TSTP Solution File: GRP273-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP273-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:46:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.57s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP273-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.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 07:41:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.57
% 0.19/0.57 SPASS V 3.9
% 0.19/0.57 SPASS beiseite: Proof found.
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.57 SPASS derived 1795 clauses, backtracked 549 clauses, performed 11 splits and kept 1116 clauses.
% 0.19/0.57 SPASS allocated 64806 KBytes.
% 0.19/0.57 SPASS spent 0:00:00.23 on the problem.
% 0.19/0.57 0:00:00.03 for the input.
% 0.19/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.57 0:00:00.01 for inferences.
% 0.19/0.57 0:00:00.00 for the backtracking.
% 0.19/0.57 0:00:00.15 for the reduction.
% 0.19/0.57
% 0.19/0.57
% 0.19/0.57 Here is a proof with depth 5, length 380 :
% 0.19/0.57 % SZS output start Refutation
% 0.19/0.57 1[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.19/0.57 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.57 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c1,sk_c11),sk_c10).
% 0.19/0.57 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.57 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.57 11[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.57 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11)** equal(inverse(sk_c1),sk_c11).
% 0.19/0.57 13[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.57 14[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c11).
% 0.19/0.57 15[0:Inp] || -> equal(inverse(sk_c1),sk_c11) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.57 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.19/0.57 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8)** equal(inverse(sk_c1),sk_c11).
% 0.19/0.57 21[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.19/0.57 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.19/0.57 23[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.19/0.57 24[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.19/0.57 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c11,sk_c9),sk_c10).
% 0.19/0.57 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.19/0.57 28[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.19/0.57 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.19/0.57 31[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 32[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 33[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 35[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 41[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.57 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.57 45[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.57 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.57 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.57 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_c9),sk_c11)** equal(inverse(v),sk_c9) 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)* -> .
% 0.19/0.57 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.57 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.57 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.57 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_c9) 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_c9),sk_c11)** equal(multiply(x1,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.19/0.57 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)** -> .
% 0.19/0.57 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) -> .
% 0.19/0.57 58[2:Spt:29.1] || -> equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.19/0.57 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)** -> .
% 0.19/0.57 61[3:Spt:49.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.57 63[4:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.57 65[5:Spt:39.1] || -> equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 69[6:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.57 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)** -> .
% 0.19/0.57 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)** -> .
% 0.19/0.57 76[3:SpR:61.0,53.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.19/0.57 77[4:SpR:63.0,53.0] || -> equal(multiply(sk_c11,sk_c1),identity)**.
% 0.19/0.57 89[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.57 90[3:SpR:76.0,54.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.57 91[4:SpR:77.0,54.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.57 93[3:Rew:52.0,90.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.19/0.57 94[4:Rew:52.0,91.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.19/0.57 95[0:Rew:52.0,89.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.57 99[5:SpR:65.0,93.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.19/0.57 108[6:SpR:69.0,94.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.57 111[6:Rew:108.0,72.5] || 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(sk_c11,sk_c11) -> .
% 0.19/0.57 113[6:Obv:111.5] || 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)** -> .
% 0.19/0.57 120[0:SpR:95.0,95.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.57 126[0:SpR:53.0,95.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.57 127[3:SpR:76.0,95.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.19/0.57 128[5:SpR:99.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c11)**.
% 0.19/0.57 139[5:Rew:53.0,128.0] || -> equal(identity,sk_c11)**.
% 0.19/0.57 140[5:Rew:139.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.57 142[5:Rew:139.0,76.0] || -> equal(multiply(sk_c9,sk_c2),sk_c11)**.
% 0.19/0.57 143[5:Rew:139.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.19/0.57 149[5:Rew:139.0,127.0] || -> equal(multiply(inverse(sk_c9),sk_c11),sk_c2)**.
% 0.19/0.57 150[5:Rew:140.0,94.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.57 151[6:Rew:140.0,108.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.57 152[5:Rew:140.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.57 165[6:Rew:151.0,113.3] || 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)** -> .
% 0.19/0.57 177[5:Rew:140.0,143.0] || -> equal(sk_c11,sk_c1)**.
% 0.19/0.57 178[5:Rew:177.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.57 179[5:Rew:177.0,139.0] || -> equal(identity,sk_c1)**.
