TSTP Solution File: GRP241-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP241-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:46:29 EDT 2022
% Result : Unsatisfiable 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP241-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 600
% 0.17/0.33 % DateTime : Mon Jun 13 11:17:37 EDT 2022
% 0.17/0.33 % CPUTime :
% 0.17/0.46
% 0.17/0.46 SPASS V 3.9
% 0.17/0.46 SPASS beiseite: Proof found.
% 0.17/0.46 % SZS status Theorem
% 0.17/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.46 SPASS derived 1044 clauses, backtracked 425 clauses, performed 13 splits and kept 777 clauses.
% 0.17/0.46 SPASS allocated 63766 KBytes.
% 0.17/0.46 SPASS spent 0:00:00.13 on the problem.
% 0.17/0.46 0:00:00.04 for the input.
% 0.17/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.46 0:00:00.01 for inferences.
% 0.17/0.46 0:00:00.00 for the backtracking.
% 0.17/0.46 0:00:00.06 for the reduction.
% 0.17/0.46
% 0.17/0.46
% 0.17/0.46 Here is a proof with depth 4, length 409 :
% 0.17/0.46 % SZS output start Refutation
% 0.17/0.46 1[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c8),sk_c7)**.
% 0.17/0.46 3[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.17/0.46 4[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.17/0.46 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c8),sk_c7)**.
% 0.17/0.46 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c7),sk_c8).
% 0.17/0.46 7[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.17/0.46 8[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.17/0.46 9[0:Inp] || -> equal(inverse(sk_c7),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.17/0.46 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c7),sk_c8).
% 0.17/0.46 11[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 12[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 13[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.17/0.46 14[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 15[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 16[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 17[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.17/0.46 18[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.17/0.46 19[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.17/0.46 20[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.46 24[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.46 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.46 26[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.46 29[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.46 30[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.46 31[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.46 33[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.17/0.46 34[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.17/0.46 35[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.46 36[0:Inp] || equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c7),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(inverse(u),sk_c7) equal(multiply(sk_c8,v),sk_c7)** equal(multiply(w,sk_c8),v)* equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(z,sk_c8),y)* equal(inverse(z),sk_c8) -> .
% 0.17/0.46 37[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.17/0.46 38[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.17/0.46 39[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.17/0.46 40[0:Con:36.9] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c8),x)*+ equal(multiply(u,sk_c7),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c8,x),sk_c7)** -> .
% 0.17/0.46 41[1:Spt:40.0,40.6] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.17/0.46 42[2:Spt:10.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.17/0.46 44[3:Spt:6.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.17/0.46 46[4:Spt:9.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.17/0.46 48[5:Spt:8.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.17/0.46 51[1:SpL:37.0,41.1] || equal(inverse(identity),sk_c8)** equal(sk_c8,sk_c7) -> .
% 0.17/0.46 52[6:Spt:7.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.17/0.46 54[6:SpL:52.0,41.1] || equal(inverse(sk_c4),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.17/0.46 55[6:Obv:54.1] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.17/0.46 56[6:Rew:44.0,55.0] || equal(sk_c8,sk_c8)* -> .
% 0.17/0.46 57[6:Obv:56.0] || -> .
% 0.17/0.46 58[6:Spt:57.0,7.1,52.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.17/0.46 59[6:Spt:57.0,7.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.17/0.46 61[6:MRR:17.1,58.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 65[6:MRR:12.0,58.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 73[6:SpL:65.0,41.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.17/0.46 74[6:Obv:73.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.17/0.46 75[6:Rew:61.0,74.0] || equal(sk_c8,sk_c7)** -> .
% 0.17/0.46 77[2:SpR:42.0,38.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.17/0.46 78[3:SpR:44.0,38.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.17/0.46 83[1:SpL:38.0,41.1] || equal(inverse(inverse(sk_c7)),sk_c8)** equal(sk_c8,identity) -> .
