TSTP Solution File: GRP233-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP233-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:46:26 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP233-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 01:14:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 962 clauses, backtracked 368 clauses, performed 12 splits and kept 741 clauses.
% 0.19/0.48 SPASS allocated 63651 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.06 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 5, length 400 :
% 0.19/0.48 % SZS output start Refutation
% 0.19/0.48 1[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.48 2[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.48 3[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.48 4[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.48 5[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.48 6[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 7[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 8[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.19/0.48 9[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 10[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 11[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 12[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.48 13[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.48 14[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.48 15[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 16[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 18[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 19[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 20[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 23[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c8),sk_c3).
% 0.19/0.48 24[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 25[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 26[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.48 28[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.48 29[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.48 30[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.48 31[0:Inp] || equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(sk_c8,v),sk_c7)** equal(multiply(w,sk_c8),v)* equal(inverse(w),sk_c8) equal(inverse(x),sk_c8) equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(z,sk_c8),y)* equal(inverse(z),sk_c8) -> .
% 0.19/0.48 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.48 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.48 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.48 35[0:Con:31.8] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(v,sk_c8),x)*+ equal(multiply(u,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c8,x),sk_c7)** -> .
% 0.19/0.48 36[1:Spt:35.1,35.4,35.7] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.19/0.48 38[2:Spt:5.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.48 40[3:Spt:1.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 42[4:Spt:4.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.48 48[1:SpL:32.0,36.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.48 49[5:Spt:3.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.48 51[6:Spt:2.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.48 54[2:SpR:38.0,33.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.48 55[3:SpR:40.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.48 56[1:SpL:33.0,36.1] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.48 63[2:SpR:54.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),multiply(identity,u))**.
% 0.19/0.48 66[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.48 69[2:Rew:32.0,63.0] || -> equal(multiply(sk_c8,multiply(sk_c5,u)),u)**.
% 0.19/0.48 71[0:Rew:32.0,66.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.48 75[4:SpR:42.0,69.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.48 76[5:Rew:49.0,75.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 79[5:Rew:76.0,40.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.48 80[5:Rew:76.0,42.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.48 81[5:Rew:76.0,49.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.48 82[6:Rew:76.0,51.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.48 83[5:Rew:76.0,54.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.19/0.48 84[5:Rew:76.0,55.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.48 87[5:Rew:76.0,56.2] || equal(inverse(inverse(sk_c8)),sk_c8) equal(identity,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 99[5:Rew:76.0,87.0] || equal(inverse(inverse(sk_c7)),sk_c7) equal(identity,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 120[0:SpR:71.0,71.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.48 123[0:SpR:33.0,71.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.48 127[5:SpR:81.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.48 128[5:SpR:83.0,71.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.19/0.48 129[5:SpR:84.0,71.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c4)**.
% 0.19/0.48 134[5:Rew:33.0,127.0] || -> equal(identity,sk_c6)**.
% 0.19/0.48 135[5:Rew:134.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.48 137[5:Rew:134.0,83.0] || -> equal(multiply(sk_c7,sk_c5),sk_c6)**.
% 0.19/0.48 141[5:Rew:134.0,99.1] || equal(inverse(inverse(sk_c7)),sk_c7) equal(sk_c6,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 144[5:Rew:134.0,128.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c5)**.
% 0.19/0.48 145[5:Rew:144.0,129.0,134.0,129.0] || -> equal(sk_c5,sk_c4)**.
% 0.19/0.48 147[5:Rew:145.0,80.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.19/0.48 149[5:Rew:145.0,137.0] || -> equal(multiply(sk_c7,sk_c4),sk_c6)**.
% 0.19/0.48 150[5:Rew:145.0,144.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c4)**.
% 0.19/0.48 151[6:Rew:82.0,147.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 155[6:Rew:151.0,135.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 157[6:Rew:151.0,149.0] || -> equal(multiply(sk_c7,sk_c4),sk_c7)**.
% 0.19/0.48 159[6:Rew:155.0,157.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.48 164[6:Rew:159.0,79.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 188[6:Rew:155.0,141.2,151.0,141.1,164.0,141.0,164.0,141.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.48 189[6:Obv:188.1] || equal(u,sk_c7)* -> .
% 0.19/0.48 190[6:UnC:189.0,76.0] || -> .
% 0.19/0.48 192[6:Spt:190.0,2.1,51.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.19/0.48 193[6:Spt:190.0,2.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.48 194[6:Rew:76.0,193.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 195[6:Rew:81.0,150.0,194.0,150.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.48 198[6:Rew:195.0,147.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.48 200[6:Rew:76.0,192.0] || equal(multiply(sk_c4,sk_c7),sk_c7)** -> .
