TSTP Solution File: GRP342-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP342-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:46:56 EDT 2022
% Result : Unsatisfiable 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP342-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n024.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 10:00:18 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.53
% 0.22/0.53 SPASS V 3.9
% 0.22/0.53 SPASS beiseite: Proof found.
% 0.22/0.53 % SZS status Theorem
% 0.22/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.53 SPASS derived 1201 clauses, backtracked 433 clauses, performed 12 splits and kept 873 clauses.
% 0.22/0.53 SPASS allocated 63823 KBytes.
% 0.22/0.53 SPASS spent 0:00:00.15 on the problem.
% 0.22/0.53 0:00:00.04 for the input.
% 0.22/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.53 0:00:00.01 for inferences.
% 0.22/0.53 0:00:00.00 for the backtracking.
% 0.22/0.53 0:00:00.08 for the reduction.
% 0.22/0.53
% 0.22/0.53
% 0.22/0.53 Here is a proof with depth 5, length 437 :
% 0.22/0.53 % SZS output start Refutation
% 0.22/0.53 1[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.22/0.53 2[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.22/0.53 3[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.53 4[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.22/0.53 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.22/0.53 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.53 7[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 8[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.22/0.53 9[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.53 10[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.22/0.53 11[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 12[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.53 13[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.22/0.53 14[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.53 15[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.53 16[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.53 17[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.53 18[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.53 19[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 20[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.22/0.53 21[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(inverse(sk_c2),sk_c7)**.
% 0.22/0.53 22[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.22/0.53 23[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 24[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c7)**.
% 0.22/0.53 25[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c6),sk_c7).
% 0.22/0.53 26[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.53 27[0:Inp] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.53 28[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.53 29[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.53 30[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.53 31[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(inverse(y),sk_c8) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(x,sk_c6),sk_c7)** equal(multiply(y,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.53 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.22/0.53 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.22/0.53 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.22/0.53 35[1:Spt:31.0,31.4,31.6] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.22/0.53 36[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.53 39[3:Spt:19.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.22/0.53 41[4:Spt:7.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.53 44[1:SpL:32.0,35.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.22/0.53 45[5:Spt:25.1] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.53 49[6:Spt:13.1] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.22/0.53 55[3:SpR:39.0,33.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.22/0.53 56[4:SpR:41.0,33.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.22/0.53 59[3:SpL:55.0,35.1] || equal(inverse(sk_c7),sk_c2) equal(sk_c8,identity) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.22/0.53 68[3:SpR:55.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.22/0.53 70[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.22/0.53 71[5:SpR:45.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.22/0.53 72[4:SpR:56.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.22/0.53 74[3:Rew:32.0,68.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.22/0.53 75[4:Rew:32.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.22/0.53 76[0:Rew:32.0,70.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.22/0.53 80[5:SpR:45.0,74.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.53 81[3:SpL:74.0,35.1] || equal(multiply(sk_c2,u),inverse(sk_c7)) equal(u,sk_c8) equal(multiply(multiply(sk_c2,u),sk_c7),sk_c8)** -> .
% 0.22/0.53 84[3:Rew:34.0,81.2] || equal(multiply(sk_c2,u),inverse(sk_c7)) equal(u,sk_c8) equal(multiply(sk_c2,multiply(u,sk_c7)),sk_c8)** -> .
% 0.22/0.53 85[5:SpR:80.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.22/0.53 92[6:SpR:49.0,75.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.22/0.53 100[0:SpR:76.0,76.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.22/0.53 103[2:SpR:36.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.22/0.53 104[3:SpR:55.0,76.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c2)**.
% 0.22/0.53 106[5:SpR:80.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.22/0.53 108[0:SpR:33.0,76.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.22/0.53 110[4:SpR:56.0,76.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.22/0.53 112[6:SpR:92.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.22/0.53 118[5:Rew:103.0,106.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 121[5:Rew:118.0,41.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.53 123[5:Rew:118.0,56.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.22/0.53 131[5:Rew:118.0,84.1] || equal(multiply(sk_c2,u),inverse(sk_c7)) equal(u,sk_c7) equal(multiply(sk_c2,multiply(u,sk_c7)),sk_c8)** -> .
