TSTP Solution File: GRP391-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP391-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:47:09 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP391-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 13:33:09 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 812 clauses, backtracked 320 clauses, performed 11 splits and kept 689 clauses.
% 0.20/0.49 SPASS allocated 63639 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.00 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.06 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 4, length 328 :
% 0.20/0.49 % SZS output start Refutation
% 0.20/0.49 1[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 2[0:Inp] || -> equal(inverse(sk_c3),sk_c8)** equal(inverse(sk_c6),sk_c8).
% 0.20/0.49 3[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c6),sk_c8).
% 0.20/0.49 5[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c6),sk_c8).
% 0.20/0.49 6[0:Inp] || -> equal(inverse(sk_c6),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 7[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.49 8[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.49 9[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.49 10[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.49 11[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.49 12[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.49 15[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 16[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.49 17[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.49 18[0:Inp] || -> equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 21[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.49 22[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.49 23[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.49 24[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.49 25[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c8).
% 0.20/0.49 26[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.20/0.49 27[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c8).
% 0.20/0.49 28[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.20/0.49 29[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.20/0.49 30[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c8).
% 0.20/0.49 31[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(inverse(y),sk_c8) equal(inverse(sk_c6),sk_c8) equal(multiply(u,v),sk_c8)**+ equal(multiply(w,sk_c8),sk_c6)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(y,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.49 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.49 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.49 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.49 35[1:Spt:31.0,31.5,31.9] || equal(inverse(u),v) equal(multiply(u,v),sk_c8)**+ equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.49 36[2:Spt:4.1] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.49 38[3:Spt:29.1] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.20/0.49 40[3:SpL:38.0,35.1] || equal(inverse(sk_c6),sk_c7) equal(sk_c8,sk_c8) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.20/0.49 41[3:Obv:40.1] || equal(inverse(sk_c6),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.20/0.49 42[3:Rew:36.0,41.0] || equal(sk_c8,sk_c7) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.20/0.49 43[4:Spt:17.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.49 46[1:SpL:32.0,35.1] || equal(inverse(identity),u) equal(u,sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.20/0.49 47[5:Spt:23.1] || -> equal(multiply(sk_c2,sk_c7),sk_c8)**.
% 0.20/0.49 51[6:Spt:11.1] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.49 53[6:SpL:51.0,35.1] || equal(inverse(sk_c1),sk_c2) equal(sk_c8,sk_c8) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.20/0.49 54[6:Obv:53.1] || equal(inverse(sk_c1),sk_c2) equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.20/0.49 55[6:Rew:47.0,54.1,43.0,54.0] || equal(sk_c2,sk_c2) equal(sk_c8,sk_c8)* -> .
% 0.20/0.49 56[6:Obv:55.1] || -> .
% 0.20/0.49 57[6:Spt:56.0,11.1,51.0] || equal(multiply(sk_c1,sk_c2),sk_c8)** -> .
% 0.20/0.49 58[6:Spt:56.0,11.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 59[6:MRR:10.1,57.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 60[6:MRR:8.1,57.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 61[6:MRR:12.1,57.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 63[6:MRR:7.1,57.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 80[2:SpR:36.0,33.0] || -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.20/0.49 82[6:SpR:58.0,33.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.20/0.49 83[6:SpR:59.0,33.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.20/0.49 84[6:SpR:60.0,33.0] || -> equal(multiply(sk_c8,sk_c3),identity)**.
% 0.20/0.49 96[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.49 99[2:SpR:80.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.20/0.49 101[2:Rew:32.0,99.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.20/0.49 102[0:Rew:32.0,96.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.49 123[0:SpR:102.0,102.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.49 125[3:SpR:38.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.20/0.49 129[0:SpR:33.0,102.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.49 132[2:SpR:80.0,102.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c6)**.
% 0.20/0.49 133[6:SpR:84.0,102.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c3)**.
% 0.20/0.49 136[6:SpR:82.0,102.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c5)**.
% 0.20/0.49 137[6:SpR:83.0,102.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.20/0.49 144[3:Rew:36.0,125.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.49 150[6:Rew:132.0,133.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.49 152[6:Rew:150.0,63.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.49 157[6:Rew:36.0,136.0] || -> equal(multiply(sk_c8,identity),sk_c5)**.
% 0.20/0.49 161[0:Rew:123.0,129.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.49 162[6:Rew:161.0,137.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.20/0.49 164[2:Rew:161.0,132.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.20/0.49 165[6:Rew:161.0,157.0] || -> equal(sk_c8,sk_c5)**.
