TSTP Solution File: GRP343-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP343-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:46:56 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP343-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 : Tue Jun 14 04:28:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 1105 clauses, backtracked 416 clauses, performed 10 splits and kept 775 clauses.
% 0.19/0.51 SPASS allocated 63836 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.04 for the input.
% 0.19/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.08 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 5, length 372 :
% 0.19/0.51 % SZS output start Refutation
% 0.19/0.51 1[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.51 2[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.51 3[0:Inp] || -> equal(inverse(sk_c3),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.19/0.51 4[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.51 5[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.51 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c9).
% 0.19/0.51 7[0:Inp] || -> equal(inverse(sk_c6),sk_c5)** equal(inverse(sk_c1),sk_c9).
% 0.19/0.51 8[0:Inp] || -> equal(inverse(sk_c5),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.19/0.51 9[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c5)**.
% 0.19/0.51 12[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.51 13[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c8),sk_c9).
% 0.19/0.51 14[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.51 15[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.51 16[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.51 17[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c5)** equal(multiply(sk_c1,sk_c8),sk_c9).
% 0.19/0.51 18[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.51 19[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.51 20[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.51 21[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.51 22[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.51 23[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.51 24[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.51 25[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c6,sk_c9),sk_c5)**.
% 0.19/0.51 26[0:Inp] || -> equal(multiply(sk_c3,sk_c9),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 27[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 28[0:Inp] || -> equal(multiply(sk_c9,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 29[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 30[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 31[0:Inp] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 32[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 33[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c5) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 34[0:Inp] || equal(multiply(sk_c8,sk_c9),sk_c7) equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(inverse(w),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c9)** equal(inverse(x),sk_c8) equal(inverse(y),z) equal(inverse(z),sk_c9)** equal(multiply(y,sk_c9),z)* -> .
% 0.19/0.51 35[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.51 36[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.51 37[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.51 38[0:Rew:1.0,34.0] || equal(sk_c7,sk_c7) equal(inverse(u),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(inverse(v),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c9),sk_c8)** equal(inverse(w),sk_c9) equal(multiply(sk_c9,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c9)** equal(inverse(x),sk_c8) equal(inverse(y),z) equal(inverse(z),sk_c9)** equal(multiply(y,sk_c9),z)* -> .
% 0.19/0.51 39[0:Obv:38.0] || equal(inverse(u),v) equal(inverse(v),sk_c9)** equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(inverse(y),sk_c8) equal(inverse(z),sk_c9) equal(multiply(u,sk_c9),v)*+ equal(multiply(w,sk_c8),sk_c9)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(y,sk_c7),sk_c8)** equal(multiply(z,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.19/0.51 40[1:Spt:39.0,39.1,39.6] || equal(inverse(u),v) equal(inverse(v),sk_c9)** equal(multiply(u,sk_c9),v)*+ -> .
% 0.19/0.51 42[2:Spt:20.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.51 44[3:Spt:4.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.51 46[4:Spt:28.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 48[5:Spt:12.1] || -> equal(multiply(sk_c1,sk_c8),sk_c9)**.
% 0.19/0.51 51[1:SpL:1.0,40.2] || equal(inverse(sk_c8),u)* equal(inverse(u),sk_c9)** equal(sk_c7,u) -> .
% 0.19/0.51 53[1:SpL:35.0,40.2] || equal(inverse(identity),u)* equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.19/0.51 55[2:SpR:42.0,36.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.19/0.51 56[3:SpR:44.0,36.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.51 65[0:SpR:36.0,37.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.51 66[2:SpR:55.0,37.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.51 68[2:Rew:35.0,66.0] || -> equal(multiply(sk_c8,multiply(sk_c2,u)),u)**.
