TSTP Solution File: GRP337-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP337-1 : 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 11:46:55 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP337-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 14:56:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 933 clauses, backtracked 410 clauses, performed 14 splits and kept 658 clauses.
% 0.20/0.50 SPASS allocated 63922 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.06 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 6, length 258 :
% 0.20/0.50 % SZS output start Refutation
% 0.20/0.50 1[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.20/0.50 2[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.20/0.50 3[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 4[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 5[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c8),sk_c6).
% 0.20/0.50 6[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 10[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.50 11[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.50 12[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.50 16[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 17[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 18[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 19[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 20[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 21[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 22[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 23[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 24[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 25[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.50 26[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.50 27[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 28[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 29[0:Inp] || -> equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.50 30[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 31[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 32[0:Inp] || -> equal(multiply(sk_c4,sk_c8),sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 33[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 34[0:Inp] || -> equal(inverse(sk_c8),sk_c6) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 36[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 37[0:Inp] || equal(inverse(u),v) equal(inverse(w),sk_c6) equal(inverse(x),sk_c8) equal(inverse(y),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(u,v),sk_c7)**+ equal(multiply(w,sk_c6),sk_c7)** equal(multiply(x,sk_c8),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(y,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.20/0.50 38[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.50 39[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.50 40[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.50 41[1:Spt:37.0,37.5,37.8] || equal(inverse(u),v) equal(multiply(u,v),sk_c7)**+ equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.20/0.50 42[2:Spt:4.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.20/0.50 44[3:Spt:1.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.50 47[4:Spt:6.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.50 49[5:Spt:3.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.50 53[6:Spt:5.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.50 55[6:SpL:53.0,41.1] || equal(inverse(sk_c5),sk_c6) equal(sk_c7,sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.50 56[6:Obv:55.1] || equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.50 57[6:Rew:47.0,56.0] || equal(sk_c6,sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.50 58[6:Obv:57.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.20/0.50 66[2:SpR:42.0,39.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.20/0.50 67[4:SpR:47.0,39.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.20/0.50 68[5:SpR:49.0,39.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.20/0.50 70[6:Rew:66.0,58.0] || equal(identity,sk_c7)** -> .
% 0.20/0.50 75[6:SpR:53.0,40.0] || -> equal(multiply(sk_c5,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.50 77[0:SpR:39.0,40.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.50 79[0:Rew:38.0,77.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.50 89[5:SpR:68.0,40.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.20/0.50 92[5:Rew:38.0,89.0] || -> equal(multiply(sk_c8,multiply(sk_c4,u)),u)**.
% 0.20/0.50 94[0:SpR:79.0,79.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.50 97[2:SpR:66.0,79.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c8)**.
% 0.20/0.50 101[0:SpR:39.0,79.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.50 103[4:SpR:67.0,79.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c5)**.
% 0.20/0.50 104[5:SpR:68.0,79.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c4)**.
% 0.20/0.50 111[4:Rew:97.0,103.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.50 113[6:Rew:111.0,53.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.50 115[6:Rew:111.0,75.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.20/0.50 117[5:Rew:42.0,104.0] || -> equal(multiply(sk_c6,identity),sk_c4)**.
% 0.20/0.50 119[0:Rew:94.0,101.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.50 120[5:Rew:119.0,117.0] || -> equal(sk_c4,sk_c6)**.
% 0.20/0.50 124[5:Rew:120.0,68.0] || -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.20/0.50 126[5:Rew:120.0,92.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),u)**.
% 0.20/0.50 131[6:Rew:126.0,115.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 132[6:Rew:131.0,44.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 135[6:Rew:132.0,66.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.20/0.50 140[6:Rew:132.0,113.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 144[6:Rew:135.0,140.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 145[6:MRR:144.0,70.0] || -> .
% 0.20/0.50 150[6:Spt:145.0,5.0,53.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.50 151[6:Spt:145.0,5.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 152[6:Rew:124.0,150.0,111.0,150.0] || equal(identity,sk_c7)** -> .
% 0.20/0.50 153[5:Rew:66.0,26.1,120.0,26.1] || -> equal(inverse(sk_c2),sk_c3)** equal(identity,sk_c7).
% 0.20/0.50 154[6:MRR:153.1,152.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 157[5:Rew:66.0,32.0,120.0,32.0] || -> equal(identity,sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 158[6:MRR:157.0,152.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 159[5:Rew:66.0,20.0,120.0,20.0] || -> equal(identity,sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 160[6:MRR:159.0,152.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 207[6:SpL:160.0,41.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c7,sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 209[6:Obv:207.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 210[6:Rew:158.0,209.1,154.0,209.0] || equal(sk_c3,sk_c3)* equal(sk_c7,sk_c7) -> .
