TSTP Solution File: GRP269-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP269-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 11:46:36 EDT 2022
% Result : Unsatisfiable 0.44s 0.60s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP269-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 14:02:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/0.60
% 0.44/0.60 SPASS V 3.9
% 0.44/0.60 SPASS beiseite: Proof found.
% 0.44/0.60 % SZS status Theorem
% 0.44/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.60 SPASS derived 2097 clauses, backtracked 600 clauses, performed 12 splits and kept 1189 clauses.
% 0.44/0.60 SPASS allocated 64944 KBytes.
% 0.44/0.60 SPASS spent 0:00:00.26 on the problem.
% 0.44/0.60 0:00:00.04 for the input.
% 0.44/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.44/0.60 0:00:00.01 for inferences.
% 0.44/0.60 0:00:00.01 for the backtracking.
% 0.44/0.60 0:00:00.17 for the reduction.
% 0.44/0.60
% 0.44/0.60
% 0.44/0.60 Here is a proof with depth 4, length 467 :
% 0.44/0.60 % SZS output start Refutation
% 0.44/0.60 1[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.44/0.60 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 3[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.44/0.60 4[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.44/0.60 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 7[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.44/0.60 8[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 11[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11)** equal(inverse(sk_c1),sk_c11).
% 0.44/0.60 15[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.60 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.44/0.60 17[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.60 18[0:Inp] || -> equal(inverse(sk_c7),sk_c6)** equal(inverse(sk_c1),sk_c11).
% 0.44/0.60 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.44/0.60 20[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.60 21[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.44/0.60 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.44/0.60 23[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.44/0.60 24[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.44/0.60 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.44/0.60 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.44/0.60 28[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.44/0.60 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.44/0.60 31[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 32[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 33[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 35[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 37[0:Inp] || -> equal(multiply(sk_c8,sk_c10),sk_c11) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 38[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 41[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c2),sk_c11)**.
% 0.44/0.60 43[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.60 44[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c11)**.
% 0.44/0.60 45[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.60 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c11)**.
% 0.44/0.60 47[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.60 48[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(inverse(sk_c2),sk_c11)**.
% 0.44/0.60 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c11)**.
% 0.44/0.60 50[0:Inp] || -> equal(inverse(sk_c2),sk_c11) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.60 51[0:Inp] || equal(multiply(u,sk_c11),sk_c10)** equal(inverse(u),sk_c11) equal(multiply(sk_c11,sk_c9),sk_c10)** equal(multiply(v,sk_c11),sk_c9)** equal(inverse(v),sk_c11) equal(multiply(w,sk_c11),sk_c10)** equal(inverse(w),sk_c11) equal(multiply(x,sk_c10),sk_c9)** equal(inverse(x),sk_c10) equal(multiply(y,z),sk_c11)** equal(inverse(y),z) equal(multiply(z,sk_c10),sk_c11)** equal(inverse(x1),x2) equal(inverse(x2),z)* equal(multiply(x1,z),x2)* -> .
% 0.44/0.60 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.44/0.60 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.44/0.60 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.44/0.60 55[0:Con:51.5] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(inverse(y),sk_c10) equal(inverse(z),sk_c11) equal(inverse(x1),sk_c11) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** equal(multiply(y,sk_c10),sk_c9)** equal(multiply(z,sk_c11),sk_c9)** equal(multiply(x1,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.44/0.60 56[1:Spt:55.0,55.1,55.2,55.6,55.7,55.8] || equal(inverse(u),v)* equal(inverse(w),u) equal(inverse(x),v) equal(multiply(w,v),u)*+ equal(multiply(x,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11)** -> .
% 0.44/0.60 57[1:EqR:56.3] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c11)** equal(multiply(v,sk_c10),sk_c11) -> .
% 0.44/0.60 58[2:Spt:29.1] || -> equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.44/0.60 60[2:SpL:58.0,56.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c11),u)* equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.44/0.60 61[3:Spt:49.1] || -> equal(inverse(sk_c2),sk_c11)**.
% 0.44/0.60 63[4:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.60 65[5:Spt:39.1] || -> equal(multiply(sk_c2,sk_c11),sk_c9)**.
% 0.44/0.60 69[6:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 71[6:SpL:69.0,56.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c1),u)* equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.44/0.60 72[6:Rew:63.0,71.1] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c10,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.44/0.60 76[3:SpR:61.0,53.0] || -> equal(multiply(sk_c11,sk_c2),identity)**.
% 0.44/0.60 77[4:SpR:63.0,53.0] || -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.44/0.60 86[3:SpR:76.0,54.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.44/0.60 91[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.44/0.60 93[3:Rew:52.0,86.0] || -> equal(multiply(sk_c11,multiply(sk_c2,u)),u)**.
% 0.44/0.60 95[0:Rew:52.0,91.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.44/0.60 99[5:SpR:65.0,93.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.44/0.60 101[5:Rew:58.0,99.0] || -> equal(sk_c10,sk_c11)**.
% 0.44/0.60 103[5:Rew:101.0,58.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.44/0.60 104[6:Rew:101.0,69.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.44/0.60 109[6:Rew:101.0,72.3] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.44/0.60 117[6:Obv:109.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.44/0.60 118[6:Rew:101.0,117.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c11),sk_c11)** -> .
