TSTP Solution File: GRP239-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP239-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:46:28 EDT 2022
% Result : Unsatisfiable 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP239-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 12:40:55 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.51
% 0.21/0.51 SPASS V 3.9
% 0.21/0.51 SPASS beiseite: Proof found.
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 SPASS derived 1167 clauses, backtracked 545 clauses, performed 15 splits and kept 903 clauses.
% 0.21/0.51 SPASS allocated 63872 KBytes.
% 0.21/0.51 SPASS spent 0:00:00.15 on the problem.
% 0.21/0.51 0:00:00.04 for the input.
% 0.21/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.51 0:00:00.01 for inferences.
% 0.21/0.51 0:00:00.00 for the backtracking.
% 0.21/0.51 0:00:00.08 for the reduction.
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 Here is a proof with depth 5, length 386 :
% 0.21/0.51 % SZS output start Refutation
% 0.21/0.51 1[0:Inp] || -> equal(inverse(sk_c4),sk_c9)** equal(inverse(sk_c9),sk_c8).
% 0.21/0.51 2[0:Inp] || -> equal(inverse(sk_c9),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.21/0.51 3[0:Inp] || -> equal(inverse(sk_c9),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 4[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c9),sk_c8).
% 0.21/0.51 5[0:Inp] || -> equal(inverse(sk_c9),sk_c8) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.21/0.51 6[0:Inp] || -> equal(inverse(sk_c6),sk_c7)** equal(inverse(sk_c9),sk_c8).
% 0.21/0.51 8[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 9[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.21/0.51 10[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 11[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 13[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 17[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.21/0.51 18[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.21/0.51 20[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.21/0.51 24[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c3),sk_c8).
% 0.21/0.51 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.21/0.51 27[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.21/0.51 28[0:Inp] || -> equal(multiply(sk_c7,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c3),sk_c8).
% 0.21/0.51 29[0:Inp] || -> equal(inverse(sk_c4),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.21/0.51 31[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.21/0.51 32[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.21/0.51 34[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.21/0.51 38[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 39[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.21/0.51 41[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c9)**.
% 0.21/0.51 43[0:Inp] || equal(inverse(sk_c9),sk_c8) equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,v),sk_c8)** equal(multiply(w,sk_c9),v)* equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(multiply(x,sk_c8),sk_c9)** equal(multiply(y,sk_c8),sk_c9)** equal(inverse(y),sk_c8) equal(multiply(z,x1),sk_c8)** equal(inverse(z),x1) equal(multiply(x1,sk_c9),sk_c8)** -> .
% 0.21/0.51 44[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.51 45[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.51 46[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.51 47[0:Con:43.6] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(inverse(y),sk_c9) equal(inverse(sk_c9),sk_c8) equal(multiply(u,v),sk_c8)**+ equal(multiply(x,sk_c9),z)* equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(y,sk_c8),sk_c9)** equal(multiply(sk_c9,z),sk_c8)** -> .
% 0.21/0.51 48[1:Spt:47.0,47.5,47.7] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.21/0.51 49[2:Spt:6.1] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.21/0.51 51[3:Spt:41.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.21/0.51 53[4:Spt:13.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.51 55[5:Spt:34.1] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.21/0.51 61[1:SpL:44.0,48.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.21/0.51 62[6:Spt:27.1] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.21/0.51 67[7:Spt:20.1] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.21/0.51 73[2:SpR:49.0,45.0] || -> equal(multiply(sk_c8,sk_c9),identity)**.
% 0.21/0.51 74[3:SpR:51.0,45.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.21/0.51 75[4:SpR:53.0,45.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.21/0.51 79[2:SpL:73.0,48.1] || equal(inverse(sk_c8),sk_c9) equal(identity,sk_c8) equal(multiply(sk_c9,sk_c9),sk_c8)** -> .
% 0.21/0.51 86[2:SpR:73.0,46.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),multiply(identity,u))**.
% 0.21/0.51 88[0:SpR:45.0,46.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.51 89[6:SpR:62.0,46.0] || -> equal(multiply(sk_c9,multiply(sk_c3,u)),multiply(sk_c8,u))**.
