TSTP Solution File: GRP362-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP362-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:47:02 EDT 2022
% Result : Unsatisfiable 0.37s 0.55s
% Output : Refutation 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP362-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 11:03:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.37/0.55
% 0.37/0.55 SPASS V 3.9
% 0.37/0.55 SPASS beiseite: Proof found.
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.55 SPASS derived 1403 clauses, backtracked 652 clauses, performed 13 splits and kept 1150 clauses.
% 0.37/0.55 SPASS allocated 64040 KBytes.
% 0.37/0.55 SPASS spent 0:00:00.19 on the problem.
% 0.37/0.55 0:00:00.04 for the input.
% 0.37/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.37/0.55 0:00:00.01 for inferences.
% 0.37/0.55 0:00:00.00 for the backtracking.
% 0.37/0.55 0:00:00.11 for the reduction.
% 0.37/0.55
% 0.37/0.55
% 0.37/0.55 Here is a proof with depth 6, length 341 :
% 0.37/0.55 % SZS output start Refutation
% 0.37/0.55 1[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.37/0.55 2[0:Inp] || -> equal(multiply(sk_c10,sk_c4),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c10).
% 0.37/0.55 3[0:Inp] || -> equal(multiply(sk_c3,sk_c10),sk_c4)** equal(multiply(sk_c9,sk_c8),sk_c10).
% 0.37/0.55 4[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.37/0.55 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(multiply(sk_c9,sk_c8),sk_c10).
% 0.37/0.55 6[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.37/0.55 8[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.37/0.55 9[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10)** equal(multiply(sk_c9,sk_c8),sk_c10).
% 0.37/0.55 10[0:Inp] || -> equal(inverse(sk_c10),sk_c9)** equal(inverse(sk_c9),sk_c10).
% 0.37/0.55 11[0:Inp] || -> equal(inverse(sk_c9),sk_c10) equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.37/0.55 12[0:Inp] || -> equal(inverse(sk_c9),sk_c10) equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.37/0.55 13[0:Inp] || -> equal(inverse(sk_c3),sk_c10)** equal(inverse(sk_c9),sk_c10).
% 0.37/0.55 14[0:Inp] || -> equal(inverse(sk_c9),sk_c10) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 15[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c9),sk_c10).
% 0.37/0.55 18[0:Inp] || -> equal(inverse(sk_c9),sk_c10) equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.37/0.55 19[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.37/0.55 20[0:Inp] || -> equal(multiply(sk_c10,sk_c4),sk_c9)** equal(multiply(sk_c10,sk_c8),sk_c9).
% 0.37/0.55 21[0:Inp] || -> equal(multiply(sk_c3,sk_c10),sk_c4) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.37/0.55 22[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.37/0.55 23[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.37/0.55 24[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.37/0.55 27[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.37/0.55 28[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.37/0.55 32[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.37/0.55 33[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.37/0.55 34[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c8) equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.37/0.55 37[0:Inp] || -> equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.37/0.55 41[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.37/0.55 42[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.37/0.55 43[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.37/0.55 44[0:Inp] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.37/0.55 46[0:Inp] || -> equal(inverse(sk_c10),sk_c9)** equal(inverse(sk_c1),sk_c10).
% 0.37/0.55 50[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 51[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c10)**.
% 0.37/0.55 52[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c6,sk_c9),sk_c8)**.
% 0.37/0.55 55[0:Inp] || equal(multiply(sk_c9,sk_c8),sk_c10) equal(inverse(sk_c9),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c10,u),sk_c9)** equal(multiply(v,sk_c10),u)* equal(inverse(v),sk_c10) equal(inverse(sk_c10),sk_c9) equal(multiply(sk_c10,w),sk_c9)** equal(multiply(x,sk_c10),w)* equal(inverse(x),sk_c10) equal(multiply(y,z),sk_c8)** equal(inverse(y),z) equal(multiply(z,sk_c9),sk_c8)** equal(inverse(x1),sk_c10) equal(multiply(x1,sk_c8),sk_c10)** -> .
% 0.37/0.55 56[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.37/0.55 57[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.37/0.55 58[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.37/0.55 59[0:Con:55.7] || equal(inverse(u),v) equal(inverse(w),sk_c10) equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c9),sk_c10) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c10),x)* equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c10,x),sk_c9)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c10) -> .
