TSTP Solution File: GRP279-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP279-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:46:39 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : GRP279-1 : TPTP v8.1.0. Released v2.5.0.
% 0.09/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 10:23:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.51
% 0.20/0.51 SPASS V 3.9
% 0.20/0.51 SPASS beiseite: Proof found.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.51 SPASS derived 1203 clauses, backtracked 478 clauses, performed 13 splits and kept 974 clauses.
% 0.20/0.51 SPASS allocated 63866 KBytes.
% 0.20/0.51 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.51 0:00:00.04 for the input.
% 0.20/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.51 0:00:00.01 for inferences.
% 0.20/0.51 0:00:00.00 for the backtracking.
% 0.20/0.51 0:00:00.08 for the reduction.
% 0.20/0.51
% 0.20/0.51
% 0.20/0.51 Here is a proof with depth 5, length 452 :
% 0.20/0.51 % SZS output start Refutation
% 0.20/0.51 1[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 3[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 4[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 6[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 8[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 10[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 11[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.51 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.51 14[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 15[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.51 16[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 18[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 20[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 21[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.51 22[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 23[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.51 24[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 25[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.51 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 28[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 30[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 31[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c7) equal(inverse(x),sk_c8) equal(inverse(y),sk_c8) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c6),sk_c7)** equal(multiply(x,sk_c7),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(y,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.20/0.51 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.51 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.51 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.51 35[1:Spt:31.0,31.4,31.7] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.51 36[2:Spt:1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.51 38[2:SpL:36.0,35.1] || equal(inverse(sk_c7),sk_c8) equal(sk_c8,sk_c6) equal(multiply(sk_c8,sk_c7),sk_c8)** -> .
% 0.20/0.51 39[3:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.51 41[4:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.51 45[5:Spt:5.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.51 47[5:SpL:45.0,35.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c8,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.51 48[5:Rew:39.0,47.0] || equal(sk_c6,sk_c7) equal(sk_c8,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.51 49[6:Spt:3.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.51 55[3:SpR:39.0,33.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.20/0.51 56[4:SpR:41.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.51 68[3:SpR:55.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.20/0.51 70[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.51 71[5:SpR:45.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.51 72[4:SpR:56.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.20/0.51 74[3:Rew:32.0,68.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.20/0.51 75[4:Rew:32.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.51 76[0:Rew:32.0,70.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.51 80[5:SpR:45.0,74.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.51 81[3:SpL:74.0,35.1] || equal(multiply(sk_c5,u),inverse(sk_c7)) equal(u,sk_c8) equal(multiply(multiply(sk_c5,u),sk_c7),sk_c8)** -> .
% 0.20/0.51 84[3:Rew:34.0,81.2] || equal(multiply(sk_c5,u),inverse(sk_c7)) equal(u,sk_c8) equal(multiply(sk_c5,multiply(u,sk_c7)),sk_c8)** -> .
% 0.20/0.51 92[6:SpR:49.0,75.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.51 100[0:SpR:76.0,76.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.51 103[2:SpR:36.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.20/0.51 104[3:SpR:55.0,76.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.20/0.51 106[5:SpR:80.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.51 108[0:SpR:33.0,76.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.51 110[4:SpR:56.0,76.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.20/0.51 112[6:SpR:92.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.51 118[5:Rew:103.0,106.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.51 121[5:Rew:118.0,41.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.51 123[5:Rew:118.0,56.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.51 131[5:Rew:118.0,84.1] || equal(multiply(sk_c5,u),inverse(sk_c7)) equal(u,sk_c7) equal(multiply(sk_c5,multiply(u,sk_c7)),sk_c8)** -> .
% 0.20/0.51 134[5:Rew:118.0,48.1] || equal(sk_c6,sk_c7) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.51 149[5:Rew:104.0,110.0,118.0,110.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.51 153[5:Rew:149.0,104.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.20/0.51 155[6:Rew:118.0,112.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.20/0.51 156[6:Rew:33.0,155.0] || -> equal(identity,sk_c7)**.
% 0.20/0.51 157[6:Rew:156.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 159[6:Rew:156.0,123.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.20/0.51 161[6:Rew:157.0,159.0] || -> equal(sk_c4,sk_c7)**.
% 0.20/0.51 162[6:Rew:161.0,121.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.51 164[6:Rew:161.0,149.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.51 168[6:Rew:156.0,108.0] || -> equal(multiply(inverse(inverse(u)),sk_c7),u)**.