% 0.22/0.53 149[5:Rew:104.0,110.0,118.0,110.0] || -> equal(sk_c2,sk_c1)**.
% 0.22/0.53 153[5:Rew:149.0,104.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c1)**.
% 0.22/0.53 155[6:Rew:118.0,112.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.22/0.53 156[6:Rew:33.0,155.0] || -> equal(identity,sk_c7)**.
% 0.22/0.53 157[6:Rew:156.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 159[6:Rew:156.0,123.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.22/0.53 161[6:Rew:157.0,159.0] || -> equal(sk_c1,sk_c7)**.
% 0.22/0.53 162[6:Rew:161.0,121.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.53 164[6:Rew:161.0,149.0] || -> equal(sk_c2,sk_c7)**.
% 0.22/0.53 168[6:Rew:156.0,108.0] || -> equal(multiply(inverse(inverse(u)),sk_c7),u)**.
% 0.22/0.53 177[6:Rew:100.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.53 204[6:Rew:157.0,131.2,164.0,131.2,177.0,131.2,118.0,131.2,157.0,131.0,164.0,131.0,162.0,131.0] || equal(u,sk_c7)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.22/0.53 205[6:Obv:204.1] || equal(u,sk_c7)* -> .
% 0.22/0.53 206[6:UnC:205.0,76.0] || -> .
% 0.22/0.53 210[6:Spt:206.0,13.1,49.0] || equal(multiply(sk_c1,sk_c7),sk_c8)** -> .
% 0.22/0.53 211[6:Spt:206.0,13.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 213[6:Rew:118.0,211.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.22/0.53 215[6:Rew:118.0,210.0] || equal(multiply(sk_c1,sk_c7),sk_c7)** -> .
% 0.22/0.53 216[0:Rew:100.0,108.0] || -> equal(multiply(u,identity),u)**.
% 0.22/0.53 217[5:Rew:216.0,153.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.22/0.53 223[5:Rew:118.0,18.1,118.0,18.0] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 224[6:MRR:223.1,215.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.22/0.53 225[5:Rew:118.0,15.1] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 226[6:MRR:225.1,215.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 227[5:Rew:149.0,71.0] || -> equal(multiply(sk_c1,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.22/0.53 229[5:Rew:118.0,17.1,118.0,17.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 230[6:MRR:229.1,215.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.53 231[5:Rew:118.0,16.1,118.0,16.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 232[6:MRR:231.1,215.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 233[5:Rew:118.0,14.1,118.0,14.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 234[6:MRR:233.1,215.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 257[5:SpR:217.0,76.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),u)**.
% 0.22/0.53 259[6:SpR:224.0,76.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.22/0.53 281[6:SpR:213.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.22/0.53 283[6:Rew:217.0,281.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.22/0.53 284[6:Rew:283.0,215.0] || equal(sk_c6,sk_c7)** -> .
% 0.22/0.53 285[6:SpR:232.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.22/0.53 289[6:SpR:234.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.22/0.53 291[6:Rew:232.0,289.0,226.0,289.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.53 297[6:Rew:291.0,285.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.22/0.53 304[6:Rew:85.0,297.0] || -> equal(multiply(sk_c6,u),multiply(sk_c7,u))**.
% 0.22/0.53 306[6:Rew:304.0,227.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.22/0.53 309[6:Rew:257.0,306.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 317[6:Rew:309.0,259.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.22/0.53 332[6:Rew:317.0,230.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 333[6:MRR:332.0,284.0] || -> .
% 0.22/0.53 337[5:Spt:333.0,25.1,45.0] || equal(multiply(sk_c2,sk_c6),sk_c7)** -> .
% 0.22/0.53 338[5:Spt:333.0,25.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 340[3:Rew:216.0,104.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.22/0.53 341[3:Rew:340.0,103.0] || -> equal(multiply(sk_c2,sk_c6),sk_c8)**.