% 0.17/0.46 98[2:SpR:77.0,39.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.17/0.46 103[0:SpR:38.0,39.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.17/0.46 105[2:Rew:37.0,98.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.17/0.46 109[0:Rew:37.0,103.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.17/0.46 119[4:SpR:46.0,105.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.17/0.46 120[5:Rew:48.0,119.0] || -> equal(sk_c8,sk_c7)**.
% 0.17/0.46 121[6:MRR:120.0,75.0] || -> .
% 0.17/0.46 123[5:Spt:121.0,8.1,48.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.17/0.46 124[5:Spt:121.0,8.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.17/0.46 125[5:Rew:119.0,123.0] || equal(sk_c8,sk_c7)** -> .
% 0.17/0.46 126[4:Rew:119.0,33.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c8,sk_c7).
% 0.17/0.46 127[5:MRR:126.1,125.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.46 128[4:Rew:119.0,18.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c8,sk_c7).
% 0.17/0.46 129[5:MRR:128.1,125.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 130[4:Rew:119.0,3.1] || -> equal(inverse(sk_c8),sk_c7)** equal(sk_c8,sk_c7).
% 0.17/0.46 131[5:MRR:130.1,125.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.17/0.46 137[4:Rew:119.0,13.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 138[5:MRR:137.0,125.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 139[5:SpR:124.0,38.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.17/0.46 141[5:SpR:127.0,38.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.17/0.46 143[5:SpR:129.0,38.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.17/0.46 145[5:SpR:131.0,38.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.17/0.46 159[5:SpR:139.0,39.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.17/0.46 161[5:Rew:37.0,159.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),u)**.
% 0.17/0.46 177[5:SpR:145.0,161.0] || -> equal(multiply(sk_c8,identity),sk_c8)**.
% 0.17/0.46 178[5:SpR:143.0,161.0] || -> equal(multiply(sk_c8,identity),sk_c1)**.
% 0.17/0.46 179[5:Rew:177.0,178.0] || -> equal(sk_c8,sk_c1)**.
% 0.17/0.46 188[5:Rew:179.0,125.0] || equal(sk_c1,sk_c7)** -> .
% 0.17/0.46 189[5:Rew:179.0,127.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.17/0.46 191[5:Rew:179.0,119.0] || -> equal(multiply(sk_c1,sk_c6),sk_c1)**.
% 0.17/0.46 194[5:Rew:179.0,138.0] || -> equal(multiply(sk_c1,sk_c7),sk_c1)**.
% 0.17/0.46 195[5:Rew:179.0,139.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.17/0.46 196[5:Rew:179.0,141.0] || -> equal(multiply(sk_c1,sk_c2),identity)**.
% 0.17/0.46 209[5:Rew:194.0,195.0] || -> equal(identity,sk_c1)**.
% 0.17/0.46 210[5:Rew:209.0,37.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.17/0.46 215[5:Rew:209.0,196.0] || -> equal(multiply(sk_c1,sk_c2),sk_c1)**.
% 0.17/0.46 218[5:Rew:210.0,215.0] || -> equal(sk_c2,sk_c1)**.
% 0.17/0.46 221[5:Rew:210.0,191.0] || -> equal(sk_c1,sk_c6)**.
% 0.17/0.46 223[5:Rew:218.0,189.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.17/0.46 226[5:Rew:221.0,129.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.17/0.46 231[5:Rew:221.0,188.0] || equal(sk_c6,sk_c7)** -> .
% 0.17/0.46 237[5:Rew:221.0,223.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.17/0.46 238[5:Rew:237.0,226.0] || -> equal(sk_c6,sk_c7)**.
% 0.17/0.46 247[5:Rew:238.0,231.0] || equal(sk_c7,sk_c7)* -> .
% 0.17/0.46 248[5:Obv:247.0] || -> .