% 0.20/0.51 177[6:Rew:100.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.51 186[5:Obv:134.1] || equal(sk_c6,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.51 204[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)* -> .
% 0.20/0.51 205[6:Obv:204.1] || equal(u,sk_c7)* -> .
% 0.20/0.51 206[6:UnC:205.0,76.0] || -> .
% 0.20/0.51 210[6:Spt:206.0,3.0,49.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.51 211[6:Spt:206.0,3.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 215[6:Rew:118.0,210.0] || equal(multiply(sk_c4,sk_c7),sk_c7)** -> .
% 0.20/0.51 216[0:Rew:100.0,108.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.51 217[5:Rew:216.0,153.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.51 223[5:Rew:118.0,23.1] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.20/0.51 224[6:MRR:223.1,215.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 227[5:Rew:149.0,71.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.51 229[5:Rew:118.0,28.1,118.0,28.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.51 230[6:MRR:229.0,215.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.51 231[5:Rew:118.0,18.1,118.0,18.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.51 232[6:MRR:231.0,215.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.51 235[5:Rew:118.0,186.1] || equal(sk_c6,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.20/0.51 257[5:SpR:217.0,76.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.20/0.51 280[6:SpR:232.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.20/0.51 282[6:Rew:230.0,280.0,224.0,280.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.51 284[6:Rew:282.0,230.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.51 289[6:Rew:80.0,284.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 293[6:Rew:289.0,227.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.20/0.51 294[6:Rew:289.0,235.0] || equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.20/0.51 301[6:Rew:257.0,293.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 318[6:Obv:294.0] || equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.20/0.51 319[6:Rew:301.0,318.0,289.0,318.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.51 320[6:Obv:319.0] || -> .
% 0.20/0.51 323[5:Spt:320.0,5.0,45.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.51 324[5:Spt:320.0,5.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 325[4:Rew:216.0,110.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.20/0.51 326[3:Rew:216.0,104.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.51 327[3:Rew:326.0,103.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.20/0.51 328[5:Rew:327.0,323.0] || equal(sk_c8,sk_c7)** -> .
% 0.20/0.51 331[3:Rew:327.0,25.1] || -> equal(inverse(sk_c2),sk_c3)** equal(sk_c8,sk_c7).
% 0.20/0.51 332[5:MRR:331.1,328.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 333[3:Rew:327.0,15.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c8,sk_c7).
% 0.20/0.51 334[5:MRR:333.1,328.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 335[3:Rew:327.0,30.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 336[5:MRR:335.0,328.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 337[3:Rew:327.0,20.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 338[5:MRR:337.0,328.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 339[3:Rew:327.0,10.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 340[5:MRR:339.0,328.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 351[5:SpR:324.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.51 353[5:Rew:325.0,351.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.51 358[4:SpR:325.0,76.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.20/0.51 360[3:SpR:326.0,76.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.20/0.51 371[5:SpR:336.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.20/0.51 372[5:SpR:336.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.20/0.51 383[3:SpR:327.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.51 388[5:SpR:338.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.20/0.51 390[5:Rew:332.0,388.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.20/0.51 392[5:SpR:340.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.51 394[5:Rew:324.0,392.0,334.0,392.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.51 397[5:Rew:394.0,325.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.51 398[5:Rew:394.0,328.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.51 408[5:Rew:394.0,358.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.20/0.51 409[5:Rew:394.0,371.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.51 424[5:Rew:394.0,372.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c7)**.
% 0.20/0.51 425[5:Rew:394.0,390.0] || -> equal(multiply(sk_c3,sk_c6),sk_c3)**.
% 0.20/0.51 445[5:SpR:353.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.51 449[5:Rew:408.0,445.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 453[5:Rew:449.0,409.0] || -> equal(multiply(sk_c3,u),multiply(sk_c6,u))**.
% 0.20/0.51 468[5:Rew:453.0,425.0] || -> equal(multiply(sk_c6,sk_c6),sk_c3)**.
% 0.20/0.51 496[5:SpR:468.0,76.0] || -> equal(multiply(inverse(sk_c6),sk_c3),sk_c6)**.
% 0.20/0.51 498[5:Rew:397.0,496.0] || -> equal(multiply(sk_c4,sk_c3),sk_c6)**.