% 0.21/0.51 93[2:Rew:44.0,86.0] || -> equal(multiply(sk_c8,multiply(sk_c9,u)),u)**.
% 0.21/0.51 95[0:Rew:44.0,88.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.51 97[4:SpR:75.0,46.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.21/0.51 100[4:Rew:44.0,97.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.21/0.51 104[6:SpR:62.0,93.0] || -> equal(multiply(sk_c8,sk_c8),sk_c3)**.
% 0.21/0.51 105[3:SpR:74.0,93.0] || -> equal(multiply(sk_c8,identity),sk_c2)**.
% 0.21/0.51 106[4:SpR:75.0,93.0] || -> equal(multiply(sk_c8,identity),sk_c1)**.
% 0.21/0.51 107[2:SpL:93.0,48.1] || equal(multiply(sk_c9,u),inverse(sk_c8)) equal(u,sk_c8) equal(multiply(multiply(sk_c9,u),sk_c9),sk_c8)** -> .
% 0.21/0.51 108[4:Rew:105.0,106.0] || -> equal(sk_c2,sk_c1)**.
% 0.21/0.51 110[5:Rew:108.0,55.0] || -> equal(multiply(sk_c1,sk_c9),sk_c3)**.
% 0.21/0.51 115[4:Rew:108.0,105.0] || -> equal(multiply(sk_c8,identity),sk_c1)**.
% 0.21/0.51 118[2:Rew:46.0,107.2] || equal(multiply(sk_c9,u),inverse(sk_c8)) equal(u,sk_c8) equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c8)** -> .
% 0.21/0.51 127[4:SpR:115.0,46.0] || -> equal(multiply(sk_c8,multiply(identity,u)),multiply(sk_c1,u))**.
% 0.21/0.51 129[4:SpL:115.0,48.1] || equal(inverse(sk_c8),identity) equal(sk_c1,sk_c8) equal(multiply(identity,sk_c9),sk_c8)** -> .
% 0.21/0.51 130[4:Rew:44.0,127.0] || -> equal(multiply(sk_c1,u),multiply(sk_c8,u))**.
% 0.21/0.51 131[7:Rew:130.0,67.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.21/0.51 132[5:Rew:130.0,110.0] || -> equal(multiply(sk_c8,sk_c9),sk_c3)**.
% 0.21/0.51 135[4:Rew:130.0,100.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),u)**.
% 0.21/0.51 136[7:Rew:104.0,131.0] || -> equal(sk_c3,sk_c9)**.
% 0.21/0.51 137[7:Rew:136.0,62.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.21/0.51 145[5:Rew:73.0,132.0] || -> equal(identity,sk_c3)**.
% 0.21/0.51 146[7:Rew:136.0,145.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 147[7:Rew:146.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 153[7:Rew:146.0,79.1] || equal(inverse(sk_c8),sk_c9) equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c9),sk_c8)** -> .
% 0.21/0.51 158[7:Rew:147.0,137.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 160[7:Rew:158.0,49.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.51 191[7:Rew:147.0,153.2,158.0,153.2,158.0,153.1,160.0,153.0,158.0,153.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.21/0.51 192[7:Obv:191.2] || -> .
% 0.21/0.51 199[7:Spt:192.0,20.1,67.0] || equal(multiply(sk_c1,sk_c8),sk_c9)** -> .
% 0.21/0.51 200[7:Spt:192.0,20.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.51 201[5:Rew:145.0,115.0] || -> equal(multiply(sk_c8,sk_c3),sk_c1)**.
% 0.21/0.51 204[5:Rew:145.0,44.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.51 205[5:Rew:145.0,45.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.21/0.51 206[7:Rew:130.0,199.0] || equal(multiply(sk_c8,sk_c8),sk_c9)** -> .
% 0.21/0.51 207[7:Rew:104.0,206.0] || equal(sk_c3,sk_c9)** -> .
% 0.21/0.51 208[6:Rew:104.0,18.1,130.0,18.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c3,sk_c9).
% 0.21/0.51 209[7:MRR:208.1,207.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.51 213[6:Rew:204.0,89.0] || -> equal(multiply(sk_c8,u),multiply(sk_c9,u))**.
% 0.21/0.51 215[6:Rew:213.0,135.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),u)**.