% 0.19/0.48 201[6:Rew:198.0,200.0,195.0,200.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.48 211[5:Rew:76.0,12.1,76.0,12.0] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.48 212[6:Rew:198.0,211.1,195.0,211.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.48 213[6:MRR:212.1,201.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 220[5:Rew:76.0,7.1,76.0,7.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 221[6:Rew:198.0,220.0,195.0,220.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 222[6:MRR:221.0,201.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 252[6:SpR:222.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.48 254[6:Rew:198.0,252.0,213.0,252.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 255[6:MRR:254.0,201.0] || -> .
% 0.19/0.48 256[5:Spt:255.0,3.1,49.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.19/0.48 257[5:Spt:255.0,3.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.48 258[5:Rew:75.0,256.0] || equal(sk_c8,sk_c7)** -> .
% 0.19/0.48 259[0:Rew:120.0,123.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.48 260[4:Rew:75.0,28.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c8,sk_c7).
% 0.19/0.48 261[5:MRR:260.1,258.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.48 264[4:Rew:75.0,23.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 265[5:MRR:264.0,258.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 266[4:Rew:75.0,18.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 267[5:MRR:266.0,258.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 287[3:SpR:55.0,71.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.19/0.48 298[5:SpR:265.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.48 300[5:Rew:261.0,298.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.48 301[5:Rew:267.0,300.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 302[5:MRR:301.0,258.0] || -> .
% 0.19/0.48 303[4:Spt:302.0,4.1,42.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.19/0.48 304[4:Spt:302.0,4.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.48 305[4:Rew:259.0,287.0,304.0,287.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.48 307[4:Rew:305.0,55.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.48 312[4:MRR:29.1,303.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.48 313[4:MRR:14.1,303.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 317[4:MRR:24.0,303.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 318[4:MRR:19.0,303.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 319[4:MRR:9.0,303.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 332[4:SpR:317.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.48 334[4:Rew:312.0,332.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.48 335[4:Rew:318.0,334.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 337[4:Rew:335.0,304.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 340[4:Rew:335.0,313.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 342[4:Rew:335.0,54.0] || -> equal(multiply(sk_c7,sk_c5),identity)**.
% 0.19/0.48 345[4:Rew:335.0,48.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 350[4:Rew:335.0,307.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.48 353[4:Rew:335.0,318.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.48 354[4:Rew:335.0,319.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 359[4:Rew:335.0,345.1,335.0,345.0] || equal(inverse(identity),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 376[4:SpR:342.0,71.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c5)**.
% 0.19/0.48 378[4:Rew:337.0,376.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.19/0.48 379[4:Rew:259.0,378.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.48 388[4:SpR:353.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.48 390[4:Rew:337.0,388.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.48 391[4:Rew:350.0,390.0] || -> equal(identity,sk_c3)**.
% 0.19/0.48 393[4:Rew:391.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.48 396[4:Rew:391.0,359.0] || equal(inverse(sk_c3),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 398[4:Rew:391.0,350.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.48 404[4:SpR:354.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.48 406[4:Rew:340.0,404.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 407[4:Rew:398.0,406.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.48 411[4:Rew:407.0,393.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 416[4:Rew:407.0,396.0] || equal(inverse(sk_c7),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 438[4:Rew:337.0,416.0] || equal(sk_c7,sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 439[4:Obv:438.0] || equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 440[4:Rew:411.0,439.1] || equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.48 441[4:Obv:440.0] || equal(u,sk_c7)* -> .
% 0.19/0.48 442[4:UnC:441.0,379.0] || -> .
% 0.19/0.48 445[3:Spt:442.0,1.0,40.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.48 446[3:Spt:442.0,1.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.48 447[3:MRR:26.0,445.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.48 448[3:MRR:11.0,445.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 449[3:MRR:21.0,445.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 450[3:MRR:16.0,445.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 451[3:MRR:6.0,445.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 462[2:SpR:54.0,71.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c5)**.
% 0.19/0.48 464[3:Rew:446.0,462.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.19/0.48 465[3:Rew:259.0,464.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.48 467[3:Rew:465.0,54.0] || -> equal(multiply(sk_c8,sk_c7),identity)**.