% 0.20/0.51 500[5:SpR:498.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c3,u)),multiply(sk_c6,u))**.
% 0.20/0.51 504[5:Rew:408.0,500.0,453.0,500.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.51 505[5:Rew:504.0,468.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.51 508[5:Rew:504.0,408.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.51 518[5:Rew:505.0,424.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.51 536[5:Rew:397.0,518.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.51 537[5:Rew:508.0,536.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 538[5:MRR:537.0,398.0] || -> .
% 0.20/0.51 540[4:Spt:538.0,2.0,41.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.51 541[4:Spt:538.0,2.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 542[3:Rew:331.1,22.0] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 548[3:Rew:335.0,27.0] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 549[3:Rew:337.0,17.0] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 557[4:Rew:541.0,38.2,326.0,38.0] || equal(sk_c8,sk_c5)** equal(sk_c8,sk_c6) equal(sk_c8,sk_c6) -> .
% 0.20/0.51 558[4:Obv:557.1] || equal(sk_c8,sk_c5)** equal(sk_c8,sk_c6) -> .
% 0.20/0.51 560[4:SpR:541.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.51 594[0:SpR:33.0,76.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.51 595[0:SpR:33.0,216.0] || -> equal(inverse(identity),identity)**.
% 0.20/0.51 597[3:SpR:326.0,33.0] || -> equal(multiply(sk_c5,sk_c7),identity)**.
% 0.20/0.51 602[0:Rew:216.0,594.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.51 609[5:Spt:331.1] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.51 610[5:Rew:609.0,541.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.51 611[5:Rew:609.0,540.0] || equal(inverse(sk_c4),sk_c7)** -> .
% 0.20/0.51 618[5:Rew:609.0,548.1] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.51 620[5:Rew:609.0,549.1] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.51 623[5:Rew:609.0,383.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.51 625[5:Rew:609.0,558.0] || equal(sk_c5,sk_c7) equal(sk_c8,sk_c6)** -> .
% 0.20/0.51 633[5:MRR:542.0,611.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 636[5:Rew:609.0,625.1] || equal(sk_c5,sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.20/0.51 637[5:MRR:618.0,611.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.20/0.51 638[5:MRR:620.0,611.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.51 650[5:SpR:633.0,76.0] || -> equal(multiply(sk_c3,multiply(sk_c2,u)),u)**.
% 0.20/0.51 651[5:SpR:633.0,33.0] || -> equal(multiply(sk_c3,sk_c2),identity)**.
% 0.20/0.51 673[5:SpR:638.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.20/0.51 675[5:Rew:637.0,673.0,633.0,673.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.51 677[5:Rew:675.0,637.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.51 679[5:Rew:675.0,651.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.20/0.51 680[5:Rew:675.0,650.0] || -> equal(multiply(sk_c7,multiply(sk_c2,u)),u)**.
% 0.20/0.51 683[5:Rew:610.0,677.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 686[5:Rew:683.0,636.1] || equal(sk_c5,sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.20/0.51 687[5:Rew:683.0,623.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.20/0.51 693[5:Obv:686.1] || equal(sk_c5,sk_c7)** -> .
% 0.20/0.51 695[5:Rew:360.0,687.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 696[5:Rew:695.0,55.0] || -> equal(identity,sk_c5)**.
% 0.20/0.51 697[5:Rew:695.0,680.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.51 698[5:Rew:695.0,679.0] || -> equal(identity,sk_c2)**.
% 0.20/0.51 709[5:Rew:696.0,597.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.20/0.51 711[5:Rew:696.0,698.0] || -> equal(sk_c2,sk_c5)**.
% 0.20/0.51 719[5:Rew:711.0,697.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.20/0.51 722[5:Rew:719.0,709.0] || -> equal(sk_c5,sk_c7)**.
% 0.20/0.51 723[5:MRR:722.0,693.0] || -> .
% 0.20/0.51 724[5:Spt:723.0,331.1,609.0] || equal(sk_c8,sk_c7)** -> .
% 0.20/0.51 725[5:Spt:723.0,331.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 726[5:MRR:333.1,724.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 727[5:MRR:335.0,724.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 728[5:MRR:337.0,724.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 729[5:MRR:339.0,724.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 762[5:SpR:728.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.20/0.51 764[5:Rew:725.0,762.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.20/0.51 766[5:SpR:729.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.51 768[5:Rew:541.0,766.0,726.0,766.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.51 770[5:Rew:768.0,724.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.51 776[5:Rew:768.0,727.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.51 779[5:Rew:768.0,560.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.51 793[5:Rew:768.0,764.0] || -> equal(multiply(sk_c3,sk_c6),sk_c3)**.