% 0.19/0.57 193[5:Rew:179.0,126.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.19/0.57 203[5:Rew:120.0,193.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.57 205[6:Obv:165.1] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11) equal(sk_c11,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.19/0.57 206[6:Rew:203.0,205.3,177.0,205.3,177.0,205.2,177.0,205.1,177.0,205.0] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c1)** equal(sk_c1,u) equal(v,sk_c1) -> .
% 0.19/0.57 512[6:SpL:178.0,206.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c1) -> .
% 0.19/0.57 515[6:Obv:512.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.57 517[6:SpL:178.0,515.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.57 520[6:Obv:517.1] || -> .
% 0.19/0.57 521[6:Spt:520.0,9.1,69.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.19/0.57 522[6:Spt:520.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.57 527[5:Rew:177.0,142.0] || -> equal(multiply(sk_c9,sk_c2),sk_c1)**.
% 0.19/0.57 528[5:Rew:152.0,527.0] || -> equal(multiply(sk_c10,sk_c2),sk_c1)**.
% 0.19/0.57 530[5:Rew:203.0,149.0,177.0,149.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.19/0.57 531[5:Rew:152.0,530.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.19/0.57 532[6:Rew:150.0,521.0,177.0,521.0] || equal(sk_c10,sk_c1)** -> .
% 0.19/0.57 544[5:Rew:177.0,2.1,150.0,2.1,177.0,2.0] || -> equal(inverse(sk_c3),sk_c1)** equal(sk_c10,sk_c1).
% 0.19/0.57 545[6:MRR:544.1,532.0] || -> equal(inverse(sk_c3),sk_c1)**.
% 0.19/0.57 555[5:Rew:177.0,1.1,150.0,1.1,203.0,1.0,177.0,1.0] || -> equal(sk_c3,sk_c10)** equal(sk_c10,sk_c1).
% 0.19/0.57 556[6:MRR:555.1,532.0] || -> equal(sk_c3,sk_c10)**.
% 0.19/0.57 557[6:Rew:556.0,545.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.19/0.57 558[6:Rew:531.0,557.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.57 561[6:Rew:558.0,528.0] || -> equal(multiply(sk_c10,sk_c1),sk_c1)**.
% 0.19/0.57 569[6:Rew:203.0,561.0] || -> equal(sk_c10,sk_c1)**.
% 0.19/0.57 570[6:MRR:569.0,532.0] || -> .
% 0.19/0.57 595[5:Spt:570.0,39.1,65.0] || equal(multiply(sk_c2,sk_c9),sk_c11)** -> .
% 0.19/0.57 596[5:Spt:570.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.57 601[5:MRR:36.1,595.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.57 603[5:MRR:32.1,595.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.57 604[0:Rew:120.0,126.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.57 608[5:MRR:35.1,595.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.57 610[5:MRR:31.1,595.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.57 651[3:SpR:76.0,95.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.19/0.57 653[3:Rew:604.0,651.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.19/0.57 672[5:SpR:608.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.57 674[5:Rew:601.0,672.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.57 680[5:SpR:610.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.57 682[5:Rew:603.0,680.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.57 691[5:SpR:674.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.57 693[5:Rew:53.0,691.0] || -> equal(identity,sk_c11)**.
% 0.19/0.57 694[5:Rew:693.0,77.0] || -> equal(multiply(sk_c11,sk_c1),sk_c11)**.
% 0.19/0.57 696[5:Rew:693.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.57 700[5:Rew:693.0,604.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.57 704[5:Rew:696.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.57 706[5:Rew:696.0,682.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.57 711[5:Rew:696.0,694.0] || -> equal(sk_c11,sk_c1)**.
% 0.19/0.57 715[5:Rew:704.0,653.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.19/0.57 718[5:Rew:704.0,595.0] || equal(multiply(sk_c2,sk_c10),sk_c11)** -> .
% 0.19/0.57 738[5:Rew:711.0,63.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.57 745[5:Rew:711.0,706.0] || -> equal(sk_c10,sk_c1)**.
% 0.19/0.57 748[5:Rew:745.0,715.0] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.19/0.57 750[5:Rew:748.0,738.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.57 753[5:Rew:711.0,700.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.57 781[5:Rew:753.0,718.0,750.0,718.0,745.0,718.0,711.0,718.0] || equal(sk_c1,sk_c1)* -> .
% 0.19/0.57 782[5:Obv:781.0] || -> .
