TSTP Solution File: GRP352-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP352-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:46:59 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP352-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 01:06:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.46
% 0.20/0.46 SPASS V 3.9
% 0.20/0.46 SPASS beiseite: Proof found.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 SPASS derived 794 clauses, backtracked 309 clauses, performed 11 splits and kept 660 clauses.
% 0.20/0.46 SPASS allocated 63577 KBytes.
% 0.20/0.46 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.46 0:00:00.03 for the input.
% 0.20/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.46 0:00:00.01 for inferences.
% 0.20/0.46 0:00:00.00 for the backtracking.
% 0.20/0.46 0:00:00.06 for the reduction.
% 0.20/0.46
% 0.20/0.46
% 0.20/0.46 Here is a proof with depth 4, length 339 :
% 0.20/0.46 % SZS output start Refutation
% 0.20/0.46 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c7).
% 0.20/0.46 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7).
% 0.20/0.46 4[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c5),sk_c7).
% 0.20/0.46 5[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 8[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 9[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 10[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.46 12[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.46 14[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.46 15[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 18[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 19[0:Inp] || -> equal(multiply(sk_c4,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 20[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 21[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.46 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 23[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.46 24[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.46 25[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 26[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c7) -> .
% 0.20/0.46 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.46 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.46 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.46 30[1:Spt:26.1,26.5] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.20/0.46 31[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.46 33[3:Spt:5.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.46 35[4:Spt:2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.46 38[1:SpL:27.0,30.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c6) -> .
% 0.20/0.46 39[5:Spt:4.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.46 41[5:SpL:39.0,30.1] || equal(inverse(sk_c4),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.46 42[5:Obv:41.1] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.20/0.46 43[5:Rew:33.0,42.0] || equal(sk_c7,sk_c6)** -> .
% 0.20/0.46 44[6:Spt:3.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.46 46[6:SpL:44.0,30.1] || equal(inverse(sk_c3),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.46 47[6:Obv:46.1] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.46 48[6:Rew:35.0,47.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.46 49[6:Obv:48.0] || -> .
% 0.20/0.46 50[6:Spt:49.0,3.0,44.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.20/0.46 51[6:Spt:49.0,3.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 52[6:MRR:23.1,50.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 54[6:MRR:18.0,50.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 64[3:SpR:33.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.46 65[4:SpR:35.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.20/0.46 66[6:SpR:52.0,28.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.20/0.46 68[1:SpL:28.0,30.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(sk_c7,identity) -> .
% 0.20/0.46 73[6:SpR:54.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.20/0.46 76[3:SpR:64.0,29.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.20/0.46 78[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.46 81[3:Rew:27.0,76.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.20/0.46 82[0:Rew:27.0,78.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.46 95[5:SpR:39.0,81.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.46 96[5:Rew:31.0,95.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 97[5:Rew:96.0,31.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.46 98[6:Rew:96.0,51.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.20/0.46 100[6:Rew:96.0,73.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.20/0.46 115[0:SpR:82.0,82.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.46 119[3:SpR:64.0,82.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.20/0.46 120[6:SpR:66.0,82.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c2)**.
% 0.20/0.46 122[5:SpR:97.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.46 123[6:SpR:98.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c6)**.
% 0.20/0.46 125[0:SpR:28.0,82.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.46 128[4:SpR:65.0,82.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.20/0.46 130[3:SpR:33.0,82.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.20/0.46 137[6:Rew:119.0,120.0] || -> equal(sk_c2,sk_c4)**.
% 0.20/0.46 142[6:Rew:137.0,100.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.20/0.46 145[5:Rew:28.0,122.0] || -> equal(sk_c7,identity)**.
% 0.20/0.46 149[5:Rew:145.0,43.0] || equal(identity,sk_c6)** -> .
% 0.20/0.46 153[5:Rew:145.0,65.0] || -> equal(multiply(identity,sk_c3),identity)**.
% 0.20/0.46 156[6:Rew:145.0,98.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.20/0.46 166[5:Rew:27.0,153.0] || -> equal(identity,sk_c3)**.
% 0.20/0.46 170[5:Rew:166.0,119.0] || -> equal(multiply(inverse(sk_c6),sk_c3),sk_c4)**.