% 0.22/0.53 342[5:Rew:341.0,337.0] || equal(sk_c8,sk_c7)** -> .
% 0.22/0.53 345[3:Rew:341.0,30.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c8,sk_c7).
% 0.22/0.53 346[5:MRR:345.1,342.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.53 347[3:Rew:341.0,27.1] || -> equal(inverse(sk_c3),sk_c4)** equal(sk_c8,sk_c7).
% 0.22/0.53 349[3:Rew:341.0,29.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(sk_c8,sk_c7).
% 0.22/0.53 350[5:MRR:349.1,342.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 351[3:Rew:341.0,28.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(sk_c8,sk_c7).
% 0.22/0.53 353[3:Rew:341.0,26.1] || -> equal(multiply(sk_c3,sk_c4),sk_c8)** equal(sk_c8,sk_c7).
% 0.22/0.53 355[3:Rew:340.0,59.0] || equal(sk_c2,sk_c2) equal(sk_c8,identity) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.22/0.53 356[3:Obv:355.0] || equal(sk_c8,identity) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.22/0.53 395[5:SpR:350.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.22/0.53 397[5:Rew:338.0,395.0,346.0,395.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 398[5:MRR:397.0,342.0] || -> .
% 0.22/0.53 399[4:Spt:398.0,7.0,41.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.53 400[4:Spt:398.0,7.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 402[3:Rew:347.1,9.1] || -> equal(inverse(sk_c3),sk_c4) equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.53 408[3:Rew:351.1,10.0] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.22/0.53 409[3:Rew:353.1,8.0] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.22/0.53 416[4:SpR:400.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.22/0.53 417[4:SpR:400.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.22/0.53 419[3:SpR:341.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.22/0.53 434[0:SpR:33.0,76.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.22/0.53 435[0:SpR:33.0,216.0] || -> equal(inverse(identity),identity)**.
% 0.22/0.53 438[3:SpR:340.0,33.0] || -> equal(multiply(sk_c2,sk_c7),identity)**.
% 0.22/0.53 440[1:Rew:435.0,44.0] || equal(identity,u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.22/0.53 441[3:Rew:438.0,356.1] || equal(sk_c8,identity)** equal(sk_c8,identity)** -> .
% 0.22/0.53 442[0:Rew:216.0,434.0] || -> equal(inverse(inverse(u)),u)**.
% 0.22/0.53 446[3:Obv:441.0] || equal(sk_c8,identity)** -> .
% 0.22/0.53 458[0:SpR:442.0,76.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.22/0.53 459[0:SpR:442.0,33.0] || -> equal(multiply(u,inverse(u)),identity)**.
% 0.22/0.53 465[5:Spt:345.1] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 466[5:Rew:465.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.53 468[5:Rew:465.0,341.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.53 469[5:Rew:465.0,399.0] || equal(inverse(sk_c1),sk_c7)** -> .
% 0.22/0.53 470[5:Rew:465.0,446.0] || equal(identity,sk_c7)** -> .
% 0.22/0.53 482[5:Rew:465.0,408.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 484[5:Rew:465.0,409.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 485[5:Rew:465.0,417.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.22/0.53 488[5:MRR:402.1,469.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 489[5:Rew:438.0,485.0,340.0,485.0] || -> equal(identity,sk_c6)**.
% 0.22/0.53 491[5:Rew:489.0,216.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.22/0.53 497[5:Rew:489.0,470.0] || equal(sk_c6,sk_c7)** -> .
% 0.22/0.53 498[5:Rew:491.0,468.0] || -> equal(sk_c2,sk_c7)**.
% 0.22/0.53 499[5:Rew:498.0,39.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.53 501[5:Rew:498.0,74.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.22/0.53 509[5:MRR:482.0,469.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 510[5:MRR:484.0,469.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 522[5:SpR:488.0,442.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.22/0.53 551[5:SpR:510.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),multiply(sk_c7,u))**.