% 0.20/0.50 211[6:Obv:210.1] || -> .
% 0.20/0.50 212[5:Spt:211.0,3.0,49.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.20/0.50 213[5:Spt:211.0,3.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 214[5:MRR:27.0,212.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 216[5:MRR:33.0,212.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 217[5:MRR:21.0,212.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 249[5:SpL:217.0,41.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c7,sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 251[5:Obv:249.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 252[5:Rew:216.0,251.1,214.0,251.0] || equal(sk_c3,sk_c3)* equal(sk_c7,sk_c7) -> .
% 0.20/0.50 253[5:Obv:252.1] || -> .
% 0.20/0.50 254[4:Spt:253.0,6.0,47.0] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.20/0.50 255[4:Spt:253.0,6.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 256[4:MRR:30.0,254.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 258[4:MRR:36.0,254.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 259[4:MRR:24.0,254.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 279[4:SpL:259.0,41.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c7,sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 281[4:Obv:279.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 282[4:Rew:258.0,281.1,256.0,281.0] || equal(sk_c3,sk_c3)* equal(sk_c7,sk_c7) -> .
% 0.20/0.50 283[4:Obv:282.1] || -> .
% 0.20/0.50 284[3:Spt:283.0,1.0,44.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.20/0.50 285[3:Spt:283.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 286[3:MRR:25.1,284.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 288[3:MRR:31.0,284.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 289[3:MRR:19.0,284.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 309[3:SpL:289.0,41.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c7,sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 311[3:Obv:309.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 312[3:Rew:288.0,311.1,286.0,311.0] || equal(sk_c3,sk_c3)* equal(sk_c7,sk_c7) -> .
% 0.20/0.50 313[3:Obv:312.1] || -> .
% 0.20/0.50 314[2:Spt:313.0,4.0,42.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.20/0.50 315[2:Spt:313.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 316[2:MRR:28.0,314.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 318[2:MRR:34.0,314.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.20/0.50 319[2:MRR:22.0,314.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 339[2:SpL:319.0,41.1] || equal(inverse(sk_c2),sk_c3) equal(sk_c7,sk_c7) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 341[2:Obv:339.1] || equal(inverse(sk_c2),sk_c3) equal(multiply(sk_c3,sk_c8),sk_c7)** -> .
% 0.20/0.50 342[2:Rew:318.0,341.1,316.0,341.0] || equal(sk_c3,sk_c3)* equal(sk_c7,sk_c7) -> .
% 0.20/0.50 343[2:Obv:342.1] || -> .
% 0.20/0.50 344[1:Spt:343.0,37.1,37.2,37.3,37.4,37.6,37.7,37.9,37.10,37.11] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c6) equal(multiply(u,sk_c6),sk_c7)**+ equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.20/0.50 346[1:SpL:39.0,344.4] || equal(inverse(inverse(sk_c6)),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c6) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.20/0.50 348[2:Spt:4.0] || -> equal(inverse(sk_c8),sk_c6)**.
% 0.20/0.50 349[2:Rew:348.0,344.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(sk_c6,sk_c6) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.20/0.50 351[2:Rew:348.0,346.3] || equal(inverse(inverse(sk_c6)),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c6,sk_c6) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.20/0.50 354[2:Obv:351.3] || equal(inverse(inverse(sk_c6)),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.20/0.50 355[2:Obv:349.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6) -> .
% 0.20/0.50 357[2:SpR:348.0,39.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.20/0.50 360[3:Spt:1.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.50 362[3:Rew:360.0,355.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(sk_c8,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.50 363[3:Rew:360.0,354.6] || equal(inverse(inverse(sk_c6)),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(sk_c8,sk_c8) equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.50 366[3:Obv:363.6] || equal(inverse(inverse(sk_c6)),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.50 367[3:Obv:362.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.50 372[4:Spt:3.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 374[4:Rew:372.0,367.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.20/0.50 375[4:Rew:372.0,366.6] || equal(inverse(inverse(sk_c6)),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** equal(sk_c6,sk_c6) -> .
% 0.20/0.50 378[4:Obv:375.6] || equal(inverse(inverse(sk_c6)),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.50 379[4:Obv:374.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.20/0.50 384[5:Spt:30.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.20/0.50 385[5:SpR:384.0,39.0] || -> equal(multiply(sk_c6,sk_c5),identity)**.
% 0.20/0.50 389[2:SpR:357.0,79.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c8)**.
