TSTP Solution File: GRP261-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP261-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:46:34 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP261-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 : Mon Jun 13 19:35:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 485 clauses, backtracked 210 clauses, performed 11 splits and kept 423 clauses.
% 0.18/0.43 SPASS allocated 63450 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.03 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 5, length 229 :
% 0.18/0.43 % SZS output start Refutation
% 0.18/0.43 1[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7)** equal(multiply(sk_c1,sk_c8),sk_c7).
% 0.18/0.43 2[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 4[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 5[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 7[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.18/0.43 8[0:Inp] || -> equal(inverse(sk_c3),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.18/0.43 9[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.43 10[0:Inp] || -> equal(inverse(sk_c4),sk_c7)** equal(inverse(sk_c1),sk_c8).
% 0.18/0.43 11[0:Inp] || -> equal(inverse(sk_c5),sk_c6)** equal(inverse(sk_c1),sk_c8).
% 0.18/0.43 12[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.18/0.43 15[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.18/0.43 16[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.18/0.43 17[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.18/0.43 18[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.18/0.43 21[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.43 22[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.43 23[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.43 24[0:Inp] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.18/0.43 25[0:Inp] || -> equal(multiply(sk_c3,sk_c8),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 26[0:Inp] || -> equal(inverse(sk_c3),sk_c8) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 27[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 28[0:Inp] || -> equal(inverse(sk_c4),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 29[0:Inp] || -> equal(inverse(sk_c5),sk_c6) equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 30[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7).
% 0.18/0.43 31[0:Inp] || equal(multiply(u,sk_c8),sk_c7)** equal(inverse(u),sk_c8) equal(multiply(v,sk_c7),sk_c6)** equal(inverse(v),sk_c7) equal(multiply(sk_c6,sk_c8),sk_c7)** equal(multiply(w,sk_c8),sk_c7)** equal(inverse(w),sk_c8) equal(multiply(x,sk_c7),sk_c6)** equal(inverse(x),sk_c7) equal(inverse(y),sk_c6) equal(multiply(y,sk_c8),sk_c6)** -> .
% 0.18/0.43 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.18/0.43 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.18/0.43 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.18/0.43 35[0:Con:31.5] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c8) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(w,sk_c8),sk_c7)** equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.43 36[1:Spt:35.2,35.5] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c8),sk_c7)** -> .
% 0.18/0.43 43[2:Spt:11.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.43 47[3:Spt:5.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 49[3:SpL:47.0,36.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 50[3:Obv:49.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.18/0.43 51[3:Rew:43.0,50.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.43 52[3:Obv:51.0] || -> .
% 0.18/0.43 53[3:Spt:52.0,5.1,47.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.18/0.43 54[3:Spt:52.0,5.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.43 56[3:MRR:2.1,53.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.18/0.43 59[3:MRR:1.1,53.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.18/0.43 68[3:SpL:59.0,36.1] || equal(inverse(sk_c3),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 69[3:Obv:68.1] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.18/0.43 70[3:Rew:56.0,69.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.43 71[3:Obv:70.0] || -> .
% 0.18/0.43 72[2:Spt:71.0,11.1,43.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.18/0.43 73[2:Spt:71.0,11.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.43 75[2:MRR:8.1,72.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.18/0.43 78[2:MRR:7.0,72.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.18/0.43 87[2:SpL:78.0,36.1] || equal(inverse(sk_c3),sk_c8)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 88[2:Obv:87.1] || equal(inverse(sk_c3),sk_c8)** -> .
% 0.18/0.43 89[2:Rew:75.0,88.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.43 90[2:Obv:89.0] || -> .
% 0.18/0.43 91[1:Spt:90.0,35.0,35.1,35.3,35.4,35.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c8),sk_c6)**+ equal(multiply(v,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.43 92[2:Spt:28.1] || -> equal(multiply(sk_c6,sk_c8),sk_c7)**.
% 0.18/0.43 93[2:Rew:92.0,91.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.18/0.43 94[2:Obv:93.4] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.18/0.43 96[3:Spt:10.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.18/0.43 98[4:Spt:22.1] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.18/0.43 100[5:Spt:4.1] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 103[6:Spt:17.1] || -> equal(multiply(sk_c2,sk_c7),sk_c6)**.