% 0.17/0.46 274[4:Spt:248.0,9.1,46.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.17/0.46 275[4:Spt:248.0,9.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.17/0.46 276[4:MRR:34.1,274.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.46 277[4:MRR:19.1,274.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 278[4:MRR:4.1,274.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.17/0.46 280[4:MRR:29.0,274.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.46 281[4:MRR:24.0,274.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.46 282[4:MRR:14.0,274.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 305[4:SpR:275.0,38.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.17/0.46 308[4:SpR:276.0,38.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.17/0.46 310[4:SpR:278.0,38.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.17/0.46 325[0:SpR:109.0,109.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.17/0.46 328[3:SpR:78.0,109.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.17/0.46 329[2:SpR:77.0,109.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.17/0.46 330[4:SpR:281.0,109.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.17/0.46 331[4:SpR:305.0,109.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c7)**.
% 0.17/0.46 332[4:SpR:308.0,109.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.17/0.46 333[4:SpR:280.0,109.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.17/0.46 335[4:SpR:282.0,109.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.17/0.46 336[0:SpR:37.0,109.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.17/0.46 337[0:SpR:38.0,109.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.17/0.46 345[4:Rew:278.0,328.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.17/0.46 352[4:Rew:278.0,330.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.17/0.46 353[4:Rew:278.0,331.0] || -> equal(multiply(sk_c7,identity),sk_c7)**.
% 0.17/0.46 354[4:Rew:345.0,353.0] || -> equal(sk_c4,sk_c7)**.
% 0.17/0.46 358[4:Rew:354.0,345.0] || -> equal(multiply(sk_c7,identity),sk_c7)**.
% 0.17/0.46 360[4:Rew:278.0,332.0] || -> equal(multiply(sk_c7,identity),sk_c2)**.
% 0.17/0.46 361[4:Rew:358.0,360.0] || -> equal(sk_c2,sk_c7)**.
% 0.17/0.46 363[4:Rew:361.0,280.0] || -> equal(multiply(sk_c7,sk_c8),sk_c3)**.
% 0.17/0.46 367[4:Rew:310.0,363.0] || -> equal(identity,sk_c3)**.
% 0.17/0.46 373[4:Rew:367.0,51.0] || equal(inverse(sk_c3),sk_c8)** equal(sk_c8,sk_c7) -> .
% 0.17/0.46 378[4:Rew:361.0,333.0] || -> equal(multiply(inverse(sk_c7),sk_c3),sk_c8)**.
% 0.17/0.46 379[4:Rew:281.0,378.0,275.0,378.0] || -> equal(sk_c8,sk_c7)**.
% 0.17/0.46 380[4:Rew:379.0,275.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.17/0.46 392[4:Rew:277.0,335.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.17/0.46 393[4:Rew:352.0,392.0,379.0,392.0] || -> equal(sk_c3,sk_c7)**.
% 0.17/0.46 425[4:Rew:379.0,373.1,380.0,373.0,393.0,373.0,379.0,373.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.17/0.46 426[4:Obv:425.1] || -> .
% 0.17/0.46 431[3:Spt:426.0,6.0,44.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.17/0.46 432[3:Spt:426.0,6.1] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.17/0.46 433[0:Rew:325.0,337.0] || -> equal(multiply(u,identity),u)**.
% 0.17/0.46 434[2:Rew:433.0,329.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.17/0.46 435[3:MRR:31.0,431.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.46 436[3:MRR:16.0,431.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 437[2:Rew:434.0,1.1] || -> equal(inverse(sk_c4),sk_c8)** equal(sk_c5,sk_c7).
% 0.17/0.46 438[3:MRR:437.0,431.0] || -> equal(sk_c5,sk_c7)**.
% 0.17/0.46 440[3:Rew:438.0,77.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.17/0.46 442[3:Rew:438.0,434.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.17/0.46 443[3:MRR:26.0,431.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.46 444[3:MRR:21.0,431.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.46 445[3:MRR:11.0,431.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 446[3:Rew:442.0,83.0,432.0,83.0] || equal(sk_c8,sk_c7) equal(sk_c8,identity)** -> .
