TSTP Solution File: GRP282-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP282-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:46:40 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP282-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.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 : Tue Jun 14 01:42:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 713 clauses, backtracked 572 clauses, performed 16 splits and kept 816 clauses.
% 0.19/0.49 SPASS allocated 63716 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.00 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.08 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 4, length 308 :
% 0.19/0.49 % SZS output start Refutation
% 0.19/0.49 1[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c7)** equal(multiply(sk_c9,sk_c8),sk_c7).
% 0.19/0.49 2[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c7).
% 0.19/0.49 3[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.19/0.49 6[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c9,sk_c8),sk_c7).
% 0.19/0.49 7[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.19/0.49 8[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(multiply(sk_c9,sk_c8),sk_c7).
% 0.19/0.49 10[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.49 11[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.49 14[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.49 15[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.49 16[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.49 18[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.19/0.49 19[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.49 22[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 23[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.49 24[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.49 25[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c7)** equal(multiply(sk_c9,sk_c3),sk_c8).
% 0.19/0.49 26[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c9,sk_c3),sk_c8).
% 0.19/0.49 27[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 30[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c9,sk_c3),sk_c8).
% 0.19/0.49 31[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 32[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(multiply(sk_c9,sk_c3),sk_c8).
% 0.19/0.49 33[0:Inp] || -> equal(multiply(sk_c8,sk_c9),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 34[0:Inp] || -> equal(multiply(sk_c8,sk_c7),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 35[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 38[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 39[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 40[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 41[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.49 42[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.19/0.49 43[0:Inp] || -> equal(inverse(sk_c9),sk_c7) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 46[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 47[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 48[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.49 49[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(inverse(y),sk_c9) equal(inverse(sk_c9),sk_c7) equal(multiply(u,v),sk_c7)**+ equal(multiply(x,sk_c9),z)* equal(multiply(v,sk_c9),sk_c7)** equal(multiply(w,sk_c7),sk_c9)** equal(multiply(y,sk_c9),sk_c8)** equal(multiply(sk_c9,z),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7) equal(multiply(sk_c9,sk_c8),sk_c7) -> .
% 0.19/0.49 50[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.49 51[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.49 52[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.49 53[1:Spt:49.0,49.5,49.7] || equal(inverse(u),v) equal(multiply(u,v),sk_c7)**+ equal(multiply(v,sk_c9),sk_c7)** -> .
% 0.19/0.49 54[2:Spt:3.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.19/0.49 58[3:Spt:43.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 60[4:Spt:19.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.49 62[5:Spt:35.1] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 67[6:Spt:27.1] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 72[7:Spt:11.1] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.49 74[7:SpL:72.0,53.1] || equal(inverse(sk_c1),sk_c9) equal(sk_c7,sk_c8) equal(multiply(sk_c9,sk_c9),sk_c7)** -> .
% 0.19/0.49 75[7:Rew:60.0,74.0] || equal(sk_c9,sk_c9) equal(sk_c7,sk_c8) equal(multiply(sk_c9,sk_c9),sk_c7)** -> .
% 0.19/0.49 76[7:Obv:75.0] || equal(sk_c7,sk_c8) equal(multiply(sk_c9,sk_c9),sk_c7)** -> .
% 0.19/0.49 78[3:SpR:58.0,51.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.19/0.49 79[4:SpR:60.0,51.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.49 93[3:SpR:78.0,52.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.19/0.49 94[4:SpR:79.0,52.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.49 96[0:SpR:51.0,52.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.49 98[3:Rew:50.0,93.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.19/0.49 99[4:Rew:50.0,94.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.19/0.49 100[0:Rew:50.0,96.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.49 104[5:SpR:62.0,98.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 106[6:Rew:67.0,104.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.49 107[6:Rew:106.0,54.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.19/0.49 109[7:Rew:106.0,72.0] || -> equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.19/0.49 112[7:Rew:106.0,76.0] || equal(sk_c7,sk_c9) equal(multiply(sk_c9,sk_c9),sk_c7)** -> .
% 0.19/0.49 119[7:Rew:107.0,112.1] || equal(sk_c7,sk_c9) equal(sk_c7,sk_c7)* -> .
