TSTP Solution File: GRP369-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP369-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:47:03 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : GRP369-1 : TPTP v8.1.0. Released v2.5.0.
% 0.09/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 14:07:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 1168 clauses, backtracked 564 clauses, performed 13 splits and kept 1035 clauses.
% 0.19/0.50 SPASS allocated 63826 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.50 0:00:00.04 for the input.
% 0.19/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.08 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 4, length 451 :
% 0.19/0.50 % SZS output start Refutation
% 0.19/0.50 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.50 2[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c9),sk_c8).
% 0.19/0.50 3[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.50 4[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9)** equal(multiply(sk_c7,sk_c9),sk_c8).
% 0.19/0.50 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.50 6[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(multiply(sk_c7,sk_c9),sk_c8).
% 0.19/0.50 7[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.50 8[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.19/0.50 13[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(multiply(sk_c9,sk_c2),sk_c8).
% 0.19/0.50 14[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.19/0.50 15[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 16[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 17[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 18[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 19[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 20[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 21[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 22[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 27[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 28[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 29[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.19/0.50 34[0:Inp] || -> equal(multiply(sk_c6,sk_c9),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.19/0.50 35[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.19/0.50 36[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.50 37[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.19/0.50 38[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.50 39[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.50 40[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.50 41[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 42[0:Inp] || -> equal(inverse(sk_c6),sk_c9) equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.50 43[0:Inp] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(inverse(y),sk_c9) equal(inverse(sk_c8),sk_c7) equal(multiply(y,sk_c9),z)*+ equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** equal(multiply(sk_c9,z),sk_c8)** equal(multiply(sk_c7,sk_c9),sk_c8) -> .
% 0.19/0.50 44[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.50 45[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.50 46[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.50 47[1:Spt:43.4,43.6,43.11] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),v)* equal(multiply(sk_c9,v),sk_c8)** -> .
% 0.19/0.50 49[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.50 52[3:Spt:22.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 54[4:Spt:36.1] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.50 56[5:Spt:15.1] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 62[1:SpL:44.0,47.1] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c9,u),sk_c8)** -> .
% 0.19/0.50 63[6:Spt:29.1] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.19/0.50 65[7:Spt:8.1] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.19/0.50 68[3:SpR:52.0,45.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.19/0.50 69[4:SpR:54.0,45.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.50 70[1:SpL:45.0,47.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c9,u),sk_c8)** -> .
% 0.19/0.50 76[5:SpR:56.0,46.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),multiply(sk_c2,u))**.
% 0.19/0.50 78[3:SpR:68.0,46.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.19/0.50 80[0:SpR:45.0,46.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.50 84[3:Rew:44.0,78.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.19/0.50 86[0:Rew:44.0,80.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.50 90[5:SpR:56.0,84.0] || -> equal(multiply(sk_c9,sk_c2),sk_c9)**.
% 0.19/0.50 91[7:Rew:65.0,90.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.50 93[7:Rew:91.0,49.0] || -> equal(multiply(sk_c7,sk_c9),sk_c9)**.
% 0.19/0.50 94[7:Rew:91.0,65.0] || -> equal(multiply(sk_c9,sk_c2),sk_c9)**.
% 0.19/0.50 97[7:Rew:91.0,70.2] || equal(inverse(inverse(sk_c9)),sk_c9) equal(identity,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 111[0:SpR:86.0,86.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.50 114[3:SpR:68.0,86.0] || -> equal(multiply(inverse(sk_c9),identity),sk_c1)**.
% 0.19/0.50 116[7:SpR:94.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c2)**.
% 0.19/0.50 118[0:SpR:45.0,86.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.50 119[6:SpR:63.0,86.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.19/0.50 120[4:SpR:69.0,86.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.50 121[7:SpR:93.0,86.0] || -> equal(multiply(inverse(sk_c7),sk_c9),sk_c9)**.
% 0.19/0.50 126[7:Rew:45.0,116.0] || -> equal(identity,sk_c2)**.
% 0.19/0.50 127[7:Rew:126.0,44.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.50 128[7:Rew:126.0,45.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.50 130[7:Rew:126.0,69.0] || -> equal(multiply(sk_c7,sk_c3),sk_c2)**.