% 0.44/0.60 131[0:SpR:95.0,95.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.44/0.60 133[3:SpR:76.0,95.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c2)**.
% 0.44/0.60 134[4:SpR:77.0,95.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c1)**.
% 0.44/0.60 136[5:SpR:103.0,95.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c9)**.
% 0.44/0.60 140[0:SpR:53.0,95.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.44/0.60 144[4:Rew:133.0,134.0] || -> equal(sk_c2,sk_c1)**.
% 0.44/0.60 146[5:Rew:144.0,65.0] || -> equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.44/0.60 152[4:Rew:144.0,133.0] || -> equal(multiply(inverse(sk_c11),identity),sk_c1)**.
% 0.44/0.60 153[6:Rew:104.0,146.0] || -> equal(sk_c9,sk_c11)**.
% 0.44/0.60 154[6:Rew:153.0,103.0] || -> equal(multiply(sk_c11,sk_c11),sk_c11)**.
% 0.44/0.60 157[6:Rew:154.0,118.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.44/0.60 158[5:Rew:53.0,136.0] || -> equal(identity,sk_c9)**.
% 0.44/0.60 159[6:Rew:153.0,158.0] || -> equal(identity,sk_c11)**.
% 0.44/0.60 160[6:Rew:159.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.60 162[6:Rew:159.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.44/0.60 168[6:Rew:160.0,162.0] || -> equal(sk_c11,sk_c1)**.
% 0.44/0.60 169[6:Rew:168.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.44/0.60 176[6:Rew:168.0,159.0] || -> equal(identity,sk_c1)**.
% 0.44/0.60 183[6:Rew:176.0,140.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.44/0.60 188[6:Rew:131.0,183.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.44/0.60 192[6:Obv:157.4] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.44/0.60 193[6:Rew:188.0,192.3,168.0,192.3,168.0,192.2,168.0,192.1,168.0,192.0] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.44/0.60 489[6:SpL:169.0,193.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.44/0.60 492[6:Obv:489.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.44/0.60 494[6:SpL:169.0,492.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.44/0.60 497[6:Obv:494.1] || -> .
% 0.44/0.60 498[6:Spt:497.0,9.1,69.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.44/0.60 499[6:Spt:497.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.60 500[5:Rew:158.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c9)**.
% 0.44/0.60 507[6:Rew:146.0,498.0,101.0,498.0] || equal(sk_c9,sk_c11)** -> .
% 0.44/0.60 508[5:Rew:158.0,140.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.44/0.60 514[5:Rew:146.0,6.1,101.0,6.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c9,sk_c11).
% 0.44/0.60 515[6:MRR:514.1,507.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.60 522[5:Rew:131.0,508.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.44/0.60 526[5:Rew:146.0,7.1,101.0,7.1,101.0,7.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)** equal(sk_c9,sk_c11).
% 0.44/0.60 527[6:MRR:526.1,507.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.44/0.60 528[5:Rew:146.0,5.1,101.0,5.1] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(sk_c9,sk_c11).
% 0.44/0.60 529[6:MRR:528.1,507.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.60 572[5:SpR:500.0,95.0] || -> equal(multiply(inverse(sk_c11),sk_c9),sk_c1)**.
% 0.44/0.60 574[5:Rew:522.0,572.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.44/0.60 582[6:SpR:527.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c11)**.
% 0.44/0.60 585[6:SpR:529.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.44/0.60 587[6:Rew:527.0,585.0,515.0,585.0] || -> equal(sk_c8,sk_c11)**.
% 0.44/0.60 597[6:Rew:587.0,582.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c11)**.
% 0.44/0.60 600[6:Rew:146.0,597.0,574.0,597.0] || -> equal(sk_c9,sk_c11)**.
% 0.44/0.60 601[6:MRR:600.0,507.0] || -> .
% 0.44/0.60 604[5:Spt:601.0,39.1,65.0] || equal(multiply(sk_c2,sk_c11),sk_c9)** -> .
% 0.44/0.60 605[5:Spt:601.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.60 606[5:Rew:144.0,604.0] || equal(multiply(sk_c1,sk_c11),sk_c9)** -> .
% 0.44/0.60 607[0:Rew:131.0,140.0] || -> equal(multiply(u,identity),u)**.
% 0.44/0.60 608[4:Rew:607.0,152.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.44/0.60 610[4:Rew:144.0,38.1] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.44/0.60 611[4:Rew:8.1,610.1] || -> equal(inverse(sk_c7),sk_c6)** equal(sk_c9,sk_c10).
% 0.44/0.60 612[4:Rew:144.0,36.1] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.44/0.60 613[4:Rew:6.1,612.1] || -> equal(inverse(sk_c5),sk_c8)** equal(sk_c9,sk_c10).
% 0.44/0.60 614[4:Rew:144.0,34.1] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.44/0.60 615[4:Rew:4.1,614.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c9,sk_c10).
% 0.44/0.60 616[4:Rew:144.0,32.1] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.44/0.60 617[4:Rew:2.1,616.1] || -> equal(inverse(sk_c3),sk_c11)** equal(sk_c9,sk_c10).
% 0.44/0.60 621[4:Rew:144.0,37.1] || -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c9).
