TSTP Solution File: GRP265-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP265-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:46:35 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP265-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 08:09:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 652 clauses, backtracked 193 clauses, performed 9 splits and kept 412 clauses.
% 0.20/0.48 SPASS allocated 63584 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.48 0:00:00.03 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.01 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.06 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 5, length 204 :
% 0.20/0.48 % SZS output start Refutation
% 0.20/0.48 1[0:Inp] || -> equal(multiply(sk_c3,sk_c9),sk_c8)** equal(multiply(sk_c1,sk_c9),sk_c8).
% 0.20/0.48 2[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.48 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.48 5[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8)** equal(multiply(sk_c1,sk_c9),sk_c8).
% 0.20/0.48 6[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6)** equal(multiply(sk_c1,sk_c9),sk_c8).
% 0.20/0.48 7[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.48 8[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.20/0.48 9[0:Inp] || -> equal(inverse(sk_c3),sk_c9)** equal(inverse(sk_c1),sk_c9).
% 0.20/0.48 10[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 11[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c1),sk_c9).
% 0.20/0.48 12[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.48 13[0:Inp] || -> equal(inverse(sk_c1),sk_c9) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.20/0.48 14[0:Inp] || -> equal(inverse(sk_c5),sk_c7)** equal(inverse(sk_c1),sk_c9).
% 0.20/0.48 19[0:Inp] || -> equal(multiply(sk_c7,sk_c6),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.20/0.48 20[0:Inp] || -> equal(multiply(sk_c5,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.20/0.48 21[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.20/0.48 22[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.20/0.48 23[0:Inp] || -> equal(inverse(sk_c3),sk_c9) equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.48 24[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 25[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.48 26[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.48 27[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.20/0.48 28[0:Inp] || -> equal(inverse(sk_c5),sk_c7) equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.48 29[0:Inp] || equal(multiply(u,sk_c9),sk_c8)** equal(inverse(u),sk_c9) equal(multiply(v,sk_c8),sk_c7)** equal(inverse(v),sk_c8) equal(multiply(w,sk_c9),sk_c8)** equal(inverse(w),sk_c9) equal(multiply(x,sk_c7),sk_c8)** equal(inverse(x),sk_c7) equal(multiply(sk_c7,y),sk_c8)** equal(multiply(z,sk_c7),y)* equal(inverse(z),sk_c7) -> .
% 0.20/0.48 30[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.20/0.48 31[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.20/0.48 32[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.20/0.48 33[0:Con:29.4] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(inverse(x),sk_c9) equal(multiply(u,sk_c7),y)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(x,sk_c9),sk_c8)** equal(multiply(sk_c7,y),sk_c8)** -> .
% 0.20/0.48 34[1:Spt:33.3,33.7] || equal(inverse(u),sk_c9) equal(multiply(u,sk_c9),sk_c8)** -> .
% 0.20/0.48 37[2:Spt:14.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.48 43[3:Spt:7.1] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.48 45[3:SpL:43.0,34.1] || equal(inverse(sk_c1),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.20/0.48 46[3:Obv:45.1] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.20/0.48 47[3:Rew:37.0,46.0] || equal(sk_c9,sk_c9)* -> .
% 0.20/0.48 48[3:Obv:47.0] || -> .
% 0.20/0.48 49[3:Spt:48.0,7.1,43.0] || equal(multiply(sk_c1,sk_c9),sk_c8)** -> .
% 0.20/0.48 50[3:Spt:48.0,7.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 52[3:MRR:2.1,49.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.20/0.48 56[3:MRR:1.1,49.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.20/0.48 64[3:SpL:56.0,34.1] || equal(inverse(sk_c3),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.20/0.48 65[3:Obv:64.1] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.20/0.48 66[3:Rew:52.0,65.0] || equal(sk_c9,sk_c9)* -> .
% 0.20/0.48 67[3:Obv:66.0] || -> .
% 0.20/0.48 68[2:Spt:67.0,14.1,37.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.20/0.48 69[2:Spt:67.0,14.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 71[2:MRR:9.1,68.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.20/0.48 75[2:MRR:8.0,68.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.20/0.48 83[2:SpL:75.0,34.1] || equal(inverse(sk_c3),sk_c9)** equal(sk_c8,sk_c8) -> .