% 0.19/0.50 132[7:Rew:126.0,97.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(sk_c2,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 137[7:Rew:93.0,119.0,54.0,119.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 154[7:Rew:137.0,121.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.50 155[7:Rew:128.0,154.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.50 157[7:Rew:155.0,127.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 158[7:Rew:155.0,130.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.50 166[7:Rew:157.0,158.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.50 167[7:Rew:166.0,54.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 195[7:Rew:157.0,132.2,137.0,132.2,155.0,132.1,167.0,132.0,167.0,132.0,137.0,132.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.50 196[7:Obv:195.1] || equal(u,sk_c7)* -> .
% 0.19/0.50 197[7:UnC:196.0,86.0] || -> .
% 0.19/0.50 200[7:Spt:197.0,8.1,65.0] || equal(multiply(sk_c9,sk_c2),sk_c8)** -> .
% 0.19/0.50 201[7:Spt:197.0,8.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 203[6:Rew:49.0,119.0,54.0,119.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 204[7:Rew:203.0,201.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 206[7:Rew:204.0,120.0] || -> equal(multiply(sk_c7,identity),sk_c3)**.
% 0.19/0.50 207[7:Rew:90.0,200.0,203.0,200.0] || equal(sk_c9,sk_c7)** -> .
% 0.19/0.50 208[0:Rew:111.0,118.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.50 209[7:Rew:208.0,206.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.50 210[3:Rew:208.0,114.0] || -> equal(inverse(sk_c9),sk_c1)**.
% 0.19/0.50 212[7:Rew:209.0,69.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.50 213[7:Rew:209.0,63.0] || -> equal(multiply(sk_c7,sk_c7),sk_c9)**.
% 0.19/0.50 215[7:Rew:212.0,213.0] || -> equal(identity,sk_c9)**.
% 0.19/0.50 217[7:Rew:215.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 220[7:Rew:215.0,208.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.50 224[7:Rew:217.0,90.0] || -> equal(sk_c2,sk_c9)**.
% 0.19/0.50 234[7:Rew:224.0,14.1,217.0,14.1,203.0,14.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c9,sk_c7).
% 0.19/0.50 235[7:MRR:234.1,207.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 243[7:Rew:224.0,13.1,217.0,13.1,203.0,13.1,220.0,13.0] || -> equal(sk_c6,sk_c7)** equal(sk_c9,sk_c7).
% 0.19/0.50 244[7:MRR:243.1,207.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.50 245[7:Rew:244.0,235.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.19/0.50 246[7:Rew:204.0,245.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 247[7:MRR:246.0,207.0] || -> .
% 0.19/0.50 263[6:Spt:247.0,29.1,63.0] || equal(multiply(sk_c3,sk_c7),sk_c9)** -> .
% 0.19/0.50 264[6:Spt:247.0,29.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 265[4:Rew:208.0,120.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.50 270[6:MRR:35.1,263.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 276[6:MRR:34.1,263.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 286[3:SpR:210.0,86.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),u)**.
% 0.19/0.50 288[5:Rew:76.0,286.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.50 292[4:SpR:265.0,86.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.19/0.50 311[6:SpR:276.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 313[6:Rew:270.0,311.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 337[6:SpR:313.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.19/0.50 339[6:Rew:56.0,337.0,210.0,337.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.50 343[6:Rew:339.0,288.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 344[6:Rew:343.0,49.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.50 345[6:Rew:343.0,69.0] || -> equal(identity,sk_c3)**.
% 0.19/0.50 346[6:Rew:343.0,292.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.50 352[6:Rew:344.0,264.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.50 360[6:Rew:344.0,62.2] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c9,u),sk_c9)** -> .
% 0.19/0.50 374[6:Rew:210.0,352.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.50 375[6:Rew:374.0,210.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.50 376[6:Rew:374.0,52.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.19/0.50 380[6:Rew:265.0,376.0] || -> equal(sk_c3,sk_c9)**.
% 0.19/0.50 384[6:Rew:380.0,345.0] || -> equal(identity,sk_c9)**.
