TSTP Solution File: GRP365-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP365-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:47:02 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP365-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 11:20:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 754 clauses, backtracked 359 clauses, performed 11 splits and kept 715 clauses.
% 0.20/0.48 SPASS allocated 63603 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.03 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.07 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 5, length 363 :
% 0.20/0.48 % SZS output start Refutation
% 0.20/0.48 1[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.20/0.48 2[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.20/0.48 3[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 4[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.20/0.48 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 7[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c8,sk_c2),sk_c7).
% 0.20/0.48 8[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 9[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c8,sk_c2),sk_c7).
% 0.20/0.48 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 12[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 13[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 14[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 15[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 17[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.48 18[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 19[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 20[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 21[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 22[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 23[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 24[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 26[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.48 27[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.48 28[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 29[0:Inp] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 30[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 31[0:Inp] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(inverse(x),sk_c8) equal(multiply(x,sk_c8),y)*+ equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7) -> .
% 0.20/0.48 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.48 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.48 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.48 35[1:Spt:31.3,31.4,31.8] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.20/0.48 37[2:Spt:1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.48 39[3:Spt:5.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 41[4:Spt:3.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 44[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.48 45[5:Spt:4.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.48 47[5:SpL:45.0,35.1] || equal(inverse(sk_c5),sk_c8) equal(sk_c6,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.48 48[5:Rew:39.0,47.0] || equal(sk_c8,sk_c8) equal(sk_c6,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.48 49[5:Obv:48.0] || equal(sk_c6,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.48 50[6:Spt:2.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.48 56[3:SpR:39.0,33.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.20/0.48 57[4:SpR:41.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.48 58[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.48 66[3:SpR:56.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.20/0.48 67[4:SpR:57.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.20/0.48 69[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.48 71[3:Rew:32.0,66.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.20/0.48 72[4:Rew:32.0,67.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.48 73[0:Rew:32.0,69.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.48 77[5:SpR:45.0,71.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 83[6:SpR:50.0,72.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.48 84[6:Rew:37.0,83.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 86[6:Rew:84.0,37.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.48 94[6:Rew:84.0,77.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.48 100[6:Rew:84.0,49.1] || equal(sk_c6,u) equal(multiply(sk_c6,u),sk_c7)** -> .
% 0.20/0.48 125[0:SpR:73.0,73.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.48 128[0:SpR:33.0,73.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.48 130[6:SpR:86.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.48 135[6:Rew:33.0,130.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 136[6:Rew:135.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 137[6:Rew:135.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.48 151[6:SpR:94.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c6)**.
% 0.20/0.48 153[6:Rew:137.0,151.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 157[6:Rew:153.0,100.1] || equal(sk_c6,u) equal(multiply(sk_c6,u),sk_c6)** -> .
% 0.20/0.48 161[6:Rew:153.0,136.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 185[6:Rew:161.0,157.1] || equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.48 186[6:Obv:185.0] || equal(u,sk_c6)* -> .
% 0.20/0.48 187[6:UnC:186.0,84.0] || -> .
% 0.20/0.48 191[6:Spt:187.0,2.0,50.0] || equal(multiply(sk_c4,sk_c8),sk_c7)** -> .
% 0.20/0.48 192[6:Spt:187.0,2.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 193[0:Rew:125.0,128.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.48 194[6:MRR:27.1,191.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 196[6:MRR:22.0,191.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 207[6:SpR:194.0,73.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.48 212[5:SpR:77.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.20/0.48 214[5:Rew:33.0,212.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 217[5:Rew:214.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 221[5:Rew:214.0,193.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 222[5:Rew:214.0,58.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(sk_c6,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.20/0.48 223[6:Rew:217.0,192.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 227[6:Rew:217.0,207.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 229[6:Rew:223.0,37.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.20/0.48 237[6:Rew:221.0,196.0] || -> equal(sk_c3,sk_c8)**.
% 0.20/0.48 238[6:Rew:237.0,194.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.20/0.48 239[6:Rew:237.0,227.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 248[6:Rew:239.0,229.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 251[6:Rew:248.0,223.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 253[6:Rew:248.0,238.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 278[6:Rew:217.0,222.2,248.0,222.2,251.0,222.2,253.0,222.0,253.0,222.0,248.0,222.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.48 279[6:Obv:278.1] || equal(u,sk_c6)* -> .
