TSTP Solution File: GRP255-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP255-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:46:33 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP255-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 11:34:06 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 899 clauses, backtracked 306 clauses, performed 10 splits and kept 684 clauses.
% 0.20/0.48 SPASS allocated 63675 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.06 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 4, length 327 :
% 0.20/0.48 % SZS output start Refutation
% 0.20/0.48 1[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.20/0.48 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 3[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.20/0.48 4[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.20/0.48 6[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.20/0.48 8[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7)** equal(inverse(sk_c1),sk_c8).
% 0.20/0.48 11[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 13[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 14[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 15[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 16[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 18[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 20[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.48 21[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 22[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 23[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 24[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 25[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.48 26[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.48 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.48 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.48 30[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.48 31[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(inverse(y),sk_c8) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c6)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(y,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.48 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.48 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.48 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.48 35[1:Spt:31.1,31.6] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.20/0.48 36[2:Spt:21.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 38[3:Spt:24.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 40[4:Spt:22.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 43[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.20/0.48 44[5:Spt:23.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 46[5:SpL:44.0,35.1] || equal(inverse(sk_c4),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.20/0.48 47[5:Obv:46.1] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.48 48[5:Rew:40.0,47.0] || equal(sk_c8,sk_c8)* -> .
% 0.20/0.48 49[5:Obv:48.0] || -> .
% 0.20/0.48 50[5:Spt:49.0,23.1,44.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.48 51[5:Spt:49.0,23.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 52[5:MRR:18.1,50.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 53[5:MRR:8.1,50.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 55[5:MRR:13.0,50.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 56[5:MRR:3.0,50.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 66[3:SpR:38.0,33.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.20/0.48 67[4:SpR:40.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.48 70[5:SpR:53.0,33.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.20/0.48 71[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c7)),sk_c8)** equal(identity,sk_c8) -> .
% 0.20/0.48 80[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.48 84[0:Rew:32.0,80.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.48 99[0:SpR:84.0,84.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.48 101[5:SpR:55.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.20/0.48 106[0:SpR:33.0,84.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.48 107[3:SpR:66.0,84.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.20/0.48 110[4:SpR:67.0,84.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.20/0.48 111[5:SpR:70.0,84.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.20/0.48 118[5:Rew:52.0,101.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 127[5:Rew:110.0,111.0] || -> equal(sk_c4,sk_c1)**.
% 0.20/0.48 132[5:Rew:127.0,110.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.20/0.48 135[0:Rew:99.0,106.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.48 136[5:Rew:135.0,132.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.20/0.48 138[3:Rew:135.0,107.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.48 145[5:SpR:136.0,33.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.20/0.48 148[5:Rew:56.0,145.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 149[5:Rew:148.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 151[5:Rew:148.0,66.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.20/0.48 154[5:Rew:148.0,43.0] || equal(inverse(sk_c7),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.20/0.48 158[5:Rew:149.0,36.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 160[5:Rew:149.0,118.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 173[5:Rew:158.0,160.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 180[5:Rew:173.0,138.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.20/0.48 182[5:Rew:173.0,149.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 185[5:Rew:136.0,180.0] || -> equal(sk_c5,sk_c1)**.
% 0.20/0.48 188[5:Rew:185.0,151.0,173.0,151.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.20/0.48 197[5:Rew:182.0,188.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.48 198[5:Rew:197.0,53.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.48 201[5:Rew:197.0,173.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.48 221[5:Rew:201.0,154.1,197.0,154.1,198.0,154.0,201.0,154.0,197.0,154.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 222[5:Obv:221.1] || -> .