% 0.19/0.50 385[6:Rew:380.0,346.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 386[6:Rew:385.0,313.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 393[6:Rew:386.0,375.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 395[6:Rew:386.0,384.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 436[6:Rew:343.0,360.2,386.0,360.2,386.0,360.1,393.0,360.0,395.0,360.0,386.0,360.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.50 437[6:Obv:436.1] || equal(u,sk_c7)* -> .
% 0.19/0.50 438[6:UnC:437.0,86.0] || -> .
% 0.19/0.50 441[5:Spt:438.0,15.1,56.0] || equal(multiply(sk_c1,sk_c9),sk_c2)** -> .
% 0.19/0.50 442[5:Spt:438.0,15.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 443[5:MRR:21.1,441.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 444[5:MRR:19.1,441.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.50 445[5:MRR:17.1,441.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.50 446[5:MRR:20.1,441.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 447[5:MRR:18.1,441.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.50 448[5:MRR:16.1,441.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.19/0.50 471[5:SpR:446.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 473[5:Rew:443.0,471.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 488[5:SpR:447.0,86.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.19/0.50 490[5:Rew:444.0,488.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.19/0.50 492[5:SpR:448.0,86.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c8)**.
% 0.19/0.50 494[5:Rew:445.0,492.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 501[5:SpR:490.0,86.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c9)**.
% 0.19/0.50 503[5:Rew:442.0,501.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.19/0.50 505[5:SpR:494.0,86.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.19/0.50 507[5:Rew:442.0,505.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.50 508[5:Rew:503.0,507.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 509[5:Rew:508.0,52.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.50 510[5:Rew:508.0,210.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.50 513[5:Rew:508.0,49.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 517[5:Rew:508.0,473.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.50 518[5:Rew:508.0,490.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 522[5:Rew:508.0,62.2] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c7,u),sk_c8)** -> .
% 0.19/0.50 536[5:Rew:265.0,510.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.50 537[5:Rew:536.0,265.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.50 539[5:Rew:536.0,69.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.50 543[5:Rew:513.0,517.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 544[5:Rew:543.0,442.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 556[5:Rew:537.0,544.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.50 557[5:Rew:556.0,509.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 561[5:Rew:543.0,518.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.50 564[5:Rew:561.0,539.0,556.0,539.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 565[5:Rew:564.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 600[5:Rew:565.0,522.2,543.0,522.2,508.0,522.1,557.0,522.0,564.0,522.0,508.0,522.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.50 601[5:Obv:600.1] || equal(u,sk_c7)* -> .
% 0.19/0.50 602[5:UnC:601.0,86.0] || -> .
% 0.19/0.50 605[4:Spt:602.0,36.1,54.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.50 606[4:Spt:602.0,36.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 607[4:MRR:42.1,605.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 608[4:MRR:40.1,605.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.50 609[4:MRR:38.1,605.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.50 610[4:MRR:41.0,605.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 611[4:MRR:39.0,605.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.50 612[4:MRR:37.0,605.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.19/0.50 634[4:SpR:610.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 636[4:Rew:607.0,634.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 638[4:SpR:611.0,86.0] || -> equal(multiply(inverse(sk_c5),sk_c9),sk_c8)**.
% 0.19/0.50 640[4:Rew:608.0,638.0] || -> equal(multiply(sk_c8,sk_c9),sk_c8)**.
% 0.19/0.50 642[4:SpR:612.0,86.0] || -> equal(multiply(inverse(sk_c4),sk_c7),sk_c8)**.
% 0.19/0.50 644[4:Rew:609.0,642.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 650[4:SpR:640.0,86.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c9)**.
% 0.19/0.50 652[4:Rew:606.0,650.0] || -> equal(multiply(sk_c7,sk_c8),sk_c9)**.
% 0.19/0.50 654[4:SpR:644.0,86.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.19/0.50 656[4:Rew:606.0,654.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.50 657[4:Rew:652.0,656.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 659[4:Rew:657.0,210.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.50 661[4:Rew:657.0,68.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.50 662[4:Rew:657.0,49.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.50 665[4:Rew:657.0,636.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.50 666[4:Rew:657.0,640.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.19/0.50 671[4:Rew:657.0,62.2] || equal(inverse(identity),sk_c9) equal(sk_c9,u) equal(multiply(sk_c7,u),sk_c8)** -> .