% 0.44/0.60 622[4:Rew:7.1,621.1] || -> equal(multiply(sk_c8,sk_c10),sk_c11)** equal(sk_c9,sk_c10).
% 0.44/0.60 623[4:Rew:144.0,35.1] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c9).
% 0.44/0.60 624[4:Rew:5.1,623.1] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(sk_c9,sk_c10).
% 0.44/0.60 625[4:Rew:144.0,33.1] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c1,sk_c11),sk_c9).
% 0.44/0.60 626[4:Rew:3.1,625.1] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(sk_c9,sk_c10).
% 0.44/0.60 627[4:Rew:144.0,31.1] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c9).
% 0.44/0.60 628[4:Rew:1.1,627.1] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(sk_c9,sk_c10).
% 0.44/0.60 639[4:SpR:608.0,95.0] || -> equal(multiply(sk_c1,multiply(sk_c11,u)),u)**.
% 0.44/0.60 642[2:SpR:58.0,95.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c9)**.
% 0.44/0.60 644[4:Rew:608.0,642.0] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.44/0.60 651[4:SpR:644.0,54.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.44/0.60 666[0:SpR:53.0,95.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.44/0.60 667[0:SpR:53.0,607.0] || -> equal(inverse(identity),identity)**.
% 0.44/0.60 670[5:SpR:605.0,53.0] || -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.44/0.60 671[4:SpR:608.0,53.0] || -> equal(multiply(sk_c1,sk_c11),identity)**.
% 0.44/0.60 674[5:Rew:671.0,606.0] || equal(identity,sk_c9)** -> .
% 0.44/0.60 675[4:Rew:671.0,1.1] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(identity,sk_c10).
% 0.44/0.60 680[4:Rew:671.0,2.1] || -> equal(inverse(sk_c3),sk_c11)** equal(identity,sk_c10).
% 0.44/0.60 684[0:Rew:607.0,666.0] || -> equal(inverse(inverse(u)),u)**.
% 0.44/0.60 693[5:SpR:670.0,95.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c6)**.
% 0.44/0.60 695[5:Rew:607.0,693.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.44/0.60 698[5:SpR:695.0,53.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.44/0.60 710[6:Spt:611.1] || -> equal(sk_c9,sk_c10)**.
% 0.44/0.60 711[6:Rew:710.0,58.0] || -> equal(multiply(sk_c11,sk_c10),sk_c10)**.
% 0.44/0.60 713[6:Rew:710.0,674.0] || equal(identity,sk_c10)** -> .
% 0.44/0.60 715[6:Rew:710.0,651.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c10,u))**.
% 0.44/0.60 719[6:MRR:680.1,713.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.60 723[6:MRR:675.1,713.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 751[6:SpR:723.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.44/0.60 753[6:Rew:711.0,751.0,719.0,751.0] || -> equal(sk_c10,sk_c11)**.
% 0.44/0.60 755[6:Rew:753.0,713.0] || equal(identity,sk_c11)** -> .
% 0.44/0.60 769[6:Rew:753.0,715.0] || -> equal(multiply(sk_c1,multiply(sk_c11,u)),multiply(sk_c11,u))**.
% 0.44/0.60 776[6:Rew:639.0,769.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.60 777[6:Rew:776.0,77.0] || -> equal(identity,sk_c1)**.
% 0.44/0.60 788[6:Rew:777.0,667.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.44/0.60 794[6:Rew:777.0,755.0] || equal(sk_c11,sk_c1)** -> .
% 0.44/0.60 801[6:Rew:63.0,788.0] || -> equal(sk_c11,sk_c1)**.
% 0.44/0.60 809[6:Rew:801.0,794.0] || equal(sk_c1,sk_c1)* -> .
% 0.44/0.60 810[6:Obv:809.0] || -> .
% 0.44/0.60 856[6:Spt:810.0,611.1,710.0] || equal(sk_c9,sk_c10)** -> .
% 0.44/0.60 857[6:Spt:810.0,611.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.60 858[6:MRR:613.1,856.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.60 859[6:MRR:615.1,856.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.60 860[6:MRR:617.1,856.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.60 862[6:MRR:622.1,856.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.60 863[6:MRR:624.1,856.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.60 864[6:MRR:626.1,856.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.60 865[6:MRR:628.1,856.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 913[6:SpR:862.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c11),sk_c10)**.
% 0.44/0.60 915[6:Rew:695.0,913.0] || -> equal(multiply(sk_c6,sk_c11),sk_c10)**.
% 0.44/0.60 922[6:SpR:863.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.44/0.60 924[6:Rew:858.0,922.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.44/0.60 926[6:SpR:864.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.44/0.60 928[6:Rew:859.0,926.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.44/0.60 946[6:SpR:924.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.44/0.60 948[6:Rew:698.0,946.0,695.0,946.0] || -> equal(identity,sk_c11)**.
% 0.44/0.60 949[6:Rew:948.0,674.0] || equal(sk_c9,sk_c11)** -> .
% 0.44/0.60 950[6:Rew:948.0,667.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.44/0.60 955[6:Rew:948.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.60 956[6:Rew:948.0,607.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.44/0.60 960[6:Rew:608.0,950.0] || -> equal(sk_c11,sk_c1)**.
