TSTP Solution File: GRP303-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP303-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:46:45 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP303-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 20:29:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 642 clauses, backtracked 273 clauses, performed 10 splits and kept 533 clauses.
% 0.19/0.46 SPASS allocated 63529 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.03 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.05 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 5, length 292 :
% 0.19/0.46 % SZS output start Refutation
% 0.19/0.46 1[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 2[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.19/0.46 3[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 4[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5).
% 0.19/0.46 5[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.46 6[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 7[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 8[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 9[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 10[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.46 12[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 13[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.46 14[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 15[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 16[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 17[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 18[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 19[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.46 20[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 21[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.46 22[0:Inp] || equal(multiply(sk_c7,sk_c6),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)** equal(multiply(u,sk_c7),sk_c6)** equal(inverse(u),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(w,sk_c6),sk_c7)** equal(inverse(x),sk_c6) equal(multiply(x,sk_c5),sk_c6)** -> .
% 0.19/0.46 23[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.46 24[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.46 25[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.46 26[0:Rew:5.0,22.1] || equal(multiply(sk_c7,sk_c6),sk_c5)** equal(sk_c5,sk_c5) equal(multiply(u,sk_c7),sk_c6)** equal(inverse(u),sk_c7) equal(multiply(v,sk_c6),sk_c7)** equal(inverse(v),sk_c6) equal(inverse(w),sk_c7) equal(multiply(w,sk_c6),sk_c7)** equal(inverse(x),sk_c6) equal(multiply(x,sk_c5),sk_c6)** -> .
% 0.19/0.46 27[0:Obv:26.1] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c6) equal(inverse(x),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c6),sk_c7)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.19/0.46 28[1:Spt:27.2,27.6] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.19/0.46 29[2:Spt:3.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.46 31[3:Spt:1.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 34[4:Spt:4.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.46 36[5:Spt:2.0] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.46 38[5:SpL:36.0,28.1] || equal(inverse(sk_c3),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 39[5:Obv:38.1] || equal(inverse(sk_c3),sk_c6)** -> .
% 0.19/0.46 40[5:Rew:31.0,39.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.46 42[1:SpL:23.0,28.1] || equal(inverse(identity),sk_c6)** equal(sk_c6,sk_c7) -> .
% 0.19/0.46 44[2:SpR:29.0,24.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.46 45[3:SpR:31.0,24.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.46 46[1:SpL:24.0,28.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c7) -> .
% 0.19/0.46 51[4:SpR:34.0,25.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c6,u))**.
% 0.19/0.46 53[0:SpR:24.0,25.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.46 55[0:Rew:23.0,53.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.46 58[2:SpR:44.0,25.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),multiply(identity,u))**.
% 0.19/0.46 59[2:Rew:23.0,58.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.46 65[4:SpR:34.0,59.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.46 69[4:SpL:65.0,28.1] || equal(inverse(sk_c6),sk_c6)** equal(sk_c5,sk_c7) -> .
% 0.19/0.46 71[0:SpR:55.0,55.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.46 74[0:SpR:5.0,55.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.46 76[2:SpR:59.0,55.0] || -> equal(multiply(inverse(sk_c6),u),multiply(sk_c4,u))**.
% 0.19/0.46 77[4:SpR:65.0,55.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.46 80[0:SpR:24.0,55.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.46 82[3:SpR:45.0,55.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.46 86[4:Rew:74.0,77.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 90[2:Rew:76.0,74.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.46 91[4:Rew:34.0,90.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 92[5:MRR:91.0,40.0] || -> .
% 0.19/0.46 93[0:Rew:71.0,80.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.46 94[3:Rew:93.0,82.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.46 96[5:Spt:92.0,2.0,36.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.46 97[5:Spt:92.0,2.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 105[4:Rew:86.0,76.0] || -> equal(multiply(inverse(sk_c7),u),multiply(sk_c4,u))**.
% 0.19/0.46 107[4:Rew:86.0,51.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.46 111[4:Rew:86.0,69.0] || equal(inverse(sk_c7),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.19/0.46 112[5:Rew:86.0,97.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.46 114[5:Rew:86.0,96.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.19/0.46 115[4:Rew:94.0,105.0] || -> equal(multiply(sk_c4,u),multiply(sk_c3,u))**.