% 0.18/0.43 106[3:SpR:96.0,33.0] || -> equal(multiply(sk_c8,sk_c1),identity)**.
% 0.18/0.43 107[4:SpR:98.0,33.0] || -> equal(multiply(sk_c7,sk_c2),identity)**.
% 0.18/0.43 113[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.18/0.43 115[0:Rew:32.0,113.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.18/0.43 117[3:SpR:106.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),multiply(identity,u))**.
% 0.18/0.43 119[3:Rew:32.0,117.0] || -> equal(multiply(sk_c8,multiply(sk_c1,u)),u)**.
% 0.18/0.43 125[5:SpR:100.0,119.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.18/0.43 130[0:SpR:115.0,115.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.18/0.43 132[2:SpR:92.0,115.0] || -> equal(multiply(inverse(sk_c6),sk_c7),sk_c8)**.
% 0.18/0.43 135[0:SpR:33.0,115.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.18/0.43 136[6:SpR:103.0,115.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c7)**.
% 0.18/0.43 138[3:SpR:106.0,115.0] || -> equal(multiply(inverse(sk_c8),identity),sk_c1)**.
% 0.18/0.43 140[5:SpR:125.0,115.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.18/0.43 145[6:Rew:98.0,136.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.43 146[5:Rew:33.0,140.0] || -> equal(sk_c7,identity)**.
% 0.18/0.43 147[5:Rew:146.0,92.0] || -> equal(multiply(sk_c6,sk_c8),identity)**.
% 0.18/0.43 151[5:Rew:146.0,107.0] || -> equal(multiply(identity,sk_c2),identity)**.
% 0.18/0.43 153[5:Rew:146.0,94.1] || equal(inverse(u),sk_c6) equal(inverse(v),identity) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.18/0.43 159[5:Rew:146.0,132.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c8)**.
% 0.18/0.43 160[6:Rew:146.0,145.0] || -> equal(multiply(identity,sk_c6),identity)**.
% 0.18/0.43 161[5:Rew:32.0,151.0] || -> equal(identity,sk_c2)**.
% 0.18/0.43 162[5:Rew:161.0,32.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.18/0.43 164[5:Rew:161.0,106.0] || -> equal(multiply(sk_c8,sk_c1),sk_c2)**.
% 0.18/0.43 167[5:Rew:161.0,146.0] || -> equal(sk_c7,sk_c2)**.
% 0.18/0.43 169[5:Rew:161.0,147.0] || -> equal(multiply(sk_c6,sk_c8),sk_c2)**.
% 0.18/0.43 173[6:Rew:161.0,160.0] || -> equal(multiply(sk_c2,sk_c6),sk_c2)**.
% 0.18/0.43 174[6:Rew:162.0,173.0] || -> equal(sk_c2,sk_c6)**.
% 0.18/0.43 175[6:Rew:174.0,161.0] || -> equal(identity,sk_c6)**.
% 0.18/0.43 176[6:Rew:174.0,167.0] || -> equal(sk_c7,sk_c6)**.
% 0.18/0.43 179[6:Rew:174.0,162.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.43 180[6:Rew:174.0,164.0] || -> equal(multiply(sk_c8,sk_c1),sk_c6)**.
% 0.18/0.43 181[6:Rew:174.0,169.0] || -> equal(multiply(sk_c6,sk_c8),sk_c6)**.
% 0.18/0.43 184[6:Rew:179.0,181.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.43 186[6:Rew:184.0,175.0] || -> equal(identity,sk_c8)**.
% 0.18/0.43 187[6:Rew:184.0,176.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.43 189[6:Rew:184.0,180.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.18/0.43 192[6:Rew:184.0,179.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.43 194[6:Rew:192.0,189.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.43 195[6:Rew:194.0,96.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.43 196[6:Rew:194.0,184.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.43 198[6:Rew:194.0,186.0] || -> equal(identity,sk_c1)**.