% 0.44/0.60 961[6:Rew:960.0,608.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.44/0.60 963[6:Rew:960.0,860.0] || -> equal(inverse(sk_c3),sk_c1)**.
% 0.44/0.60 967[6:Rew:960.0,865.0] || -> equal(multiply(sk_c3,sk_c1),sk_c10)**.
% 0.44/0.60 968[6:Rew:960.0,915.0] || -> equal(multiply(sk_c6,sk_c1),sk_c10)**.
% 0.44/0.60 985[6:Rew:960.0,949.0] || equal(sk_c9,sk_c1)** -> .
% 0.44/0.60 990[6:Rew:960.0,955.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.44/0.60 994[6:Rew:960.0,956.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.44/0.60 997[6:Rew:994.0,967.0] || -> equal(sk_c3,sk_c10)**.
% 0.44/0.60 998[6:Rew:997.0,963.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.44/0.60 999[6:Rew:994.0,968.0] || -> equal(sk_c6,sk_c10)**.
% 0.44/0.60 1001[6:Rew:999.0,695.0] || -> equal(inverse(sk_c8),sk_c10)**.
% 0.44/0.60 1002[6:Rew:999.0,605.0] || -> equal(inverse(sk_c10),sk_c8)**.
% 0.44/0.60 1013[6:Rew:998.0,1002.0] || -> equal(sk_c8,sk_c1)**.
% 0.44/0.60 1018[6:Rew:1013.0,1001.0] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.44/0.60 1019[6:Rew:961.0,1018.0] || -> equal(sk_c10,sk_c1)**.
% 0.44/0.60 1022[6:Rew:1019.0,864.0] || -> equal(multiply(sk_c4,sk_c1),sk_c9)**.
% 0.44/0.60 1025[6:Rew:1019.0,928.0] || -> equal(multiply(sk_c1,sk_c9),sk_c1)**.
% 0.44/0.60 1040[6:Rew:994.0,1022.0] || -> equal(sk_c9,sk_c4)**.
% 0.44/0.60 1041[6:Rew:1040.0,985.0] || equal(sk_c4,sk_c1)** -> .
% 0.44/0.60 1042[6:Rew:990.0,1025.0,1040.0,1025.0] || -> equal(sk_c4,sk_c1)**.
% 0.44/0.60 1043[6:MRR:1042.0,1041.0] || -> .
% 0.44/0.60 1072[4:Spt:1043.0,19.1,63.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.44/0.60 1073[4:Spt:1043.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.60 1074[3:Rew:607.0,133.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.44/0.60 1078[4:MRR:16.1,1072.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.60 1080[4:MRR:12.1,1072.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.60 1084[4:MRR:15.0,1072.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.60 1086[4:MRR:11.0,1072.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 1130[4:SpR:1084.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.44/0.60 1132[4:Rew:1078.0,1130.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.44/0.60 1138[4:SpR:1086.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.44/0.60 1140[4:Rew:1080.0,1138.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.44/0.60 1150[4:SpR:1132.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.44/0.60 1152[4:Rew:53.0,1150.0] || -> equal(identity,sk_c11)**.
% 0.44/0.60 1153[4:Rew:1152.0,667.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.44/0.60 1155[4:Rew:1152.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.60 1156[4:Rew:1152.0,607.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.44/0.60 1157[4:Rew:1152.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.44/0.60 1160[4:Rew:1074.0,1153.0] || -> equal(sk_c2,sk_c11)**.
% 0.44/0.60 1161[4:Rew:1160.0,61.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.44/0.60 1172[4:Rew:1155.0,1140.0] || -> equal(sk_c10,sk_c11)**.
% 0.44/0.60 1185[4:Rew:1172.0,57.4] || equal(inverse(multiply(u,v)),v)** equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c11)** equal(multiply(v,sk_c11),sk_c11) -> .
% 0.44/0.60 1236[4:Rew:1156.0,1185.4] || equal(inverse(multiply(u,v)),v)**+ equal(multiply(u,v),inverse(u)) equal(inverse(w),v) equal(multiply(w,v),sk_c11)** equal(v,sk_c11) -> .
% 0.44/0.60 1252[0:SpR:684.0,95.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.44/0.60 1277[4:SpR:684.0,1157.0] || -> equal(multiply(u,inverse(u)),sk_c11)**.
% 0.44/0.60 1673[4:SpL:1157.0,1236.0] || equal(inverse(sk_c11),u) equal(multiply(inverse(u),u),inverse(inverse(u)))** equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.44/0.60 1683[4:Rew:1157.0,1673.1,684.0,1673.1,1161.0,1673.0] || equal(sk_c11,u) equal(sk_c11,u) equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.44/0.60 1684[4:Obv:1683.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c11)** equal(v,sk_c11) -> .
% 0.44/0.60 1922[4:SpL:1277.0,1684.1] || equal(inverse(u),inverse(u))* equal(sk_c11,sk_c11) equal(inverse(u),sk_c11) -> .
% 0.44/0.60 1944[4:Obv:1922.1] || equal(inverse(u),sk_c11)** -> .
% 0.44/0.60 1945[4:UnC:1944.0,684.0] || -> .
% 0.44/0.60 1951[3:Spt:1945.0,49.1,61.0] || equal(inverse(sk_c2),sk_c11)** -> .