% 0.19/0.50 684[4:Rew:662.0,665.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 685[4:Rew:684.0,606.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 696[4:Rew:659.0,685.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.50 697[4:Rew:696.0,659.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 699[4:Rew:696.0,661.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.50 700[4:Rew:684.0,666.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.50 703[4:Rew:700.0,699.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 705[4:Rew:703.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 735[4:Rew:705.0,671.2,684.0,671.2,657.0,671.1,697.0,671.0,703.0,671.0,657.0,671.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.50 736[4:Obv:735.1] || equal(u,sk_c7)* -> .
% 0.19/0.50 737[4:UnC:736.0,86.0] || -> .
% 0.19/0.50 740[3:Spt:737.0,22.1,52.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.50 741[3:Spt:737.0,22.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 742[3:MRR:28.1,740.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 745[3:MRR:27.0,740.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 748[3:SpR:741.0,86.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.50 750[3:SpR:742.0,86.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.19/0.50 760[3:SpR:745.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 762[3:Rew:742.0,760.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 772[3:SpR:762.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.19/0.50 774[3:Rew:45.0,772.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 775[3:Rew:774.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 780[3:Rew:774.0,70.1] || equal(inverse(inverse(sk_c9)),sk_c9) equal(sk_c7,u) equal(multiply(sk_c9,u),sk_c8)** -> .
% 0.19/0.50 781[3:Rew:775.0,49.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.50 782[3:Rew:775.0,748.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 786[3:Rew:781.0,741.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.50 801[3:Rew:781.0,782.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 802[3:Rew:801.0,750.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.50 803[3:Rew:802.0,745.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 806[3:Rew:803.0,781.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 807[3:Rew:803.0,786.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 833[3:Rew:775.0,780.2,803.0,780.2,806.0,780.2,807.0,780.0,807.0,780.0,803.0,780.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.50 834[3:Obv:833.1] || equal(u,sk_c7)* -> .
% 0.19/0.50 835[3:UnC:834.0,86.0] || -> .
% 0.19/0.50 838[2:Spt:835.0,1.1,49.0] || equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.19/0.50 839[2:Spt:835.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 840[2:MRR:7.1,838.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 841[2:MRR:5.1,838.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.50 842[2:MRR:3.1,838.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.50 843[2:MRR:6.1,838.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 844[2:MRR:4.1,838.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.50 845[2:MRR:2.1,838.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.19/0.50 846[2:SpR:839.0,86.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.50 850[2:SpR:841.0,86.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.19/0.50 852[2:SpR:842.0,86.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.19/0.50 854[2:SpR:843.0,46.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),multiply(sk_c7,u))**.
% 0.19/0.50 855[2:SpR:843.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 857[2:Rew:840.0,855.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 858[2:SpR:844.0,46.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.19/0.50 867[2:SpR:857.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.19/0.50 869[2:Rew:45.0,867.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 871[2:Rew:869.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 876[2:Rew:871.0,838.0] || equal(sk_c8,sk_c9)** -> .
% 0.19/0.50 877[2:Rew:871.0,854.0] || -> equal(multiply(sk_c6,multiply(sk_c9,u)),u)**.
% 0.19/0.50 879[2:Rew:871.0,846.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 881[2:Rew:879.0,858.0] || -> equal(multiply(sk_c5,u),multiply(sk_c9,u))**.
% 0.19/0.50 882[2:Rew:879.0,852.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.50 883[2:Rew:879.0,850.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.50 885[2:Rew:882.0,845.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 893[2:Rew:885.0,876.0] || equal(sk_c9,sk_c7)** -> .
% 0.19/0.50 899[2:Rew:883.0,881.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 900[2:Rew:899.0,877.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.50 902[2:Rew:900.0,843.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 903[2:MRR:902.0,893.0] || -> .
