TSTP Solution File: GRP325-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP325-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:46:51 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Refutation 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP325-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 05:01:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.53
% 0.20/0.53 SPASS V 3.9
% 0.20/0.53 SPASS beiseite: Proof found.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.53 SPASS derived 1446 clauses, backtracked 553 clauses, performed 11 splits and kept 1007 clauses.
% 0.20/0.53 SPASS allocated 64006 KBytes.
% 0.20/0.53 SPASS spent 0:00:00.18 on the problem.
% 0.20/0.53 0:00:00.03 for the input.
% 0.20/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.53 0:00:00.01 for inferences.
% 0.20/0.53 0:00:00.00 for the backtracking.
% 0.20/0.53 0:00:00.10 for the reduction.
% 0.20/0.53
% 0.20/0.53
% 0.20/0.53 Here is a proof with depth 4, length 401 :
% 0.20/0.53 % SZS output start Refutation
% 0.20/0.53 1[0:Inp] || -> equal(multiply(sk_c9,sk_c10),sk_c8)**.
% 0.20/0.53 4[0:Inp] || -> equal(inverse(sk_c9),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.53 5[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.53 11[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 12[0:Inp] || -> equal(inverse(sk_c4),sk_c10)** equal(inverse(sk_c1),sk_c9).
% 0.20/0.53 13[0:Inp] || -> equal(inverse(sk_c9),sk_c8) equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.53 14[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.53 15[0:Inp] || -> equal(inverse(sk_c5),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.20/0.53 16[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 17[0:Inp] || -> equal(inverse(sk_c7),sk_c6)** equal(inverse(sk_c1),sk_c9).
% 0.20/0.53 18[0:Inp] || -> equal(inverse(sk_c6),sk_c10)** equal(inverse(sk_c1),sk_c9).
% 0.20/0.53 19[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c7,sk_c10),sk_c6)**.
% 0.20/0.53 20[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(multiply(sk_c10,sk_c3),sk_c9).
% 0.20/0.53 21[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.20/0.53 22[0:Inp] || -> equal(inverse(sk_c9),sk_c8) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.20/0.53 23[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.20/0.53 24[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.20/0.53 25[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c10,sk_c3),sk_c9).
% 0.20/0.53 29[0:Inp] || -> equal(multiply(sk_c4,sk_c10),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 30[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 31[0:Inp] || -> equal(inverse(sk_c9),sk_c8) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 32[0:Inp] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 33[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 34[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 35[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 36[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 37[0:Inp] || -> equal(multiply(sk_c7,sk_c10),sk_c6) equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 38[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 39[0:Inp] || -> equal(inverse(sk_c4),sk_c10) equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.53 40[0:Inp] || -> equal(inverse(sk_c9),sk_c8) equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.53 41[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.53 42[0:Inp] || -> equal(inverse(sk_c5),sk_c9) equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.53 43[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 44[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.53 45[0:Inp] || -> equal(inverse(sk_c6),sk_c10) equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.53 46[0:Inp] || -> equal(inverse(sk_c2),sk_c10) equal(multiply(sk_c7,sk_c10),sk_c6)**.
% 0.20/0.53 47[0:Inp] || equal(multiply(sk_c9,sk_c10),sk_c8) equal(multiply(u,sk_c9),sk_c10)** equal(inverse(u),sk_c9) equal(multiply(sk_c10,v),sk_c9)** equal(multiply(w,sk_c10),v)* equal(inverse(w),sk_c10) equal(multiply(x,sk_c10),sk_c9)** equal(inverse(x),sk_c10) equal(inverse(sk_c9),sk_c8) equal(multiply(sk_c10,sk_c8),sk_c9)** equal(inverse(y),sk_c9) equal(multiply(y,sk_c8),sk_c9)** equal(inverse(z),x1) equal(inverse(x1),sk_c10)** equal(multiply(z,sk_c10),x1)* -> .
% 0.20/0.53 48[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.53 49[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.53 50[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.53 51[0:Rew:1.0,47.0] || equal(sk_c8,sk_c8) equal(multiply(u,sk_c9),sk_c10)** equal(inverse(u),sk_c9) equal(multiply(sk_c10,v),sk_c9)** equal(multiply(w,sk_c10),v)* equal(inverse(w),sk_c10) equal(multiply(x,sk_c10),sk_c9)** equal(inverse(x),sk_c10) equal(inverse(sk_c9),sk_c8) equal(multiply(sk_c10,sk_c8),sk_c9)** equal(inverse(y),sk_c9) equal(multiply(y,sk_c8),sk_c9)** equal(inverse(z),x1) equal(inverse(x1),sk_c10)** equal(multiply(z,sk_c10),x1)* -> .
% 0.20/0.53 52[0:Obv:51.0] || equal(inverse(u),v) equal(inverse(v),sk_c10)** equal(inverse(w),sk_c9) equal(inverse(x),sk_c10) equal(inverse(y),sk_c10) equal(inverse(z),sk_c9) equal(inverse(sk_c9),sk_c8) equal(multiply(u,sk_c10),v)*+ equal(multiply(y,sk_c10),x1)* equal(multiply(w,sk_c8),sk_c9)** equal(multiply(x,sk_c10),sk_c9)** equal(multiply(z,sk_c9),sk_c10)** equal(multiply(sk_c10,x1),sk_c9)** equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.20/0.53 53[1:Spt:52.0,52.1,52.7] || equal(inverse(u),v) equal(inverse(v),sk_c10)** equal(multiply(u,sk_c10),v)*+ -> .