% 0.20/0.51 794[5:Rew:33.0,779.0] || -> equal(identity,sk_c7)**.
% 0.20/0.51 798[5:Rew:794.0,216.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.51 800[5:Rew:794.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.51 810[5:Rew:798.0,776.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.51 814[5:Rew:810.0,793.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.51 856[5:SpR:814.0,76.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.20/0.51 858[5:Rew:800.0,856.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 859[5:MRR:858.0,770.0] || -> .
% 0.20/0.51 860[3:Spt:859.0,4.0,39.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.20/0.51 861[3:Spt:859.0,4.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 862[3:MRR:24.0,860.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 863[3:MRR:14.0,860.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 864[3:MRR:29.0,860.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 865[3:MRR:19.0,860.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 866[3:MRR:9.0,860.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 867[3:Rew:861.0,38.2] || equal(inverse(sk_c7),sk_c8)** equal(sk_c8,sk_c6) equal(sk_c8,sk_c6) -> .
% 0.20/0.51 868[3:Obv:867.1] || equal(inverse(sk_c7),sk_c8)** equal(sk_c8,sk_c6) -> .
% 0.20/0.51 870[3:SpR:861.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.51 886[3:SpR:865.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.20/0.51 888[3:Rew:862.0,886.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.20/0.51 890[3:SpR:866.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.51 892[3:Rew:861.0,890.0,863.0,890.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.51 896[3:Rew:892.0,864.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.51 905[3:Rew:892.0,868.0] || equal(inverse(sk_c7),sk_c6)** equal(sk_c8,sk_c6) -> .
% 0.20/0.51 909[3:Rew:892.0,870.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.51 913[3:Rew:892.0,888.0] || -> equal(multiply(sk_c3,sk_c6),sk_c3)**.
% 0.20/0.51 914[3:Rew:33.0,909.0] || -> equal(identity,sk_c7)**.
% 0.20/0.51 915[3:Rew:914.0,595.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.51 917[3:Rew:914.0,216.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.51 918[3:Rew:914.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.51 920[3:Rew:917.0,896.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.51 924[3:Rew:920.0,913.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.51 929[3:Rew:892.0,905.1,915.0,905.0] || equal(sk_c6,sk_c7) equal(sk_c6,sk_c6)* -> .
% 0.20/0.51 930[3:Obv:929.1] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.51 958[3:SpR:924.0,76.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.20/0.51 960[3:Rew:918.0,958.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 961[3:MRR:960.0,930.0] || -> .
% 0.20/0.51 962[2:Spt:961.0,1.0,36.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.51 963[2:Spt:961.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 965[2:MRR:11.1,962.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 968[2:MRR:6.0,962.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 970[2:SpR:963.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.51 987[2:SpR:968.0,76.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.20/0.51 989[2:Rew:963.0,987.0,965.0,987.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.51 995[2:Rew:989.0,962.0] || equal(multiply(sk_c7,sk_c6),sk_c6)** -> .
% 0.20/0.51 1001[2:Rew:989.0,970.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.51 1008[2:Rew:33.0,1001.0] || -> equal(identity,sk_c7)**.
% 0.20/0.51 1011[2:Rew:1008.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 1018[2:UnC:1011.0,995.0] || -> .
% 0.20/0.51 1029[1:Spt:1018.0,31.1,31.2,31.3,31.5,31.6,31.8,31.9,31.10] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.20/0.51 1031[2:Spt:1.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.51 1032[2:Rew:1031.0,1029.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c6,sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.20/0.51 1034[2:Obv:1032.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.20/0.51 1037[2:SpR:1031.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.20/0.51 1039[3:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.51 1040[3:SpR:1039.0,76.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.51 1042[4:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.51 1045[5:Spt:3.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.51 1047[5:SpR:1045.0,76.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.20/0.51 1049[5:Rew:1039.0,1047.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.51 1053[6:Spt:5.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.51 1055[6:SpR:1053.0,76.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.20/0.51 1057[6:Rew:1042.0,1055.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.20/0.51 1058[5:SpR:1049.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.20/0.51 1062[6:SpR:1057.0,76.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.51 1064[6:Rew:1037.0,1062.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.51 1068[6:Rew:1064.0,1049.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.20/0.51 1070[6:Rew:1064.0,1034.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c7),sk_c6)** -> .
