TSTP Solution File: GRP330-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP330-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:46:53 EDT 2022
% Result : Unsatisfiable 0.40s 0.59s
% Output : Refutation 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP330-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 08:45:54 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.40/0.59
% 0.40/0.59 SPASS V 3.9
% 0.40/0.59 SPASS beiseite: Proof found.
% 0.40/0.59 % SZS status Theorem
% 0.40/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.59 SPASS derived 1612 clauses, backtracked 549 clauses, performed 11 splits and kept 1088 clauses.
% 0.40/0.59 SPASS allocated 64326 KBytes.
% 0.40/0.59 SPASS spent 0:00:00.22 on the problem.
% 0.40/0.59 0:00:00.03 for the input.
% 0.40/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.59 0:00:00.01 for inferences.
% 0.40/0.59 0:00:00.00 for the backtracking.
% 0.40/0.59 0:00:00.14 for the reduction.
% 0.40/0.59
% 0.40/0.59
% 0.40/0.59 Here is a proof with depth 5, length 365 :
% 0.40/0.59 % SZS output start Refutation
% 0.40/0.59 1[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.40/0.59 2[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.40/0.59 3[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.40/0.59 4[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.40/0.59 5[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9).
% 0.40/0.59 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.40/0.59 8[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.40/0.59 9[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.40/0.59 11[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 12[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 13[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 14[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 15[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 16[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 19[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 21[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 22[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c1),sk_c10)**.
% 0.40/0.59 23[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.40/0.59 24[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c1),sk_c10)**.
% 0.40/0.59 25[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 26[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c10)**.
% 0.40/0.59 29[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c1),sk_c10)**.
% 0.40/0.59 31[0:Inp] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.40/0.59 32[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.40/0.59 33[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.40/0.59 34[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.40/0.59 35[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c11) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.40/0.59 36[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.40/0.59 39[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.40/0.59 41[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 42[0:Inp] || -> equal(inverse(sk_c3),sk_c11) equal(inverse(sk_c2),sk_c9)**.
% 0.40/0.59 45[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 46[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.40/0.59 49[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(inverse(sk_c2),sk_c9)**.
% 0.40/0.59 51[0:Inp] || 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_c9) equal(inverse(x2),sk_c10) 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_c10)** equal(multiply(x1,sk_c9),sk_c10)** equal(multiply(x2,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.40/0.59 52[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.40/0.59 53[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.40/0.59 54[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.40/0.59 55[1:Spt:51.0,51.1,51.2,51.7,51.8,51.9] || 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)** -> .
% 0.40/0.59 57[2:Spt:9.1] || -> equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.40/0.59 59[2:SpL:57.0,55.3] || equal(inverse(u),sk_c11)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** equal(multiply(sk_c11,sk_c10),sk_c11)** -> .
% 0.40/0.59 60[3:Spt:49.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.40/0.59 62[4:Spt:29.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.40/0.59 64[5:Spt:39.1] || -> equal(multiply(sk_c2,sk_c9),sk_c10)**.
% 0.40/0.59 66[5:SpL:64.0,55.3] || equal(inverse(u),sk_c9)** equal(inverse(sk_c2),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)** -> .
% 0.40/0.59 67[5:Rew:60.0,66.1] || equal(inverse(u),sk_c9)** equal(sk_c9,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)** -> .
% 0.40/0.59 68[6:Spt:19.1] || -> equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 75[3:SpR:60.0,53.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.40/0.59 76[4:SpR:62.0,53.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.40/0.59 88[4:SpR:76.0,54.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.40/0.59 89[5:SpR:64.0,54.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),multiply(sk_c10,u))**.
% 0.40/0.59 91[0:SpR:53.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.40/0.59 92[3:SpR:75.0,54.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.40/0.59 94[4:Rew:52.0,88.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.40/0.59 95[3:Rew:52.0,92.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.40/0.59 96[0:Rew:52.0,91.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.40/0.59 100[6:SpR:68.0,94.0] || -> equal(multiply(sk_c10,sk_c11),sk_c10)**.
% 0.40/0.59 102[6:Rew:57.0,100.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 103[6:Rew:102.0,57.0] || -> equal(multiply(sk_c10,sk_c11),sk_c10)**.