% 0.19/0.57 812[4:Spt:782.0,19.1,63.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.19/0.57 813[4:Spt:782.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.57 815[4:MRR:16.1,812.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.57 816[4:MRR:14.1,812.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.57 817[4:MRR:12.1,812.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.57 820[4:MRR:15.0,812.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.57 821[4:MRR:13.0,812.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.57 822[4:MRR:11.0,812.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.57 853[4:SpR:820.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.57 855[4:Rew:815.0,853.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.57 861[4:SpR:822.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.57 863[4:Rew:817.0,861.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.57 869[4:SpR:855.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.57 871[4:Rew:53.0,869.0] || -> equal(identity,sk_c11)**.
% 0.19/0.57 873[4:Rew:871.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.57 874[4:Rew:871.0,604.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.57 877[4:Rew:871.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.19/0.57 880[4:Rew:873.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.57 881[4:Rew:873.0,863.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.57 887[4:Rew:880.0,653.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.19/0.57 889[4:Rew:880.0,821.0] || -> equal(multiply(sk_c4,sk_c10),sk_c10)**.
% 0.19/0.57 897[4:Rew:881.0,816.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.19/0.57 902[4:Rew:881.0,57.4] || 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) -> .
% 0.19/0.57 908[4:Rew:881.0,887.0] || -> equal(inverse(sk_c11),sk_c2)**.
% 0.19/0.57 910[4:Rew:874.0,889.0,881.0,889.0] || -> equal(sk_c4,sk_c11)**.
% 0.19/0.57 911[4:Rew:910.0,897.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.19/0.57 912[4:Rew:908.0,911.0] || -> equal(sk_c2,sk_c11)**.
% 0.19/0.57 913[4:Rew:912.0,908.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.19/0.57 961[4:Rew:874.0,902.4] || 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) -> .
% 0.19/0.57 991[4:SpR:877.0,95.0] || -> equal(multiply(inverse(inverse(u)),sk_c11),u)**.
% 0.19/0.57 999[4:Rew:874.0,991.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.57 1006[4:SpR:999.0,877.0] || -> equal(multiply(u,inverse(u)),sk_c11)**.
% 0.19/0.57 1403[4:SpL:877.0,961.0] || 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) -> .
% 0.19/0.57 1413[4:Rew:877.0,1403.1,999.0,1403.1,913.0,1403.0] || equal(sk_c11,u) equal(sk_c11,u) equal(inverse(v),u) equal(multiply(v,u),sk_c11)** equal(u,sk_c11) -> .
% 0.19/0.57 1414[4:Obv:1413.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c11)** equal(v,sk_c11) -> .
% 0.19/0.57 1652[4:SpL:1006.0,1414.1] || equal(inverse(u),inverse(u))* equal(sk_c11,sk_c11) equal(inverse(u),sk_c11) -> .
% 0.19/0.57 1674[4:Obv:1652.1] || equal(inverse(u),sk_c11)** -> .
% 0.19/0.57 1675[4:UnC:1674.0,999.0] || -> .
% 0.19/0.57 1681[3:Spt:1675.0,49.1,61.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.19/0.57 1682[3:Spt:1675.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.57 1684[3:MRR:46.1,1681.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.57 1686[3:MRR:42.1,1681.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.57 1689[3:MRR:45.0,1681.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.57 1691[3:MRR:41.0,1681.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.57 1713[3:SpR:1689.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.57 1715[3:Rew:1684.0,1713.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.57 1721[3:SpR:1691.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.57 1723[3:Rew:1686.0,1721.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.57 1729[3:SpR:1715.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.57 1731[3:Rew:53.0,1729.0] || -> equal(identity,sk_c11)**.
% 0.19/0.57 1732[3:Rew:1731.0,604.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.57 1733[3:Rew:1731.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.57 1738[3:Rew:1732.0,1691.0] || -> equal(sk_c3,sk_c10)**.
% 0.19/0.57 1740[3:Rew:1738.0,1686.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.19/0.57 1743[3:Rew:1733.0,58.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.57 1744[3:Rew:1733.0,1723.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.57 1752[3:Rew:1743.0,60.0] || equal(inverse(u),sk_c10)** 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)** -> .
% 0.19/0.57 1763[3:Rew:1744.0,1740.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.19/0.57 1764[3:Rew:1744.0,1743.0] || -> equal(sk_c9,sk_c11)**.