% 0.19/0.46 118[4:Rew:86.0,19.1,86.0,19.0] || -> equal(inverse(sk_c2),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.46 119[5:MRR:118.1,114.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.46 120[4:Rew:86.0,11.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.46 121[5:MRR:120.1,114.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 124[4:Rew:115.0,107.0] || -> equal(multiply(sk_c3,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.46 125[4:Rew:94.0,111.0] || equal(sk_c3,sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.19/0.46 126[4:Rew:86.0,15.1,86.0,15.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.46 127[5:MRR:126.0,114.0] || -> equal(multiply(sk_c2,sk_c7),sk_c7)**.
% 0.19/0.46 136[3:SpR:94.0,24.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.19/0.46 137[3:SpR:94.0,55.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),u)**.
% 0.19/0.46 147[5:SpR:121.0,24.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.46 148[5:SpR:121.0,55.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.46 166[5:SpR:127.0,55.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c7)**.
% 0.19/0.46 168[5:Rew:112.0,166.0,119.0,166.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 171[5:Rew:168.0,124.0] || -> equal(multiply(sk_c3,multiply(sk_c7,u)),multiply(sk_c7,u))**.
% 0.19/0.46 173[5:Rew:168.0,125.1] || equal(sk_c3,sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 176[5:Obv:173.1] || equal(sk_c3,sk_c7)** -> .
% 0.19/0.46 177[5:Rew:137.0,171.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 178[5:Rew:177.0,45.0] || -> equal(identity,sk_c3)**.
% 0.19/0.46 179[5:Rew:177.0,147.0] || -> equal(identity,sk_c1)**.
% 0.19/0.46 181[5:Rew:177.0,148.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.46 192[5:Rew:178.0,136.0] || -> equal(multiply(sk_c3,sk_c7),sk_c3)**.
% 0.19/0.46 193[5:Rew:178.0,179.0] || -> equal(sk_c1,sk_c3)**.
% 0.19/0.46 199[5:Rew:193.0,181.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.46 204[5:Rew:199.0,192.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.46 205[5:MRR:204.0,176.0] || -> .
% 0.19/0.46 207[4:Spt:205.0,4.0,34.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.46 208[4:Spt:205.0,4.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 209[4:Rew:90.0,207.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.46 210[2:Rew:90.0,21.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.19/0.46 211[4:MRR:210.1,209.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 212[2:Rew:90.0,13.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.46 213[4:MRR:212.1,209.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 214[2:Rew:90.0,17.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 215[4:MRR:214.0,209.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 216[2:Rew:90.0,9.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 217[4:MRR:216.0,209.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 243[2:SpR:44.0,55.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.46 245[2:Rew:93.0,243.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.46 251[2:SpR:245.0,55.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.19/0.46 254[4:SpR:215.0,55.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.46 256[4:Rew:5.0,254.0,211.0,254.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 257[4:Rew:256.0,208.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.19/0.46 265[4:SpR:217.0,55.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.46 267[4:Rew:213.0,265.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.46 268[4:Rew:257.0,267.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 269[4:MRR:268.0,209.0] || -> .
% 0.19/0.46 270[3:Spt:269.0,1.0,31.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.46 271[3:Spt:269.0,1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 272[3:MRR:18.0,270.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 273[3:MRR:10.0,270.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 274[3:MRR:14.0,270.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 275[3:MRR:6.0,270.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 281[3:SpR:273.0,55.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.46 287[2:SpR:90.0,25.0] || -> equal(multiply(sk_c4,multiply(sk_c5,u)),multiply(sk_c7,u))**.
% 0.19/0.46 292[3:SpR:274.0,55.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.46 294[3:Rew:5.0,292.0,272.0,292.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 300[3:Rew:294.0,287.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.46 302[3:Rew:251.0,300.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 305[3:Rew:302.0,281.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.46 306[3:Rew:305.0,275.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 307[3:Rew:306.0,29.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.46 308[3:Rew:306.0,44.0] || -> equal(multiply(sk_c7,sk_c4),identity)**.