% 0.20/0.51 1071[6:Rew:1064.0,1037.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.20/0.51 1077[6:Rew:1057.0,1068.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 1081[6:Rew:33.0,1071.0,1077.0,1071.0] || -> equal(identity,sk_c7)**.
% 0.20/0.51 1082[6:Rew:1081.0,595.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.51 1083[6:Rew:1081.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 1084[6:Rew:1081.0,216.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.51 1098[6:Rew:1083.0,1070.6,1077.0,1070.6,1084.0,1070.5,1064.0,1070.5,1084.0,1070.4,1064.0,1070.4,1084.0,1070.3,1077.0,1070.3,1064.0,1070.2,1064.0,1070.1] || 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) -> .
% 0.20/0.51 1099[6:Obv:1098.6] || 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) -> .
% 0.20/0.51 1100[6:Con:1099.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.51 1122[0:SpR:602.0,76.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.20/0.51 1143[6:SpL:1082.0,1100.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.51 1145[6:Obv:1143.1] || -> .
% 0.20/0.51 1146[6:Spt:1145.0,5.0,1053.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.51 1147[6:Spt:1145.0,5.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 1148[6:MRR:25.1,1146.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 1150[6:MRR:30.0,1146.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 1151[6:MRR:20.0,1146.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 1161[3:SpR:1039.0,602.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.20/0.51 1170[4:SpR:1042.0,602.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.20/0.51 1172[4:Rew:1170.0,1037.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.20/0.51 1173[6:Rew:1172.0,1146.0] || equal(sk_c8,sk_c7)** -> .
% 0.20/0.51 1175[6:SpR:1148.0,602.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.20/0.51 1191[6:SpR:1150.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.20/0.51 1192[6:SpR:1150.0,76.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c7)**.
% 0.20/0.51 1194[6:Rew:1175.0,1192.0] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.20/0.51 1195[6:SpR:1175.0,76.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.51 1210[6:SpR:1151.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c8,u))**.
% 0.20/0.51 1211[6:SpR:1151.0,76.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.20/0.51 1213[6:Rew:1148.0,1211.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.20/0.51 1214[6:Rew:1195.0,1210.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.51 1218[6:Rew:1214.0,1058.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.20/0.51 1219[6:Rew:1214.0,1040.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.51 1223[6:Rew:1214.0,1191.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.20/0.51 1235[6:Rew:1214.0,1218.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 1244[6:Rew:1235.0,1223.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.51 1248[6:Rew:1244.0,1213.0] || -> equal(sk_c8,sk_c3)**.
% 0.20/0.51 1251[6:Rew:1248.0,1161.0] || -> equal(inverse(sk_c3),sk_c4)**.
% 0.20/0.51 1252[6:Rew:1248.0,1173.0] || equal(sk_c3,sk_c7)** -> .
% 0.20/0.51 1254[6:Rew:1248.0,1194.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.51 1256[6:Rew:1175.0,1251.0] || -> equal(sk_c2,sk_c4)**.
% 0.20/0.51 1262[6:Rew:1219.0,1254.0,1256.0,1254.0] || -> equal(sk_c3,sk_c7)**.
% 0.20/0.51 1263[6:MRR:1262.0,1252.0] || -> .
% 0.20/0.51 1266[5:Spt:1263.0,3.0,1045.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.20/0.51 1267[5:Spt:1263.0,3.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 1268[4:Rew:1172.0,25.1] || -> equal(inverse(sk_c2),sk_c3)** equal(sk_c8,sk_c7).
% 0.20/0.51 1269[4:Rew:1172.0,15.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c8,sk_c7).
% 0.20/0.51 1271[4:Rew:1269.1,13.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.20/0.51 1272[4:Rew:1172.0,30.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 1273[4:Rew:1172.0,20.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 1274[4:Rew:1172.0,10.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 1277[4:Rew:1274.0,8.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 1283[5:SpR:1267.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.51 1285[5:Rew:1161.0,1283.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.51 1323[3:SpR:1161.0,33.0] || -> equal(multiply(sk_c4,sk_c8),identity)**.
