TSTP Solution File: GRP245-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP245-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:46:30 EDT 2022
% Result : Unsatisfiable 0.18s 0.55s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP245-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 17:48:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.55
% 0.18/0.55 SPASS V 3.9
% 0.18/0.55 SPASS beiseite: Proof found.
% 0.18/0.55 % SZS status Theorem
% 0.18/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.55 SPASS derived 1938 clauses, backtracked 474 clauses, performed 13 splits and kept 872 clauses.
% 0.18/0.55 SPASS allocated 64689 KBytes.
% 0.18/0.55 SPASS spent 0:00:00.21 on the problem.
% 0.18/0.55 0:00:00.04 for the input.
% 0.18/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.55 0:00:00.01 for inferences.
% 0.18/0.55 0:00:00.00 for the backtracking.
% 0.18/0.55 0:00:00.13 for the reduction.
% 0.18/0.55
% 0.18/0.55
% 0.18/0.55 Here is a proof with depth 5, length 394 :
% 0.18/0.55 % SZS output start Refutation
% 0.18/0.55 1[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.55 2[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c10)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.18/0.55 3[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.55 4[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.18/0.55 5[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.18/0.55 6[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.55 7[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.18/0.55 8[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c10).
% 0.18/0.55 9[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.18/0.55 10[0:Inp] || -> equal(inverse(sk_c5),sk_c9)** equal(inverse(sk_c1),sk_c10).
% 0.18/0.55 11[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 12[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 13[0:Inp] || -> equal(inverse(sk_c6),sk_c7)** equal(inverse(sk_c1),sk_c10).
% 0.18/0.55 14[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.55 17[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.18/0.55 18[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.18/0.55 19[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.18/0.55 20[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.18/0.55 21[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.18/0.55 22[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c9)**.
% 0.18/0.55 23[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.18/0.55 24[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.18/0.55 25[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 26[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 27[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c9)**.
% 0.18/0.55 28[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.55 29[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c3),sk_c10)**.
% 0.18/0.55 30[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.18/0.55 31[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c3),sk_c10)**.
% 0.18/0.55 32[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 33[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 34[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c3),sk_c10)**.
% 0.18/0.55 35[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.55 36[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.18/0.55 37[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.18/0.55 38[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.18/0.55 43[0:Inp] || equal(multiply(u,sk_c10),sk_c9)** equal(inverse(u),sk_c10) equal(multiply(v,sk_c9),sk_c8)** equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(multiply(w,sk_c9),sk_c10)** equal(inverse(x),sk_c10) equal(multiply(x,sk_c9),sk_c10)** equal(inverse(y),sk_c9) equal(multiply(y,sk_c8),sk_c9)** equal(multiply(z,x1),sk_c9)** equal(inverse(z),x1) equal(multiply(x1,sk_c8),sk_c9)** -> .
% 0.18/0.55 44[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.55 45[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.55 46[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.55 47[0:Con:43.6] || equal(inverse(u),v) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(inverse(y),sk_c9) equal(inverse(z),sk_c10) equal(multiply(u,v),sk_c9)**+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(y,sk_c9),sk_c8)** equal(multiply(z,sk_c10),sk_c9)** -> .
% 0.18/0.55 48[1:Spt:47.0,47.5,47.6] || equal(inverse(u),v) equal(multiply(u,v),sk_c9)**+ equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.18/0.55 51[2:Spt:27.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.18/0.55 53[3:Spt:13.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.18/0.55 61[1:SpL:44.0,48.1] || equal(inverse(identity),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.18/0.55 62[4:Spt:20.1] || -> equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.18/0.55 64[4:SpL:62.0,48.1] || equal(inverse(sk_c2),sk_c9) equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.18/0.55 65[4:Rew:51.0,64.0] || equal(sk_c9,sk_c9) equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.18/0.55 66[4:Obv:65.0] || equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.18/0.55 67[5:Spt:6.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.55 75[2:SpR:51.0,45.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.18/0.55 85[0:SpR:45.0,46.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.55 90[0:Rew:44.0,85.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.55 111[0:SpR:90.0,90.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.55 114[4:SpR:62.0,90.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c9)**.