% 0.21/0.51 218[6:Rew:213.0,201.0] || -> equal(multiply(sk_c9,sk_c3),sk_c1)**.
% 0.21/0.51 219[6:Rew:213.0,132.0] || -> equal(multiply(sk_c9,sk_c9),sk_c3)**.
% 0.21/0.51 220[6:Rew:213.0,104.0] || -> equal(multiply(sk_c9,sk_c8),sk_c3)**.
% 0.21/0.51 221[6:Rew:62.0,218.0] || -> equal(sk_c1,sk_c8)**.
% 0.21/0.51 232[6:Rew:220.0,17.1,213.0,17.1,221.0,17.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(sk_c3,sk_c9).
% 0.21/0.51 233[7:MRR:232.1,207.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 268[7:SpR:233.0,46.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.21/0.51 270[7:Rew:213.0,268.0] || -> equal(multiply(sk_c5,multiply(sk_c9,u)),multiply(sk_c9,u))**.
% 0.21/0.51 280[7:SpR:209.0,205.0] || -> equal(multiply(sk_c8,sk_c5),sk_c3)**.
% 0.21/0.51 284[7:Rew:213.0,280.0] || -> equal(multiply(sk_c9,sk_c5),sk_c3)**.
% 0.21/0.51 302[6:SpR:219.0,215.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.21/0.51 303[6:SpR:220.0,215.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.21/0.51 304[7:SpR:284.0,215.0] || -> equal(multiply(sk_c9,sk_c3),sk_c5)**.
% 0.21/0.51 306[6:Rew:62.0,302.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 324[6:Rew:306.0,303.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.21/0.51 325[7:Rew:324.0,304.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.51 327[7:Rew:325.0,270.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),multiply(sk_c9,u))**.
% 0.21/0.51 341[7:Rew:215.0,327.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 346[7:Rew:341.0,324.0] || -> equal(sk_c3,sk_c9)**.
% 0.21/0.51 348[7:MRR:346.0,207.0] || -> .
% 0.21/0.51 367[6:Spt:348.0,27.1,62.0] || equal(multiply(sk_c9,sk_c3),sk_c8)** -> .
% 0.21/0.51 368[6:Spt:348.0,27.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.51 371[6:MRR:25.1,367.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.51 378[6:MRR:28.1,367.0] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.21/0.51 380[6:MRR:24.1,367.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 402[6:SpR:378.0,46.0] || -> equal(multiply(sk_c7,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.21/0.51 406[6:SpR:380.0,46.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.21/0.51 415[6:SpR:371.0,205.0] || -> equal(multiply(sk_c8,sk_c5),sk_c3)**.
% 0.21/0.51 455[5:SpR:132.0,135.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.21/0.51 456[6:SpR:415.0,135.0] || -> equal(multiply(sk_c9,sk_c3),sk_c5)**.
% 0.21/0.51 460[6:Rew:455.0,367.0] || equal(sk_c8,sk_c9)** -> .
% 0.21/0.51 461[6:Rew:455.0,456.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.51 465[6:Rew:461.0,406.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.21/0.51 469[6:Rew:135.0,465.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 470[6:Rew:469.0,93.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.51 477[6:Rew:469.0,402.0] || -> equal(multiply(sk_c7,u),multiply(sk_c8,u))**.
% 0.21/0.51 506[6:Rew:470.0,477.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 507[6:Rew:506.0,378.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 510[6:MRR:507.0,460.0] || -> .
% 0.21/0.51 525[5:Spt:510.0,34.1,55.0] || equal(multiply(sk_c2,sk_c9),sk_c3)** -> .
% 0.21/0.51 526[5:Spt:510.0,34.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.51 527[5:Rew:108.0,525.0] || equal(multiply(sk_c1,sk_c9),sk_c3)** -> .
% 0.21/0.51 528[5:Rew:130.0,527.0] || equal(multiply(sk_c8,sk_c9),sk_c3)** -> .
% 0.21/0.51 529[5:Rew:73.0,528.0] || equal(identity,sk_c3)** -> .
% 0.21/0.51 530[4:Rew:73.0,32.1,130.0,32.1,108.0,32.1] || -> equal(inverse(sk_c5),sk_c8)** equal(identity,sk_c3).