% 0.20/0.48 84[2:Obv:83.1] || equal(inverse(sk_c3),sk_c9)** -> .
% 0.20/0.48 85[2:Rew:71.0,84.0] || equal(sk_c9,sk_c9)* -> .
% 0.20/0.48 86[2:Obv:85.0] || -> .
% 0.20/0.48 87[1:Spt:86.0,33.0,33.1,33.2,33.4,33.5,33.6,33.8] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c7),x)* equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,x),sk_c8)** -> .
% 0.20/0.48 88[1:EqR:87.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c8)** -> .
% 0.20/0.48 90[2:Spt:11.1] || -> equal(inverse(sk_c1),sk_c9)**.
% 0.20/0.48 92[3:Spt:25.1] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.20/0.48 94[4:Spt:4.1] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.48 96[5:Spt:21.1] || -> equal(multiply(sk_c2,sk_c8),sk_c7)**.
% 0.20/0.48 99[2:SpR:90.0,31.0] || -> equal(multiply(sk_c9,sk_c1),identity)**.
% 0.20/0.48 100[3:SpR:92.0,31.0] || -> equal(multiply(sk_c8,sk_c2),identity)**.
% 0.20/0.48 107[0:SpR:31.0,32.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.20/0.48 110[2:SpR:99.0,32.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.20/0.48 113[2:Rew:30.0,110.0] || -> equal(multiply(sk_c9,multiply(sk_c1,u)),u)**.
% 0.20/0.48 115[0:Rew:30.0,107.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.20/0.48 119[4:SpR:94.0,113.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.48 122[0:SpR:115.0,115.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.20/0.48 125[0:SpR:31.0,115.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.20/0.48 129[2:SpR:113.0,115.0] || -> equal(multiply(inverse(sk_c9),u),multiply(sk_c1,u))**.
% 0.20/0.48 130[3:SpR:100.0,115.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c2)**.
% 0.20/0.48 137[0:Rew:122.0,125.0] || -> equal(multiply(u,identity),u)**.
% 0.20/0.48 138[3:Rew:137.0,130.0] || -> equal(inverse(sk_c8),sk_c2)**.
% 0.20/0.48 140[3:SpR:138.0,31.0] || -> equal(multiply(sk_c2,sk_c8),identity)**.
% 0.20/0.48 143[5:Rew:96.0,140.0] || -> equal(identity,sk_c7)**.
% 0.20/0.48 144[5:Rew:143.0,30.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.20/0.48 145[5:Rew:143.0,31.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.20/0.48 147[5:Rew:143.0,100.0] || -> equal(multiply(sk_c8,sk_c2),sk_c7)**.
% 0.20/0.48 151[5:Rew:143.0,137.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.20/0.48 155[5:Rew:144.0,88.5] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.20/0.48 156[5:Con:155.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.20/0.48 157[5:Rew:151.0,156.2] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.20/0.48 165[4:SpR:119.0,115.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.20/0.48 166[5:Rew:145.0,165.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 169[5:Rew:166.0,144.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 171[5:Rew:166.0,147.0] || -> equal(multiply(sk_c8,sk_c2),sk_c8)**.
% 0.20/0.48 172[5:Rew:166.0,151.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 175[5:Rew:166.0,157.0] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8) equal(u,sk_c8) equal(multiply(v,sk_c8),sk_c7)** -> .
% 0.20/0.48 179[5:Rew:169.0,171.0] || -> equal(sk_c2,sk_c8)**.
% 0.20/0.48 180[5:Rew:179.0,92.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 187[5:Rew:172.0,175.3,166.0,175.3] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.20/0.48 188[5:Con:187.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 279[5:SpL:180.0,188.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.48 282[5:Obv:279.1] || -> .
% 0.20/0.48 283[5:Spt:282.0,21.1,96.0] || equal(multiply(sk_c2,sk_c8),sk_c7)** -> .
% 0.20/0.48 284[5:Spt:282.0,21.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 285[4:Rew:31.0,165.0] || -> equal(identity,sk_c8)**.
% 0.20/0.48 287[4:Rew:285.0,100.0] || -> equal(multiply(sk_c8,sk_c2),sk_c8)**.
% 0.20/0.48 289[4:Rew:285.0,30.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 290[4:Rew:285.0,137.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 293[4:Rew:289.0,287.0] || -> equal(sk_c2,sk_c8)**.