% 0.19/0.46 316[3:Rew:306.0,42.1] || equal(inverse(identity),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 322[3:Rew:302.0,308.0] || -> equal(identity,sk_c4)**.
% 0.19/0.46 334[3:Obv:316.1] || equal(inverse(identity),sk_c6)** -> .
% 0.19/0.46 335[3:Rew:307.0,334.0,322.0,334.0,306.0,334.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 336[3:Obv:335.0] || -> .
% 0.19/0.46 339[2:Spt:336.0,3.0,29.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.46 340[2:Spt:336.0,3.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 341[2:MRR:20.0,339.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 342[2:MRR:12.0,339.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 343[2:MRR:16.0,339.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 344[2:MRR:8.0,339.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 348[2:SpR:341.0,55.0] || -> equal(multiply(sk_c6,multiply(sk_c2,u)),u)**.
% 0.19/0.46 350[2:SpR:342.0,55.0] || -> equal(multiply(sk_c7,multiply(sk_c1,u)),u)**.
% 0.19/0.46 356[2:SpR:343.0,55.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.46 358[2:Rew:5.0,356.0,341.0,356.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 361[2:Rew:358.0,74.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c7)**.
% 0.19/0.46 365[2:Rew:24.0,361.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 366[2:Rew:365.0,93.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 367[2:Rew:365.0,23.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 371[2:Rew:365.0,46.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.46 372[2:Rew:366.0,344.0] || -> equal(sk_c1,sk_c6)**.
% 0.19/0.46 373[2:Rew:372.0,342.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.46 374[2:Rew:372.0,350.0] || -> equal(multiply(sk_c7,multiply(sk_c6,u)),u)**.
% 0.19/0.46 375[2:Rew:367.0,374.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.46 376[2:Rew:375.0,348.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.46 377[2:Rew:376.0,343.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 384[2:Rew:377.0,373.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 391[2:Obv:371.1] || equal(inverse(inverse(sk_c6)),sk_c6)** -> .
% 0.19/0.46 392[2:Rew:384.0,391.0,384.0,391.0,377.0,391.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 393[2:Obv:392.0] || -> .
% 0.19/0.46 396[1:Spt:393.0,27.0,27.1,27.3,27.4,27.5,27.7,27.8] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.19/0.46 398[2:Spt:1.1] || -> equal(multiply(sk_c7,sk_c6),sk_c5)**.
% 0.19/0.46 399[2:Rew:398.0,396.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) -> .
% 0.19/0.46 401[2:Obv:399.6] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.46 406[3:Spt:20.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.46 409[4:Spt:18.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 434[0:SpR:24.0,55.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.46 435[0:SpR:24.0,93.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.46 437[3:SpR:406.0,24.0] || -> equal(multiply(sk_c6,sk_c4),identity)**.
% 0.19/0.46 438[4:SpR:409.0,24.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.46 440[0:Rew:93.0,434.0] || -> equal(inverse(inverse(u)),u)**.
% 0.19/0.46 448[3:SpR:437.0,55.0] || -> equal(multiply(inverse(sk_c6),identity),sk_c4)**.
% 0.19/0.46 450[3:Rew:93.0,448.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.46 451[3:Rew:450.0,74.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.46 453[3:Rew:451.0,9.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 454[3:Rew:451.0,17.0] || -> equal(sk_c6,sk_c7) equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 455[3:Rew:451.0,13.1] || -> equal(inverse(sk_c1),sk_c7)** equal(sk_c6,sk_c7).
% 0.19/0.46 456[3:Rew:451.0,21.1] || -> equal(inverse(sk_c2),sk_c6)** equal(sk_c6,sk_c7).
% 0.19/0.46 457[3:Rew:455.1,11.1] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.46 459[3:Rew:453.0,7.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 463[3:SpR:450.0,24.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.19/0.46 466[4:SpR:438.0,55.0] || -> equal(multiply(inverse(sk_c7),identity),sk_c3)**.
% 0.19/0.46 468[4:Rew:93.0,466.0] || -> equal(inverse(sk_c7),sk_c3)**.