% 0.20/0.48 280[6:UnC:279.0,73.0] || -> .
% 0.20/0.48 283[5:Spt:280.0,4.0,45.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.20/0.48 284[5:Spt:280.0,4.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 285[5:MRR:29.1,283.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 286[5:MRR:19.1,283.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 287[5:MRR:24.0,283.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 288[5:MRR:14.0,283.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 289[5:MRR:9.0,283.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 291[5:SpR:284.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.48 297[5:SpR:285.0,73.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.48 299[5:SpR:286.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.48 305[3:SpR:56.0,73.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.20/0.48 307[3:Rew:193.0,305.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.20/0.48 316[5:SpR:287.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.48 318[5:Rew:284.0,316.0,285.0,316.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 323[5:Rew:318.0,289.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.48 329[5:Rew:318.0,291.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.48 331[5:Rew:33.0,329.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 332[5:Rew:331.0,56.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.20/0.48 333[5:Rew:331.0,193.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 334[5:Rew:331.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 338[5:Rew:333.0,288.0] || -> equal(sk_c1,sk_c2)**.
% 0.20/0.48 339[5:Rew:333.0,283.0] || equal(sk_c5,sk_c6)** -> .
% 0.20/0.48 341[5:Rew:338.0,299.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.20/0.48 343[5:Rew:334.0,332.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.48 344[5:Rew:334.0,323.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.48 350[5:Rew:343.0,339.0] || equal(sk_c8,sk_c6)** -> .
% 0.20/0.48 359[5:Rew:334.0,341.0,344.0,341.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 360[5:Rew:359.0,297.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 361[5:Rew:360.0,287.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 362[5:MRR:361.0,350.0] || -> .
% 0.20/0.48 371[4:Spt:362.0,3.0,41.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.48 372[4:Spt:362.0,3.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 373[4:MRR:28.0,371.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 374[4:MRR:18.0,371.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 375[4:MRR:23.0,371.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 376[4:MRR:13.0,371.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 377[4:MRR:8.0,371.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 379[4:SpR:372.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.48 385[4:SpR:373.0,73.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.48 387[4:SpR:374.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.48 403[4:SpR:375.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.48 405[4:Rew:372.0,403.0,373.0,403.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 412[4:Rew:405.0,377.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.48 413[4:Rew:405.0,44.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c6)** -> .
% 0.20/0.48 418[4:Rew:405.0,379.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.48 419[4:Rew:33.0,418.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 420[4:Rew:419.0,56.0] || -> equal(multiply(sk_c8,sk_c5),sk_c8)**.
% 0.20/0.48 421[4:Rew:419.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 422[4:Rew:419.0,193.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 426[4:Rew:421.0,420.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.48 427[4:Rew:421.0,412.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.48 428[4:Rew:421.0,387.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 430[4:Rew:426.0,307.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 433[4:Rew:427.0,376.0] || -> equal(multiply(sk_c1,sk_c8),sk_c6)**.
% 0.20/0.48 436[4:Rew:422.0,433.0] || -> equal(sk_c1,sk_c6)**.
% 0.20/0.48 438[4:Rew:436.0,428.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 439[4:Rew:438.0,385.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 440[4:Rew:439.0,375.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 442[4:Rew:440.0,419.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 445[4:Rew:440.0,430.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 458[4:Rew:438.0,413.2,440.0,413.2,440.0,413.1,445.0,413.0,442.0,413.0,440.0,413.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.48 459[4:Obv:458.1] || equal(u,sk_c6)* -> .
% 0.20/0.48 460[4:UnC:459.0,373.0] || -> .
% 0.20/0.48 463[3:Spt:460.0,5.0,39.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.20/0.48 464[3:Spt:460.0,5.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 465[3:MRR:30.0,463.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 466[3:MRR:20.0,463.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 467[3:MRR:25.0,463.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 468[3:MRR:15.0,463.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 469[3:MRR:10.0,463.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 471[3:SpR:464.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.48 473[3:SpR:465.0,73.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.48 475[3:SpR:466.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.48 481[3:SpR:467.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.48 483[3:Rew:464.0,481.0,465.0,481.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 489[3:Rew:483.0,469.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.48 491[3:Rew:483.0,58.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c6)** -> .
% 0.20/0.48 495[3:Rew:483.0,471.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.48 496[3:Rew:33.0,495.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 497[3:Rew:496.0,193.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 498[3:Rew:496.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 501[3:Rew:497.0,468.0] || -> equal(sk_c1,sk_c2)**.