% 0.19/0.51 69[0:Rew:35.0,65.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.51 71[3:SpR:56.0,37.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.51 73[3:Rew:35.0,71.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.19/0.51 76[4:SpR:46.0,68.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.51 82[5:SpR:48.0,73.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 85[0:SpR:69.0,69.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.51 87[0:SpR:1.0,69.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.19/0.51 91[0:SpR:36.0,69.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.51 92[2:SpR:55.0,69.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.19/0.51 93[2:SpR:68.0,69.0] || -> equal(multiply(inverse(sk_c8),u),multiply(sk_c2,u))**.
% 0.19/0.51 94[4:SpR:76.0,69.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.51 96[3:SpR:56.0,69.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c1)**.
% 0.19/0.51 102[4:Rew:87.0,94.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.51 104[4:Rew:102.0,44.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.51 107[4:Rew:102.0,56.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.19/0.51 111[4:Rew:102.0,53.1] || equal(inverse(identity),u)* equal(inverse(u),sk_c8)** equal(sk_c9,u) -> .
% 0.19/0.51 116[5:Rew:102.0,82.0] || -> equal(multiply(sk_c8,sk_c8),sk_c8)**.
% 0.19/0.51 117[4:Rew:102.0,87.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.19/0.51 118[5:Rew:76.0,116.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.51 123[4:Rew:92.0,96.0,102.0,96.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.51 129[5:Rew:118.0,117.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c8)**.
% 0.19/0.51 130[5:Rew:36.0,129.0] || -> equal(identity,sk_c8)**.
% 0.19/0.51 131[5:Rew:130.0,35.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.51 134[5:Rew:130.0,107.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.19/0.51 135[5:Rew:131.0,134.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.51 136[5:Rew:135.0,104.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.51 154[5:Rew:102.0,111.2,136.0,111.0,130.0,111.0] || equal(sk_c8,u) equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.19/0.51 155[5:Obv:154.0] || equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.19/0.51 224[5:SpL:136.0,155.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.51 226[5:Obv:224.1] || -> .
% 0.19/0.51 227[5:Spt:226.0,12.1,48.0] || equal(multiply(sk_c1,sk_c8),sk_c9)** -> .
% 0.19/0.51 228[5:Spt:226.0,12.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.51 230[5:Rew:102.0,228.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.51 231[5:Rew:102.0,227.0] || equal(multiply(sk_c1,sk_c8),sk_c8)** -> .
% 0.19/0.51 234[4:Rew:123.0,93.0] || -> equal(multiply(inverse(sk_c8),u),multiply(sk_c1,u))**.
% 0.19/0.51 242[4:Rew:102.0,14.1] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.51 243[5:MRR:242.1,231.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.51 247[0:Rew:85.0,91.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.51 250[4:Rew:102.0,13.1,102.0,13.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)** equal(multiply(sk_c1,sk_c8),sk_c8).
% 0.19/0.51 251[5:MRR:250.1,231.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.19/0.51 284[5:SpR:230.0,69.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.19/0.51 286[5:Rew:234.0,284.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.51 287[5:Rew:286.0,231.0] || equal(sk_c7,sk_c8)** -> .
% 0.19/0.51 293[5:SpR:251.0,69.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c8)**.
% 0.19/0.51 295[5:Rew:76.0,293.0,243.0,293.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.51 296[5:MRR:295.0,287.0] || -> .
% 0.19/0.51 297[4:Spt:296.0,28.1,46.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.19/0.51 298[4:Spt:296.0,28.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.51 300[2:Rew:247.0,92.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.19/0.51 301[2:Rew:300.0,87.0] || -> equal(multiply(sk_c2,sk_c7),sk_c9)**.
% 0.19/0.51 302[4:Rew:301.0,297.0] || equal(sk_c9,sk_c8)** -> .
% 0.19/0.51 305[2:Rew:301.0,32.1] || -> equal(inverse(sk_c5),sk_c9)** equal(sk_c9,sk_c8).
% 0.19/0.51 307[2:Rew:301.0,31.1] || -> equal(inverse(sk_c6),sk_c5)** equal(sk_c9,sk_c8).