% 0.20/0.48 226[4:Spt:222.0,22.0,40.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.48 227[4:Spt:222.0,22.1] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 228[4:MRR:17.0,226.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 229[4:MRR:7.0,226.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 231[4:MRR:12.0,226.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 232[4:MRR:2.0,226.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 261[4:SpR:231.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.20/0.48 263[4:Rew:228.0,261.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 265[4:SpR:232.0,84.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.48 267[4:Rew:229.0,265.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.48 279[4:SpR:267.0,84.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.20/0.48 281[4:Rew:33.0,279.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 283[4:Rew:281.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 284[4:Rew:281.0,135.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 287[4:Rew:281.0,43.0] || equal(inverse(sk_c7),sk_c8)** equal(sk_c7,sk_c8) -> .
% 0.20/0.48 289[4:Rew:283.0,263.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.48 290[4:Rew:283.0,36.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 310[4:Rew:289.0,290.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 314[4:Rew:310.0,232.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.48 325[4:Rew:310.0,284.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 334[4:Rew:325.0,314.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.48 335[4:Rew:334.0,229.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.48 337[4:Rew:334.0,310.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.48 360[4:Rew:337.0,287.1,334.0,287.1,335.0,287.0,337.0,287.0,334.0,287.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 361[4:Obv:360.1] || -> .
% 0.20/0.48 367[3:Spt:361.0,24.0,38.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.20/0.48 368[3:Spt:361.0,24.1] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 369[3:MRR:19.0,367.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 370[3:MRR:9.0,367.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 371[3:MRR:29.0,367.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.48 372[3:MRR:14.0,367.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 373[3:MRR:4.0,367.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 384[3:SpR:371.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c8)**.
% 0.20/0.48 386[3:Rew:368.0,384.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.48 388[3:SpR:372.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.20/0.48 390[3:Rew:369.0,388.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 399[3:SpR:390.0,84.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 401[3:Rew:33.0,399.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 402[3:Rew:401.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 403[3:Rew:401.0,135.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 407[3:Rew:401.0,71.1] || equal(inverse(inverse(sk_c7)),sk_c8)** equal(sk_c6,sk_c8) -> .
% 0.20/0.48 408[3:Rew:402.0,386.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 415[3:Rew:408.0,36.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.20/0.48 423[3:Rew:408.0,403.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 424[3:Rew:423.0,373.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.48 432[3:Rew:423.0,415.0,424.0,415.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.48 433[3:Rew:432.0,370.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.48 435[3:Rew:432.0,408.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.48 459[3:Rew:435.0,407.1,432.0,407.1,433.0,407.0,433.0,407.0,424.0,407.0,432.0,407.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.48 460[3:Obv:459.1] || -> .
% 0.20/0.48 463[2:Spt:460.0,21.1,36.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.48 464[2:Spt:460.0,21.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 465[2:MRR:16.1,463.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 466[2:MRR:6.1,463.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 467[2:MRR:26.0,463.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.48 468[2:MRR:11.0,463.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 469[2:MRR:1.0,463.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 477[2:SpR:467.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c8)**.
% 0.20/0.48 479[2:Rew:464.0,477.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.48 481[2:SpR:468.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.20/0.48 483[2:Rew:465.0,481.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 485[2:SpR:469.0,84.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.48 487[2:Rew:466.0,485.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.48 492[2:SpR:483.0,84.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 494[2:Rew:33.0,492.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 495[2:Rew:494.0,135.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 496[2:Rew:494.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 500[2:Rew:494.0,71.1] || equal(inverse(inverse(sk_c7)),sk_c8)** equal(sk_c6,sk_c8) -> .
% 0.20/0.48 501[2:Rew:495.0,479.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 504[2:Rew:501.0,468.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.48 512[2:Rew:501.0,495.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 513[2:Rew:501.0,496.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 514[2:Rew:513.0,487.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 517[2:Rew:514.0,465.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.48 522[2:Rew:514.0,504.0] || -> equal(multiply(sk_c2,sk_c8),sk_c8)**.
% 0.20/0.48 523[2:Rew:512.0,522.0] || -> equal(sk_c2,sk_c8)**.