% 0.17/0.46 462[3:SpR:443.0,109.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.17/0.46 464[3:Rew:435.0,462.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.17/0.46 465[3:Rew:444.0,464.0] || -> equal(sk_c8,sk_c7)**.
% 0.17/0.46 466[3:Rew:465.0,432.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.17/0.46 470[3:Rew:465.0,440.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.17/0.46 474[3:Rew:465.0,446.0] || equal(sk_c7,sk_c7) equal(sk_c8,identity)** -> .
% 0.17/0.46 475[3:Rew:465.0,444.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.17/0.46 476[3:Rew:465.0,445.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.17/0.46 481[3:Obv:474.0] || equal(sk_c8,identity)** -> .
% 0.17/0.46 482[3:Rew:465.0,481.0] || equal(identity,sk_c7)** -> .
% 0.17/0.46 503[3:SpR:475.0,109.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.17/0.46 505[3:Rew:470.0,503.0,466.0,503.0] || -> equal(identity,sk_c3)**.
% 0.17/0.46 506[3:Rew:505.0,482.0] || equal(sk_c3,sk_c7)** -> .
% 0.17/0.46 507[3:Rew:505.0,470.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.17/0.46 517[3:SpR:476.0,109.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.17/0.46 519[3:Rew:436.0,517.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.17/0.46 520[3:Rew:507.0,519.0] || -> equal(sk_c3,sk_c7)**.
% 0.17/0.46 521[3:MRR:520.0,506.0] || -> .
% 0.17/0.46 522[2:Spt:521.0,10.0,42.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.17/0.46 523[2:Spt:521.0,10.1] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.17/0.46 524[2:MRR:35.0,522.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.46 525[2:MRR:20.0,522.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 526[2:MRR:5.0,522.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.17/0.46 527[2:MRR:30.0,522.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.46 528[2:MRR:25.0,522.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.46 529[2:MRR:15.0,522.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 530[2:Rew:526.0,83.0,523.0,83.0] || equal(sk_c8,sk_c7) equal(sk_c8,identity)** -> .
% 0.17/0.46 531[2:SpR:523.0,109.0] || -> equal(multiply(sk_c8,multiply(sk_c7,u)),u)**.
% 0.17/0.46 540[2:SpR:527.0,109.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.17/0.46 542[2:Rew:524.0,540.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.17/0.46 543[2:Rew:528.0,542.0] || -> equal(sk_c8,sk_c7)**.
% 0.17/0.46 544[2:Rew:543.0,523.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.17/0.46 550[2:Rew:543.0,530.0] || equal(sk_c7,sk_c7) equal(sk_c8,identity)** -> .
% 0.17/0.46 551[2:Rew:543.0,528.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.17/0.46 552[2:Rew:543.0,529.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.17/0.46 555[2:Rew:543.0,531.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.17/0.46 558[2:Obv:550.0] || equal(sk_c8,identity)** -> .
% 0.17/0.46 559[2:Rew:543.0,558.0] || equal(identity,sk_c7)** -> .
% 0.17/0.46 574[2:SpR:551.0,39.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.17/0.46 575[2:SpR:551.0,109.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.17/0.46 577[2:Rew:544.0,575.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.17/0.46 579[2:SpR:552.0,109.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.17/0.46 581[2:Rew:525.0,579.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.17/0.46 582[2:Rew:577.0,581.0] || -> equal(sk_c3,sk_c7)**.
% 0.17/0.46 586[2:Rew:582.0,574.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.17/0.46 588[2:Rew:555.0,586.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.17/0.46 607[2:SpR:588.0,433.0] || -> equal(identity,sk_c7)**.
% 0.17/0.46 609[2:MRR:607.0,559.0] || -> .
% 0.17/0.46 611[1:Spt:609.0,40.1,40.2,40.3,40.4,40.5,40.7,40.8] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),w)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,w),sk_c7)** -> .