% 0.20/0.49 167[6:Rew:165.0,36.0] || -> equal(inverse(sk_c6),sk_c5)**.
% 0.20/0.49 170[6:Rew:165.0,61.0] || -> equal(multiply(sk_c5,sk_c5),sk_c6)**.
% 0.20/0.49 174[6:Rew:165.0,46.1] || equal(inverse(identity),u) equal(u,sk_c5) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.20/0.49 184[6:Rew:165.0,144.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.20/0.49 188[6:Rew:165.0,152.0] || -> equal(multiply(sk_c6,sk_c5),sk_c7)**.
% 0.20/0.49 192[6:Rew:170.0,184.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 195[6:Rew:192.0,83.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.20/0.49 199[6:Rew:192.0,162.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.49 203[6:Rew:167.0,199.0] || -> equal(sk_c5,sk_c4)**.
% 0.20/0.49 207[6:Rew:203.0,165.0] || -> equal(sk_c8,sk_c4)**.
% 0.20/0.49 208[6:Rew:203.0,167.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.20/0.49 215[6:Rew:203.0,188.0,192.0,188.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.20/0.49 218[6:Rew:215.0,195.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 223[6:Rew:218.0,161.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 268[6:Rew:223.0,174.2,192.0,174.2,207.0,174.2,203.0,174.1,208.0,174.0,218.0,174.0] || equal(sk_c4,u)* equal(u,sk_c4)* equal(u,sk_c4)* -> .
% 0.20/0.49 269[6:Obv:268.1] || equal(u,sk_c4)* -> .
% 0.20/0.49 270[6:UnC:269.0,102.0] || -> .
% 0.20/0.49 278[5:Spt:270.0,23.1,47.0] || equal(multiply(sk_c2,sk_c7),sk_c8)** -> .
% 0.20/0.49 279[5:Spt:270.0,23.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 282[5:MRR:22.1,278.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 284[5:MRR:24.1,278.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 285[5:MRR:21.1,278.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 292[2:SpR:164.0,102.0] || -> equal(multiply(sk_c6,multiply(sk_c8,u)),u)**.
% 0.20/0.49 312[5:SpR:284.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 314[5:Rew:279.0,312.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 325[5:SpR:285.0,102.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 327[5:Rew:282.0,325.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 335[5:SpR:314.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.49 336[5:SpR:314.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.20/0.49 338[5:Rew:144.0,336.0,36.0,336.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 349[5:Rew:338.0,42.0] || equal(sk_c8,sk_c6) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.20/0.49 355[5:Rew:338.0,327.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.49 357[5:Rew:314.0,355.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 365[5:Rew:357.0,101.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.49 375[5:Rew:365.0,335.0,357.0,335.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 383[5:Rew:375.0,349.1,338.0,349.1,357.0,349.1,357.0,349.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 384[5:Obv:383.1] || -> .
% 0.20/0.49 389[4:Spt:384.0,17.1,43.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.20/0.49 390[4:Spt:384.0,17.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 391[4:MRR:16.1,389.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 393[4:MRR:18.0,389.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 394[4:MRR:15.0,389.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 420[4:SpR:393.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 422[4:Rew:390.0,420.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 424[4:SpR:394.0,102.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 426[4:Rew:391.0,424.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 431[4:SpR:422.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.49 432[4:SpR:422.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.20/0.49 434[4:Rew:144.0,432.0,36.0,432.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 444[4:Rew:434.0,42.0] || equal(sk_c8,sk_c6) equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.20/0.49 450[4:Rew:434.0,426.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.49 452[4:Rew:422.0,450.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 460[4:Rew:452.0,292.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.49 469[4:Rew:460.0,431.0,452.0,431.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 477[4:Rew:469.0,444.1,434.0,444.1,452.0,444.1,452.0,444.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 478[4:Obv:477.1] || -> .
% 0.20/0.49 483[3:Spt:478.0,29.1,38.0] || equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.49 484[3:Spt:478.0,29.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 485[3:MRR:28.1,483.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 486[3:MRR:26.1,483.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 487[3:MRR:30.1,483.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 488[3:MRR:27.1,483.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 489[3:MRR:25.1,483.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 498[3:SpR:486.0,102.0] || -> equal(multiply(sk_c8,multiply(sk_c3,u)),u)**.
