TSTP Solution File: GRP305-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP305-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:46:46 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP305-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 21:09:24 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 749 clauses, backtracked 262 clauses, performed 11 splits and kept 588 clauses.
% 0.21/0.48 SPASS allocated 63560 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.21/0.48 0:00:00.04 for the input.
% 0.21/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.00 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.05 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 5, length 312 :
% 0.21/0.48 % SZS output start Refutation
% 0.21/0.48 1[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c4)** equal(multiply(sk_c6,sk_c5),sk_c4).
% 0.21/0.48 2[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.21/0.48 3[0:Inp] || -> equal(multiply(sk_c2,sk_c5),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c4).
% 0.21/0.48 4[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.21/0.48 5[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c5)** equal(multiply(sk_c6,sk_c5),sk_c4).
% 0.21/0.48 6[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c4) equal(multiply(sk_c5,sk_c4),sk_c6)**.
% 0.21/0.48 7[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c5,sk_c4),sk_c6)**.
% 0.21/0.48 8[0:Inp] || -> equal(multiply(sk_c2,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c4),sk_c6).
% 0.21/0.48 9[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c5,sk_c4),sk_c6)**.
% 0.21/0.48 10[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c5)** equal(multiply(sk_c5,sk_c4),sk_c6).
% 0.21/0.48 11[0:Inp] || -> equal(inverse(sk_c6),sk_c4) equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.48 12[0:Inp] || -> equal(inverse(sk_c2),sk_c6)** equal(inverse(sk_c6),sk_c4).
% 0.21/0.48 13[0:Inp] || -> equal(inverse(sk_c6),sk_c4) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.48 14[0:Inp] || -> equal(inverse(sk_c3),sk_c5)** equal(inverse(sk_c6),sk_c4).
% 0.21/0.48 15[0:Inp] || -> equal(inverse(sk_c6),sk_c4) equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.48 16[0:Inp] || -> equal(multiply(sk_c5,sk_c6),sk_c4) equal(multiply(sk_c1,sk_c6),sk_c4)**.
% 0.21/0.48 17[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c4)**.
% 0.21/0.48 18[0:Inp] || -> equal(multiply(sk_c2,sk_c5),sk_c6) equal(multiply(sk_c1,sk_c6),sk_c4)**.
% 0.21/0.48 19[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c4)**.
% 0.21/0.48 20[0:Inp] || -> equal(multiply(sk_c3,sk_c4),sk_c5) equal(multiply(sk_c1,sk_c6),sk_c4)**.
% 0.21/0.48 21[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.48 22[0:Inp] || -> equal(inverse(sk_c2),sk_c6) equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.48 23[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.48 24[0:Inp] || -> equal(inverse(sk_c3),sk_c5) equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.48 25[0:Inp] || -> equal(inverse(sk_c1),sk_c6) equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.48 26[0:Inp] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(w),sk_c6) equal(inverse(sk_c6),sk_c4) equal(multiply(u,sk_c4),sk_c5)**+ equal(multiply(v,sk_c5),sk_c6)** equal(multiply(w,sk_c6),sk_c4)** equal(multiply(sk_c5,sk_c6),sk_c4) equal(multiply(sk_c5,sk_c4),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c4) -> .
% 0.21/0.48 27[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.21/0.48 28[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.21/0.48 29[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.21/0.48 30[1:Spt:26.2,26.6] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c4)** -> .
% 0.21/0.48 31[2:Spt:11.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.21/0.48 35[3:Spt:1.1] || -> equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.21/0.48 39[4:Spt:21.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.48 41[5:Spt:16.1] || -> equal(multiply(sk_c1,sk_c6),sk_c4)**.
% 0.21/0.48 43[5:SpL:41.0,30.1] || equal(inverse(sk_c1),sk_c6)** equal(sk_c4,sk_c4) -> .
% 0.21/0.48 44[5:Obv:43.1] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.21/0.48 45[5:Rew:39.0,44.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.48 46[5:Obv:45.0] || -> .
% 0.21/0.48 47[5:Spt:46.0,16.1,41.0] || equal(multiply(sk_c1,sk_c6),sk_c4)** -> .
% 0.21/0.48 48[5:Spt:46.0,16.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.48 49[5:MRR:19.1,47.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.48 50[5:MRR:17.1,47.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 51[5:MRR:20.1,47.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.48 52[5:MRR:18.1,47.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.48 54[5:SpL:48.0,30.1] || equal(inverse(sk_c5),sk_c6)** equal(sk_c4,sk_c4) -> .
% 0.21/0.48 55[5:Obv:54.1] || equal(inverse(sk_c5),sk_c6)** -> .
% 0.21/0.48 61[2:SpR:31.0,28.0] || -> equal(multiply(sk_c4,sk_c6),identity)**.
% 0.21/0.48 62[4:SpR:39.0,28.0] || -> equal(multiply(sk_c6,sk_c1),identity)**.
% 0.21/0.48 63[5:SpR:49.0,28.0] || -> equal(multiply(sk_c5,sk_c3),identity)**.