% 0.19/0.49 120[7:Obv:119.1] || equal(sk_c7,sk_c9)** -> .
% 0.19/0.49 138[7:SpR:109.0,99.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.19/0.49 140[7:Rew:107.0,138.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 141[7:MRR:140.0,120.0] || -> .
% 0.19/0.49 144[7:Spt:141.0,11.1,72.0] || equal(multiply(sk_c1,sk_c9),sk_c8)** -> .
% 0.19/0.49 145[7:Spt:141.0,11.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.49 149[7:Rew:106.0,144.0] || equal(multiply(sk_c1,sk_c9),sk_c9)** -> .
% 0.19/0.49 150[6:Rew:106.0,15.1] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.19/0.49 151[7:MRR:150.1,149.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.49 154[6:Rew:106.0,16.1] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.19/0.49 155[7:MRR:154.1,149.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.49 156[6:Rew:106.0,14.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.19/0.49 157[7:MRR:156.1,149.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 178[7:SpL:157.0,53.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 179[7:Obv:178.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 180[7:Rew:155.0,179.1,151.0,179.0] || equal(sk_c6,sk_c6)* equal(sk_c7,sk_c7) -> .
% 0.19/0.49 181[7:Obv:180.1] || -> .
% 0.19/0.49 182[6:Spt:181.0,27.1,67.0] || equal(multiply(sk_c9,sk_c3),sk_c8)** -> .
% 0.19/0.49 183[6:Spt:181.0,27.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.49 184[6:Rew:104.0,182.0] || equal(sk_c8,sk_c9)** -> .
% 0.19/0.49 185[5:Rew:104.0,31.1] || -> equal(inverse(sk_c5),sk_c6)** equal(sk_c8,sk_c9).
% 0.19/0.49 186[6:MRR:185.1,184.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.49 189[5:Rew:104.0,32.1] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(sk_c8,sk_c9).
% 0.19/0.49 190[6:MRR:189.1,184.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.49 191[5:Rew:104.0,30.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(sk_c8,sk_c9).
% 0.19/0.49 192[6:MRR:191.1,184.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 226[6:SpL:192.0,53.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 227[6:Obv:226.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 228[6:Rew:190.0,227.1,186.0,227.0] || equal(sk_c6,sk_c6)* equal(sk_c7,sk_c7) -> .
% 0.19/0.49 229[6:Obv:228.1] || -> .
% 0.19/0.49 230[5:Spt:229.0,35.1,62.0] || equal(multiply(sk_c2,sk_c9),sk_c3)** -> .
% 0.19/0.49 231[5:Spt:229.0,35.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.49 232[5:MRR:39.1,230.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.49 234[5:MRR:40.1,230.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.49 235[5:MRR:38.1,230.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 262[5:SpL:235.0,53.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 263[5:Obv:262.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 264[5:Rew:234.0,263.1,232.0,263.0] || equal(sk_c6,sk_c6)* equal(sk_c7,sk_c7) -> .
% 0.19/0.49 265[5:Obv:264.1] || -> .
% 0.19/0.49 266[4:Spt:265.0,19.1,60.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.49 267[4:Spt:265.0,19.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.49 268[4:MRR:23.1,266.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.49 270[4:MRR:24.0,266.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.49 271[4:MRR:22.0,266.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 298[4:SpL:271.0,53.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 299[4:Obv:298.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 300[4:Rew:270.0,299.1,268.0,299.0] || equal(sk_c6,sk_c6)* equal(sk_c7,sk_c7) -> .
% 0.19/0.49 301[4:Obv:300.1] || -> .
% 0.19/0.49 302[3:Spt:301.0,43.1,58.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.19/0.49 303[3:Spt:301.0,43.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.49 304[3:MRR:47.1,302.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.49 306[3:MRR:48.0,302.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.49 307[3:MRR:46.0,302.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 334[3:SpL:307.0,53.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 335[3:Obv:334.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 336[3:Rew:306.0,335.1,304.0,335.0] || equal(sk_c6,sk_c6)* equal(sk_c7,sk_c7) -> .
% 0.19/0.49 337[3:Obv:336.1] || -> .