% 0.19/0.51 309[2:Rew:301.0,30.1] || -> equal(inverse(sk_c4),sk_c8)** equal(sk_c9,sk_c8).
% 0.19/0.51 310[4:MRR:309.1,302.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.51 311[2:Rew:301.0,27.1] || -> equal(inverse(sk_c3),sk_c9)** equal(sk_c9,sk_c8).
% 0.19/0.51 312[4:MRR:311.1,302.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.19/0.51 313[2:Rew:301.0,33.1] || -> equal(multiply(sk_c6,sk_c9),sk_c5)** equal(sk_c9,sk_c8).
% 0.19/0.51 315[2:Rew:301.0,29.1] || -> equal(multiply(sk_c4,sk_c8),sk_c9)** equal(sk_c9,sk_c8).
% 0.19/0.51 316[4:MRR:315.1,302.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.51 317[2:Rew:301.0,26.1] || -> equal(multiply(sk_c3,sk_c9),sk_c8)** equal(sk_c9,sk_c8).
% 0.19/0.51 318[4:MRR:317.1,302.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.51 331[2:SpR:300.0,69.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),u)**.
% 0.19/0.51 339[4:SpR:312.0,69.0] || -> equal(multiply(sk_c9,multiply(sk_c3,u)),u)**.
% 0.19/0.51 359[2:SpR:301.0,37.0] || -> equal(multiply(sk_c2,multiply(sk_c7,u)),multiply(sk_c9,u))**.
% 0.19/0.51 364[4:SpR:316.0,69.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c8)**.
% 0.19/0.51 366[4:Rew:1.0,364.0,310.0,364.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.51 372[4:Rew:366.0,359.0] || -> equal(multiply(sk_c2,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.19/0.51 375[4:Rew:331.0,372.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.51 377[4:Rew:375.0,339.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.51 391[4:Rew:377.0,318.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.51 392[4:MRR:391.0,302.0] || -> .
% 0.19/0.51 418[3:Spt:392.0,4.0,44.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.51 419[3:Spt:392.0,4.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.51 420[2:Rew:305.1,8.1] || -> equal(inverse(sk_c5),sk_c9)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.51 421[2:Rew:307.1,7.1] || -> equal(inverse(sk_c6),sk_c5)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.51 432[2:Rew:313.1,9.0] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c6,sk_c9),sk_c5)**.
% 0.19/0.51 442[3:SpR:419.0,69.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c7)**.
% 0.19/0.51 472[0:SpR:36.0,69.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.51 473[0:SpR:36.0,247.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.51 476[2:SpR:300.0,36.0] || -> equal(multiply(sk_c2,sk_c8),identity)**.
% 0.19/0.51 478[1:Rew:473.0,53.0] || equal(identity,u) equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.19/0.51 479[0:Rew:247.0,472.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.51 492[0:SpR:479.0,69.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.51 509[4:Spt:305.1] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.51 511[4:Rew:509.0,301.0] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.19/0.51 512[4:Rew:509.0,1.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.51 513[4:Rew:509.0,418.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.51 514[4:Rew:509.0,442.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.19/0.51 516[4:Rew:509.0,420.0] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.51 520[4:Rew:509.0,432.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.51 527[4:Rew:509.0,478.1] || equal(identity,u) equal(inverse(u),sk_c8)** equal(sk_c9,u) -> .
% 0.19/0.51 534[4:MRR:421.1,513.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.51 536[4:Rew:476.0,514.0,300.0,514.0] || -> equal(identity,sk_c7)**.
% 0.19/0.51 538[4:Rew:536.0,247.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.51 545[4:Rew:538.0,511.0] || -> equal(sk_c2,sk_c8)**.