% 0.20/0.53 55[2:Spt:40.1] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.53 57[3:Spt:13.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.53 59[4:Spt:31.1] || -> equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 61[4:SpL:59.0,53.2] || equal(inverse(sk_c2),u)* equal(inverse(u),sk_c10)** equal(sk_c3,u) -> .
% 0.20/0.53 62[4:Rew:55.0,61.0] || equal(sk_c10,u) equal(inverse(u),sk_c10)** equal(sk_c3,u) -> .
% 0.20/0.53 63[5:Spt:22.1] || -> equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.20/0.53 65[6:Spt:4.1] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.20/0.53 68[1:SpL:1.0,53.2] || equal(inverse(sk_c9),u)* equal(inverse(u),sk_c10)** equal(sk_c8,u) -> .
% 0.20/0.53 72[2:SpR:55.0,49.0] || -> equal(multiply(sk_c10,sk_c2),identity)**.
% 0.20/0.53 73[3:SpR:57.0,49.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.20/0.53 79[0:SpR:1.0,50.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),multiply(sk_c8,u))**.
% 0.20/0.53 81[2:SpR:72.0,50.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),multiply(identity,u))**.
% 0.20/0.53 84[0:SpR:49.0,50.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.53 86[2:Rew:48.0,81.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.20/0.53 87[0:Rew:48.0,84.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.53 94[4:SpR:59.0,86.0] || -> equal(multiply(sk_c10,sk_c3),sk_c10)**.
% 0.20/0.53 95[5:Rew:63.0,94.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 98[5:Rew:95.0,59.0] || -> equal(multiply(sk_c2,sk_c9),sk_c3)**.
% 0.20/0.53 99[5:Rew:95.0,63.0] || -> equal(multiply(sk_c9,sk_c3),sk_c9)**.
% 0.20/0.53 100[6:Rew:95.0,65.0] || -> equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.20/0.53 102[5:Rew:95.0,72.0] || -> equal(multiply(sk_c9,sk_c2),identity)**.
% 0.20/0.53 106[5:Rew:95.0,62.0] || equal(sk_c9,u) equal(inverse(u),sk_c10)** equal(sk_c3,u) -> .
% 0.20/0.53 116[5:Rew:95.0,106.1] || equal(sk_c9,u) equal(inverse(u),sk_c9)** equal(sk_c3,u) -> .
% 0.20/0.53 137[0:SpR:87.0,87.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.53 140[0:SpR:49.0,87.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.53 142[3:SpR:73.0,87.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c1)**.
% 0.20/0.53 144[5:SpR:99.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c3)**.
% 0.20/0.53 145[5:SpR:102.0,87.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c2)**.
% 0.20/0.53 150[5:Rew:49.0,144.0] || -> equal(identity,sk_c3)**.
% 0.20/0.53 151[5:Rew:150.0,48.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.53 153[5:Rew:150.0,73.0] || -> equal(multiply(sk_c9,sk_c1),sk_c3)**.
% 0.20/0.53 154[5:Rew:150.0,102.0] || -> equal(multiply(sk_c9,sk_c2),sk_c3)**.
% 0.20/0.53 158[5:Rew:150.0,142.0] || -> equal(multiply(inverse(sk_c9),sk_c3),sk_c1)**.
% 0.20/0.53 161[5:Rew:150.0,145.0] || -> equal(multiply(inverse(sk_c9),sk_c3),sk_c2)**.
% 0.20/0.53 168[5:Rew:161.0,158.0] || -> equal(sk_c2,sk_c1)**.
% 0.20/0.53 170[5:Rew:168.0,98.0] || -> equal(multiply(sk_c1,sk_c9),sk_c3)**.
% 0.20/0.53 172[5:Rew:168.0,154.0] || -> equal(multiply(sk_c9,sk_c1),sk_c3)**.
% 0.20/0.53 173[5:Rew:168.0,161.0] || -> equal(multiply(inverse(sk_c9),sk_c3),sk_c1)**.
% 0.20/0.53 174[6:Rew:100.0,170.0] || -> equal(sk_c3,sk_c9)**.
% 0.20/0.53 176[6:Rew:174.0,116.2] || equal(sk_c9,u) equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.20/0.53 178[6:Rew:174.0,151.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.53 182[6:Rew:174.0,172.0] || -> equal(multiply(sk_c9,sk_c1),sk_c9)**.
% 0.20/0.53 183[6:Rew:178.0,182.0] || -> equal(sk_c1,sk_c9)**.
% 0.20/0.53 186[6:Rew:183.0,57.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 206[6:Obv:176.0] || equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.20/0.53 271[6:SpL:186.0,206.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.20/0.53 273[6:Obv:271.1] || -> .