% 0.44/0.60 1952[3:Spt:1945.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.60 1953[3:MRR:48.1,1951.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.60 1954[3:MRR:46.1,1951.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.60 1956[3:MRR:42.1,1951.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.60 1957[3:MRR:50.0,1951.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.60 1958[3:MRR:47.0,1951.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.60 1959[3:MRR:45.0,1951.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.60 1961[3:MRR:41.0,1951.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 1963[3:SpR:1952.0,684.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.44/0.60 1967[3:SpR:1953.0,684.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.44/0.60 1970[3:Rew:1952.0,1967.0] || -> equal(sk_c7,sk_c8)**.
% 0.44/0.60 1972[3:Rew:1970.0,1957.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.44/0.60 1983[3:SpR:1954.0,684.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.60 1984[3:SpR:1954.0,1252.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.44/0.60 1986[3:Rew:1963.0,1983.0] || -> equal(sk_c6,sk_c5)**.
% 0.44/0.60 1988[3:Rew:1986.0,1963.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.60 1991[3:Rew:1986.0,1972.0] || -> equal(multiply(sk_c8,sk_c8),sk_c5)**.
% 0.44/0.60 1997[3:SpR:1956.0,95.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.44/0.60 1998[3:SpR:1956.0,684.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.60 2002[3:Rew:1998.0,60.1] || equal(inverse(u),sk_c9)** equal(sk_c3,u) equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.44/0.60 2023[3:SpR:1959.0,54.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c11,u))**.
% 0.44/0.60 2024[3:SpR:1959.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.44/0.60 2026[3:Rew:1954.0,2024.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.44/0.60 2027[3:Rew:1984.0,2023.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.60 2028[3:Rew:2027.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.44/0.60 2029[3:Rew:2027.0,1997.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.44/0.60 2035[3:Rew:2028.0,2002.0] || equal(inverse(u),sk_c10)** equal(sk_c3,u) equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.44/0.60 2036[3:Rew:2029.0,1961.0] || -> equal(sk_c10,sk_c11)**.
% 0.44/0.60 2039[3:Rew:2036.0,1958.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.44/0.60 2047[3:Rew:2036.0,2028.0] || -> equal(sk_c9,sk_c11)**.
% 0.44/0.60 2051[3:Rew:2026.0,2039.0] || -> equal(sk_c8,sk_c11)**.
% 0.44/0.60 2054[3:Rew:2051.0,1988.0] || -> equal(inverse(sk_c11),sk_c5)**.
% 0.44/0.60 2056[3:Rew:2051.0,1991.0] || -> equal(multiply(sk_c11,sk_c11),sk_c5)**.
% 0.44/0.60 2060[3:Rew:1998.0,2054.0] || -> equal(sk_c5,sk_c3)**.
% 0.44/0.60 2065[3:Rew:2027.0,2056.0,2060.0,2056.0] || -> equal(sk_c3,sk_c11)**.
% 0.44/0.60 2066[3:Rew:2065.0,1956.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.44/0.60 2078[3:Rew:2027.0,2035.5,2047.0,2035.5,2036.0,2035.5,2047.0,2035.4,2036.0,2035.3,2047.0,2035.2,2065.0,2035.1,2036.0,2035.0] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.44/0.60 2079[3:Obv:2078.5] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.44/0.60 2115[3:SpR:2066.0,53.0] || -> equal(multiply(sk_c11,sk_c11),identity)**.
% 0.44/0.60 2116[3:Rew:2027.0,2115.0] || -> equal(identity,sk_c11)**.
% 0.44/0.60 2119[3:Rew:2116.0,607.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.44/0.60 2126[3:Rew:2119.0,2079.3] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.44/0.60 2510[3:SpL:2066.0,2126.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.44/0.60 2513[3:Obv:2510.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.44/0.60 2516[3:SpL:2066.0,2513.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.44/0.60 2519[3:Obv:2516.1] || -> .
% 0.44/0.60 2520[2:Spt:2519.0,29.1,58.0] || equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.44/0.60 2521[2:Spt:2519.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.60 2524[2:MRR:26.1,2520.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.60 2525[2:MRR:24.1,2520.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.60 2526[2:MRR:22.1,2520.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.60 2530[2:MRR:25.1,2520.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.60 2531[2:MRR:23.1,2520.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.60 2532[2:MRR:21.1,2520.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 2555[2:SpR:2524.0,1252.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.44/0.60 2565[2:SpR:2525.0,684.0] || -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.60 2568[2:SpR:2526.0,95.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.44/0.60 2569[2:SpR:2526.0,684.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.60 2588[2:SpR:2530.0,54.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c11,u))**.
% 0.44/0.60 2592[2:Rew:2555.0,2588.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.60 2593[2:Rew:2592.0,2568.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.44/0.60 2594[2:Rew:2592.0,2520.0] || equal(sk_c9,sk_c10)** -> .
% 0.44/0.60 2597[2:Rew:2593.0,2532.0] || -> equal(sk_c10,sk_c11)**.
% 0.44/0.60 2600[2:Rew:2597.0,2565.0] || -> equal(inverse(sk_c11),sk_c4)**.
% 0.44/0.60 2601[2:Rew:2597.0,2531.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.44/0.60 2609[2:Rew:2597.0,2594.0] || equal(sk_c9,sk_c11)** -> .