% 0.37/0.55 60[1:Spt:59.1,59.5,59.7] || equal(inverse(u),sk_c10) equal(multiply(u,sk_c10),v)*+ equal(multiply(sk_c10,v),sk_c9)** -> .
% 0.37/0.55 61[1:EqR:60.1] || equal(inverse(u),sk_c10) equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.37/0.55 62[2:Spt:10.1] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.37/0.55 64[3:Spt:19.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.37/0.55 66[4:Spt:1.1] || -> equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.37/0.55 68[5:Spt:46.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.37/0.55 70[6:Spt:37.1] || -> equal(multiply(sk_c1,sk_c10),sk_c2)**.
% 0.37/0.55 77[7:Spt:28.1] || -> equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.37/0.55 80[2:SpR:62.0,57.0] || -> equal(multiply(sk_c10,sk_c9),identity)**.
% 0.37/0.55 81[5:SpR:68.0,57.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.37/0.55 82[1:SpL:57.0,60.1] || equal(inverse(inverse(sk_c10)),sk_c10) equal(identity,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.37/0.55 88[3:SpR:64.0,58.0] || -> equal(multiply(sk_c10,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.37/0.55 90[2:SpR:80.0,58.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),multiply(identity,u))**.
% 0.37/0.55 91[5:SpR:81.0,58.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.37/0.55 92[4:SpR:66.0,58.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.37/0.55 94[0:SpR:57.0,58.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.37/0.55 96[2:Rew:56.0,90.0] || -> equal(multiply(sk_c10,multiply(sk_c9,u)),u)**.
% 0.37/0.55 97[5:Rew:56.0,91.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.37/0.55 98[0:Rew:56.0,94.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.37/0.55 102[4:SpR:66.0,96.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.37/0.55 109[6:SpR:70.0,97.0] || -> equal(multiply(sk_c10,sk_c2),sk_c10)**.
% 0.37/0.55 110[7:Rew:77.0,109.0] || -> equal(sk_c10,sk_c9)**.
% 0.37/0.55 118[7:Rew:110.0,80.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.37/0.55 121[7:Rew:110.0,102.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.37/0.55 123[7:Rew:110.0,61.0] || equal(inverse(u),sk_c9) equal(multiply(sk_c10,multiply(u,sk_c10)),sk_c9)** -> .
% 0.37/0.55 134[7:Rew:118.0,121.0] || -> equal(identity,sk_c8)**.
% 0.37/0.55 136[7:Rew:134.0,57.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.37/0.55 144[7:Rew:110.0,123.1] || equal(inverse(u),sk_c9) equal(multiply(sk_c9,multiply(u,sk_c9)),sk_c9)** -> .
% 0.37/0.55 177[0:SpR:98.0,98.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.37/0.55 181[7:SpR:136.0,98.0] || -> equal(multiply(inverse(inverse(u)),sk_c8),u)**.
% 0.37/0.55 204[7:Rew:177.0,181.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.55 241[7:SpR:177.0,204.0] || -> equal(multiply(u,sk_c8),inverse(inverse(u)))**.
% 0.37/0.55 243[0:SpR:177.0,98.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.37/0.55 248[7:Rew:204.0,241.0] || -> equal(inverse(inverse(u)),u)**.
% 0.37/0.55 434[7:SpL:136.0,144.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.37/0.55 450[7:Rew:204.0,434.1,248.0,434.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.37/0.55 451[7:Obv:450.1] || -> .
% 0.37/0.55 457[7:Spt:451.0,28.1,77.0] || equal(multiply(sk_c10,sk_c2),sk_c9)** -> .
% 0.37/0.55 458[7:Spt:451.0,28.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 459[7:Rew:109.0,457.0] || equal(sk_c10,sk_c9)** -> .
% 0.37/0.55 462[6:Rew:109.0,33.1] || -> equal(inverse(sk_c5),sk_c6)** equal(sk_c10,sk_c9).
% 0.37/0.55 463[7:MRR:462.1,459.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 471[6:Rew:109.0,32.1] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(sk_c10,sk_c9).
