TSTP Solution File: GRP274-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP274-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:46:38 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP274-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 04:22:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 843 clauses, backtracked 350 clauses, performed 11 splits and kept 689 clauses.
% 0.19/0.47 SPASS allocated 63641 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.01 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 5, length 342 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 6[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.19/0.47 8[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6)** equal(inverse(sk_c1),sk_c7).
% 0.19/0.47 10[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 11[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.47 12[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 13[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.47 14[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 15[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c5),sk_c6).
% 0.19/0.47 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 18[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 21[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 23[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 25[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 26[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) -> .
% 0.19/0.47 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 30[1:Spt:26.3,26.7] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.19/0.47 31[2:Spt:11.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 33[2:SpL:31.0,30.1] || equal(inverse(sk_c6),sk_c7)** equal(sk_c5,sk_c6) -> .
% 0.19/0.47 34[3:Spt:14.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.47 36[4:Spt:12.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 40[5:Spt:15.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 42[6:Spt:13.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 45[3:SpR:34.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.47 46[4:SpR:36.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.47 47[1:SpL:28.0,30.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,sk_c6) -> .
% 0.19/0.47 54[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 57[3:SpR:45.0,29.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.47 58[4:SpR:46.0,29.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.19/0.47 60[3:Rew:27.0,57.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.47 61[4:Rew:27.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.47 62[0:Rew:27.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 66[5:SpR:40.0,60.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.47 72[6:SpR:42.0,61.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 76[6:SpL:72.0,30.1] || equal(inverse(sk_c7),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 77[6:Obv:76.1] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.47 79[0:SpR:62.0,62.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 81[2:SpR:31.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.47 83[0:SpR:28.0,62.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 86[3:SpR:45.0,62.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.47 88[5:SpR:66.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.47 89[4:SpR:46.0,62.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.47 91[6:SpR:72.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.19/0.47 97[5:Rew:81.0,88.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 99[5:Rew:97.0,31.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 100[5:Rew:97.0,34.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.47 103[5:Rew:97.0,45.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.47 121[6:Rew:97.0,91.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.47 122[6:Rew:28.0,121.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 123[6:Rew:122.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 127[6:Rew:122.0,103.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.19/0.47 134[6:Rew:123.0,127.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 135[6:Rew:134.0,100.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 137[6:MRR:135.0,77.0] || -> .
% 0.19/0.47 160[6:Spt:137.0,13.0,42.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.47 161[6:Spt:137.0,13.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 162[6:Rew:97.0,161.0] || -> equal(multiply(sk_c7,sk_c5),sk_c7)**.
% 0.19/0.47 167[6:Rew:97.0,160.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.19/0.47 168[0:Rew:79.0,83.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 169[4:Rew:168.0,89.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.47 177[5:Rew:97.0,8.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 178[6:MRR:177.1,167.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 184[5:Rew:97.0,3.1,97.0,3.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c7).
% 0.19/0.47 185[6:MRR:184.0,167.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 212[6:SpR:162.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c5)**.
% 0.19/0.47 214[6:Rew:169.0,212.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.47 215[6:Rew:214.0,167.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.47 221[6:SpR:185.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 223[6:Rew:99.0,221.0,178.0,221.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 224[6:MRR:223.0,215.0] || -> .
% 0.19/0.47 225[5:Spt:224.0,15.0,40.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.47 226[5:Spt:224.0,15.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 227[3:Rew:168.0,86.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.47 228[3:Rew:227.0,81.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.47 229[5:Rew:228.0,225.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.47 231[3:Rew:228.0,25.1] || -> equal(inverse(sk_c2),sk_c5)** equal(sk_c6,sk_c7).
% 0.19/0.47 232[5:MRR:231.1,229.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 233[3:Rew:228.0,10.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 234[5:MRR:233.1,229.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 235[3:Rew:227.0,33.0] || equal(sk_c4,sk_c7)** equal(sk_c5,sk_c6) -> .
% 0.19/0.47 236[3:Rew:228.0,20.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 237[5:MRR:236.0,229.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 238[3:Rew:228.0,5.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 239[5:MRR:238.0,229.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 268[5:SpR:237.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c5)**.
% 0.19/0.47 270[5:Rew:232.0,268.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.19/0.47 280[5:SpR:270.0,62.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.19/0.47 282[5:Rew:28.0,280.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 286[5:Rew:282.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 289[5:Rew:282.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 290[5:Rew:286.0,226.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 308[5:Rew:290.0,235.1] || equal(sk_c4,sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 313[5:Rew:289.0,239.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 317[5:Rew:313.0,227.0] || -> equal(inverse(sk_c1),sk_c4)**.