% 0.22/0.53 552[5:SpR:510.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.22/0.53 554[5:Rew:509.0,552.0,488.0,552.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.53 556[5:Rew:554.0,522.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.22/0.53 562[5:Rew:499.0,556.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.53 574[5:Rew:501.0,551.0,562.0,551.0,554.0,551.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 575[5:Rew:574.0,466.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 577[5:MRR:575.0,497.0] || -> .
% 0.22/0.53 578[5:Spt:577.0,345.1,465.0] || equal(sk_c8,sk_c7)** -> .
% 0.22/0.53 579[5:Spt:577.0,345.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.53 581[5:MRR:349.1,578.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 585[5:SpR:579.0,442.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.22/0.53 601[5:SpR:585.0,76.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.22/0.53 615[5:SpR:581.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.22/0.53 620[5:Rew:601.0,615.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.53 621[5:Rew:620.0,416.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.22/0.53 622[5:Rew:620.0,419.0] || -> equal(multiply(sk_c8,u),multiply(sk_c2,u))**.
% 0.22/0.53 624[5:Rew:621.0,400.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.22/0.53 628[5:Rew:621.0,622.0] || -> equal(multiply(sk_c2,u),multiply(sk_c7,u))**.
% 0.22/0.53 629[5:Rew:628.0,341.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.22/0.53 633[5:Rew:624.0,629.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 634[5:MRR:633.0,578.0] || -> .
% 0.22/0.53 637[3:Spt:634.0,19.0,39.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.22/0.53 638[3:Spt:634.0,19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 639[3:MRR:24.1,637.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.53 640[3:MRR:21.1,637.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 641[3:MRR:23.0,637.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 642[3:MRR:22.0,637.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.22/0.53 643[3:MRR:20.0,637.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.22/0.53 648[3:SpR:639.0,442.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.22/0.53 654[3:SpR:648.0,76.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.22/0.53 663[3:SpR:641.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.22/0.53 664[3:SpR:641.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.22/0.53 666[3:Rew:638.0,664.0,639.0,664.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 670[3:Rew:666.0,36.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.53 672[3:Rew:666.0,440.1] || equal(identity,u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.22/0.53 679[3:Rew:666.0,654.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.22/0.53 680[3:Rew:666.0,642.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 681[3:Rew:666.0,643.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 686[3:Rew:679.0,663.0,666.0,663.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.53 690[3:Rew:666.0,672.2] || equal(identity,u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.22/0.53 723[3:SpR:681.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.22/0.53 725[3:Rew:680.0,723.0,640.0,723.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.53 726[3:Rew:725.0,640.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.22/0.53 728[3:Rew:725.0,680.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.53 741[3:Rew:670.0,728.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 744[3:Rew:741.0,686.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 779[3:SpR:744.0,216.0] || -> equal(identity,sk_c7)**.
% 0.22/0.53 783[3:Rew:779.0,216.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.53 787[3:Rew:779.0,690.0] || equal(sk_c7,u) equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.22/0.53 797[3:Obv:787.0] || equal(u,sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.22/0.53 798[3:Rew:783.0,797.1] || equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.22/0.53 799[3:Obv:798.0] || equal(u,sk_c7)* -> .
% 0.22/0.53 800[3:UnC:799.0,726.0] || -> .
% 0.22/0.53 801[2:Spt:800.0,1.1,36.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.53 802[2:Spt:800.0,1.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 803[2:MRR:6.1,801.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.53 804[2:MRR:3.1,801.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 805[2:MRR:5.1,801.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 806[2:MRR:4.1,801.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.22/0.53 807[2:MRR:2.1,801.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.22/0.53 820[2:SpR:804.0,442.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.22/0.53 825[2:SpR:820.0,76.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),u)**.