% 0.37/0.55 472[7:MRR:471.1,459.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 499[7:SpR:463.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.37/0.55 514[5:SpR:81.0,98.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.37/0.55 516[7:Rew:458.0,514.0] || -> equal(multiply(sk_c9,identity),sk_c1)**.
% 0.37/0.55 523[2:SpR:80.0,98.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c9)**.
% 0.37/0.55 525[7:Rew:458.0,523.0] || -> equal(multiply(sk_c9,identity),sk_c9)**.
% 0.37/0.55 526[7:Rew:516.0,525.0] || -> equal(sk_c1,sk_c9)**.
% 0.37/0.55 532[7:Rew:526.0,516.0] || -> equal(multiply(sk_c9,identity),sk_c9)**.
% 0.37/0.55 540[3:SpR:64.0,98.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c8)**.
% 0.37/0.55 542[7:Rew:458.0,540.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.37/0.55 546[7:SpR:472.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.37/0.55 550[7:Rew:499.0,546.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.55 552[7:Rew:550.0,88.0] || -> equal(multiply(sk_c10,u),multiply(sk_c9,u))**.
% 0.37/0.55 557[7:Rew:552.0,80.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.37/0.55 576[7:Rew:542.0,557.0] || -> equal(identity,sk_c8)**.
% 0.37/0.55 580[7:Rew:576.0,532.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.37/0.55 585[7:Rew:66.0,580.0] || -> equal(sk_c10,sk_c9)**.
% 0.37/0.55 586[7:MRR:585.0,459.0] || -> .
% 0.37/0.55 595[6:Spt:586.0,37.1,70.0] || equal(multiply(sk_c1,sk_c10),sk_c2)** -> .
% 0.37/0.55 596[6:Spt:586.0,37.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 598[6:Rew:596.0,514.0] || -> equal(multiply(sk_c9,identity),sk_c1)**.
% 0.37/0.55 599[6:Rew:598.0,523.0,596.0,523.0] || -> equal(sk_c1,sk_c9)**.
% 0.37/0.55 603[6:Rew:596.0,540.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.37/0.55 604[6:Rew:599.0,595.0] || equal(multiply(sk_c9,sk_c10),sk_c2)** -> .
% 0.37/0.55 609[6:Rew:599.0,42.1] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c9,sk_c10),sk_c2)**.
% 0.37/0.55 610[6:MRR:609.1,604.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 617[6:Rew:599.0,41.1] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(multiply(sk_c9,sk_c10),sk_c2).
% 0.37/0.55 618[6:MRR:617.1,604.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 624[6:Rew:596.0,82.0] || equal(inverse(sk_c9),sk_c10) equal(identity,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.37/0.55 625[6:Rew:62.0,624.0] || equal(sk_c10,sk_c10) equal(identity,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.37/0.55 626[6:Obv:625.0] || equal(identity,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.37/0.55 635[6:SpR:610.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.37/0.55 668[6:SpR:618.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.37/0.55 672[6:Rew:635.0,668.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.55 673[6:Rew:672.0,92.0] || -> equal(multiply(sk_c10,u),multiply(sk_c9,u))**.
% 0.37/0.55 680[6:Rew:673.0,80.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.37/0.55 690[6:Rew:673.0,626.1] || equal(identity,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.37/0.55 705[6:Rew:603.0,680.0] || -> equal(identity,sk_c8)**.
% 0.37/0.55 709[6:Rew:705.0,57.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.37/0.55 718[6:Rew:705.0,690.0] || equal(sk_c8,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.37/0.55 759[6:SpR:709.0,243.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.55 865[6:SpL:759.0,718.1] || equal(sk_c8,sk_c8)* equal(sk_c9,sk_c9) -> .
% 0.37/0.55 868[6:Obv:865.1] || -> .
% 0.37/0.55 871[5:Spt:868.0,46.1,68.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.37/0.55 872[5:Spt:868.0,46.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 875[5:Rew:872.0,540.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.37/0.55 880[5:MRR:51.1,871.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 885[5:MRR:50.0,871.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 889[5:Rew:62.0,82.0,872.0,82.0] || equal(sk_c10,sk_c10) equal(identity,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.37/0.55 890[5:Obv:889.0] || equal(identity,u) equal(multiply(sk_c10,u),sk_c9)** -> .