% 0.40/0.59 105[6:Rew:102.0,64.0] || -> equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.40/0.59 107[6:Rew:102.0,67.1] || equal(inverse(u),sk_c9)** equal(sk_c10,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)** -> .
% 0.40/0.59 112[6:Rew:102.0,95.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.40/0.59 114[6:Obv:107.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9) equal(sk_c10,u) equal(multiply(v,sk_c9),sk_c11)** equal(multiply(sk_c9,sk_c10),sk_c11)** -> .
% 0.40/0.59 115[6:Rew:102.0,114.4,102.0,114.3,102.0,114.1,102.0,114.0] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c10,u) equal(multiply(v,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c10),sk_c11)** -> .
% 0.40/0.59 134[6:SpR:105.0,112.0] || -> equal(multiply(sk_c10,sk_c10),sk_c10)**.
% 0.40/0.59 136[6:Rew:134.0,115.4] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c10,u) equal(multiply(v,sk_c10),sk_c11)** equal(sk_c11,sk_c10) -> .
% 0.40/0.59 144[0:SpR:96.0,96.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.40/0.59 151[6:SpR:103.0,96.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c11)**.
% 0.40/0.59 153[6:SpR:134.0,96.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c10)**.
% 0.40/0.59 154[0:SpR:52.0,96.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.40/0.59 155[0:SpR:53.0,96.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.40/0.59 162[6:Rew:53.0,151.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 163[6:Rew:162.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 164[6:Rew:162.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.40/0.59 165[6:Rew:162.0,76.0] || -> equal(multiply(sk_c10,sk_c1),sk_c11)**.
% 0.40/0.59 177[6:Rew:164.0,153.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 182[6:Rew:177.0,136.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10) equal(sk_c10,u) equal(multiply(v,sk_c10),sk_c10)** equal(sk_c11,sk_c10) -> .
% 0.40/0.59 186[6:Rew:177.0,162.0] || -> equal(identity,sk_c10)**.
% 0.40/0.59 187[6:Rew:177.0,163.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.40/0.59 188[6:Rew:177.0,165.0] || -> equal(multiply(sk_c10,sk_c1),sk_c10)**.
% 0.40/0.59 196[6:Rew:187.0,188.0] || -> equal(sk_c1,sk_c10)**.
% 0.40/0.59 197[6:Rew:196.0,62.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.40/0.59 208[6:Rew:186.0,155.0] || -> equal(multiply(inverse(inverse(u)),sk_c10),u)**.
% 0.40/0.59 214[6:Rew:144.0,208.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.40/0.59 216[6:Rew:177.0,182.4,214.0,182.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) equal(sk_c10,sk_c10) -> .
% 0.40/0.59 217[6:Obv:216.4] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.40/0.59 396[6:SpL:197.0,217.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c10) -> .
% 0.40/0.59 398[6:Obv:396.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.40/0.59 400[6:SpL:197.0,398.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 402[6:Obv:400.1] || -> .
% 0.40/0.59 403[6:Spt:402.0,19.1,68.0] || equal(multiply(sk_c1,sk_c10),sk_c11)** -> .
% 0.40/0.59 404[6:Spt:402.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 408[6:MRR:14.1,403.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.40/0.59 410[0:Rew:144.0,155.0] || -> equal(multiply(u,identity),u)**.
% 0.40/0.59 414[6:MRR:13.1,403.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.40/0.59 427[6:SpR:408.0,96.0] || -> equal(multiply(sk_c10,multiply(sk_c4,u)),u)**.
% 0.40/0.59 432[3:SpR:75.0,96.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.40/0.59 434[3:Rew:410.0,432.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.40/0.59 437[3:SpR:434.0,96.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),u)**.
% 0.40/0.59 439[5:Rew:89.0,437.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.40/0.59 440[6:Rew:439.0,427.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.40/0.59 443[5:Rew:439.0,94.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.40/0.59 445[5:Rew:439.0,57.0] || -> equal(sk_c9,sk_c11)**.
% 0.40/0.59 458[6:Rew:445.0,414.0] || -> equal(multiply(sk_c4,sk_c10),sk_c11)**.
