TSTP Solution File: GRP248-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP248-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:46:31 EDT 2022
% Result : Unsatisfiable 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP248-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 08:34:37 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.55
% 0.20/0.55 SPASS V 3.9
% 0.20/0.55 SPASS beiseite: Proof found.
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.55 SPASS derived 1819 clauses, backtracked 569 clauses, performed 13 splits and kept 994 clauses.
% 0.20/0.55 SPASS allocated 64543 KBytes.
% 0.20/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.20/0.55 0:00:00.04 for the input.
% 0.20/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.55 0:00:00.01 for inferences.
% 0.20/0.55 0:00:00.00 for the backtracking.
% 0.20/0.55 0:00:00.11 for the reduction.
% 0.20/0.55
% 0.20/0.55
% 0.20/0.55 Here is a proof with depth 5, length 452 :
% 0.20/0.55 % SZS output start Refutation
% 0.20/0.55 1[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.20/0.55 2[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c10)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.20/0.55 3[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.20/0.55 4[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.20/0.55 5[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.20/0.55 6[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.20/0.55 7[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c10),sk_c9).
% 0.20/0.55 8[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c10).
% 0.20/0.55 9[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.20/0.55 10[0:Inp] || -> equal(inverse(sk_c5),sk_c9)** equal(inverse(sk_c1),sk_c10).
% 0.20/0.55 11[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 12[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 13[0:Inp] || -> equal(inverse(sk_c6),sk_c7)** equal(inverse(sk_c1),sk_c10).
% 0.20/0.55 14[0:Inp] || -> equal(inverse(sk_c1),sk_c10) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.55 15[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 16[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c10) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 17[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 18[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 19[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 20[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 21[0:Inp] || -> equal(multiply(sk_c7,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 22[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.55 23[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.20/0.55 24[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.55 25[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 26[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 27[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.55 28[0:Inp] || -> equal(inverse(sk_c2),sk_c9) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.55 29[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c3),sk_c10)**.
% 0.20/0.55 30[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.20/0.55 31[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c3),sk_c10)**.
% 0.20/0.55 32[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 33[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 34[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(inverse(sk_c3),sk_c10)**.
% 0.20/0.55 35[0:Inp] || -> equal(inverse(sk_c3),sk_c10) equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.55 36[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c3,sk_c8),sk_c10)**.
% 0.20/0.55 37[0:Inp] || -> equal(multiply(sk_c4,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c8),sk_c10)**.
% 0.20/0.55 38[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c3,sk_c8),sk_c10)**.
% 0.20/0.55 39[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c3,sk_c8),sk_c10)**.
% 0.20/0.55 40[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c9) equal(multiply(sk_c3,sk_c8),sk_c10)**.
% 0.20/0.55 41[0:Inp] || -> equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c10)**.
% 0.20/0.55 43[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(inverse(y),sk_c10) equal(inverse(z),sk_c9) equal(inverse(x1),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_c8),sk_c10)** equal(multiply(z,sk_c9),sk_c8)** equal(multiply(x1,sk_c10),sk_c9)** -> .
% 0.20/0.55 44[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.55 45[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.55 46[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.55 47[1:Spt:43.0,43.6,43.7] || equal(inverse(u),v) equal(multiply(u,v),sk_c9)**+ equal(multiply(v,sk_c8),sk_c9)** -> .
% 0.20/0.55 48[2:Spt:34.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.20/0.55 50[3:Spt:27.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.55 52[4:Spt:13.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.55 54[5:Spt:41.1] || -> equal(multiply(sk_c3,sk_c8),sk_c10)**.
% 0.20/0.55 59[1:SpL:44.0,47.1] || equal(inverse(identity),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.55 60[6:Spt:20.1] || -> equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 62[6:SpL:60.0,47.1] || equal(inverse(sk_c2),sk_c9) equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.20/0.55 63[6:Rew:50.0,62.0] || equal(sk_c9,sk_c9) equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.20/0.55 64[6:Obv:63.0] || equal(sk_c8,sk_c9) equal(multiply(sk_c9,sk_c8),sk_c9)** -> .
% 0.20/0.55 65[7:Spt:6.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.20/0.55 72[2:SpR:48.0,45.0] || -> equal(multiply(sk_c10,sk_c3),identity)**.
% 0.20/0.55 73[3:SpR:50.0,45.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.20/0.55 74[4:SpR:52.0,45.0] || -> equal(multiply(sk_c10,sk_c1),identity)**.
% 0.20/0.55 83[0:SpR:45.0,46.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.55 85[7:SpR:65.0,46.0] || -> equal(multiply(sk_c1,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.20/0.55 86[2:SpR:72.0,46.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.20/0.55 88[2:Rew:44.0,86.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.20/0.55 89[0:Rew:44.0,83.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.55 101[5:SpR:54.0,88.0] || -> equal(multiply(sk_c10,sk_c10),sk_c8)**.
