TSTP Solution File: GRP232-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP232-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 11:46:26 EDT 2022
% Result : Unsatisfiable 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP232-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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 23:54:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.50
% 0.21/0.50 SPASS V 3.9
% 0.21/0.50 SPASS beiseite: Proof found.
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50 SPASS derived 1025 clauses, backtracked 430 clauses, performed 12 splits and kept 772 clauses.
% 0.21/0.50 SPASS allocated 63814 KBytes.
% 0.21/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.21/0.50 0:00:00.04 for the input.
% 0.21/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.50 0:00:00.01 for inferences.
% 0.21/0.50 0:00:00.00 for the backtracking.
% 0.21/0.50 0:00:00.08 for the reduction.
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 Here is a proof with depth 4, length 381 :
% 0.21/0.50 % SZS output start Refutation
% 0.21/0.50 1[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.50 2[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.21/0.50 3[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.21/0.50 4[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.21/0.50 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.50 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 8[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.21/0.50 9[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 11[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.21/0.50 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.21/0.50 15[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 17[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.21/0.50 18[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c3),sk_c8).
% 0.21/0.50 20[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.21/0.50 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.50 22[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.21/0.50 23[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.21/0.50 24[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.21/0.50 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.50 27[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.21/0.50 28[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c3,sk_c7),sk_c8).
% 0.21/0.50 31[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(inverse(y),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),z)* equal(multiply(x,sk_c7),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(y,sk_c8),sk_c7)** equal(multiply(sk_c8,z),sk_c7)** -> .
% 0.21/0.50 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.50 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.50 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.50 35[1:Spt:31.0,31.5,31.8] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.21/0.50 36[2:Spt:5.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.50 38[3:Spt:1.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.21/0.50 40[4:Spt:4.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.21/0.50 46[1:SpL:32.0,35.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.21/0.50 47[5:Spt:3.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.21/0.50 49[5:SpL:47.0,35.1] || equal(inverse(sk_c8),sk_c6) equal(sk_c8,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.21/0.50 50[6:Spt:2.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.21/0.50 56[2:SpR:36.0,33.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.50 57[3:SpR:38.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.21/0.50 60[2:SpL:56.0,35.1] || equal(inverse(sk_c8),sk_c5) equal(sk_c8,identity) equal(multiply(sk_c5,sk_c7),sk_c8)** -> .
% 0.21/0.50 68[4:SpR:40.0,34.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.21/0.50 70[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.50 72[2:SpR:56.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.21/0.50 73[3:SpR:57.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.21/0.50 75[2:Rew:32.0,72.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.21/0.50 76[3:Rew:32.0,73.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.21/0.50 77[0:Rew:32.0,70.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.50 81[4:SpR:40.0,75.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.21/0.50 82[2:SpL:75.0,35.1] || equal(multiply(sk_c5,u),inverse(sk_c8)) equal(u,sk_c8) equal(multiply(multiply(sk_c5,u),sk_c7),sk_c8)** -> .
% 0.21/0.50 83[5:Rew:47.0,81.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 86[5:Rew:83.0,38.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.50 87[5:Rew:83.0,40.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.21/0.50 88[5:Rew:83.0,47.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.21/0.50 89[6:Rew:83.0,50.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.21/0.50 90[5:Rew:83.0,56.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.21/0.50 91[5:Rew:83.0,57.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.21/0.50 93[5:Rew:83.0,49.0] || equal(inverse(sk_c7),sk_c6) equal(sk_c8,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.21/0.50 94[5:Rew:83.0,60.0] || equal(inverse(sk_c7),sk_c5) equal(sk_c8,identity) equal(multiply(sk_c5,sk_c7),sk_c8)** -> .
% 0.21/0.50 103[5:Rew:83.0,76.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.21/0.50 111[5:Rew:83.0,93.2,83.0,93.1] || equal(inverse(sk_c7),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.21/0.50 112[5:Obv:111.1] || equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c7)** -> .
% 0.21/0.50 113[5:Rew:87.0,94.2,83.0,94.2,83.0,94.1] || equal(inverse(sk_c7),sk_c5)** equal(identity,sk_c7) equal(sk_c6,sk_c7) -> .