% 0.18/0.55 116[0:SpR:45.0,90.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.55 117[5:SpR:67.0,90.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c10)**.
% 0.18/0.55 123[2:SpR:75.0,90.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.18/0.55 129[4:Rew:51.0,114.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.18/0.55 130[4:Rew:129.0,66.1] || equal(sk_c8,sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.18/0.55 132[5:Rew:53.0,117.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.18/0.55 146[4:Obv:130.1] || equal(sk_c8,sk_c9)** -> .
% 0.18/0.55 148[0:Rew:111.0,116.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.55 149[2:Rew:148.0,123.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.18/0.55 157[2:SpR:149.0,45.0] || -> equal(multiply(sk_c2,sk_c9),identity)**.
% 0.18/0.55 160[4:Rew:62.0,157.0] || -> equal(identity,sk_c8)**.
% 0.18/0.55 162[4:Rew:160.0,45.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.18/0.55 170[4:Rew:160.0,148.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.55 184[5:SpR:132.0,90.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.18/0.55 186[5:Rew:162.0,184.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 187[5:MRR:186.0,146.0] || -> .
% 0.18/0.55 188[5:Spt:187.0,6.1,67.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.18/0.55 189[5:Spt:187.0,6.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 190[5:MRR:3.1,188.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 192[4:Rew:170.0,7.0] || -> equal(sk_c7,sk_c9) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.55 193[5:MRR:192.1,188.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.55 194[5:Rew:193.0,189.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.18/0.55 195[5:Rew:193.0,5.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.18/0.55 196[5:MRR:195.1,188.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.18/0.55 197[4:Rew:170.0,4.0] || -> equal(sk_c5,sk_c9) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.55 198[5:MRR:197.1,188.0] || -> equal(sk_c5,sk_c9)**.
% 0.18/0.55 199[5:Rew:198.0,190.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.18/0.55 200[5:Rew:149.0,199.0] || -> equal(sk_c2,sk_c9)**.
% 0.18/0.55 202[5:Rew:200.0,62.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.18/0.55 223[5:SpR:196.0,90.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c9)**.
% 0.18/0.55 225[5:Rew:194.0,223.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.18/0.55 226[5:Rew:202.0,225.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 227[5:MRR:226.0,146.0] || -> .
% 0.18/0.55 228[4:Spt:227.0,20.1,62.0] || equal(multiply(sk_c2,sk_c9),sk_c8)** -> .
% 0.18/0.55 229[4:Spt:227.0,20.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 230[4:Rew:157.0,228.0] || equal(identity,sk_c8)** -> .
% 0.18/0.55 231[2:Rew:157.0,17.1] || -> equal(inverse(sk_c5),sk_c9)** equal(identity,sk_c8).
% 0.18/0.55 232[4:MRR:231.1,230.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 235[2:Rew:157.0,21.1] || -> equal(multiply(sk_c7,sk_c8),sk_c9)** equal(identity,sk_c8).
% 0.18/0.55 236[4:MRR:235.1,230.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.55 237[2:Rew:157.0,19.1] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(identity,sk_c8).
% 0.18/0.55 238[4:MRR:237.1,230.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 239[2:Rew:157.0,18.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(identity,sk_c8).
% 0.18/0.55 240[4:MRR:239.1,230.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 243[4:SpR:229.0,90.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.18/0.55 249[4:SpR:232.0,90.0] || -> equal(multiply(sk_c9,multiply(sk_c5,u)),u)**.
% 0.18/0.55 268[4:SpR:236.0,46.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.18/0.55 269[4:SpR:236.0,90.0] || -> equal(multiply(inverse(sk_c7),sk_c9),sk_c8)**.
% 0.18/0.55 272[4:SpR:238.0,90.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.18/0.55 274[4:Rew:229.0,272.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.18/0.55 275[4:SpR:240.0,46.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.18/0.55 284[4:SpR:274.0,90.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.18/0.55 286[4:Rew:45.0,284.0] || -> equal(identity,sk_c9)**.