% 0.19/0.47 324[5:Rew:234.0,317.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 346[5:Obv:308.1] || equal(sk_c4,sk_c7)** -> .
% 0.19/0.47 347[5:Rew:324.0,346.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 348[5:Obv:347.0] || -> .
% 0.19/0.47 353[4:Spt:348.0,12.0,36.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.47 354[4:Spt:348.0,12.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 355[4:MRR:22.0,353.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 356[4:MRR:7.0,353.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 357[4:MRR:17.0,353.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 358[4:MRR:2.0,353.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 384[4:SpR:357.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c5)**.
% 0.19/0.47 386[4:Rew:355.0,384.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.19/0.47 388[4:SpR:358.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 390[4:Rew:356.0,388.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 392[4:SpR:386.0,62.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.19/0.47 394[4:Rew:28.0,392.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 396[4:Rew:394.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 397[4:Rew:394.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 401[4:Rew:394.0,47.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.47 402[4:Rew:396.0,358.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 416[4:Rew:402.0,390.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.19/0.47 429[4:Rew:397.0,416.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 430[4:Rew:429.0,356.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 459[4:Rew:402.0,401.1,429.0,401.1,430.0,401.0,430.0,401.0,429.0,401.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 460[4:Obv:459.1] || -> .
% 0.19/0.47 462[3:Spt:460.0,14.0,34.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.47 463[3:Spt:460.0,14.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 464[3:MRR:24.0,462.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 465[3:MRR:9.0,462.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 466[3:MRR:19.0,462.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 467[3:MRR:4.0,462.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 479[3:SpR:466.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c5)**.
% 0.19/0.47 481[3:Rew:464.0,479.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.19/0.47 483[3:SpR:467.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 485[3:Rew:465.0,483.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 487[3:SpR:481.0,62.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.19/0.47 489[3:Rew:28.0,487.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 490[3:Rew:489.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 491[3:Rew:489.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 495[3:Rew:489.0,47.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.47 496[3:Rew:490.0,463.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 497[3:Rew:490.0,485.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 503[3:Rew:496.0,464.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 505[3:Rew:496.0,466.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.47 516[3:Rew:497.0,503.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.47 517[3:Rew:491.0,505.0,497.0,505.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.47 518[3:Rew:517.0,516.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 532[3:Rew:497.0,495.1,518.0,495.0,518.0,495.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 533[3:Obv:532.1] || -> .
% 0.19/0.47 536[2:Spt:533.0,11.0,31.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.47 537[2:Spt:533.0,11.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 538[2:MRR:21.1,536.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 539[2:MRR:6.1,536.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 540[2:MRR:16.0,536.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 541[2:MRR:1.0,536.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 550[2:SpR:540.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c5)**.
% 0.19/0.47 552[2:Rew:538.0,550.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.19/0.47 554[2:SpR:541.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 556[2:Rew:539.0,554.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 558[2:SpR:552.0,62.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.19/0.47 560[2:Rew:28.0,558.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 561[2:Rew:560.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 562[2:Rew:560.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 566[2:Rew:560.0,47.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.47 567[2:Rew:561.0,541.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 575[2:Rew:567.0,556.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.19/0.47 581[2:Rew:562.0,575.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 582[2:Rew:581.0,539.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 601[2:Rew:567.0,566.1,581.0,566.1,582.0,566.0,582.0,566.0,581.0,566.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 602[2:Obv:601.1] || -> .
% 0.19/0.47 604[1:Spt:602.0,26.0,26.1,26.2,26.4,26.5,26.6,26.8,26.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c7,sk_c5),sk_c6) -> .
% 0.19/0.47 606[2:Spt:11.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 607[2:Rew:606.0,604.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(sk_c5,sk_c5) equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.47 609[2:Obv:607.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.47 612[2:SpR:606.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.47 614[3:Spt:12.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 616[3:Rew:614.0,609.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 617[3:Obv:616.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.19/0.47 620[3:SpR:614.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.47 622[4:Spt:24.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.47 628[5:Spt:22.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 643[0:SpR:28.0,62.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 644[0:SpR:28.0,168.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.47 646[4:SpR:622.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.47 647[5:SpR:628.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.47 649[0:Rew:168.0,643.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.47 657[4:SpR:646.0,62.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.47 659[4:Rew:168.0,657.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.47 660[4:Rew:659.0,612.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.47 662[4:Rew:660.0,5.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 663[4:Rew:660.0,20.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 664[4:Rew:660.0,10.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 665[4:Rew:660.0,25.1] || -> equal(inverse(sk_c2),sk_c5)** equal(sk_c6,sk_c7).
