TSTP Solution File: GRP321-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP321-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:46:50 EDT 2022
% Result : Unsatisfiable 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP321-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 07:02:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.51
% 0.21/0.51 SPASS V 3.9
% 0.21/0.51 SPASS beiseite: Proof found.
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 SPASS derived 1049 clauses, backtracked 377 clauses, performed 12 splits and kept 816 clauses.
% 0.21/0.51 SPASS allocated 63711 KBytes.
% 0.21/0.51 SPASS spent 0:00:00.14 on the problem.
% 0.21/0.51 0:00:00.04 for the input.
% 0.21/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.51 0:00:00.01 for inferences.
% 0.21/0.51 0:00:00.00 for the backtracking.
% 0.21/0.51 0:00:00.07 for the reduction.
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 Here is a proof with depth 5, length 403 :
% 0.21/0.51 % SZS output start Refutation
% 0.21/0.51 1[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.21/0.51 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 3[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.21/0.51 4[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 5[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.21/0.51 6[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 7[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 8[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 9[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 10[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.21/0.51 12[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.51 14[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 15[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.21/0.51 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 18[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.21/0.51 19[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 20[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c3),sk_c7).
% 0.21/0.51 22[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 23[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 24[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 25[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 28[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.51 29[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 30[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.21/0.51 31[0:Inp] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(w,sk_c8),y)*+ equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.21/0.51 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.51 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.51 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.51 35[1:Spt:31.3,31.7] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.21/0.51 36[2:Spt:5.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.21/0.51 38[2:SpL:36.0,35.1] || equal(inverse(sk_c6),sk_c7)** equal(sk_c8,sk_c8) -> .
% 0.21/0.51 39[2:Obv:38.1] || equal(inverse(sk_c6),sk_c7)** -> .
% 0.21/0.51 40[3:Spt:4.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.21/0.51 42[4:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.21/0.51 44[5:Spt:3.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.51 46[5:SpL:44.0,35.1] || equal(inverse(sk_c5),sk_c7)** equal(sk_c6,sk_c8) -> .
% 0.21/0.51 47[5:Rew:40.0,46.0] || equal(sk_c7,sk_c7) equal(sk_c6,sk_c8)** -> .
% 0.21/0.51 48[5:Obv:47.0] || equal(sk_c6,sk_c8)** -> .
% 0.21/0.51 49[6:Spt:1.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.21/0.51 52[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c7)** equal(sk_c8,sk_c7) -> .
% 0.21/0.51 54[3:SpR:40.0,33.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.21/0.51 55[4:SpR:42.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.21/0.51 56[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c8) -> .
% 0.21/0.51 60[5:SpR:44.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.21/0.51 61[6:SpR:49.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.21/0.51 63[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.51 65[0:Rew:32.0,63.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.51 67[3:SpR:54.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.21/0.51 69[3:Rew:32.0,67.0] || -> equal(multiply(sk_c7,multiply(sk_c5,u)),u)**.
% 0.21/0.51 75[5:SpR:44.0,69.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.51 80[0:SpR:65.0,65.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.51 82[2:SpR:36.0,65.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.21/0.51 86[0:SpR:33.0,65.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.51 88[3:SpR:54.0,65.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.21/0.51 90[5:SpR:75.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.21/0.51 91[4:SpR:55.0,65.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.21/0.51 96[5:Rew:33.0,90.0] || -> equal(identity,sk_c6)**.
% 0.21/0.51 97[5:Rew:96.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.51 100[5:Rew:96.0,55.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.21/0.51 104[5:Rew:96.0,88.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.51 105[5:Rew:97.0,36.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 106[5:Rew:97.0,60.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.21/0.51 110[5:Rew:105.0,42.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.51 112[5:Rew:105.0,48.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.51 113[6:Rew:105.0,61.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.21/0.51 118[5:Rew:105.0,100.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.21/0.51 119[5:Rew:105.0,91.0,96.0,91.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c4)**.
% 0.21/0.51 120[5:Rew:119.0,104.0] || -> equal(sk_c5,sk_c4)**.