% 0.22/0.53 829[2:SpR:805.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.22/0.53 831[2:Rew:802.0,829.0,803.0,829.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 832[2:Rew:831.0,802.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.22/0.53 836[2:Rew:831.0,801.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.22/0.53 839[2:Rew:831.0,806.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 840[2:Rew:831.0,807.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 875[2:SpR:840.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),multiply(sk_c7,u))**.
% 0.22/0.53 876[2:SpR:840.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.22/0.53 878[2:Rew:839.0,876.0,804.0,876.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.53 881[2:Rew:878.0,839.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.53 884[2:Rew:878.0,825.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.22/0.53 892[2:Rew:881.0,836.0] || equal(sk_c6,sk_c7)** -> .
% 0.22/0.53 895[2:Rew:884.0,875.0,878.0,875.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 896[2:Rew:895.0,832.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 899[2:MRR:896.0,892.0] || -> .
% 0.22/0.53 900[1:Spt:899.0,31.1,31.2,31.3,31.5,31.7,31.8,31.9,31.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.22/0.53 902[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.22/0.53 903[2:Rew:902.0,900.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.22/0.53 905[2:Obv:903.7] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.22/0.53 908[2:SpR:902.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.22/0.53 910[3:Spt:7.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.22/0.53 912[3:SpR:910.0,442.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.22/0.53 914[4:Spt:19.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.22/0.53 916[4:SpR:914.0,442.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.22/0.53 918[4:Rew:916.0,908.0] || -> equal(multiply(sk_c2,sk_c6),sk_c8)**.
% 0.22/0.53 919[4:Rew:918.0,26.1] || -> equal(multiply(sk_c3,sk_c4),sk_c8)** equal(sk_c8,sk_c7).
% 0.22/0.53 920[4:Rew:918.0,28.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(sk_c8,sk_c7).
% 0.22/0.53 921[4:Rew:918.0,29.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(sk_c8,sk_c7).
% 0.22/0.53 922[4:Rew:918.0,25.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(sk_c8,sk_c7).
% 0.22/0.53 923[4:Rew:918.0,27.1] || -> equal(inverse(sk_c3),sk_c4)** equal(sk_c8,sk_c7).
% 0.22/0.53 924[4:Rew:918.0,30.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c8,sk_c7).
% 0.22/0.53 925[4:Rew:923.1,15.1] || -> equal(inverse(sk_c3),sk_c4) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 926[4:Rew:924.1,18.1] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 927[4:Rew:919.1,14.1] || -> equal(multiply(sk_c3,sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 928[4:Rew:920.1,16.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 929[4:Rew:921.1,17.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 959[3:SpR:910.0,459.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.22/0.53 996[5:Spt:923.1] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 997[5:Rew:996.0,902.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.53 998[5:Rew:996.0,910.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.22/0.53 999[5:Rew:996.0,912.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.22/0.53 1000[5:Rew:996.0,918.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.22/0.53 1001[5:Rew:996.0,959.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.22/0.53 1005[5:Rew:996.0,905.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c7)** -> .
% 0.22/0.53 1010[5:Rew:996.0,926.0] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 1011[5:Rew:996.0,927.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 1012[5:Rew:996.0,928.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 1013[5:Rew:996.0,929.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.22/0.53 1014[5:Rew:916.0,999.0] || -> equal(sk_c2,sk_c1)**.
% 0.22/0.53 1016[5:Rew:1014.0,916.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.22/0.53 1021[5:Rew:1014.0,1000.0] || -> equal(multiply(sk_c1,sk_c6),sk_c7)**.
% 0.22/0.53 1022[5:Rew:1001.0,925.1] || -> equal(inverse(sk_c3),sk_c4)** equal(identity,sk_c7).
% 0.22/0.53 1024[5:Rew:1001.0,1010.1] || -> equal(inverse(sk_c5),sk_c7)** equal(identity,sk_c7).
% 0.22/0.53 1026[5:Rew:1001.0,1011.1] || -> equal(multiply(sk_c3,sk_c4),sk_c7)** equal(identity,sk_c7).
% 0.22/0.53 1027[5:Rew:1001.0,1012.1] || -> equal(multiply(sk_c4,sk_c7),sk_c7)** equal(identity,sk_c7).