% 0.20/0.49 506[3:SpR:487.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 508[3:Rew:484.0,506.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 509[3:SpR:488.0,34.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.20/0.49 510[3:SpR:488.0,102.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 512[3:Rew:485.0,510.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 522[3:SpR:512.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 524[3:Rew:33.0,522.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 525[3:Rew:524.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 527[3:Rew:524.0,161.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 532[3:Rew:525.0,508.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 538[3:Rew:525.0,509.0] || -> equal(multiply(sk_c4,multiply(sk_c7,u)),u)**.
% 0.20/0.49 539[3:Rew:525.0,483.0] || equal(sk_c8,sk_c7)** -> .
% 0.20/0.49 544[3:Rew:532.0,489.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.49 549[3:Rew:532.0,498.0] || -> equal(multiply(sk_c6,multiply(sk_c3,u)),u)**.
% 0.20/0.49 552[3:Rew:532.0,539.0] || equal(sk_c7,sk_c6)** -> .
% 0.20/0.49 556[3:Rew:527.0,544.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.49 558[3:Rew:556.0,488.0] || -> equal(multiply(sk_c4,sk_c3),sk_c6)**.
% 0.20/0.49 560[3:Rew:556.0,552.0] || equal(sk_c3,sk_c6)** -> .
% 0.20/0.49 566[3:Rew:556.0,538.0] || -> equal(multiply(sk_c4,multiply(sk_c3,u)),u)**.
% 0.20/0.49 567[3:Rew:525.0,549.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.20/0.49 568[3:Rew:567.0,566.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.20/0.49 569[3:Rew:568.0,558.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.49 570[3:MRR:569.0,560.0] || -> .
% 0.20/0.49 581[2:Spt:570.0,4.1,36.0] || equal(inverse(sk_c6),sk_c8)** -> .
% 0.20/0.49 582[2:Spt:570.0,4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 583[2:MRR:5.1,581.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 584[2:MRR:2.1,581.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 585[2:MRR:6.0,581.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 586[2:MRR:3.0,581.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 587[2:MRR:1.0,581.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 595[2:SpR:585.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 597[2:Rew:583.0,595.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 599[2:SpR:586.0,102.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 601[2:Rew:582.0,599.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 603[2:SpR:587.0,102.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.20/0.49 605[2:Rew:584.0,603.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.49 610[2:SpR:601.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 612[2:Rew:33.0,610.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 613[2:Rew:612.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 614[2:Rew:612.0,161.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 619[2:Rew:613.0,597.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 625[2:Rew:619.0,581.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.20/0.49 627[2:Rew:619.0,587.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.49 633[2:Rew:619.0,605.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 635[2:Rew:614.0,627.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.49 636[2:Rew:635.0,582.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.20/0.49 637[2:Rew:635.0,586.0] || -> equal(multiply(sk_c4,sk_c3),sk_c6)**.
% 0.20/0.49 639[2:Rew:613.0,633.0,635.0,633.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.49 642[2:Rew:639.0,636.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.49 644[2:Rew:614.0,637.0,639.0,637.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.49 645[2:Rew:644.0,642.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 646[2:MRR:645.0,625.0] || -> .
% 0.20/0.49 661[1:Spt:646.0,31.1,31.2,31.3,31.4,31.6,31.7,31.8,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(sk_c6),sk_c8) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.49 663[2:Spt:5.1] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.49 664[2:Rew:663.0,661.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(sk_c8,sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.49 666[2:Obv:664.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.49 668[2:SpR:663.0,102.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.20/0.49 670[3:Spt:28.1] || -> equal(multiply(sk_c6,sk_c7),sk_c8)**.
% 0.20/0.49 672[3:Rew:670.0,666.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(sk_c8,sk_c8) -> .
% 0.20/0.49 673[3:Obv:672.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.20/0.49 676[3:SpR:670.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c7)**.
% 0.20/0.49 678[3:Rew:663.0,676.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.49 679[4:Spt:16.1] || -> equal(inverse(sk_c1),sk_c2)**.
% 0.20/0.49 682[5:Spt:11.1] || -> equal(multiply(sk_c1,sk_c2),sk_c8)**.
% 0.20/0.49 684[5:SpR:682.0,102.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c2)**.
% 0.20/0.49 686[5:Rew:679.0,684.0] || -> equal(multiply(sk_c2,sk_c8),sk_c2)**.
% 0.20/0.49 695[5:SpR:686.0,102.0] || -> equal(multiply(inverse(sk_c2),sk_c2),sk_c8)**.