% 0.20/0.55 105[5:SpR:101.0,46.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),multiply(sk_c8,u))**.
% 0.20/0.55 109[0:SpR:89.0,89.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.55 113[0:SpR:45.0,89.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.55 114[6:SpR:60.0,89.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c9)**.
% 0.20/0.55 116[2:SpR:72.0,89.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c3)**.
% 0.20/0.55 117[4:SpR:74.0,89.0] || -> equal(multiply(inverse(sk_c10),identity),sk_c1)**.
% 0.20/0.55 121[3:SpR:73.0,89.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.20/0.55 127[6:Rew:50.0,114.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.55 128[6:Rew:127.0,64.1] || equal(sk_c8,sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.20/0.55 130[4:Rew:116.0,117.0] || -> equal(sk_c3,sk_c1)**.
% 0.20/0.55 132[5:Rew:130.0,54.0] || -> equal(multiply(sk_c1,sk_c8),sk_c10)**.
% 0.20/0.55 144[6:Obv:128.1] || equal(sk_c8,sk_c9)** -> .
% 0.20/0.55 145[0:Rew:109.0,113.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.55 146[3:Rew:145.0,121.0] || -> equal(inverse(sk_c9),sk_c2)**.
% 0.20/0.55 153[3:SpR:146.0,45.0] || -> equal(multiply(sk_c2,sk_c9),identity)**.
% 0.20/0.55 156[6:Rew:60.0,153.0] || -> equal(identity,sk_c8)**.
% 0.20/0.55 157[6:Rew:156.0,44.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.55 159[6:Rew:156.0,73.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.20/0.55 161[6:Rew:156.0,59.0] || equal(inverse(sk_c8),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.55 166[6:Rew:156.0,145.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.55 168[6:Rew:157.0,105.0] || -> equal(multiply(sk_c10,multiply(sk_c10,u)),u)**.
% 0.20/0.55 175[6:Rew:166.0,132.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.55 179[6:Rew:175.0,101.0] || -> equal(multiply(sk_c1,sk_c1),sk_c8)**.
% 0.20/0.55 180[7:Rew:175.0,85.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),multiply(sk_c9,u))**.
% 0.20/0.55 190[6:Rew:175.0,168.0] || -> equal(multiply(sk_c1,multiply(sk_c1,u)),u)**.
% 0.20/0.55 193[7:Rew:190.0,180.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.55 194[7:Rew:193.0,159.0] || -> equal(sk_c2,sk_c8)**.
% 0.20/0.55 197[7:Rew:194.0,50.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.20/0.55 205[7:Rew:166.0,161.2,197.0,161.0] || equal(sk_c9,u)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.20/0.55 206[7:Obv:205.1] || equal(u,sk_c9)* -> .
% 0.20/0.55 207[7:UnC:206.0,89.0] || -> .
% 0.20/0.55 209[7:Spt:207.0,6.1,65.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.20/0.55 210[7:Spt:207.0,6.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 212[6:Rew:179.0,3.1,175.0,3.1] || -> equal(inverse(sk_c5),sk_c9)** equal(sk_c8,sk_c9).
% 0.20/0.55 213[6:MRR:212.1,144.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.55 216[6:Rew:179.0,7.1,175.0,7.1,166.0,7.0] || -> equal(sk_c7,sk_c9)** equal(sk_c8,sk_c9).
% 0.20/0.55 217[6:MRR:216.1,144.0] || -> equal(sk_c7,sk_c9)**.
% 0.20/0.55 218[7:Rew:217.0,210.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.55 219[6:Rew:179.0,5.1,175.0,5.1,217.0,5.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)** equal(sk_c8,sk_c9).
% 0.20/0.55 220[6:MRR:219.1,144.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.20/0.55 221[6:Rew:179.0,4.1,175.0,4.1,166.0,4.0] || -> equal(sk_c5,sk_c9) equal(sk_c8,sk_c9)**.
% 0.20/0.55 222[6:MRR:221.1,144.0] || -> equal(sk_c5,sk_c9)**.
% 0.20/0.55 223[6:Rew:222.0,213.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.55 224[6:Rew:146.0,223.0] || -> equal(sk_c2,sk_c9)**.
% 0.20/0.55 227[6:Rew:224.0,159.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.55 254[6:SpR:220.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c9)**.
% 0.20/0.55 256[7:Rew:218.0,254.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.55 257[7:Rew:227.0,256.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 258[7:MRR:257.0,144.0] || -> .
% 0.20/0.55 259[6:Spt:258.0,20.1,60.0] || equal(multiply(sk_c2,sk_c9),sk_c8)** -> .
% 0.20/0.55 260[6:Spt:258.0,20.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 261[6:Rew:153.0,259.0] || equal(identity,sk_c8)** -> .