% 0.19/0.48 476[3:SpR:449.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.48 478[3:Rew:447.0,476.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.48 479[3:Rew:450.0,478.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 480[3:Rew:479.0,446.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 482[3:Rew:479.0,448.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 486[3:Rew:479.0,450.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.48 487[3:Rew:479.0,451.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 490[3:Rew:479.0,48.0] || equal(inverse(identity),sk_c7) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.48 496[3:Rew:479.0,467.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.48 500[3:Rew:479.0,490.2,479.0,490.1] || equal(inverse(identity),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 515[3:SpR:486.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.48 517[3:Rew:480.0,515.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.48 518[3:Rew:496.0,517.0] || -> equal(identity,sk_c3)**.
% 0.19/0.48 520[3:Rew:518.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.48 522[3:Rew:518.0,500.0] || equal(inverse(sk_c3),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 524[3:Rew:518.0,496.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.48 530[3:SpR:487.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.48 532[3:Rew:482.0,530.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 533[3:Rew:524.0,532.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.48 537[3:Rew:533.0,520.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 540[3:Rew:533.0,522.0] || equal(inverse(sk_c7),sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 563[3:Rew:480.0,540.0] || equal(sk_c7,sk_c7) equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 564[3:Obv:563.0] || equal(sk_c7,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 565[3:Rew:537.0,564.1] || equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.48 566[3:Obv:565.0] || equal(u,sk_c7)* -> .
% 0.19/0.48 567[3:UnC:566.0,480.0] || -> .
% 0.19/0.48 570[2:Spt:567.0,5.0,38.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.48 571[2:Spt:567.0,5.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.48 572[2:MRR:30.0,570.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.48 573[2:MRR:15.0,570.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 574[2:MRR:25.0,570.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 575[2:MRR:20.0,570.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 576[2:MRR:10.0,570.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 577[2:Rew:571.0,56.0] || equal(inverse(sk_c7),sk_c8) equal(identity,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.48 578[2:SpR:571.0,71.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.48 585[2:SpR:574.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.48 587[2:Rew:572.0,585.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.48 588[2:Rew:575.0,587.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 589[2:Rew:588.0,571.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 591[2:Rew:588.0,573.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 594[2:Rew:588.0,575.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.48 595[2:Rew:588.0,576.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 599[2:Rew:588.0,577.2] || equal(inverse(sk_c7),sk_c8) equal(identity,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 600[2:Rew:588.0,578.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.48 607[2:Rew:589.0,599.0,588.0,599.0] || equal(sk_c7,sk_c7) equal(identity,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 608[2:Obv:607.0] || equal(identity,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.48 622[2:SpR:594.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.19/0.48 623[2:SpR:594.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.48 625[2:Rew:589.0,623.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.48 627[2:SpR:595.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.48 629[2:Rew:591.0,627.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 630[2:Rew:625.0,629.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.48 634[2:Rew:630.0,622.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.48 636[2:Rew:600.0,634.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 643[2:Rew:636.0,608.1] || equal(identity,u)* equal(u,sk_c7) -> .
% 0.19/0.48 662[2:SpR:636.0,259.0] || -> equal(identity,sk_c7)**.
% 0.19/0.48 669[2:Rew:662.0,643.0] || equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.48 677[2:Obv:669.0] || equal(u,sk_c7)* -> .
% 0.19/0.48 678[2:AED:677.0] || -> .
% 0.19/0.48 679[1:Spt:678.0,35.0,35.2,35.3,35.5,35.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c7),sk_c8)**+ equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.48 681[2:Spt:1.1] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.48 682[2:Rew:681.0,679.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c7,sk_c7) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.48 684[2:Obv:682.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.48 686[2:SpR:681.0,71.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.48 688[3:Spt:30.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.48 691[4:Spt:26.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.48 694[5:Spt:29.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.48 696[5:SpR:694.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.48 698[5:Rew:688.0,696.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.19/0.48 699[5:Rew:698.0,8.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 702[5:Rew:698.0,13.1] || -> equal(inverse(sk_c1),sk_c8)** equal(sk_c8,sk_c7).
% 0.19/0.48 704[5:Rew:702.1,12.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.48 706[5:Rew:699.0,7.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 710[5:SpR:698.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.19/0.48 712[5:Rew:681.0,710.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.48 713[5:SpR:712.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(sk_c6,u))**.
% 0.19/0.48 714[5:SpR:712.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c6),sk_c8)**.
% 0.19/0.48 716[5:Rew:686.0,713.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.48 731[5:SpR:716.0,259.0] || -> equal(identity,sk_c6)**.
% 0.19/0.48 734[5:Rew:731.0,259.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.48 736[5:Rew:731.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.48 737[5:Rew:734.0,714.0] || -> equal(inverse(sk_c7),sk_c8)**.
