TSTP Solution File: GRP262-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP262-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:46:34 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP262-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 04:44:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 919 clauses, backtracked 378 clauses, performed 12 splits and kept 796 clauses.
% 0.19/0.47 SPASS allocated 63679 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 5, length 398 :
% 0.19/0.47 % SZS output start Refutation
% 0.19/0.47 1[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 3[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 5[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 6[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 7[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c1),sk_c7).
% 0.19/0.47 8[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 9[0:Inp] || -> equal(inverse(sk_c4),sk_c6)** equal(inverse(sk_c1),sk_c7).
% 0.19/0.47 10[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 11[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c2,sk_c6),sk_c5).
% 0.19/0.47 12[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 14[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 15[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 16[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 20[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 21[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.19/0.47 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 23[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.19/0.47 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 25[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c7),sk_c6).
% 0.19/0.47 26[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.19/0.47 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.47 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.47 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.47 30[1:Spt:26.3,26.7] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c6)** -> .
% 0.19/0.47 31[2:Spt:21.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 34[3:Spt:24.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.47 36[4:Spt:22.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 40[5:Spt:25.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.47 42[6:Spt:23.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 45[3:SpR:34.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.47 46[4:SpR:36.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.47 47[1:SpL:28.0,30.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,identity) -> .
% 0.19/0.47 54[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.47 55[5:SpR:40.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.19/0.47 57[3:SpR:45.0,29.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.47 58[4:SpR:46.0,29.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.19/0.47 60[3:Rew:27.0,57.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.47 61[4:Rew:27.0,58.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.47 62[0:Rew:27.0,54.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.47 66[5:SpR:40.0,60.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.47 72[6:SpR:42.0,61.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.47 76[6:SpL:72.0,30.1] || equal(inverse(sk_c7),sk_c7)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 77[6:Obv:76.1] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.47 79[0:SpR:62.0,62.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.47 81[2:SpR:31.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.47 82[0:SpR:27.0,62.0] || -> equal(multiply(inverse(identity),u),u)**.
% 0.19/0.47 83[0:SpR:28.0,62.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 86[3:SpR:45.0,62.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.47 88[5:SpR:66.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.47 89[4:SpR:46.0,62.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.47 91[6:SpR:72.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.19/0.47 97[5:Rew:81.0,88.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 99[5:Rew:97.0,31.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 100[5:Rew:97.0,34.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.47 103[5:Rew:97.0,45.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.47 109[5:Rew:97.0,86.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.19/0.47 113[5:Rew:97.0,55.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 121[6:Rew:97.0,91.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.47 122[6:Rew:28.0,121.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 123[6:Rew:122.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 127[6:Rew:122.0,103.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.19/0.47 134[6:Rew:123.0,127.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 135[6:Rew:134.0,100.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 137[6:MRR:135.0,77.0] || -> .
% 0.19/0.47 160[6:Spt:137.0,23.0,42.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.47 161[6:Spt:137.0,23.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 163[5:Rew:89.0,109.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.47 167[6:Rew:97.0,160.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.19/0.47 168[0:Rew:79.0,83.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.47 169[4:Rew:168.0,89.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.47 177[5:Rew:97.0,8.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 178[6:MRR:177.1,167.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 181[5:Rew:163.0,113.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 184[5:Rew:97.0,3.1,97.0,3.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c7).
% 0.19/0.47 185[6:MRR:184.0,167.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 192[4:SpR:169.0,62.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.19/0.47 219[6:SpR:185.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.47 221[6:Rew:99.0,219.0,178.0,219.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 228[6:Rew:221.0,181.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.47 237[6:Rew:192.0,228.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 238[6:Rew:237.0,46.0] || -> equal(identity,sk_c3)**.
% 0.19/0.47 246[6:Rew:238.0,27.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.47 254[6:UnC:246.0,167.0] || -> .