% 0.20/0.48 502[3:Rew:501.0,466.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.48 503[3:Rew:501.0,475.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.20/0.48 504[3:Rew:498.0,489.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.48 506[3:Rew:504.0,502.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.48 507[3:Rew:498.0,503.0,504.0,503.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 508[3:Rew:507.0,473.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 509[3:Rew:508.0,467.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 511[3:Rew:509.0,496.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 514[3:Rew:509.0,506.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 525[3:Rew:507.0,491.2,509.0,491.2,511.0,491.1,514.0,491.0,514.0,491.0,509.0,491.0] || equal(sk_c6,sk_c6)* equal(sk_c6,u)* equal(u,sk_c6)* -> .
% 0.20/0.48 526[3:Obv:525.1] || equal(u,sk_c6)* -> .
% 0.20/0.48 527[3:UnC:526.0,465.0] || -> .
% 0.20/0.48 530[2:Spt:527.0,1.0,37.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.20/0.48 531[2:Spt:527.0,1.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 532[2:MRR:26.1,530.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 534[2:MRR:21.0,530.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 538[2:SpR:531.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.48 545[2:SpR:534.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.48 547[2:Rew:531.0,545.0,532.0,545.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 549[2:Rew:547.0,530.0] || equal(multiply(sk_c8,sk_c6),sk_c6)** -> .
% 0.20/0.48 556[2:Rew:547.0,538.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.48 558[2:Rew:33.0,556.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 559[2:Rew:558.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 563[2:UnC:559.0,549.0] || -> .
% 0.20/0.48 572[1:Spt:563.0,31.0,31.1,31.2,31.5,31.6,31.7,31.9,31.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7) -> .
% 0.20/0.48 574[2:Spt:1.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.20/0.48 575[2:Rew:574.0,572.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** equal(sk_c6,sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.48 577[2:Obv:575.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.48 580[2:SpR:574.0,73.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c7)**.
% 0.20/0.48 582[3:Spt:3.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 585[4:Spt:5.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.20/0.48 588[5:Spt:2.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.48 590[5:SpR:588.0,73.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c8)**.
% 0.20/0.48 592[5:Rew:574.0,590.0,582.0,590.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 594[5:Rew:592.0,582.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 595[5:Rew:592.0,585.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.48 596[5:Rew:592.0,588.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.20/0.48 599[5:Rew:592.0,577.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** equal(multiply(sk_c6,sk_c6),sk_c7)** -> .
% 0.20/0.48 603[5:Rew:592.0,24.0] || -> equal(multiply(sk_c5,sk_c6),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 604[5:Rew:592.0,29.1] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c6)**.
% 0.20/0.48 605[5:Rew:592.0,580.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.20/0.48 609[5:Rew:33.0,605.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 610[5:Rew:609.0,193.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 611[5:Rew:609.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 613[5:Rew:609.0,33.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.48 620[5:Rew:592.0,603.1] || -> equal(multiply(sk_c5,sk_c6),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.20/0.48 621[5:Rew:592.0,599.5,592.0,599.4,592.0,599.3,592.0,599.1,592.0,599.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c6)** equal(multiply(sk_c6,sk_c6),sk_c7)** -> .
% 0.20/0.48 622[5:Con:621.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c6),sk_c7)** -> .
% 0.20/0.48 646[5:SpR:613.0,73.0] || -> equal(multiply(inverse(inverse(u)),sk_c7),u)**.
% 0.20/0.48 647[5:SpR:613.0,610.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.20/0.48 649[5:SpR:594.0,613.0] || -> equal(multiply(sk_c6,sk_c4),sk_c7)**.
% 0.20/0.48 650[5:SpR:595.0,613.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.48 652[5:Rew:610.0,646.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.48 660[5:SpR:649.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c4)**.
% 0.20/0.48 662[5:Rew:610.0,660.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.48 668[5:SpR:650.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c5)**.
% 0.20/0.48 670[5:Rew:610.0,668.0,662.0,668.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.48 674[5:Rew:670.0,620.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.20/0.48 678[5:Rew:670.0,604.1] || -> equal(inverse(sk_c3),sk_c6) equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.20/0.48 682[5:Rew:596.0,678.1] || -> equal(inverse(sk_c3),sk_c6)** equal(sk_c7,sk_c6).