% 0.21/0.50 117[2:Rew:34.0,82.2] || equal(multiply(sk_c5,u),inverse(sk_c8)) equal(u,sk_c8) equal(multiply(sk_c5,multiply(u,sk_c7)),sk_c8)** -> .
% 0.21/0.50 138[0:SpR:77.0,77.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.50 140[0:SpR:32.0,77.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.21/0.50 141[0:SpR:33.0,77.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.50 145[5:SpR:88.0,77.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.21/0.50 146[5:SpR:90.0,77.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.21/0.50 147[5:SpR:91.0,77.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.21/0.50 153[5:Rew:33.0,145.0] || -> equal(identity,sk_c6)**.
% 0.21/0.50 154[5:Rew:153.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.50 159[5:Rew:153.0,113.1] || equal(inverse(sk_c7),sk_c5)** equal(sk_c6,sk_c7) equal(sk_c6,sk_c7) -> .
% 0.21/0.50 162[5:Rew:153.0,140.0] || -> equal(multiply(inverse(sk_c6),u),u)**.
% 0.21/0.50 165[5:Rew:154.0,112.1] || equal(inverse(sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.21/0.50 166[5:Rew:153.0,146.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.21/0.50 167[5:Rew:166.0,147.0,153.0,147.0] || -> equal(sk_c5,sk_c4)**.
% 0.21/0.50 169[5:Rew:167.0,87.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.21/0.50 173[5:Rew:167.0,166.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c4)**.
% 0.21/0.50 174[6:Rew:89.0,169.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.50 183[6:Rew:174.0,162.0] || -> equal(multiply(inverse(sk_c7),u),u)**.
% 0.21/0.50 184[6:Rew:183.0,173.0,174.0,173.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.50 185[6:Rew:184.0,86.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 189[6:Rew:184.0,167.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.50 204[5:Obv:165.1] || equal(inverse(sk_c7),sk_c6)** -> .
% 0.21/0.50 210[5:Obv:159.1] || equal(inverse(sk_c7),sk_c5)** equal(sk_c6,sk_c7) -> .
% 0.21/0.50 211[6:Rew:174.0,210.1,185.0,210.0,189.0,210.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.50 212[6:Obv:211.1] || -> .
% 0.21/0.50 218[6:Spt:212.0,2.1,50.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.21/0.50 219[6:Spt:212.0,2.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.50 220[6:Rew:83.0,219.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 221[6:Rew:220.0,204.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.50 222[6:Rew:88.0,173.0,220.0,173.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.50 225[6:Rew:222.0,169.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.50 229[6:Rew:222.0,103.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.21/0.50 235[5:Rew:83.0,22.1] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.21/0.50 236[6:Rew:225.0,235.1,222.0,235.1] || -> equal(inverse(sk_c2),sk_c3)** equal(sk_c6,sk_c7).
% 0.21/0.50 237[6:MRR:236.1,221.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.50 243[5:Rew:83.0,27.1,83.0,27.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.50 244[6:Rew:225.0,243.0,222.0,243.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.50 245[6:MRR:244.0,221.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.21/0.50 246[5:Rew:83.0,17.1,83.0,17.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.21/0.50 247[6:Rew:225.0,246.0,222.0,246.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.21/0.50 248[6:MRR:247.0,221.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.21/0.50 271[6:SpR:245.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.21/0.50 275[6:SpR:248.0,77.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.21/0.50 277[6:Rew:245.0,275.0,237.0,275.0] || -> equal(sk_c3,sk_c7)**.
% 0.21/0.50 283[6:Rew:277.0,271.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.21/0.50 289[6:Rew:229.0,283.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 290[6:Rew:289.0,225.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.50 296[6:MRR:290.0,221.0] || -> .
% 0.21/0.50 299[5:Spt:296.0,3.1,47.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.21/0.50 300[5:Spt:296.0,3.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.50 301[5:Rew:81.0,299.0] || equal(sk_c8,sk_c7)** -> .
% 0.21/0.50 302[0:Rew:138.0,141.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.50 305[4:Rew:81.0,13.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c8,sk_c7).
% 0.21/0.50 306[5:MRR:305.1,301.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 307[4:Rew:81.0,28.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.21/0.50 308[5:MRR:307.0,301.0] || -> equal(multiply(sk_c3,sk_c7),sk_c8)**.