% 0.20/0.49 697[5:Rew:33.0,695.0] || -> equal(sk_c8,identity)**.
% 0.20/0.49 698[5:Rew:697.0,663.0] || -> equal(inverse(sk_c6),identity)**.
% 0.20/0.49 699[5:Rew:697.0,670.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.20/0.49 701[5:Rew:697.0,678.0] || -> equal(multiply(identity,identity),sk_c7)**.
% 0.20/0.49 705[5:Rew:697.0,673.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),identity) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.20/0.49 713[5:Rew:32.0,701.0] || -> equal(identity,sk_c7)**.
% 0.20/0.49 714[5:Rew:713.0,161.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.49 718[5:Rew:713.0,697.0] || -> equal(sk_c8,sk_c7)**.
% 0.20/0.49 719[5:Rew:713.0,698.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.20/0.49 720[5:Rew:713.0,699.0] || -> equal(multiply(sk_c6,sk_c7),sk_c7)**.
% 0.20/0.49 727[5:Rew:714.0,720.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 728[5:Rew:727.0,713.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 729[5:Rew:727.0,718.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 730[5:Rew:727.0,719.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 733[5:Rew:727.0,714.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 750[5:Rew:733.0,705.5,729.0,705.5,727.0,705.5,733.0,705.4,727.0,705.4,733.0,705.3,729.0,705.3,728.0,705.2,727.0,705.1] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(inverse(w),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(w,sk_c6) -> .
% 0.20/0.49 751[5:Con:750.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.49 780[5:SpL:730.0,751.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 781[5:Obv:780.1] || -> .
% 0.20/0.49 782[5:Spt:781.0,11.1,682.0] || equal(multiply(sk_c1,sk_c2),sk_c8)** -> .
% 0.20/0.49 783[5:Spt:781.0,11.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 784[5:MRR:10.1,782.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 786[5:MRR:12.1,782.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 787[5:MRR:9.1,782.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 803[5:SpR:786.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 805[5:Rew:783.0,803.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 811[5:SpR:787.0,102.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 813[5:Rew:784.0,811.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 818[5:SpR:805.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.49 819[5:SpR:805.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.20/0.49 821[5:Rew:678.0,819.0,663.0,819.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 835[5:Rew:821.0,813.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.49 837[5:Rew:805.0,835.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 842[5:Rew:837.0,782.0] || equal(multiply(sk_c1,sk_c2),sk_c6)** -> .
% 0.20/0.49 843[5:Rew:837.0,668.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.49 850[5:Rew:843.0,818.0,837.0,818.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 885[5:SpR:850.0,161.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 888[5:Rew:885.0,161.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 890[5:Rew:885.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.49 928[5:SpR:679.0,890.0] || -> equal(multiply(sk_c2,sk_c1),sk_c6)**.
% 0.20/0.49 936[5:SpR:928.0,102.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c1)**.
% 0.20/0.49 938[5:Rew:888.0,936.0] || -> equal(inverse(sk_c2),sk_c1)**.
% 0.20/0.49 941[5:SpR:938.0,890.0] || -> equal(multiply(sk_c1,sk_c2),sk_c6)**.
% 0.20/0.49 943[5:MRR:941.0,842.0] || -> .
% 0.20/0.49 944[4:Spt:943.0,16.1,679.0] || equal(inverse(sk_c1),sk_c2)** -> .
% 0.20/0.49 945[4:Spt:943.0,16.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 946[4:MRR:17.1,944.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 948[4:MRR:18.0,944.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 949[4:MRR:15.0,944.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 967[4:SpR:948.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 969[4:Rew:946.0,967.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 971[4:SpR:949.0,102.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 973[4:Rew:945.0,971.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 978[4:SpR:969.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),multiply(sk_c8,u))**.
% 0.20/0.49 979[4:SpR:969.0,102.0] || -> equal(multiply(inverse(sk_c6),sk_c8),sk_c6)**.
% 0.20/0.49 981[4:Rew:678.0,979.0,663.0,979.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 992[4:Rew:981.0,673.1] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** -> .
% 0.20/0.49 995[4:Rew:981.0,973.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.20/0.49 997[4:Rew:969.0,995.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 998[4:Rew:997.0,663.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.49 1002[4:Rew:997.0,668.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.20/0.49 1009[4:Rew:1002.0,978.0,997.0,978.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 1017[4:Rew:997.0,992.5,981.0,992.5,981.0,992.4,997.0,992.3,997.0,992.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c6)** equal(multiply(w,sk_c6),sk_c6)** -> .