% 0.19/0.46 472[5:Spt:455.1] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 473[5:Rew:472.0,398.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.46 477[5:Rew:472.0,450.0] || -> equal(inverse(sk_c7),sk_c4)**.
% 0.19/0.46 479[5:Rew:472.0,401.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.46 486[5:Rew:472.0,459.1] || -> equal(multiply(sk_c3,sk_c7),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.46 488[5:Rew:472.0,463.0] || -> equal(multiply(sk_c4,sk_c7),identity)**.
% 0.19/0.46 490[5:Rew:468.0,477.0] || -> equal(sk_c4,sk_c3)**.
% 0.19/0.46 495[5:Rew:490.0,488.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.19/0.46 496[5:Rew:495.0,457.1] || -> equal(inverse(sk_c1),sk_c7)** equal(identity,sk_c7).
% 0.19/0.46 500[5:Rew:495.0,486.0] || -> equal(identity,sk_c7) equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.46 502[5:Rew:472.0,479.5,472.0,479.4,472.0,479.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.46 503[5:Con:502.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.46 509[4:SpR:468.0,24.0] || -> equal(multiply(sk_c3,sk_c7),identity)**.
% 0.19/0.46 520[6:Spt:496.1] || -> equal(identity,sk_c7)**.
% 0.19/0.46 521[6:Rew:520.0,23.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 522[6:Rew:520.0,93.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 524[6:Rew:520.0,435.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 527[6:Rew:468.0,524.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.46 528[6:Rew:527.0,409.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 535[6:Rew:521.0,473.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 537[6:Rew:535.0,503.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.46 546[6:Con:537.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.46 547[6:Rew:522.0,546.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.46 561[0:SpR:440.0,55.0] || -> equal(multiply(u,multiply(inverse(u),v)),v)**.
% 0.19/0.46 588[6:SpL:528.0,547.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 590[6:Obv:588.1] || -> .
% 0.19/0.46 591[6:Spt:590.0,496.1,520.0] || equal(identity,sk_c7)** -> .
% 0.19/0.46 592[6:Spt:590.0,496.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 594[6:MRR:500.0,591.0] || -> equal(multiply(sk_c1,sk_c7),sk_c7)**.
% 0.19/0.46 597[6:SpR:592.0,440.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.46 599[6:Rew:468.0,597.0] || -> equal(sk_c1,sk_c3)**.
% 0.19/0.46 601[6:Rew:599.0,594.0] || -> equal(multiply(sk_c3,sk_c7),sk_c7)**.
% 0.19/0.46 602[6:Rew:495.0,601.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 603[6:MRR:602.0,591.0] || -> .
% 0.19/0.46 605[5:Spt:603.0,455.1,472.0] || equal(sk_c6,sk_c7)** -> .
% 0.19/0.46 606[5:Spt:603.0,455.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 607[5:MRR:456.1,605.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 608[5:MRR:453.0,605.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 609[5:MRR:454.0,605.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 611[5:SpR:606.0,440.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.46 613[5:Rew:468.0,611.0] || -> equal(sk_c1,sk_c3)**.
% 0.19/0.46 615[5:Rew:613.0,608.0] || -> equal(multiply(sk_c3,sk_c7),sk_c6)**.
% 0.19/0.46 616[5:Rew:509.0,615.0] || -> equal(identity,sk_c6)**.
% 0.19/0.46 618[5:Rew:616.0,438.0] || -> equal(multiply(sk_c7,sk_c3),sk_c6)**.
% 0.19/0.46 619[5:Rew:616.0,93.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.46 634[5:Rew:619.0,609.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.46 636[5:Rew:634.0,607.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.46 642[5:Rew:468.0,636.0] || -> equal(sk_c3,sk_c6)**.
% 0.19/0.46 648[5:Rew:642.0,618.0] || -> equal(multiply(sk_c7,sk_c6),sk_c6)**.
% 0.19/0.46 658[5:Rew:619.0,648.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 659[5:MRR:658.0,605.0] || -> .