% 0.20/0.55 264[3:Rew:153.0,15.1] || -> equal(inverse(sk_c4),sk_c10)** equal(identity,sk_c8).
% 0.20/0.55 265[6:MRR:264.1,261.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.55 266[3:Rew:153.0,21.1] || -> equal(multiply(sk_c7,sk_c8),sk_c9)** equal(identity,sk_c8).
% 0.20/0.55 267[6:MRR:266.1,261.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.55 268[3:Rew:153.0,19.1] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(identity,sk_c8).
% 0.20/0.55 269[6:MRR:268.1,261.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 272[3:Rew:153.0,16.1] || -> equal(multiply(sk_c4,sk_c9),sk_c10)** equal(identity,sk_c8).
% 0.20/0.55 273[6:MRR:272.1,261.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.20/0.55 306[6:SpR:267.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c9),sk_c8)**.
% 0.20/0.55 313[6:SpR:269.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.55 315[6:Rew:260.0,313.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.55 321[6:SpR:273.0,89.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.20/0.55 323[6:Rew:101.0,321.0,265.0,321.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 324[6:Rew:323.0,261.0] || equal(identity,sk_c9)** -> .
% 0.20/0.55 326[6:Rew:323.0,267.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.20/0.55 342[6:Rew:323.0,306.0] || -> equal(multiply(inverse(sk_c7),sk_c9),sk_c9)**.
% 0.20/0.55 344[6:Rew:315.0,326.0] || -> equal(sk_c7,sk_c9)**.
% 0.20/0.55 350[6:Rew:45.0,342.0,344.0,342.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 351[6:MRR:350.0,324.0] || -> .
% 0.20/0.55 358[5:Spt:351.0,41.1,54.0] || equal(multiply(sk_c3,sk_c8),sk_c10)** -> .
% 0.20/0.55 359[5:Spt:351.0,41.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 360[5:Rew:130.0,358.0] || equal(multiply(sk_c1,sk_c8),sk_c10)** -> .
% 0.20/0.55 363[4:Rew:130.0,38.1] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c1,sk_c8),sk_c10)**.
% 0.20/0.55 364[5:MRR:363.1,360.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.55 373[4:Rew:130.0,40.1] || -> equal(multiply(sk_c6,sk_c7),sk_c9)** equal(multiply(sk_c1,sk_c8),sk_c10).
% 0.20/0.55 374[5:MRR:373.1,360.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 375[4:Rew:130.0,39.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c1,sk_c8),sk_c10).
% 0.20/0.55 376[5:MRR:375.1,360.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 390[5:SpR:374.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.55 392[5:Rew:359.0,390.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.55 394[5:SpR:376.0,89.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.55 396[5:Rew:364.0,394.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.55 402[5:SpR:392.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.20/0.55 404[5:Rew:45.0,402.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 407[5:Rew:404.0,73.0] || -> equal(multiply(sk_c9,sk_c2),sk_c9)**.
% 0.20/0.55 408[5:Rew:404.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.55 409[5:Rew:404.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.55 412[5:Rew:404.0,59.0] || equal(inverse(sk_c9),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.55 416[5:Rew:408.0,407.0] || -> equal(sk_c2,sk_c9)**.
% 0.20/0.55 417[5:Rew:408.0,396.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 425[5:Rew:416.0,50.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.55 465[5:Rew:409.0,412.2,417.0,412.2,425.0,412.0] || equal(sk_c9,u)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.20/0.55 466[5:Obv:465.1] || equal(u,sk_c9)* -> .
% 0.20/0.55 467[5:UnC:466.0,364.0] || -> .
% 0.20/0.55 476[4:Spt:467.0,13.1,52.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.20/0.55 477[4:Spt:467.0,13.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 479[4:MRR:10.1,476.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.55 483[4:MRR:12.0,476.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 484[4:MRR:11.0,476.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 522[4:SpR:483.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.55 524[4:Rew:477.0,522.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.55 526[4:SpR:484.0,89.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.55 528[4:Rew:479.0,526.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.55 534[4:SpR:524.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.20/0.55 536[4:Rew:45.0,534.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 538[4:Rew:536.0,153.0] || -> equal(multiply(sk_c2,sk_c9),sk_c9)**.
% 0.20/0.55 540[4:Rew:536.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.55 543[4:Rew:536.0,59.0] || equal(inverse(sk_c9),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.55 549[4:Rew:540.0,538.0] || -> equal(sk_c2,sk_c9)**.
% 0.20/0.55 550[4:Rew:540.0,528.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 555[4:Rew:549.0,146.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.55 601[4:Rew:540.0,543.2,550.0,543.2,555.0,543.0] || equal(sk_c9,u)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.20/0.55 602[4:Obv:601.1] || equal(u,sk_c9)* -> .
% 0.20/0.55 603[4:UnC:602.0,89.0] || -> .