% 0.44/0.60 2610[2:Rew:2569.0,2600.0] || -> equal(sk_c4,sk_c3)**.
% 0.44/0.60 2624[2:Rew:2593.0,2601.0,2610.0,2601.0] || -> equal(sk_c9,sk_c11)**.
% 0.44/0.60 2625[2:MRR:2624.0,2609.0] || -> .
% 0.44/0.60 2640[1:Spt:2625.0,55.3,55.4,55.5,55.9,55.10,55.11,55.12] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c11),sk_c9)** equal(multiply(w,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.44/0.60 2642[2:Spt:28.1] || -> equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.44/0.60 2643[2:Rew:2642.0,2640.6] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c9)** equal(multiply(w,sk_c11),sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.44/0.60 2645[2:Obv:2643.6] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c9)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.44/0.60 2648[2:SpR:2642.0,95.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c9)**.
% 0.44/0.60 2650[3:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.44/0.60 2652[3:SpR:2650.0,684.0] || -> equal(inverse(sk_c11),sk_c1)**.
% 0.44/0.60 2655[3:Rew:2652.0,2648.0] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.44/0.60 2656[4:Spt:49.1] || -> equal(inverse(sk_c2),sk_c11)**.
% 0.44/0.60 2658[4:SpR:2656.0,684.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.44/0.60 2661[4:Rew:2652.0,2658.0] || -> equal(sk_c2,sk_c1)**.
% 0.44/0.60 2664[4:Rew:2661.0,33.1] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c1,sk_c11),sk_c9).
% 0.44/0.60 2669[4:Rew:2661.0,34.1] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c11),sk_c9)**.
% 0.44/0.60 2676[4:Rew:4.1,2669.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c9,sk_c10).
% 0.44/0.60 2681[4:Rew:3.1,2664.1] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(sk_c9,sk_c10).
% 0.44/0.60 2685[5:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 2730[3:SpR:2652.0,53.0] || -> equal(multiply(sk_c1,sk_c11),identity)**.
% 0.44/0.60 2731[5:Rew:2685.0,2730.0] || -> equal(identity,sk_c10)**.
% 0.44/0.60 2732[5:Rew:2731.0,667.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.60 2734[5:Rew:2731.0,607.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.60 2738[5:Rew:2734.0,2655.0] || -> equal(sk_c9,sk_c1)**.
% 0.44/0.60 2740[5:Rew:2734.0,2645.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(u,sk_c9) equal(multiply(v,sk_c11),sk_c9)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.44/0.60 2741[5:Rew:2734.0,2681.0] || -> equal(sk_c9,sk_c4)** equal(sk_c9,sk_c10).
% 0.44/0.60 2750[5:Rew:2738.0,2676.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c10,sk_c1).
% 0.44/0.60 2754[5:Rew:2738.0,2741.1,2738.0,2741.0] || -> equal(sk_c4,sk_c1)** equal(sk_c10,sk_c1).
% 0.44/0.60 2760[5:Rew:2754.0,2750.0] || -> equal(inverse(sk_c1),sk_c10)** equal(sk_c10,sk_c1).
% 0.44/0.60 2761[5:Rew:2650.0,2760.0] || -> equal(sk_c10,sk_c11)** equal(sk_c10,sk_c1).
% 0.44/0.60 2767[5:Rew:2738.0,2740.4,2738.0,2740.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(u,sk_c1) equal(multiply(v,sk_c11),sk_c1)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.44/0.60 2782[6:Spt:2754.1] || -> equal(sk_c10,sk_c1)**.
% 0.44/0.60 2785[6:Rew:2782.0,2732.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.44/0.60 2788[6:Rew:2782.0,2734.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.44/0.60 2791[6:Rew:2782.0,2767.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(u,sk_c1) equal(multiply(v,sk_c11),sk_c1)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.44/0.60 2792[6:Rew:2650.0,2785.0] || -> equal(sk_c11,sk_c1)**.
% 0.44/0.60 2793[6:Rew:2792.0,2650.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.44/0.60 2801[6:Rew:2788.0,2791.5,2792.0,2791.5,2782.0,2791.5,2788.0,2791.4,2792.0,2791.4,2792.0,2791.2,2792.0,2791.1] || 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) -> .
% 0.44/0.60 2802[6:Con:2801.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.44/0.60 2846[6:SpL:2793.0,2802.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.44/0.60 2847[6:Obv:2846.1] || -> .
% 0.44/0.60 2848[6:Spt:2847.0,2754.1,2782.0] || equal(sk_c10,sk_c1)** -> .
% 0.44/0.60 2849[6:Spt:2847.0,2754.0] || -> equal(sk_c4,sk_c1)**.
% 0.44/0.60 2851[6:MRR:2761.1,2848.0] || -> equal(sk_c10,sk_c11)**.
% 0.44/0.60 2853[6:Rew:2851.0,2732.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.44/0.60 2854[6:Rew:2851.0,2848.0] || equal(sk_c11,sk_c1)** -> .
% 0.44/0.60 2859[6:Rew:2652.0,2853.0] || -> equal(sk_c11,sk_c1)**.
% 0.44/0.60 2865[6:Rew:2859.0,2854.0] || equal(sk_c1,sk_c1)* -> .