% 0.21/0.51 531[5:MRR:530.1,529.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.51 532[4:Rew:73.0,29.1,130.0,29.1,108.0,29.1] || -> equal(inverse(sk_c4),sk_c9)** equal(identity,sk_c3).
% 0.21/0.51 533[5:MRR:532.1,529.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.51 538[4:Rew:73.0,31.1,130.0,31.1,108.0,31.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(identity,sk_c3).
% 0.21/0.51 539[5:MRR:538.1,529.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 548[4:Rew:44.0,129.2] || equal(inverse(sk_c8),identity)** equal(sk_c1,sk_c8) equal(sk_c8,sk_c9) -> .
% 0.21/0.51 567[5:SpR:539.0,46.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.21/0.51 578[5:SpR:531.0,45.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.51 579[5:SpR:533.0,45.0] || -> equal(multiply(sk_c9,sk_c4),identity)**.
% 0.21/0.51 596[4:SpR:73.0,135.0] || -> equal(multiply(sk_c9,identity),sk_c9)**.
% 0.21/0.51 597[5:SpR:578.0,135.0] || -> equal(multiply(sk_c9,identity),sk_c5)**.
% 0.21/0.51 598[5:Rew:596.0,597.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.51 600[5:Rew:598.0,539.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.51 602[5:Rew:598.0,567.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.21/0.51 604[5:Rew:135.0,602.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 606[5:Rew:604.0,579.0] || -> equal(identity,sk_c4)**.
% 0.21/0.51 607[5:Rew:604.0,75.0] || -> equal(identity,sk_c1)**.
% 0.21/0.51 608[5:Rew:604.0,600.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 609[5:Rew:604.0,596.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 625[5:Rew:606.0,548.0] || equal(inverse(sk_c8),sk_c4)** equal(sk_c1,sk_c8) equal(sk_c8,sk_c9) -> .
% 0.21/0.51 626[5:Rew:606.0,607.0] || -> equal(sk_c1,sk_c4)**.
% 0.21/0.51 628[5:Rew:626.0,53.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.51 637[5:Rew:606.0,609.0] || -> equal(sk_c4,sk_c9)**.
% 0.21/0.51 640[5:Rew:637.0,626.0] || -> equal(sk_c1,sk_c9)**.
% 0.21/0.51 643[5:Rew:637.0,628.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.51 671[5:Rew:608.0,625.2,640.0,625.1,608.0,625.1,643.0,625.0,608.0,625.0,637.0,625.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.21/0.51 672[5:Obv:671.2] || -> .
% 0.21/0.51 681[4:Spt:672.0,13.1,53.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.21/0.51 682[4:Spt:672.0,13.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.51 683[4:MRR:11.1,681.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.51 684[4:MRR:8.1,681.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.51 687[4:MRR:10.0,681.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 688[4:MRR:9.0,681.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.21/0.51 701[3:SpR:105.0,46.0] || -> equal(multiply(sk_c8,multiply(identity,u)),multiply(sk_c2,u))**.
% 0.21/0.51 703[3:Rew:44.0,701.0] || -> equal(multiply(sk_c2,u),multiply(sk_c8,u))**.
% 0.21/0.51 722[4:SpR:683.0,45.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.51 724[4:SpR:684.0,45.0] || -> equal(multiply(sk_c9,sk_c4),identity)**.
% 0.21/0.51 738[4:SpR:724.0,93.0] || -> equal(multiply(sk_c8,identity),sk_c4)**.
% 0.21/0.51 739[4:Rew:105.0,738.0] || -> equal(sk_c2,sk_c4)**.
% 0.21/0.51 743[4:Rew:739.0,703.0] || -> equal(multiply(sk_c4,u),multiply(sk_c8,u))**.
% 0.21/0.51 745[4:Rew:743.0,688.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.21/0.51 756[0:SpR:95.0,95.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.51 759[2:SpR:73.0,95.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c9)**.
% 0.21/0.51 760[4:SpR:722.0,95.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.21/0.51 768[4:SpR:687.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.21/0.51 770[0:SpR:45.0,95.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.51 775[4:Rew:759.0,760.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.51 783[4:Rew:775.0,768.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.21/0.51 784[4:Rew:73.0,783.0,49.0,783.0] || -> equal(identity,sk_c8)**.