% 0.19/0.50 911[1:Spt:903.0,43.0,43.1,43.2,43.3,43.5,43.7,43.8,43.9,43.10,43.12] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c9),sk_c7)**+ equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.19/0.50 913[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c9),sk_c8)**.
% 0.19/0.50 914[2:Rew:913.0,911.9] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.19/0.50 916[2:Obv:914.9] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** -> .
% 0.19/0.50 919[2:SpR:913.0,86.0] || -> equal(multiply(inverse(sk_c7),sk_c8),sk_c9)**.
% 0.19/0.50 921[3:Spt:36.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 923[3:Rew:921.0,916.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(sk_c7,sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** -> .
% 0.19/0.50 924[3:Obv:923.4] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** -> .
% 0.19/0.50 926[3:SpR:921.0,86.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.50 928[4:Spt:28.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 931[5:Spt:42.1] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.50 934[6:Spt:21.1] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 935[6:SpR:934.0,46.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),multiply(sk_c2,u))**.
% 0.19/0.50 936[6:SpR:934.0,86.0] || -> equal(multiply(inverse(sk_c1),sk_c2),sk_c9)**.
% 0.19/0.50 938[6:Rew:928.0,936.0] || -> equal(multiply(sk_c9,sk_c2),sk_c9)**.
% 0.19/0.50 941[6:Rew:938.0,13.1] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(sk_c8,sk_c9).
% 0.19/0.50 944[6:Rew:938.0,14.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c8,sk_c9).
% 0.19/0.50 948[7:Spt:35.1] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.19/0.50 950[7:SpR:948.0,86.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.19/0.50 952[7:Rew:913.0,950.0,931.0,950.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 954[7:Rew:952.0,921.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 959[7:Rew:952.0,919.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.19/0.50 961[7:Rew:952.0,926.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.50 962[7:Rew:952.0,924.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** -> .
% 0.19/0.50 964[7:Rew:952.0,941.1] || -> equal(multiply(sk_c6,sk_c9),sk_c7)** equal(sk_c9,sk_c7).
% 0.19/0.50 965[7:Rew:952.0,944.1] || -> equal(inverse(sk_c6),sk_c9)** equal(sk_c9,sk_c7).
% 0.19/0.50 966[7:Rew:954.0,959.0] || -> equal(multiply(sk_c7,sk_c7),sk_c9)**.
% 0.19/0.50 971[7:Rew:952.0,962.6,952.0,962.5,952.0,962.2] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(inverse(x),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c7),sk_c9)** equal(multiply(w,sk_c7),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** -> .
% 0.19/0.50 972[7:Con:971.3] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c7),sk_c9)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.50 979[6:SpR:938.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c2)**.
% 0.19/0.50 981[6:Rew:45.0,979.0] || -> equal(identity,sk_c2)**.
% 0.19/0.50 982[6:Rew:981.0,44.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.50 983[6:Rew:981.0,208.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.50 984[6:Rew:981.0,45.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.19/0.50 986[6:Rew:982.0,935.0] || -> equal(multiply(sk_c1,multiply(sk_c9,u)),u)**.
% 0.19/0.50 996[7:SpR:966.0,46.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c9,u))**.
% 0.19/0.50 1000[7:Rew:961.0,996.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 1003[7:Rew:1000.0,986.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.50 1005[7:Rew:1003.0,934.0] || -> equal(sk_c2,sk_c9)**.
% 0.19/0.50 1008[7:Rew:1005.0,983.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.50 1012[7:Rew:1008.0,964.0] || -> equal(sk_c6,sk_c7)** equal(sk_c9,sk_c7).
% 0.19/0.50 1013[7:Rew:1008.0,972.3] || equal(inverse(u),sk_c9)** equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(u,sk_c7) equal(multiply(v,sk_c7),sk_c9)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.50 1014[7:Rew:1012.0,965.0] || -> equal(inverse(sk_c7),sk_c9)** equal(sk_c9,sk_c7).
% 0.19/0.50 1015[7:Rew:954.0,1014.0] || -> equal(sk_c9,sk_c7)** equal(sk_c9,sk_c7)**.
