0.52 932[7:Rew:923.0,504.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.22/0.52 940[7:Rew:923.0,875.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.22/0.52 942[7:Rew:846.0,924.0] || -> equal(sk_c5,sk_c6)**.
% 0.22/0.52 950[7:Rew:906.0,940.0,942.0,940.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.52 955[7:Rew:932.0,920.0,923.0,920.0,950.0,920.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.52 957[7:Rew:955.0,932.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.52 968[7:Rew:957.0,516.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 969[7:MRR:968.0,925.0] || -> .
% 0.22/0.52 981[6:Spt:969.0,33.0,533.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.22/0.52 982[6:Spt:969.0,33.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 985[6:MRR:15.0,981.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 986[6:MRR:27.0,981.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 987[6:MRR:21.0,981.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 988[6:MRR:9.0,981.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 990[6:SpR:982.0,693.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.22/0.52 992[6:Rew:497.0,990.0] || -> equal(sk_c2,sk_c6)**.
% 0.22/0.52 994[6:Rew:992.0,986.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.22/0.52 997[6:SpR:985.0,693.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.22/0.52 999[6:Rew:846.0,997.0] || -> equal(sk_c1,sk_c5)**.
% 0.22/0.52 1001[6:Rew:999.0,988.0] || -> equal(multiply(sk_c5,sk_c7),sk_c8)**.
% 0.22/0.52 1005[2:SpR:880.0,106.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.22/0.52 1026[6:SpR:987.0,106.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.22/0.52 1028[6:Rew:497.0,1026.0] || -> equal(multiply(sk_c6,sk_c7),sk_c3)**.
% 0.22/0.52 1047[6:SpR:994.0,106.0] || -> equal(multiply(inverse(sk_c6),sk_c3),sk_c8)**.
% 0.22/0.52 1049[6:Rew:987.0,1047.0,880.0,1047.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 1050[6:Rew:1049.0,880.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.22/0.52 1051[6:Rew:1049.0,497.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.22/0.52 1054[6:Rew:1049.0,987.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.22/0.52 1055[6:Rew:1049.0,517.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.52 1064[6:Rew:1049.0,521.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.22/0.52 1066[6:Rew:1049.0,1001.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.22/0.52 1068[6:Rew:846.0,1051.0] || -> equal(sk_c5,sk_c6)**.
% 0.22/0.52 1072[6:Rew:1068.0,611.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.22/0.52 1076[6:Rew:1028.0,1066.0,1068.0,1066.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.52 1078[6:Rew:1076.0,1054.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.52 1079[6:Rew:1055.0,1078.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 1081[6:Rew:1079.0,516.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.52 1083[6:Rew:1079.0,1050.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.52 1088[6:Rew:1079.0,1072.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.22/0.52 1090[6:Rew:1081.0,1088.0] || -> equal(identity,sk_c7)**.
% 0.22/0.52 1092[6:Rew:1090.0,360.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.52 1093[6:Rew:1090.0,38.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.52 1104[6:Rew:1092.0,1064.5,1093.0,1064.5,1049.0,1064.5,1092.0,1064.4,1049.0,1064.4,1092.0,1064.3,1049.0,1064.3,1049.0,1064.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(w,sk_c7) equal(v,sk_c7) -> .
% 0.22/0.52 1105[6:Con:1104.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.22/0.52 1166[6:SpL:1083.0,1105.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.22/0.52 1167[6:Obv:1166.1] || -> .
% 0.22/0.52 1168[5:Spt:1167.0,36.0,527.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.22/0.52 1169[5:Spt:1167.0,36.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 1170[5:MRR:18.0,1168.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 1173[5:MRR:12.0,1168.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 1199[5:SpR:1170.0,693.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.22/0.52 1202[5:Rew:1199.0,525.0] || -> equal(multiply(sk_c1,sk_c6),sk_c8)**.