% 0.20/0.55 610[3:Spt:603.0,27.1,50.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.20/0.55 611[3:Spt:603.0,27.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 612[3:MRR:24.1,610.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.55 614[3:MRR:28.0,610.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.55 615[3:MRR:26.0,610.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 616[3:MRR:25.0,610.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 637[3:SpR:615.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.55 639[3:Rew:611.0,637.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.55 641[3:SpR:616.0,89.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.55 643[3:Rew:612.0,641.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.55 649[3:SpR:639.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.20/0.55 651[3:Rew:45.0,649.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 653[3:Rew:651.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.55 654[3:Rew:651.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.55 657[3:Rew:651.0,59.0] || equal(inverse(sk_c9),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.55 660[3:Rew:653.0,643.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 666[3:Rew:660.0,614.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.20/0.55 682[3:Rew:654.0,666.0] || -> equal(sk_c7,sk_c9)**.
% 0.20/0.55 683[3:Rew:682.0,611.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.55 684[3:Rew:682.0,615.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.20/0.55 686[3:Rew:654.0,684.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.55 687[3:Rew:686.0,683.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.55 698[3:Rew:654.0,657.2,660.0,657.2,687.0,657.0] || equal(sk_c9,u)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.20/0.55 699[3:Obv:698.1] || equal(u,sk_c9)* -> .
% 0.20/0.55 700[3:UnC:699.0,612.0] || -> .
% 0.20/0.55 707[2:Spt:700.0,34.1,48.0] || equal(inverse(sk_c3),sk_c10)** -> .
% 0.20/0.55 708[2:Spt:700.0,34.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 709[2:MRR:31.1,707.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.55 711[2:MRR:35.0,707.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.55 712[2:MRR:33.0,707.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 713[2:MRR:32.0,707.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 725[2:SpR:712.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.55 727[2:Rew:708.0,725.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.55 729[2:SpR:713.0,89.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.55 731[2:Rew:709.0,729.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.55 740[2:SpR:727.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.20/0.55 742[2:Rew:45.0,740.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 743[2:Rew:742.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.55 744[2:Rew:742.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.55 746[2:Rew:742.0,59.0] || equal(inverse(sk_c9),u) equal(u,sk_c9) equal(multiply(u,sk_c8),sk_c9)** -> .
% 0.20/0.55 749[2:Rew:743.0,731.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 755[2:Rew:749.0,711.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.20/0.55 764[2:Rew:744.0,755.0] || -> equal(sk_c7,sk_c9)**.
% 0.20/0.55 765[2:Rew:764.0,708.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.55 766[2:Rew:764.0,712.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.20/0.55 768[2:Rew:744.0,766.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.55 769[2:Rew:768.0,765.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.55 778[2:Rew:744.0,746.2,749.0,746.2,769.0,746.0] || equal(sk_c9,u)* equal(u,sk_c9)* equal(u,sk_c9)* -> .
% 0.20/0.55 779[2:Obv:778.1] || equal(u,sk_c9)* -> .
% 0.20/0.55 780[2:UnC:779.0,709.0] || -> .
% 0.20/0.55 786[1:Spt:780.0,43.1,43.2,43.3,43.4,43.5,43.8,43.9,43.10,43.11,43.12] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(inverse(y),sk_c10) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c8),sk_c10)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.55 788[2:Spt:13.1] || -> equal(inverse(sk_c1),sk_c10)**.
% 0.20/0.55 791[3:Spt:27.1] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.20/0.55 792[3:SpR:791.0,89.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.20/0.55 794[4:Spt:31.1] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.20/0.55 797[5:Spt:6.1] || -> equal(multiply(sk_c1,sk_c10),sk_c9)**.
% 0.20/0.55 799[5:SpR:797.0,89.0] || -> equal(multiply(inverse(sk_c1),sk_c9),sk_c10)**.
% 0.20/0.55 801[5:Rew:788.0,799.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.55 802[6:Spt:20.1] || -> equal(multiply(sk_c2,sk_c9),sk_c8)**.
% 0.20/0.55 804[6:SpR:802.0,89.0] || -> equal(multiply(inverse(sk_c2),sk_c8),sk_c9)**.
% 0.20/0.55 806[6:Rew:791.0,804.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.55 808[5:SpR:801.0,89.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c9)**.
% 0.20/0.55 810[5:Rew:45.0,808.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 811[5:Rew:810.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.55 812[5:Rew:810.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.55 813[5:Rew:810.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.20/0.55 815[6:Rew:811.0,806.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 818[5:Rew:811.0,792.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.20/0.55 819[6:Rew:815.0,786.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(inverse(y),sk_c10) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c8),sk_c10)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.55 821[6:Rew:815.0,37.1] || -> equal(multiply(sk_c4,sk_c9),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.20/0.55 826[6:Rew:815.0,36.1] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c3,sk_c9),sk_c10)**.