% 0.18/0.55 287[4:Rew:286.0,230.0] || equal(sk_c8,sk_c9)** -> .
% 0.18/0.55 290[4:Rew:286.0,75.0] || -> equal(multiply(sk_c9,sk_c2),sk_c9)**.
% 0.18/0.55 291[4:Rew:286.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.55 292[4:Rew:286.0,148.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.55 301[4:Rew:291.0,249.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.18/0.55 303[4:Rew:291.0,290.0] || -> equal(sk_c2,sk_c9)**.
% 0.18/0.55 307[4:Rew:291.0,268.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.18/0.55 309[4:Rew:291.0,275.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),u)**.
% 0.18/0.55 312[4:Rew:303.0,149.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.18/0.55 317[4:Rew:292.0,269.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.18/0.55 336[4:Rew:301.0,309.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.55 337[4:Rew:336.0,307.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.18/0.55 339[4:Rew:337.0,243.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.55 342[4:Rew:339.0,238.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.55 344[4:Rew:342.0,317.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.18/0.55 346[4:Rew:312.0,344.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 347[4:MRR:346.0,287.0] || -> .
% 0.18/0.55 361[3:Spt:347.0,13.1,53.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.18/0.55 362[3:Spt:347.0,13.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 364[3:MRR:10.1,361.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 368[3:MRR:12.0,361.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 369[3:MRR:11.0,361.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 407[3:SpR:368.0,90.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.18/0.55 409[3:Rew:362.0,407.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.18/0.55 411[3:SpR:369.0,90.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.18/0.55 413[3:Rew:364.0,411.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.18/0.55 419[3:SpR:409.0,90.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.18/0.55 421[3:Rew:45.0,419.0] || -> equal(identity,sk_c9)**.
% 0.18/0.55 423[3:Rew:421.0,157.0] || -> equal(multiply(sk_c2,sk_c9),sk_c9)**.
% 0.18/0.55 425[3:Rew:421.0,148.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.55 428[3:Rew:421.0,61.0] || equal(inverse(sk_c9),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.18/0.55 434[3:Rew:425.0,423.0] || -> equal(sk_c2,sk_c9)**.
% 0.18/0.55 435[3:Rew:425.0,413.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 440[3:Rew:434.0,51.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.18/0.55 486[3:Rew:425.0,428.2,435.0,428.2,440.0,428.0] || equal(sk_c9,u)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.18/0.55 487[3:Obv:486.1] || equal(u,sk_c9)* -> .
% 0.18/0.55 488[3:UnC:487.0,90.0] || -> .
% 0.18/0.55 495[2:Spt:488.0,27.1,51.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.18/0.55 496[2:Spt:488.0,27.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 497[2:MRR:24.1,495.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 499[2:MRR:28.0,495.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.55 500[2:MRR:26.0,495.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 501[2:MRR:25.0,495.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 522[2:SpR:500.0,90.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.18/0.55 524[2:Rew:496.0,522.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.18/0.55 526[2:SpR:501.0,90.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.18/0.55 528[2:Rew:497.0,526.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.18/0.55 534[2:SpR:524.0,90.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.18/0.55 536[2:Rew:45.0,534.0] || -> equal(identity,sk_c9)**.
% 0.18/0.55 538[2:Rew:536.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.55 539[2:Rew:536.0,148.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.55 542[2:Rew:536.0,61.0] || equal(inverse(sk_c9),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.18/0.55 545[2:Rew:538.0,528.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 551[2:Rew:545.0,499.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.18/0.55 567[2:Rew:539.0,551.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.55 568[2:Rew:567.0,496.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.18/0.55 569[2:Rew:567.0,500.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.18/0.55 571[2:Rew:539.0,569.0] || -> equal(sk_c6,sk_c9)**.
% 0.18/0.55 572[2:Rew:571.0,568.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.18/0.55 583[2:Rew:539.0,542.2,545.0,542.2,572.0,542.0] || equal(sk_c9,u)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.18/0.55 584[2:Obv:583.1] || equal(u,sk_c9)* -> .
% 0.18/0.55 585[2:UnC:584.0,497.0] || -> .