% 0.19/0.47 667[4:Rew:665.1,23.1] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 669[4:Rew:663.0,18.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 672[4:SpR:659.0,28.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.19/0.47 675[5:SpR:647.0,62.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.47 677[5:Rew:168.0,675.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.47 678[5:Rew:677.0,620.0] || -> equal(multiply(sk_c3,sk_c6),sk_c5)**.
% 0.19/0.47 680[6:Spt:664.1] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 685[6:Rew:680.0,659.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.47 687[6:Rew:680.0,617.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.19/0.47 693[6:Rew:680.0,672.0] || -> equal(multiply(sk_c4,sk_c7),identity)**.
% 0.19/0.47 694[6:Rew:680.0,678.0] || -> equal(multiply(sk_c3,sk_c7),sk_c5)**.
% 0.19/0.47 695[6:Rew:677.0,685.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.47 696[6:Rew:695.0,660.0] || -> equal(multiply(sk_c3,sk_c5),sk_c7)**.
% 0.19/0.47 700[6:Rew:695.0,693.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.19/0.47 701[6:Rew:700.0,669.0] || -> equal(identity,sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 702[6:Rew:700.0,667.1] || -> equal(inverse(sk_c2),sk_c5)** equal(identity,sk_c7).
% 0.19/0.47 704[6:Rew:700.0,694.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 706[6:Rew:704.0,168.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 711[6:Rew:706.0,696.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 712[6:Rew:711.0,628.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 720[6:Rew:704.0,702.1] || -> equal(inverse(sk_c2),sk_c5)** equal(sk_c5,sk_c7).
% 0.19/0.47 722[6:Rew:706.0,701.1,704.0,701.0] || -> equal(sk_c5,sk_c7) equal(sk_c2,sk_c7)**.
% 0.19/0.47 723[6:Rew:722.1,720.0] || -> equal(inverse(sk_c7),sk_c5)** equal(sk_c5,sk_c7).
% 0.19/0.47 724[6:Rew:712.0,723.0] || -> equal(sk_c5,sk_c7)** equal(sk_c5,sk_c7)**.
% 0.19/0.47 725[6:Obv:724.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 730[6:Rew:725.0,706.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 737[6:Rew:730.0,687.5,725.0,687.5,730.0,687.4,680.0,687.4,730.0,687.3,725.0,687.3,680.0,687.3,725.0,687.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.19/0.47 738[6:Con:737.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 753[0:SpR:649.0,62.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.47 772[6:SpL:712.0,738.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 774[6:Obv:772.1] || -> .
% 0.19/0.47 775[6:Spt:774.0,664.1,680.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.47 776[6:Spt:774.0,664.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 777[6:MRR:665.1,775.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 778[6:MRR:662.0,775.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 779[6:MRR:663.0,775.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 781[6:SpR:776.0,649.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 783[6:Rew:677.0,781.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.47 785[6:Rew:783.0,677.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 801[6:SpR:777.0,649.0] || -> equal(inverse(sk_c5),sk_c2)**.
% 0.19/0.47 803[6:SpR:785.0,62.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),u)**.
% 0.19/0.47 814[6:SpR:778.0,29.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.47 818[6:Rew:803.0,814.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.47 824[6:Rew:818.0,606.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 832[6:Rew:824.0,801.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.47 835[6:Rew:824.0,779.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.47 846[6:Rew:785.0,832.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.47 855[6:Rew:846.0,835.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 856[6:Rew:778.0,855.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 857[6:MRR:856.0,775.0] || -> .
% 0.19/0.47 876[5:Spt:857.0,22.0,628.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.47 877[5:Spt:857.0,22.1] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 878[5:MRR:7.0,876.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 879[5:MRR:17.0,876.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 880[5:MRR:2.0,876.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 882[5:SpR:877.0,649.0] || -> equal(inverse(sk_c5),sk_c2)**.
% 0.19/0.47 895[5:SpR:878.0,649.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 898[5:SpR:882.0,62.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),u)**.
% 0.19/0.47 901[5:SpR:895.0,62.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),u)**.
% 0.19/0.47 913[5:SpR:879.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 917[5:Rew:898.0,913.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 918[5:Rew:917.0,614.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 921[5:Rew:917.0,901.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.47 930[5:Rew:918.0,617.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.19/0.47 937[5:Rew:921.0,880.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 939[5:Rew:937.0,659.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.47 940[5:Rew:937.0,646.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.47 944[5:Rew:937.0,918.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 945[5:Rew:895.0,939.0] || -> equal(sk_c4,sk_c1)**.
% 0.19/0.47 952[5:Rew:917.0,940.0,945.0,940.0] || -> equal(identity,sk_c1)**.