% 0.20/0.48 297[5:Rew:289.0,283.0,293.0,283.0] || equal(sk_c7,sk_c8)** -> .
% 0.20/0.48 307[4:Rew:293.0,20.1,290.0,20.1] || -> equal(multiply(sk_c5,sk_c7),sk_c6)** equal(sk_c7,sk_c8).
% 0.20/0.48 308[5:MRR:307.1,297.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.20/0.48 309[4:Rew:293.0,19.1,290.0,19.1] || -> equal(multiply(sk_c7,sk_c6),sk_c8)** equal(sk_c7,sk_c8).
% 0.20/0.48 310[5:MRR:309.1,297.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.48 337[5:SpR:308.0,115.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.20/0.48 339[5:Rew:284.0,337.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 340[5:Rew:310.0,339.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 341[5:MRR:340.0,297.0] || -> .
% 0.20/0.48 342[4:Spt:341.0,4.1,94.0] || equal(multiply(sk_c1,sk_c9),sk_c8)** -> .
% 0.20/0.48 343[4:Spt:341.0,4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.48 346[4:MRR:2.1,342.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.20/0.48 347[4:MRR:7.1,342.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 352[4:MRR:6.1,342.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.20/0.48 353[4:MRR:5.1,342.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.48 355[4:MRR:1.1,342.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.20/0.48 367[4:SpR:352.0,115.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.20/0.48 369[4:Rew:347.0,367.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 370[4:Rew:353.0,369.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 374[4:Rew:370.0,353.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 407[4:SpR:355.0,115.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c9)**.
% 0.20/0.48 409[4:Rew:346.0,407.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.48 425[4:SpR:374.0,115.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.20/0.48 427[4:Rew:140.0,425.0,138.0,425.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 431[4:Rew:427.0,137.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 435[4:Rew:427.0,31.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 445[4:SpR:409.0,115.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.20/0.48 447[4:Rew:435.0,445.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 453[4:Rew:447.0,431.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 457[4:Rew:447.0,435.0] || -> equal(multiply(inverse(u),u),sk_c8)**.
% 0.20/0.48 523[4:SpR:346.0,457.0] || -> equal(multiply(sk_c9,sk_c3),sk_c8)**.
% 0.20/0.48 530[4:SpR:523.0,115.0] || -> equal(multiply(inverse(sk_c9),sk_c8),sk_c3)**.
% 0.20/0.48 531[4:Rew:453.0,530.0] || -> equal(inverse(sk_c9),sk_c3)**.
% 0.20/0.48 532[4:Rew:531.0,129.0] || -> equal(multiply(sk_c3,u),multiply(sk_c1,u))**.
% 0.20/0.48 533[4:Rew:532.0,355.0] || -> equal(multiply(sk_c1,sk_c9),sk_c8)**.
% 0.20/0.48 536[4:MRR:533.0,342.0] || -> .
% 0.20/0.48 539[3:Spt:536.0,25.1,92.0] || equal(inverse(sk_c2),sk_c8)** -> .
% 0.20/0.48 540[3:Spt:536.0,25.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.48 541[3:MRR:23.1,539.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.20/0.48 542[3:MRR:28.1,539.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 543[3:MRR:27.0,539.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.20/0.48 544[3:MRR:26.0,539.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.48 545[3:MRR:24.0,539.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 546[3:MRR:22.0,539.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.20/0.48 559[3:SpR:543.0,115.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.20/0.48 561[3:Rew:542.0,559.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 562[3:Rew:544.0,561.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 563[3:Rew:562.0,540.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 566[3:Rew:562.0,544.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 567[3:Rew:562.0,545.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.20/0.48 571[3:Rew:562.0,88.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c8)** -> .
% 0.20/0.48 576[3:Rew:562.0,571.5,562.0,571.4,562.0,571.3,562.0,571.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.48 577[3:Con:576.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.48 592[3:SpR:546.0,115.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c9)**.