% 0.21/0.51 786[4:Rew:784.0,44.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.51 798[4:Rew:786.0,745.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 799[4:Rew:786.0,93.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 806[4:Rew:798.0,49.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.51 809[4:Rew:798.0,118.0] || equal(multiply(sk_c9,u),inverse(sk_c9)) equal(u,sk_c8) equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c8)** -> .
% 0.21/0.51 816[4:Rew:798.0,784.0] || -> equal(identity,sk_c9)**.
% 0.21/0.51 840[4:Rew:816.0,770.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.21/0.51 854[4:Rew:756.0,840.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 866[4:Rew:854.0,809.2,799.0,809.2,798.0,809.2,798.0,809.1,799.0,809.0,806.0,809.0] || equal(u,sk_c9)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.21/0.51 867[4:Obv:866.1] || equal(u,sk_c9)* -> .
% 0.21/0.51 868[4:UnC:867.0,95.0] || -> .
% 0.21/0.51 870[3:Spt:868.0,41.1,51.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.21/0.51 871[3:Spt:868.0,41.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.51 872[0:Rew:756.0,770.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.51 873[2:Rew:872.0,759.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.21/0.51 875[3:MRR:39.1,870.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.51 879[3:MRR:38.0,870.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 883[2:Rew:873.0,118.0] || equal(multiply(sk_c9,u),sk_c9) equal(u,sk_c8) equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c8)** -> .
% 0.21/0.51 888[2:SpR:873.0,95.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),u)**.
% 0.21/0.51 907[3:SpR:879.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.21/0.51 909[3:Rew:73.0,907.0,875.0,907.0] || -> equal(identity,sk_c8)**.
% 0.21/0.51 910[3:Rew:909.0,73.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.21/0.51 911[3:Rew:909.0,44.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.51 915[3:Rew:909.0,872.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.51 918[3:Rew:911.0,910.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 919[3:Rew:911.0,888.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.51 931[3:Rew:918.0,883.1] || equal(multiply(sk_c9,u),sk_c9) equal(u,sk_c9) equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c8)** -> .
% 0.21/0.51 938[3:Rew:918.0,915.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 964[3:Rew:938.0,931.2,919.0,931.2,918.0,931.2,919.0,931.0] || equal(u,sk_c9)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.21/0.51 965[3:Obv:964.1] || equal(u,sk_c9)* -> .
% 0.21/0.51 966[3:UnC:965.0,95.0] || -> .
% 0.21/0.51 968[2:Spt:966.0,6.1,49.0] || equal(inverse(sk_c9),sk_c8)** -> .
% 0.21/0.51 969[2:Spt:966.0,6.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.51 970[2:MRR:4.1,968.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.51 971[2:MRR:1.1,968.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.51 973[2:MRR:5.0,968.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.21/0.51 974[2:MRR:3.0,968.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.51 975[2:MRR:2.0,968.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.21/0.51 986[2:SpR:973.0,95.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.21/0.51 988[2:Rew:969.0,986.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.21/0.51 998[2:SpR:988.0,95.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c8)**.
% 0.21/0.51 1000[2:Rew:45.0,998.0] || -> equal(identity,sk_c8)**.
% 0.21/0.51 1001[2:Rew:1000.0,872.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.21/0.51 1004[2:Rew:1000.0,61.0] || equal(inverse(sk_c8),u) equal(u,sk_c8) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.21/0.51 1007[2:Rew:1001.0,975.0] || -> equal(sk_c4,sk_c9)**.
% 0.21/0.51 1008[2:Rew:1001.0,974.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.51 1010[2:Rew:1007.0,971.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.51 1013[2:Rew:1008.0,970.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.21/0.51 1017[2:Rew:1010.0,1013.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.51 1027[2:Rew:1017.0,1001.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.51 1048[2:Rew:1027.0,1004.2,1017.0,1004.2,1017.0,1004.1,1010.0,1004.0,1017.0,1004.0] || equal(sk_c9,u)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.21/0.51 1049[2:Obv:1048.1] || equal(u,sk_c9)* -> .
% 0.21/0.51 1050[2:UnC:1049.0,95.0] || -> .