% 0.22/0.53 1028[5:Rew:1001.0,1013.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)** equal(identity,sk_c7).
% 0.22/0.53 1029[5:Rew:996.0,1005.5,996.0,1005.3,996.0,1005.2,996.0,1005.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c7)** -> .
% 0.22/0.53 1032[6:Spt:1022.1] || -> equal(identity,sk_c7)**.
% 0.22/0.53 1033[6:Rew:1032.0,435.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.53 1034[6:Rew:1032.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 1035[6:Rew:1032.0,216.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.53 1041[6:Rew:1016.0,1033.0] || -> equal(sk_c1,sk_c7)**.
% 0.22/0.53 1042[6:Rew:1041.0,998.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.53 1050[6:Rew:1034.0,1029.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.22/0.53 1052[6:Rew:1034.0,997.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 1060[6:Rew:1052.0,1050.6,1035.0,1050.5,1035.0,1050.4,1052.0,1050.4,1035.0,1050.3,1052.0,1050.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.22/0.53 1061[6:Obv:1060.6] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.22/0.53 1062[6:Con:1061.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.22/0.53 1119[6:SpL:1042.0,1062.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.22/0.53 1120[6:Obv:1119.1] || -> .
% 0.22/0.53 1121[6:Spt:1120.0,1022.1,1032.0] || equal(identity,sk_c7)** -> .
% 0.22/0.53 1122[6:Spt:1120.0,1022.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 1123[6:MRR:1024.1,1121.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.22/0.53 1125[6:MRR:1026.1,1121.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 1126[6:MRR:1027.1,1121.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 1127[6:MRR:1028.1,1121.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.22/0.53 1133[6:SpR:1122.0,442.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.22/0.53 1151[6:SpR:1123.0,76.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.22/0.53 1152[6:SpR:1123.0,442.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.22/0.53 1155[6:Rew:1016.0,1152.0] || -> equal(sk_c1,sk_c5)**.
% 0.22/0.53 1160[6:Rew:1155.0,1001.0] || -> equal(multiply(sk_c5,sk_c7),identity)**.
% 0.22/0.53 1161[6:Rew:1155.0,1021.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.22/0.53 1165[6:Rew:1127.0,1160.0] || -> equal(identity,sk_c6)**.
% 0.22/0.53 1167[6:Rew:1165.0,1121.0] || equal(sk_c6,sk_c7)** -> .
% 0.22/0.53 1168[6:Rew:1165.0,216.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.22/0.53 1174[6:Rew:1168.0,1161.0] || -> equal(sk_c5,sk_c7)**.
% 0.22/0.53 1177[6:Rew:1174.0,1123.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.53 1184[6:Rew:1174.0,1151.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.22/0.53 1207[6:SpR:1125.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),multiply(sk_c7,u))**.
% 0.22/0.53 1208[6:SpR:1125.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.22/0.53 1210[6:Rew:1122.0,1208.0] || -> equal(multiply(sk_c4,sk_c7),sk_c4)**.
% 0.22/0.53 1211[6:Rew:1126.0,1210.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.53 1213[6:Rew:1211.0,1133.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.22/0.53 1218[6:Rew:1177.0,1213.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.53 1226[6:Rew:1184.0,1207.0,1218.0,1207.0,1211.0,1207.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 1227[6:Rew:1226.0,997.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 1229[6:MRR:1227.0,1167.0] || -> .
% 0.22/0.53 1230[5:Spt:1229.0,923.1,996.0] || equal(sk_c8,sk_c7)** -> .
% 0.22/0.53 1231[5:Spt:1229.0,923.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 1232[5:MRR:924.1,1230.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.53 1235[5:MRR:921.1,1230.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 1236[5:MRR:922.1,1230.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 1268[5:SpR:1232.0,442.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.22/0.53 1271[5:Rew:912.0,1268.0] || -> equal(sk_c1,sk_c5)**.