% 0.19/0.51 546[4:Rew:545.0,42.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.51 552[4:MRR:516.1,513.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.51 554[4:MRR:520.0,513.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.51 561[4:Rew:509.0,527.2,536.0,527.0] || equal(sk_c7,u) equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.19/0.51 570[4:SpR:534.0,479.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.51 572[4:Rew:552.0,570.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.51 573[4:Rew:572.0,534.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.19/0.51 574[4:Rew:572.0,554.0] || -> equal(multiply(sk_c8,sk_c8),sk_c5)**.
% 0.19/0.51 575[4:Rew:546.0,573.0] || -> equal(sk_c5,sk_c8)**.
% 0.19/0.51 577[4:Rew:512.0,574.0,575.0,574.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.51 586[4:Rew:577.0,561.0] || equal(sk_c8,u) equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.19/0.51 597[4:Obv:586.0] || equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.19/0.51 658[4:SpL:546.0,597.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.51 659[4:Obv:658.1] || -> .
% 0.19/0.51 660[4:Spt:659.0,305.1,509.0] || equal(sk_c9,sk_c8)** -> .
% 0.19/0.51 661[4:Spt:659.0,305.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.19/0.51 663[4:MRR:309.1,660.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.51 664[4:MRR:311.1,660.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.19/0.51 666[4:MRR:315.1,660.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.51 667[4:MRR:317.1,660.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.51 699[4:SpR:663.0,479.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.51 702[4:Rew:300.0,699.0] || -> equal(sk_c2,sk_c4)**.
% 0.19/0.51 703[4:Rew:702.0,300.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.51 706[4:Rew:702.0,476.0] || -> equal(multiply(sk_c4,sk_c8),identity)**.
% 0.19/0.51 707[4:Rew:702.0,55.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.51 712[4:Rew:666.0,706.0] || -> equal(identity,sk_c9)**.
% 0.19/0.51 715[4:Rew:712.0,247.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.51 728[4:Rew:712.0,707.0] || -> equal(multiply(sk_c8,sk_c4),sk_c9)**.
% 0.19/0.51 737[4:Rew:715.0,667.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.51 738[4:Rew:737.0,664.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.19/0.51 739[4:Rew:703.0,738.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.51 744[4:Rew:739.0,728.0] || -> equal(multiply(sk_c8,sk_c9),sk_c9)**.
% 0.19/0.51 752[4:Rew:715.0,744.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.51 753[4:MRR:752.0,660.0] || -> .
% 0.19/0.51 767[2:Spt:753.0,20.0,42.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.51 768[2:Spt:753.0,20.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.51 769[2:MRR:24.1,767.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.19/0.51 770[2:MRR:23.1,767.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.51 771[2:MRR:22.1,767.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.51 772[2:MRR:19.1,767.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.19/0.51 773[2:MRR:25.0,767.0] || -> equal(multiply(sk_c6,sk_c9),sk_c5)**.
% 0.19/0.51 774[2:MRR:21.0,767.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.51 775[2:MRR:18.0,767.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.51 786[2:SpR:769.0,479.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.19/0.51 791[2:SpR:770.0,479.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.51 794[2:Rew:769.0,791.0] || -> equal(sk_c6,sk_c9)**.
% 0.19/0.51 796[2:Rew:794.0,773.0] || -> equal(multiply(sk_c9,sk_c9),sk_c5)**.
% 0.19/0.51 801[2:SpR:771.0,479.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.51 802[2:SpR:771.0,492.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.19/0.51 805[2:Rew:801.0,51.0] || equal(sk_c4,u) equal(inverse(u),sk_c9)** equal(sk_c7,u) -> .
% 0.19/0.51 807[2:SpR:772.0,479.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.19/0.51 810[2:Rew:786.0,807.0] || -> equal(sk_c5,sk_c3)**.
% 0.19/0.51 816[2:Rew:810.0,796.0] || -> equal(multiply(sk_c9,sk_c9),sk_c3)**.
% 0.19/0.51 830[2:SpR:774.0,37.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.19/0.51 831[2:SpR:774.0,69.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c8)**.