% 0.21/0.51 122[5:Rew:120.0,44.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.51 130[5:Rew:120.0,106.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.21/0.51 135[6:Rew:130.0,113.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 138[6:Rew:135.0,118.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.51 139[6:Rew:138.0,110.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.51 143[6:MRR:139.0,39.0] || -> .
% 0.21/0.51 149[6:Spt:143.0,1.0,49.0] || equal(multiply(sk_c4,sk_c8),sk_c7)** -> .
% 0.21/0.51 150[6:Spt:143.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 151[6:Rew:105.0,150.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 155[5:Rew:122.0,11.1,105.0,11.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.21/0.51 156[5:MRR:155.1,112.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 161[5:Rew:105.0,6.1,122.0,6.0,105.0,6.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 162[5:MRR:161.0,112.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 218[5:SpR:162.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 220[6:Rew:151.0,218.0,156.0,218.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 221[6:MRR:220.0,112.0] || -> .
% 0.21/0.51 222[5:Spt:221.0,3.0,44.0] || equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.21/0.51 223[5:Spt:221.0,3.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 224[0:Rew:80.0,86.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.51 225[4:Rew:224.0,91.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.21/0.51 226[3:Rew:224.0,88.0] || -> equal(inverse(sk_c7),sk_c5)**.
% 0.21/0.51 228[5:MRR:28.1,222.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 229[5:MRR:13.1,222.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 230[5:MRR:23.0,222.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 231[5:MRR:18.0,222.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 232[5:MRR:8.0,222.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 247[3:SpR:226.0,65.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),u)**.
% 0.21/0.51 252[5:SpR:230.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.21/0.51 254[5:Rew:228.0,252.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.21/0.51 255[5:Rew:231.0,254.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 256[5:Rew:255.0,223.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 259[5:Rew:255.0,225.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.21/0.51 263[5:Rew:255.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c7)**.
% 0.21/0.51 269[5:Rew:255.0,231.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.51 270[5:Rew:255.0,232.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 276[5:Rew:226.0,259.0] || -> equal(sk_c5,sk_c4)**.
% 0.21/0.51 278[5:Rew:276.0,226.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.21/0.51 280[5:Rew:276.0,222.0] || equal(multiply(sk_c4,sk_c7),sk_c6)** -> .
% 0.21/0.51 308[5:SpR:269.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.21/0.51 310[5:Rew:278.0,308.0] || -> equal(multiply(sk_c4,sk_c7),sk_c3)**.
% 0.21/0.51 311[5:Rew:310.0,280.0] || equal(sk_c3,sk_c6)** -> .
% 0.21/0.51 316[5:SpR:270.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 318[5:Rew:256.0,316.0,229.0,316.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 321[5:Rew:318.0,311.0] || equal(sk_c3,sk_c7)** -> .
% 0.21/0.51 324[5:Rew:318.0,263.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 330[5:Rew:278.0,324.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.21/0.51 331[5:Rew:310.0,330.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 332[5:MRR:331.0,321.0] || -> .
% 0.21/0.51 333[4:Spt:332.0,2.0,42.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.21/0.51 334[4:Spt:332.0,2.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 335[4:MRR:27.0,333.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 336[4:MRR:12.0,333.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 337[4:MRR:22.0,333.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 338[4:MRR:17.0,333.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 339[4:MRR:7.0,333.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 341[4:SpR:334.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.21/0.51 343[4:Rew:226.0,341.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.21/0.51 361[4:SpR:337.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.21/0.51 363[4:Rew:335.0,361.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.21/0.51 364[4:Rew:338.0,363.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 365[4:Rew:364.0,334.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 374[4:Rew:364.0,52.1] || equal(inverse(identity),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.21/0.51 375[4:Rew:364.0,338.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.51 376[4:Rew:364.0,339.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 379[4:Rew:364.0,343.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.21/0.51 382[4:Obv:374.1] || equal(inverse(identity),sk_c7)** -> .
% 0.21/0.51 398[4:SpR:375.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.21/0.51 400[4:Rew:226.0,398.0] || -> equal(multiply(sk_c5,sk_c7),sk_c3)**.