% 0.20/0.48 594[3:Rew:541.0,592.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.48 600[3:SpR:566.0,115.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.20/0.48 602[3:Rew:31.0,600.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 604[3:Rew:602.0,30.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 605[3:Rew:602.0,137.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 606[3:Rew:602.0,31.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 618[3:SpR:594.0,115.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.20/0.48 620[3:Rew:606.0,618.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 624[3:Rew:620.0,604.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 625[3:Rew:620.0,605.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 637[3:Rew:624.0,577.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.48 638[3:Rew:625.0,567.0] || -> equal(sk_c4,sk_c8)**.
% 0.20/0.48 640[3:Rew:638.0,563.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 648[3:Con:637.0] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.48 649[3:Rew:625.0,648.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 780[3:SpL:640.0,649.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.48 783[3:Obv:780.1] || -> .
% 0.20/0.48 784[2:Spt:783.0,11.1,90.0] || equal(inverse(sk_c1),sk_c9)** -> .
% 0.20/0.48 785[2:Spt:783.0,11.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.20/0.48 786[2:MRR:9.1,784.0] || -> equal(inverse(sk_c3),sk_c9)**.
% 0.20/0.48 787[2:MRR:14.1,784.0] || -> equal(inverse(sk_c5),sk_c7)**.
% 0.20/0.48 788[2:MRR:13.0,784.0] || -> equal(multiply(sk_c5,sk_c7),sk_c6)**.
% 0.20/0.48 789[2:MRR:12.0,784.0] || -> equal(multiply(sk_c7,sk_c6),sk_c8)**.
% 0.20/0.48 790[2:MRR:10.0,784.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.20/0.48 791[2:MRR:8.0,784.0] || -> equal(multiply(sk_c3,sk_c9),sk_c8)**.
% 0.20/0.48 799[2:SpR:788.0,115.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c7)**.
% 0.20/0.48 801[2:Rew:787.0,799.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.20/0.48 802[2:Rew:789.0,801.0] || -> equal(sk_c7,sk_c8)**.
% 0.20/0.48 803[2:Rew:802.0,785.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.20/0.48 806[2:Rew:802.0,789.0] || -> equal(multiply(sk_c8,sk_c6),sk_c8)**.
% 0.20/0.48 807[2:Rew:802.0,790.0] || -> equal(multiply(sk_c4,sk_c8),sk_c8)**.
% 0.20/0.48 811[2:Rew:802.0,88.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(v,sk_c7),sk_c8)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c7,multiply(u,sk_c7)),sk_c8)** -> .
% 0.20/0.48 816[2:Rew:802.0,811.5,802.0,811.4,802.0,811.3,802.0,811.1] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(w),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(w,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.48 817[2:Con:816.2] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(sk_c8,multiply(u,sk_c8)),sk_c8)** -> .
% 0.20/0.48 832[2:SpR:791.0,115.0] || -> equal(multiply(inverse(sk_c3),sk_c8),sk_c9)**.
% 0.20/0.48 834[2:Rew:786.0,832.0] || -> equal(multiply(sk_c9,sk_c8),sk_c9)**.
% 0.20/0.48 840[2:SpR:806.0,115.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c6)**.
% 0.20/0.48 842[2:Rew:31.0,840.0] || -> equal(identity,sk_c6)**.
% 0.20/0.48 843[2:Rew:842.0,137.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.20/0.48 844[2:Rew:842.0,30.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.20/0.48 847[2:Rew:842.0,31.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.20/0.48 860[2:SpR:834.0,115.0] || -> equal(multiply(inverse(sk_c9),sk_c9),sk_c8)**.
% 0.20/0.48 862[2:Rew:847.0,860.0] || -> equal(sk_c6,sk_c8)**.
% 0.20/0.48 865[2:Rew:862.0,844.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.20/0.48 866[2:Rew:862.0,843.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.20/0.48 878[2:Rew:865.0,817.3] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(multiply(v,sk_c8),sk_c8)** equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.48 879[2:Rew:866.0,807.0] || -> equal(sk_c4,sk_c8)**.
% 0.20/0.48 881[2:Rew:879.0,803.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.20/0.48 889[2:Con:878.0] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c8)** -> .
% 0.20/0.48 890[2:Rew:866.0,889.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.20/0.48 995[2:SpL:881.0,890.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.20/0.48 998[2:Obv:995.1] || -> .
% 0.20/0.48 % SZS output end Refutation
% 0.20/0.48 Formulae used in the proof : prove_this_1 prove_this_2 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_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 left_identity left_inverse associativity
% 0.20/0.48
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