% 0.18/0.43 199[6:Rew:194.0,187.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.43 208[6:Rew:198.0,135.0] || -> equal(multiply(inverse(inverse(u)),sk_c1),u)**.
% 0.18/0.43 213[6:Rew:130.0,208.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.43 219[6:Rew:213.0,153.3,199.0,153.3,196.0,153.3,213.0,153.2,194.0,153.2,196.0,153.2,198.0,153.1,196.0,153.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) -> .
% 0.18/0.43 220[6:Con:219.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.18/0.43 248[6:SpL:195.0,220.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.43 249[6:Obv:248.1] || -> .
% 0.18/0.43 250[6:Spt:249.0,17.1,103.0] || equal(multiply(sk_c2,sk_c7),sk_c6)** -> .
% 0.18/0.43 251[6:Spt:249.0,17.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.43 253[5:Rew:161.0,159.0] || -> equal(multiply(inverse(sk_c6),sk_c2),sk_c8)**.
% 0.18/0.43 255[6:Rew:162.0,250.0,167.0,250.0] || equal(sk_c2,sk_c6)** -> .
% 0.18/0.43 256[5:Rew:161.0,135.0] || -> equal(multiply(inverse(inverse(u)),sk_c2),u)**.
% 0.18/0.43 260[5:Rew:167.0,16.1,162.0,16.1,167.0,16.0] || -> equal(inverse(sk_c4),sk_c2)** equal(sk_c2,sk_c6).
% 0.18/0.43 261[6:MRR:260.1,255.0] || -> equal(inverse(sk_c4),sk_c2)**.
% 0.18/0.43 267[5:Rew:130.0,256.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.18/0.43 268[5:Rew:267.0,253.0] || -> equal(inverse(sk_c6),sk_c8)**.
% 0.18/0.43 269[5:Rew:167.0,18.1,162.0,18.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(sk_c2,sk_c6).
% 0.18/0.43 270[6:MRR:269.1,255.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.18/0.43 271[5:Rew:167.0,15.1,162.0,15.1,267.0,15.0,167.0,15.0] || -> equal(sk_c6,sk_c4) equal(sk_c2,sk_c6)**.
% 0.18/0.43 272[6:MRR:271.1,255.0] || -> equal(sk_c6,sk_c4)**.
% 0.18/0.43 273[6:Rew:272.0,251.0] || -> equal(inverse(sk_c5),sk_c4)**.
% 0.18/0.43 275[6:Rew:272.0,255.0] || equal(sk_c2,sk_c4)** -> .
% 0.18/0.43 277[6:Rew:272.0,268.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.43 278[6:Rew:272.0,270.0] || -> equal(multiply(sk_c5,sk_c8),sk_c4)**.
% 0.18/0.43 279[6:Rew:261.0,277.0] || -> equal(sk_c2,sk_c8)**.
% 0.18/0.43 283[6:Rew:279.0,162.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.43 284[6:Rew:279.0,164.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.18/0.43 287[6:Rew:279.0,261.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.43 288[6:Rew:279.0,267.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.43 289[6:Rew:279.0,275.0] || equal(sk_c4,sk_c8)** -> .
% 0.18/0.43 294[6:Rew:283.0,284.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.43 301[6:Rew:294.0,287.0] || -> equal(inverse(sk_c4),sk_c1)**.
% 0.18/0.43 302[6:Rew:294.0,289.0] || equal(sk_c4,sk_c1)** -> .
% 0.18/0.43 304[6:Rew:294.0,278.0] || -> equal(multiply(sk_c5,sk_c1),sk_c4)**.
% 0.18/0.43 307[6:Rew:294.0,288.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.43 310[6:Rew:307.0,304.0] || -> equal(sk_c5,sk_c4)**.
% 0.18/0.43 311[6:Rew:310.0,273.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.18/0.43 312[6:Rew:301.0,311.0] || -> equal(sk_c4,sk_c1)**.
% 0.18/0.43 313[6:MRR:312.0,302.0] || -> .
% 0.18/0.43 321[5:Spt:313.0,4.1,100.0] || equal(multiply(sk_c1,sk_c8),sk_c7)** -> .