% 0.20/0.46 171[5:Rew:166.0,145.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.46 173[5:Rew:166.0,149.0] || equal(sk_c3,sk_c6)** -> .
% 0.20/0.46 179[6:Rew:166.0,156.0] || -> equal(multiply(sk_c6,sk_c6),sk_c3)**.
% 0.20/0.46 185[6:Rew:171.0,123.0] || -> equal(multiply(inverse(sk_c6),sk_c3),sk_c6)**.
% 0.20/0.46 192[6:Rew:185.0,170.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.46 201[6:Rew:192.0,130.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.46 210[6:Rew:201.0,142.0,192.0,142.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.46 212[6:Rew:210.0,179.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.46 213[6:MRR:212.0,173.0] || -> .
% 0.20/0.46 223[5:Spt:213.0,4.0,39.0] || equal(multiply(sk_c4,sk_c6),sk_c7)** -> .
% 0.20/0.46 224[5:Spt:213.0,4.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 225[0:Rew:115.0,125.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.46 226[4:Rew:225.0,128.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.20/0.46 227[3:Rew:225.0,119.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.46 229[5:MRR:24.1,223.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 230[5:MRR:14.1,223.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 231[5:MRR:19.0,223.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 232[5:MRR:9.0,223.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 235[5:SpR:224.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.46 237[5:Rew:227.0,235.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.20/0.46 244[3:SpR:227.0,82.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.20/0.46 251[2:SpR:31.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.46 253[3:Rew:227.0,251.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.20/0.46 265[5:SpR:231.0,82.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 267[5:Rew:224.0,265.0,229.0,265.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 270[5:Rew:267.0,226.0] || -> equal(inverse(sk_c6),sk_c3)**.
% 0.20/0.46 271[5:Rew:267.0,230.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.46 272[5:Rew:267.0,31.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.46 274[5:Rew:267.0,223.0] || equal(multiply(sk_c4,sk_c6),sk_c6)** -> .
% 0.20/0.46 281[5:Rew:267.0,232.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.46 284[5:Rew:267.0,237.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.20/0.46 287[5:Rew:227.0,270.0] || -> equal(sk_c4,sk_c3)**.
% 0.20/0.46 293[5:Rew:287.0,284.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.20/0.46 295[5:Rew:293.0,274.0,287.0,274.0] || equal(sk_c5,sk_c6)** -> .
% 0.20/0.46 319[5:SpR:281.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.46 321[5:Rew:272.0,319.0,271.0,319.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 322[5:MRR:321.0,295.0] || -> .
% 0.20/0.46 323[4:Spt:322.0,2.0,35.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.46 324[4:Spt:322.0,2.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 325[4:MRR:22.0,323.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 326[4:MRR:12.0,323.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 327[4:MRR:17.0,323.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 328[4:MRR:7.0,323.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 345[3:SpR:253.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.20/0.46 355[4:SpR:327.0,82.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 357[4:Rew:324.0,355.0,325.0,355.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 359[4:Rew:357.0,326.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.46 361[4:Rew:357.0,31.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.46 363[4:Rew:357.0,38.1] || equal(inverse(identity),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.46 367[4:Rew:357.0,345.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.20/0.46 368[4:Rew:357.0,328.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.46 375[4:Obv:363.1] || equal(inverse(identity),sk_c7)** -> .
% 0.20/0.46 376[4:Rew:357.0,375.0] || equal(inverse(identity),sk_c6)** -> .
% 0.20/0.46 387[4:SpR:368.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.46 389[4:Rew:359.0,387.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.46 390[4:Rew:361.0,389.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 399[4:Rew:390.0,367.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.20/0.46 400[4:Rew:244.0,399.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.46 401[4:Rew:400.0,64.0] || -> equal(identity,sk_c4)**.
% 0.20/0.46 412[4:Rew:401.0,376.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.46 414[4:Rew:33.0,412.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.46 415[4:Obv:414.0] || -> .
% 0.20/0.46 417[3:Spt:415.0,5.0,33.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.46 418[3:Spt:415.0,5.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 419[3:MRR:25.0,417.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 420[3:MRR:15.0,417.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 421[3:MRR:20.0,417.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 422[3:MRR:10.0,417.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 424[3:SpR:418.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.46 434[3:SpR:421.0,82.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 436[3:Rew:418.0,434.0,419.0,434.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 438[3:Rew:436.0,420.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.46 439[3:Rew:436.0,31.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.46 440[3:Rew:436.0,251.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.46 444[3:Rew:436.0,422.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.46 445[3:Rew:436.0,68.0] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(sk_c7,identity) -> .