% 0.21/0.51 402[4:SpR:376.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 404[4:Rew:365.0,402.0,336.0,402.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 408[4:Rew:404.0,379.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.21/0.51 413[4:Rew:400.0,408.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 418[4:Rew:413.0,400.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.21/0.51 430[4:SpR:418.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.21/0.51 434[4:Rew:247.0,430.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 435[4:Rew:434.0,54.0] || -> equal(identity,sk_c5)**.
% 0.21/0.51 443[4:Rew:435.0,382.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.21/0.51 448[4:Rew:40.0,443.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 449[4:Obv:448.0] || -> .
% 0.21/0.51 451[3:Spt:449.0,4.0,40.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.21/0.51 452[3:Spt:449.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 453[3:MRR:29.0,451.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 454[3:MRR:14.0,451.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 455[3:MRR:24.0,451.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 456[3:MRR:19.0,451.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 457[3:MRR:9.0,451.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 459[3:SpR:452.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.21/0.51 469[3:SpR:455.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.21/0.51 471[3:Rew:453.0,469.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.21/0.51 472[3:Rew:456.0,471.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 473[3:Rew:472.0,452.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 477[3:Rew:472.0,82.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c7)**.
% 0.21/0.51 481[3:Rew:472.0,456.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.51 482[3:Rew:472.0,457.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 486[3:Rew:472.0,459.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.21/0.51 504[3:SpR:481.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.21/0.51 506[3:Rew:33.0,504.0] || -> equal(identity,sk_c3)**.
% 0.21/0.51 507[3:Rew:506.0,224.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.21/0.51 511[3:Rew:506.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.21/0.51 517[3:SpR:482.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 519[3:Rew:473.0,517.0,454.0,517.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 520[3:Rew:519.0,39.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.21/0.51 523[3:Rew:519.0,477.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 524[3:Rew:519.0,486.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 527[3:Rew:511.0,523.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 530[3:Rew:527.0,507.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 547[3:Rew:530.0,524.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 548[3:MRR:547.0,520.0] || -> .
% 0.21/0.51 554[2:Spt:548.0,5.0,36.0] || equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.21/0.51 555[2:Spt:548.0,5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 556[2:MRR:30.1,554.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 557[2:MRR:15.1,554.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 558[2:MRR:25.0,554.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 559[2:MRR:20.0,554.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 560[2:MRR:10.0,554.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 562[2:SpR:555.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.21/0.51 569[2:SpR:558.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.21/0.51 571[2:Rew:556.0,569.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.21/0.51 572[2:Rew:559.0,571.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 573[2:Rew:572.0,555.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 578[2:Rew:572.0,56.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c7) -> .
% 0.21/0.51 579[2:Rew:572.0,559.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.51 580[2:Rew:572.0,560.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 583[2:Rew:572.0,562.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.21/0.51 599[2:SpR:579.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.21/0.51 601[2:Rew:33.0,599.0] || -> equal(identity,sk_c3)**.
% 0.21/0.51 603[2:Rew:601.0,224.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.21/0.51 604[2:Rew:601.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.21/0.51 607[2:Rew:601.0,578.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c3,sk_c7) -> .
% 0.21/0.51 612[2:SpR:580.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 614[2:Rew:573.0,612.0,557.0,612.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 617[2:Rew:614.0,583.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 621[2:Rew:604.0,617.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 625[2:Rew:621.0,603.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 629[2:Rew:621.0,607.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.21/0.51 633[2:Rew:625.0,580.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.51 637[2:Rew:633.0,557.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 646[2:Obv:629.1] || equal(inverse(inverse(sk_c7)),sk_c7)** -> .
% 0.21/0.51 647[2:Rew:637.0,646.0,637.0,646.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 648[2:Obv:647.0] || -> .