% 0.19/0.47 256[5:Spt:254.0,25.0,40.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.47 257[5:Spt:254.0,25.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 258[3:Rew:168.0,86.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.47 259[3:Rew:258.0,81.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.47 260[5:Rew:259.0,256.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.47 262[3:Rew:259.0,20.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.19/0.47 263[5:MRR:262.1,260.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 264[3:Rew:259.0,10.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 265[5:MRR:264.1,260.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 267[3:Rew:259.0,15.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 268[5:MRR:267.0,260.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 269[3:Rew:259.0,5.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 270[5:MRR:269.0,260.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 274[5:SpR:257.0,62.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.19/0.47 278[3:SpR:258.0,62.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.19/0.47 285[5:SpR:268.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.47 287[5:Rew:263.0,285.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.47 303[5:SpR:270.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 305[5:Rew:265.0,303.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 306[3:SpR:259.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.47 311[5:SpR:287.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.47 313[5:Rew:258.0,311.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.19/0.47 318[5:SpR:313.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.19/0.47 322[5:Rew:278.0,318.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 326[5:Rew:322.0,306.0] || -> equal(multiply(sk_c4,u),multiply(sk_c7,u))**.
% 0.19/0.47 330[5:Rew:326.0,313.0] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.47 334[5:Rew:305.0,330.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 339[5:Rew:334.0,274.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c7)**.
% 0.19/0.47 340[5:Rew:334.0,322.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 346[5:Rew:340.0,192.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.47 374[5:Rew:169.0,339.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.47 375[5:Rew:346.0,374.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 376[5:MRR:375.0,260.0] || -> .
% 0.19/0.47 383[4:Spt:376.0,22.0,36.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.47 384[4:Spt:376.0,22.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 385[4:MRR:17.0,383.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 386[4:MRR:7.0,383.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 387[4:MRR:12.0,383.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 388[4:MRR:2.0,383.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 414[4:SpR:387.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.47 416[4:Rew:385.0,414.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.47 418[4:SpR:388.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 420[4:Rew:386.0,418.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 429[4:SpR:420.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.47 431[4:Rew:28.0,429.0] || -> equal(sk_c6,identity)**.
% 0.19/0.47 434[4:Rew:431.0,258.0] || -> equal(inverse(identity),sk_c4)**.
% 0.19/0.47 436[4:Rew:431.0,31.0] || -> equal(multiply(identity,sk_c7),sk_c5)**.
% 0.19/0.47 437[4:Rew:431.0,45.0] || -> equal(multiply(identity,sk_c4),identity)**.
% 0.19/0.47 439[4:Rew:431.0,388.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.19/0.47 440[4:Rew:431.0,416.0] || -> equal(multiply(identity,sk_c5),identity)**.
% 0.19/0.47 452[4:Rew:431.0,47.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(identity,identity) -> .
% 0.19/0.47 457[4:Rew:434.0,82.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.47 458[4:Rew:27.0,436.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 462[4:Rew:27.0,437.0] || -> equal(identity,sk_c4)**.
% 0.19/0.47 464[4:Rew:462.0,168.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.47 471[4:Rew:462.0,439.0] || -> equal(multiply(sk_c1,sk_c7),sk_c4)**.
% 0.19/0.47 472[4:Rew:458.0,440.0,462.0,440.0] || -> equal(multiply(sk_c4,sk_c7),sk_c4)**.
% 0.19/0.47 475[4:Rew:457.0,472.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 482[4:Rew:475.0,471.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 489[4:Rew:475.0,464.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 492[4:Rew:489.0,482.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 493[4:Rew:492.0,386.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 521[4:Obv:452.1] || equal(inverse(inverse(sk_c7)),sk_c7)** -> .
% 0.19/0.47 522[4:Rew:493.0,521.0,493.0,521.0,492.0,521.0] || equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 523[4:Obv:522.0] || -> .
% 0.19/0.47 526[3:Spt:523.0,24.0,34.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.47 527[3:Spt:523.0,24.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 528[3:MRR:19.0,526.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 529[3:MRR:9.0,526.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 530[3:MRR:14.0,526.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 531[3:MRR:4.0,526.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 543[3:SpR:530.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.47 545[3:Rew:528.0,543.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.47 547[3:SpR:531.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 549[3:Rew:529.0,547.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 551[3:SpR:545.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.47 553[3:Rew:28.0,551.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 554[3:Rew:553.0,27.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 555[3:Rew:553.0,168.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 559[3:Rew:553.0,47.1] || equal(inverse(inverse(sk_c7)),sk_c7)** equal(sk_c6,sk_c5) -> .