% 0.19/0.50 1016[7:Obv:1015.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 1023[7:Rew:1016.0,1008.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.50 1034[7:Rew:1023.0,1013.5,1023.0,1013.4,1016.0,1013.4,1016.0,1013.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.19/0.50 1035[7:Con:1034.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.50 1057[7:SpL:954.0,1035.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.50 1058[7:Obv:1057.1] || -> .
% 0.19/0.50 1059[7:Spt:1058.0,35.1,948.0] || equal(multiply(sk_c3,sk_c7),sk_c9)** -> .
% 0.19/0.50 1060[7:Spt:1058.0,35.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 1063[7:MRR:34.1,1059.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 1066[7:SpR:1060.0,86.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.19/0.50 1088[7:SpR:1063.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 1090[7:Rew:1060.0,1088.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 1100[7:SpR:1090.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.19/0.50 1102[7:Rew:984.0,1100.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.50 1105[7:Rew:1102.0,982.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1106[7:Rew:1102.0,983.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.50 1108[7:Rew:1102.0,984.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.50 1109[7:Rew:1105.0,913.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.50 1112[7:Rew:1105.0,926.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1128[7:Rew:1106.0,1059.0] || equal(sk_c3,sk_c9)** -> .
% 0.19/0.50 1129[7:Rew:1109.0,1112.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 1130[7:Rew:1129.0,1066.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.50 1133[7:Rew:1130.0,1063.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 1141[7:Rew:1133.0,1128.0] || equal(sk_c3,sk_c7)** -> .
% 0.19/0.50 1192[7:SpR:931.0,1108.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.50 1196[7:Rew:1105.0,1192.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.50 1197[7:MRR:1196.0,1141.0] || -> .
% 0.19/0.50 1207[6:Spt:1197.0,21.1,934.0] || equal(multiply(sk_c1,sk_c9),sk_c2)** -> .
% 0.19/0.50 1208[6:Spt:1197.0,21.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 1211[6:MRR:20.1,1207.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 1214[6:SpR:1208.0,86.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.19/0.50 1225[6:SpR:1211.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 1227[6:Rew:1208.0,1225.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 1240[6:SpR:1227.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.19/0.50 1242[6:Rew:45.0,1240.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 1243[6:Rew:1242.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1244[6:Rew:1242.0,208.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.50 1247[6:Rew:1243.0,913.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.50 1250[6:Rew:1243.0,926.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1253[6:Rew:1247.0,921.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.50 1260[6:Rew:1247.0,924.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** -> .
% 0.19/0.50 1266[6:Rew:1247.0,1250.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 1267[6:Rew:1266.0,1214.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.50 1269[6:Rew:1267.0,1211.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 1273[6:Rew:1269.0,1247.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 1274[6:Rew:1269.0,1253.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 1294[6:Rew:1244.0,1260.7,1269.0,1260.7,1244.0,1260.6,1273.0,1260.6,1244.0,1260.5,1273.0,1260.5,1269.0,1260.5,1244.0,1260.4,1269.0,1260.4,1273.0,1260.2,1269.0,1260.1,1269.0,1260.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(inverse(x),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) equal(x,sk_c7) -> .
% 0.19/0.50 1295[6:Con:1294.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.50 1345[6:SpL:1274.0,1295.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.50 1346[6:Obv:1345.1] || -> .
% 0.19/0.50 1347[5:Spt:1346.0,42.1,931.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.50 1348[5:Spt:1346.0,42.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 1351[5:MRR:41.0,1347.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 1354[5:SpR:1348.0,86.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.19/0.50 1368[5:SpR:1351.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 1370[5:Rew:1348.0,1368.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 1383[5:SpR:1370.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.19/0.50 1385[5:Rew:45.0,1383.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 1386[5:Rew:1385.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1387[5:Rew:1385.0,208.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.50 1390[5:Rew:1386.0,913.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.50 1392[5:Rew:1386.0,926.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1395[5:Rew:1390.0,921.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.50 1402[5:Rew:1390.0,924.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** -> .