% 0.20/0.50 391[2:Rew:119.0,389.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.20/0.50 392[4:Rew:391.0,378.0] || equal(inverse(sk_c8),sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.50 394[4:Rew:348.0,392.0] || equal(sk_c6,sk_c6) equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.50 395[4:Obv:394.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(identity,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.50 400[6:Spt:29.1] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.20/0.50 409[2:SpR:391.0,39.0] || -> equal(multiply(sk_c8,sk_c6),identity)**.
% 0.20/0.50 413[5:SpR:385.0,79.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c5)**.
% 0.20/0.50 415[5:Rew:391.0,413.0] || -> equal(multiply(sk_c8,identity),sk_c5)**.
% 0.20/0.50 416[5:Rew:119.0,415.0] || -> equal(sk_c5,sk_c8)**.
% 0.20/0.50 418[6:Rew:416.0,400.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.50 422[6:Rew:409.0,418.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 423[6:Rew:422.0,38.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 425[6:Rew:422.0,357.0] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.20/0.50 428[6:Rew:422.0,119.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.50 429[6:Rew:422.0,395.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(sk_c7,sk_c7) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.50 434[6:Rew:423.0,372.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 438[6:Rew:434.0,348.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.50 448[6:Rew:434.0,425.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 457[6:Obv:429.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.50 458[6:Rew:428.0,457.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8)** equal(multiply(u,sk_c8),sk_c7)**+ equal(v,sk_c8) -> .
% 0.20/0.50 550[0:SpR:94.0,79.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.20/0.50 864[6:SpL:448.0,458.2] || equal(inverse(sk_c8),sk_c8)** equal(inverse(u),sk_c8)** equal(sk_c7,sk_c7) equal(u,sk_c8) -> .
% 0.20/0.50 867[6:Obv:864.2] || equal(inverse(sk_c8),sk_c8)** equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 868[6:Rew:438.0,867.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 869[6:Obv:868.0] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 942[6:SpL:438.0,869.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 951[6:Obv:942.1] || -> .
% 0.20/0.50 953[6:Spt:951.0,29.1,400.0] || equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.20/0.50 954[6:Spt:951.0,29.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 955[6:Rew:416.0,953.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.20/0.50 956[6:Rew:409.0,955.0] || equal(identity,sk_c7)** -> .
% 0.20/0.50 957[5:Rew:416.0,11.1] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.20/0.50 958[5:Rew:409.0,957.1] || -> equal(inverse(sk_c1),sk_c8)** equal(identity,sk_c7).
% 0.20/0.50 959[6:MRR:958.1,956.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.50 966[5:Rew:416.0,23.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 967[5:Rew:409.0,966.0] || -> equal(identity,sk_c7) equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 968[6:MRR:967.0,956.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 969[5:Rew:416.0,17.0] || -> equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 970[5:Rew:409.0,969.0] || -> equal(identity,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 971[6:MRR:970.0,956.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 979[6:SpR:954.0,550.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.50 1023[6:SpR:968.0,40.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1027[6:Rew:979.0,1023.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 1028[6:Rew:1027.0,360.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 1035[6:Rew:1028.0,357.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.20/0.50 1052[6:SpR:971.0,79.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.50 1054[6:Rew:959.0,1052.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 1055[6:Rew:1035.0,1054.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 1056[6:MRR:1055.0,956.0] || -> .
% 0.20/0.50 1061[5:Spt:1056.0,30.0,384.0] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.20/0.50 1062[5:Spt:1056.0,30.1] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 1063[5:MRR:12.0,1061.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.50 1065[5:MRR:24.0,1061.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 1066[5:MRR:18.0,1061.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 1068[5:SpR:1062.0,550.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.50 1098[5:SpR:1065.0,40.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1102[5:Rew:1068.0,1098.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 1103[5:Rew:1102.0,360.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 1108[5:Rew:1103.0,348.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.50 1111[5:Rew:1103.0,409.0] || -> equal(multiply(sk_c8,sk_c8),identity)**.
% 0.20/0.50 1118[5:Rew:1103.0,379.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c6),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.20/0.50 1123[5:Rew:1103.0,1118.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c8),sk_c7)** equal(multiply(w,sk_c7),sk_c8)** -> .
% 0.20/0.50 1124[5:Con:1123.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(u,sk_c8),sk_c7)** equal(multiply(v,sk_c7),sk_c8)** -> .
% 0.20/0.50 1130[5:SpR:1066.0,79.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.50 1132[5:Rew:1063.0,1130.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 1133[5:Rew:1111.0,1132.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 1135[5:Rew:1133.0,119.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.50 1138[5:Rew:1133.0,1111.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 1140[5:Rew:1135.0,1124.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8)** equal(multiply(u,sk_c8),sk_c7)**+ equal(v,sk_c8) -> .