% 0.20/0.53 274[6:Spt:273.0,4.1,65.0] || equal(multiply(sk_c1,sk_c9),sk_c10)** -> .
% 0.20/0.53 275[6:Spt:273.0,4.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.20/0.53 277[6:Rew:275.0,173.0] || -> equal(multiply(sk_c8,sk_c3),sk_c1)**.
% 0.20/0.53 278[6:Rew:95.0,274.0] || equal(multiply(sk_c1,sk_c9),sk_c9)** -> .
% 0.20/0.53 279[6:Rew:170.0,278.0] || equal(sk_c3,sk_c9)** -> .
% 0.20/0.53 280[5:Rew:150.0,140.0] || -> equal(multiply(inverse(inverse(u)),sk_c3),u)**.
% 0.20/0.53 295[5:Rew:137.0,280.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.20/0.53 296[6:Rew:295.0,277.0] || -> equal(sk_c1,sk_c8)**.
% 0.20/0.53 299[6:Rew:296.0,170.0] || -> equal(multiply(sk_c8,sk_c9),sk_c3)**.
% 0.20/0.53 300[6:Rew:296.0,153.0] || -> equal(multiply(sk_c9,sk_c8),sk_c3)**.
% 0.20/0.53 309[5:Rew:95.0,5.1,95.0,5.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.20/0.53 310[6:Rew:299.0,309.1,296.0,309.1,300.0,309.0] || -> equal(sk_c3,sk_c9)** equal(sk_c3,sk_c9)**.
% 0.20/0.53 311[6:Obv:310.0] || -> equal(sk_c3,sk_c9)**.
% 0.20/0.53 312[6:MRR:311.0,279.0] || -> .
% 0.20/0.53 319[5:Spt:312.0,22.1,63.0] || equal(multiply(sk_c10,sk_c3),sk_c9)** -> .
% 0.20/0.53 320[5:Spt:312.0,22.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.20/0.53 322[5:Rew:94.0,319.0] || equal(sk_c10,sk_c9)** -> .
% 0.20/0.53 323[0:Rew:137.0,140.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.53 336[4:Rew:94.0,24.1] || -> equal(inverse(sk_c5),sk_c9)** equal(sk_c10,sk_c9).
% 0.20/0.53 337[5:MRR:336.1,322.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.53 346[4:Rew:94.0,25.1] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(sk_c10,sk_c9).
% 0.20/0.53 347[5:MRR:346.1,322.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 386[0:SpR:1.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c10)**.
% 0.20/0.53 388[5:Rew:320.0,386.0] || -> equal(multiply(sk_c8,sk_c8),sk_c10)**.
% 0.20/0.53 399[5:SpR:347.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.53 401[5:Rew:337.0,399.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.53 436[5:SpR:401.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.20/0.53 438[5:Rew:388.0,436.0,320.0,436.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 439[5:MRR:438.0,322.0] || -> .
% 0.20/0.53 440[4:Spt:439.0,31.1,59.0] || equal(multiply(sk_c2,sk_c10),sk_c3)** -> .
% 0.20/0.53 441[4:Spt:439.0,31.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.20/0.53 445[4:Rew:441.0,386.0] || -> equal(multiply(sk_c8,sk_c8),sk_c10)**.
% 0.20/0.53 453[4:MRR:33.1,440.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.53 454[4:MRR:30.1,440.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.53 460[4:MRR:34.1,440.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 462[4:MRR:29.1,440.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 463[4:Rew:441.0,68.0] || equal(sk_c8,u) equal(inverse(u),sk_c10)** equal(sk_c8,u) -> .
% 0.20/0.53 464[4:Obv:463.0] || equal(inverse(u),sk_c10)** equal(sk_c8,u) -> .
% 0.20/0.53 501[4:SpR:460.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.53 503[4:Rew:453.0,501.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.53 509[4:SpR:462.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.20/0.53 511[4:Rew:454.0,509.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.53 517[4:SpR:503.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.20/0.53 519[4:Rew:445.0,517.0,441.0,517.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 544[4:Rew:519.0,464.0] || equal(inverse(u),sk_c9)** equal(sk_c8,u) -> .
% 0.20/0.53 548[4:Rew:519.0,511.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 560[4:Rew:503.0,548.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.53 561[4:Rew:560.0,441.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 602[4:Rew:560.0,544.1] || equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.20/0.53 678[4:SpL:561.0,602.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.20/0.53 680[4:Obv:678.1] || -> .
% 0.20/0.53 681[3:Spt:680.0,13.1,57.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.20/0.53 682[3:Spt:680.0,13.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.20/0.53 683[3:Rew:682.0,386.0] || -> equal(multiply(sk_c8,sk_c8),sk_c10)**.
% 0.20/0.53 686[3:MRR:15.1,681.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.53 687[3:MRR:12.1,681.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.53 689[3:MRR:16.0,681.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 691[3:MRR:11.0,681.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 692[3:Rew:682.0,68.0] || equal(sk_c8,u) equal(inverse(u),sk_c10)** equal(sk_c8,u) -> .
% 0.20/0.53 693[3:Obv:692.0] || equal(inverse(u),sk_c10)** equal(sk_c8,u) -> .