% 0.19/0.48 742[5:SpR:736.0,71.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.19/0.48 746[5:SpR:691.0,736.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.19/0.48 747[5:SpR:737.0,736.0] || -> equal(multiply(sk_c8,sk_c7),sk_c6)**.
% 0.19/0.48 748[5:Rew:734.0,742.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.48 765[5:SpR:746.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c6),sk_c4)**.
% 0.19/0.48 767[5:Rew:681.0,765.0] || -> equal(multiply(sk_c7,sk_c6),sk_c4)**.
% 0.19/0.48 768[5:Rew:734.0,767.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.48 774[5:Rew:768.0,706.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 776[5:Rew:768.0,704.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 780[6:Spt:702.1] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 781[6:Rew:780.0,681.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 782[6:Rew:780.0,712.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.48 784[6:Rew:780.0,684.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.48 787[6:Rew:780.0,776.0] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 789[6:Rew:780.0,774.1] || -> equal(multiply(sk_c7,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 794[6:Rew:782.0,787.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.48 796[6:Rew:782.0,789.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 799[6:Rew:780.0,784.3,780.0,784.2,780.0,784.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.48 800[6:Con:799.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.48 824[7:Spt:794.1] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 829[7:Rew:824.0,734.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 832[7:Rew:829.0,800.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.48 883[7:SpL:781.0,832.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 885[7:Obv:883.1] || -> .
% 0.19/0.48 886[7:Spt:885.0,794.1,824.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.48 887[7:Spt:885.0,794.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 889[7:MRR:796.0,886.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 893[7:SpR:887.0,748.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.48 896[7:Rew:781.0,893.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.48 898[7:Rew:896.0,889.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 899[7:Rew:782.0,898.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 900[7:MRR:899.0,886.0] || -> .
% 0.19/0.48 903[6:Spt:900.0,702.1,780.0] || equal(sk_c8,sk_c7)** -> .
% 0.19/0.48 904[6:Spt:900.0,702.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 906[6:MRR:699.0,903.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 910[6:SpR:904.0,748.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.19/0.48 913[6:Rew:681.0,910.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.48 915[6:Rew:913.0,906.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.48 916[6:Rew:712.0,915.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.48 919[6:Rew:916.0,734.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 923[6:Rew:916.0,747.0] || -> equal(multiply(sk_c8,sk_c7),sk_c7)**.
% 0.19/0.48 932[6:Rew:919.0,923.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 933[6:MRR:932.0,903.0] || -> .
% 0.19/0.48 938[5:Spt:933.0,29.1,694.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.19/0.48 939[5:Spt:933.0,29.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.48 940[5:MRR:14.1,938.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 941[5:MRR:24.0,938.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 942[5:MRR:19.0,938.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 943[5:MRR:9.0,938.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 955[5:SpR:941.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.48 957[5:Rew:939.0,955.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.48 958[5:Rew:942.0,957.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 960[5:Rew:958.0,681.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 961[5:Rew:958.0,940.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 966[5:Rew:958.0,686.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.48 969[5:Rew:958.0,942.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.48 970[5:Rew:958.0,943.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.48 971[5:Rew:958.0,684.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.48 976[5:Rew:958.0,971.3,958.0,971.2,958.0,971.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.48 977[5:Con:976.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.48 994[5:SpR:969.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.19/0.48 995[5:SpR:969.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.48 997[5:Rew:960.0,995.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.48 999[5:SpR:970.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.48 1001[5:Rew:961.0,999.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.48 1002[5:Rew:997.0,1001.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.48 1006[5:Rew:1002.0,994.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.48 1008[5:Rew:966.0,1006.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.48 1030[5:SpR:1008.0,259.0] || -> equal(identity,sk_c7)**.
% 0.19/0.48 1033[5:Rew:1030.0,259.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.48 1036[5:Rew:1033.0,977.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.48 1071[5:SpL:960.0,1036.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.48 1072[5:Obv:1071.1] || -> .