% 0.17/0.46 612[1:EqR:611.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(sk_c7),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.46 615[2:Spt:6.1] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.17/0.46 619[2:Rew:615.0,612.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(sk_c8,sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.46 620[2:Obv:619.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.46 626[3:Spt:5.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.17/0.46 630[3:Rew:626.0,620.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(sk_c7,sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.46 631[3:Obv:630.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.46 637[4:Spt:35.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.17/0.46 640[5:Spt:31.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.17/0.46 645[0:SpR:336.0,433.0] || -> equal(inverse(identity),identity)**.
% 0.17/0.46 652[6:Spt:34.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.17/0.46 654[6:SpR:652.0,109.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.17/0.46 656[6:Rew:637.0,654.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.17/0.46 657[6:Rew:656.0,13.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 660[6:Rew:656.0,18.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c8,sk_c7).
% 0.17/0.46 662[6:Rew:660.1,17.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.17/0.46 664[6:Rew:657.0,12.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 671[6:SpR:656.0,109.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.17/0.46 673[6:Rew:626.0,671.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.17/0.46 675[0:SpR:38.0,109.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.17/0.46 678[2:SpR:615.0,38.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.17/0.46 679[3:SpR:626.0,38.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.17/0.46 681[5:SpR:640.0,38.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.17/0.46 683[6:Rew:673.0,679.0] || -> equal(identity,sk_c6)**.
% 0.17/0.46 684[6:Rew:683.0,433.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.17/0.46 685[6:Rew:683.0,37.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.17/0.46 686[6:Rew:683.0,645.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.17/0.46 689[6:Rew:683.0,678.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.17/0.46 691[6:Rew:683.0,681.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.17/0.46 695[6:Rew:684.0,675.0,683.0,675.0] || -> equal(inverse(inverse(u)),u)**.
% 0.17/0.46 725[6:SpR:691.0,109.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c4)**.
% 0.17/0.46 727[6:Rew:626.0,725.0] || -> equal(multiply(sk_c7,sk_c6),sk_c4)**.
% 0.17/0.46 728[6:Rew:684.0,727.0] || -> equal(sk_c4,sk_c7)**.
% 0.17/0.46 734[6:Rew:728.0,664.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 736[6:Rew:728.0,662.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.17/0.46 778[7:Spt:660.1] || -> equal(sk_c8,sk_c7)**.
% 0.17/0.46 779[7:Rew:778.0,615.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.17/0.46 781[7:Rew:778.0,673.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.17/0.46 785[7:Rew:778.0,631.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.46 789[7:Rew:778.0,734.1] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.17/0.46 793[7:Rew:781.0,736.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.17/0.46 795[7:Rew:781.0,789.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.17/0.46 798[7:Rew:778.0,785.3,778.0,785.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.17/0.46 803[8:Spt:793.1] || -> equal(sk_c6,sk_c7)**.
% 0.17/0.46 806[8:Rew:803.0,685.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.17/0.46 808[8:Rew:803.0,684.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.17/0.46 815[8:Rew:806.0,798.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.17/0.46 817[8:Con:815.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.17/0.46 818[8:Rew:808.0,817.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.17/0.46 876[8:SpL:779.0,818.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.17/0.46 877[8:Obv:876.1] || -> .
% 0.17/0.46 878[8:Spt:877.0,793.1,803.0] || equal(sk_c6,sk_c7)** -> .
% 0.17/0.46 879[8:Spt:877.0,793.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 881[8:MRR:795.0,878.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.17/0.46 885[8:SpR:879.0,695.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.17/0.46 888[8:Rew:779.0,885.0] || -> equal(sk_c1,sk_c7)**.
% 0.17/0.46 890[8:Rew:888.0,881.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.17/0.46 891[8:Rew:781.0,890.0] || -> equal(sk_c6,sk_c7)**.
% 0.17/0.46 892[8:MRR:891.0,878.0] || -> .
% 0.17/0.46 895[7:Spt:892.0,660.1,778.0] || equal(sk_c8,sk_c7)** -> .