% 0.40/0.59 462[6:Rew:443.0,403.0] || equal(sk_c11,sk_c10)** -> .
% 0.40/0.59 465[6:Rew:440.0,458.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 466[6:MRR:465.0,462.0] || -> .
% 0.40/0.59 473[5:Spt:466.0,39.1,64.0] || equal(multiply(sk_c2,sk_c9),sk_c10)** -> .
% 0.40/0.59 474[5:Spt:466.0,39.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 476[5:MRR:36.1,473.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 477[5:MRR:34.1,473.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.40/0.59 478[5:MRR:32.1,473.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 481[5:MRR:35.1,473.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 482[5:MRR:33.1,473.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.40/0.59 483[5:MRR:31.1,473.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 520[5:SpR:481.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 522[5:Rew:476.0,520.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 528[5:SpR:483.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 530[5:Rew:478.0,528.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 545[5:SpR:522.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 547[5:Rew:53.0,545.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 550[5:Rew:547.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 551[5:Rew:547.0,410.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 558[5:Rew:550.0,530.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 566[5:Rew:558.0,57.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.40/0.59 582[5:Rew:558.0,550.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.40/0.59 583[5:Rew:558.0,551.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.40/0.59 584[5:Rew:583.0,482.0] || -> equal(sk_c4,sk_c9)**.
% 0.40/0.59 585[5:Rew:584.0,477.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.40/0.59 588[5:Rew:434.0,585.0] || -> equal(sk_c2,sk_c10)**.
% 0.40/0.59 591[5:Rew:588.0,473.0] || equal(multiply(sk_c10,sk_c9),sk_c10)** -> .
% 0.40/0.59 595[5:Rew:583.0,566.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 629[5:Rew:582.0,591.0,595.0,591.0] || equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 630[5:Obv:629.0] || -> .
% 0.40/0.59 661[4:Spt:630.0,29.1,62.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.40/0.59 662[4:Spt:630.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 664[4:MRR:26.1,661.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 665[4:MRR:24.1,661.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.40/0.59 666[4:MRR:22.1,661.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 669[4:MRR:25.0,661.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 670[4:MRR:23.0,661.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.40/0.59 671[4:MRR:21.0,661.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 702[4:SpR:669.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 704[4:Rew:664.0,702.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 710[4:SpR:671.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 712[4:Rew:666.0,710.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 713[4:Rew:712.0,59.5] || equal(inverse(u),sk_c11)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.40/0.59 714[4:Obv:713.5] || equal(inverse(u),sk_c11)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.40/0.59 720[4:SpR:704.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 722[4:Rew:53.0,720.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 724[4:Rew:722.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 725[4:Rew:722.0,410.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 731[4:Rew:724.0,712.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 738[4:Rew:731.0,57.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.40/0.59 749[4:Rew:731.0,714.0] || equal(inverse(u),sk_c10)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.40/0.59 753[4:Rew:731.0,725.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.40/0.59 754[4:Rew:753.0,670.0] || -> equal(sk_c4,sk_c9)**.
% 0.40/0.59 755[4:Rew:754.0,665.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.40/0.59 758[4:Rew:434.0,755.0] || -> equal(sk_c2,sk_c10)**.
% 0.40/0.59 759[4:Rew:758.0,60.0] || -> equal(inverse(sk_c10),sk_c9)**.
% 0.40/0.59 763[4:Rew:753.0,738.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 766[4:Rew:763.0,759.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.40/0.59 808[4:Rew:753.0,749.4,731.0,749.4,763.0,749.3,731.0,749.2,766.0,749.1] || equal(inverse(u),sk_c10)** equal(sk_c10,u) equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.40/0.59 809[4:Obv:808.1] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.40/0.59 1119[4:SpL:766.0,809.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c10) -> .
% 0.40/0.59 1122[4:Obv:1119.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.40/0.59 1124[4:SpL:766.0,1122.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 1127[4:Obv:1124.1] || -> .