% 0.21/0.51 649[1:Spt:648.0,31.0,31.1,31.2,31.4,31.5,31.6,31.8,31.9,31.10] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(w,sk_c8),x)*+ equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.21/0.51 650[1:EqR:649.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(w,sk_c8)),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.21/0.51 652[2:Spt:5.0] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.21/0.51 655[2:Rew:652.0,650.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(w,sk_c8)),sk_c7)** equal(sk_c8,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.21/0.51 656[2:Obv:655.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(w,sk_c8)),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.21/0.51 660[2:SpR:652.0,65.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.21/0.51 662[3:Spt:2.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 665[3:Rew:662.0,656.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(w,sk_c8)),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.21/0.51 666[3:Obv:665.6] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(w,sk_c8)),sk_c7)** -> .
% 0.21/0.51 670[3:SpR:662.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.21/0.51 672[4:Spt:29.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.21/0.51 675[5:Spt:27.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.21/0.51 684[6:Spt:28.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.51 686[6:SpR:684.0,65.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.21/0.51 688[6:Rew:672.0,686.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.51 694[6:SpR:688.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.21/0.51 696[6:Rew:33.0,694.0] || -> equal(identity,sk_c6)**.
% 0.21/0.51 697[6:Rew:696.0,224.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.51 698[6:Rew:696.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.51 700[6:Rew:696.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.21/0.51 701[6:Rew:697.0,670.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.21/0.51 702[6:Rew:698.0,652.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 706[6:Rew:702.0,662.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 707[6:Rew:702.0,675.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.51 709[6:Rew:702.0,6.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 712[6:Rew:702.0,11.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.21/0.51 716[6:Rew:702.0,666.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(w,sk_c8)),sk_c7)** -> .
% 0.21/0.51 718[6:Rew:702.0,701.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 723[6:Rew:702.0,709.1] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 726[6:Rew:702.0,716.5,702.0,716.4,702.0,716.2] || 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_c7),sk_c7)** equal(multiply(sk_c7,multiply(w,sk_c7)),sk_c7)** -> .
% 0.21/0.51 759[6:SpR:700.0,65.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.21/0.51 763[6:SpR:707.0,700.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.21/0.51 765[6:Rew:697.0,759.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.51 785[6:SpR:763.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c4)**.
% 0.21/0.51 787[6:Rew:697.0,785.0,718.0,785.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.51 793[6:Rew:787.0,723.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 794[6:Rew:787.0,712.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.51 798[6:Rew:706.0,794.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.21/0.51 802[6:Rew:706.0,793.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 803[7:Spt:798.1] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 805[7:Rew:803.0,698.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 807[7:Rew:803.0,697.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 812[7:Rew:803.0,726.3] || 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_c7),sk_c7)** equal(multiply(sk_c7,multiply(w,sk_c7)),sk_c7)** -> .
% 0.21/0.51 814[7:Con:812.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c7)** -> .
% 0.21/0.51 815[7:Rew:807.0,814.3,805.0,814.3,807.0,814.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.51 816[7:Con:815.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.51 872[7:SpL:718.0,816.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 874[7:Obv:872.1] || -> .
% 0.21/0.51 875[7:Spt:874.0,798.1,803.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.51 876[7:Spt:874.0,798.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 880[7:MRR:802.0,875.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 882[7:SpR:876.0,765.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.21/0.51 885[7:Rew:718.0,882.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.51 887[7:Rew:885.0,880.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.51 888[7:Rew:706.0,887.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 889[7:MRR:888.0,875.0] || -> .
% 0.21/0.51 892[6:Spt:889.0,28.1,684.0] || equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.21/0.51 893[6:Spt:889.0,28.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 894[6:MRR:13.1,892.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 895[6:MRR:23.0,892.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 896[6:MRR:18.0,892.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 897[6:MRR:8.0,892.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 913[6:SpR:895.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.21/0.51 915[6:Rew:893.0,913.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.21/0.51 916[6:Rew:896.0,915.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 920[6:Rew:916.0,662.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 922[6:Rew:916.0,670.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.21/0.51 927[6:Rew:916.0,896.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.51 928[6:Rew:916.0,897.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 953[6:SpR:927.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.21/0.51 955[6:Rew:33.0,953.0] || -> equal(identity,sk_c3)**.