% 0.19/0.47 953[5:Rew:952.0,644.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 955[5:Rew:952.0,168.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.47 957[5:Rew:878.0,953.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 958[5:Rew:957.0,878.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 962[5:Rew:957.0,937.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 963[5:Rew:957.0,944.0] || -> equal(sk_c5,sk_c1)**.
% 0.19/0.47 972[5:Rew:955.0,930.5,963.0,930.5,957.0,930.5,955.0,930.4,962.0,930.4,957.0,930.4,955.0,930.3,963.0,930.3,962.0,930.3,962.0,930.2,957.0,930.1,962.0,930.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) -> .
% 0.19/0.47 973[5:Con:972.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.47 1031[5:SpL:958.0,973.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 1032[5:Obv:1031.1] || -> .
% 0.19/0.47 1033[4:Spt:1032.0,24.0,622.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.47 1034[4:Spt:1032.0,24.1] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 1035[4:MRR:9.0,1033.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 1036[4:MRR:19.0,1033.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 1037[4:MRR:4.0,1033.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 1040[4:SpR:1034.0,753.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),u)**.
% 0.19/0.47 1042[4:SpR:1035.0,62.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.47 1043[4:SpR:1035.0,649.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 1068[4:SpR:1036.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 1072[4:Rew:1040.0,1068.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 1073[4:Rew:1072.0,614.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 1074[4:Rew:1072.0,1042.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.47 1083[4:Rew:1073.0,612.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.47 1085[4:Rew:1073.0,617.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** -> .
% 0.19/0.47 1090[4:Rew:1074.0,1037.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1092[4:Rew:1090.0,1073.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 1100[4:Rew:28.0,1083.0,1090.0,1083.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 1101[4:Rew:1100.0,644.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 1102[4:Rew:1100.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 1105[4:Rew:1043.0,1101.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 1106[4:Rew:1105.0,1035.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 1109[4:Rew:1105.0,1090.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 1110[4:Rew:1105.0,1092.0] || -> equal(sk_c5,sk_c1)**.
% 0.19/0.47 1113[4:Rew:1105.0,1102.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.47 1121[4:Rew:1113.0,1085.5,1110.0,1085.5,1105.0,1085.5,1113.0,1085.4,1109.0,1085.4,1105.0,1085.4,1113.0,1085.3,1110.0,1085.3,1109.0,1085.3,1109.0,1085.2,1105.0,1085.1,1109.0,1085.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) -> .
% 0.19/0.47 1122[4:Con:1121.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.47 1170[4:SpL:1106.0,1122.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 1171[4:Obv:1170.1] || -> .
% 0.19/0.47 1172[3:Spt:1171.0,12.1,614.0] || equal(multiply(sk_c7,sk_c5),sk_c6)** -> .
% 0.19/0.47 1173[3:Spt:1171.0,12.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 1174[3:MRR:14.1,1172.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.47 1175[3:MRR:13.1,1172.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 1176[3:MRR:15.1,1172.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 1182[3:SpR:1174.0,649.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.47 1185[3:Rew:1182.0,612.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.47 1187[3:Rew:1176.0,1185.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1189[3:Rew:1187.0,606.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 1190[3:Rew:1187.0,1172.0] || equal(multiply(sk_c7,sk_c5),sk_c7)** -> .
% 0.19/0.47 1192[3:Rew:1187.0,1175.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 1214[3:SpR:1192.0,62.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.19/0.47 1216[3:Rew:1173.0,1214.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 1217[3:Rew:1189.0,1216.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 1218[3:Rew:1217.0,1189.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 1220[3:Rew:1217.0,1190.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.19/0.47 1223[3:Rew:1218.0,1220.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 1224[3:Obv:1223.0] || -> .
% 0.19/0.47 1228[2:Spt:1224.0,11.0,606.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.47 1229[2:Spt:1224.0,11.1] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.47 1230[2:MRR:21.1,1228.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.47 1231[2:MRR:6.1,1228.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 1232[2:MRR:16.0,1228.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.47 1233[2:MRR:1.0,1228.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 1239[2:SpR:1230.0,753.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),u)**.
% 0.19/0.47 1241[2:SpR:1231.0,62.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.47 1254[2:SpR:1232.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 1258[2:Rew:1239.0,1254.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 1259[2:Rew:1258.0,1229.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.47 1260[2:Rew:1258.0,1241.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.47 1266[2:Rew:1259.0,1228.0] || equal(multiply(sk_c6,sk_c7),sk_c6)** -> .
% 0.19/0.47 1271[2:Rew:1260.0,1233.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1279[2:Rew:1258.0,1266.0,1271.0,1266.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 1280[2:Obv:1279.0] || -> .
% 0.19/0.47 % SZS output end Refutation
% 0.19/0.47 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 left_identity left_inverse associativity
% 0.19/0.47
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