% 0.40/0.59 1128[3:Spt:1127.0,49.1,60.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.40/0.59 1129[3:Spt:1127.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 1131[3:MRR:46.1,1128.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 1133[3:MRR:42.1,1128.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 1137[3:MRR:45.0,1128.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 1139[3:MRR:41.0,1128.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 1169[3:SpR:1137.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 1171[3:Rew:1131.0,1169.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 1177[3:SpR:1139.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 1179[3:Rew:1133.0,1177.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 1180[3:Rew:1179.0,59.5] || equal(inverse(u),sk_c11)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** equal(sk_c11,sk_c11) -> .
% 0.40/0.59 1181[3:Obv:1180.5] || equal(inverse(u),sk_c11)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11) equal(sk_c9,u) equal(multiply(v,sk_c11),sk_c11)** -> .
% 0.40/0.59 1187[3:SpR:1171.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 1189[3:Rew:53.0,1187.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 1190[3:Rew:1189.0,410.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 1191[3:Rew:1189.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 1196[3:Rew:1190.0,1139.0] || -> equal(sk_c3,sk_c10)**.
% 0.40/0.59 1197[3:Rew:1190.0,57.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 1198[3:Rew:1190.0,1181.4] || equal(inverse(u),sk_c11)** equal(inverse(sk_c10),u)* equal(inverse(v),sk_c11)** equal(sk_c9,u) equal(v,sk_c11) -> .
% 0.40/0.59 1200[3:Rew:1196.0,1133.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.40/0.59 1209[3:Rew:1191.0,1179.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 1220[3:Rew:1209.0,1200.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.40/0.59 1264[3:Rew:1209.0,1198.4,1197.0,1198.3,1209.0,1198.2,1220.0,1198.1,1209.0,1198.0] || equal(inverse(u),sk_c10)** equal(sk_c10,u) equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.40/0.59 1265[3:Obv:1264.1] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c10)** equal(sk_c10,u) equal(v,sk_c10) -> .
% 0.40/0.59 1618[3:SpL:1220.0,1265.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c10) -> .
% 0.40/0.59 1622[3:Obv:1618.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.40/0.59 1624[3:SpL:1220.0,1622.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 1628[3:Obv:1624.1] || -> .
% 0.40/0.59 1629[2:Spt:1628.0,9.1,57.0] || equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.40/0.59 1630[2:Spt:1628.0,9.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 1633[2:MRR:6.1,1629.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 1634[2:MRR:4.1,1629.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.40/0.59 1635[2:MRR:2.1,1629.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 1638[2:MRR:5.1,1629.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 1639[2:MRR:3.1,1629.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.40/0.59 1640[2:MRR:1.1,1629.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 1667[2:SpR:1638.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 1669[2:Rew:1633.0,1667.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 1671[2:SpR:1639.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.40/0.59 1673[2:Rew:1634.0,1671.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.40/0.59 1675[2:SpR:1640.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 1677[2:Rew:1635.0,1675.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 1683[2:SpR:1669.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 1685[2:Rew:53.0,1683.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 1686[2:Rew:1685.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 1687[2:Rew:1685.0,410.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 1692[2:Rew:1686.0,1677.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 1702[2:Rew:1692.0,1629.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.40/0.59 1709[2:Rew:1692.0,1686.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.40/0.59 1710[2:Rew:1692.0,1687.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.40/0.59 1727[2:Rew:1709.0,1673.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 1741[2:Rew:1710.0,1702.0,1727.0,1702.0] || equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 1742[2:Obv:1741.0] || -> .
% 0.40/0.59 1761[1:Spt:1742.0,51.3,51.4,51.5,51.6,51.10,51.11,51.12,51.13,51.14] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c9)**+ equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.40/0.59 1763[2:Spt:8.1] || -> equal(multiply(sk_c10,sk_c11),sk_c9)**.
% 0.40/0.59 1764[2:Rew:1763.0,1761.8] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** equal(sk_c9,sk_c9) -> .
% 0.40/0.59 1766[2:Obv:1764.8] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.40/0.59 1769[2:SpR:1763.0,96.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c11)**.
% 0.40/0.59 1771[3:Spt:29.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.40/0.59 1772[3:SpR:1771.0,96.0] || -> equal(multiply(sk_c10,multiply(sk_c1,u)),u)**.