% 0.18/0.55 592[1:Spt:585.0,47.1,47.2,47.3,47.4,47.7,47.8,47.9,47.10] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** -> .
% 0.18/0.55 594[2:Spt:13.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.18/0.55 597[3:Spt:24.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.18/0.55 598[3:SpR:597.0,90.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.18/0.55 600[4:Spt:31.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.18/0.55 603[5:Spt:6.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.18/0.55 605[5:SpR:603.0,90.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c10)**.
% 0.18/0.55 607[5:Rew:594.0,605.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.18/0.55 608[6:Spt:20.1] || -> equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.18/0.55 610[6:SpR:608.0,90.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c9)**.
% 0.18/0.55 612[6:Rew:597.0,610.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.18/0.55 616[1:SpL:44.0,592.4] || equal(inverse(identity),sk_c9) equal(inverse(u),sk_c10) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(sk_c8,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 617[7:Spt:38.1] || -> equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.18/0.55 623[5:SpR:607.0,90.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.18/0.55 625[5:Rew:45.0,623.0] || -> equal(identity,sk_c9)**.
% 0.18/0.55 626[5:Rew:625.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.55 627[5:Rew:625.0,148.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.55 630[5:Rew:625.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.18/0.55 631[6:Rew:626.0,612.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 635[5:Rew:626.0,598.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.55 636[6:Rew:631.0,592.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c9),sk_c8)** equal(multiply(x,sk_c10),sk_c9)** -> .
% 0.18/0.55 639[7:Rew:627.0,617.0] || -> equal(sk_c3,sk_c10)**.
% 0.18/0.55 640[7:Rew:639.0,600.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.55 647[6:Rew:627.0,636.6,631.0,636.6,627.0,636.5,627.0,636.4] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c9)** equal(inverse(x),sk_c10) equal(u,sk_c9) equal(v,sk_c10) equal(w,sk_c9) equal(multiply(x,sk_c10),sk_c9)** -> .
% 0.18/0.55 648[6:Con:647.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10) equal(u,sk_c9) equal(v,sk_c10) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 673[5:SpR:635.0,627.0] || -> equal(sk_c2,sk_c9)**.
% 0.18/0.55 675[5:Rew:673.0,597.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.18/0.55 681[5:SpR:630.0,90.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.18/0.55 684[5:SpR:594.0,630.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.18/0.55 686[5:Rew:627.0,681.0] || -> equal(inverse(inverse(u)),u)**.
% 0.18/0.55 695[5:SpR:684.0,90.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.18/0.55 697[7:Rew:627.0,695.0,640.0,695.0] || -> equal(sk_c10,sk_c1)**.
% 0.18/0.55 698[7:Rew:697.0,594.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.55 699[7:Rew:697.0,603.0] || -> equal(multiply(sk_c1,sk_c1),sk_c9)**.
% 0.18/0.55 707[7:Rew:697.0,648.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c10) equal(u,sk_c9) equal(v,sk_c10) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 710[7:Rew:697.0,707.5,697.0,707.4,697.0,707.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1) equal(u,sk_c9) equal(v,sk_c1) equal(multiply(w,sk_c1),sk_c9)**+ -> .
% 0.18/0.55 739[7:SpL:699.0,710.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c9) equal(v,sk_c1) equal(sk_c9,sk_c9) -> .
% 0.18/0.55 740[7:Obv:739.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.18/0.55 741[7:Rew:698.0,740.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.18/0.55 742[7:Obv:741.2] || equal(inverse(u),sk_c9)**+ equal(inverse(v),sk_c1)** equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.18/0.55 1021[7:SpL:675.0,742.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c1)** equal(sk_c9,sk_c9) equal(u,sk_c1) -> .
% 0.18/0.55 1024[7:Obv:1021.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.18/0.55 1027[7:SpL:698.0,1024.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.55 1030[7:Obv:1027.1] || -> .
% 0.18/0.55 1031[7:Spt:1030.0,38.1,617.0] || equal(multiply(sk_c3,sk_c9),sk_c10)** -> .