% 0.19/0.47 560[3:Rew:554.0,527.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 566[3:Rew:560.0,31.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 568[3:Rew:560.0,531.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 577[3:Rew:560.0,549.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 578[3:Rew:566.0,577.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 581[3:Rew:578.0,555.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 585[3:Rew:581.0,568.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 586[3:Rew:585.0,529.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 587[3:Rew:585.0,560.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.47 590[3:Rew:585.0,578.0] || -> equal(sk_c5,sk_c1)**.
% 0.19/0.47 611[3:Rew:587.0,559.1,590.0,559.1,586.0,559.0,586.0,559.0,585.0,559.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 612[3:Obv:611.1] || -> .
% 0.19/0.47 615[2:Spt:612.0,21.0,31.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.47 616[2:Spt:612.0,21.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 617[2:MRR:16.1,615.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 618[2:MRR:6.1,615.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 619[2:MRR:11.0,615.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 620[2:MRR:1.0,615.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 629[2:SpR:619.0,62.0] || -> equal(multiply(inverse(sk_c2),sk_c5),sk_c6)**.
% 0.19/0.47 631[2:Rew:617.0,629.0] || -> equal(multiply(sk_c6,sk_c5),sk_c6)**.
% 0.19/0.47 633[2:SpR:620.0,62.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.47 635[2:Rew:618.0,633.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.47 637[2:SpR:631.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c5)**.
% 0.19/0.47 639[2:Rew:28.0,637.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 641[2:Rew:639.0,27.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 642[2:Rew:639.0,28.0] || -> equal(multiply(inverse(u),u),sk_c5)**.
% 0.19/0.47 646[2:Rew:641.0,616.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 652[2:Rew:646.0,615.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.19/0.47 658[2:Rew:646.0,635.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.47 659[2:Rew:658.0,652.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.47 680[2:SpR:658.0,62.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.47 682[2:Rew:642.0,680.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 683[2:MRR:682.0,659.0] || -> .
% 0.19/0.47 684[1:Spt:683.0,26.0,26.1,26.2,26.4,26.5,26.6,26.8,26.9] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6) -> .
% 0.19/0.47 686[2:Spt:21.0] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.47 687[2:Rew:686.0,684.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(sk_c5,sk_c5) equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.19/0.47 689[2:Obv:687.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.19/0.47 692[2:SpR:686.0,62.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.47 694[3:Spt:22.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.47 696[3:Rew:694.0,689.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** equal(sk_c6,sk_c6) -> .
% 0.19/0.47 697[3:Obv:696.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** -> .
% 0.19/0.47 700[3:SpR:694.0,62.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.19/0.47 702[4:Spt:19.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.47 708[5:Spt:17.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.47 723[0:SpR:28.0,62.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.47 724[0:SpR:28.0,168.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.47 726[4:SpR:702.0,28.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.47 727[5:SpR:708.0,28.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.47 729[0:Rew:168.0,723.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.47 737[4:SpR:726.0,62.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.47 739[4:Rew:168.0,737.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.47 740[4:Rew:739.0,692.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.47 742[4:Rew:740.0,5.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 743[4:Rew:740.0,15.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 744[4:Rew:740.0,10.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.47 745[4:Rew:740.0,20.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.19/0.47 746[4:Rew:744.1,8.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.47 748[4:Rew:742.0,3.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c6).
% 0.19/0.47 752[4:SpR:739.0,28.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.19/0.47 755[5:SpR:727.0,62.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.47 757[5:Rew:168.0,755.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.47 759[6:Spt:744.1] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 760[6:Rew:759.0,686.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 764[6:Rew:759.0,739.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.47 766[6:Rew:759.0,697.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** -> .
% 0.19/0.47 773[6:Rew:759.0,748.1] || -> equal(multiply(sk_c3,sk_c7),sk_c7)** equal(multiply(sk_c1,sk_c7),sk_c7).
% 0.19/0.47 775[6:Rew:759.0,752.0] || -> equal(multiply(sk_c4,sk_c7),identity)**.