% 0.20/0.55 832[6:Rew:812.0,826.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c3,sk_c10).
% 0.20/0.55 834[6:Rew:812.0,821.1,812.0,821.0] || -> equal(sk_c4,sk_c10) equal(sk_c3,sk_c10)**.
% 0.20/0.55 835[6:Rew:834.0,832.0] || -> equal(inverse(sk_c10),sk_c10)** equal(sk_c3,sk_c10).
% 0.20/0.55 844[6:Rew:812.0,819.8,815.0,819.8,812.0,819.7,815.0,819.7,812.0,819.6,812.0,819.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10)** equal(inverse(x),sk_c9)** equal(inverse(y),sk_c10) equal(u,sk_c9) equal(v,sk_c10) equal(w,sk_c10) equal(x,sk_c9) equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.55 845[6:Con:844.2] || 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)** -> .
% 0.20/0.55 862[5:SpR:818.0,812.0] || -> equal(sk_c2,sk_c9)**.
% 0.20/0.55 864[5:Rew:862.0,791.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.55 873[7:Spt:834.1] || -> equal(sk_c3,sk_c10)**.
% 0.20/0.55 874[7:Rew:873.0,794.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.55 880[5:SpR:813.0,89.0] || -> equal(multiply(inverse(inverse(u)),sk_c9),u)**.
% 0.20/0.55 883[5:SpR:788.0,813.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.20/0.55 886[5:Rew:812.0,880.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.55 890[5:SpR:883.0,89.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.20/0.55 892[7:Rew:812.0,890.0,874.0,890.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.55 893[7:Rew:892.0,788.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.55 894[7:Rew:892.0,797.0] || -> equal(multiply(sk_c1,sk_c1),sk_c9)**.
% 0.20/0.55 900[7:Rew:892.0,845.1] || 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)** -> .
% 0.20/0.55 905[7:Rew:892.0,900.5,892.0,900.4,892.0,900.2] || 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)**+ -> .
% 0.20/0.55 934[7:SpL:894.0,905.5] || 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) -> .
% 0.20/0.55 935[7:Obv:934.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.20/0.55 936[7:Rew:893.0,935.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.20/0.55 937[7:Obv:936.2] || equal(inverse(u),sk_c9)**+ equal(inverse(v),sk_c1)** equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.20/0.55 1216[7:SpL:864.0,937.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c1)** equal(sk_c9,sk_c9) equal(u,sk_c1) -> .
% 0.20/0.55 1219[7:Obv:1216.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.55 1222[7:SpL:893.0,1219.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.55 1225[7:Obv:1222.1] || -> .
% 0.20/0.55 1226[7:Spt:1225.0,834.1,873.0] || equal(sk_c3,sk_c10)** -> .
% 0.20/0.55 1227[7:Spt:1225.0,834.0] || -> equal(sk_c4,sk_c10)**.
% 0.20/0.55 1231[5:Rew:812.0,890.0] || -> equal(inverse(sk_c10),sk_c1)**.
% 0.20/0.55 1232[6:Rew:1231.0,835.0] || -> equal(sk_c10,sk_c1) equal(sk_c3,sk_c10)**.
% 0.20/0.55 1233[7:MRR:1232.1,1226.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.55 1235[7:Rew:1233.0,794.0] || -> equal(inverse(sk_c3),sk_c1)**.
% 0.20/0.55 1236[7:Rew:1233.0,788.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.55 1237[7:Rew:1233.0,1226.0] || equal(sk_c3,sk_c1)** -> .
% 0.20/0.55 1255[7:SpR:1235.0,886.0] || -> equal(inverse(sk_c1),sk_c3)**.
% 0.20/0.55 1259[7:Rew:1236.0,1255.0] || -> equal(sk_c3,sk_c1)**.
% 0.20/0.55 1260[7:MRR:1259.0,1237.0] || -> .
% 0.20/0.55 1261[6:Spt:1260.0,20.1,802.0] || equal(multiply(sk_c2,sk_c9),sk_c8)** -> .
% 0.20/0.55 1262[6:Spt:1260.0,20.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 1263[6:Rew:811.0,1261.0,862.0,1261.0] || equal(sk_c8,sk_c9)** -> .
% 0.20/0.55 1265[5:Rew:862.0,17.1,812.0,17.1] || -> equal(inverse(sk_c5),sk_c9)** equal(sk_c8,sk_c9).
% 0.20/0.55 1266[6:MRR:1265.1,1263.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.55 1273[5:Rew:862.0,18.1,812.0,18.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(sk_c8,sk_c9).
% 0.20/0.55 1274[6:MRR:1273.1,1263.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 1304[6:SpR:1266.0,886.0] || -> equal(inverse(sk_c9),sk_c5)**.
% 0.20/0.55 1308[6:Rew:864.0,1304.0] || -> equal(sk_c5,sk_c9)**.