% 0.21/0.50 311[4:Rew:81.0,8.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 312[5:MRR:311.0,301.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 319[5:SpR:300.0,77.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.21/0.50 334[3:SpR:57.0,77.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.21/0.50 336[5:Rew:300.0,334.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.21/0.50 337[5:Rew:302.0,336.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.50 339[5:Rew:337.0,57.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.21/0.50 349[5:SpR:308.0,34.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c8,u))**.
% 0.21/0.50 353[2:SpR:56.0,77.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.21/0.50 355[5:Rew:300.0,353.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.21/0.50 356[5:Rew:302.0,355.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.50 362[5:Rew:356.0,68.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.21/0.50 365[5:Rew:319.0,362.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.50 376[5:SpR:312.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.21/0.50 378[5:Rew:306.0,376.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.50 379[5:Rew:339.0,378.0] || -> equal(sk_c8,identity)**.
% 0.21/0.50 380[5:Rew:379.0,300.0] || -> equal(inverse(identity),sk_c7)**.
% 0.21/0.50 381[5:Rew:379.0,301.0] || equal(identity,sk_c7)** -> .
% 0.21/0.50 383[5:Rew:379.0,81.0] || -> equal(multiply(identity,sk_c6),identity)**.
% 0.21/0.50 385[5:Rew:379.0,308.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.21/0.50 389[5:Rew:379.0,349.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.21/0.50 404[5:Rew:380.0,140.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 405[5:Rew:32.0,383.0] || -> equal(identity,sk_c6)**.
% 0.21/0.50 411[5:Rew:405.0,381.0] || equal(sk_c6,sk_c7)** -> .
% 0.21/0.50 414[5:Rew:405.0,385.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.21/0.50 431[5:Rew:404.0,389.0,365.0,389.0,405.0,389.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.21/0.50 432[5:Rew:431.0,414.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.50 434[5:MRR:432.0,411.0] || -> .
% 0.21/0.50 448[4:Spt:434.0,4.1,40.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.21/0.50 449[4:Spt:434.0,4.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.50 450[4:Rew:302.0,334.0,449.0,334.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.50 452[4:Rew:450.0,57.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.21/0.50 453[4:Rew:302.0,353.0,449.0,353.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.50 456[4:Rew:453.0,448.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.21/0.50 465[4:Rew:453.0,14.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.50 466[4:MRR:465.1,456.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 474[4:Rew:453.0,9.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 475[4:MRR:474.0,456.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 480[4:Rew:453.0,117.2,453.0,117.0,449.0,117.0] || equal(multiply(sk_c7,u),sk_c7) equal(u,sk_c8) equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c8)** -> .
% 0.21/0.50 507[4:SpR:475.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.21/0.50 509[4:Rew:452.0,507.0,466.0,507.0] || -> equal(sk_c8,identity)**.
% 0.21/0.50 510[4:Rew:509.0,449.0] || -> equal(inverse(identity),sk_c7)**.
% 0.21/0.50 514[4:Rew:509.0,452.0] || -> equal(multiply(identity,sk_c7),identity)**.
% 0.21/0.50 521[4:Rew:509.0,480.1] || equal(multiply(sk_c7,u),sk_c7) equal(u,identity) equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c8)** -> .
% 0.21/0.50 531[4:Rew:510.0,140.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 532[4:Rew:32.0,514.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 533[4:Rew:532.0,302.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 536[4:Rew:532.0,509.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 570[4:Rew:533.0,521.2,531.0,521.2,536.0,521.2,532.0,521.1,531.0,521.0] || equal(u,sk_c7)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.21/0.50 571[4:Obv:570.1] || equal(u,sk_c7)* -> .
% 0.21/0.50 572[4:UnC:571.0,453.0] || -> .
% 0.21/0.50 574[3:Spt:572.0,1.0,38.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.21/0.50 575[3:Spt:572.0,1.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.50 576[3:Rew:302.0,353.0,575.0,353.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.50 578[3:Rew:576.0,56.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.21/0.50 581[3:MRR:11.0,574.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 585[3:MRR:6.0,574.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 588[3:Rew:576.0,117.2,576.0,117.0,575.0,117.0] || equal(multiply(sk_c7,u),sk_c7) equal(u,sk_c8) equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c8)** -> .