% 0.20/0.48 525[2:Rew:523.0,517.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 539[2:Rew:501.0,500.1,525.0,500.0,525.0,500.0,514.0,500.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.48 540[2:Obv:539.1] || -> .
% 0.20/0.48 543[1:Spt:540.0,31.0,31.2,31.3,31.4,31.5,31.7,31.8,31.9,31.10] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.48 545[2:Spt:16.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.48 546[2:Rew:545.0,543.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.48 548[2:Obv:546.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** -> .
% 0.20/0.48 551[2:SpR:545.0,84.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.20/0.48 553[3:Spt:22.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 556[4:Spt:24.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 559[5:Spt:25.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.48 561[5:SpR:559.0,84.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.20/0.48 563[5:Rew:556.0,561.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.48 567[6:Spt:23.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 569[6:SpR:567.0,84.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.20/0.48 571[6:Rew:553.0,569.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.48 573[5:SpR:563.0,84.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.48 575[5:Rew:551.0,573.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 576[5:Rew:575.0,545.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.48 577[5:Rew:575.0,556.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 578[5:Rew:575.0,559.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.20/0.48 581[5:Rew:575.0,548.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** -> .
% 0.20/0.48 583[5:Rew:575.0,551.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c8)**.
% 0.20/0.48 588[6:Rew:575.0,571.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.20/0.48 589[6:Rew:576.0,588.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 591[6:Rew:589.0,578.0] || -> equal(multiply(sk_c5,sk_c8),sk_c8)**.
% 0.20/0.48 592[6:Rew:33.0,583.0,589.0,583.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 594[6:Rew:592.0,135.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 598[6:Rew:594.0,591.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.48 600[6:Rew:598.0,577.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 609[6:Rew:594.0,581.7,575.0,581.7,594.0,581.6,575.0,581.6,589.0,581.6,594.0,581.5,589.0,581.5,594.0,581.4,589.0,581.4,575.0,581.4,575.0,581.2,589.0,581.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(inverse(x),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) equal(x,sk_c8) -> .
% 0.20/0.48 610[6:Con:609.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 670[6:SpL:600.0,610.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.48 672[6:Obv:670.1] || -> .
% 0.20/0.48 673[6:Spt:672.0,23.1,567.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.48 674[6:Spt:672.0,23.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 675[6:Rew:575.0,673.0] || equal(multiply(sk_c4,sk_c8),sk_c8)** -> .
% 0.20/0.48 678[5:Rew:575.0,8.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.20/0.48 679[6:MRR:678.1,675.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 685[5:Rew:575.0,3.1,575.0,3.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)** equal(multiply(sk_c1,sk_c8),sk_c8).
% 0.20/0.48 686[6:MRR:685.0,675.0] || -> equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.20/0.48 697[6:SpR:679.0,84.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.48 715[6:SpR:686.0,84.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c8)**.
% 0.20/0.48 717[6:Rew:576.0,715.0,679.0,715.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 723[6:Rew:717.0,583.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.20/0.48 733[6:Rew:33.0,723.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 734[6:Rew:733.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 735[6:Rew:733.0,135.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 736[6:Rew:733.0,33.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.48 738[6:Rew:734.0,697.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 742[6:Rew:735.0,686.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.48 746[6:Rew:735.0,675.0] || equal(sk_c4,sk_c8)** -> .
% 0.20/0.48 750[6:Rew:742.0,553.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.20/0.48 760[6:Rew:742.0,746.0] || equal(sk_c4,sk_c1)** -> .
% 0.20/0.48 766[6:Rew:742.0,736.0] || -> equal(multiply(inverse(u),u),sk_c1)**.
% 0.20/0.48 799[6:SpR:750.0,766.0] || -> equal(multiply(sk_c1,sk_c4),sk_c1)**.
% 0.20/0.48 800[6:Rew:738.0,799.0] || -> equal(sk_c4,sk_c1)**.
% 0.20/0.48 801[6:MRR:800.0,760.0] || -> .