% 0.44/0.60 2866[6:Obv:2865.0] || -> .
% 0.44/0.60 2877[5:Spt:2866.0,9.1,2685.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.44/0.60 2878[5:Spt:2866.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.60 2879[5:Rew:2730.0,2877.0] || equal(identity,sk_c10)** -> .
% 0.44/0.60 2887[3:Rew:2730.0,2.1] || -> equal(inverse(sk_c3),sk_c11)** equal(identity,sk_c10).
% 0.44/0.60 2888[5:MRR:2887.1,2879.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.60 2897[3:Rew:2730.0,1.1] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(identity,sk_c10).
% 0.44/0.60 2898[5:MRR:2897.1,2879.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 2944[5:SpR:2888.0,684.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.60 2947[5:Rew:2652.0,2944.0] || -> equal(sk_c3,sk_c1)**.
% 0.44/0.60 2949[5:Rew:2947.0,2898.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 2950[5:Rew:2730.0,2949.0] || -> equal(identity,sk_c10)**.
% 0.44/0.60 2951[5:MRR:2950.0,2879.0] || -> .
% 0.44/0.60 2954[4:Spt:2951.0,49.1,2656.0] || equal(inverse(sk_c2),sk_c11)** -> .
% 0.44/0.60 2955[4:Spt:2951.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.60 2958[4:MRR:44.1,2954.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.60 2959[4:MRR:42.1,2954.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.60 2963[4:MRR:43.0,2954.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.60 2964[4:MRR:41.0,2954.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.60 2991[4:SpR:2958.0,684.0] || -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.60 2995[4:SpR:2959.0,684.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.60 2998[4:Rew:2652.0,2995.0] || -> equal(sk_c3,sk_c1)**.
% 0.44/0.60 3000[4:Rew:2998.0,2964.0] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.44/0.60 3001[4:Rew:2730.0,3000.0] || -> equal(identity,sk_c10)**.
% 0.44/0.60 3002[4:Rew:3001.0,667.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.60 3004[4:Rew:3001.0,607.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.44/0.60 3005[4:Rew:3001.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.44/0.60 3009[4:Rew:2991.0,3002.0] || -> equal(sk_c4,sk_c10)**.
% 0.44/0.60 3010[4:Rew:3009.0,2958.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.44/0.60 3011[4:Rew:3009.0,2963.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.44/0.60 3017[4:Rew:3004.0,2645.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(u,sk_c9) equal(multiply(v,sk_c11),sk_c9)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.44/0.60 3018[4:Rew:3004.0,2655.0] || -> equal(sk_c9,sk_c1)**.
% 0.44/0.60 3032[4:Rew:3005.0,3011.0,3018.0,3011.0] || -> equal(sk_c10,sk_c1)**.
% 0.44/0.60 3035[4:Rew:3032.0,3010.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.44/0.60 3037[4:Rew:3032.0,3004.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.44/0.60 3040[4:Rew:2650.0,3035.0] || -> equal(sk_c11,sk_c1)**.
% 0.44/0.60 3041[4:Rew:3040.0,2650.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.44/0.60 3065[4:Rew:3037.0,3017.5,3040.0,3017.5,3032.0,3017.5,3037.0,3017.4,3040.0,3017.4,3018.0,3017.4,3018.0,3017.3,3040.0,3017.2,3040.0,3017.1,3032.0,3017.0] || 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) -> .
% 0.44/0.60 3066[4:Con:3065.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.44/0.60 3109[4:SpL:3041.0,3066.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.44/0.60 3110[4:Obv:3109.1] || -> .
% 0.44/0.60 3111[3:Spt:3110.0,19.1,2650.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.44/0.60 3112[3:Spt:3110.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.44/0.60 3113[3:MRR:18.1,3111.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.61 3114[3:MRR:16.1,3111.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61 3116[3:MRR:12.1,3111.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61 3117[3:MRR:20.0,3111.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.44/0.61 3118[3:MRR:17.0,3111.0] || -> equal(multiply(sk_c8,sk_c10),sk_c11)**.
% 0.44/0.61 3119[3:MRR:15.0,3111.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61 3121[3:MRR:11.0,3111.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61 3123[3:SpR:3112.0,684.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.44/0.61 3133[3:SpR:3113.0,684.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.44/0.61 3136[3:Rew:3112.0,3133.0] || -> equal(sk_c7,sk_c8)**.
% 0.44/0.61 3138[3:Rew:3136.0,3117.0] || -> equal(multiply(sk_c8,sk_c8),sk_c6)**.
% 0.44/0.61 3143[3:SpR:3114.0,684.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.61 3144[3:SpR:3114.0,1252.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.44/0.61 3146[3:Rew:3123.0,3143.0] || -> equal(sk_c6,sk_c5)**.
% 0.44/0.61 3148[3:Rew:3146.0,3123.0] || -> equal(inverse(sk_c8),sk_c5)**.
% 0.44/0.61 3151[3:Rew:3146.0,3138.0] || -> equal(multiply(sk_c8,sk_c8),sk_c5)**.
% 0.44/0.61 3157[3:SpR:3116.0,95.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.44/0.61 3158[3:SpR:3116.0,684.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.61 3182[3:SpR:3119.0,54.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c11,u))**.