% 0.19/0.49 338[2:Spt:337.0,3.1,54.0] || equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.19/0.49 339[2:Spt:337.0,3.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.49 340[2:MRR:7.1,338.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.49 342[2:MRR:8.1,338.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.49 343[2:MRR:6.1,338.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 359[2:SpL:343.0,53.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 360[2:Obv:359.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c9),sk_c7)** -> .
% 0.19/0.49 361[2:Rew:342.0,360.1,340.0,360.0] || equal(sk_c6,sk_c6)* equal(sk_c7,sk_c7) -> .
% 0.19/0.49 362[2:Obv:361.1] || -> .
% 0.19/0.49 363[1:Spt:362.0,49.1,49.2,49.3,49.4,49.6,49.8,49.9,49.10,49.11,49.12,49.13] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(sk_c9),sk_c7) equal(multiply(v,sk_c9),x)*+ equal(multiply(u,sk_c7),sk_c9)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(sk_c9,x),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7) equal(multiply(sk_c9,sk_c8),sk_c7) -> .
% 0.19/0.49 366[1:SpL:51.0,363.4] || equal(inverse(u),sk_c9) equal(inverse(inverse(sk_c9)),sk_c9) equal(inverse(v),sk_c9) equal(inverse(sk_c9),sk_c7) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7) equal(multiply(sk_c9,sk_c8),sk_c7) -> .
% 0.19/0.49 368[2:Spt:3.1] || -> equal(multiply(sk_c9,sk_c8),sk_c7)**.
% 0.19/0.49 371[2:Rew:368.0,366.10] || equal(inverse(u),sk_c9) equal(inverse(inverse(sk_c9)),sk_c9) equal(inverse(v),sk_c9) equal(inverse(sk_c9),sk_c7) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7) equal(sk_c7,sk_c7) -> .
% 0.19/0.49 376[2:Obv:371.10] || equal(inverse(u),sk_c9) equal(inverse(inverse(sk_c9)),sk_c9) equal(inverse(v),sk_c9) equal(inverse(sk_c9),sk_c7) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.19/0.49 379[2:SpR:368.0,52.0] || -> equal(multiply(sk_c9,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.19/0.49 381[3:Spt:19.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.49 384[3:Rew:381.0,376.3] || equal(inverse(u),sk_c9) equal(inverse(inverse(sk_c9)),sk_c9) equal(inverse(v),sk_c9) equal(sk_c7,sk_c7) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.19/0.49 389[3:Obv:384.3] || equal(inverse(u),sk_c9) equal(inverse(inverse(sk_c9)),sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.19/0.49 390[3:Rew:381.0,389.1] || equal(inverse(u),sk_c9) equal(inverse(sk_c7),sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(multiply(sk_c8,sk_c7),sk_c9)** equal(multiply(sk_c8,sk_c9),sk_c7) -> .
% 0.19/0.49 393[3:SpR:381.0,51.0] || -> equal(multiply(sk_c7,sk_c9),identity)**.
% 0.19/0.49 395[4:Spt:42.1] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.19/0.49 398[4:Rew:395.0,390.7] || equal(inverse(u),sk_c9) equal(inverse(sk_c7),sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(sk_c9,sk_c9) equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.19/0.49 402[4:Obv:398.7] || equal(inverse(u),sk_c9) equal(inverse(sk_c7),sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.19/0.49 408[5:Spt:41.1] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.49 412[5:Rew:408.0,402.7] || equal(inverse(u),sk_c9) equal(inverse(sk_c7),sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.19/0.49 416[5:Obv:412.7] || equal(inverse(u),sk_c9) equal(inverse(sk_c7),sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.49 421[6:Spt:47.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.49 422[6:SpR:421.0,51.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.19/0.49 433[7:Spt:46.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 440[0:SpR:100.0,100.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.49 443[0:SpR:51.0,100.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.49 445[2:SpR:368.0,100.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c8)**.
% 0.19/0.49 447[5:SpR:408.0,100.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.19/0.49 448[3:SpR:393.0,100.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c9)**.