% 0.20/0.50 1208[5:SpL:1138.0,1140.2] || equal(inverse(sk_c8),sk_c8)** equal(inverse(u),sk_c8)** equal(sk_c7,sk_c7) equal(u,sk_c8) -> .
% 0.20/0.50 1210[5:Obv:1208.2] || equal(inverse(sk_c8),sk_c8)** equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 1211[5:Rew:1108.0,1210.0] || equal(sk_c8,sk_c8) equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 1212[5:Obv:1211.0] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.50 1299[5:SpL:1108.0,1212.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 1302[5:Obv:1299.1] || -> .
% 0.20/0.50 1304[4:Spt:1302.0,3.1,372.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.20/0.50 1305[4:Spt:1302.0,3.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.50 1307[4:MRR:2.1,1304.0] || -> equal(multiply(sk_c4,sk_c8),sk_c7)**.
% 0.20/0.50 1331[4:SpR:1305.0,550.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),u)**.
% 0.20/0.50 1342[4:SpR:1307.0,40.0] || -> equal(multiply(sk_c4,multiply(sk_c8,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1346[4:Rew:1331.0,1342.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 1348[4:Rew:1346.0,1304.0] || equal(sk_c6,sk_c8)** -> .
% 0.20/0.50 1349[4:Rew:1346.0,360.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 1361[4:Rew:1349.0,1348.0] || equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 1362[4:Obv:1361.0] || -> .
% 0.20/0.50 1364[3:Spt:1362.0,1.0,360.0] || equal(multiply(sk_c7,sk_c6),sk_c8)** -> .
% 0.20/0.50 1365[3:Spt:1362.0,1.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 1366[3:MRR:25.1,1364.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 1369[3:MRR:19.0,1364.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 1381[3:SpR:1366.0,550.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.50 1399[3:SpR:1369.0,40.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1403[3:Rew:1381.0,1399.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 1404[3:Rew:1403.0,1365.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 1406[3:Rew:1403.0,1364.0] || equal(sk_c6,sk_c8)** -> .
% 0.20/0.50 1415[3:Rew:1404.0,1406.0] || equal(sk_c8,sk_c8)* -> .
% 0.20/0.50 1416[3:Obv:1415.0] || -> .
% 0.20/0.50 1418[2:Spt:1416.0,4.0,348.0] || equal(inverse(sk_c8),sk_c6)** -> .
% 0.20/0.50 1419[2:Spt:1416.0,4.1] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.20/0.50 1420[2:MRR:28.0,1418.0] || -> equal(inverse(sk_c2),sk_c3)**.
% 0.20/0.50 1421[2:MRR:10.0,1418.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.20/0.50 1423[2:MRR:22.0,1418.0] || -> equal(multiply(sk_c2,sk_c3),sk_c7)**.
% 0.20/0.50 1424[2:MRR:16.0,1418.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.20/0.50 1429[2:SpR:1420.0,550.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),u)**.
% 0.20/0.50 1437[2:SpR:1423.0,40.0] || -> equal(multiply(sk_c2,multiply(sk_c3,u)),multiply(sk_c7,u))**.
% 0.20/0.50 1438[2:SpR:1423.0,79.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c3)**.
% 0.20/0.50 1440[2:Rew:1420.0,1438.0] || -> equal(multiply(sk_c3,sk_c7),sk_c3)**.
% 0.20/0.50 1441[2:Rew:1429.0,1437.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.50 1442[2:Rew:1441.0,1419.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.50 1445[2:Rew:1442.0,1418.0] || equal(inverse(sk_c8),sk_c8)** -> .
% 0.20/0.50 1450[2:SpR:1424.0,79.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.20/0.50 1452[2:Rew:1421.0,1450.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.20/0.50 1458[2:SpR:1440.0,79.0] || -> equal(multiply(inverse(sk_c3),sk_c3),sk_c7)**.
% 0.20/0.50 1460[2:Rew:39.0,1458.0] || -> equal(identity,sk_c7)**.
% 0.20/0.50 1461[2:Rew:1460.0,119.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.50 1482[2:SpR:1452.0,79.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c8)**.
% 0.20/0.50 1484[2:Rew:1461.0,1482.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.50 1485[2:MRR:1484.0,1445.0] || -> .
% 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_10 prove_this_11 prove_this_12 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 prove_this_32 prove_this_33 prove_this_34 prove_this_36 prove_this_37 left_identity left_inverse associativity
% 0.20/0.50
%------------------------------------------------------------------------------