% 0.40/0.59 1774[4:Spt:49.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.40/0.59 1777[5:Spt:19.1] || -> equal(multiply(sk_c1,sk_c10),sk_c11)**.
% 0.40/0.59 1779[5:SpR:1777.0,96.0] || -> equal(multiply(inverse(sk_c1),sk_c11),sk_c10)**.
% 0.40/0.59 1781[5:Rew:1763.0,1779.0,1771.0,1779.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 1783[5:Rew:1781.0,1774.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.40/0.59 1784[5:Rew:1781.0,31.1] || -> equal(multiply(sk_c3,sk_c11),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.40/0.59 1789[5:Rew:1781.0,32.1] || -> equal(inverse(sk_c3),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.40/0.59 1794[5:Rew:1781.0,1766.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11) equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.40/0.59 1796[5:Rew:1781.0,1769.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c11)**.
% 0.40/0.59 1799[5:Rew:53.0,1796.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 1800[5:Rew:1799.0,410.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 1802[5:Rew:1799.0,154.0] || -> equal(multiply(inverse(sk_c11),u),u)**.
% 0.40/0.59 1803[5:Rew:1799.0,53.0] || -> equal(multiply(inverse(u),u),sk_c11)**.
% 0.40/0.59 1806[5:Rew:1800.0,1784.0] || -> equal(sk_c3,sk_c10) equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.40/0.59 1807[5:Rew:1806.0,1789.0] || -> equal(inverse(sk_c10),sk_c11) equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.40/0.59 1809[5:Rew:1781.0,1794.6,1800.0,1794.5,1781.0,1794.4] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11)** equal(inverse(w),sk_c10) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(v,sk_c10) equal(multiply(w,sk_c10),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.40/0.59 1810[5:Con:1809.2] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11)** equal(inverse(w),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(v,sk_c10) equal(multiply(w,sk_c10),sk_c11)** -> .
% 0.40/0.59 1828[5:SpR:1802.0,1800.0] || -> equal(inverse(sk_c11),sk_c11)**.
% 0.40/0.59 1841[5:SpR:1771.0,1803.0] || -> equal(multiply(sk_c10,sk_c1),sk_c11)**.
% 0.40/0.59 1842[5:SpR:1783.0,1803.0] || -> equal(multiply(sk_c10,sk_c2),sk_c11)**.
% 0.40/0.59 1848[5:SpR:1841.0,96.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c1)**.
% 0.40/0.59 1850[5:Rew:1800.0,1848.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.40/0.59 1851[5:Rew:1850.0,1807.0] || -> equal(sk_c1,sk_c11) equal(multiply(sk_c2,sk_c10),sk_c10)**.
% 0.40/0.59 1857[5:SpR:1842.0,96.0] || -> equal(multiply(inverse(sk_c10),sk_c11),sk_c2)**.
% 0.40/0.59 1859[5:Rew:1800.0,1857.0,1850.0,1857.0] || -> equal(sk_c2,sk_c1)**.
% 0.40/0.59 1863[5:Rew:1859.0,1851.1] || -> equal(sk_c1,sk_c11) equal(multiply(sk_c1,sk_c10),sk_c10)**.
% 0.40/0.59 1873[5:Rew:1777.0,1863.1] || -> equal(sk_c1,sk_c11)** equal(sk_c11,sk_c10).
% 0.40/0.59 1886[6:Spt:1873.1] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 1890[6:Rew:1886.0,1800.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.40/0.59 1891[6:Rew:1886.0,1828.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.40/0.59 1894[6:Rew:1886.0,1810.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10) equal(multiply(u,sk_c10),sk_c10)** equal(v,sk_c10) equal(multiply(w,sk_c10),sk_c11)** -> .
% 0.40/0.59 1895[6:Rew:1850.0,1891.0] || -> equal(sk_c1,sk_c10)**.
% 0.40/0.59 1896[6:Rew:1895.0,1771.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.40/0.59 1905[6:Rew:1890.0,1894.5,1886.0,1894.5,1890.0,1894.3] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) equal(w,sk_c10) -> .
% 0.40/0.59 1906[6:Con:1905.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.40/0.59 1945[6:SpL:1896.0,1906.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 1947[6:Obv:1945.1] || -> .