% 0.19/0.49 455[3:Rew:381.0,445.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.49 458[0:Rew:440.0,443.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.49 459[3:Rew:458.0,448.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.19/0.49 460[5:Rew:459.0,416.1] || equal(inverse(u),sk_c9) equal(sk_c9,sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.49 462[5:Obv:460.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.49 463[3:SpR:459.0,51.0] || -> equal(multiply(sk_c9,sk_c7),identity)**.
% 0.19/0.49 464[3:SpR:459.0,100.0] || -> equal(multiply(sk_c9,multiply(sk_c7,u)),u)**.
% 0.19/0.49 467[6:SpR:422.0,100.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c5)**.
% 0.19/0.49 469[6:Rew:458.0,467.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.19/0.49 472[6:SpR:469.0,51.0] || -> equal(multiply(sk_c5,sk_c6),identity)**.
% 0.19/0.49 475[7:Rew:433.0,472.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 476[7:Rew:475.0,50.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 483[7:Rew:475.0,458.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 484[7:Rew:475.0,462.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(sk_c7,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.49 485[7:Rew:475.0,463.0] || -> equal(multiply(sk_c9,sk_c7),sk_c7)**.
% 0.19/0.49 492[7:Rew:476.0,464.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.49 493[7:Rew:476.0,455.0] || -> equal(sk_c7,sk_c8)**.
% 0.19/0.49 496[7:Rew:493.0,381.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.19/0.49 516[7:Rew:493.0,483.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.49 517[7:Rew:516.0,485.0,493.0,485.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.49 518[7:Rew:517.0,493.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 520[7:Rew:517.0,496.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.49 525[7:Rew:517.0,516.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.49 560[7:Rew:492.0,484.5,517.0,484.5,525.0,484.4,517.0,484.4,525.0,484.3,518.0,484.3,518.0,484.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(sk_c9,w)* equal(u,sk_c9) equal(v,sk_c9) equal(w,sk_c9)* -> .
% 0.19/0.49 561[7:Obv:560.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(u,sk_c9) equal(v,sk_c9) equal(w,sk_c9)* -> .
% 0.19/0.49 562[7:Con:561.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.19/0.49 605[7:SpL:520.0,562.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.19/0.49 607[7:Obv:605.1] || -> .
% 0.19/0.49 608[7:Spt:607.0,46.1,433.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.19/0.49 609[7:Spt:607.0,46.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 610[7:Rew:472.0,608.0] || equal(identity,sk_c7)** -> .
% 0.19/0.49 613[6:Rew:472.0,38.0] || -> equal(identity,sk_c7) equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 614[7:MRR:613.0,610.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 615[6:Rew:472.0,30.0] || -> equal(identity,sk_c7) equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 616[7:MRR:615.0,610.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 644[7:SpR:614.0,100.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.49 646[7:Rew:609.0,644.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 647[7:Rew:616.0,646.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.49 650[7:Rew:647.0,395.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.49 652[7:Rew:647.0,447.0] || -> equal(multiply(inverse(sk_c9),sk_c7),sk_c9)**.
% 0.19/0.49 664[7:Rew:463.0,650.0] || -> equal(identity,sk_c9)**.
% 0.19/0.49 665[7:Rew:664.0,610.0] || equal(sk_c7,sk_c9)** -> .
% 0.19/0.49 669[7:Rew:664.0,50.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.49 680[7:Rew:669.0,464.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 716[7:Rew:381.0,652.0] || -> equal(multiply(sk_c7,sk_c7),sk_c9)**.
% 0.19/0.49 717[7:Rew:680.0,716.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 718[7:MRR:717.0,665.0] || -> .
% 0.19/0.49 738[6:Spt:718.0,47.0,421.0] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.19/0.49 739[6:Spt:718.0,47.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 741[6:MRR:39.0,738.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 742[6:MRR:31.0,738.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 773[6:SpR:741.0,100.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.49 775[6:Rew:739.0,773.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 776[6:Rew:742.0,775.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.49 778[6:Rew:776.0,395.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.49 790[6:Rew:776.0,462.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(identity,w) equal(multiply(u,sk_c7),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(sk_c9,w),sk_c8)** -> .
% 0.19/0.49 794[6:Rew:463.0,778.0] || -> equal(identity,sk_c9)**.