% 0.19/0.47 776[6:Rew:757.0,764.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.47 781[6:Rew:776.0,775.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.19/0.47 782[6:Rew:781.0,746.1] || -> equal(inverse(sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.19/0.47 786[6:Rew:781.0,773.0] || -> equal(identity,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 788[6:Rew:759.0,766.5,759.0,766.4,759.0,766.3,759.0,766.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c5)** -> .
% 0.19/0.47 793[5:SpR:757.0,28.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.19/0.47 802[7:Spt:782.1] || -> equal(identity,sk_c7)**.
% 0.19/0.47 803[7:Rew:802.0,27.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.47 804[7:Rew:802.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.47 806[7:Rew:802.0,724.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 809[7:Rew:757.0,806.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.47 810[7:Rew:809.0,708.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 817[7:Rew:803.0,760.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 822[7:Rew:817.0,788.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c5)** -> .
% 0.19/0.47 832[7:Con:822.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c5)** -> .
% 0.19/0.47 833[7:Rew:804.0,832.3,817.0,832.3,804.0,832.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) -> .
% 0.19/0.47 834[7:Con:833.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.47 848[0:SpR:729.0,62.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.47 875[7:SpL:810.0,834.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.47 877[7:Obv:875.1] || -> .
% 0.19/0.47 878[7:Spt:877.0,782.1,802.0] || equal(identity,sk_c7)** -> .
% 0.19/0.47 879[7:Spt:877.0,782.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 881[7:MRR:786.0,878.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 884[7:SpR:879.0,729.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 886[7:Rew:757.0,884.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.47 891[7:Rew:886.0,781.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.19/0.47 896[7:Rew:881.0,891.0] || -> equal(identity,sk_c7)**.
% 0.19/0.47 897[7:MRR:896.0,878.0] || -> .
% 0.19/0.47 898[6:Spt:897.0,744.1,759.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.47 899[6:Spt:897.0,744.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 900[6:MRR:745.1,898.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 901[6:MRR:742.0,898.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 902[6:MRR:743.0,898.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 904[6:SpR:899.0,729.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 906[6:Rew:757.0,904.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.47 908[6:Rew:906.0,757.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 910[6:Rew:906.0,793.0] || -> equal(multiply(sk_c1,sk_c7),identity)**.
% 0.19/0.47 913[6:Rew:901.0,910.0] || -> equal(sk_c6,identity)**.
% 0.19/0.47 914[6:Rew:913.0,739.0] || -> equal(inverse(identity),sk_c4)**.
% 0.19/0.47 915[6:Rew:913.0,702.0] || -> equal(inverse(sk_c4),identity)**.
% 0.19/0.47 916[6:Rew:913.0,898.0] || equal(identity,sk_c7)** -> .
% 0.19/0.47 919[6:Rew:913.0,686.0] || -> equal(multiply(identity,sk_c7),sk_c5)**.
% 0.19/0.47 922[6:Rew:913.0,900.0] || -> equal(inverse(sk_c2),identity)**.
% 0.19/0.47 927[6:Rew:913.0,902.0] || -> equal(multiply(sk_c2,identity),sk_c5)**.
% 0.19/0.47 931[6:Rew:724.0,914.0] || -> equal(identity,sk_c4)**.
% 0.19/0.47 933[6:Rew:931.0,168.0] || -> equal(multiply(u,sk_c4),u)**.
% 0.19/0.47 934[6:Rew:931.0,27.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.47 938[6:Rew:931.0,915.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.19/0.47 939[6:Rew:931.0,916.0] || equal(sk_c4,sk_c7)** -> .
% 0.19/0.47 940[6:Rew:931.0,922.0] || -> equal(inverse(sk_c2),sk_c4)**.
% 0.19/0.47 943[6:Rew:931.0,919.0] || -> equal(multiply(sk_c4,sk_c7),sk_c5)**.
% 0.19/0.47 946[6:Rew:931.0,927.0] || -> equal(multiply(sk_c2,sk_c4),sk_c5)**.
% 0.19/0.47 947[6:Rew:933.0,946.0] || -> equal(sk_c2,sk_c5)**.
% 0.19/0.47 948[6:Rew:947.0,940.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.19/0.47 949[6:Rew:934.0,943.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.47 954[6:Rew:949.0,948.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.47 955[6:Rew:908.0,954.0] || -> equal(sk_c4,sk_c1)**.