% 0.37/0.55 901[5:SpR:880.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.37/0.55 938[5:SpR:885.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.37/0.55 942[5:Rew:901.0,938.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.55 944[5:Rew:942.0,88.0] || -> equal(multiply(sk_c10,u),multiply(sk_c9,u))**.
% 0.37/0.55 950[5:Rew:944.0,80.0] || -> equal(multiply(sk_c9,sk_c9),identity)**.
% 0.37/0.55 956[5:Rew:944.0,890.1] || equal(identity,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.37/0.55 976[5:Rew:875.0,950.0] || -> equal(identity,sk_c8)**.
% 0.37/0.55 979[5:Rew:976.0,57.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.37/0.55 988[5:Rew:976.0,956.0] || equal(sk_c8,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.37/0.55 1040[5:SpR:979.0,243.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.55 1130[5:SpL:1040.0,988.1] || equal(sk_c8,sk_c8)* equal(sk_c9,sk_c9) -> .
% 0.37/0.55 1133[5:Obv:1130.1] || -> .
% 0.37/0.55 1136[4:Spt:1133.0,1.1,66.0] || equal(multiply(sk_c9,sk_c8),sk_c10)** -> .
% 0.37/0.55 1137[4:Spt:1133.0,1.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 1145[4:MRR:6.1,1136.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 1147[4:MRR:9.1,1136.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.37/0.55 1149[4:MRR:5.1,1136.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 1164[4:SpR:1145.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.37/0.55 1169[4:SpR:1147.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.37/0.55 1193[4:SpR:1149.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.37/0.55 1197[4:Rew:1164.0,1193.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.55 1198[4:Rew:1197.0,88.0] || -> equal(multiply(sk_c10,u),multiply(sk_c9,u))**.
% 0.37/0.55 1199[4:Rew:1197.0,1169.0] || -> equal(multiply(sk_c10,u),multiply(sk_c7,u))**.
% 0.37/0.55 1202[4:Rew:1198.0,64.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.37/0.55 1217[4:Rew:1202.0,1136.0] || equal(sk_c10,sk_c9)** -> .
% 0.37/0.55 1223[4:Rew:1198.0,1199.0] || -> equal(multiply(sk_c7,u),multiply(sk_c9,u))**.
% 0.37/0.55 1224[4:Rew:1223.0,1147.0] || -> equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.37/0.55 1225[4:Rew:1202.0,1224.0] || -> equal(sk_c10,sk_c9)**.
% 0.37/0.55 1226[4:MRR:1225.0,1217.0] || -> .
% 0.37/0.55 1231[3:Spt:1226.0,19.1,64.0] || equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.37/0.55 1232[3:Spt:1226.0,19.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 1238[3:MRR:24.1,1231.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 1239[3:MRR:22.1,1231.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.37/0.55 1240[3:MRR:27.1,1231.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.37/0.55 1242[3:MRR:23.1,1231.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 1243[3:MRR:21.1,1231.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.37/0.55 1244[3:MRR:20.1,1231.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.37/0.55 1255[3:SpR:1238.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.37/0.55 1260[3:SpR:1240.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.37/0.55 1276[3:SpR:1242.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.37/0.55 1280[3:Rew:1255.0,1276.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.55 1281[3:Rew:1280.0,1260.0] || -> equal(multiply(sk_c10,u),multiply(sk_c7,u))**.
% 0.37/0.55 1287[3:Rew:1281.0,1244.0] || -> equal(multiply(sk_c7,sk_c4),sk_c9)**.
% 0.37/0.55 1297[3:Rew:1281.0,1231.0] || equal(multiply(sk_c7,sk_c8),sk_c9)** -> .
% 0.37/0.55 1298[3:Rew:1240.0,1297.0] || equal(sk_c10,sk_c9)** -> .
% 0.37/0.55 1300[3:SpR:1243.0,98.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.37/0.55 1302[3:Rew:1239.0,1300.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.37/0.55 1303[3:Rew:1287.0,1302.0,1281.0,1302.0] || -> equal(sk_c10,sk_c9)**.
% 0.37/0.55 1304[3:MRR:1303.0,1298.0] || -> .
% 0.37/0.55 1306[2:Spt:1304.0,10.1,62.0] || equal(inverse(sk_c9),sk_c10)** -> .