% 0.19/0.57 1808[3:Rew:1764.0,1752.5,1732.0,1752.5,1744.0,1752.5,1732.0,1752.4,1764.0,1752.4,1744.0,1752.3,1764.0,1752.2,1763.0,1752.1,1744.0,1752.0] || equal(inverse(u),sk_c11)** equal(sk_c11,u) equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) equal(sk_c11,sk_c11) -> .
% 0.19/0.57 1809[3:Obv:1808.5] || equal(inverse(u),sk_c11)**+ equal(inverse(v),sk_c11)** equal(sk_c11,u) equal(v,sk_c11) -> .
% 0.19/0.57 2014[3:SpL:1763.0,1809.0] || equal(sk_c11,sk_c11) equal(inverse(u),sk_c11)** equal(sk_c11,sk_c11) equal(u,sk_c11) -> .
% 0.19/0.57 2016[3:Obv:2014.2] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.19/0.57 2018[3:SpL:1763.0,2016.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.19/0.57 2020[3:Obv:2018.1] || -> .
% 0.19/0.57 2021[2:Spt:2020.0,29.1,58.0] || equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.19/0.57 2022[2:Spt:2020.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.57 2024[2:MRR:26.1,2021.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.57 2025[2:MRR:24.1,2021.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.57 2026[2:MRR:22.1,2021.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.57 2029[2:MRR:25.1,2021.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.57 2030[2:MRR:23.1,2021.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.57 2031[2:MRR:21.1,2021.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.57 2050[2:SpR:2029.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.57 2052[2:Rew:2024.0,2050.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.57 2054[2:SpR:2030.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.19/0.57 2056[2:Rew:2025.0,2054.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.19/0.57 2058[2:SpR:2031.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.57 2060[2:Rew:2026.0,2058.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.57 2066[2:SpR:2052.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.57 2068[2:Rew:53.0,2066.0] || -> equal(identity,sk_c11)**.
% 0.19/0.57 2069[2:Rew:2068.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.57 2070[2:Rew:2068.0,604.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.57 2075[2:Rew:2069.0,2060.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.57 2077[2:Rew:2069.0,2021.0] || equal(sk_c9,sk_c10)** -> .
% 0.19/0.57 2083[2:Rew:2075.0,2030.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.19/0.57 2092[2:Rew:2075.0,2056.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.19/0.57 2093[2:Rew:2075.0,2077.0] || equal(sk_c9,sk_c11)** -> .
% 0.19/0.57 2105[2:Rew:2070.0,2083.0] || -> equal(sk_c9,sk_c4)**.
% 0.19/0.57 2106[2:Rew:2105.0,2093.0] || equal(sk_c4,sk_c11)** -> .
% 0.19/0.57 2107[2:Rew:2069.0,2092.0,2105.0,2092.0] || -> equal(sk_c4,sk_c11)**.
% 0.19/0.57 2108[2:MRR:2107.0,2106.0] || -> .
% 0.19/0.57 2139[1:Spt:2108.0,55.3,55.4,55.5,55.9,55.10,55.11,55.12] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c9) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c9),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.19/0.57 2141[2:Spt:28.1] || -> equal(multiply(sk_c11,sk_c9),sk_c10)**.
% 0.19/0.57 2142[2:Rew:2141.0,2139.6] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c9) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c9),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** equal(sk_c10,sk_c10) -> .
% 0.19/0.57 2144[2:Obv:2142.6] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c9) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c9),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.19/0.57 2147[2:SpR:2141.0,95.0] || -> equal(multiply(inverse(sk_c11),sk_c10),sk_c9)**.
% 0.19/0.57 2149[3:Spt:19.1] || -> equal(inverse(sk_c1),sk_c11)**.
% 0.19/0.57 2150[3:SpR:2149.0,95.0] || -> equal(multiply(sk_c11,multiply(sk_c1,u)),u)**.
% 0.19/0.57 2152[4:Spt:49.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.57 2153[4:SpR:2152.0,95.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.19/0.57 2155[5:Spt:9.1] || -> equal(multiply(sk_c1,sk_c11),sk_c10)**.
% 0.19/0.57 2157[5:SpR:2155.0,95.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c11)**.
% 0.19/0.57 2159[5:Rew:2149.0,2157.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.57 2160[6:Spt:39.1] || -> equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 2162[6:SpR:2160.0,95.0] || -> equal(multiply(inverse(sk_c2),sk_c11),sk_c9)**.
% 0.19/0.57 2164[6:Rew:2152.0,2162.0] || -> equal(multiply(sk_c9,sk_c11),sk_c9)**.