% 0.44/0.61 3183[3:SpR:3119.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.44/0.61 3185[3:Rew:3114.0,3183.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.44/0.61 3186[3:Rew:3144.0,3182.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.61 3187[3:Rew:3186.0,2642.0] || -> equal(sk_c9,sk_c10)**.
% 0.44/0.61 3188[3:Rew:3186.0,3157.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.44/0.61 3193[3:Rew:3187.0,2645.3] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c10)** equal(multiply(v,sk_c11),sk_c9)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.44/0.61 3196[3:Rew:3188.0,3121.0] || -> equal(sk_c10,sk_c11)**.
% 0.44/0.61 3199[3:Rew:3196.0,3118.0] || -> equal(multiply(sk_c8,sk_c11),sk_c11)**.
% 0.44/0.61 3203[3:Rew:3196.0,3187.0] || -> equal(sk_c9,sk_c11)**.
% 0.44/0.61 3207[3:Rew:3185.0,3199.0] || -> equal(sk_c8,sk_c11)**.
% 0.44/0.61 3210[3:Rew:3207.0,3148.0] || -> equal(inverse(sk_c11),sk_c5)**.
% 0.44/0.61 3212[3:Rew:3207.0,3151.0] || -> equal(multiply(sk_c11,sk_c11),sk_c5)**.
% 0.44/0.61 3216[3:Rew:3158.0,3210.0] || -> equal(sk_c5,sk_c3)**.
% 0.44/0.61 3221[3:Rew:3186.0,3212.0,3216.0,3212.0] || -> equal(sk_c3,sk_c11)**.
% 0.44/0.61 3222[3:Rew:3221.0,3116.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.44/0.61 3234[3:Rew:3196.0,3193.5,3203.0,3193.4,3196.0,3193.3,3196.0,3193.0] || equal(inverse(u),sk_c11) equal(inverse(v),sk_c11) equal(inverse(w),sk_c11) equal(multiply(u,sk_c11),sk_c11)** equal(multiply(v,sk_c11),sk_c11)** equal(multiply(w,sk_c11),sk_c11)** -> .
% 0.44/0.61 3235[3:Con:3234.1] || equal(inverse(u),sk_c11) equal(multiply(u,sk_c11),sk_c11)** -> .
% 0.44/0.61 3264[3:SpR:3222.0,53.0] || -> equal(multiply(sk_c11,sk_c11),identity)**.
% 0.44/0.61 3265[3:Rew:3186.0,3264.0] || -> equal(identity,sk_c11)**.
% 0.44/0.61 3269[3:Rew:3265.0,607.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.44/0.61 3271[3:Rew:3269.0,3235.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.44/0.61 3312[3:SpL:3222.0,3271.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.44/0.61 3313[3:Obv:3312.1] || -> .
% 0.44/0.61 3314[2:Spt:3313.0,28.1,2642.0] || equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.44/0.61 3315[2:Spt:3313.0,28.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.44/0.61 3317[2:MRR:26.1,3314.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.44/0.61 3318[2:MRR:24.1,3314.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.44/0.61 3319[2:MRR:22.1,3314.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.44/0.61 3324[2:MRR:25.1,3314.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.44/0.61 3325[2:MRR:23.1,3314.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.44/0.61 3326[2:MRR:21.1,3314.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.44/0.61 3345[2:SpR:3317.0,1252.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.44/0.61 3354[2:SpR:3318.0,684.0] || -> equal(inverse(sk_c10),sk_c4)**.
% 0.44/0.61 3358[2:SpR:3319.0,95.0] || -> equal(multiply(sk_c11,multiply(sk_c3,u)),u)**.
% 0.44/0.61 3359[2:SpR:3319.0,684.0] || -> equal(inverse(sk_c11),sk_c3)**.
% 0.44/0.61 3378[2:SpR:3324.0,54.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c11,u))**.
% 0.44/0.61 3382[2:Rew:3345.0,3378.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.44/0.61 3383[2:Rew:3382.0,3358.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.44/0.61 3384[2:Rew:3382.0,3314.0] || equal(sk_c9,sk_c10)** -> .
% 0.44/0.61 3387[2:Rew:3383.0,3326.0] || -> equal(sk_c10,sk_c11)**.
% 0.44/0.61 3389[2:Rew:3387.0,3354.0] || -> equal(inverse(sk_c11),sk_c4)**.
% 0.44/0.61 3391[2:Rew:3387.0,3325.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.44/0.61 3395[2:Rew:3387.0,3384.0] || equal(sk_c9,sk_c11)** -> .
% 0.44/0.61 3396[2:Rew:3359.0,3389.0] || -> equal(sk_c4,sk_c3)**.
% 0.44/0.61 3410[2:Rew:3383.0,3391.0,3396.0,3391.0] || -> equal(sk_c9,sk_c11)**.
% 0.44/0.61 3411[2:MRR:3410.0,3395.0] || -> .
% 0.44/0.61 % SZS output end Refutation
% 0.44/0.61 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_11 prove_this_12 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_28 prove_this_29 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_38 prove_this_39 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 prove_this_48 prove_this_49 prove_this_50 prove_this_51 left_identity left_inverse associativity
% 0.44/0.61
%------------------------------------------------------------------------------