% 0.20/0.51 1327[6:Spt:1268.1] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.51 1329[6:Rew:1327.0,1161.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.51 1333[6:Rew:1327.0,1266.0] || equal(multiply(sk_c4,sk_c7),sk_c7)** -> .
% 0.20/0.51 1338[6:Rew:1327.0,1271.0] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.20/0.51 1341[6:Rew:1327.0,1277.1] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.51 1345[6:Rew:1327.0,1323.0] || -> equal(multiply(sk_c4,sk_c7),identity)**.
% 0.20/0.51 1347[6:Rew:1170.0,1329.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.51 1349[6:Rew:1347.0,1170.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.51 1356[6:Rew:1345.0,1333.0] || equal(identity,sk_c7)** -> .
% 0.20/0.51 1359[6:Rew:1345.0,1338.1] || -> equal(inverse(sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.20/0.51 1360[6:MRR:1359.1,1356.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.51 1365[6:Rew:1345.0,1341.0] || -> equal(identity,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.51 1366[6:MRR:1365.0,1356.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.20/0.51 1386[6:SpR:1360.0,602.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.20/0.51 1389[6:Rew:1349.0,1386.0] || -> equal(sk_c1,sk_c4)**.
% 0.20/0.51 1391[6:Rew:1389.0,1366.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.20/0.51 1393[6:Rew:1345.0,1391.0] || -> equal(identity,sk_c7)**.
% 0.20/0.51 1394[6:MRR:1393.0,1356.0] || -> .
% 0.20/0.51 1396[6:Spt:1394.0,1268.1,1327.0] || equal(sk_c8,sk_c7)** -> .
% 0.20/0.51 1397[6:Spt:1394.0,1268.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 1398[6:MRR:1269.1,1396.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 1399[6:MRR:1272.0,1396.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 1400[6:MRR:1273.0,1396.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 1401[6:MRR:1274.0,1396.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 1403[6:SpR:1397.0,602.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.20/0.51 1423[6:SpR:1398.0,602.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.20/0.51 1426[6:Rew:1161.0,1423.0] || -> equal(sk_c1,sk_c4)**.
% 0.20/0.51 1428[6:Rew:1426.0,1401.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.51 1430[6:Rew:1323.0,1428.0] || -> equal(identity,sk_c7)**.
% 0.20/0.51 1432[6:Rew:1430.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.51 1433[6:Rew:1430.0,216.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.51 1449[6:Rew:1432.0,1031.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.51 1453[6:Rew:1449.0,1161.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.51 1454[6:Rew:1449.0,1396.0] || equal(sk_c6,sk_c7)** -> .
% 0.20/0.51 1459[6:Rew:1449.0,1399.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.20/0.51 1460[6:Rew:1449.0,1400.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.20/0.51 1468[6:Rew:1433.0,1459.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.51 1470[6:Rew:1468.0,1403.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.20/0.51 1473[6:Rew:1453.0,1470.0] || -> equal(sk_c2,sk_c4)**.
% 0.20/0.51 1475[6:Rew:1473.0,1460.0,1468.0,1460.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.20/0.51 1476[6:Rew:1285.0,1475.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 1477[6:MRR:1476.0,1454.0] || -> .
% 0.20/0.51 1489[4:Spt:1477.0,4.0,1042.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.20/0.51 1490[4:Spt:1477.0,4.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 1491[4:MRR:24.0,1489.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 1492[4:MRR:14.0,1489.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 1493[4:MRR:29.0,1489.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.20/0.51 1494[4:MRR:19.0,1489.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 1495[4:MRR:9.0,1489.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 1496[4:Rew:1490.0,1034.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.51 1497[4:Obv:1496.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.20/0.51 1501[4:SpR:1490.0,76.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.51 1503[4:Rew:1161.0,1501.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.51 1512[4:SpR:1491.0,602.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.20/0.51 1518[4:SpR:1492.0,602.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.20/0.51 1520[4:Rew:1161.0,1518.0] || -> equal(sk_c1,sk_c4)**.
% 0.20/0.51 1522[4:Rew:1520.0,1495.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.51 1523[4:Rew:1323.0,1522.0] || -> equal(identity,sk_c7)**.