% 0.18/0.55 1032[7:Spt:1030.0,38.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 1033[5:Rew:627.0,695.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.18/0.55 1034[7:Rew:627.0,1031.0] || equal(sk_c3,sk_c10)** -> .
% 0.18/0.55 1035[5:Rew:627.0,36.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c3,sk_c10).
% 0.18/0.55 1036[7:MRR:1035.1,1034.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.18/0.55 1051[5:Rew:627.0,37.1,627.0,37.0] || -> equal(sk_c4,sk_c10) equal(sk_c3,sk_c10)**.
% 0.18/0.55 1052[7:MRR:1051.1,1034.0] || -> equal(sk_c4,sk_c10)**.
% 0.18/0.55 1053[7:Rew:1052.0,1036.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.55 1054[7:Rew:1033.0,1053.0] || -> equal(sk_c10,sk_c1)**.
% 0.18/0.55 1055[7:Rew:1054.0,600.0] || -> equal(inverse(sk_c3),sk_c1)**.
% 0.18/0.55 1056[7:Rew:1054.0,594.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.55 1060[7:Rew:1054.0,1034.0] || equal(sk_c3,sk_c1)** -> .
% 0.18/0.55 1073[7:SpR:1055.0,686.0] || -> equal(inverse(sk_c1),sk_c3)**.
% 0.18/0.55 1077[7:Rew:1056.0,1073.0] || -> equal(sk_c3,sk_c1)**.
% 0.18/0.55 1078[7:MRR:1077.0,1060.0] || -> .
% 0.18/0.55 1079[6:Spt:1078.0,20.1,608.0] || equal(multiply(sk_c2,sk_c9),sk_c8)** -> .
% 0.18/0.55 1080[6:Spt:1078.0,20.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 1081[6:Rew:626.0,1079.0,673.0,1079.0] || equal(sk_c8,sk_c9)** -> .
% 0.18/0.55 1087[5:Rew:673.0,17.1,627.0,17.1] || -> equal(inverse(sk_c5),sk_c9)** equal(sk_c8,sk_c9).
% 0.18/0.55 1088[6:MRR:1087.1,1081.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 1100[5:Rew:673.0,18.1,627.0,18.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(sk_c8,sk_c9).
% 0.18/0.55 1101[6:MRR:1100.1,1081.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 1130[6:SpR:1088.0,686.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.18/0.55 1134[6:Rew:675.0,1130.0] || -> equal(sk_c5,sk_c9)**.
% 0.18/0.55 1136[6:Rew:1134.0,1101.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.18/0.55 1139[6:Rew:626.0,1136.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 1140[6:MRR:1139.0,1081.0] || -> .
% 0.18/0.55 1145[5:Spt:1140.0,6.1,603.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.18/0.55 1146[5:Spt:1140.0,6.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 1148[5:MRR:1.1,1145.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.18/0.55 1151[5:MRR:5.1,1145.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 1153[5:MRR:2.1,1145.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.18/0.55 1178[5:SpR:1151.0,90.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.18/0.55 1180[5:Rew:1146.0,1178.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.18/0.55 1186[5:SpR:1153.0,90.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.18/0.55 1188[5:Rew:1148.0,1186.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.18/0.55 1190[5:SpR:1180.0,90.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.18/0.55 1192[5:Rew:45.0,1190.0] || -> equal(identity,sk_c9)**.
% 0.18/0.55 1194[5:Rew:1192.0,148.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.55 1195[5:Rew:1192.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.18/0.55 1210[5:Rew:1194.0,1153.0] || -> equal(sk_c4,sk_c10)**.
% 0.18/0.55 1211[5:Rew:1210.0,1148.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.55 1284[5:SpR:594.0,1195.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.18/0.55 1301[5:SpR:1284.0,90.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.18/0.55 1303[5:Rew:1194.0,1301.0,1211.0,1301.0] || -> equal(sk_c10,sk_c1)**.
% 0.18/0.55 1307[5:Rew:1303.0,1188.0] || -> equal(multiply(sk_c1,sk_c1),sk_c9)**.
% 0.18/0.55 1308[5:Rew:1303.0,1145.0] || equal(multiply(sk_c1,sk_c1),sk_c9)** -> .