% 0.19/0.50 1408[5:Rew:1390.0,1392.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 1409[5:Rew:1408.0,1354.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.50 1411[5:Rew:1409.0,1351.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 1414[5:Rew:1411.0,1390.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 1415[5:Rew:1411.0,1395.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 1434[5:Rew:1387.0,1402.7,1411.0,1402.7,1387.0,1402.6,1414.0,1402.6,1387.0,1402.5,1414.0,1402.5,1411.0,1402.5,1387.0,1402.4,1411.0,1402.4,1414.0,1402.2,1411.0,1402.1,1411.0,1402.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(inverse(x),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) equal(x,sk_c7) -> .
% 0.19/0.50 1435[5:Con:1434.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.50 1521[5:SpL:1415.0,1435.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.50 1523[5:Obv:1521.1] || -> .
% 0.19/0.50 1524[4:Spt:1523.0,28.1,928.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.19/0.50 1525[4:Spt:1523.0,28.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 1528[4:MRR:27.0,1524.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 1531[4:SpR:1525.0,86.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.19/0.50 1543[4:SpR:1528.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 1545[4:Rew:1525.0,1543.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 1555[4:SpR:1545.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.19/0.50 1557[4:Rew:45.0,1555.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 1558[4:Rew:1557.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1559[4:Rew:1557.0,208.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.50 1562[4:Rew:1558.0,913.0] || -> equal(sk_c8,sk_c9)**.
% 0.19/0.50 1564[4:Rew:1558.0,926.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1567[4:Rew:1562.0,921.0] || -> equal(inverse(sk_c9),sk_c7)**.
% 0.19/0.50 1574[4:Rew:1562.0,924.1] || equal(inverse(u),sk_c9) equal(inverse(v),sk_c9) equal(inverse(w),sk_c8) equal(inverse(x),sk_c7) equal(multiply(u,sk_c9),sk_c7)** equal(multiply(v,sk_c8),sk_c9)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c7),sk_c9)** -> .
% 0.19/0.50 1580[4:Rew:1562.0,1564.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 1581[4:Rew:1580.0,1531.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.50 1582[4:Rew:1581.0,1528.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 1585[4:Rew:1582.0,1562.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 1586[4:Rew:1582.0,1567.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.50 1605[4:Rew:1559.0,1574.7,1582.0,1574.7,1559.0,1574.6,1585.0,1574.6,1559.0,1574.5,1585.0,1574.5,1582.0,1574.5,1559.0,1574.4,1582.0,1574.4,1585.0,1574.2,1582.0,1574.1,1582.0,1574.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(inverse(x),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) equal(x,sk_c7) -> .
% 0.19/0.50 1606[4:Con:1605.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.50 1674[4:SpL:1586.0,1606.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.50 1676[4:Obv:1674.1] || -> .
% 0.19/0.50 1677[3:Spt:1676.0,36.0,921.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.50 1678[3:Spt:1676.0,36.1] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.50 1679[3:MRR:22.0,1677.0] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.19/0.50 1680[3:MRR:8.0,1677.0] || -> equal(multiply(sk_c9,sk_c2),sk_c8)**.
% 0.19/0.50 1681[3:MRR:29.0,1677.0] || -> equal(multiply(sk_c3,sk_c7),sk_c9)**.
% 0.19/0.50 1682[3:MRR:15.0,1677.0] || -> equal(multiply(sk_c1,sk_c9),sk_c2)**.
% 0.19/0.50 1683[3:SpR:1678.0,86.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.50 1685[3:SpR:1679.0,86.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.19/0.50 1694[3:SpR:1681.0,86.0] || -> equal(multiply(inverse(sk_c3),sk_c9),sk_c7)**.
% 0.19/0.50 1696[3:Rew:913.0,1694.0,1678.0,1694.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 1698[3:Rew:1696.0,1677.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.50 1699[3:Rew:1696.0,1680.0] || -> equal(multiply(sk_c9,sk_c2),sk_c7)**.
% 0.19/0.50 1700[3:Rew:1696.0,919.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c9)**.
% 0.19/0.50 1704[3:Rew:45.0,1700.0] || -> equal(identity,sk_c9)**.
% 0.19/0.50 1705[3:Rew:1704.0,208.0] || -> equal(multiply(u,sk_c9),u)**.