% 0.19/0.57 2166[5:SpR:2159.0,95.0] || -> equal(multiply(inverse(sk_c11),sk_c11),sk_c10)**.
% 0.19/0.57 2168[5:Rew:53.0,2166.0] || -> equal(identity,sk_c10)**.
% 0.19/0.57 2169[5:Rew:2168.0,604.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.19/0.57 2170[5:Rew:2168.0,52.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.19/0.57 2171[5:Rew:2168.0,53.0] || -> equal(multiply(inverse(u),u),sk_c10)**.
% 0.19/0.57 2173[5:Rew:2169.0,2147.0] || -> equal(inverse(sk_c11),sk_c9)**.
% 0.19/0.57 2175[5:Rew:2169.0,2144.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c11) equal(u,sk_c9) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.19/0.57 2183[5:SpR:2173.0,95.0] || -> equal(multiply(sk_c9,multiply(sk_c11,u)),u)**.
% 0.19/0.57 2186[6:SpR:2164.0,95.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c11)**.
% 0.19/0.57 2188[6:Rew:2171.0,2186.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.57 2189[6:Rew:2188.0,2141.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.19/0.57 2190[6:Rew:2188.0,2155.0] || -> equal(multiply(sk_c1,sk_c11),sk_c11)**.
% 0.19/0.57 2192[6:Rew:2188.0,2170.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.57 2193[6:Rew:2188.0,2169.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.57 2196[6:Rew:2188.0,2175.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c11) equal(u,sk_c9) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.19/0.57 2197[6:Rew:2192.0,2189.0] || -> equal(sk_c9,sk_c11)**.
% 0.19/0.57 2208[6:Rew:2193.0,2190.0] || -> equal(sk_c11,sk_c1)**.
% 0.19/0.57 2209[6:Rew:2208.0,2149.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.57 2210[6:Rew:2208.0,2188.0] || -> equal(sk_c10,sk_c1)**.
% 0.19/0.57 2213[6:Rew:2208.0,2197.0] || -> equal(sk_c9,sk_c1)**.
% 0.19/0.57 2216[6:Rew:2208.0,2193.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.57 2228[6:Rew:2216.0,2196.5,2208.0,2196.5,2210.0,2196.5,2216.0,2196.4,2213.0,2196.4,2208.0,2196.4,2213.0,2196.3,2208.0,2196.2,2213.0,2196.1,2208.0,2196.0] || 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) -> .
% 0.19/0.57 2229[6:Con:2228.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.57 2244[6:SpL:2209.0,2229.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.57 2245[6:Obv:2244.1] || -> .
% 0.19/0.57 2246[6:Spt:2245.0,39.1,2160.0] || equal(multiply(sk_c2,sk_c9),sk_c11)** -> .
% 0.19/0.57 2247[6:Spt:2245.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.57 2250[6:MRR:34.1,2246.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.57 2260[5:Rew:2169.0,33.0] || -> equal(sk_c9,sk_c4) equal(multiply(sk_c2,sk_c9),sk_c11)**.
% 0.19/0.57 2261[6:MRR:2260.1,2246.0] || -> equal(sk_c9,sk_c4)**.
% 0.19/0.57 2264[6:Rew:2261.0,2141.0] || -> equal(multiply(sk_c11,sk_c4),sk_c10)**.
% 0.19/0.57 2265[6:Rew:2261.0,2246.0] || equal(multiply(sk_c2,sk_c4),sk_c11)** -> .
% 0.19/0.57 2266[6:Rew:2261.0,2183.0] || -> equal(multiply(sk_c4,multiply(sk_c11,u)),u)**.
% 0.19/0.57 2268[6:Rew:2261.0,2153.0] || -> equal(multiply(sk_c4,multiply(sk_c2,u)),u)**.
% 0.19/0.57 2279[6:SpR:2250.0,95.0] || -> equal(multiply(sk_c10,multiply(sk_c4,u)),u)**.
% 0.19/0.57 2281[6:Rew:2170.0,2279.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.57 2282[6:Rew:2281.0,2268.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.57 2283[6:Rew:2281.0,2266.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.57 2285[6:Rew:2282.0,2265.0] || equal(sk_c4,sk_c11)** -> .
% 0.19/0.57 2286[6:Rew:2283.0,2264.0] || -> equal(sk_c4,sk_c10)**.