% 0.19/0.51 833[2:Rew:1.0,831.0,771.0,831.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.51 839[2:Rew:833.0,805.2] || equal(sk_c4,u) equal(inverse(u),sk_c9)** equal(sk_c8,u) -> .
% 0.19/0.51 841[2:Rew:802.0,830.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.51 843[2:Rew:841.0,816.0] || -> equal(sk_c3,sk_c9)**.
% 0.19/0.51 845[2:Rew:843.0,772.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.51 848[2:Rew:843.0,775.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 852[2:Rew:841.0,848.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.51 863[2:Rew:852.0,845.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.51 864[2:Rew:801.0,863.0] || -> equal(sk_c4,sk_c8)**.
% 0.19/0.51 865[2:Rew:864.0,771.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.51 875[2:Rew:852.0,839.1,864.0,839.0] || equal(sk_c8,u) equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.19/0.51 876[2:Obv:875.0] || equal(inverse(u),sk_c8)** equal(sk_c8,u) -> .
% 0.19/0.51 953[2:SpL:865.0,876.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.51 954[2:Obv:953.1] || -> .
% 0.19/0.51 955[1:Spt:954.0,39.2,39.3,39.4,39.5,39.7,39.8,39.9,39.10,39.11] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.19/0.51 957[2:Spt:4.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.51 959[2:SpR:957.0,479.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.19/0.51 962[3:Spt:20.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.51 964[3:SpR:962.0,479.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.19/0.51 967[3:Rew:964.0,87.0] || -> equal(multiply(sk_c2,sk_c7),sk_c9)**.
% 0.19/0.51 968[3:Rew:967.0,26.1] || -> equal(multiply(sk_c3,sk_c9),sk_c8)** equal(sk_c9,sk_c8).
% 0.19/0.51 969[3:Rew:967.0,29.1] || -> equal(multiply(sk_c4,sk_c8),sk_c9)** equal(sk_c9,sk_c8).
% 0.19/0.51 970[3:Rew:967.0,33.1] || -> equal(multiply(sk_c6,sk_c9),sk_c5)** equal(sk_c9,sk_c8).
% 0.19/0.51 971[3:Rew:967.0,28.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)** equal(sk_c9,sk_c8).
% 0.19/0.51 972[3:Rew:967.0,27.1] || -> equal(inverse(sk_c3),sk_c9)** equal(sk_c9,sk_c8).
% 0.19/0.51 973[3:Rew:967.0,30.1] || -> equal(inverse(sk_c4),sk_c8)** equal(sk_c9,sk_c8).
% 0.19/0.51 974[3:Rew:967.0,31.1] || -> equal(inverse(sk_c6),sk_c5)** equal(sk_c9,sk_c8).
% 0.19/0.51 975[3:Rew:967.0,32.1] || -> equal(inverse(sk_c5),sk_c9)** equal(sk_c9,sk_c8).
% 0.19/0.51 978[3:Rew:974.1,15.1] || -> equal(inverse(sk_c6),sk_c5) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.51 979[3:Rew:975.1,16.1] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.51 982[3:Rew:970.1,17.1] || -> equal(multiply(sk_c6,sk_c9),sk_c5)** equal(multiply(sk_c1,sk_c8),sk_c8).
% 0.19/0.51 983[3:Rew:971.1,12.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.51 1028[2:SpR:957.0,36.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.51 1031[2:SpR:959.0,36.0] || -> equal(multiply(sk_c1,sk_c9),identity)**.
% 0.19/0.51 1033[1:SpL:36.0,955.4] || equal(inverse(inverse(sk_c8)),sk_c8) equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.19/0.51 1036[1:Rew:479.0,1033.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.19/0.51 1037[1:Obv:1036.0] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.19/0.51 1059[4:Spt:972.1] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.51 1060[4:Rew:1059.0,955.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c7),sk_c8)** -> .