% 0.19/0.50 1706[3:Rew:1704.0,44.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 1709[3:Rew:1705.0,1682.0] || -> equal(sk_c1,sk_c2)**.
% 0.19/0.50 1710[3:Rew:1709.0,1679.0] || -> equal(inverse(sk_c2),sk_c9)**.
% 0.19/0.50 1711[3:Rew:1709.0,1685.0] || -> equal(multiply(sk_c9,multiply(sk_c2,u)),u)**.
% 0.19/0.50 1712[3:Rew:1706.0,1699.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.50 1714[3:Rew:1712.0,1710.0] || -> equal(inverse(sk_c7),sk_c9)**.
% 0.19/0.50 1715[3:Rew:1714.0,1698.0] || equal(sk_c9,sk_c7)** -> .
% 0.19/0.50 1717[3:Rew:1706.0,1711.0,1712.0,1711.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1718[3:Rew:1717.0,1683.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.50 1719[3:Rew:1718.0,1681.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 1720[3:MRR:1719.0,1715.0] || -> .
% 0.19/0.50 1724[2:Spt:1720.0,1.1,913.0] || equal(multiply(sk_c7,sk_c9),sk_c8)** -> .
% 0.19/0.50 1725[2:Spt:1720.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.50 1726[2:MRR:7.1,1724.0] || -> equal(inverse(sk_c6),sk_c9)**.
% 0.19/0.50 1727[2:MRR:5.1,1724.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.50 1728[2:MRR:3.1,1724.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.50 1729[2:MRR:6.1,1724.0] || -> equal(multiply(sk_c6,sk_c9),sk_c7)**.
% 0.19/0.50 1730[2:MRR:4.1,1724.0] || -> equal(multiply(sk_c5,sk_c8),sk_c9)**.
% 0.19/0.50 1731[2:MRR:2.1,1724.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.19/0.50 1732[2:SpR:1725.0,86.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.50 1734[2:SpR:1726.0,86.0] || -> equal(multiply(sk_c9,multiply(sk_c6,u)),u)**.
% 0.19/0.50 1736[2:SpR:1727.0,86.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.19/0.50 1738[2:SpR:1728.0,86.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.19/0.50 1741[2:SpR:1729.0,86.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c9)**.
% 0.19/0.50 1743[2:Rew:1726.0,1741.0] || -> equal(multiply(sk_c9,sk_c7),sk_c9)**.
% 0.19/0.50 1744[2:SpR:1730.0,46.0] || -> equal(multiply(sk_c5,multiply(sk_c8,u)),multiply(sk_c9,u))**.
% 0.19/0.50 1753[2:SpR:1743.0,86.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c7)**.
% 0.19/0.50 1755[2:Rew:45.0,1753.0] || -> equal(identity,sk_c7)**.
% 0.19/0.50 1756[2:Rew:1755.0,44.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.50 1760[2:Rew:1756.0,1732.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.50 1761[2:Rew:1756.0,1724.0] || equal(sk_c8,sk_c9)** -> .
% 0.19/0.50 1764[2:Rew:1760.0,1738.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.50 1765[2:Rew:1760.0,1736.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.50 1767[2:Rew:1760.0,1744.0] || -> equal(multiply(sk_c5,u),multiply(sk_c9,u))**.
% 0.19/0.50 1769[2:Rew:1764.0,1731.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.50 1774[2:Rew:1769.0,1761.0] || equal(sk_c9,sk_c7)** -> .
% 0.19/0.50 1780[2:Rew:1765.0,1767.0] || -> equal(multiply(sk_c9,u),u)**.
% 0.19/0.50 1781[2:Rew:1780.0,1734.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.50 1783[2:Rew:1781.0,1729.0] || -> equal(sk_c9,sk_c7)**.
% 0.19/0.50 1784[2:MRR:1783.0,1774.0] || -> .
% 0.19/0.50 % SZS output end Refutation
% 0.19/0.50 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_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_27 prove_this_28 prove_this_29 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 left_identity left_inverse associativity
% 0.19/0.50
%------------------------------------------------------------------------------