% 0.20/0.53 725[3:SpR:689.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.53 727[3:Rew:686.0,725.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.53 733[3:SpR:691.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.20/0.53 735[3:Rew:687.0,733.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.53 741[3:SpR:727.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.20/0.53 743[3:Rew:683.0,741.0,682.0,741.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 764[3:Rew:743.0,693.0] || equal(inverse(u),sk_c9)** equal(sk_c8,u) -> .
% 0.20/0.53 772[3:Rew:743.0,735.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 784[3:Rew:727.0,772.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.53 785[3:Rew:784.0,682.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 823[3:Rew:784.0,764.1] || equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.20/0.53 893[3:SpL:785.0,823.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.20/0.53 895[3:Obv:893.1] || -> .
% 0.20/0.53 896[2:Spt:895.0,40.1,55.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.20/0.53 897[2:Spt:895.0,40.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.20/0.53 898[2:Rew:897.0,386.0] || -> equal(multiply(sk_c8,sk_c8),sk_c10)**.
% 0.20/0.53 902[2:MRR:42.1,896.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.53 903[2:MRR:39.1,896.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.53 905[2:MRR:43.0,896.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 907[2:MRR:38.0,896.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 908[2:Rew:897.0,68.0] || equal(sk_c8,u) equal(inverse(u),sk_c10)** equal(sk_c8,u) -> .
% 0.20/0.53 909[2:Obv:908.0] || equal(inverse(u),sk_c10)** equal(sk_c8,u) -> .
% 0.20/0.53 932[2:SpR:905.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.53 934[2:Rew:902.0,932.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.53 939[2:SpR:907.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.20/0.53 941[2:Rew:903.0,939.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.53 947[2:SpR:934.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.20/0.53 949[2:Rew:898.0,947.0,897.0,947.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 966[2:Rew:949.0,909.0] || equal(inverse(u),sk_c9)** equal(sk_c8,u) -> .
% 0.20/0.53 975[2:Rew:949.0,941.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 977[2:Rew:934.0,975.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.53 978[2:Rew:977.0,897.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 1004[2:Rew:977.0,966.1] || equal(inverse(u),sk_c9)** equal(sk_c9,u) -> .
% 0.20/0.53 1117[2:SpL:978.0,1004.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.20/0.53 1119[2:Obv:1117.1] || -> .
% 0.20/0.53 1120[1:Spt:1119.0,52.2,52.3,52.4,52.5,52.6,52.8,52.9,52.10,52.11,52.12,52.13] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(inverse(sk_c9),sk_c8) equal(multiply(w,sk_c10),y)*+ equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,y),sk_c9)** equal(multiply(sk_c10,sk_c8),sk_c9)** -> .
% 0.20/0.53 1121[1:EqR:1120.5] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(inverse(sk_c9),sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** equal(multiply(sk_c10,sk_c8),sk_c9) -> .
% 0.20/0.53 1123[2:Spt:13.0] || -> equal(inverse(sk_c9),sk_c8)**.
% 0.20/0.53 1125[2:Rew:1123.0,386.0] || -> equal(multiply(sk_c8,sk_c8),sk_c10)**.
% 0.20/0.53 1127[2:Rew:1123.0,1121.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(sk_c8,sk_c8) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** equal(multiply(sk_c10,sk_c8),sk_c9) -> .
% 0.20/0.53 1128[2:Obv:1127.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** equal(multiply(sk_c10,sk_c8),sk_c9) -> .
% 0.20/0.53 1133[3:Spt:41.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.20/0.53 1136[4:Spt:14.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.53 1139[5:Spt:32.1] || -> equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.20/0.53 1141[5:SpR:1139.0,87.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c10)**.
% 0.20/0.53 1143[5:Rew:1133.0,1141.0] || -> equal(multiply(sk_c10,sk_c3),sk_c10)**.
% 0.20/0.53 1144[5:Rew:1143.0,20.1] || -> equal(multiply(sk_c4,sk_c10),sk_c9)** equal(sk_c10,sk_c9).
% 0.20/0.53 1145[5:Rew:1143.0,23.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)** equal(sk_c10,sk_c9).
% 0.20/0.53 1148[5:Rew:1143.0,21.1] || -> equal(inverse(sk_c4),sk_c10)** equal(sk_c10,sk_c9).
% 0.20/0.53 1157[5:Rew:1145.1,5.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.20/0.53 1168[5:SpR:1143.0,87.0] || -> equal(multiply(inverse(sk_c10),sk_c10),sk_c3)**.
% 0.20/0.53 1170[5:Rew:49.0,1168.0] || -> equal(identity,sk_c3)**.
% 0.20/0.53 1171[5:Rew:1170.0,323.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.20/0.53 1172[5:Rew:1170.0,48.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.53 1173[5:Rew:1170.0,49.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.20/0.53 1193[5:SpR:1173.0,87.0] || -> equal(multiply(inverse(inverse(u)),sk_c3),u)**.
% 0.20/0.53 1194[5:SpR:1173.0,1171.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.20/0.53 1196[5:SpR:1123.0,1173.0] || -> equal(multiply(sk_c8,sk_c9),sk_c3)**.