% 0.20/0.55 1310[6:Rew:1308.0,1274.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.55 1313[6:Rew:811.0,1310.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 1314[6:MRR:1313.0,1263.0] || -> .
% 0.20/0.55 1319[5:Spt:1314.0,6.1,797.0] || equal(multiply(sk_c1,sk_c10),sk_c9)** -> .
% 0.20/0.55 1320[5:Spt:1314.0,6.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 1322[5:MRR:1.1,1319.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.55 1325[5:MRR:5.1,1319.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 1327[5:MRR:2.1,1319.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.20/0.55 1352[5:SpR:1325.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.55 1354[5:Rew:1320.0,1352.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.55 1360[5:SpR:1327.0,89.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.20/0.55 1362[5:Rew:1322.0,1360.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.20/0.55 1364[5:SpR:1354.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.20/0.55 1366[5:Rew:45.0,1364.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 1367[5:Rew:1366.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.55 1370[5:Rew:1366.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.20/0.55 1371[5:Rew:1367.0,1327.0] || -> equal(sk_c4,sk_c10)**.
% 0.20/0.55 1376[5:Rew:1371.0,1322.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.55 1450[5:SpR:788.0,1370.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.20/0.55 1467[5:SpR:1450.0,89.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.20/0.55 1469[5:Rew:1367.0,1467.0,1376.0,1467.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.55 1473[5:Rew:1469.0,1362.0] || -> equal(multiply(sk_c1,sk_c1),sk_c9)**.
% 0.20/0.55 1474[5:Rew:1469.0,1319.0] || equal(multiply(sk_c1,sk_c1),sk_c9)** -> .
% 0.20/0.55 1480[5:Rew:1473.0,1474.0] || equal(sk_c9,sk_c9)* -> .
% 0.20/0.55 1481[5:Obv:1480.0] || -> .
% 0.20/0.55 1485[4:Spt:1481.0,31.1,794.0] || equal(inverse(sk_c3),sk_c10)** -> .
% 0.20/0.55 1486[4:Spt:1481.0,31.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.55 1487[4:MRR:29.1,1485.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.55 1488[4:MRR:34.1,1485.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 1489[4:MRR:35.0,1485.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.55 1490[4:MRR:33.0,1485.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 1491[4:MRR:32.0,1485.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 1492[4:MRR:30.0,1485.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.20/0.55 1507[4:SpR:1490.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.55 1509[4:Rew:1488.0,1507.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.55 1511[4:SpR:1491.0,89.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.55 1513[4:Rew:1486.0,1511.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.55 1515[4:SpR:1492.0,89.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.20/0.55 1517[4:Rew:1487.0,1515.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.20/0.55 1519[4:SpR:1509.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.20/0.55 1521[4:Rew:45.0,1519.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 1522[4:Rew:1521.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.55 1523[4:Rew:1521.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.55 1524[4:Rew:1521.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.20/0.55 1526[4:Rew:1522.0,1513.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 1533[4:Rew:1526.0,1489.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.20/0.55 1535[4:Rew:1526.0,786.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(inverse(y),sk_c10) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c8),sk_c10)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.55 1538[4:Rew:1523.0,1492.0] || -> equal(sk_c4,sk_c10)**.
% 0.20/0.55 1539[4:Rew:1538.0,1487.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.55 1541[4:Rew:1523.0,1533.0] || -> equal(sk_c7,sk_c9)**.
% 0.20/0.55 1542[4:Rew:1541.0,1488.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.55 1543[4:Rew:1541.0,1490.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.20/0.55 1545[4:Rew:1523.0,1543.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.55 1546[4:Rew:1545.0,1542.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.55 1555[4:Rew:1523.0,1535.8,1526.0,1535.8,1523.0,1535.7,1526.0,1535.7,1523.0,1535.6,1523.0,1535.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10)** equal(inverse(x),sk_c9)** equal(inverse(y),sk_c10) equal(u,sk_c9) equal(v,sk_c10) equal(w,sk_c10) equal(x,sk_c9) equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.55 1556[4:Con:1555.2] || 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)** -> .
% 0.20/0.55 1591[4:SpR:788.0,1524.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.20/0.55 1606[4:SpR:1591.0,89.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.20/0.55 1608[4:Rew:1523.0,1606.0,1539.0,1606.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.55 1609[4:Rew:1608.0,788.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.55 1613[4:Rew:1608.0,1517.0] || -> equal(multiply(sk_c1,sk_c1),sk_c9)**.
% 0.20/0.55 1617[4:Rew:1608.0,1556.1] || 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)** -> .
% 0.20/0.55 1620[4:Rew:1608.0,1617.5,1608.0,1617.4,1608.0,1617.2] || 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)**+ -> .
% 0.20/0.55 1640[4:SpL:1613.0,1620.5] || 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) -> .