% 0.18/0.55 1314[5:Rew:1307.0,1308.0] || equal(sk_c9,sk_c9)* -> .
% 0.18/0.55 1315[5:Obv:1314.0] || -> .
% 0.18/0.55 1319[4:Spt:1315.0,31.1,600.0] || equal(inverse(sk_c3),sk_c10)** -> .
% 0.18/0.55 1320[4:Spt:1315.0,31.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 1321[4:MRR:29.1,1319.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.18/0.55 1322[4:MRR:34.1,1319.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 1323[4:MRR:35.0,1319.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.55 1324[4:MRR:33.0,1319.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 1325[4:MRR:32.0,1319.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 1326[4:MRR:30.0,1319.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.18/0.55 1341[4:SpR:1324.0,90.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.18/0.55 1343[4:Rew:1322.0,1341.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.18/0.55 1345[4:SpR:1325.0,90.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.18/0.55 1347[4:Rew:1320.0,1345.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.18/0.55 1349[4:SpR:1326.0,90.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.18/0.55 1351[4:Rew:1321.0,1349.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.18/0.55 1356[4:SpR:1343.0,90.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.18/0.55 1358[4:Rew:45.0,1356.0] || -> equal(identity,sk_c9)**.
% 0.18/0.55 1359[4:Rew:1358.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.55 1360[4:Rew:1358.0,148.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.55 1362[4:Rew:1358.0,616.0] || equal(inverse(sk_c9),sk_c9) equal(inverse(u),sk_c10) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(sk_c8,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 1363[4:Rew:1358.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.18/0.55 1364[4:Rew:1359.0,1347.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 1371[4:Rew:1364.0,1323.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.18/0.55 1376[4:Rew:1360.0,1326.0] || -> equal(sk_c4,sk_c10)**.
% 0.18/0.55 1377[4:Rew:1376.0,1321.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.55 1379[4:Rew:1360.0,1371.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.55 1380[4:Rew:1379.0,1322.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.18/0.55 1381[4:Rew:1379.0,1324.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.18/0.55 1383[4:Rew:1360.0,1381.0] || -> equal(sk_c6,sk_c9)**.
% 0.18/0.55 1384[4:Rew:1383.0,1380.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.18/0.55 1393[4:Rew:1360.0,1362.6,1364.0,1362.6,1360.0,1362.5,1364.0,1362.4,1384.0,1362.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(sk_c9,sk_c9) equal(u,sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 1394[4:Obv:1393.4] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(u,sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 1448[4:SpR:594.0,1363.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.18/0.55 1456[4:SpR:1448.0,90.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.18/0.55 1458[4:Rew:1360.0,1456.0,1377.0,1456.0] || -> equal(sk_c10,sk_c1)**.
% 0.18/0.55 1459[4:Rew:1458.0,594.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.55 1463[4:Rew:1458.0,1351.0] || -> equal(multiply(sk_c1,sk_c1),sk_c9)**.
% 0.18/0.55 1467[4:Rew:1458.0,1394.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(u,sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 1470[4:Rew:1458.0,1467.5,1458.0,1467.3,1458.0,1467.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c1) equal(u,sk_c1) equal(v,sk_c9) equal(multiply(w,sk_c1),sk_c9)**+ -> .
% 0.18/0.55 1814[4:SpL:1463.0,1470.5] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(v,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.18/0.55 1815[4:Obv:1814.5] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(v,sk_c9) -> .
% 0.18/0.55 1816[4:Rew:1459.0,1815.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(sk_c1,sk_c1) equal(u,sk_c1) equal(v,sk_c9) -> .
% 0.18/0.55 1817[4:Obv:1816.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c9)** equal(u,sk_c1) equal(v,sk_c9) -> .
% 0.18/0.55 2014[4:SpL:1459.0,1817.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c9)** equal(sk_c1,sk_c1) equal(u,sk_c9) -> .
% 0.18/0.55 2019[4:Obv:2014.2] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.18/0.55 2020[4:SpL:1384.0,2019.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.18/0.55 2025[4:Obv:2020.1] || -> .