% 0.20/0.53 1197[5:SpR:1133.0,1173.0] || -> equal(multiply(sk_c10,sk_c2),sk_c3)**.
% 0.20/0.53 1198[5:SpR:1136.0,1173.0] || -> equal(multiply(sk_c9,sk_c1),sk_c3)**.
% 0.20/0.53 1200[5:Rew:1171.0,1193.0] || -> equal(inverse(inverse(u)),u)**.
% 0.20/0.53 1208[5:SpR:1196.0,87.0] || -> equal(multiply(inverse(sk_c8),sk_c3),sk_c9)**.
% 0.20/0.53 1210[5:Rew:1171.0,1208.0] || -> equal(inverse(sk_c8),sk_c9)**.
% 0.20/0.53 1214[6:Spt:1148.1] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 1219[6:Rew:1214.0,1157.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.20/0.53 1222[6:Rew:1214.0,1128.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c9) -> .
% 0.20/0.53 1232[6:Rew:1214.0,1222.7,1214.0,1222.6,1214.0,1222.5,1214.0,1222.2,1214.0,1222.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(x,sk_c9),sk_c9)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c9) -> .
% 0.20/0.53 1233[6:Con:1232.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c9)** equal(multiply(sk_c9,sk_c8),sk_c9) -> .
% 0.20/0.53 1240[5:SpR:1210.0,1173.0] || -> equal(multiply(sk_c9,sk_c8),sk_c3)**.
% 0.20/0.53 1244[6:Rew:1240.0,1233.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c9)** equal(sk_c3,sk_c9) -> .
% 0.20/0.53 1245[6:Rew:1240.0,1219.0] || -> equal(sk_c3,sk_c9) equal(multiply(sk_c1,sk_c9),sk_c9)**.
% 0.20/0.53 1250[5:SpR:1198.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c3),sk_c1)**.
% 0.20/0.53 1252[5:Rew:1171.0,1250.0,1123.0,1250.0] || -> equal(sk_c1,sk_c8)**.
% 0.20/0.53 1256[6:Rew:1252.0,1245.1] || -> equal(sk_c3,sk_c9) equal(multiply(sk_c8,sk_c9),sk_c9)**.
% 0.20/0.53 1264[6:Rew:1196.0,1256.1] || -> equal(sk_c3,sk_c9)** equal(sk_c3,sk_c9)**.
% 0.20/0.53 1265[6:Obv:1264.0] || -> equal(sk_c3,sk_c9)**.
% 0.20/0.53 1267[6:Rew:1265.0,1171.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.53 1268[6:Rew:1265.0,1172.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.53 1270[6:Rew:1265.0,1194.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 1277[6:Rew:1265.0,1244.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.20/0.53 1278[6:Rew:1123.0,1270.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.53 1279[6:Rew:1278.0,1123.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 1307[6:Obv:1277.6] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(sk_c9,multiply(w,sk_c9)),sk_c9)** -> .
% 0.20/0.53 1308[6:Rew:1267.0,1307.5,1268.0,1307.5,1267.0,1307.4,1267.0,1307.3,1278.0,1307.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c9)** equal(inverse(w),sk_c9)** equal(u,sk_c9) equal(v,sk_c9) equal(w,sk_c9) -> .
% 0.20/0.53 1309[6:Con:1308.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.20/0.53 1355[6:SpL:1279.0,1309.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.20/0.53 1357[6:Obv:1355.1] || -> .
% 0.20/0.53 1358[6:Spt:1357.0,1148.1,1214.0] || equal(sk_c10,sk_c9)** -> .
% 0.20/0.53 1359[6:Spt:1357.0,1148.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.53 1363[6:MRR:1144.1,1358.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 1375[6:SpR:1359.0,1200.0] || -> equal(inverse(sk_c10),sk_c4)**.
% 0.20/0.53 1380[5:SpR:1133.0,1200.0] || -> equal(inverse(sk_c10),sk_c2)**.
% 0.20/0.53 1382[6:Rew:1375.0,1380.0] || -> equal(sk_c2,sk_c4)**.
% 0.20/0.53 1384[6:Rew:1382.0,1139.0] || -> equal(multiply(sk_c4,sk_c10),sk_c3)**.
% 0.20/0.53 1385[6:Rew:1382.0,1197.0] || -> equal(multiply(sk_c10,sk_c4),sk_c3)**.
% 0.20/0.53 1388[6:Rew:1363.0,1384.0] || -> equal(sk_c3,sk_c9)**.
% 0.20/0.53 1390[6:Rew:1388.0,1194.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 1392[6:Rew:1388.0,1172.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.53 1396[6:Rew:1123.0,1390.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.53 1403[6:Rew:1396.0,79.0] || -> equal(multiply(sk_c9,multiply(sk_c10,u)),multiply(sk_c9,u))**.
% 0.20/0.53 1411[6:Rew:1388.0,1385.0] || -> equal(multiply(sk_c10,sk_c4),sk_c9)**.
% 0.20/0.53 1425[6:Rew:1392.0,1403.0,1392.0,1403.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.20/0.53 1427[6:Rew:1425.0,1411.0] || -> equal(sk_c4,sk_c9)**.