% 0.18/0.43 322[5:Spt:313.0,4.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.43 323[0:Rew:130.0,135.0] || -> equal(multiply(u,identity),u)**.
% 0.18/0.43 325[3:Rew:323.0,138.0] || -> equal(inverse(sk_c8),sk_c1)**.
% 0.18/0.43 327[5:MRR:2.1,321.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.18/0.43 331[5:MRR:1.1,321.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.18/0.43 368[5:SpR:331.0,115.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.18/0.43 370[5:Rew:327.0,368.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.18/0.43 382[5:SpR:370.0,115.0] || -> equal(multiply(inverse(sk_c8),sk_c8),sk_c7)**.
% 0.18/0.43 384[5:Rew:325.0,382.0] || -> equal(multiply(sk_c1,sk_c8),sk_c7)**.
% 0.18/0.43 385[5:MRR:384.0,321.0] || -> .
% 0.18/0.43 386[4:Spt:385.0,22.1,98.0] || equal(inverse(sk_c2),sk_c7)** -> .
% 0.18/0.43 387[4:Spt:385.0,22.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.43 389[4:MRR:23.1,386.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.43 390[4:MRR:24.0,386.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.18/0.43 391[4:MRR:21.0,386.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.43 400[4:SpR:390.0,115.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.18/0.43 402[4:Rew:389.0,400.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.18/0.43 404[4:SpR:391.0,115.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.18/0.43 406[4:Rew:387.0,404.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.43 415[4:SpR:406.0,115.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.18/0.43 417[4:Rew:33.0,415.0] || -> equal(identity,sk_c6)**.
% 0.18/0.43 419[4:Rew:417.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.43 422[4:Rew:417.0,323.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.43 423[4:Rew:419.0,402.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.43 424[4:Rew:419.0,92.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.43 432[4:Rew:423.0,391.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.43 435[4:Rew:423.0,94.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.18/0.43 440[4:Rew:424.0,387.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.43 446[4:Rew:423.0,422.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.43 447[4:Rew:446.0,432.0,424.0,432.0] || -> equal(sk_c4,sk_c8)**.
% 0.18/0.43 448[4:Rew:447.0,440.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.43 449[4:Rew:325.0,448.0] || -> equal(sk_c8,sk_c1)**.
% 0.18/0.43 450[4:Rew:449.0,96.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.18/0.43 456[4:Rew:449.0,423.0] || -> equal(sk_c6,sk_c1)**.
% 0.18/0.43 457[4:Rew:449.0,424.0] || -> equal(sk_c7,sk_c1)**.
% 0.18/0.43 460[4:Rew:449.0,446.0] || -> equal(multiply(u,sk_c1),u)**.
% 0.18/0.43 484[4:Rew:460.0,435.3,457.0,435.3,456.0,435.3,460.0,435.2,449.0,435.2,456.0,435.2,457.0,435.1,449.0,435.0] || equal(inverse(u),sk_c1)** equal(inverse(v),sk_c1)** equal(u,sk_c1) equal(v,sk_c1) -> .
% 0.18/0.43 485[4:Con:484.1] || equal(inverse(u),sk_c1)** equal(u,sk_c1) -> .
% 0.18/0.43 530[4:SpL:450.0,485.0] || equal(sk_c1,sk_c1)* equal(sk_c1,sk_c1)* -> .
% 0.18/0.43 532[4:Obv:530.1] || -> .
% 0.18/0.43 533[3:Spt:532.0,10.1,96.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.18/0.43 534[3:Spt:532.0,10.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.43 536[3:MRR:11.1,533.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.43 537[3:MRR:12.0,533.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.18/0.43 538[3:MRR:9.0,533.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.43 550[3:SpR:537.0,115.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.18/0.43 552[3:Rew:536.0,550.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.18/0.43 554[3:SpR:538.0,115.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.18/0.43 556[3:Rew:534.0,554.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.43 565[3:SpR:556.0,115.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.18/0.43 567[3:Rew:33.0,565.0] || -> equal(identity,sk_c6)**.