% 0.20/0.46 448[3:Rew:436.0,424.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.46 450[3:Rew:28.0,448.0] || -> equal(identity,sk_c5)**.
% 0.20/0.46 451[3:Rew:450.0,225.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.46 455[3:Rew:451.0,440.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.46 461[3:Rew:436.0,445.1,450.0,445.1,455.0,445.0,455.0,445.0] || equal(sk_c6,sk_c6) equal(sk_c5,sk_c6)** -> .
% 0.20/0.46 462[3:Obv:461.0] || equal(sk_c5,sk_c6)** -> .
% 0.20/0.46 472[3:SpR:444.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.46 474[3:Rew:438.0,472.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.46 475[3:Rew:439.0,474.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 476[3:MRR:475.0,462.0] || -> .
% 0.20/0.46 477[2:Spt:476.0,1.0,31.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.46 478[2:Spt:476.0,1.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 479[2:MRR:21.1,477.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 480[2:MRR:11.1,477.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 481[2:MRR:16.0,477.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 482[2:MRR:6.0,477.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 484[2:SpR:478.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.46 491[2:SpR:481.0,82.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 493[2:Rew:478.0,491.0,479.0,491.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 495[2:Rew:493.0,480.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.46 496[2:Rew:493.0,477.0] || equal(multiply(sk_c6,sk_c6),sk_c5)** -> .
% 0.20/0.46 499[2:Rew:493.0,482.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.46 502[2:Rew:493.0,484.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.46 505[2:Rew:28.0,502.0] || -> equal(identity,sk_c5)**.
% 0.20/0.46 508[2:Rew:505.0,28.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.46 522[2:SpR:499.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.46 524[2:Rew:495.0,522.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.46 525[2:Rew:524.0,496.0] || equal(sk_c5,sk_c6)** -> .
% 0.20/0.46 530[2:SpR:524.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.20/0.46 532[2:Rew:508.0,530.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 533[2:MRR:532.0,525.0] || -> .
% 0.20/0.46 534[1:Spt:533.0,26.0,26.2,26.3,26.4,26.6,26.7,26.8,26.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c7) -> .
% 0.20/0.46 536[2:Spt:1.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.20/0.46 537[2:Rew:536.0,534.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.46 539[2:Obv:537.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.46 542[2:SpR:536.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.20/0.46 544[3:Spt:2.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 546[3:Rew:544.0,539.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.20/0.46 547[3:Obv:546.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.20/0.46 550[3:SpR:544.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.46 552[4:Spt:25.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.46 561[5:Spt:22.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.46 562[5:SpR:561.0,82.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.20/0.46 564[6:Spt:24.1] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.46 566[6:SpR:564.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c6)**.
% 0.20/0.46 568[6:Rew:536.0,566.0,552.0,566.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 572[6:Rew:568.0,542.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.46 575[6:Rew:568.0,547.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c6)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.20/0.46 577[6:Rew:568.0,550.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c6)**.
% 0.20/0.46 578[6:Rew:28.0,572.0] || -> equal(sk_c7,identity)**.
% 0.20/0.46 581[6:Rew:578.0,13.0] || -> equal(inverse(sk_c1),identity) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.46 582[6:Rew:578.0,8.0] || -> equal(multiply(sk_c3,sk_c6),identity) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 584[6:Rew:578.0,562.0] || -> equal(multiply(identity,multiply(sk_c3,u)),u)**.
% 0.20/0.46 587[6:Rew:578.0,577.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c6)**.
% 0.20/0.46 588[6:Rew:225.0,587.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.46 589[6:Rew:27.0,584.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.46 593[6:Rew:589.0,581.1,578.0,581.1] || -> equal(inverse(sk_c1),identity)** equal(identity,sk_c6).
% 0.20/0.46 596[6:Rew:578.0,582.1,589.0,582.0] || -> equal(identity,sk_c6) equal(multiply(sk_c1,identity),sk_c6)**.