% 0.19/0.57 2287[6:Rew:2283.0,2150.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.57 2295[6:Rew:2286.0,2285.0] || equal(sk_c10,sk_c11)** -> .
% 0.19/0.57 2297[6:Rew:2287.0,2155.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.57 2298[6:MRR:2297.0,2295.0] || -> .
% 0.19/0.57 2300[5:Spt:2298.0,9.1,2155.0] || equal(multiply(sk_c1,sk_c11),sk_c10)** -> .
% 0.19/0.57 2301[5:Spt:2298.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.57 2303[5:MRR:6.1,2300.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.57 2305[5:MRR:2.1,2300.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.57 2308[5:MRR:5.1,2300.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.57 2310[5:MRR:1.1,2300.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.57 2334[5:SpR:2308.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.57 2336[5:Rew:2303.0,2334.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.57 2342[5:SpR:2310.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.57 2344[5:Rew:2305.0,2342.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.57 2350[5:SpR:2336.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.57 2352[5:Rew:53.0,2350.0] || -> equal(identity,sk_c11)**.
% 0.19/0.57 2353[5:Rew:2352.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.57 2358[5:Rew:2353.0,2344.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.57 2361[5:Rew:2353.0,2150.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.57 2376[5:Rew:2358.0,2300.0] || equal(multiply(sk_c1,sk_c11),sk_c11)** -> .
% 0.19/0.57 2408[5:Rew:2361.0,2376.0] || equal(sk_c11,sk_c11)* -> .
% 0.19/0.57 2409[5:Obv:2408.0] || -> .
% 0.19/0.57 2428[4:Spt:2409.0,49.1,2152.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.19/0.57 2429[4:Spt:2409.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.57 2431[4:MRR:46.1,2428.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.57 2433[4:MRR:42.1,2428.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 2436[4:MRR:45.0,2428.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 2438[4:MRR:41.0,2428.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 2460[4:SpR:2436.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 2462[4:Rew:2431.0,2460.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 2468[4:SpR:2438.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 2470[4:Rew:2433.0,2468.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 2476[4:SpR:2462.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 2478[4:Rew:53.0,2476.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 2479[4:Rew:2478.0,604.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 2480[4:Rew:2478.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 2486[4:Rew:2479.0,2144.5] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c9) equal(inverse(w),sk_c11)** equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c9),sk_c11)** equal(w,sk_c10) -> .
% 0.19/0.58 2490[4:Rew:2480.0,2141.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.58 2491[4:Rew:2480.0,2470.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.58 2493[4:Rew:2480.0,2150.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.58 2507[4:Rew:2491.0,2490.0] || -> equal(sk_c9,sk_c11)**.
% 0.19/0.58 2550[4:Rew:2491.0,2486.5,2479.0,2486.4,2507.0,2486.4,2479.0,2486.3,2491.0,2486.3,2507.0,2486.3,2507.0,2486.1,2491.0,2486.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(w,sk_c11) -> .
% 0.19/0.58 2551[4:Con:2550.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.19/0.58 2579[4:SpR:2493.0,2479.0] || -> equal(sk_c11,sk_c1)**.
% 0.19/0.58 2581[4:Rew:2579.0,2149.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.58 2596[4:Rew:2579.0,2551.0] || equal(inverse(u),sk_c1)** equal(u,sk_c11) -> .
% 0.19/0.58 2598[4:Rew:2579.0,2596.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.58 2657[4:SpL:2581.0,2598.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.58 2659[4:Obv:2657.1] || -> .
% 0.19/0.58 2660[3:Spt:2659.0,19.1,2149.0] || equal(inverse(sk_c1),sk_c11)** -> .
% 0.19/0.58 2661[3:Spt:2659.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.19/0.58 2663[3:MRR:16.1,2660.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 2664[3:MRR:14.1,2660.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.58 2665[3:MRR:12.1,2660.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 2668[3:MRR:15.0,2660.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 2669[3:MRR:13.0,2660.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.58 2670[3:MRR:11.0,2660.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 2692[3:SpR:2668.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 2694[3:Rew:2663.0,2692.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 2700[3:SpR:2670.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 2702[3:Rew:2665.0,2700.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 2708[3:SpR:2694.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 2710[3:Rew:53.0,2708.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 2711[3:Rew:2710.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 2712[3:Rew:2710.0,604.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 2715[3:Rew:2711.0,2141.0] || -> equal(sk_c9,sk_c10)**.