% 0.21/0.50 615[3:SpR:585.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.21/0.50 617[3:Rew:578.0,615.0,581.0,615.0] || -> equal(sk_c8,identity)**.
% 0.21/0.50 618[3:Rew:617.0,575.0] || -> equal(inverse(identity),sk_c7)**.
% 0.21/0.50 622[3:Rew:617.0,578.0] || -> equal(multiply(identity,sk_c7),identity)**.
% 0.21/0.50 629[3:Rew:617.0,588.1] || equal(multiply(sk_c7,u),sk_c7) equal(u,identity) equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c8)** -> .
% 0.21/0.50 639[3:Rew:618.0,140.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 640[3:Rew:32.0,622.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 642[3:Rew:640.0,302.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 644[3:Rew:640.0,617.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 678[3:Rew:642.0,629.2,639.0,629.2,644.0,629.2,640.0,629.1,639.0,629.0] || equal(u,sk_c7)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.21/0.50 679[3:Obv:678.1] || equal(u,sk_c7)* -> .
% 0.21/0.50 680[3:UnC:679.0,576.0] || -> .
% 0.21/0.50 682[2:Spt:680.0,5.0,36.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.50 683[2:Spt:680.0,5.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.50 684[2:MRR:25.0,682.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.50 685[2:MRR:15.0,682.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 687[2:MRR:20.0,682.0] || -> equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.21/0.50 688[2:MRR:10.0,682.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 699[2:SpR:687.0,77.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c3)**.
% 0.21/0.50 701[2:Rew:684.0,699.0] || -> equal(multiply(sk_c3,sk_c8),sk_c3)**.
% 0.21/0.50 703[2:SpR:688.0,77.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c8)**.
% 0.21/0.50 705[2:Rew:685.0,703.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.21/0.50 707[2:SpR:701.0,77.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c8)**.
% 0.21/0.50 709[2:Rew:33.0,707.0] || -> equal(sk_c8,identity)**.
% 0.21/0.50 710[2:Rew:709.0,683.0] || -> equal(inverse(identity),sk_c7)**.
% 0.21/0.50 717[2:Rew:709.0,46.1] || equal(inverse(identity),u) equal(u,identity) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.21/0.50 727[2:Rew:709.0,705.0] || -> equal(multiply(identity,sk_c7),identity)**.
% 0.21/0.50 731[2:Rew:32.0,727.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 732[2:Rew:731.0,302.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 735[2:Rew:731.0,709.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 736[2:Rew:731.0,710.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 754[2:Rew:732.0,717.2,735.0,717.2,731.0,717.1,736.0,717.0,731.0,717.0] || equal(sk_c7,u)* equal(u,sk_c7)* equal(u,sk_c7)* -> .
% 0.21/0.50 755[2:Obv:754.1] || equal(u,sk_c7)* -> .
% 0.21/0.50 756[2:UnC:755.0,77.0] || -> .
% 0.21/0.50 761[1:Spt:756.0,31.1,31.2,31.3,31.4,31.6,31.7,31.9,31.10] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),x)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c7)** -> .
% 0.21/0.50 762[1:EqR:761.4] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.21/0.50 764[2:Spt:1.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.21/0.50 767[2:Rew:764.0,762.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(sk_c7,sk_c7) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.21/0.50 768[2:Obv:767.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.21/0.50 773[3:Spt:25.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.50 776[4:Spt:21.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.21/0.50 791[0:SpR:140.0,302.0] || -> equal(inverse(identity),identity)**.
% 0.21/0.50 801[0:SpR:33.0,77.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.50 804[2:SpR:764.0,33.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.21/0.50 805[3:SpR:773.0,33.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.21/0.50 806[4:SpR:776.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.21/0.50 808[0:Rew:302.0,801.0] || -> equal(inverse(inverse(u)),u)**.
% 0.21/0.50 811[5:Spt:22.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.50 813[5:SpR:811.0,33.0] || -> equal(multiply(sk_c3,sk_c2),identity)**.
% 0.21/0.50 816[2:SpR:804.0,77.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c8)**.