% 0.20/0.46 597[6:Rew:225.0,596.1] || -> equal(identity,sk_c6)** equal(sk_c1,sk_c6).
% 0.20/0.46 598[6:Rew:597.1,593.0] || -> equal(inverse(sk_c6),identity)** equal(identity,sk_c6).
% 0.20/0.46 599[6:Rew:588.0,598.0] || -> equal(identity,sk_c6)** equal(identity,sk_c6)**.
% 0.20/0.46 600[6:Obv:599.0] || -> equal(identity,sk_c6)**.
% 0.20/0.46 601[6:Rew:600.0,225.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.46 605[6:Rew:600.0,578.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 617[6:Rew:601.0,575.5,605.0,575.5,601.0,575.4,601.0,575.3,605.0,575.3,605.0,575.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.20/0.46 618[6:Con:617.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.46 668[6:SpL:588.0,618.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.46 670[6:Obv:668.1] || -> .
% 0.20/0.46 671[6:Spt:670.0,24.1,564.0] || equal(multiply(sk_c4,sk_c6),sk_c7)** -> .
% 0.20/0.46 672[6:Spt:670.0,24.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 673[6:MRR:14.1,671.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 674[6:MRR:19.0,671.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 675[6:MRR:9.0,671.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 688[6:SpR:674.0,82.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 690[6:Rew:544.0,688.0,672.0,688.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 692[6:Rew:690.0,673.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.46 694[6:Rew:690.0,536.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.46 695[6:Rew:690.0,550.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.46 697[6:Rew:690.0,671.0] || equal(multiply(sk_c4,sk_c6),sk_c6)** -> .
% 0.20/0.46 701[6:Rew:690.0,675.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.46 705[6:Rew:28.0,695.0] || -> equal(identity,sk_c5)**.
% 0.20/0.46 706[6:Rew:705.0,225.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.46 707[6:Rew:705.0,27.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.46 708[6:Rew:705.0,28.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.46 724[6:SpR:701.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.46 726[6:Rew:692.0,724.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.46 727[6:Rew:694.0,726.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 731[6:Rew:727.0,706.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.46 732[6:Rew:727.0,707.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.46 733[6:Rew:727.0,708.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.46 738[6:Rew:731.0,697.0] || equal(sk_c4,sk_c6)** -> .
% 0.20/0.46 785[6:SpR:552.0,733.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.20/0.46 787[6:Rew:732.0,785.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.46 788[6:MRR:787.0,738.0] || -> .
% 0.20/0.46 792[5:Spt:788.0,22.0,561.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.20/0.46 793[5:Spt:788.0,22.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 794[5:MRR:12.0,792.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 795[5:MRR:17.0,792.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 796[5:MRR:7.0,792.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 808[5:SpR:795.0,82.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 810[5:Rew:544.0,808.0,793.0,808.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 811[5:Rew:810.0,794.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.46 813[5:Rew:810.0,536.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.46 815[5:Rew:810.0,542.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.46 816[5:Rew:810.0,550.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.46 819[5:Rew:810.0,796.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.46 820[5:Rew:810.0,547.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.20/0.46 823[5:Rew:28.0,816.0] || -> equal(identity,sk_c5)**.
% 0.20/0.46 825[5:Rew:823.0,225.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.46 828[5:Rew:825.0,815.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.46 832[5:Rew:810.0,820.5,810.0,820.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.20/0.46 833[5:Con:832.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.20/0.46 847[5:SpR:819.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.46 849[5:Rew:813.0,847.0,811.0,847.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 854[5:Rew:849.0,825.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.46 857[5:Rew:849.0,833.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c6)** -> .
% 0.20/0.46 872[5:Con:857.1] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.46 873[5:Rew:854.0,872.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.46 937[5:SpL:828.0,873.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.46 939[5:Obv:937.1] || -> .
% 0.20/0.46 940[4:Spt:939.0,25.0,552.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.20/0.46 941[4:Spt:939.0,25.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 942[4:MRR:15.0,940.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 943[4:MRR:20.0,940.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.46 944[4:MRR:10.0,940.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.46 956[4:SpR:943.0,82.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.46 958[4:Rew:544.0,956.0,941.0,956.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 959[4:Rew:958.0,942.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.46 960[4:Rew:958.0,536.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.20/0.46 962[4:Rew:958.0,550.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.46 963[4:Rew:958.0,542.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.20/0.46 966[4:Rew:958.0,944.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.46 967[4:Rew:958.0,547.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.20/0.46 970[4:Rew:28.0,962.0] || -> equal(identity,sk_c5)**.