% 0.19/0.51 1061[4:Rew:1059.0,957.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.51 1062[4:Rew:1059.0,959.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.19/0.51 1063[4:Rew:1059.0,1.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.51 1065[4:Rew:1059.0,1028.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.19/0.51 1066[4:Rew:1059.0,1031.0] || -> equal(multiply(sk_c1,sk_c8),identity)**.
% 0.19/0.51 1069[4:Rew:1059.0,983.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.51 1076[4:Rew:1059.0,979.0] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c8)**.
% 0.19/0.51 1079[4:Rew:1059.0,982.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)** equal(multiply(sk_c1,sk_c8),sk_c8).
% 0.19/0.51 1080[4:Rew:964.0,1062.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.51 1082[4:Rew:1080.0,964.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.19/0.51 1088[4:Rew:1066.0,978.1] || -> equal(inverse(sk_c6),sk_c5)** equal(identity,sk_c8).
% 0.19/0.51 1092[4:Rew:1066.0,1076.1] || -> equal(inverse(sk_c5),sk_c8)** equal(identity,sk_c8).
% 0.19/0.51 1093[4:Rew:1066.0,1069.1] || -> equal(multiply(sk_c8,sk_c7),sk_c8)** equal(identity,sk_c8).
% 0.19/0.51 1096[4:Rew:1066.0,1079.1] || -> equal(multiply(sk_c6,sk_c8),sk_c5)** equal(identity,sk_c8).
% 0.19/0.51 1102[4:Rew:1059.0,1060.8,1059.0,1060.7,1059.0,1060.5,1059.0,1060.4,1059.0,1060.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c8)** -> .
% 0.19/0.51 1103[4:Con:1102.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c8)** -> .
% 0.19/0.51 1122[5:Spt:1088.1] || -> equal(identity,sk_c8)**.
% 0.19/0.51 1123[5:Rew:1122.0,473.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.51 1124[5:Rew:1122.0,247.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.51 1125[5:Rew:1122.0,35.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.51 1131[5:Rew:1082.0,1123.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.51 1133[5:Rew:1131.0,1061.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.51 1139[5:Rew:1124.0,1063.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.51 1140[5:Rew:1124.0,1103.2] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c8)** -> .
% 0.19/0.51 1148[5:Rew:1139.0,1140.4,1125.0,1140.4,1124.0,1140.3,1139.0,1140.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(sk_c8,sk_c8) -> .
% 0.19/0.51 1149[5:Obv:1148.4] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.19/0.51 1150[5:Con:1149.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.51 1195[5:SpL:1133.0,1150.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.51 1196[5:Obv:1195.1] || -> .
% 0.19/0.51 1197[5:Spt:1196.0,1088.1,1122.0] || equal(identity,sk_c8)** -> .
% 0.19/0.51 1198[5:Spt:1196.0,1088.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.51 1201[5:MRR:1092.1,1197.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.51 1202[5:MRR:1093.1,1197.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.51 1205[5:MRR:1096.1,1197.0] || -> equal(multiply(sk_c6,sk_c8),sk_c5)**.
% 0.19/0.51 1209[5:SpR:1198.0,479.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.51 1212[5:Rew:1201.0,1209.0] || -> equal(sk_c6,sk_c8)**.
% 0.19/0.51 1213[5:Rew:1212.0,1198.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.19/0.51 1214[5:Rew:1212.0,1205.0] || -> equal(multiply(sk_c8,sk_c8),sk_c5)**.
% 0.19/0.51 1215[5:Rew:1082.0,1213.0] || -> equal(sk_c5,sk_c1)**.
% 0.19/0.51 1217[5:Rew:1063.0,1214.0,1215.0,1214.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.51 1222[5:Rew:1217.0,1065.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.51 1228[5:Rew:1202.0,1222.0] || -> equal(identity,sk_c8)**.