% 0.21/0.50 818[2:Rew:302.0,816.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.21/0.50 821[2:SpR:818.0,33.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.21/0.50 824[3:SpR:805.0,77.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.21/0.50 826[3:Rew:302.0,824.0,764.0,824.0] || -> equal(sk_c5,sk_c7)**.
% 0.21/0.50 829[3:Rew:826.0,9.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 832[3:Rew:826.0,14.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.50 836[3:Rew:804.0,832.1] || -> equal(inverse(sk_c1),sk_c8)** equal(identity,sk_c6).
% 0.21/0.50 837[3:Rew:804.0,829.0] || -> equal(identity,sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 841[6:Spt:836.1] || -> equal(identity,sk_c6)**.
% 0.21/0.50 842[6:Rew:841.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.50 843[6:Rew:841.0,302.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.50 844[6:Rew:841.0,791.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.50 845[6:Rew:841.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.21/0.50 846[6:Rew:841.0,804.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.50 847[6:Rew:841.0,806.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.21/0.50 848[6:Rew:841.0,813.0] || -> equal(multiply(sk_c3,sk_c2),sk_c6)**.
% 0.21/0.50 851[6:Rew:843.0,18.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.21/0.50 856[6:Rew:851.0,17.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.21/0.50 868[6:SpR:847.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c4)**.
% 0.21/0.50 870[6:Rew:764.0,868.0] || -> equal(multiply(sk_c7,sk_c6),sk_c4)**.
% 0.21/0.50 871[6:Rew:843.0,870.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.50 876[6:Rew:871.0,856.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c8)**.
% 0.21/0.50 886[6:SpR:848.0,77.0] || -> equal(multiply(inverse(sk_c3),sk_c6),sk_c2)**.
% 0.21/0.50 888[6:Rew:843.0,886.0] || -> equal(inverse(sk_c3),sk_c2)**.
% 0.21/0.50 897[0:SpR:808.0,77.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.21/0.50 912[6:SpR:888.0,845.0] || -> equal(multiply(sk_c2,sk_c3),sk_c6)**.
% 0.21/0.50 914[6:Rew:912.0,876.1] || -> equal(multiply(sk_c7,sk_c7),sk_c7)** equal(sk_c8,sk_c6).
% 0.21/0.50 915[6:Rew:912.0,851.1] || -> equal(sk_c8,sk_c7) equal(sk_c8,sk_c6)**.
% 0.21/0.50 943[7:Spt:915.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 944[7:Rew:943.0,764.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 946[7:Rew:943.0,846.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.50 949[7:Rew:943.0,768.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.21/0.50 953[7:Rew:943.0,914.1] || -> equal(multiply(sk_c7,sk_c7),sk_c7)** equal(sk_c6,sk_c7).
% 0.21/0.50 956[7:Rew:946.0,953.0] || -> equal(sk_c6,sk_c7)** equal(sk_c6,sk_c7)**.
% 0.21/0.50 957[7:Obv:956.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.50 960[7:Rew:957.0,842.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 964[7:Rew:957.0,843.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 968[7:Rew:964.0,949.5,960.0,949.5,943.0,949.5,964.0,949.4,943.0,949.4,964.0,949.3,943.0,949.3,943.0,949.2,943.0,949.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(v,sk_c7) equal(w,sk_c7) equal(u,sk_c7) -> .
% 0.21/0.50 969[7:Con:968.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.50 1045[7:SpL:944.0,969.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.50 1046[7:Obv:1045.1] || -> .
% 0.21/0.50 1047[7:Spt:1046.0,915.0,943.0] || equal(sk_c8,sk_c7)** -> .
% 0.21/0.50 1048[7:Spt:1046.0,915.1] || -> equal(sk_c8,sk_c6)**.
% 0.21/0.50 1050[7:Rew:1048.0,764.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.21/0.50 1051[7:Rew:1050.0,844.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.50 1053[7:Rew:1051.0,1048.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 1056[7:Rew:1053.0,1047.0] || equal(sk_c7,sk_c7)* -> .
% 0.21/0.50 1057[7:Obv:1056.0] || -> .
% 0.21/0.50 1074[6:Spt:1057.0,836.1,841.0] || equal(identity,sk_c6)** -> .