% 0.40/0.59 1948[6:Spt:1947.0,1873.1,1886.0] || equal(sk_c11,sk_c10)** -> .
% 0.40/0.59 1949[6:Spt:1947.0,1873.0] || -> equal(sk_c1,sk_c11)**.
% 0.40/0.59 1952[6:Rew:1828.0,1771.0,1949.0,1771.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 1958[6:Rew:1952.0,1948.0] || equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 1959[6:Obv:1958.0] || -> .
% 0.40/0.59 1969[5:Spt:1959.0,19.1,1777.0] || equal(multiply(sk_c1,sk_c10),sk_c11)** -> .
% 0.40/0.59 1970[5:Spt:1959.0,19.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 1972[5:MRR:16.1,1969.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 1974[5:MRR:12.1,1969.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 1977[5:MRR:15.1,1969.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 1979[5:MRR:11.1,1969.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 2005[5:SpR:1977.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 2007[5:Rew:1972.0,2005.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 2013[5:SpR:1979.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 2015[5:Rew:1974.0,2013.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 2021[5:SpR:2007.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 2023[5:Rew:53.0,2021.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 2024[5:Rew:2023.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 2028[5:Rew:2024.0,2015.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 2041[5:Rew:2028.0,1969.0] || equal(multiply(sk_c1,sk_c10),sk_c10)** -> .
% 0.40/0.59 2046[5:Rew:2028.0,2024.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.40/0.59 2070[5:Rew:2046.0,1772.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.40/0.59 2083[5:Rew:2070.0,2041.0] || equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 2084[5:Obv:2083.0] || -> .
% 0.40/0.59 2103[4:Spt:2084.0,49.1,1774.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.40/0.59 2104[4:Spt:2084.0,49.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 2106[4:MRR:46.1,2103.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 2108[4:MRR:42.1,2103.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 2111[4:MRR:45.0,2103.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 2113[4:MRR:41.0,2103.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 2135[4:SpR:2111.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 2137[4:Rew:2106.0,2135.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 2143[4:SpR:2113.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 2145[4:Rew:2108.0,2143.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 2151[4:SpR:2137.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 2153[4:Rew:53.0,2151.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 2154[4:Rew:2153.0,410.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 2155[4:Rew:2153.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 2158[4:Rew:2154.0,2113.0] || -> equal(sk_c3,sk_c10)**.
% 0.40/0.59 2159[4:Rew:2154.0,1763.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 2161[4:Rew:2154.0,1766.5] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c11)** equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(v,sk_c10) equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.40/0.59 2163[4:Rew:2158.0,2108.0] || -> equal(inverse(sk_c10),sk_c11)**.
% 0.40/0.59 2172[4:Rew:2155.0,2145.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 2178[4:Rew:2172.0,2154.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.40/0.59 2179[4:Rew:2172.0,2163.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.40/0.59 2224[4:Rew:2178.0,2161.7,2172.0,2161.7,2178.0,2161.6,2159.0,2161.6,2178.0,2161.4,2159.0,2161.4,2159.0,2161.2,2172.0,2161.1] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10)** equal(inverse(x),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) equal(w,sk_c10) equal(x,sk_c10) -> .
% 0.40/0.59 2225[4:Con:2224.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.40/0.59 2274[4:SpL:2179.0,2225.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 2276[4:Obv:2274.1] || -> .
% 0.40/0.59 2277[3:Spt:2276.0,29.1,1771.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.40/0.59 2278[3:Spt:2276.0,29.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.40/0.59 2280[3:MRR:26.1,2277.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 2281[3:MRR:24.1,2277.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.40/0.59 2282[3:MRR:22.1,2277.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 2285[3:MRR:25.0,2277.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 2286[3:MRR:23.0,2277.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.40/0.59 2287[3:MRR:21.0,2277.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 2309[3:SpR:2285.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 2311[3:Rew:2280.0,2309.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 2317[3:SpR:2287.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 2319[3:Rew:2282.0,2317.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 2325[3:SpR:2311.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 2327[3:Rew:53.0,2325.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 2328[3:Rew:2327.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 2329[3:Rew:2327.0,410.0] || -> equal(multiply(u,sk_c11),u)**.