% 0.18/0.43 568[3:Rew:567.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.43 569[3:Rew:567.0,323.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.43 572[3:Rew:568.0,552.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.43 573[3:Rew:568.0,92.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.43 581[3:Rew:572.0,538.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.18/0.43 584[3:Rew:572.0,94.0] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c7) equal(multiply(u,sk_c8),sk_c6)** equal(multiply(v,sk_c7),sk_c6)** -> .
% 0.18/0.43 588[3:Rew:573.0,534.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.18/0.43 593[3:Rew:572.0,569.0] || -> equal(multiply(u,sk_c8),u)**.
% 0.18/0.43 594[3:Rew:593.0,581.0,573.0,581.0] || -> equal(sk_c4,sk_c8)**.
% 0.18/0.43 595[3:Rew:594.0,588.0] || -> equal(inverse(sk_c8),sk_c8)**.
% 0.18/0.43 610[3:Rew:593.0,584.3,573.0,584.3,572.0,584.3,593.0,584.2,572.0,584.2,573.0,584.1] || equal(inverse(u),sk_c8)** equal(inverse(v),sk_c8)** equal(u,sk_c8) equal(v,sk_c8) -> .
% 0.18/0.43 611[3:Con:610.1] || equal(inverse(u),sk_c8)** equal(u,sk_c8) -> .
% 0.18/0.43 682[3:SpL:595.0,611.0] || equal(sk_c8,sk_c8)* equal(sk_c8,sk_c8)* -> .
% 0.18/0.43 684[3:Obv:682.1] || -> .
% 0.18/0.43 685[2:Spt:684.0,28.1,92.0] || equal(multiply(sk_c6,sk_c8),sk_c7)** -> .
% 0.18/0.43 686[2:Spt:684.0,28.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.18/0.43 687[2:MRR:26.1,685.0] || -> equal(inverse(sk_c3),sk_c8)**.
% 0.18/0.43 688[2:MRR:29.1,685.0] || -> equal(inverse(sk_c5),sk_c6)**.
% 0.18/0.43 689[2:MRR:30.1,685.0] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.18/0.43 690[2:MRR:27.1,685.0] || -> equal(multiply(sk_c4,sk_c7),sk_c6)**.
% 0.18/0.43 691[2:MRR:25.1,685.0] || -> equal(multiply(sk_c3,sk_c8),sk_c7)**.
% 0.18/0.43 699[2:SpR:689.0,115.0] || -> equal(multiply(inverse(sk_c5),sk_c6),sk_c8)**.
% 0.18/0.43 701[2:Rew:688.0,699.0] || -> equal(multiply(sk_c6,sk_c6),sk_c8)**.
% 0.18/0.43 703[2:SpR:690.0,115.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c7)**.
% 0.18/0.43 705[2:Rew:686.0,703.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.18/0.43 707[2:SpR:691.0,115.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c8)**.
% 0.18/0.43 709[2:Rew:687.0,707.0] || -> equal(multiply(sk_c8,sk_c7),sk_c8)**.
% 0.18/0.43 714[2:SpR:705.0,115.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c6)**.
% 0.18/0.43 716[2:Rew:33.0,714.0] || -> equal(identity,sk_c6)**.
% 0.18/0.43 717[2:Rew:716.0,323.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.18/0.43 718[2:Rew:716.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.18/0.44 721[2:Rew:717.0,701.0] || -> equal(sk_c6,sk_c8)**.
% 0.18/0.44 725[2:Rew:721.0,685.0] || equal(multiply(sk_c8,sk_c8),sk_c7)** -> .
% 0.18/0.44 733[2:Rew:721.0,718.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.18/0.44 734[2:Rew:733.0,709.0] || -> equal(sk_c7,sk_c8)**.
% 0.18/0.44 747[2:Rew:733.0,725.0,734.0,725.0] || equal(sk_c8,sk_c8)* -> .
% 0.18/0.44 748[2:Obv:747.0] || -> .
% 0.18/0.44 % SZS output end Refutation
% 0.18/0.44 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_4 prove_this_5 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.18/0.44
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