% 0.20/0.48 804[5:Spt:801.0,25.1,559.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.48 805[5:Spt:801.0,25.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 806[5:MRR:20.1,804.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.48 808[5:MRR:30.0,804.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.48 809[5:MRR:15.0,804.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.48 810[5:MRR:5.0,804.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.48 822[5:SpR:808.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c8)**.
% 0.20/0.48 824[5:Rew:805.0,822.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.48 829[5:SpR:809.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.20/0.48 831[5:Rew:806.0,829.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 843[5:SpR:831.0,84.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.48 845[5:Rew:33.0,843.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 846[5:Rew:845.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 847[5:Rew:845.0,135.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 849[5:Rew:845.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.49 850[5:Rew:846.0,824.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 858[5:Rew:850.0,545.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.20/0.49 862[5:Rew:850.0,804.0] || equal(multiply(sk_c5,sk_c8),sk_c7)** -> .
% 0.20/0.49 867[5:Rew:850.0,846.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 868[5:Rew:850.0,847.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 869[5:Rew:868.0,810.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.49 870[5:Rew:869.0,556.0] || -> equal(inverse(sk_c5),sk_c1)**.
% 0.20/0.49 876[5:Rew:868.0,858.0,869.0,858.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.49 881[5:Rew:876.0,850.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.49 884[5:Rew:876.0,868.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.49 887[5:Rew:876.0,867.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 892[5:Rew:881.0,849.0] || -> equal(multiply(inverse(u),u),sk_c1)**.
% 0.20/0.49 894[5:Rew:884.0,862.0,876.0,862.0,869.0,862.0] || equal(sk_c5,sk_c1)** -> .
% 0.20/0.49 949[5:SpR:870.0,892.0] || -> equal(multiply(sk_c1,sk_c5),sk_c1)**.
% 0.20/0.49 952[5:Rew:887.0,949.0] || -> equal(sk_c5,sk_c1)**.
% 0.20/0.49 953[5:MRR:952.0,894.0] || -> .
% 0.20/0.49 960[4:Spt:953.0,24.0,556.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.20/0.49 961[4:Spt:953.0,24.1] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 962[4:MRR:19.0,960.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 963[4:MRR:9.0,960.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 964[4:MRR:29.0,960.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.49 965[4:MRR:14.0,960.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.49 966[4:MRR:4.0,960.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.49 979[4:SpR:964.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c8)**.
% 0.20/0.49 981[4:Rew:961.0,979.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 983[4:SpR:965.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.20/0.49 985[4:Rew:962.0,983.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 997[4:SpR:985.0,84.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 999[4:Rew:33.0,997.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 1000[4:Rew:999.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 1001[4:Rew:999.0,135.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1004[4:Rew:1000.0,981.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 1011[4:Rew:1004.0,545.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.20/0.49 1016[4:Rew:1004.0,548.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** -> .
% 0.20/0.49 1021[4:Rew:1004.0,1001.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 1022[4:Rew:1021.0,966.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.49 1028[4:Rew:1021.0,1011.0,1022.0,1011.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.49 1030[4:Rew:1028.0,963.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.49 1033[4:Rew:1028.0,1004.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.49 1036[4:Rew:1028.0,1021.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.49 1056[4:Rew:1036.0,1016.7,1028.0,1016.7,1022.0,1016.7,1036.0,1016.6,1022.0,1016.6,1033.0,1016.6,1036.0,1016.5,1028.0,1016.5,1033.0,1016.5,1036.0,1016.4,1033.0,1016.4,1022.0,1016.4,1028.0,1016.3,1022.0,1016.2,1028.0,1016.1,1022.0,1016.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(inverse(x),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) equal(x,sk_c1) -> .
% 0.20/0.49 1057[4:Con:1056.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.49 1136[4:SpL:1030.0,1057.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.49 1138[4:Obv:1136.1] || -> .