% 0.22/0.52 1223[5:SpR:1173.0,40.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.22/0.52 1224[5:SpR:1173.0,106.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.22/0.52 1226[5:Rew:517.0,1224.0,1170.0,1224.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 1228[5:Rew:1226.0,497.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.22/0.52 1229[5:Rew:1226.0,880.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.22/0.52 1230[5:Rew:1226.0,506.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.22/0.52 1233[5:Rew:1226.0,1005.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),u)**.
% 0.22/0.52 1239[5:Rew:1226.0,1202.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 1241[5:Rew:1199.0,1229.0] || -> equal(sk_c1,sk_c8)**.
% 0.22/0.52 1250[5:Rew:1230.0,1239.0,1241.0,1239.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 1253[5:Rew:1250.0,521.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(v,sk_c8)),sk_c7)** -> .
% 0.22/0.52 1254[5:Rew:1250.0,1228.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.52 1255[5:Rew:1250.0,1241.0] || -> equal(sk_c1,sk_c7)**.
% 0.22/0.52 1262[5:Rew:1250.0,1233.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.22/0.52 1266[5:Rew:1262.0,1223.0,1255.0,1223.0,1250.0,1223.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.52 1271[5:Rew:1266.0,1253.5,1250.0,1253.5,1250.0,1253.4,1250.0,1253.3,1250.0,1253.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.22/0.52 1272[5:Con:1271.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.22/0.52 1300[5:SpR:1254.0,39.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.22/0.52 1301[5:Rew:1266.0,1300.0] || -> equal(identity,sk_c7)**.
% 0.22/0.52 1305[5:Rew:1301.0,360.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.52 1306[5:Rew:1305.0,1272.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.22/0.52 1347[5:SpL:1254.0,1306.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.22/0.52 1348[5:Obv:1347.1] || -> .
% 0.22/0.52 1349[4:Spt:1348.0,3.1,517.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.52 1350[4:Spt:1348.0,3.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.22/0.52 1352[4:MRR:6.1,1349.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.22/0.52 1354[4:MRR:2.1,1349.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.22/0.52 1355[4:MRR:5.1,1349.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.52 1357[4:SpR:1350.0,693.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.22/0.52 1360[4:Rew:497.0,1357.0] || -> equal(sk_c4,sk_c6)**.
% 0.22/0.52 1362[4:Rew:1360.0,1354.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.22/0.52 1376[4:SpR:1352.0,837.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.22/0.52 1396[4:SpR:1355.0,40.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.22/0.52 1400[4:Rew:1376.0,1396.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.52 1401[4:Rew:1400.0,516.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 1402[4:Rew:1400.0,1005.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.22/0.52 1405[4:Rew:1400.0,1362.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 1412[4:Rew:1401.0,1349.0] || equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.22/0.52 1422[4:Rew:1405.0,1402.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.52 1426[4:Rew:1422.0,1412.0,1405.0,1412.0] || equal(sk_c7,sk_c7)* -> .
% 0.22/0.52 1427[4:Obv:1426.0] || -> .
% 0.22/0.52 1432[3:Spt:1427.0,1.0,506.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.22/0.52 1433[3:Spt:1427.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 1434[3:MRR:31.1,1432.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 1435[3:MRR:13.1,1432.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 1436[3:MRR:25.0,1432.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 1437[3:MRR:19.0,1432.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 1438[3:MRR:7.0,1432.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 1440[3:SpR:1433.0,106.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.22/0.52 1451[3:SpR:1434.0,693.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.22/0.52 1454[3:Rew:497.0,1451.0] || -> equal(sk_c2,sk_c6)**.
% 0.22/0.52 1456[3:Rew:1454.0,1436.0] || -> equal(multiply(sk_c6,sk_c8),sk_c3)**.
% 0.22/0.52 1461[3:SpR:1435.0,693.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.22/0.52 1464[3:Rew:1461.0,1440.0] || -> equal(multiply(sk_c1,sk_c6),sk_c8)**.
% 0.22/0.52 1470[3:SpR:1437.0,106.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.22/0.52 1472[3:Rew:497.0,1470.0] || -> equal(multiply(sk_c6,sk_c7),sk_c3)**.