% 0.20/0.53 1430[6:Rew:1427.0,1363.0] || -> equal(multiply(sk_c9,sk_c10),sk_c9)**.
% 0.20/0.53 1437[6:Rew:1392.0,1430.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 1438[6:MRR:1437.0,1358.0] || -> .
% 0.20/0.53 1444[5:Spt:1438.0,32.1,1139.0] || equal(multiply(sk_c2,sk_c10),sk_c3)** -> .
% 0.20/0.53 1445[5:Spt:1438.0,32.0] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.53 1446[5:MRR:36.1,1444.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.20/0.53 1447[5:MRR:35.1,1444.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.53 1448[5:MRR:33.1,1444.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.53 1449[5:MRR:30.1,1444.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.53 1450[5:MRR:37.1,1444.0] || -> equal(multiply(sk_c7,sk_c10),sk_c6)**.
% 0.20/0.53 1451[5:MRR:34.1,1444.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 1452[5:MRR:29.1,1444.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 1453[5:Rew:1445.0,1128.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.20/0.53 1454[5:Obv:1453.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** -> .
% 0.20/0.53 1464[5:SpR:1446.0,87.0] || -> equal(multiply(sk_c10,multiply(sk_c6,u)),u)**.
% 0.20/0.53 1484[5:SpR:1450.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c10)**.
% 0.20/0.53 1486[5:Rew:1447.0,1484.0] || -> equal(multiply(sk_c6,sk_c6),sk_c10)**.
% 0.20/0.53 1488[5:SpR:1451.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.53 1490[5:Rew:1448.0,1488.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.53 1492[5:SpR:1452.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.20/0.53 1494[5:Rew:1449.0,1492.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.53 1496[5:SpR:1486.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c10),sk_c6)**.
% 0.20/0.53 1498[5:Rew:1446.0,1496.0] || -> equal(multiply(sk_c10,sk_c10),sk_c6)**.
% 0.20/0.53 1499[5:SpR:1490.0,50.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.20/0.53 1500[5:SpR:1490.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.20/0.53 1502[5:Rew:1125.0,1500.0,1123.0,1500.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 1523[5:Rew:1502.0,1454.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** -> .
% 0.20/0.53 1526[5:Rew:1502.0,1464.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.20/0.53 1528[5:Rew:1502.0,1494.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 1529[5:Rew:1502.0,1498.0] || -> equal(multiply(sk_c9,sk_c9),sk_c6)**.
% 0.20/0.53 1530[5:Rew:1490.0,1528.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.53 1531[5:Rew:1530.0,1123.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 1533[5:Rew:1530.0,1490.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 1538[5:Rew:1529.0,1533.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.53 1547[5:Rew:1538.0,1526.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),u)**.
% 0.20/0.53 1548[5:Rew:1547.0,1499.0,1530.0,1499.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.53 1562[5:Rew:1548.0,1523.7,1502.0,1523.7,1502.0,1523.6,1502.0,1523.5,1530.0,1523.4,1502.0,1523.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(x,sk_c9),sk_c9)** equal(multiply(w,sk_c9),sk_c9)** -> .
% 0.20/0.53 1563[5:Con:1562.1] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.20/0.53 1595[5:SpR:1548.0,323.0] || -> equal(identity,sk_c9)**.
% 0.20/0.53 1598[5:Rew:1595.0,323.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.53 1601[5:Rew:1598.0,1563.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.20/0.53 1675[5:SpL:1531.0,1601.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.20/0.53 1677[5:Obv:1675.1] || -> .
% 0.20/0.53 1678[4:Spt:1677.0,14.0,1136.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.20/0.53 1679[4:Spt:1677.0,14.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.53 1680[4:MRR:18.1,1678.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.20/0.53 1681[4:MRR:17.1,1678.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.53 1682[4:MRR:15.1,1678.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.53 1683[4:MRR:12.1,1678.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.53 1684[4:MRR:19.0,1678.0] || -> equal(multiply(sk_c7,sk_c10),sk_c6)**.
% 0.20/0.53 1685[4:MRR:16.0,1678.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 1686[4:MRR:11.0,1678.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 1687[4:Rew:1679.0,1128.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.20/0.53 1688[4:Obv:1687.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** -> .
% 0.20/0.53 1700[4:SpR:1680.0,87.0] || -> equal(multiply(sk_c10,multiply(sk_c6,u)),u)**.
% 0.20/0.53 1716[4:SpR:1684.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c10)**.
% 0.20/0.53 1718[4:Rew:1681.0,1716.0] || -> equal(multiply(sk_c6,sk_c6),sk_c10)**.
% 0.20/0.53 1720[4:SpR:1685.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.53 1722[4:Rew:1682.0,1720.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.53 1724[4:SpR:1686.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.20/0.53 1726[4:Rew:1683.0,1724.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.53 1728[4:SpR:1718.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c10),sk_c6)**.
% 0.20/0.53 1730[4:Rew:1680.0,1728.0] || -> equal(multiply(sk_c10,sk_c10),sk_c6)**.
% 0.20/0.53 1731[4:SpR:1722.0,50.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.20/0.53 1732[4:SpR:1722.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.20/0.53 1734[4:Rew:1125.0,1732.0,1123.0,1732.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 1754[4:Rew:1734.0,1688.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** -> .