% 0.20/0.55 1641[4:Obv:1640.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(inverse(sk_c1),sk_c1)** equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.20/0.55 1642[4:Rew:1609.0,1641.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(sk_c1,sk_c1) equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.20/0.55 1643[4:Obv:1642.2] || equal(inverse(u),sk_c9)**+ equal(inverse(v),sk_c1)** equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.20/0.55 1895[4:SpL:1546.0,1643.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c1)** equal(sk_c9,sk_c9) equal(u,sk_c1) -> .
% 0.20/0.55 1898[4:Obv:1895.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.55 1901[4:SpL:1609.0,1898.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.55 1904[4:Obv:1901.1] || -> .
% 0.20/0.55 1905[3:Spt:1904.0,27.1,791.0] || equal(inverse(sk_c2),sk_c9)** -> .
% 0.20/0.55 1906[3:Spt:1904.0,27.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.55 1907[3:MRR:24.1,1905.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.55 1908[3:MRR:22.1,1905.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.55 1910[3:MRR:28.0,1905.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.55 1911[3:MRR:26.0,1905.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.55 1912[3:MRR:25.0,1905.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.55 1913[3:MRR:23.0,1905.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.20/0.55 1934[3:SpR:1911.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.55 1936[3:Rew:1906.0,1934.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.55 1938[3:SpR:1912.0,89.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.55 1940[3:Rew:1907.0,1938.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.55 1942[3:SpR:1913.0,89.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.20/0.55 1944[3:Rew:1908.0,1942.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.20/0.55 1949[3:SpR:1936.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.20/0.55 1951[3:Rew:45.0,1949.0] || -> equal(identity,sk_c9)**.
% 0.20/0.55 1952[3:Rew:1951.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.55 1953[3:Rew:1951.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.55 1955[3:Rew:1951.0,45.0] || -> equal(multiply(inverse(u),u),sk_c9)**.
% 0.20/0.55 1956[3:Rew:1952.0,1940.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.55 1962[3:Rew:1956.0,1910.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.20/0.55 1964[3:Rew:1956.0,786.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(inverse(y),sk_c10) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c8),sk_c10)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.55 1967[3:Rew:1953.0,1913.0] || -> equal(sk_c4,sk_c10)**.
% 0.20/0.55 1968[3:Rew:1967.0,1908.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.55 1970[3:Rew:1953.0,1962.0] || -> equal(sk_c7,sk_c9)**.
% 0.20/0.55 1971[3:Rew:1970.0,1906.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.55 1972[3:Rew:1970.0,1911.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.20/0.55 1974[3:Rew:1953.0,1972.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.55 1975[3:Rew:1974.0,1971.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.55 1984[3:Rew:1953.0,1964.8,1956.0,1964.8,1953.0,1964.7,1956.0,1964.7,1953.0,1964.6,1953.0,1964.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10)** equal(inverse(x),sk_c9)** equal(inverse(y),sk_c10) equal(u,sk_c9) equal(v,sk_c10) equal(w,sk_c10) equal(x,sk_c9) equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.55 1985[3:Con:1984.2] || 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)**+ -> .
% 0.20/0.55 2028[3:SpR:788.0,1955.0] || -> equal(multiply(sk_c10,sk_c1),sk_c9)**.
% 0.20/0.55 2035[3:SpL:1944.0,1985.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(sk_c10),sk_c10)** equal(u,sk_c9) equal(v,sk_c10) equal(sk_c9,sk_c9) -> .
% 0.20/0.55 2041[3:Obv:2035.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(sk_c10),sk_c10)** equal(u,sk_c9) equal(v,sk_c10) -> .
% 0.20/0.55 2042[3:Rew:1968.0,2041.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c9) equal(v,sk_c10) -> .
% 0.20/0.55 2043[3:Obv:2042.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(u,sk_c9) equal(v,sk_c10) -> .
% 0.20/0.55 2046[3:SpR:2028.0,89.0] || -> equal(multiply(inverse(sk_c10),sk_c9),sk_c1)**.
% 0.20/0.55 2048[3:Rew:1953.0,2046.0,1968.0,2046.0] || -> equal(sk_c10,sk_c1)**.
% 0.20/0.55 2049[3:Rew:2048.0,788.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.20/0.55 2057[3:Rew:2048.0,2043.1] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c1)** equal(u,sk_c9) equal(v,sk_c10) -> .
% 0.20/0.55 2060[3:Rew:2048.0,2057.3] || equal(inverse(u),sk_c9)**+ equal(inverse(v),sk_c1)** equal(u,sk_c9) equal(v,sk_c1) -> .
% 0.20/0.56 2390[3:SpL:1975.0,2060.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c1)** equal(sk_c9,sk_c9) equal(u,sk_c1) -> .
% 0.20/0.56 2394[3:Obv:2390.2] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.20/0.56 2397[3:SpL:2049.0,2394.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.20/0.56 2401[3:Obv:2397.1] || -> .