% 0.17/0.46 896[7:Spt:892.0,660.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 898[7:MRR:657.0,895.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 902[7:SpR:896.0,695.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.17/0.46 905[7:Rew:615.0,902.0] || -> equal(sk_c8,sk_c1)**.
% 0.17/0.46 908[7:Rew:905.0,895.0] || equal(sk_c1,sk_c7)** -> .
% 0.17/0.46 909[7:Rew:905.0,689.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.17/0.46 914[7:Rew:905.0,898.0] || -> equal(multiply(sk_c1,sk_c7),sk_c1)**.
% 0.17/0.46 921[7:Rew:909.0,914.0] || -> equal(sk_c1,sk_c6)**.
% 0.17/0.46 922[7:Rew:921.0,896.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.17/0.46 925[7:Rew:921.0,908.0] || equal(sk_c6,sk_c7)** -> .
% 0.17/0.46 929[7:Rew:686.0,922.0] || -> equal(sk_c6,sk_c7)**.
% 0.17/0.46 940[7:Rew:929.0,925.0] || equal(sk_c7,sk_c7)* -> .
% 0.17/0.46 941[7:Obv:940.0] || -> .
% 0.17/0.46 963[6:Spt:941.0,34.1,652.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.17/0.46 964[6:Spt:941.0,34.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.46 965[0:Rew:433.0,675.0] || -> equal(inverse(inverse(u)),u)**.
% 0.17/0.46 966[6:MRR:19.1,963.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 968[6:MRR:29.0,963.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.46 969[6:MRR:24.0,963.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.46 970[6:MRR:14.0,963.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 988[6:SpR:968.0,109.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.17/0.46 990[6:Rew:964.0,988.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.17/0.46 991[6:Rew:969.0,990.0] || -> equal(sk_c8,sk_c7)**.
% 0.17/0.46 993[6:Rew:991.0,615.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.17/0.46 998[6:Rew:991.0,679.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.17/0.46 1007[6:Rew:991.0,969.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.17/0.46 1008[6:Rew:991.0,970.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.17/0.46 1010[6:Rew:991.0,631.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.46 1015[6:Rew:991.0,1010.3,991.0,1010.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.17/0.46 1060[6:SpR:1007.0,109.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.17/0.46 1062[6:Rew:998.0,1060.0,993.0,1060.0] || -> equal(identity,sk_c3)**.
% 0.17/0.46 1064[6:Rew:1062.0,998.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.17/0.46 1066[6:Rew:1062.0,37.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.17/0.46 1067[6:Rew:1062.0,433.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.17/0.46 1077[6:SpR:1008.0,109.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.17/0.46 1079[6:Rew:966.0,1077.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.17/0.46 1080[6:Rew:1064.0,1079.0] || -> equal(sk_c3,sk_c7)**.
% 0.17/0.46 1086[6:Rew:1080.0,1066.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.17/0.46 1087[6:Rew:1080.0,1067.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.17/0.46 1092[6:Rew:1086.0,1015.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.17/0.46 1105[6:Con:1092.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.17/0.46 1106[6:Rew:1087.0,1105.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.17/0.46 1117[0:SpR:965.0,109.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.17/0.46 1165[6:SpL:993.0,1106.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.17/0.46 1167[6:Obv:1165.1] || -> .
% 0.17/0.46 1168[5:Spt:1167.0,31.0,640.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.17/0.46 1169[5:Spt:1167.0,31.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.46 1170[5:MRR:16.0,1168.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.46 1171[5:MRR:26.0,1168.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.46 1172[5:MRR:21.0,1168.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.46 1173[5:MRR:11.0,1168.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.46 1175[5:SpR:1169.0,965.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.17/0.46 1178[5:Rew:626.0,1175.0] || -> equal(sk_c2,sk_c7)**.
% 0.17/0.46 1180[5:Rew:1178.0,1171.0] || -> equal(multiply(sk_c7,sk_c8),sk_c3)**.
% 0.17/0.46 1181[5:Rew:679.0,1180.0] || -> equal(identity,sk_c3)**.