% 0.20/0.49 1139[3:Spt:1138.0,22.0,553.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.49 1140[3:Spt:1138.0,22.1] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 1141[3:MRR:17.0,1139.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 1142[3:MRR:7.0,1139.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 1143[3:MRR:27.0,1139.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.49 1144[3:MRR:12.0,1139.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.49 1145[3:MRR:2.0,1139.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.49 1156[3:SpR:1143.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c8)**.
% 0.20/0.49 1158[3:Rew:1140.0,1156.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 1160[3:SpR:1144.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.20/0.49 1162[3:Rew:1141.0,1160.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 1171[3:SpR:1162.0,84.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 1173[3:Rew:33.0,1171.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 1174[3:Rew:1173.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 1175[3:Rew:1173.0,135.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1178[3:Rew:1174.0,1158.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 1185[3:Rew:1178.0,545.0] || -> equal(multiply(sk_c7,sk_c8),sk_c8)**.
% 0.20/0.49 1190[3:Rew:1178.0,548.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(x,sk_c8),sk_c7)** -> .
% 0.20/0.49 1195[3:Rew:1178.0,1175.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 1196[3:Rew:1195.0,1145.0] || -> equal(sk_c7,sk_c1)**.
% 0.20/0.49 1201[3:Rew:1195.0,1185.0,1196.0,1185.0] || -> equal(sk_c8,sk_c1)**.
% 0.20/0.49 1202[3:Rew:1201.0,1142.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.49 1205[3:Rew:1201.0,1178.0] || -> equal(sk_c6,sk_c1)**.
% 0.20/0.49 1208[3:Rew:1201.0,1195.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.49 1227[3:Rew:1208.0,1190.7,1201.0,1190.7,1196.0,1190.7,1208.0,1190.6,1196.0,1190.6,1205.0,1190.6,1208.0,1190.5,1201.0,1190.5,1205.0,1190.5,1208.0,1190.4,1205.0,1190.4,1196.0,1190.4,1201.0,1190.3,1196.0,1190.2,1201.0,1190.1,1196.0,1190.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(inverse(x),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) equal(x,sk_c1) -> .
% 0.20/0.49 1228[3:Con:1227.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.49 1283[3:SpL:1202.0,1228.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.49 1285[3:Obv:1283.1] || -> .
% 0.20/0.49 1286[2:Spt:1285.0,16.1,545.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.49 1287[2:Spt:1285.0,16.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.20/0.49 1288[2:MRR:6.1,1286.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.49 1289[2:MRR:21.1,1286.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 1290[2:MRR:26.0,1286.0] || -> equal(multiply(sk_c3,sk_c8),sk_c6)**.
% 0.20/0.49 1291[2:MRR:11.0,1286.0] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.20/0.49 1292[2:MRR:1.0,1286.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.49 1300[2:SpR:1290.0,84.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c8)**.
% 0.20/0.49 1302[2:Rew:1289.0,1300.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 1304[2:SpR:1291.0,84.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.20/0.49 1306[2:Rew:1287.0,1304.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 1308[2:SpR:1292.0,84.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.49 1310[2:Rew:1288.0,1308.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.49 1315[2:SpR:1306.0,84.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 1317[2:Rew:33.0,1315.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 1318[2:Rew:1317.0,135.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1319[2:Rew:1317.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 1322[2:Rew:1318.0,1302.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.49 1326[2:Rew:1322.0,1286.0] || equal(multiply(sk_c7,sk_c8),sk_c8)** -> .
% 0.20/0.49 1334[2:Rew:1322.0,1319.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 1335[2:Rew:1334.0,1310.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.49 1348[2:Rew:1334.0,1326.0,1335.0,1326.0] || equal(sk_c8,sk_c8)* -> .
% 0.20/0.49 1349[2:Obv:1348.0] || -> .
% 0.20/0.49 % SZS output end Refutation
% 0.20/0.49 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_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 prove_this_26 prove_this_27 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.20/0.49
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