% 0.21/0.50 1075[6:Spt:1057.0,836.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 1076[6:MRR:837.0,1074.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 1081[6:SpR:1075.0,808.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.21/0.50 1083[6:Rew:764.0,1081.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.50 1085[6:Rew:1083.0,1076.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.21/0.50 1086[6:Rew:804.0,1085.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 1087[6:Rew:1086.0,791.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 1090[6:Rew:1086.0,302.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 1091[6:Rew:1086.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 1096[6:Rew:818.0,1087.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 1097[6:Rew:1096.0,818.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 1106[6:Rew:1096.0,768.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.21/0.50 1127[6:Rew:1090.0,1106.5,1091.0,1106.5,1096.0,1106.5,1090.0,1106.4,1096.0,1106.4,1090.0,1106.3,1096.0,1106.3,1096.0,1106.2,1096.0,1106.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(v,sk_c7) equal(w,sk_c7) equal(u,sk_c7) -> .
% 0.21/0.50 1128[6:Con:1127.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.50 1188[6:SpL:1097.0,1128.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.50 1189[6:Obv:1188.1] || -> .
% 0.21/0.50 1190[5:Spt:1189.0,22.0,811.0] || equal(inverse(sk_c2),sk_c3)** -> .
% 0.21/0.50 1191[5:Spt:1189.0,22.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.21/0.50 1192[3:Rew:826.0,24.1] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.21/0.50 1193[3:Rew:804.0,1192.1] || -> equal(inverse(sk_c2),sk_c3)** equal(identity,sk_c6).
% 0.21/0.50 1194[5:MRR:1193.0,1190.0] || -> equal(identity,sk_c6)**.
% 0.21/0.50 1197[5:Rew:1194.0,821.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.21/0.50 1198[5:Rew:1194.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.50 1199[5:Rew:1194.0,302.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.50 1203[5:Rew:1199.0,23.1] || -> equal(inverse(sk_c2),sk_c3)** equal(sk_c8,sk_c7).
% 0.21/0.50 1204[5:MRR:1203.0,1190.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 1205[5:Rew:1204.0,776.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.21/0.50 1206[5:Rew:1204.0,764.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 1208[5:Rew:1204.0,1191.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.21/0.50 1213[5:Rew:1204.0,1197.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.21/0.50 1221[5:Rew:1204.0,768.5,1204.0,768.4,1204.0,768.3,1204.0,768.2,1204.0,768.1,1204.0,768.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c7)** -> .
% 0.21/0.50 1222[5:Con:1221.2] || 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)** -> .
% 0.21/0.50 1236[5:SpR:1205.0,808.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.21/0.50 1239[5:Rew:1206.0,1236.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.50 1241[5:Rew:1239.0,1208.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.21/0.50 1244[5:Rew:1213.0,1241.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.50 1247[5:Rew:1244.0,1198.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 1248[5:Rew:1244.0,1199.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 1255[5:Rew:1247.0,1222.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.21/0.50 1259[5:Con:1255.0] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.21/0.50 1260[5:Rew:1248.0,1259.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.50 1306[5:SpL:1206.0,1260.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.50 1307[5:Obv:1306.1] || -> .
% 0.21/0.50 1308[4:Spt:1307.0,21.0,776.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.21/0.50 1309[4:Spt:1307.0,21.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.50 1310[4:MRR:11.0,1308.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 1313[4:MRR:6.0,1308.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 1325[4:SpR:1310.0,808.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.21/0.50 1328[4:Rew:764.0,1325.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.50 1330[4:Rew:1328.0,1313.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.21/0.50 1331[4:Rew:804.0,1330.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 1332[4:Rew:1331.0,791.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 1334[4:Rew:1331.0,302.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 1335[4:Rew:1331.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 1338[4:Rew:818.0,1332.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 1339[4:Rew:1338.0,818.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 1347[4:Rew:1338.0,768.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.21/0.50 1365[4:Rew:1334.0,1347.5,1335.0,1347.5,1338.0,1347.5,1334.0,1347.4,1338.0,1347.4,1334.0,1347.3,1338.0,1347.3,1338.0,1347.2,1338.0,1347.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(v,sk_c7) equal(w,sk_c7) equal(u,sk_c7) -> .
% 0.21/0.50 1366[4:Con:1365.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.50 1416[4:SpL:1339.0,1366.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.50 1417[4:Obv:1416.1] || -> .