% 0.37/0.55 1307[2:Spt:1304.0,10.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 1309[2:MRR:15.1,1306.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 1310[2:MRR:13.1,1306.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.37/0.55 1311[2:MRR:18.0,1306.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.37/0.55 1313[2:MRR:14.0,1306.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 1314[2:MRR:12.0,1306.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.37/0.55 1315[2:MRR:11.0,1306.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.37/0.55 1324[2:SpR:1309.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.37/0.55 1329[2:SpR:1311.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.37/0.55 1336[2:SpR:1313.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.37/0.55 1340[2:Rew:1324.0,1336.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.55 1341[2:Rew:1340.0,1329.0] || -> equal(multiply(sk_c10,u),multiply(sk_c7,u))**.
% 0.37/0.55 1354[2:Rew:1341.0,1315.0] || -> equal(multiply(sk_c7,sk_c4),sk_c9)**.
% 0.37/0.55 1356[2:SpR:1314.0,98.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.37/0.55 1358[2:Rew:1310.0,1356.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.37/0.55 1359[2:Rew:1354.0,1358.0,1341.0,1358.0] || -> equal(sk_c10,sk_c9)**.
% 0.37/0.55 1360[2:Rew:1359.0,1307.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.37/0.55 1363[2:Rew:1359.0,1306.0] || equal(inverse(sk_c9),sk_c9)** -> .
% 0.37/0.55 1372[2:Rew:1360.0,1363.0] || equal(sk_c9,sk_c9)* -> .
% 0.37/0.55 1373[2:Obv:1372.0] || -> .
% 0.37/0.55 1388[1:Spt:1373.0,59.0,59.2,59.3,59.4,59.6,59.8,59.9] || equal(inverse(u),v) equal(inverse(sk_c10),sk_c9) equal(inverse(sk_c9),sk_c10) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c10) -> .
% 0.37/0.55 1394[2:Spt:10.1] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.37/0.55 1395[2:Rew:1394.0,1388.2] || equal(inverse(u),v) equal(inverse(sk_c10),sk_c9) equal(sk_c10,sk_c10) equal(multiply(u,v),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c10) -> .
% 0.37/0.55 1399[2:Obv:1395.2] || equal(inverse(u),v) equal(inverse(sk_c10),sk_c9) equal(multiply(u,v),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c10) -> .
% 0.37/0.55 1406[3:Spt:1.1] || -> equal(multiply(sk_c9,sk_c8),sk_c10)**.
% 0.37/0.55 1410[3:Rew:1406.0,1399.5] || equal(inverse(u),v) equal(inverse(sk_c10),sk_c9) equal(multiply(u,v),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c10,sk_c8),sk_c9)** equal(sk_c10,sk_c10) -> .
% 0.37/0.55 1411[3:Obv:1410.5] || equal(inverse(u),v) equal(inverse(sk_c10),sk_c9) equal(multiply(u,v),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.37/0.55 1415[3:SpR:1406.0,58.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.37/0.55 1416[3:SpR:1406.0,98.0] || -> equal(multiply(inverse(sk_c9),sk_c10),sk_c8)**.
% 0.37/0.55 1418[3:Rew:1394.0,1416.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.37/0.55 1419[4:Spt:19.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.37/0.55 1423[4:Rew:1419.0,1411.4] || equal(inverse(u),v) equal(inverse(sk_c10),sk_c9) equal(multiply(u,v),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** equal(sk_c9,sk_c9) -> .
% 0.37/0.55 1424[4:Obv:1423.4] || equal(inverse(u),v) equal(inverse(sk_c10),sk_c9) equal(multiply(u,v),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.37/0.55 1429[4:SpR:1419.0,98.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c8)**.
% 0.37/0.55 1431[5:Spt:46.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.37/0.55 1435[6:Spt:28.1] || -> equal(multiply(sk_c10,sk_c2),sk_c9)**.
% 0.37/0.55 1437[6:SpR:1435.0,98.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c2)**.
% 0.37/0.55 1439[6:Rew:1429.0,1437.0] || -> equal(sk_c2,sk_c8)**.
% 0.37/0.55 1443[6:Rew:1439.0,41.1] || -> equal(multiply(sk_c5,sk_c6),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c8)**.