% 0.17/0.46 1184[5:Rew:1181.0,678.0] || -> equal(multiply(sk_c8,sk_c7),sk_c3)**.
% 0.17/0.46 1186[5:Rew:1181.0,433.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.17/0.46 1187[5:Rew:1181.0,37.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.17/0.46 1190[5:Rew:1186.0,1172.0] || -> equal(sk_c8,sk_c7)**.
% 0.17/0.46 1192[5:Rew:1190.0,626.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.17/0.46 1198[5:Rew:1190.0,1173.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.17/0.46 1200[5:Rew:1190.0,631.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.46 1203[5:Rew:1190.0,1184.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.17/0.46 1207[5:Rew:1190.0,1200.3,1190.0,1200.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.17/0.46 1215[5:SpR:1170.0,965.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.17/0.46 1218[5:Rew:1192.0,1215.0] || -> equal(sk_c1,sk_c7)**.
% 0.17/0.46 1220[5:Rew:1218.0,1198.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.17/0.46 1221[5:Rew:1203.0,1220.0] || -> equal(sk_c3,sk_c7)**.
% 0.17/0.47 1224[5:Rew:1221.0,1186.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.17/0.47 1225[5:Rew:1221.0,1187.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.17/0.47 1232[5:Rew:1224.0,1207.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.17/0.47 1240[5:Rew:1224.0,1232.3,1225.0,1232.3] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(v,sk_c7) equal(u,sk_c7) -> .
% 0.17/0.47 1241[5:Con:1240.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.17/0.47 1290[5:SpL:1192.0,1241.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.17/0.47 1291[5:Obv:1290.1] || -> .
% 0.17/0.47 1292[4:Spt:1291.0,35.0,637.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.17/0.47 1293[4:Spt:1291.0,35.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.17/0.47 1294[4:MRR:20.0,1292.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.17/0.47 1295[4:MRR:30.0,1292.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.17/0.47 1296[4:MRR:25.0,1292.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.17/0.47 1297[4:MRR:15.0,1292.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.17/0.47 1299[4:SpR:1293.0,965.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.17/0.47 1302[4:Rew:626.0,1299.0] || -> equal(sk_c2,sk_c7)**.
% 0.17/0.47 1304[4:Rew:1302.0,1295.0] || -> equal(multiply(sk_c7,sk_c8),sk_c3)**.
% 0.17/0.47 1305[4:Rew:679.0,1304.0] || -> equal(identity,sk_c3)**.
% 0.17/0.47 1307[4:Rew:1305.0,37.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.17/0.47 1308[4:Rew:1305.0,433.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.17/0.47 1309[4:Rew:1305.0,679.0] || -> equal(multiply(sk_c7,sk_c8),sk_c3)**.
% 0.17/0.47 1313[4:Rew:1308.0,1296.0] || -> equal(sk_c8,sk_c7)**.
% 0.17/0.47 1314[4:Rew:1313.0,615.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.17/0.47 1319[4:Rew:1313.0,1297.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.17/0.47 1321[4:Rew:1313.0,631.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.17/0.47 1323[4:Rew:1313.0,1309.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.17/0.47 1327[4:Rew:1313.0,1321.3,1313.0,1321.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.17/0.47 1335[4:SpR:1294.0,965.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.17/0.47 1338[4:Rew:1314.0,1335.0] || -> equal(sk_c1,sk_c7)**.
% 0.17/0.47 1340[4:Rew:1338.0,1319.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.17/0.47 1341[4:Rew:1323.0,1340.0] || -> equal(sk_c3,sk_c7)**.
% 0.17/0.47 1344[4:Rew:1341.0,1307.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.17/0.47 1345[4:Rew:1341.0,1308.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.17/0.47 1351[4:Rew:1344.0,1327.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.17/0.47 1355[4:Con:1351.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.17/0.47 1356[4:Rew:1345.0,1355.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.17/0.47 1406[4:SpL:1314.0,1356.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.17/0.47 1407[4:Obv:1406.1] || -> .