% 0.21/0.50 1418[3:Spt:1417.0,25.0,773.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.21/0.50 1419[3:Spt:1417.0,25.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.21/0.50 1420[3:MRR:15.0,1418.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.21/0.50 1423[3:MRR:10.0,1418.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.21/0.50 1439[3:SpR:1420.0,808.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.21/0.50 1442[3:Rew:764.0,1439.0] || -> equal(sk_c1,sk_c7)**.
% 0.21/0.50 1444[3:Rew:1442.0,1423.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.21/0.50 1445[3:Rew:804.0,1444.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 1446[3:Rew:1445.0,791.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 1448[3:Rew:1445.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 1449[3:Rew:1445.0,302.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.21/0.50 1452[3:Rew:818.0,1446.0] || -> equal(sk_c8,sk_c7)**.
% 0.21/0.50 1453[3:Rew:1452.0,764.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 1461[3:Rew:1452.0,768.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c7)** -> .
% 0.21/0.50 1479[3:Rew:1449.0,1461.5,1448.0,1461.5,1452.0,1461.5,1449.0,1461.4,1452.0,1461.4,1449.0,1461.3,1452.0,1461.3,1452.0,1461.2,1452.0,1461.1] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(v,sk_c7) equal(w,sk_c7) equal(u,sk_c7) -> .
% 0.21/0.50 1480[3:Con:1479.0] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.21/0.50 1530[3:SpL:1453.0,1480.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.21/0.50 1531[3:Obv:1530.1] || -> .
% 0.21/0.50 1532[2:Spt:1531.0,1.1,764.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.21/0.50 1533[2:Spt:1531.0,1.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.21/0.50 1534[2:MRR:5.1,1532.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.21/0.50 1535[2:MRR:2.0,1532.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.21/0.50 1536[2:MRR:3.0,1532.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.21/0.50 1537[2:MRR:4.0,1532.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.21/0.50 1539[2:SpR:1533.0,808.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.21/0.50 1540[2:SpR:1533.0,897.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.21/0.50 1542[2:Rew:1539.0,1532.0] || equal(sk_c4,sk_c7)** -> .
% 0.21/0.50 1550[2:SpR:1534.0,808.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.21/0.50 1553[2:Rew:1539.0,1550.0] || -> equal(sk_c5,sk_c4)**.
% 0.21/0.50 1555[2:Rew:1553.0,1537.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.21/0.50 1568[2:SpR:1536.0,77.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.21/0.50 1570[2:Rew:1535.0,1568.0,1539.0,1568.0] || -> equal(sk_c8,sk_c6)**.
% 0.21/0.50 1571[2:Rew:1570.0,1533.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.50 1572[2:Rew:1570.0,1539.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.21/0.50 1574[2:Rew:1570.0,1536.0] || -> equal(multiply(sk_c6,sk_c6),sk_c7)**.
% 0.21/0.50 1576[2:Rew:1570.0,1540.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.21/0.50 1578[2:Rew:1570.0,1555.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.21/0.50 1598[2:SpR:1578.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c6,u))**.
% 0.21/0.50 1599[2:SpR:1578.0,77.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c6)**.
% 0.21/0.50 1601[2:Rew:1574.0,1599.0,1571.0,1599.0] || -> equal(sk_c6,sk_c7)**.
% 0.21/0.50 1605[2:Rew:1601.0,1572.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.21/0.50 1609[2:Rew:1601.0,1576.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.21/0.50 1612[2:Rew:1609.0,1598.0,1601.0,1598.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.21/0.50 1646[2:SpR:1612.0,302.0] || -> equal(identity,sk_c7)**.
% 0.21/0.50 1648[2:Rew:1646.0,791.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.21/0.50 1653[2:Rew:1605.0,1648.0] || -> equal(sk_c4,sk_c7)**.
% 0.21/0.50 1654[2:MRR:1653.0,1542.0] || -> .
% 0.21/0.50 % SZS output end Refutation
% 0.21/0.50 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_8 prove_this_9 prove_this_10 prove_this_11 prove_this_13 prove_this_14 prove_this_15 prove_this_17 prove_this_18 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_27 prove_this_28 prove_this_31 left_identity left_inverse associativity
% 0.21/0.50
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