% 0.20/0.51 1524[4:Rew:1523.0,595.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.51 1525[4:Rew:1523.0,216.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.51 1532[4:Rew:1525.0,1490.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.51 1534[4:Rew:1525.0,1497.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(v,sk_c8) equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.20/0.51 1535[4:Rew:1525.0,1493.0] || -> equal(sk_c8,sk_c3)**.
% 0.20/0.51 1536[4:Rew:1532.0,1161.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.51 1542[4:Rew:1532.0,1494.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.20/0.51 1544[4:Rew:1532.0,1535.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.51 1546[4:Rew:1544.0,1512.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.20/0.51 1548[4:Rew:1536.0,1546.0] || -> equal(sk_c2,sk_c4)**.
% 0.20/0.51 1553[4:Rew:1503.0,1542.0,1548.0,1542.0,1544.0,1542.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 1555[4:Rew:1553.0,1532.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.51 1571[4:Rew:1525.0,1534.5,1555.0,1534.5,1555.0,1534.4,1525.0,1534.3,1553.0,1534.3,1555.0,1534.2,1555.0,1534.1] || 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) -> .
% 0.20/0.51 1572[4:Con:1571.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.51 1606[4:SpL:1524.0,1572.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.51 1607[4:Obv:1606.1] || -> .
% 0.20/0.51 1608[3:Spt:1607.0,2.0,1039.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.51 1609[3:Spt:1607.0,2.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.51 1610[3:MRR:22.0,1608.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.51 1611[3:MRR:12.0,1608.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.51 1613[3:MRR:17.0,1608.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.51 1614[3:MRR:7.0,1608.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.51 1615[3:Rew:1609.0,1034.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.20/0.51 1616[3:Obv:1615.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.20/0.51 1627[3:SpR:1610.0,602.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.20/0.51 1629[3:SpR:1611.0,76.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.51 1633[3:SpR:1627.0,76.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.51 1646[3:SpR:1613.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c8,u))**.
% 0.20/0.51 1650[3:Rew:1633.0,1646.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.51 1651[3:Rew:1650.0,1609.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.51 1652[3:Rew:1650.0,1629.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.51 1659[3:Rew:1651.0,1616.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.20/0.51 1662[3:Rew:1652.0,1614.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.51 1663[3:Rew:1662.0,1611.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.20/0.51 1689[3:Rew:1662.0,1659.5,1662.0,1659.4,1662.0,1659.2,1662.0,1659.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.20/0.52 1690[3:Con:1689.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.20/0.52 1718[3:SpR:1652.0,216.0] || -> equal(identity,sk_c1)**.
% 0.20/0.52 1720[3:Rew:1718.0,595.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.52 1722[3:Rew:1718.0,216.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.20/0.52 1725[3:Rew:1663.0,1720.0] || -> equal(sk_c1,sk_c7)**.
% 0.20/0.52 1727[3:Rew:1725.0,1663.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.52 1732[3:Rew:1725.0,1722.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.52 1733[3:Rew:1732.0,1690.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.20/0.52 1790[3:SpL:1727.0,1733.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.20/0.52 1791[3:Obv:1790.1] || -> .
% 0.20/0.52 1792[2:Spt:1791.0,1.0,1031.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.52 1793[2:Spt:1791.0,1.1] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.52 1794[2:MRR:21.1,1792.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.52 1795[2:MRR:11.1,1792.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.52 1797[2:MRR:16.0,1792.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.20/0.52 1798[2:MRR:6.0,1792.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.20/0.52 1804[2:SpR:1794.0,1122.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.52 1812[2:SpR:1795.0,76.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.52 1829[2:SpR:1797.0,34.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c8,u))**.
% 0.20/0.52 1833[2:Rew:1804.0,1829.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.52 1834[2:Rew:1833.0,1793.0] || -> equal(sk_c6,sk_c7)**.
% 0.20/0.52 1835[2:Rew:1833.0,1812.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.52 1839[2:Rew:1834.0,1792.0] || equal(multiply(sk_c7,sk_c8),sk_c7)** -> .
% 0.20/0.52 1841[2:Rew:1835.0,1798.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.52 1848[2:Rew:1841.0,1833.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.52 1860[2:Rew:1848.0,1839.0,1841.0,1839.0] || equal(sk_c7,sk_c7)* -> .
% 0.20/0.52 1861[2:Obv:1860.0] || -> .
% 0.20/0.52 % SZS output end Refutation
% 0.20/0.52 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_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_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.20/0.52
%------------------------------------------------------------------------------