% 0.19/0.49 796[6:Rew:794.0,393.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.19/0.49 797[6:Rew:794.0,458.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.49 798[6:Rew:794.0,50.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.49 802[6:Rew:797.0,796.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 807[6:Rew:802.0,459.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.49 830[6:Rew:798.0,790.5,776.0,790.5,797.0,790.4,797.0,790.3,802.0,790.3,794.0,790.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(sk_c9,w)* equal(u,sk_c9) equal(v,sk_c9) equal(w,sk_c9)* -> .
% 0.19/0.49 831[6:Obv:830.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(u,sk_c9) equal(v,sk_c9) equal(w,sk_c9)* -> .
% 0.19/0.49 832[6:Con:831.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.19/0.49 900[6:SpL:807.0,832.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.19/0.49 902[6:Obv:900.1] || -> .
% 0.19/0.49 903[5:Spt:902.0,41.1,408.0] || equal(multiply(sk_c8,sk_c9),sk_c7)** -> .
% 0.19/0.49 904[5:Spt:902.0,41.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 906[5:MRR:33.0,903.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 907[5:MRR:25.0,903.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 929[5:SpR:906.0,100.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.49 931[5:Rew:904.0,929.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 932[5:Rew:907.0,931.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.49 934[5:Rew:932.0,395.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.49 937[5:Rew:932.0,903.0] || equal(multiply(sk_c9,sk_c9),sk_c7)** -> .
% 0.19/0.49 943[5:Rew:463.0,934.0] || -> equal(identity,sk_c9)**.
% 0.19/0.49 945[5:Rew:943.0,463.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.49 946[5:Rew:943.0,50.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.49 951[5:Rew:946.0,945.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 968[5:Rew:946.0,937.0,951.0,937.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.49 969[5:Obv:968.0] || -> .
% 0.19/0.49 975[4:Spt:969.0,42.1,395.0] || equal(multiply(sk_c8,sk_c7),sk_c9)** -> .
% 0.19/0.49 976[4:Spt:969.0,42.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 977[4:MRR:18.1,975.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.49 978[4:MRR:34.0,975.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 979[4:MRR:26.0,975.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 980[4:MRR:10.0,975.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.49 993[4:SpR:978.0,52.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),multiply(sk_c3,u))**.
% 0.19/0.49 994[4:SpR:978.0,100.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.49 996[4:Rew:976.0,994.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 997[4:Rew:979.0,996.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.49 998[4:Rew:997.0,368.0] || -> equal(multiply(sk_c9,sk_c9),sk_c7)**.
% 0.19/0.49 1000[4:Rew:997.0,975.0] || equal(multiply(sk_c9,sk_c7),sk_c9)** -> .
% 0.19/0.49 1001[4:Rew:997.0,379.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),multiply(sk_c7,u))**.
% 0.19/0.49 1003[4:Rew:997.0,979.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.19/0.49 1004[4:Rew:997.0,980.0] || -> equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.19/0.49 1005[4:Rew:463.0,1000.0] || equal(identity,sk_c9)** -> .
% 0.19/0.49 1018[4:SpR:1003.0,100.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c3)**.
% 0.19/0.49 1020[4:Rew:393.0,1018.0,381.0,1018.0] || -> equal(identity,sk_c3)**.
% 0.19/0.49 1021[4:Rew:1020.0,1005.0] || equal(sk_c3,sk_c9)** -> .
% 0.19/0.49 1025[4:Rew:1020.0,50.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.49 1028[4:Rew:1025.0,993.0] || -> equal(multiply(sk_c2,multiply(sk_c9,u)),u)**.
% 0.19/0.49 1040[4:SpR:1004.0,100.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c9)**.
% 0.19/0.49 1042[4:Rew:998.0,1040.0,977.0,1040.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 1047[4:Rew:1042.0,464.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),u)**.
% 0.19/0.49 1048[4:Rew:1042.0,1001.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),multiply(sk_c9,u))**.
% 0.19/0.49 1057[4:Rew:1047.0,1048.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.49 1058[4:Rew:1057.0,1028.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.49 1063[4:Rew:1058.0,978.0] || -> equal(sk_c3,sk_c9)**.
% 0.19/0.49 1064[4:MRR:1063.0,1021.0] || -> .