% 0.19/0.58 2717[3:Rew:2711.0,2702.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.58 2722[3:Rew:2715.0,2669.0] || -> equal(multiply(sk_c4,sk_c10),sk_c10)**.
% 0.19/0.58 2725[3:Rew:2715.0,2144.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c11) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c9),sk_c11)** equal(multiply(w,sk_c11),sk_c10)** -> .
% 0.19/0.58 2728[3:Rew:2717.0,2664.0] || -> equal(inverse(sk_c4),sk_c11)**.
% 0.19/0.58 2733[3:Rew:2717.0,2715.0] || -> equal(sk_c9,sk_c11)**.
% 0.19/0.58 2734[3:Rew:2712.0,2722.0,2717.0,2722.0] || -> equal(sk_c4,sk_c11)**.
% 0.19/0.58 2735[3:Rew:2734.0,2728.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.19/0.58 2774[3:Rew:2712.0,2725.5,2717.0,2725.5,2712.0,2725.4,2733.0,2725.4,2712.0,2725.3,2717.0,2725.3,2733.0,2725.3,2717.0,2725.1,2717.0,2725.0] || equal(inverse(u),sk_c11)** equal(inverse(v),sk_c11)** equal(inverse(w),sk_c11)** equal(u,sk_c11) equal(v,sk_c11) equal(w,sk_c11) -> .
% 0.19/0.58 2775[3:Con:2774.1] || equal(inverse(u),sk_c11)** equal(u,sk_c11) -> .
% 0.19/0.58 2848[3:SpL:2735.0,2775.0] || equal(sk_c11,sk_c11)* equal(sk_c11,sk_c11)* -> .
% 0.19/0.58 2850[3:Obv:2848.1] || -> .
% 0.19/0.58 2851[2:Spt:2850.0,28.1,2141.0] || equal(multiply(sk_c11,sk_c9),sk_c10)** -> .
% 0.19/0.58 2852[2:Spt:2850.0,28.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.58 2853[2:MRR:26.1,2851.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.58 2854[2:MRR:24.1,2851.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.19/0.58 2855[2:MRR:22.1,2851.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.19/0.58 2859[2:MRR:25.1,2851.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.19/0.58 2860[2:MRR:23.1,2851.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.19/0.58 2861[2:MRR:21.1,2851.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.19/0.58 2880[2:SpR:2859.0,95.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.19/0.58 2882[2:Rew:2853.0,2880.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.19/0.58 2884[2:SpR:2860.0,95.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.19/0.58 2886[2:Rew:2854.0,2884.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.19/0.58 2888[2:SpR:2861.0,95.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.19/0.58 2890[2:Rew:2855.0,2888.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.19/0.58 2899[2:SpR:2882.0,95.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.19/0.58 2901[2:Rew:53.0,2899.0] || -> equal(identity,sk_c11)**.
% 0.19/0.58 2902[2:Rew:2901.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.19/0.58 2903[2:Rew:2901.0,604.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.19/0.58 2906[2:Rew:2902.0,2890.0] || -> equal(sk_c10,sk_c11)**.
% 0.19/0.58 2908[2:Rew:2902.0,2851.0] || equal(sk_c9,sk_c10)** -> .
% 0.19/0.58 2914[2:Rew:2906.0,2860.0] || -> equal(multiply(sk_c4,sk_c11),sk_c9)**.
% 0.19/0.58 2919[2:Rew:2906.0,2886.0] || -> equal(multiply(sk_c11,sk_c9),sk_c11)**.
% 0.19/0.58 2920[2:Rew:2906.0,2908.0] || equal(sk_c9,sk_c11)** -> .
% 0.19/0.58 2932[2:Rew:2903.0,2914.0] || -> equal(sk_c9,sk_c4)**.
% 0.19/0.58 2933[2:Rew:2932.0,2920.0] || equal(sk_c4,sk_c11)** -> .
% 0.19/0.58 2934[2:Rew:2902.0,2919.0,2932.0,2919.0] || -> equal(sk_c4,sk_c11)**.
% 0.19/0.58 2935[2:MRR:2934.0,2933.0] || -> .
% 0.19/0.58 % SZS output end Refutation
% 0.19/0.58 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_5 prove_this_6 prove_this_9 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_19 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_39 prove_this_41 prove_this_42 prove_this_45 prove_this_46 prove_this_49 prove_this_51 left_identity left_inverse associativity
% 0.19/0.58
%------------------------------------------------------------------------------