% 0.37/0.55 1444[6:Rew:1439.0,43.1] || -> equal(multiply(sk_c6,sk_c9),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c8)**.
% 0.37/0.55 1447[6:Rew:1439.0,42.1] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c10),sk_c8)**.
% 0.37/0.55 1448[6:Rew:1439.0,44.1] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c8)**.
% 0.37/0.55 1471[0:SpR:57.0,243.0] || -> equal(multiply(u,identity),u)**.
% 0.37/0.55 1473[2:SpR:1394.0,57.0] || -> equal(multiply(sk_c10,sk_c9),identity)**.
% 0.37/0.55 1474[5:SpR:1431.0,57.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.37/0.55 1478[2:SpR:1473.0,98.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c9)**.
% 0.37/0.55 1480[2:Rew:1471.0,1478.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 1486[4:Rew:1480.0,1424.1] || equal(inverse(u),v) equal(sk_c9,sk_c9) equal(multiply(u,v),sk_c8)** equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.37/0.55 1490[4:Obv:1486.1] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c9),sk_c8)** -> .
% 0.37/0.55 1496[2:SpR:1480.0,57.0] || -> equal(multiply(sk_c9,sk_c10),identity)**.
% 0.37/0.55 1499[5:SpR:1474.0,98.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.37/0.55 1501[5:Rew:1480.0,1499.0] || -> equal(multiply(sk_c9,identity),sk_c1)**.
% 0.37/0.55 1502[5:Rew:1471.0,1501.0] || -> equal(sk_c1,sk_c9)**.
% 0.37/0.55 1508[6:Rew:1502.0,1444.1] || -> equal(multiply(sk_c6,sk_c9),sk_c8)** equal(multiply(sk_c9,sk_c10),sk_c8).
% 0.37/0.55 1509[6:Rew:1502.0,1443.1] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(multiply(sk_c9,sk_c10),sk_c8).
% 0.37/0.55 1512[6:Rew:1502.0,1448.1] || -> equal(inverse(sk_c7),sk_c10) equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.37/0.55 1513[6:Rew:1502.0,1447.1] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.37/0.55 1517[6:Rew:1496.0,1512.1] || -> equal(inverse(sk_c7),sk_c10)** equal(identity,sk_c8).
% 0.37/0.55 1518[6:Rew:1496.0,1513.1] || -> equal(inverse(sk_c5),sk_c6)** equal(identity,sk_c8).
% 0.37/0.55 1521[6:Rew:1496.0,1508.1] || -> equal(multiply(sk_c6,sk_c9),sk_c8)** equal(identity,sk_c8).
% 0.37/0.55 1522[6:Rew:1496.0,1509.1] || -> equal(multiply(sk_c5,sk_c6),sk_c8)** equal(identity,sk_c8).
% 0.37/0.55 1526[7:Spt:1517.1] || -> equal(identity,sk_c8)**.
% 0.37/0.55 1528[7:Rew:1526.0,57.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.37/0.55 1531[7:Rew:1526.0,1471.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.55 1574[7:SpR:1531.0,243.0] || -> equal(multiply(u,inverse(u)),sk_c8)**.
% 0.37/0.55 1611[7:SpL:1574.0,1490.1] || equal(inverse(u),inverse(u)) equal(sk_c8,sk_c8) equal(multiply(inverse(u),sk_c9),sk_c8)** -> .
% 0.37/0.55 1626[7:Obv:1611.1] || equal(multiply(inverse(u),sk_c9),sk_c8)** -> .
% 0.37/0.55 1627[7:UnC:1626.0,1528.0] || -> .
% 0.37/0.55 1630[7:Spt:1627.0,1517.1,1526.0] || equal(identity,sk_c8)** -> .
% 0.37/0.55 1631[7:Spt:1627.0,1517.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.37/0.55 1633[7:MRR:1518.1,1630.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 1636[7:MRR:1521.1,1630.0] || -> equal(multiply(sk_c6,sk_c9),sk_c8)**.
% 0.37/0.55 1637[7:MRR:1522.1,1630.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 1711[7:SpL:1637.0,1490.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c8,sk_c8) equal(multiply(sk_c6,sk_c9),sk_c8)** -> .