% 0.19/0.51 1229[5:MRR:1228.0,1197.0] || -> .
% 0.19/0.51 1232[4:Spt:1229.0,972.1,1059.0] || equal(sk_c9,sk_c8)** -> .
% 0.19/0.51 1233[4:Spt:1229.0,972.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.19/0.51 1234[4:MRR:973.1,1232.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.51 1237[4:MRR:968.1,1232.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.51 1238[4:MRR:969.1,1232.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.51 1240[4:MRR:971.1,1232.0] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.51 1247[4:SpR:1233.0,69.0] || -> equal(multiply(sk_c9,multiply(sk_c3,u)),u)**.
% 0.19/0.51 1248[4:SpR:1233.0,479.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.19/0.51 1251[4:Rew:959.0,1248.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.51 1253[4:Rew:1251.0,1237.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.51 1254[4:Rew:1031.0,1253.0] || -> equal(identity,sk_c8)**.
% 0.19/0.51 1256[4:Rew:1254.0,35.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.51 1257[4:Rew:1254.0,247.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.51 1274[4:Rew:1256.0,1.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.51 1275[4:Rew:1274.0,1240.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.51 1278[4:Rew:1257.0,1238.0] || -> equal(sk_c4,sk_c9)**.
% 0.19/0.51 1279[4:Rew:1278.0,1234.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.19/0.51 1280[4:Rew:959.0,1279.0] || -> equal(sk_c1,sk_c8)**.
% 0.19/0.51 1285[4:Rew:1280.0,1251.0] || -> equal(sk_c3,sk_c8)**.
% 0.19/0.51 1295[4:Rew:1256.0,1247.0,1285.0,1247.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.51 1296[4:Rew:1295.0,1275.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.51 1297[4:MRR:1296.0,1232.0] || -> .
% 0.19/0.51 1307[3:Spt:1297.0,20.0,962.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.19/0.51 1308[3:Spt:1297.0,20.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.51 1311[3:MRR:22.1,1307.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.52 1312[3:MRR:19.1,1307.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.19/0.52 1314[3:MRR:21.0,1307.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.52 1315[3:MRR:18.0,1307.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.52 1316[3:Rew:1308.0,1037.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.52 1317[3:Obv:1316.7] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(identity,sk_c9) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** -> .
% 0.19/0.52 1354[3:SpR:1311.0,479.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.52 1359[3:SpR:1312.0,479.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.19/0.52 1362[3:Rew:959.0,1359.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.52 1364[3:Rew:1362.0,1315.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.52 1365[3:Rew:1031.0,1364.0] || -> equal(identity,sk_c8)**.
% 0.19/0.52 1366[3:Rew:1365.0,473.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.52 1369[3:Rew:1365.0,247.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.52 1370[3:Rew:1365.0,35.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.52 1374[3:Rew:1365.0,1317.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c9) equal(sk_c9,sk_c8) equal(multiply(u,sk_c9),sk_c8)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c9)** -> .
% 0.19/0.52 1376[3:Rew:1354.0,1366.0] || -> equal(sk_c4,sk_c8)**.
% 0.19/0.52 1377[3:Rew:1376.0,1311.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.52 1378[3:Rew:1376.0,1314.0] || -> equal(multiply(sk_c8,sk_c8),sk_c9)**.
% 0.19/0.52 1398[3:Rew:1370.0,1.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.52 1406[3:Rew:1370.0,1378.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.52 1407[3:Rew:1406.0,1398.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.52 1427[3:Rew:1369.0,1374.6,1406.0,1374.6,1369.0,1374.5,1407.0,1374.5,1369.0,1374.4,1406.0,1374.4,1406.0,1374.3,1406.0,1374.2,1406.0,1374.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(sk_c8,sk_c8) equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.19/0.52 1428[3:Obv:1427.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(inverse(w),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) equal(w,sk_c8) -> .