% 0.19/0.46 670[4:Spt:659.0,18.0,409.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.46 671[4:Spt:659.0,18.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 672[4:MRR:10.0,670.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 673[4:MRR:14.0,670.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 674[4:MRR:6.0,670.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 676[4:SpR:671.0,440.0] || -> equal(inverse(sk_c6),sk_c2)**.
% 0.19/0.46 678[4:Rew:450.0,676.0] || -> equal(sk_c2,sk_c4)**.
% 0.19/0.46 680[4:Rew:678.0,673.0] || -> equal(multiply(sk_c4,sk_c6),sk_c7)**.
% 0.19/0.46 681[4:Rew:463.0,680.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 682[4:Rew:681.0,435.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 685[4:Rew:681.0,23.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 686[4:Rew:681.0,93.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 690[4:Rew:685.0,398.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 696[4:Rew:690.0,401.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.46 698[4:Rew:686.0,674.0] || -> equal(sk_c1,sk_c6)**.
% 0.19/0.46 699[4:Rew:698.0,672.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.46 700[4:Rew:450.0,699.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.46 701[4:Rew:700.0,406.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.46 708[4:Rew:682.0,701.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 723[4:Rew:686.0,696.5,708.0,696.5,686.0,696.4,708.0,696.4,686.0,696.3,708.0,696.3,708.0,696.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) -> .
% 0.19/0.46 724[4:Con:723.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.46 782[4:SpL:682.0,724.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 783[4:Obv:782.1] || -> .
% 0.19/0.46 784[3:Spt:783.0,20.0,406.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.46 785[3:Spt:783.0,20.1] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.19/0.46 786[3:MRR:12.0,784.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.46 787[3:MRR:16.0,784.0] || -> equal(multiply(sk_c2,sk_c6),sk_c7)**.
% 0.19/0.46 788[3:MRR:8.0,784.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.46 791[3:SpR:785.0,561.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),u)**.
% 0.19/0.46 796[3:SpR:786.0,440.0] || -> equal(inverse(sk_c7),sk_c1)**.
% 0.19/0.46 797[3:SpR:786.0,561.0] || -> equal(multiply(sk_c1,multiply(sk_c7,u)),u)**.
% 0.19/0.46 823[3:SpR:787.0,25.0] || -> equal(multiply(sk_c2,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.46 824[3:SpR:787.0,55.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c6)**.
% 0.19/0.46 826[3:Rew:5.0,824.0,785.0,824.0] || -> equal(sk_c5,sk_c6)**.
% 0.19/0.46 833[3:Rew:826.0,401.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.46 837[3:Rew:791.0,823.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 838[3:Rew:837.0,797.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.46 840[3:Rew:838.0,788.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 856[3:Rew:840.0,833.5,840.0,833.4,840.0,833.3,840.0,833.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(inverse(w),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.46 857[3:Con:856.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.46 880[3:SpR:837.0,93.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 882[3:Rew:880.0,435.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 883[3:Rew:880.0,93.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 887[3:Rew:796.0,882.0] || -> equal(sk_c1,sk_c7)**.
% 0.19/0.46 888[3:Rew:887.0,786.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 892[3:Rew:883.0,857.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.46 932[3:SpL:888.0,892.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 933[3:Obv:932.1] || -> .
% 0.19/0.46 934[2:Spt:933.0,1.1,398.0] || equal(multiply(sk_c7,sk_c6),sk_c5)** -> .
% 0.19/0.46 935[2:Spt:933.0,1.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.46 936[2:MRR:3.1,934.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.46 938[2:MRR:4.1,934.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.46 950[2:SpR:936.0,440.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.19/0.46 953[2:Rew:950.0,74.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.46 955[2:Rew:938.0,953.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 957[2:Rew:955.0,5.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.46 958[2:Rew:955.0,934.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.19/0.46 966[2:Rew:957.0,958.0] || equal(sk_c5,sk_c5)* -> .
% 0.19/0.46 967[2:Obv:966.0] || -> .
% 0.19/0.46 % SZS output end Refutation
% 0.19/0.46 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_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 left_identity left_inverse associativity
% 0.19/0.46
%------------------------------------------------------------------------------