% 0.37/0.55 1745[7:Obv:1711.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c8)** -> .
% 0.37/0.55 1746[7:Rew:1636.0,1745.1,1633.0,1745.0] || equal(sk_c6,sk_c6)* equal(sk_c8,sk_c8) -> .
% 0.37/0.55 1747[7:Obv:1746.1] || -> .
% 0.37/0.55 1748[6:Spt:1747.0,28.1,1435.0] || equal(multiply(sk_c10,sk_c2),sk_c9)** -> .
% 0.37/0.55 1749[6:Spt:1747.0,28.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 1751[6:MRR:33.1,1748.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 1754[6:MRR:34.1,1748.0] || -> equal(multiply(sk_c6,sk_c9),sk_c8)**.
% 0.37/0.55 1755[6:MRR:32.1,1748.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 1802[6:SpL:1755.0,1490.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c8,sk_c8) equal(multiply(sk_c6,sk_c9),sk_c8)** -> .
% 0.37/0.55 1836[6:Obv:1802.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c8)** -> .
% 0.37/0.55 1837[6:Rew:1754.0,1836.1,1751.0,1836.0] || equal(sk_c6,sk_c6)* equal(sk_c8,sk_c8) -> .
% 0.37/0.55 1838[6:Obv:1837.1] || -> .
% 0.37/0.55 1839[5:Spt:1838.0,46.1,1431.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.37/0.55 1840[5:Spt:1838.0,46.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 1842[5:MRR:51.1,1839.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 1845[5:MRR:52.0,1839.0] || -> equal(multiply(sk_c6,sk_c9),sk_c8)**.
% 0.37/0.55 1846[5:MRR:50.0,1839.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 1891[5:SpL:1846.0,1490.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c8,sk_c8) equal(multiply(sk_c6,sk_c9),sk_c8)** -> .
% 0.37/0.55 1925[5:Obv:1891.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c8)** -> .
% 0.37/0.55 1926[5:Rew:1845.0,1925.1,1842.0,1925.0] || equal(sk_c6,sk_c6)* equal(sk_c8,sk_c8) -> .
% 0.37/0.55 1927[5:Obv:1926.1] || -> .
% 0.37/0.55 1928[4:Spt:1927.0,19.1,1419.0] || equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.37/0.55 1929[4:Spt:1927.0,19.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 1931[4:MRR:24.1,1928.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 1935[4:MRR:23.1,1928.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 1942[4:SpR:1931.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.37/0.55 1963[4:SpR:1935.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.37/0.55 1967[4:Rew:1942.0,1963.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.37/0.55 1968[4:Rew:1967.0,1415.0] || -> equal(multiply(sk_c10,u),multiply(sk_c9,u))**.
% 0.37/0.55 1972[4:Rew:1968.0,1418.0] || -> equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.37/0.55 1981[4:Rew:1968.0,1928.0] || equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.37/0.55 1982[4:Rew:1496.0,1972.0] || -> equal(identity,sk_c8)**.
% 0.37/0.55 1985[4:Rew:1982.0,1471.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.37/0.55 2007[4:Rew:1985.0,1981.0] || equal(sk_c9,sk_c9)* -> .
% 0.37/0.55 2008[4:Obv:2007.0] || -> .
% 0.37/0.55 2014[3:Spt:2008.0,1.1,1406.0] || equal(multiply(sk_c9,sk_c8),sk_c10)** -> .
% 0.37/0.55 2015[3:Spt:2008.0,1.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.37/0.55 2016[3:MRR:8.1,2014.0] || -> equal(inverse(sk_c7),sk_c10)**.
% 0.37/0.55 2017[3:MRR:6.1,2014.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.37/0.55 2018[3:MRR:4.1,2014.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.37/0.55 2019[3:MRR:9.1,2014.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.37/0.55 2021[3:MRR:5.1,2014.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.37/0.55 2022[3:MRR:3.1,2014.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.37/0.55 2023[3:MRR:2.1,2014.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.37/0.55 2034[3:SpR:2017.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.37/0.55 2049[3:SpR:2019.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.39/0.56 2050[3:SpR:2019.0,98.0] || -> equal(multiply(inverse(sk_c7),sk_c10),sk_c8)**.