% 0.20/0.48 684[5:Rew:596.0,674.0] || -> equal(sk_c7,sk_c6) equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.20/0.48 688[6:Spt:682.1] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 690[6:Rew:688.0,611.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 692[6:Rew:688.0,610.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 694[6:Rew:688.0,647.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 696[6:Rew:688.0,622.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(sk_c6,sk_c6),sk_c6)** -> .
% 0.20/0.48 697[6:Rew:662.0,694.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 698[6:Rew:697.0,594.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 707[6:Rew:690.0,696.4,692.0,696.3,688.0,696.3,692.0,696.2] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(sk_c6,sk_c6) -> .
% 0.20/0.48 708[6:Obv:707.4] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) -> .
% 0.20/0.48 709[6:Con:708.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.48 748[6:SpL:698.0,709.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.48 750[6:Obv:748.1] || -> .
% 0.20/0.48 751[6:Spt:750.0,682.1,688.0] || equal(sk_c7,sk_c6)** -> .
% 0.20/0.48 752[6:Spt:750.0,682.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 754[6:MRR:684.0,751.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.20/0.48 761[6:SpR:752.0,652.0] || -> equal(inverse(sk_c6),sk_c3)**.
% 0.20/0.48 763[6:Rew:662.0,761.0] || -> equal(sk_c3,sk_c4)**.
% 0.20/0.48 765[6:Rew:763.0,754.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.20/0.48 766[6:Rew:596.0,765.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 767[6:MRR:766.0,751.0] || -> .
% 0.20/0.48 769[5:Spt:767.0,2.0,588.0] || equal(multiply(sk_c4,sk_c8),sk_c7)** -> .
% 0.20/0.48 770[5:Spt:767.0,2.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 771[5:MRR:27.1,769.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 772[5:MRR:17.1,769.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 773[5:MRR:22.0,769.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 774[5:MRR:12.0,769.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 775[5:MRR:7.0,769.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 781[5:SpR:770.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.48 789[5:SpR:772.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.48 792[5:SpR:773.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.48 794[5:Rew:770.0,792.0,771.0,792.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 798[5:Rew:794.0,769.0] || equal(multiply(sk_c4,sk_c8),sk_c6)** -> .
% 0.20/0.48 801[5:Rew:794.0,775.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.48 804[5:Rew:794.0,781.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.48 805[5:Rew:33.0,804.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 806[5:Rew:805.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 807[5:Rew:805.0,193.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 808[5:Rew:805.0,33.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.48 810[5:Rew:806.0,801.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.48 811[5:Rew:806.0,789.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.48 814[5:Rew:810.0,774.0] || -> equal(multiply(sk_c1,sk_c8),sk_c6)**.
% 0.20/0.48 815[5:Rew:807.0,798.0] || equal(sk_c4,sk_c6)** -> .
% 0.20/0.48 816[5:Rew:811.0,814.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 818[5:Rew:816.0,582.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.48 823[5:Rew:816.0,806.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 829[5:Rew:816.0,808.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 876[5:SpR:818.0,829.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.20/0.48 882[5:Rew:823.0,876.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.48 883[5:MRR:882.0,815.0] || -> .
% 0.20/0.48 889[4:Spt:883.0,5.0,585.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.20/0.48 890[4:Spt:883.0,5.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 891[4:MRR:30.0,889.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 892[4:MRR:20.0,889.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 893[4:MRR:25.0,889.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.48 894[4:MRR:15.0,889.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.48 895[4:MRR:10.0,889.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 896[4:Rew:890.0,577.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.20/0.48 897[4:Obv:896.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** -> .
% 0.20/0.48 901[4:SpR:890.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.48 905[4:SpR:891.0,73.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.48 907[4:SpR:892.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.48 913[4:SpR:893.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.48 915[4:Rew:890.0,913.0,891.0,913.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.48 921[4:Rew:915.0,895.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.48 922[4:Rew:915.0,897.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c6),sk_c8)** -> .
% 0.20/0.48 924[4:Rew:915.0,901.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.48 925[4:Rew:33.0,924.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 926[4:Rew:925.0,193.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 927[4:Rew:925.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 930[4:Rew:926.0,894.0] || -> equal(sk_c1,sk_c2)**.