% 0.18/0.55 2027[3:Spt:2025.0,24.1,597.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.18/0.55 2028[3:Spt:2025.0,24.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 2029[3:MRR:22.1,2027.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.18/0.55 2030[3:MRR:27.1,2027.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 2032[3:MRR:28.0,2027.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.55 2033[3:MRR:26.0,2027.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 2034[3:MRR:25.0,2027.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 2035[3:MRR:23.0,2027.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.18/0.55 2056[3:SpR:2033.0,90.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.18/0.55 2058[3:Rew:2030.0,2056.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.18/0.55 2060[3:SpR:2034.0,90.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.18/0.55 2062[3:Rew:2028.0,2060.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.18/0.55 2064[3:SpR:2035.0,90.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.18/0.55 2066[3:Rew:2029.0,2064.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.18/0.55 2071[3:SpR:2058.0,90.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.18/0.55 2073[3:Rew:45.0,2071.0] || -> equal(identity,sk_c9)**.
% 0.18/0.55 2074[3:Rew:2073.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.55 2075[3:Rew:2073.0,148.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.55 2076[3:Rew:2073.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.18/0.55 2078[3:Rew:2073.0,616.0] || equal(inverse(sk_c9),sk_c9) equal(inverse(u),sk_c10) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(sk_c8,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 2079[3:Rew:2074.0,2062.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 2085[3:Rew:2079.0,2032.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.18/0.55 2090[3:Rew:2075.0,2035.0] || -> equal(sk_c4,sk_c10)**.
% 0.18/0.55 2091[3:Rew:2090.0,2029.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.55 2093[3:Rew:2075.0,2085.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.55 2094[3:Rew:2093.0,2030.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.18/0.55 2095[3:Rew:2093.0,2033.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.18/0.55 2097[3:Rew:2075.0,2095.0] || -> equal(sk_c6,sk_c9)**.
% 0.18/0.55 2098[3:Rew:2097.0,2094.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.18/0.55 2107[3:Rew:2075.0,2078.6,2079.0,2078.6,2075.0,2078.5,2079.0,2078.4,2098.0,2078.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(sk_c9,sk_c9) equal(u,sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 2108[3:Obv:2107.4] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(u,sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 2153[3:SpR:594.0,2076.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.18/0.55 2160[3:SpR:2153.0,90.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.18/0.55 2162[3:Rew:2075.0,2160.0,2091.0,2160.0] || -> equal(sk_c10,sk_c1)**.
% 0.18/0.55 2163[3:Rew:2162.0,594.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.55 2166[3:Rew:2162.0,2066.0] || -> equal(multiply(sk_c1,sk_c1),sk_c9)**.
% 0.18/0.55 2170[3:Rew:2162.0,2108.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(u,sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 2173[3:Rew:2162.0,2170.5,2162.0,2170.3,2162.0,2170.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c1) equal(u,sk_c1) equal(v,sk_c9) equal(multiply(w,sk_c1),sk_c9)**+ -> .
% 0.18/0.55 2443[3:SpL:2166.0,2173.5] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(v,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.18/0.55 2444[3:Obv:2443.5] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c1) equal(v,sk_c9) -> .
% 0.18/0.55 2445[3:Rew:2163.0,2444.2] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c9)** equal(sk_c1,sk_c1) equal(u,sk_c1) equal(v,sk_c9) -> .
% 0.18/0.55 2446[3:Obv:2445.2] || equal(inverse(u),sk_c1)**+ equal(inverse(v),sk_c9)** equal(u,sk_c1) equal(v,sk_c9) -> .
% 0.18/0.55 2602[3:SpL:2163.0,2446.0] || equal(sk_c1,sk_c1) equal(inverse(u),sk_c9)** equal(sk_c1,sk_c1) equal(u,sk_c9) -> .
% 0.18/0.55 2607[3:Obv:2602.2] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.18/0.55 2608[3:SpL:2098.0,2607.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.18/0.55 2613[3:Obv:2608.1] || -> .