% 0.22/0.53 1275[5:Rew:1271.0,959.0] || -> equal(multiply(sk_c5,sk_c8),identity)**.
% 0.22/0.53 1278[5:Rew:1235.0,1275.0] || -> equal(identity,sk_c6)**.
% 0.22/0.53 1281[5:Rew:1278.0,216.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.22/0.53 1291[5:Rew:1281.0,918.0] || -> equal(sk_c8,sk_c2)**.
% 0.22/0.53 1292[5:Rew:1281.0,1236.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 1294[5:Rew:1291.0,1230.0] || equal(sk_c2,sk_c7)** -> .
% 0.22/0.53 1301[5:Rew:1291.0,1292.0] || -> equal(sk_c2,sk_c7)**.
% 0.22/0.53 1307[5:Rew:1301.0,1294.0] || equal(sk_c7,sk_c7)* -> .
% 0.22/0.53 1308[5:Obv:1307.0] || -> .
% 0.22/0.53 1330[4:Spt:1308.0,19.0,914.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.22/0.53 1331[4:Spt:1308.0,19.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 1332[4:MRR:24.1,1330.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.53 1333[4:MRR:21.1,1330.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 1334[4:MRR:23.0,1330.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 1335[4:MRR:22.0,1330.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.22/0.53 1336[4:MRR:20.0,1330.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.22/0.53 1337[4:Rew:1331.0,905.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.22/0.53 1338[4:Obv:1337.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.22/0.53 1354[4:SpR:1332.0,442.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.22/0.53 1357[4:Rew:912.0,1354.0] || -> equal(sk_c1,sk_c5)**.
% 0.22/0.53 1360[4:Rew:1357.0,959.0] || -> equal(multiply(sk_c5,sk_c8),identity)**.
% 0.22/0.53 1365[4:Rew:1334.0,1360.0] || -> equal(identity,sk_c6)**.
% 0.22/0.53 1367[4:Rew:1365.0,216.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.22/0.53 1373[4:Rew:1367.0,1331.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 1375[4:Rew:1367.0,908.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.22/0.53 1376[4:Rew:1367.0,1338.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(v,sk_c7) equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.22/0.53 1378[4:Rew:1373.0,902.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.53 1381[4:Rew:1373.0,1335.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 1382[4:Rew:1373.0,1336.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 1386[4:Rew:1373.0,1375.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.53 1399[4:Rew:1373.0,1376.5,1373.0,1376.3,1373.0,1376.2,1373.0,1376.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(v,sk_c7) equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.22/0.53 1433[4:SpR:1382.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.22/0.53 1435[4:Rew:1381.0,1433.0,1333.0,1433.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.53 1438[4:Rew:1435.0,1381.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.53 1446[4:Rew:1378.0,1438.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 1450[4:Rew:1446.0,1367.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.53 1455[4:Rew:1446.0,1399.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(v,sk_c7) equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.22/0.53 1462[4:Con:1455.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** equal(v,sk_c7) -> .
% 0.22/0.53 1463[4:Rew:1450.0,1462.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.22/0.53 1464[4:Con:1463.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.22/0.53 1493[4:SpL:1386.0,1464.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.22/0.53 1494[4:Obv:1493.1] || -> .