% 0.22/0.52 1474[3:SpR:1438.0,106.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.22/0.52 1476[3:Rew:1433.0,1474.0,1435.0,1474.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 1477[3:Rew:1476.0,1433.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.22/0.52 1479[3:Rew:1476.0,880.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.22/0.52 1481[3:Rew:1476.0,1432.0] || equal(multiply(sk_c8,sk_c7),sk_c7)** -> .
% 0.22/0.52 1485[3:Rew:1476.0,1456.0] || -> equal(multiply(sk_c7,sk_c8),sk_c3)**.
% 0.22/0.52 1486[3:Rew:1476.0,1464.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 1487[3:Rew:1476.0,1472.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.22/0.52 1488[3:Rew:1461.0,1479.0] || -> equal(sk_c1,sk_c8)**.
% 0.22/0.52 1494[3:Rew:1477.0,1485.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.52 1495[3:Rew:1494.0,1437.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.22/0.52 1497[3:Rew:1488.0,1486.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.22/0.52 1498[3:Rew:1494.0,1487.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.52 1499[3:Rew:1497.0,1495.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 1505[3:Rew:1498.0,1481.0,1499.0,1481.0] || equal(sk_c7,sk_c7)* -> .
% 0.22/0.52 1506[3:Obv:1505.0] || -> .
% 0.22/0.52 1515[2:Spt:1506.0,4.0,497.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.22/0.52 1516[2:Spt:1506.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.52 1517[2:MRR:34.0,1515.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.22/0.52 1518[2:MRR:16.0,1515.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.52 1519[2:MRR:28.0,1515.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.22/0.52 1520[2:MRR:22.0,1515.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.22/0.52 1521[2:MRR:10.0,1515.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.52 1526[2:SpR:1517.0,693.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.22/0.52 1529[2:Rew:1526.0,1515.0] || equal(sk_c2,sk_c6)** -> .
% 0.22/0.52 1531[2:SpR:1518.0,693.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.22/0.52 1532[2:SpR:1518.0,837.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),u)**.
% 0.22/0.52 1543[2:SpR:1519.0,40.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),multiply(sk_c3,u))**.
% 0.22/0.52 1544[2:SpR:1519.0,106.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.22/0.52 1546[2:Rew:1517.0,1544.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.22/0.52 1547[2:Rew:1520.0,1546.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.52 1548[2:Rew:1547.0,1516.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.52 1550[2:Rew:1547.0,1526.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.22/0.52 1551[2:Rew:1547.0,1519.0] || -> equal(multiply(sk_c2,sk_c7),sk_c3)**.
% 0.22/0.52 1552[2:Rew:1547.0,1520.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.22/0.52 1553[2:Rew:1547.0,1521.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.52 1558[2:Rew:1531.0,1550.0] || -> equal(sk_c2,sk_c1)**.
% 0.22/0.52 1559[2:Rew:1558.0,1529.0] || equal(sk_c1,sk_c6)** -> .
% 0.22/0.52 1561[2:Rew:1558.0,1551.0] || -> equal(multiply(sk_c1,sk_c7),sk_c3)**.
% 0.22/0.52 1562[2:Rew:1561.0,1553.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.52 1564[2:Rew:1562.0,1552.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.52 1565[2:Rew:1548.0,1564.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.52 1566[2:Rew:1565.0,1559.0] || equal(sk_c1,sk_c7)** -> .
% 0.22/0.52 1571[2:Rew:1532.0,1543.0,1558.0,1543.0,1547.0,1543.0,1562.0,1543.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.52 1596[2:SpR:1571.0,360.0] || -> equal(identity,sk_c7)**.
% 0.22/0.52 1598[2:Rew:1596.0,609.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.52 1603[2:Rew:1531.0,1598.0] || -> equal(sk_c1,sk_c7)**.
% 0.22/0.52 1604[2:MRR:1603.0,1566.0] || -> .
% 0.22/0.52 % SZS output end Refutation
% 0.22/0.52 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_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 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 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.22/0.52
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