% 0.20/0.53 1757[4:Rew:1734.0,1700.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.20/0.53 1759[4:Rew:1734.0,1726.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 1760[4:Rew:1734.0,1730.0] || -> equal(multiply(sk_c9,sk_c9),sk_c6)**.
% 0.20/0.53 1761[4:Rew:1722.0,1759.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.53 1762[4:Rew:1761.0,1123.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 1764[4:Rew:1761.0,1722.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 1769[4:Rew:1760.0,1764.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.53 1778[4:Rew:1769.0,1757.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),u)**.
% 0.20/0.53 1779[4:Rew:1778.0,1731.0,1761.0,1731.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.53 1791[4:Rew:1779.0,1754.7,1734.0,1754.7,1734.0,1754.6,1734.0,1754.5,1761.0,1754.4,1734.0,1754.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(x,sk_c9),sk_c9)** equal(multiply(w,sk_c9),sk_c9)** -> .
% 0.20/0.53 1792[4:Con:1791.1] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.20/0.53 1824[4:SpR:1779.0,323.0] || -> equal(identity,sk_c9)**.
% 0.20/0.53 1826[4:Rew:1824.0,323.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.20/0.53 1830[4:Rew:1826.0,1792.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.20/0.53 1899[4:SpL:1762.0,1830.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.20/0.53 1901[4:Obv:1899.1] || -> .
% 0.20/0.53 1902[3:Spt:1901.0,41.0,1133.0] || equal(inverse(sk_c2),sk_c10)** -> .
% 0.20/0.53 1903[3:Spt:1901.0,41.1] || -> equal(multiply(sk_c10,sk_c8),sk_c9)**.
% 0.20/0.53 1904[3:MRR:45.1,1902.0] || -> equal(inverse(sk_c6),sk_c10)**.
% 0.20/0.53 1905[3:MRR:44.1,1902.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.20/0.53 1906[3:MRR:42.1,1902.0] || -> equal(inverse(sk_c5),sk_c9)**.
% 0.20/0.53 1907[3:MRR:39.1,1902.0] || -> equal(inverse(sk_c4),sk_c10)**.
% 0.20/0.53 1908[3:MRR:46.0,1902.0] || -> equal(multiply(sk_c7,sk_c10),sk_c6)**.
% 0.20/0.53 1909[3:MRR:43.0,1902.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.20/0.53 1910[3:MRR:38.0,1902.0] || -> equal(multiply(sk_c4,sk_c10),sk_c9)**.
% 0.20/0.53 1911[3:Rew:1903.0,1128.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** equal(sk_c9,sk_c9) -> .
% 0.20/0.53 1912[3:Obv:1911.8] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c10) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** -> .
% 0.20/0.53 1922[3:SpR:1904.0,87.0] || -> equal(multiply(sk_c10,multiply(sk_c6,u)),u)**.
% 0.20/0.53 1938[3:SpR:1908.0,87.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c10)**.
% 0.20/0.53 1940[3:Rew:1905.0,1938.0] || -> equal(multiply(sk_c6,sk_c6),sk_c10)**.
% 0.20/0.53 1942[3:SpR:1909.0,87.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.20/0.53 1944[3:Rew:1906.0,1942.0] || -> equal(multiply(sk_c9,sk_c9),sk_c8)**.
% 0.20/0.53 1946[3:SpR:1910.0,87.0] || -> equal(multiply(inverse(sk_c4),sk_c9),sk_c10)**.
% 0.20/0.53 1948[3:Rew:1907.0,1946.0] || -> equal(multiply(sk_c10,sk_c9),sk_c10)**.
% 0.20/0.53 1950[3:SpR:1940.0,87.0] || -> equal(multiply(inverse(sk_c6),sk_c10),sk_c6)**.
% 0.20/0.53 1952[3:Rew:1904.0,1950.0] || -> equal(multiply(sk_c10,sk_c10),sk_c6)**.
% 0.20/0.53 1953[3:SpR:1944.0,50.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),multiply(sk_c8,u))**.
% 0.20/0.53 1954[3:SpR:1944.0,87.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c9)**.
% 0.20/0.53 1956[3:Rew:1125.0,1954.0,1123.0,1954.0] || -> equal(sk_c10,sk_c9)**.
% 0.20/0.53 1975[3:Rew:1956.0,1912.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c10) equal(inverse(x),sk_c9) equal(multiply(u,sk_c8),sk_c9)** equal(multiply(v,sk_c10),sk_c9)** equal(multiply(x,sk_c9),sk_c10)** equal(multiply(sk_c10,multiply(w,sk_c10)),sk_c9)** -> .
% 0.20/0.53 1978[3:Rew:1956.0,1922.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.20/0.53 1980[3:Rew:1956.0,1948.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 1981[3:Rew:1956.0,1952.0] || -> equal(multiply(sk_c9,sk_c9),sk_c6)**.
% 0.20/0.53 1982[3:Rew:1944.0,1980.0] || -> equal(sk_c8,sk_c9)**.