% 0.40/0.59 2333[3:Rew:2328.0,2319.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 2339[3:Rew:2333.0,1763.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.40/0.59 2345[3:Rew:2333.0,1766.1] || equal(inverse(u),sk_c10) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c10),sk_c9)** equal(multiply(v,sk_c11),sk_c10)** equal(multiply(w,sk_c9),sk_c10)** equal(multiply(x,sk_c10),sk_c11)** -> .
% 0.40/0.59 2350[3:Rew:2333.0,2329.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.40/0.59 2351[3:Rew:2350.0,2286.0] || -> equal(sk_c4,sk_c9)**.
% 0.40/0.59 2352[3:Rew:2351.0,2281.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.40/0.59 2355[3:Rew:2350.0,2339.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 2358[3:Rew:2355.0,2352.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.40/0.59 2396[3:Rew:2350.0,2345.7,2333.0,2345.7,2350.0,2345.6,2355.0,2345.6,2350.0,2345.5,2333.0,2345.5,2350.0,2345.4,2355.0,2345.4,2355.0,2345.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10)** equal(inverse(x),sk_c10)** equal(u,sk_c10) equal(v,sk_c10) equal(w,sk_c10) equal(x,sk_c10) -> .
% 0.40/0.59 2397[3:Con:2396.1] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.40/0.59 2448[3:SpL:2358.0,2397.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 2450[3:Obv:2448.1] || -> .
% 0.40/0.59 2451[2:Spt:2450.0,8.1,1763.0] || equal(multiply(sk_c10,sk_c11),sk_c9)** -> .
% 0.40/0.59 2452[2:Spt:2450.0,8.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.40/0.59 2453[2:MRR:6.1,2451.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.40/0.59 2454[2:MRR:4.1,2451.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.40/0.59 2455[2:MRR:2.1,2451.0] || -> equal(inverse(sk_c3),sk_c11)**.
% 0.40/0.59 2459[2:MRR:5.1,2451.0] || -> equal(multiply(sk_c5,sk_c8),sk_c11)**.
% 0.40/0.59 2460[2:MRR:3.1,2451.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.40/0.59 2461[2:MRR:1.1,2451.0] || -> equal(multiply(sk_c3,sk_c11),sk_c10)**.
% 0.40/0.59 2480[2:SpR:2459.0,96.0] || -> equal(multiply(inverse(sk_c5),sk_c11),sk_c8)**.
% 0.40/0.59 2482[2:Rew:2453.0,2480.0] || -> equal(multiply(sk_c8,sk_c11),sk_c8)**.
% 0.40/0.59 2484[2:SpR:2460.0,96.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.40/0.59 2486[2:Rew:2454.0,2484.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.40/0.59 2488[2:SpR:2461.0,96.0] || -> equal(multiply(inverse(sk_c3),sk_c10),sk_c11)**.
% 0.40/0.59 2490[2:Rew:2455.0,2488.0] || -> equal(multiply(sk_c11,sk_c10),sk_c11)**.
% 0.40/0.59 2499[2:SpR:2482.0,96.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c11)**.
% 0.40/0.59 2501[2:Rew:53.0,2499.0] || -> equal(identity,sk_c11)**.
% 0.40/0.59 2502[2:Rew:2501.0,52.0] || -> equal(multiply(sk_c11,u),u)**.
% 0.40/0.59 2506[2:Rew:2502.0,2490.0] || -> equal(sk_c11,sk_c10)**.
% 0.40/0.59 2516[2:Rew:2506.0,2451.0] || equal(multiply(sk_c10,sk_c10),sk_c9)** -> .
% 0.40/0.59 2519[2:Rew:2506.0,2502.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.40/0.59 2537[2:Rew:2519.0,2486.0] || -> equal(sk_c9,sk_c10)**.
% 0.40/0.59 2551[2:Rew:2519.0,2516.0,2537.0,2516.0] || equal(sk_c10,sk_c10)* -> .
% 0.40/0.59 2552[2:Obv:2551.0] || -> .
% 0.40/0.59 % SZS output end Refutation
% 0.40/0.59 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_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_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
% 0.40/0.59
%------------------------------------------------------------------------------