% 0.39/0.56 2052[3:Rew:2016.0,2050.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.39/0.56 2056[3:SpR:2021.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.39/0.56 2060[3:Rew:2034.0,2056.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.39/0.56 2061[3:Rew:2060.0,2049.0] || -> equal(multiply(sk_c10,u),multiply(sk_c7,u))**.
% 0.39/0.56 2063[3:Rew:2061.0,1473.0] || -> equal(multiply(sk_c7,sk_c9),identity)**.
% 0.39/0.56 2064[3:Rew:2061.0,2052.0] || -> equal(multiply(sk_c7,sk_c10),sk_c8)**.
% 0.39/0.56 2065[3:Rew:2061.0,2023.0] || -> equal(multiply(sk_c7,sk_c4),sk_c9)**.
% 0.39/0.56 2073[3:SpR:2022.0,98.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.39/0.56 2075[3:Rew:2018.0,2073.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.39/0.56 2076[3:Rew:2065.0,2075.0,2061.0,2075.0] || -> equal(sk_c10,sk_c9)**.
% 0.39/0.56 2084[3:Rew:2076.0,2014.0] || equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.39/0.56 2086[3:Rew:2076.0,2064.0] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.39/0.56 2087[3:Rew:2063.0,2086.0] || -> equal(identity,sk_c8)**.
% 0.39/0.56 2088[3:Rew:2087.0,1471.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.39/0.56 2104[3:Rew:2088.0,2084.0] || equal(sk_c9,sk_c9)* -> .
% 0.39/0.56 2105[3:Obv:2104.0] || -> .
% 0.39/0.56 2108[2:Spt:2105.0,10.1,1394.0] || equal(inverse(sk_c9),sk_c10)** -> .
% 0.39/0.56 2109[2:Spt:2105.0,10.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.39/0.56 2111[2:MRR:15.1,2108.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.39/0.56 2112[2:MRR:13.1,2108.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.39/0.56 2113[2:MRR:18.0,2108.0] || -> equal(multiply(sk_c7,sk_c8),sk_c10)**.
% 0.39/0.56 2115[2:MRR:14.0,2108.0] || -> equal(multiply(sk_c5,sk_c6),sk_c8)**.
% 0.39/0.56 2116[2:MRR:12.0,2108.0] || -> equal(multiply(sk_c3,sk_c10),sk_c4)**.
% 0.39/0.56 2117[2:MRR:11.0,2108.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.39/0.56 2125[2:SpR:2111.0,243.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),u)**.
% 0.39/0.56 2130[2:SpR:2113.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c10,u))**.
% 0.39/0.56 2137[2:SpR:2115.0,58.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.39/0.56 2141[2:Rew:2125.0,2137.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.39/0.56 2142[2:Rew:2141.0,2130.0] || -> equal(multiply(sk_c10,u),multiply(sk_c7,u))**.
% 0.39/0.56 2148[2:Rew:2142.0,2117.0] || -> equal(multiply(sk_c7,sk_c4),sk_c9)**.
% 0.39/0.56 2153[2:SpR:2116.0,98.0] || -> equal(multiply(inverse(sk_c3),sk_c4),sk_c10)**.
% 0.39/0.56 2155[2:Rew:2112.0,2153.0] || -> equal(multiply(sk_c10,sk_c4),sk_c10)**.
% 0.39/0.56 2156[2:Rew:2148.0,2155.0,2142.0,2155.0] || -> equal(sk_c10,sk_c9)**.
% 0.39/0.56 2157[2:Rew:2156.0,2109.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.39/0.56 2160[2:Rew:2156.0,2108.0] || equal(inverse(sk_c9),sk_c9)** -> .
% 0.39/0.56 2165[2:Rew:2157.0,2160.0] || equal(sk_c9,sk_c9)* -> .
% 0.39/0.56 2166[2:Obv:2165.0] || -> .
% 0.39/0.56 % SZS output end Refutation
% 0.39/0.56 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_27 prove_this_28 prove_this_32 prove_this_33 prove_this_34 prove_this_37 prove_this_41 prove_this_42 prove_this_43 prove_this_44 prove_this_46 prove_this_50 prove_this_51 prove_this_52 prove_this_55 left_identity left_inverse associativity
% 0.39/0.56
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