% 0.21/0.51 1055[1:Spt:1050.0,47.1,47.2,47.3,47.4,47.6,47.8,47.9,47.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(sk_c9),sk_c8) equal(multiply(v,sk_c9),x)*+ equal(multiply(u,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,x),sk_c8)** -> .
% 0.21/0.51 1056[1:EqR:1055.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.51 1058[2:Spt:4.1] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.21/0.51 1061[2:Rew:1058.0,1056.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(sk_c8,sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1062[2:Obv:1061.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1067[3:Spt:13.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.21/0.52 1070[4:Spt:41.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.21/0.52 1073[5:Spt:20.1] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.21/0.52 1075[5:SpR:1073.0,95.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c8)**.
% 0.21/0.52 1077[5:Rew:1067.0,1075.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.21/0.52 1078[6:Spt:27.1] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.21/0.52 1080[6:SpR:1078.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c3)**.
% 0.21/0.52 1082[6:Rew:1058.0,1080.0] || -> equal(multiply(sk_c8,sk_c8),sk_c3)**.
% 0.21/0.52 1084[5:SpR:1077.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.21/0.52 1086[5:Rew:1058.0,1084.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.21/0.52 1087[6:Rew:1082.0,1086.0] || -> equal(sk_c3,sk_c9)**.
% 0.21/0.52 1090[6:Rew:1087.0,31.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c9)**.
% 0.21/0.52 1095[6:Rew:1087.0,32.1] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c9)**.
% 0.21/0.52 1117[0:SpR:45.0,95.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.52 1118[0:SpR:45.0,872.0] || -> equal(inverse(identity),identity)**.
% 0.21/0.52 1120[2:SpR:1058.0,45.0] || -> equal(multiply(sk_c8,sk_c9),identity)**.
% 0.21/0.52 1121[3:SpR:1067.0,45.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.21/0.52 1122[4:SpR:1070.0,45.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.21/0.52 1124[0:Rew:872.0,1117.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.52 1136[2:SpR:1120.0,95.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c9)**.
% 0.21/0.52 1138[2:Rew:872.0,1136.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.21/0.52 1143[2:SpR:1138.0,45.0] || -> equal(multiply(sk_c9,sk_c8),identity)**.
% 0.21/0.52 1146[3:SpR:1121.0,95.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c1)**.
% 0.21/0.52 1148[3:Rew:872.0,1146.0,1058.0,1146.0] || -> equal(sk_c1,sk_c8)**.
% 0.21/0.52 1162[4:SpR:1122.0,95.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.21/0.52 1164[4:Rew:872.0,1162.0,1058.0,1162.0] || -> equal(sk_c2,sk_c8)**.
% 0.21/0.52 1170[6:Rew:1164.0,1090.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c9).
% 0.21/0.52 1172[6:Rew:1164.0,1095.1] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c9),sk_c9)**.
% 0.21/0.52 1175[6:Rew:1120.0,1172.1] || -> equal(inverse(sk_c5),sk_c8)** equal(identity,sk_c9).
% 0.21/0.52 1178[6:Rew:1120.0,1170.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(identity,sk_c9).
% 0.21/0.52 1186[7:Spt:1175.1] || -> equal(identity,sk_c9)**.
% 0.21/0.52 1187[7:Rew:1186.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.52 1188[7:Rew:1186.0,872.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.52 1190[7:Rew:1186.0,1118.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1195[7:Rew:1058.0,1190.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.52 1196[7:Rew:1195.0,1058.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1204[7:Rew:1195.0,1062.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1217[7:Con:1204.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1218[7:Rew:1188.0,1217.3,1187.0,1217.3,1195.0,1217.3,1188.0,1217.2,1195.0,1217.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(u,sk_c9) equal(v,sk_c9) -> .
% 0.21/0.52 1219[7:Con:1218.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.21/0.52 1243[0:SpR:1124.0,95.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.21/0.52 1292[7:SpL:1196.0,1219.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.21/0.52 1294[7:Obv:1292.1] || -> .
% 0.21/0.52 1295[7:Spt:1294.0,1175.1,1186.0] || equal(identity,sk_c9)** -> .