% 0.21/0.51 956[6:Rew:955.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.51 957[6:Rew:955.0,224.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.21/0.51 958[6:Rew:955.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.21/0.51 964[6:SpR:928.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 966[6:Rew:920.0,964.0,894.0,964.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 969[6:Rew:966.0,892.0] || equal(multiply(sk_c5,sk_c7),sk_c7)** -> .
% 0.21/0.51 970[6:Rew:966.0,922.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 977[6:Rew:958.0,970.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 980[6:Rew:977.0,956.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 981[6:Rew:977.0,957.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 982[6:Rew:977.0,958.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.21/0.51 991[6:Rew:981.0,969.0] || equal(sk_c5,sk_c7)** -> .
% 0.21/0.51 1039[6:SpR:672.0,982.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.21/0.51 1041[6:Rew:980.0,1039.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.51 1042[6:MRR:1041.0,991.0] || -> .
% 0.21/0.51 1046[5:Spt:1042.0,27.0,675.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.21/0.51 1047[5:Spt:1042.0,27.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 1048[5:MRR:12.0,1046.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 1049[5:MRR:22.0,1046.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 1050[5:MRR:17.0,1046.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 1051[5:MRR:7.0,1046.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 1063[5:SpR:1049.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.21/0.51 1065[5:Rew:1047.0,1063.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.21/0.51 1066[5:Rew:1050.0,1065.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 1068[5:Rew:1066.0,662.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 1072[5:Rew:1066.0,660.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c7)**.
% 0.21/0.51 1076[5:Rew:1066.0,1050.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.51 1077[5:Rew:1066.0,1051.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 1080[5:Rew:1066.0,666.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(w,sk_c8)),sk_c7)** -> .
% 0.21/0.51 1083[5:Rew:1066.0,1080.5,1066.0,1080.4,1066.0,1080.2] || 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_c7),sk_c7)** equal(multiply(sk_c7,multiply(w,sk_c7)),sk_c7)** -> .
% 0.21/0.51 1100[5:SpR:1076.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.21/0.51 1102[5:Rew:33.0,1100.0] || -> equal(identity,sk_c3)**.
% 0.21/0.51 1103[5:Rew:1102.0,224.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.21/0.51 1104[5:Rew:1102.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.51 1106[5:Rew:1102.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.21/0.51 1111[5:SpR:1077.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 1113[5:Rew:1068.0,1111.0,1048.0,1111.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 1116[5:Rew:1113.0,1072.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 1122[5:Rew:1113.0,1083.3] || 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_c7),sk_c7)** equal(multiply(sk_c7,multiply(w,sk_c7)),sk_c7)** -> .
% 0.21/0.51 1123[5:Rew:1106.0,1116.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 1126[5:Rew:1123.0,1103.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 1127[5:Rew:1123.0,1104.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 1130[5:Rew:1126.0,1077.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.51 1132[5:Rew:1130.0,1048.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 1144[5:Con:1122.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c7)** -> .
% 0.21/0.51 1145[5:Rew:1126.0,1144.3,1127.0,1144.3,1126.0,1144.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.51 1146[5:Con:1145.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.51 1218[5:SpL:1132.0,1146.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1220[5:Obv:1218.1] || -> .
% 0.21/0.51 1221[4:Spt:1220.0,29.0,672.0] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.21/0.51 1222[4:Spt:1220.0,29.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 1223[4:MRR:14.0,1221.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 1224[4:MRR:24.0,1221.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 1225[4:MRR:19.0,1221.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 1226[4:MRR:9.0,1221.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 1238[4:SpR:1224.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.21/0.51 1240[4:Rew:1222.0,1238.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.21/0.51 1241[4:Rew:1225.0,1240.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 1244[4:Rew:1241.0,662.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 1246[4:Rew:1241.0,670.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.21/0.51 1250[4:Rew:1241.0,1225.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.21/0.51 1251[4:Rew:1241.0,1226.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 1254[4:Rew:1241.0,666.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(w,sk_c8)),sk_c7)** -> .
% 0.21/0.51 1257[4:Rew:1241.0,1254.5,1241.0,1254.4,1241.0,1254.2] || 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_c7),sk_c7)** equal(multiply(sk_c7,multiply(w,sk_c7)),sk_c7)** -> .