% 0.20/0.46 971[4:Rew:970.0,225.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.20/0.46 975[4:Rew:971.0,963.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.46 979[4:Rew:958.0,967.5,958.0,967.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.20/0.46 980[4:Con:979.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c5)** -> .
% 0.20/0.46 989[4:SpR:966.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.46 991[4:Rew:959.0,989.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.46 992[4:Rew:960.0,991.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 996[4:Rew:992.0,971.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.46 1000[4:Rew:992.0,980.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c6)** -> .
% 0.20/0.46 1014[4:Con:1000.1] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.46 1015[4:Rew:996.0,1014.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.46 1052[4:SpL:975.0,1015.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.46 1054[4:Obv:1052.1] || -> .
% 0.20/0.46 1055[3:Spt:1054.0,2.1,544.0] || equal(multiply(sk_c6,sk_c5),sk_c7)** -> .
% 0.20/0.46 1056[3:Spt:1054.0,2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.20/0.46 1057[3:MRR:5.1,1055.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.46 1058[3:MRR:3.1,1055.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.46 1059[3:MRR:4.1,1055.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.46 1068[3:SpR:1058.0,82.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.20/0.46 1070[3:Rew:1056.0,1068.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.46 1072[3:SpR:1059.0,82.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c6)**.
% 0.20/0.46 1074[3:Rew:536.0,1072.0,1057.0,1072.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.46 1076[3:Rew:1074.0,542.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.46 1077[3:Rew:1074.0,1055.0] || equal(multiply(sk_c6,sk_c6),sk_c7)** -> .
% 0.20/0.46 1079[3:Rew:28.0,1076.0] || -> equal(sk_c7,identity)**.
% 0.20/0.46 1085[3:Rew:1079.0,1070.0] || -> equal(multiply(identity,identity),sk_c6)**.
% 0.20/0.46 1087[3:Rew:27.0,1085.0] || -> equal(identity,sk_c6)**.
% 0.20/0.46 1088[3:Rew:1087.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.46 1092[3:Rew:1087.0,1079.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.46 1103[3:Rew:1088.0,1077.0,1092.0,1077.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.46 1104[3:Obv:1103.0] || -> .
% 0.20/0.46 1110[2:Spt:1104.0,1.0,536.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.20/0.46 1111[2:Spt:1104.0,1.1] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.46 1112[2:MRR:21.1,1110.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.20/0.46 1113[2:MRR:11.1,1110.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.46 1114[2:MRR:16.0,1110.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.20/0.47 1115[2:MRR:6.0,1110.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.20/0.47 1117[2:SpR:1111.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.47 1124[2:SpR:1114.0,82.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.20/0.47 1126[2:Rew:1111.0,1124.0,1112.0,1124.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.47 1128[2:Rew:1126.0,1113.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.20/0.47 1129[2:Rew:1126.0,1110.0] || equal(multiply(sk_c6,sk_c6),sk_c5)** -> .
% 0.20/0.47 1130[2:Rew:1126.0,1115.0] || -> equal(multiply(sk_c1,sk_c6),sk_c6)**.
% 0.20/0.47 1131[2:Rew:1126.0,1117.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.20/0.47 1134[2:Rew:28.0,1131.0] || -> equal(identity,sk_c5)**.
% 0.20/0.47 1137[2:Rew:1134.0,28.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.20/0.47 1146[2:SpR:1130.0,82.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c6)**.
% 0.20/0.47 1148[2:Rew:1128.0,1146.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.47 1149[2:Rew:1148.0,1129.0] || equal(sk_c5,sk_c6)** -> .
% 0.20/0.47 1151[2:SpR:1148.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.20/0.47 1153[2:Rew:1137.0,1151.0] || -> equal(sk_c5,sk_c6)**.
% 0.20/0.47 1154[2:MRR:1153.0,1149.0] || -> .
% 0.20/0.47 % SZS output end Refutation
% 0.20/0.47 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 left_identity left_inverse associativity
% 0.20/0.47
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