% 0.19/0.49 1065[3:Spt:1064.0,19.0,381.0] || equal(inverse(sk_c9),sk_c7)** -> .
% 0.19/0.49 1066[3:Spt:1064.0,19.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.49 1067[3:MRR:43.0,1065.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.49 1068[3:MRR:11.0,1065.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.19/0.49 1069[3:MRR:27.0,1065.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.19/0.49 1070[3:MRR:35.0,1065.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.19/0.49 1079[3:SpR:1068.0,100.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c9)**.
% 0.19/0.49 1081[3:Rew:368.0,1079.0,1066.0,1079.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 1083[3:Rew:1081.0,1065.0] || equal(inverse(sk_c9),sk_c9)** -> .
% 0.19/0.49 1084[3:Rew:1081.0,445.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.19/0.49 1086[3:Rew:51.0,1084.0] || -> equal(identity,sk_c8)**.
% 0.19/0.49 1088[3:Rew:1086.0,458.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.19/0.49 1094[3:SpR:1069.0,100.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c3)**.
% 0.19/0.49 1096[3:Rew:1088.0,1094.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.19/0.49 1097[3:Rew:1096.0,1083.0] || equal(sk_c3,sk_c9)** -> .
% 0.19/0.49 1104[3:SpR:1070.0,100.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c9)**.
% 0.19/0.49 1106[3:Rew:1069.0,1104.0,1067.0,1104.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.49 1107[3:Rew:1106.0,1068.0] || -> equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.19/0.49 1111[3:Rew:1106.0,1088.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.49 1122[3:Rew:1111.0,1107.0] || -> equal(sk_c1,sk_c9)**.
% 0.19/0.49 1124[3:Rew:1122.0,1066.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.49 1125[3:Rew:1096.0,1124.0] || -> equal(sk_c3,sk_c9)**.
% 0.19/0.49 1126[3:MRR:1125.0,1097.0] || -> .
% 0.19/0.49 1132[2:Spt:1126.0,3.1,368.0] || equal(multiply(sk_c9,sk_c8),sk_c7)** -> .
% 0.19/0.49 1133[2:Spt:1126.0,3.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.49 1134[2:MRR:7.1,1132.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.19/0.49 1137[2:MRR:6.1,1132.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.49 1139[2:MRR:2.1,1132.0] || -> equal(multiply(sk_c8,sk_c7),sk_c9)**.
% 0.19/0.49 1140[2:MRR:1.1,1132.0] || -> equal(multiply(sk_c8,sk_c9),sk_c7)**.
% 0.19/0.49 1151[2:SpR:1137.0,100.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c6)**.
% 0.19/0.49 1153[2:Rew:1134.0,1151.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.49 1162[2:SpR:1140.0,100.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c9)**.
% 0.19/0.49 1165[2:SpR:1153.0,100.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.49 1167[2:Rew:51.0,1165.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 1168[2:Rew:1167.0,458.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 1169[2:Rew:1167.0,50.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 1172[2:Rew:1168.0,1139.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.49 1174[2:Rew:1168.0,1162.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.19/0.49 1177[2:Rew:1172.0,1132.0] || equal(multiply(sk_c9,sk_c9),sk_c7)** -> .
% 0.19/0.49 1184[2:Rew:1172.0,1174.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.19/0.49 1185[2:Rew:1133.0,1184.0] || -> equal(sk_c7,sk_c9)**.
% 0.19/0.49 1195[2:Rew:1185.0,1169.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.49 1206[2:Rew:1195.0,1177.0,1185.0,1177.0] || equal(sk_c9,sk_c9)* -> .
% 0.19/0.49 1207[2:Obv:1206.0] || -> .
% 0.19/0.49 % SZS output end Refutation
% 0.19/0.49 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_6 prove_this_7 prove_this_8 prove_this_10 prove_this_11 prove_this_14 prove_this_15 prove_this_16 prove_this_18 prove_this_19 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_38 prove_this_39 prove_this_40 prove_this_41 prove_this_42 prove_this_43 prove_this_46 prove_this_47 prove_this_48 prove_this_49 left_identity left_inverse associativity
% 0.19/0.49
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