% 0.19/0.48 1073[4:Spt:1072.0,26.0,691.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.48 1074[4:Spt:1072.0,26.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.48 1075[4:MRR:11.0,1073.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.48 1076[4:MRR:21.0,1073.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.48 1077[4:MRR:16.0,1073.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.48 1078[4:MRR:6.0,1073.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.48 1088[4:SpR:1076.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.48 1090[4:Rew:1074.0,1088.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.48 1091[4:Rew:1077.0,1090.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.48 1094[4:Rew:1091.0,681.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.48 1095[4:Rew:1091.0,1075.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.48 1099[4:Rew:1091.0,686.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.48 1100[4:Rew:1091.0,1077.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.49 1101[4:Rew:1091.0,1078.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.49 1102[4:Rew:1091.0,684.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.49 1107[4:Rew:1091.0,1102.3,1091.0,1102.2,1091.0,1102.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.49 1108[4:Con:1107.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 1123[4:SpR:1100.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.19/0.49 1124[4:SpR:1100.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.49 1126[4:Rew:1094.0,1124.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.49 1128[4:SpR:1101.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.49 1130[4:Rew:1095.0,1128.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 1131[4:Rew:1126.0,1130.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.49 1135[4:Rew:1131.0,1123.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.49 1137[4:Rew:1099.0,1135.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 1157[4:SpR:1137.0,259.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 1160[4:Rew:1157.0,259.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 1163[4:Rew:1160.0,1108.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.49 1197[4:SpL:1094.0,1163.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.49 1198[4:Obv:1197.1] || -> .
% 0.19/0.49 1199[3:Spt:1198.0,30.0,688.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.49 1200[3:Spt:1198.0,30.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.49 1201[3:MRR:15.0,1199.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.49 1202[3:MRR:25.0,1199.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.49 1203[3:MRR:20.0,1199.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.49 1204[3:MRR:10.0,1199.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.19/0.49 1212[3:SpR:1202.0,71.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.49 1214[3:Rew:1200.0,1212.0] || -> equal(multiply(sk_c8,sk_c3),sk_c8)**.
% 0.19/0.49 1215[3:Rew:1203.0,1214.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 1217[3:Rew:1215.0,681.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 1218[3:Rew:1215.0,1201.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.49 1221[3:Rew:1215.0,686.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.49 1222[3:Rew:1215.0,1203.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.49 1223[3:Rew:1215.0,1204.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.49 1224[3:Rew:1215.0,684.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.19/0.49 1229[3:Rew:1215.0,1224.3,1215.0,1224.2,1215.0,1224.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.49 1230[3:Con:1229.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.49 1243[3:SpR:1222.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.19/0.49 1244[3:SpR:1222.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.49 1246[3:Rew:1217.0,1244.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.49 1248[3:SpR:1223.0,71.0] || -> equal(multiply(inverse(sk_c1),sk_c7),sk_c7)**.
% 0.19/0.49 1250[3:Rew:1218.0,1248.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 1251[3:Rew:1246.0,1250.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.49 1255[3:Rew:1251.0,1243.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.49 1257[3:Rew:1221.0,1255.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.49 1276[3:SpR:1257.0,259.0] || -> equal(identity,sk_c7)**.
% 0.19/0.49 1278[3:Rew:1276.0,259.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 1282[3:Rew:1278.0,1230.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.49 1324[3:SpL:1217.0,1282.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.49 1326[3:Obv:1324.1] || -> .
% 0.19/0.49 1327[2:Spt:1326.0,1.1,681.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.49 1328[2:Spt:1326.0,1.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.49 1329[2:MRR:5.1,1327.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.49 1330[2:MRR:2.0,1327.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.49 1331[2:MRR:3.0,1327.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.49 1332[2:MRR:4.0,1327.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.49 1338[2:SpR:1330.0,71.0] || -> equal(multiply(inverse(sk_c4),sk_c8),sk_c7)**.
% 0.19/0.49 1340[2:Rew:1328.0,1338.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.49 1342[2:SpR:1331.0,71.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c6)**.
% 0.19/0.49 1345[2:SpR:1332.0,71.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.19/0.49 1347[2:Rew:1331.0,1345.0,1329.0,1345.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.49 1349[2:Rew:1347.0,1329.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.19/0.49 1350[2:Rew:1347.0,1327.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.49 1353[2:Rew:1347.0,1332.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.19/0.49 1356[2:Rew:1347.0,1340.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.49 1358[2:Rew:1347.0,1342.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.19/0.49 1360[2:Rew:33.0,1358.0] || -> equal(identity,sk_c6)**.
% 0.19/0.49 1362[2:Rew:1360.0,259.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.49 1364[2:Rew:1360.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.49 1383[2:SpR:1356.0,71.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.49 1385[2:Rew:1364.0,1383.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.49 1387[2:Rew:1385.0,1353.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.19/0.49 1389[2:Rew:1385.0,1362.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.49 1397[2:Rew:1389.0,1387.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.49 1399[2:Rew:1397.0,1349.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.49 1401[2:MRR:1399.0,1350.0] || -> .
% 0.19/0.49 % SZS output end Refutation
% 0.19/0.49 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.19/0.49
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