% 0.22/0.53 1495[3:Spt:1494.0,7.0,910.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.22/0.53 1496[3:Spt:1494.0,7.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 1497[3:MRR:12.1,1495.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.53 1498[3:MRR:9.1,1495.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 1499[3:MRR:11.0,1495.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 1500[3:MRR:10.0,1495.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.22/0.53 1501[3:MRR:8.0,1495.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.22/0.53 1502[3:Rew:1496.0,905.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.22/0.53 1503[3:Obv:1502.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.22/0.53 1517[3:SpR:1497.0,458.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.22/0.53 1535[3:SpR:1499.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.22/0.53 1536[3:SpR:1499.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.22/0.53 1538[3:Rew:1496.0,1536.0,1497.0,1536.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 1543[3:Rew:1538.0,902.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.22/0.53 1547[3:Rew:1538.0,1517.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.22/0.53 1548[3:Rew:1538.0,1500.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 1549[3:Rew:1538.0,1501.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 1550[3:Rew:1538.0,1503.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.22/0.53 1555[3:Rew:1547.0,1535.0,1538.0,1535.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.22/0.53 1558[3:Rew:1538.0,1550.5,1538.0,1550.3,1538.0,1550.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.22/0.53 1589[3:SpR:1549.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.22/0.53 1591[3:Rew:1548.0,1589.0,1498.0,1589.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.53 1592[3:Rew:1591.0,1498.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.22/0.53 1594[3:Rew:1591.0,1548.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.53 1606[3:Rew:1543.0,1594.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 1609[3:Rew:1606.0,1555.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 1610[3:Rew:1606.0,1558.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.22/0.53 1620[3:Con:1610.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c6),sk_c7)** -> .
% 0.22/0.53 1621[3:Rew:1606.0,1620.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.22/0.53 1622[3:Con:1621.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.22/0.53 1659[3:SpR:1592.0,33.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.22/0.53 1661[3:Rew:1609.0,1659.0] || -> equal(identity,sk_c3)**.
% 0.22/0.53 1662[3:Rew:1661.0,435.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.22/0.53 1664[3:Rew:1661.0,216.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.22/0.53 1668[3:Rew:1592.0,1662.0] || -> equal(sk_c3,sk_c7)**.
% 0.22/0.53 1670[3:Rew:1668.0,1592.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.22/0.53 1676[3:Rew:1668.0,1664.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.22/0.53 1677[3:Rew:1676.0,1622.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.22/0.53 1729[3:SpL:1670.0,1677.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.22/0.53 1730[3:Obv:1729.1] || -> .
% 0.22/0.53 1731[2:Spt:1730.0,1.1,902.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.22/0.53 1732[2:Spt:1730.0,1.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.22/0.53 1734[2:MRR:6.1,1731.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.22/0.53 1735[2:MRR:3.1,1731.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.22/0.53 1737[2:MRR:5.1,1731.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.22/0.53 1738[2:MRR:4.1,1731.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.22/0.53 1739[2:MRR:2.1,1731.0] || -> equal(multiply(sk_c3,sk_c4),sk_c8)**.
% 0.22/0.53 1756[2:SpR:1735.0,458.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),u)**.
% 0.22/0.53 1767[2:SpR:1737.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.22/0.53 1769[2:Rew:1732.0,1767.0,1734.0,1767.0] || -> equal(sk_c8,sk_c7)**.
% 0.22/0.53 1770[2:Rew:1769.0,1732.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.22/0.53 1774[2:Rew:1769.0,1731.0] || equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.22/0.53 1775[2:Rew:1769.0,1738.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.22/0.53 1776[2:Rew:1769.0,1739.0] || -> equal(multiply(sk_c3,sk_c4),sk_c7)**.
% 0.22/0.53 1805[2:SpR:1776.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c4,u)),multiply(sk_c7,u))**.
% 0.22/0.53 1806[2:SpR:1776.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c4)**.
% 0.22/0.53 1808[2:Rew:1775.0,1806.0,1735.0,1806.0] || -> equal(sk_c4,sk_c7)**.
% 0.22/0.53 1811[2:Rew:1808.0,1775.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.22/0.53 1814[2:Rew:1808.0,1756.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.22/0.53 1822[2:Rew:1811.0,1774.0] || equal(sk_c6,sk_c7)** -> .
% 0.22/0.53 1825[2:Rew:1814.0,1805.0,1808.0,1805.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.22/0.53 1826[2:Rew:1825.0,1770.0] || -> equal(sk_c6,sk_c7)**.
% 0.22/0.53 1829[2:MRR:1826.0,1822.0] || -> .
% 0.22/0.53 % SZS output end Refutation
% 0.22/0.53 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 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.22/0.53
%------------------------------------------------------------------------------