% 0.17/0.47 1408[3:Spt:1407.0,5.1,626.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.17/0.47 1409[3:Spt:1407.0,5.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.17/0.47 1410[3:MRR:1.1,1408.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.17/0.47 1415[3:SpR:1409.0,965.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.17/0.47 1418[3:Rew:1415.0,1408.0] || equal(sk_c5,sk_c7)** -> .
% 0.17/0.47 1426[3:SpR:1410.0,965.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.17/0.47 1429[3:Rew:1415.0,1426.0] || -> equal(sk_c5,sk_c4)**.
% 0.17/0.47 1432[3:Rew:1429.0,1415.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.17/0.47 1433[3:Rew:1429.0,1418.0] || equal(sk_c4,sk_c7)** -> .
% 0.17/0.47 1438[2:SpR:615.0,965.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.17/0.47 1441[3:Rew:1432.0,1438.0] || -> equal(sk_c4,sk_c7)**.
% 0.17/0.47 1442[3:MRR:1441.0,1433.0] || -> .
% 0.17/0.47 1443[2:Spt:1442.0,6.1,615.0] || equal(inverse(sk_c7),sk_c8)** -> .
% 0.17/0.47 1444[2:Spt:1442.0,6.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.17/0.47 1445[2:MRR:10.1,1443.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.17/0.47 1446[2:MRR:7.0,1443.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.17/0.47 1447[2:MRR:8.0,1443.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.17/0.47 1448[2:MRR:9.0,1443.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.17/0.47 1450[2:SpR:1444.0,965.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.17/0.47 1451[2:SpR:1444.0,1117.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.17/0.47 1454[2:SpR:1445.0,965.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.17/0.47 1457[2:Rew:1450.0,1454.0] || -> equal(sk_c5,sk_c4)**.
% 0.17/0.47 1459[2:Rew:1457.0,1448.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.17/0.47 1472[2:SpR:1447.0,109.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.17/0.47 1474[2:Rew:1446.0,1472.0,1450.0,1472.0] || -> equal(sk_c8,sk_c6)**.
% 0.17/0.47 1475[2:Rew:1474.0,1444.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.17/0.47 1476[2:Rew:1474.0,1443.0] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.17/0.47 1477[2:Rew:1474.0,1450.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.17/0.47 1479[2:Rew:1474.0,1447.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.17/0.47 1481[2:Rew:1474.0,1451.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.17/0.47 1483[2:Rew:1474.0,1459.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.17/0.47 1503[2:SpR:1483.0,39.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.17/0.47 1504[2:SpR:1483.0,109.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c6)**.
% 0.17/0.47 1506[2:Rew:1479.0,1504.0,1475.0,1504.0] || -> equal(sk_c6,sk_c7)**.
% 0.17/0.47 1508[2:Rew:1506.0,1476.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.17/0.47 1510[2:Rew:1506.0,1477.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.17/0.47 1515[2:Rew:1506.0,1481.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.17/0.47 1518[2:Rew:1510.0,1508.0] || equal(sk_c4,sk_c7)** -> .
% 0.17/0.47 1519[2:Rew:1515.0,1503.0,1506.0,1503.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.17/0.47 1553[2:SpR:1519.0,433.0] || -> equal(identity,sk_c7)**.
% 0.17/0.47 1555[2:Rew:1553.0,645.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.17/0.47 1560[2:Rew:1510.0,1555.0] || -> equal(sk_c4,sk_c7)**.
% 0.17/0.47 1561[2:MRR:1560.0,1518.0] || -> .
% 0.17/0.47 % SZS output end Refutation
% 0.17/0.47 Formulae used in the proof : prove_this_1 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_24 prove_this_25 prove_this_26 prove_this_29 prove_this_30 prove_this_31 prove_this_33 prove_this_34 prove_this_35 prove_this_36 left_identity left_inverse associativity
% 0.17/0.47
%------------------------------------------------------------------------------