% 0.20/0.49 1018[4:Con:1017.1] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.20/0.49 1044[4:SpR:1009.0,161.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 1047[4:Rew:1044.0,161.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1050[4:Rew:1047.0,1018.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.20/0.49 1087[4:SpL:998.0,1050.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 1088[4:Obv:1087.1] || -> .
% 0.20/0.49 1089[3:Spt:1088.0,28.1,670.0] || equal(multiply(sk_c6,sk_c7),sk_c8)** -> .
% 0.20/0.49 1090[3:Spt:1088.0,28.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 1091[3:MRR:26.1,1089.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 1092[3:MRR:29.1,1089.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 1093[3:MRR:30.1,1089.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 1094[3:MRR:27.1,1089.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 1095[3:MRR:25.1,1089.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 1105[3:SpR:1093.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 1107[3:Rew:1092.0,1105.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 1109[3:SpR:1094.0,102.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 1111[3:Rew:1090.0,1109.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 1113[3:SpR:1095.0,102.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.20/0.49 1115[3:Rew:1091.0,1113.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.49 1121[3:SpR:1111.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 1123[3:Rew:33.0,1121.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 1124[3:Rew:1123.0,161.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1125[3:Rew:1123.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 1128[3:Rew:1124.0,1107.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 1132[3:Rew:1128.0,1095.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.49 1133[3:Rew:1128.0,1089.0] || equal(multiply(sk_c6,sk_c7),sk_c6)** -> .
% 0.20/0.49 1139[3:Rew:1128.0,1115.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 1145[3:Rew:1124.0,1132.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.49 1149[3:Rew:1125.0,1139.0,1145.0,1139.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.49 1151[3:Rew:1149.0,1145.0] || -> equal(sk_c7,sk_c6)**.
% 0.20/0.49 1157[3:Rew:1125.0,1133.0,1151.0,1133.0] || equal(sk_c6,sk_c6)* -> .
% 0.20/0.49 1158[3:Obv:1157.0] || -> .
% 0.20/0.49 1166[2:Spt:1158.0,5.1,663.0] || equal(inverse(sk_c6),sk_c8)** -> .
% 0.20/0.49 1167[2:Spt:1158.0,5.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.49 1168[2:MRR:2.1,1166.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.20/0.49 1169[2:MRR:4.1,1166.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.49 1170[2:MRR:6.0,1166.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.20/0.49 1171[2:MRR:3.0,1166.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.20/0.49 1172[2:MRR:1.0,1166.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.49 1180[2:SpR:1170.0,102.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.20/0.49 1182[2:Rew:1167.0,1180.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.20/0.49 1184[2:SpR:1171.0,102.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.20/0.49 1186[2:Rew:1169.0,1184.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.49 1188[2:SpR:1172.0,102.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.20/0.49 1190[2:Rew:1168.0,1188.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.20/0.49 1198[2:SpR:1186.0,102.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.20/0.49 1200[2:Rew:33.0,1198.0] || -> equal(identity,sk_c6)**.
% 0.20/0.49 1201[2:Rew:1200.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.49 1202[2:Rew:1200.0,161.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.49 1205[2:Rew:1201.0,1182.0] || -> equal(sk_c8,sk_c6)**.
% 0.20/0.49 1211[2:Rew:1205.0,1166.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.20/0.49 1213[2:Rew:1205.0,1172.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.20/0.49 1216[2:Rew:1205.0,1190.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.20/0.49 1218[2:Rew:1202.0,1213.0] || -> equal(sk_c7,sk_c3)**.
% 0.20/0.49 1219[2:Rew:1218.0,1169.0] || -> equal(inverse(sk_c4),sk_c3)**.
% 0.20/0.49 1220[2:Rew:1218.0,1171.0] || -> equal(multiply(sk_c4,sk_c3),sk_c6)**.
% 0.20/0.49 1222[2:Rew:1201.0,1216.0,1218.0,1216.0] || -> equal(sk_c3,sk_c6)**.
% 0.20/0.49 1225[2:Rew:1222.0,1219.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.20/0.49 1227[2:Rew:1202.0,1220.0,1222.0,1220.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.50 1228[2:Rew:1227.0,1225.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.20/0.50 1229[2:MRR:1228.0,1211.0] || -> .
% 0.20/0.50 % SZS output end Refutation
% 0.20/0.50 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_15 prove_this_16 prove_this_17 prove_this_18 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 left_identity left_inverse associativity
% 0.20/0.50
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