% 0.21/0.52 1296[7:Spt:1294.0,1175.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.52 1299[7:MRR:1178.1,1295.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.52 1302[7:SpR:1296.0,1124.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.52 1304[7:Rew:1138.0,1302.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.52 1306[7:Rew:1304.0,1299.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.52 1307[7:Rew:1143.0,1306.0] || -> equal(identity,sk_c9)**.
% 0.21/0.52 1308[7:MRR:1307.0,1295.0] || -> .
% 0.21/0.52 1310[6:Spt:1308.0,27.1,1078.0] || equal(multiply(sk_c9,sk_c3),sk_c8)** -> .
% 0.21/0.52 1311[6:Spt:1308.0,27.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.52 1313[6:MRR:25.1,1310.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.52 1317[6:MRR:24.1,1310.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.52 1332[6:SpR:1313.0,1124.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.52 1334[6:Rew:1138.0,1332.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.52 1336[6:Rew:1334.0,1317.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.52 1337[6:Rew:1143.0,1336.0] || -> equal(identity,sk_c9)**.
% 0.21/0.52 1338[6:Rew:1337.0,1118.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1340[6:Rew:1337.0,872.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.52 1341[6:Rew:1337.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.52 1344[6:Rew:1058.0,1338.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.52 1347[6:Rew:1344.0,1138.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1355[6:Rew:1344.0,1062.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1378[6:Con:1355.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1379[6:Rew:1340.0,1378.3,1341.0,1378.3,1344.0,1378.3,1340.0,1378.2,1344.0,1378.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(u,sk_c9) equal(v,sk_c9) -> .
% 0.21/0.52 1380[6:Con:1379.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.21/0.52 1425[6:SpL:1347.0,1380.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.21/0.52 1426[6:Obv:1425.1] || -> .
% 0.21/0.52 1427[5:Spt:1426.0,20.1,1073.0] || equal(multiply(sk_c1,sk_c8),sk_c9)** -> .
% 0.21/0.52 1428[5:Spt:1426.0,20.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.52 1429[5:Rew:1148.0,1427.0] || equal(multiply(sk_c8,sk_c8),sk_c9)** -> .
% 0.21/0.52 1432[3:Rew:1148.0,18.1] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.21/0.52 1433[5:MRR:1432.1,1429.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.52 1444[3:Rew:1148.0,17.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c8,sk_c8),sk_c9).
% 0.21/0.52 1445[5:MRR:1444.1,1429.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.52 1461[5:SpR:1433.0,1124.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.52 1463[5:Rew:1138.0,1461.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.52 1465[5:Rew:1463.0,1445.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.52 1466[5:Rew:1143.0,1465.0] || -> equal(identity,sk_c9)**.
% 0.21/0.52 1467[5:Rew:1466.0,1118.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1469[5:Rew:1466.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.52 1473[5:Rew:1058.0,1467.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.52 1478[5:Rew:1473.0,1429.0] || equal(multiply(sk_c9,sk_c9),sk_c9)** -> .
% 0.21/0.52 1498[5:Rew:1469.0,1478.0] || equal(sk_c9,sk_c9)* -> .
% 0.21/0.52 1499[5:Obv:1498.0] || -> .
% 0.21/0.52 1511[4:Spt:1499.0,41.1,1070.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.21/0.52 1512[4:Spt:1499.0,41.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.52 1513[4:MRR:39.1,1511.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.52 1517[4:MRR:38.0,1511.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.52 1534[4:SpR:1513.0,1124.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.52 1536[4:Rew:1138.0,1534.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.52 1538[4:Rew:1536.0,1517.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.52 1539[4:Rew:1143.0,1538.0] || -> equal(identity,sk_c9)**.
% 0.21/0.52 1540[4:Rew:1539.0,1118.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1542[4:Rew:1539.0,872.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.52 1543[4:Rew:1539.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.52 1546[4:Rew:1058.0,1540.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.52 1548[4:Rew:1546.0,1138.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1557[4:Rew:1546.0,1062.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1573[4:Con:1557.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1574[4:Rew:1542.0,1573.3,1543.0,1573.3,1546.0,1573.3,1542.0,1573.2,1546.0,1573.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(u,sk_c9) equal(v,sk_c9) -> .