% 0.21/0.51 1274[4:SpR:1250.0,65.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.21/0.51 1276[4:Rew:33.0,1274.0] || -> equal(identity,sk_c3)**.
% 0.21/0.51 1277[4:Rew:1276.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.51 1278[4:Rew:1276.0,224.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.21/0.51 1279[4:Rew:1276.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.21/0.51 1285[4:SpR:1251.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 1287[4:Rew:1244.0,1285.0,1223.0,1285.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 1290[4:Rew:1287.0,1246.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.21/0.51 1296[4:Rew:1287.0,1257.3] || 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_c7),sk_c7)** equal(multiply(sk_c7,multiply(w,sk_c7)),sk_c7)** -> .
% 0.21/0.51 1297[4:Rew:1279.0,1290.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.51 1300[4:Rew:1297.0,1277.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 1301[4:Rew:1297.0,1278.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 1307[4:Rew:1301.0,1251.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.51 1309[4:Rew:1307.0,1223.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.51 1317[4:Con:1296.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(v,sk_c7)),sk_c7)** -> .
% 0.21/0.51 1318[4:Rew:1301.0,1317.3,1300.0,1317.3,1301.0,1317.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.21/0.51 1319[4:Con:1318.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.51 1350[4:SpL:1309.0,1319.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1351[4:Obv:1350.1] || -> .
% 0.21/0.51 1352[3:Spt:1351.0,2.1,662.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.21/0.51 1353[3:Spt:1351.0,2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.21/0.51 1354[3:MRR:4.1,1352.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.21/0.51 1355[3:MRR:1.1,1352.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.21/0.51 1356[3:MRR:3.1,1352.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.51 1365[3:SpR:1355.0,65.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c8)**.
% 0.21/0.51 1367[3:Rew:1353.0,1365.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.51 1369[3:SpR:1356.0,65.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.21/0.51 1371[3:Rew:1354.0,1369.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.51 1373[3:SpR:1367.0,65.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.21/0.51 1375[3:Rew:33.0,1373.0] || -> equal(identity,sk_c7)**.
% 0.21/0.51 1376[3:Rew:1375.0,224.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.51 1377[3:Rew:1375.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.51 1381[3:Rew:1376.0,652.0] || -> equal(sk_c6,sk_c8)**.
% 0.21/0.51 1386[3:Rew:1381.0,1352.0] || equal(multiply(sk_c7,sk_c8),sk_c8)** -> .
% 0.21/0.51 1388[3:Rew:1381.0,1371.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.21/0.51 1392[3:Rew:1377.0,1388.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 1402[3:Rew:1377.0,1386.0,1392.0,1386.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1403[3:Obv:1402.0] || -> .
% 0.21/0.51 1410[2:Spt:1403.0,5.0,652.0] || equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.21/0.51 1411[2:Spt:1403.0,5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.51 1412[2:MRR:30.1,1410.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.21/0.51 1413[2:MRR:15.1,1410.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.21/0.51 1414[2:MRR:25.0,1410.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.21/0.51 1415[2:MRR:20.0,1410.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.21/0.51 1416[2:MRR:10.0,1410.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.21/0.51 1425[2:SpR:1414.0,65.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.21/0.51 1427[2:Rew:1412.0,1425.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.21/0.51 1428[2:Rew:1415.0,1427.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.51 1429[2:Rew:1428.0,1411.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.51 1432[2:Rew:1428.0,1410.0] || equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.21/0.51 1434[2:Rew:1428.0,1416.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.21/0.51 1461[2:SpR:1434.0,65.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.21/0.51 1463[2:Rew:1429.0,1461.0,1413.0,1461.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.51 1464[2:Rew:1463.0,1429.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.51 1465[2:Rew:1463.0,1432.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.21/0.51 1468[2:Rew:1464.0,1465.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.51 1469[2:Obv:1468.0] || -> .
% 0.21/0.51 % SZS output end Refutation
% 0.21/0.51 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_17 prove_this_18 prove_this_19 prove_this_20 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
% 0.21/0.51
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