% 0.20/0.48 931[4:Rew:930.0,892.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.48 932[4:Rew:930.0,907.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.20/0.48 933[4:Rew:927.0,921.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.48 936[4:Rew:933.0,931.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.48 937[4:Rew:927.0,932.0,933.0,932.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 938[4:Rew:937.0,905.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.48 939[4:Rew:938.0,893.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.48 943[4:Rew:939.0,926.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 945[4:Rew:939.0,936.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.48 952[4:Con:922.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c8)** -> .
% 0.20/0.48 953[4:Rew:943.0,952.3,939.0,952.3,943.0,952.2,939.0,952.2,939.0,952.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) -> .
% 0.20/0.48 954[4:Con:953.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.48 996[4:SpL:945.0,954.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.48 997[4:Obv:996.1] || -> .
% 0.20/0.48 998[3:Spt:997.0,3.0,582.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.48 999[3:Spt:997.0,3.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.48 1000[3:MRR:28.0,998.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.48 1001[3:MRR:18.0,998.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.48 1002[3:MRR:23.0,998.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 1003[3:MRR:13.0,998.0] || -> equal(multiply(sk_c1,sk_c8),sk_c2)**.
% 0.20/0.49 1004[3:MRR:8.0,998.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.49 1005[3:Rew:999.0,577.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.20/0.49 1006[3:Obv:1005.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c6),sk_c8)** -> .
% 0.20/0.49 1010[3:SpR:999.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.49 1014[3:SpR:1001.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.20/0.49 1020[3:SpR:1002.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 1022[3:Rew:999.0,1020.0,1000.0,1020.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 1028[3:Rew:1022.0,1004.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.20/0.49 1029[3:Rew:1022.0,1006.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c8),sk_c6)** equal(multiply(w,sk_c6),sk_c8)** -> .
% 0.20/0.49 1031[3:Rew:1022.0,1010.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 1032[3:Rew:33.0,1031.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 1033[3:Rew:1032.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 1034[3:Rew:1032.0,193.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.49 1037[3:Rew:1033.0,1028.0] || -> equal(sk_c2,sk_c6)**.
% 0.20/0.49 1038[3:Rew:1033.0,1014.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.20/0.49 1039[3:Rew:1037.0,1003.0] || -> equal(multiply(sk_c1,sk_c8),sk_c6)**.
% 0.20/0.49 1040[3:Rew:1038.0,1039.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 1043[3:Rew:1040.0,1002.0] || -> equal(multiply(sk_c3,sk_c6),sk_c6)**.
% 0.20/0.49 1047[3:Rew:1040.0,1034.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1049[3:Rew:1047.0,1043.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.49 1050[3:Rew:1049.0,1000.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 1057[3:Con:1029.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c6) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c6),sk_c8)** -> .
% 0.20/0.49 1058[3:Rew:1047.0,1057.3,1040.0,1057.3,1047.0,1057.2,1040.0,1057.2,1040.0,1057.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) -> .
% 0.20/0.49 1059[3:Con:1058.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.49 1105[3:SpL:1050.0,1059.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 1107[3:Obv:1105.1] || -> .
% 0.20/0.49 1108[2:Spt:1107.0,1.0,574.0] || equal(multiply(sk_c8,sk_c7),sk_c6)** -> .
% 0.20/0.49 1109[2:Spt:1107.0,1.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 1110[2:MRR:26.1,1108.0] || -> equal(inverse(sk_c3),sk_c6)**.
% 0.20/0.49 1112[2:MRR:21.0,1108.0] || -> equal(multiply(sk_c3,sk_c6),sk_c8)**.
% 0.20/0.49 1116[2:SpR:1109.0,73.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.20/0.49 1123[2:SpR:1112.0,73.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c6)**.
% 0.20/0.49 1125[2:Rew:1109.0,1123.0,1110.0,1123.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 1127[2:Rew:1125.0,1108.0] || equal(multiply(sk_c8,sk_c6),sk_c6)** -> .
% 0.20/0.49 1129[2:Rew:1125.0,1116.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c8)**.
% 0.20/0.49 1131[2:Rew:33.0,1129.0] || -> equal(identity,sk_c8)**.
% 0.20/0.49 1133[2:Rew:1131.0,32.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.49 1139[2:UnC:1133.0,1127.0] || -> .
% 0.20/0.49 % SZS output end Refutation
% 0.20/0.49 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_7 prove_this_8 prove_this_9 prove_this_10 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_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
% 0.20/0.49
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