% 0.19/0.47 958[6:Rew:955.0,938.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 959[6:Rew:955.0,939.0] || equal(sk_c7,sk_c1)** -> .
% 0.19/0.47 963[6:Rew:899.0,958.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 968[6:Rew:963.0,959.0] || equal(sk_c1,sk_c1)* -> .
% 0.19/0.47 969[6:Obv:968.0] || -> .
% 0.19/0.47 987[5:Spt:969.0,17.0,708.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.47 988[5:Spt:969.0,17.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.47 989[5:MRR:7.0,987.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.47 990[5:MRR:12.0,987.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.47 991[5:MRR:2.0,987.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.47 993[5:SpR:988.0,729.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.19/0.47 995[5:Rew:739.0,993.0] || -> equal(sk_c2,sk_c4)**.
% 0.19/0.47 997[5:Rew:995.0,990.0] || -> equal(multiply(sk_c4,sk_c6),sk_c5)**.
% 0.19/0.47 998[5:Rew:752.0,997.0] || -> equal(identity,sk_c5)**.
% 0.19/0.47 1002[5:Rew:998.0,27.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.47 1003[5:Rew:998.0,168.0] || -> equal(multiply(u,sk_c5),u)**.
% 0.19/0.47 1008[5:Rew:1002.0,694.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.47 1010[5:Rew:1008.0,702.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.47 1012[5:Rew:1008.0,686.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.47 1015[5:Rew:1008.0,991.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.47 1016[5:Rew:1008.0,697.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** -> .
% 0.19/0.47 1020[5:Rew:1003.0,740.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.47 1022[5:Rew:1020.0,1010.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.47 1033[5:Rew:1008.0,1016.5,1008.0,1016.4,1003.0,1016.3,1008.0,1016.3,1008.0,1016.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c5)** -> .
% 0.19/0.47 1040[5:SpR:989.0,729.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.47 1042[5:Rew:1022.0,1040.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.47 1046[5:Rew:1042.0,989.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.47 1049[5:Rew:1042.0,1012.0] || -> equal(multiply(sk_c1,sk_c1),sk_c5)**.
% 0.19/0.47 1050[5:Rew:1042.0,1015.0] || -> equal(multiply(sk_c1,sk_c1),sk_c1)**.
% 0.19/0.47 1052[5:Rew:1042.0,1033.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c5)** -> .
% 0.19/0.47 1053[5:Rew:1049.0,1050.0] || -> equal(sk_c5,sk_c1)**.
% 0.19/0.47 1057[5:Rew:1053.0,1003.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.47 1062[5:Rew:1057.0,1052.5,1042.0,1052.5,1053.0,1052.5,1057.0,1052.4,1042.0,1052.4,1042.0,1052.3,1042.0,1052.2,1042.0,1052.1] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) -> .
% 0.19/0.47 1063[5:Con:1062.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.48 1119[5:SpL:1046.0,1063.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.48 1120[5:Obv:1119.1] || -> .
% 0.19/0.48 1121[4:Spt:1120.0,19.0,702.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.48 1122[4:Spt:1120.0,19.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.48 1123[4:MRR:9.0,1121.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 1124[4:MRR:14.0,1121.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.48 1125[4:MRR:4.0,1121.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.48 1127[4:SpR:1122.0,729.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.19/0.48 1128[4:SpR:1122.0,848.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.19/0.48 1133[4:SpR:1123.0,729.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.48 1157[4:SpR:1124.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.19/0.48 1161[4:Rew:1128.0,1157.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.48 1162[4:Rew:1161.0,694.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 1167[4:Rew:1162.0,1127.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.48 1170[4:Rew:1162.0,1124.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.48 1171[4:Rew:1162.0,700.0] || -> equal(multiply(inverse(sk_c5),sk_c7),sk_c7)**.
% 0.19/0.48 1173[4:Rew:1162.0,1125.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 1174[4:Rew:1162.0,697.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c5)** -> .
% 0.19/0.48 1178[4:Rew:1133.0,1167.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.48 1181[4:Rew:1178.0,1170.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.19/0.48 1182[4:Rew:1181.0,1173.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.48 1190[4:Rew:28.0,1171.0,1182.0,1171.0] || -> equal(identity,sk_c7)**.