% 0.21/0.52 1575[4:Con:1574.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.21/0.52 1636[4:SpL:1548.0,1575.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.21/0.52 1637[4:Obv:1636.1] || -> .
% 0.21/0.52 1638[3:Spt:1637.0,13.1,1067.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.21/0.52 1639[3:Spt:1637.0,13.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.52 1640[3:MRR:11.1,1638.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.52 1644[3:MRR:10.0,1638.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.52 1665[3:SpR:1640.0,1124.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.52 1668[3:Rew:1138.0,1665.0] || -> equal(sk_c5,sk_c9)**.
% 0.21/0.52 1670[3:Rew:1668.0,1644.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.21/0.52 1671[3:Rew:1143.0,1670.0] || -> equal(identity,sk_c9)**.
% 0.21/0.52 1672[3:Rew:1671.0,1118.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1674[3:Rew:1671.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.21/0.52 1675[3:Rew:1671.0,872.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.21/0.52 1678[3:Rew:1058.0,1672.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.52 1679[3:Rew:1678.0,1058.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.21/0.52 1688[3:Rew:1678.0,1062.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1707[3:Con:1688.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(sk_c9,multiply(v,sk_c9)),sk_c8)** -> .
% 0.21/0.52 1708[3:Rew:1675.0,1707.3,1674.0,1707.3,1678.0,1707.3,1675.0,1707.2,1678.0,1707.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(u,sk_c9) equal(v,sk_c9) -> .
% 0.21/0.52 1709[3:Con:1708.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.21/0.52 1760[3:SpL:1679.0,1709.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.21/0.52 1761[3:Obv:1760.1] || -> .
% 0.21/0.52 1762[2:Spt:1761.0,4.1,1058.0] || equal(inverse(sk_c9),sk_c8)** -> .
% 0.21/0.52 1763[2:Spt:1761.0,4.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.52 1764[2:MRR:1.1,1762.0] || -> equal(inverse(sk_c4),sk_c9)**.
% 0.21/0.52 1765[2:MRR:6.1,1762.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.52 1767[2:MRR:5.0,1762.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.21/0.52 1768[2:MRR:3.0,1762.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.21/0.52 1770[2:SpR:1763.0,95.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.21/0.52 1771[2:SpR:1763.0,1124.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.52 1772[2:SpR:1763.0,1243.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.21/0.52 1781[2:SpR:1764.0,1124.0] || -> equal(inverse(sk_c9),sk_c4)**.
% 0.21/0.52 1784[2:Rew:1781.0,1762.0] || equal(sk_c4,sk_c8)** -> .
% 0.21/0.52 1787[2:SpR:1765.0,1243.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.21/0.52 1805[2:SpR:1767.0,46.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.21/0.52 1809[2:Rew:1787.0,1805.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.21/0.52 1810[2:Rew:1809.0,1772.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.52 1812[2:Rew:1809.0,1770.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.21/0.52 1813[2:Rew:1810.0,1768.0] || -> equal(sk_c8,sk_c9)**.
% 0.21/0.52 1815[2:Rew:1813.0,1771.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.21/0.52 1816[2:Rew:1813.0,1784.0] || equal(sk_c4,sk_c9)** -> .
% 0.21/0.52 1823[2:Rew:1781.0,1815.0] || -> equal(sk_c5,sk_c4)**.
% 0.21/0.52 1826[2:Rew:1823.0,1812.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.21/0.52 1864[2:SpR:1826.0,872.0] || -> equal(identity,sk_c4)**.
% 0.21/0.52 1866[2:Rew:1864.0,1118.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.21/0.52 1871[2:Rew:1764.0,1866.0] || -> equal(sk_c4,sk_c9)**.
% 0.21/0.52 1872[2:MRR:1871.0,1816.0] || -> .
% 0.21/0.52 % SZS output end Refutation
% 0.21/0.52 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_8 prove_this_9 prove_this_10 prove_this_11 prove_this_13 prove_this_17 prove_this_18 prove_this_20 prove_this_24 prove_this_25 prove_this_27 prove_this_28 prove_this_29 prove_this_31 prove_this_32 prove_this_34 prove_this_38 prove_this_39 prove_this_41 prove_this_43 left_identity left_inverse associativity
% 0.21/0.52
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