% 0.20/0.53 1983[3:Rew:1982.0,1123.0] || -> equal(inverse(sk_c9),sk_c9)**.
% 0.20/0.53 1985[3:Rew:1982.0,1944.0] || -> equal(multiply(sk_c9,sk_c9),sk_c9)**.
% 0.20/0.53 1990[3:Rew:1981.0,1985.0] || -> equal(sk_c6,sk_c9)**.
% 0.20/0.53 1999[3:Rew:1990.0,1978.0] || -> equal(multiply(sk_c9,multiply(sk_c9,u)),u)**.
% 0.20/0.53 2000[3:Rew:1999.0,1953.0,1982.0,1953.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.20/0.53 2011[3:Rew:2000.0,1975.7,1956.0,1975.7,1956.0,1975.6,1956.0,1975.5,1982.0,1975.4,1956.0,1975.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c9) equal(inverse(x),sk_c9) equal(multiply(u,sk_c9),sk_c9)** equal(multiply(v,sk_c9),sk_c9)** equal(multiply(x,sk_c9),sk_c9)** equal(multiply(w,sk_c9),sk_c9)** -> .
% 0.37/0.54 2012[3:Con:2011.1] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c9)** -> .
% 0.37/0.54 2041[3:SpR:2000.0,323.0] || -> equal(identity,sk_c9)**.
% 0.37/0.54 2044[3:Rew:2041.0,323.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.37/0.54 2047[3:Rew:2044.0,2012.1] || equal(inverse(u),sk_c9)** equal(u,sk_c9) -> .
% 0.37/0.54 2111[3:SpL:1983.0,2047.0] || equal(sk_c9,sk_c9)* equal(sk_c9,sk_c9)* -> .
% 0.37/0.54 2113[3:Obv:2111.1] || -> .
% 0.37/0.54 2114[2:Spt:2113.0,13.0,1123.0] || equal(inverse(sk_c9),sk_c8)** -> .
% 0.37/0.54 2115[2:Spt:2113.0,13.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.37/0.54 2116[2:MRR:40.0,2114.0] || -> equal(inverse(sk_c2),sk_c10)**.
% 0.37/0.54 2117[2:MRR:4.0,2114.0] || -> equal(multiply(sk_c1,sk_c9),sk_c10)**.
% 0.37/0.54 2118[2:MRR:22.0,2114.0] || -> equal(multiply(sk_c10,sk_c3),sk_c9)**.
% 0.37/0.54 2119[2:MRR:31.0,2114.0] || -> equal(multiply(sk_c2,sk_c10),sk_c3)**.
% 0.37/0.54 2120[2:SpR:2115.0,87.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.37/0.54 2122[2:SpR:2116.0,87.0] || -> equal(multiply(sk_c10,multiply(sk_c2,u)),u)**.
% 0.37/0.54 2128[2:SpR:2117.0,87.0] || -> equal(multiply(inverse(sk_c1),sk_c10),sk_c9)**.
% 0.37/0.54 2130[2:Rew:1.0,2128.0,2115.0,2128.0] || -> equal(sk_c8,sk_c9)**.
% 0.37/0.54 2132[2:Rew:2130.0,2114.0] || equal(inverse(sk_c9),sk_c9)** -> .
% 0.37/0.54 2133[2:Rew:2130.0,386.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c10)**.
% 0.37/0.54 2135[2:Rew:49.0,2133.0] || -> equal(identity,sk_c10)**.
% 0.37/0.54 2136[2:Rew:2135.0,323.0] || -> equal(multiply(u,sk_c10),u)**.
% 0.37/0.54 2137[2:Rew:2135.0,48.0] || -> equal(multiply(sk_c10,u),u)**.
% 0.37/0.54 2140[2:Rew:2136.0,2119.0] || -> equal(sk_c2,sk_c3)**.
% 0.37/0.54 2141[2:Rew:2140.0,2116.0] || -> equal(inverse(sk_c3),sk_c10)**.
% 0.37/0.54 2142[2:Rew:2140.0,2122.0] || -> equal(multiply(sk_c10,multiply(sk_c3,u)),u)**.
% 0.37/0.54 2143[2:Rew:2137.0,2118.0] || -> equal(sk_c3,sk_c9)**.
% 0.37/0.54 2145[2:Rew:2143.0,2141.0] || -> equal(inverse(sk_c9),sk_c10)**.
% 0.37/0.54 2146[2:Rew:2145.0,2132.0] || equal(sk_c10,sk_c9)** -> .
% 0.37/0.54 2147[2:Rew:2137.0,2142.0,2143.0,2142.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.37/0.54 2148[2:Rew:2147.0,2120.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.37/0.54 2149[2:Rew:2148.0,2117.0] || -> equal(sk_c10,sk_c9)**.
% 0.37/0.54 2150[2:MRR:2149.0,2146.0] || -> .
% 0.37/0.54 % SZS output end Refutation
% 0.37/0.54 Formulae used in the proof : prove_this_1 prove_this_4 prove_this_5 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_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_42 prove_this_43 prove_this_44 prove_this_45 prove_this_46 prove_this_47 left_identity left_inverse associativity
% 0.37/0.54
%------------------------------------------------------------------------------