% 0.18/0.55 2615[2:Spt:2613.0,13.1,594.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.18/0.55 2616[2:Spt:2613.0,13.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.18/0.55 2617[2:MRR:10.1,2615.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.18/0.55 2618[2:MRR:8.1,2615.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.18/0.55 2620[2:MRR:14.0,2615.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.18/0.55 2621[2:MRR:12.0,2615.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.18/0.55 2622[2:MRR:11.0,2615.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.18/0.55 2623[2:MRR:9.0,2615.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.18/0.55 2642[2:SpR:2621.0,90.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.18/0.55 2644[2:Rew:2616.0,2642.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.18/0.55 2646[2:SpR:2622.0,90.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.18/0.55 2648[2:Rew:2617.0,2646.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.18/0.55 2650[2:SpR:2623.0,90.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.18/0.55 2652[2:Rew:2618.0,2650.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.18/0.55 2654[2:SpR:2644.0,90.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.18/0.55 2656[2:Rew:45.0,2654.0] || -> equal(identity,sk_c9)**.
% 0.18/0.55 2657[2:Rew:2656.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.18/0.55 2658[2:Rew:2656.0,148.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.18/0.55 2660[2:Rew:2656.0,616.0] || equal(inverse(sk_c9),sk_c9) equal(inverse(u),sk_c10) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(sk_c8,sk_c9) equal(multiply(u,sk_c9),sk_c10)** equal(multiply(v,sk_c9),sk_c8)** equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 2663[2:Rew:2657.0,2648.0] || -> equal(sk_c8,sk_c9)**.
% 0.18/0.55 2668[2:Rew:2663.0,2620.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.18/0.55 2673[2:Rew:2658.0,2623.0] || -> equal(sk_c4,sk_c10)**.
% 0.18/0.55 2674[2:Rew:2673.0,2618.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.18/0.55 2676[2:Rew:2658.0,2668.0] || -> equal(sk_c7,sk_c9)**.
% 0.18/0.55 2677[2:Rew:2676.0,2616.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.18/0.55 2678[2:Rew:2676.0,2621.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.18/0.55 2680[2:Rew:2658.0,2678.0] || -> equal(sk_c6,sk_c9)**.
% 0.18/0.55 2681[2:Rew:2680.0,2677.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.18/0.55 2690[2:Rew:2658.0,2660.6,2663.0,2660.6,2658.0,2660.5,2663.0,2660.4,2681.0,2660.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(sk_c9,sk_c9) equal(u,sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)** -> .
% 0.18/0.55 2691[2:Obv:2690.4] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c10) equal(u,sk_c10) equal(v,sk_c9) equal(multiply(w,sk_c10),sk_c9)**+ -> .
% 0.18/0.55 2920[2:SpL:2652.0,2691.5] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(inverse(sk_c10),sk_c10)** equal(u,sk_c10) equal(v,sk_c9) equal(sk_c9,sk_c9) -> .
% 0.18/0.55 2927[2:Obv:2920.5] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(inverse(sk_c10),sk_c10)** equal(u,sk_c10) equal(v,sk_c9) -> .
% 0.18/0.55 2928[2:Rew:2674.0,2927.2] || equal(inverse(u),sk_c10)** equal(inverse(v),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c10) equal(v,sk_c9) -> .
% 0.18/0.55 2929[2:Obv:2928.2] || equal(inverse(u),sk_c10)**+ equal(inverse(v),sk_c9)** equal(u,sk_c10) equal(v,sk_c9) -> .
% 0.18/0.55 3208[2:SpL:2674.0,2929.0] || equal(sk_c10,sk_c10) equal(inverse(u),sk_c9)** equal(sk_c10,sk_c10) equal(u,sk_c9) -> .
% 0.18/0.55 3213[2:Obv:3208.2] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.18/0.55 3216[2:SpL:2681.0,3213.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.18/0.55 3221[2:Obv:3216.1] || -> .
% 0.18/0.55 % SZS output end Refutation
% 0.18/0.55 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_35 prove_this_36 prove_this_37 prove_this_38 prove_this_43 left_identity left_inverse associativity
% 0.18/0.56
%------------------------------------------------------------------------------