% 0.19/0.48 1191[4:Rew:1190.0,724.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 1192[4:Rew:1190.0,168.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 1195[4:Rew:1133.0,1191.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.48 1196[4:Rew:1195.0,1123.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.48 1198[4:Rew:1195.0,1162.0] || -> equal(sk_c6,sk_c1)**.
% 0.19/0.48 1200[4:Rew:1195.0,1182.0] || -> equal(sk_c5,sk_c1)**.
% 0.19/0.48 1203[4:Rew:1195.0,1192.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.19/0.48 1211[4:Rew:1203.0,1174.5,1198.0,1174.5,1200.0,1174.5,1203.0,1174.4,1198.0,1174.4,1195.0,1174.4,1203.0,1174.3,1200.0,1174.3,1198.0,1174.3,1198.0,1174.2,1195.0,1174.1,1195.0,1174.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(inverse(w),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) equal(w,sk_c1) -> .
% 0.19/0.48 1212[4:Con:1211.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.19/0.48 1260[4:SpL:1196.0,1212.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.19/0.48 1261[4:Obv:1260.1] || -> .
% 0.19/0.48 1262[3:Spt:1261.0,22.1,694.0] || equal(multiply(sk_c5,sk_c7),sk_c6)** -> .
% 0.19/0.48 1263[3:Spt:1261.0,22.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.48 1264[3:MRR:24.1,1262.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.48 1265[3:MRR:23.1,1262.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.48 1266[3:MRR:25.1,1262.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.48 1272[3:SpR:1264.0,729.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.48 1275[3:Rew:1272.0,692.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.48 1277[3:Rew:1266.0,1275.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 1279[3:Rew:1277.0,686.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.48 1280[3:Rew:1277.0,1262.0] || equal(multiply(sk_c5,sk_c7),sk_c7)** -> .
% 0.19/0.48 1282[3:Rew:1277.0,1265.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.48 1304[3:SpR:1282.0,62.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c7)**.
% 0.19/0.48 1306[3:Rew:1263.0,1304.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 1307[3:Rew:1279.0,1306.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.48 1308[3:Rew:1307.0,1279.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 1310[3:Rew:1307.0,1280.0] || equal(multiply(sk_c7,sk_c7),sk_c7)** -> .
% 0.19/0.48 1313[3:Rew:1308.0,1310.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 1314[3:Obv:1313.0] || -> .
% 0.19/0.48 1318[2:Spt:1314.0,21.0,686.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.48 1319[2:Spt:1314.0,21.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.48 1320[2:MRR:16.1,1318.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.48 1321[2:MRR:6.1,1318.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 1322[2:MRR:11.0,1318.0] || -> equal(multiply(sk_c2,sk_c6),sk_c5)**.
% 0.19/0.48 1323[2:MRR:1.0,1318.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.48 1328[2:SpR:1320.0,729.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.19/0.48 1329[2:SpR:1320.0,848.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.19/0.48 1332[2:SpR:1321.0,729.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.48 1343[2:SpR:1322.0,29.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c5,u))**.
% 0.19/0.48 1347[2:Rew:1329.0,1343.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.48 1348[2:Rew:1347.0,1319.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 1351[2:Rew:1348.0,1328.0] || -> equal(inverse(sk_c7),sk_c2)**.
% 0.19/0.48 1352[2:Rew:1348.0,1322.0] || -> equal(multiply(sk_c2,sk_c7),sk_c5)**.
% 0.19/0.48 1353[2:Rew:1348.0,1318.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.19/0.48 1354[2:Rew:1348.0,1323.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 1359[2:Rew:1332.0,1351.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.48 1361[2:Rew:1359.0,1352.0] || -> equal(multiply(sk_c1,sk_c7),sk_c5)**.
% 0.19/0.48 1362[2:Rew:1361.0,1354.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.48 1363[2:Rew:1362.0,1347.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 1368[2:Rew:1363.0,1353.0,1362.0,1353.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 1369[2:Obv:1368.0] || -> .
% 0.19/0.48 % SZS output end Refutation
% 0.19/0.48 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_14 prove_this_15 prove_this_16 prove_this_17 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 left_identity left_inverse associativity
% 0.19/0.48
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