% 0.20/0.56 2402[2:Spt:2401.0,13.1,788.0] || equal(inverse(sk_c1),sk_c10)** -> .
% 0.20/0.56 2403[2:Spt:2401.0,13.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.56 2404[2:MRR:10.1,2402.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.56 2405[2:MRR:8.1,2402.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.56 2407[2:MRR:14.0,2402.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.20/0.56 2408[2:MRR:12.0,2402.0] || -> equal(multiply(sk_c6,sk_c7),sk_c9)**.
% 0.20/0.56 2409[2:MRR:11.0,2402.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.56 2410[2:MRR:9.0,2402.0] || -> equal(multiply(sk_c4,sk_c9),sk_c10)**.
% 0.20/0.56 2429[2:SpR:2408.0,89.0] || -> equal(multiply(inverse(sk_c6),sk_c9),sk_c7)**.
% 0.20/0.56 2431[2:Rew:2403.0,2429.0] || -> equal(multiply(sk_c7,sk_c9),sk_c7)**.
% 0.20/0.56 2433[2:SpR:2409.0,89.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.56 2435[2:Rew:2404.0,2433.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.56 2437[2:SpR:2410.0,89.0] || -> equal(multiply(inverse(sk_c4),sk_c10),sk_c9)**.
% 0.20/0.56 2439[2:Rew:2405.0,2437.0] || -> equal(multiply(sk_c10,sk_c10),sk_c9)**.
% 0.20/0.56 2441[2:SpR:2431.0,89.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.20/0.56 2443[2:Rew:45.0,2441.0] || -> equal(identity,sk_c9)**.
% 0.20/0.56 2444[2:Rew:2443.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.56 2445[2:Rew:2443.0,145.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.56 2449[2:Rew:2444.0,2435.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.56 2454[2:Rew:2449.0,2407.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.20/0.56 2456[2:Rew:2449.0,786.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(inverse(y),sk_c10) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c9),sk_c10)** equal(multiply(w,sk_c8),sk_c10)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.56 2459[2:Rew:2445.0,2410.0] || -> equal(sk_c4,sk_c10)**.
% 0.20/0.56 2460[2:Rew:2459.0,2405.0] || -> equal(inverse(sk_c10),sk_c10)**.
% 0.20/0.56 2462[2:Rew:2445.0,2454.0] || -> equal(sk_c7,sk_c9)**.
% 0.20/0.56 2463[2:Rew:2462.0,2403.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.20/0.56 2464[2:Rew:2462.0,2408.0] || -> equal(multiply(sk_c6,sk_c9),sk_c9)**.
% 0.20/0.56 2466[2:Rew:2445.0,2464.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.56 2467[2:Rew:2466.0,2463.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.56 2476[2:Rew:2445.0,2456.8,2449.0,2456.8,2445.0,2456.7,2449.0,2456.7,2445.0,2456.6,2445.0,2456.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(w),sk_c10)** equal(inverse(x),sk_c9)** equal(inverse(y),sk_c10) equal(u,sk_c9) equal(v,sk_c10) equal(w,sk_c10) equal(x,sk_c9) equal(multiply(y,sk_c10),sk_c9)** -> .
% 0.20/0.56 2477[2:Con:2476.2] || 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)**+ -> .
% 0.20/0.56 2546[2:SpL:2439.0,2477.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(sk_c10),sk_c10)** equal(u,sk_c9) equal(v,sk_c10) equal(sk_c9,sk_c9) -> .
% 0.20/0.56 2552[2:Obv:2546.5] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(inverse(sk_c10),sk_c10)** equal(u,sk_c9) equal(v,sk_c10) -> .
% 0.20/0.56 2553[2:Rew:2460.0,2552.2] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c10)** equal(sk_c10,sk_c10) equal(u,sk_c9) equal(v,sk_c10) -> .
% 0.20/0.56 2554[2:Obv:2553.2] || equal(inverse(u),sk_c9)**+ equal(inverse(v),sk_c10)** equal(u,sk_c9) equal(v,sk_c10) -> .
% 0.20/0.56 3006[2:SpL:2467.0,2554.0] || equal(sk_c9,sk_c9) equal(inverse(u),sk_c10)** equal(sk_c9,sk_c9) equal(u,sk_c10) -> .
% 0.20/0.56 3011[2:Obv:3006.2] || equal(inverse(u),sk_c10)** equal(u,sk_c10) -> .
% 0.20/0.56 3012[2:SpL:2460.0,3011.0] || equal(sk_c10,sk_c10)* equal(sk_c10,sk_c10)* -> .
% 0.20/0.56 3017[2:Obv:3012.1] || -> .
% 0.20/0.56 % SZS output end Refutation
% 0.20/0.56 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 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_39 prove_this_40 prove_this_41 prove_this_43 left_identity left_inverse associativity
% 0.20/0.56
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