% 0.19/0.52 1429[3:Con:1428.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.52 1486[3:SpL:1377.0,1429.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.52 1487[3:Obv:1486.1] || -> .
% 0.19/0.52 1488[2:Spt:1487.0,4.0,957.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.52 1489[2:Spt:1487.0,4.1] || -> equal(multiply(sk_c9,sk_c7),sk_c8)**.
% 0.19/0.52 1490[2:MRR:8.1,1488.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.19/0.52 1491[2:MRR:7.1,1488.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.52 1492[2:MRR:6.1,1488.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.52 1493[2:MRR:3.1,1488.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.19/0.52 1494[2:MRR:9.0,1488.0] || -> equal(multiply(sk_c6,sk_c9),sk_c5)**.
% 0.19/0.52 1495[2:MRR:5.0,1488.0] || -> equal(multiply(sk_c4,sk_c8),sk_c9)**.
% 0.19/0.52 1496[2:MRR:2.0,1488.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.19/0.52 1501[2:Rew:1489.0,955.8] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.52 1502[2:Obv:1501.8] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(x,sk_c8),sk_c9)** -> .
% 0.19/0.52 1515[2:SpR:1490.0,479.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.19/0.52 1520[2:SpR:1491.0,479.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.52 1523[2:Rew:1490.0,1520.0] || -> equal(sk_c6,sk_c9)**.
% 0.19/0.52 1525[2:Rew:1523.0,1494.0] || -> equal(multiply(sk_c9,sk_c9),sk_c5)**.
% 0.19/0.52 1529[2:SpR:1492.0,479.0] || -> equal(inverse(sk_c8),sk_c4)**.
% 0.19/0.52 1530[2:SpR:1492.0,492.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.19/0.52 1535[2:SpR:1493.0,479.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.19/0.52 1538[2:Rew:1515.0,1535.0] || -> equal(sk_c5,sk_c3)**.
% 0.19/0.52 1544[2:Rew:1538.0,1525.0] || -> equal(multiply(sk_c9,sk_c9),sk_c3)**.
% 0.19/0.52 1558[2:SpR:1495.0,37.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.19/0.52 1559[2:SpR:1495.0,69.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c8)**.
% 0.19/0.52 1561[2:Rew:1.0,1559.0,1492.0,1559.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.52 1568[2:Rew:1561.0,1502.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(x,sk_c8),sk_c9)** -> .
% 0.19/0.52 1572[2:Rew:1530.0,1558.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.52 1574[2:Rew:1572.0,1544.0] || -> equal(sk_c3,sk_c9)**.
% 0.19/0.52 1576[2:Rew:1574.0,1493.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.52 1579[2:Rew:1574.0,1496.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.19/0.52 1583[2:Rew:1572.0,1579.0] || -> equal(sk_c9,sk_c8)**.
% 0.19/0.52 1588[2:Rew:1583.0,1572.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.52 1591[2:Rew:1583.0,1576.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.52 1592[2:Rew:1529.0,1591.0] || -> equal(sk_c4,sk_c8)**.
% 0.19/0.52 1593[2:Rew:1592.0,1492.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.19/0.52 1605[2:Rew:1583.0,1568.7,1583.0,1568.5,1583.0,1568.4,1583.0,1568.3,1583.0,1568.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(multiply(u,sk_c8),sk_c8)** equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(x,sk_c8),sk_c8)** -> .
% 0.19/0.52 1606[2:Con:1605.1] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.19/0.52 1636[2:SpR:1588.0,247.0] || -> equal(identity,sk_c8)**.
% 0.19/0.52 1640[2:Rew:1636.0,247.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.52 1644[2:Rew:1640.0,1606.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.19/0.52 1676[2:SpL:1593.0,1644.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.19/0.52 1677[2:Obv:1676.1] || -> .
% 0.19/0.52 % SZS output end Refutation
% 0.19/0.52 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_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 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 left_identity left_inverse associativity
% 0.19/0.52
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