% 0.21/0.48 64[5:SpR:50.0,28.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.21/0.48 65[1:SpL:28.0,30.1] || equal(inverse(inverse(sk_c6)),sk_c6)** equal(identity,sk_c4) -> .
% 0.21/0.48 66[2:Rew:31.0,65.0] || equal(inverse(sk_c4),sk_c6)** equal(identity,sk_c4) -> .
% 0.21/0.48 71[2:SpR:61.0,29.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),multiply(identity,u))**.
% 0.21/0.48 77[0:SpR:28.0,29.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.21/0.48 80[2:Rew:27.0,71.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.21/0.48 81[0:Rew:27.0,77.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.21/0.48 87[5:SpR:63.0,29.0] || -> equal(multiply(sk_c5,multiply(sk_c3,u)),multiply(identity,u))**.
% 0.21/0.48 88[5:Rew:27.0,87.0] || -> equal(multiply(sk_c5,multiply(sk_c3,u)),u)**.
% 0.21/0.48 94[3:SpR:35.0,80.0] || -> equal(multiply(sk_c4,sk_c4),sk_c5)**.
% 0.21/0.48 95[4:SpR:62.0,80.0] || -> equal(multiply(sk_c4,identity),sk_c1)**.
% 0.21/0.48 96[5:SpR:64.0,80.0] || -> equal(multiply(sk_c4,identity),sk_c2)**.
% 0.21/0.48 97[5:Rew:95.0,96.0] || -> equal(sk_c1,sk_c2)**.
% 0.21/0.48 102[5:Rew:97.0,95.0] || -> equal(multiply(sk_c4,identity),sk_c2)**.
% 0.21/0.48 107[5:SpR:102.0,29.0] || -> equal(multiply(sk_c4,multiply(identity,u)),multiply(sk_c2,u))**.
% 0.21/0.48 109[5:Rew:27.0,107.0] || -> equal(multiply(sk_c2,u),multiply(sk_c4,u))**.
% 0.21/0.48 110[5:Rew:109.0,52.0] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.21/0.48 119[5:SpR:51.0,88.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.48 139[0:SpR:81.0,81.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.21/0.48 141[2:SpR:61.0,81.0] || -> equal(multiply(inverse(sk_c4),identity),sk_c6)**.
% 0.21/0.48 143[5:SpR:48.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.48 146[5:SpR:119.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.48 149[0:SpR:28.0,81.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.21/0.48 155[2:SpR:80.0,81.0] || -> equal(multiply(inverse(sk_c4),u),multiply(sk_c6,u))**.
% 0.21/0.48 156[3:SpR:94.0,81.0] || -> equal(multiply(inverse(sk_c4),sk_c5),sk_c4)**.
% 0.21/0.48 162[5:Rew:143.0,146.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.48 168[5:Rew:162.0,55.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.21/0.48 171[5:Rew:162.0,110.0] || -> equal(multiply(sk_c4,sk_c6),sk_c6)**.
% 0.21/0.48 185[5:Rew:31.0,168.0] || equal(sk_c4,sk_c6)** -> .
% 0.21/0.48 186[5:Rew:61.0,171.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 187[5:Rew:186.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.48 231[5:Rew:162.0,156.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c4)**.
% 0.21/0.48 257[5:Rew:187.0,155.0] || -> equal(multiply(inverse(sk_c4),u),u)**.
% 0.21/0.48 258[5:Rew:257.0,231.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.48 259[5:MRR:258.0,185.0] || -> .
% 0.21/0.48 270[4:Spt:259.0,21.0,39.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.21/0.48 271[4:Spt:259.0,21.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.48 273[0:Rew:139.0,149.0] || -> equal(multiply(u,identity),u)**.
% 0.21/0.48 274[2:Rew:273.0,141.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.21/0.48 277[4:MRR:24.1,270.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.48 278[4:MRR:22.1,270.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 279[2:Rew:274.0,66.0] || equal(sk_c6,sk_c6) equal(identity,sk_c4)** -> .
% 0.21/0.48 280[2:Obv:279.0] || equal(identity,sk_c4)** -> .
% 0.21/0.48 281[4:MRR:25.0,270.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.48 282[4:MRR:23.0,270.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.48 284[4:SpR:271.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.48 286[2:SpR:274.0,81.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.21/0.48 309[4:SpR:281.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.21/0.48 311[4:Rew:277.0,309.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.48 313[4:SpR:282.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.21/0.48 315[4:Rew:278.0,313.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.48 316[4:SpR:311.0,29.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),multiply(sk_c4,u))**.
% 0.21/0.48 317[4:SpR:311.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.48 319[4:Rew:284.0,317.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.48 320[4:Rew:319.0,271.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.48 337[4:Rew:319.0,315.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.48 338[4:Rew:320.0,337.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.48 341[4:Rew:338.0,280.0] || equal(identity,sk_c6)** -> .
% 0.21/0.48 342[4:Rew:338.0,61.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.21/0.48 343[4:Rew:338.0,80.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.21/0.48 362[4:Rew:343.0,316.0,319.0,316.0,338.0,316.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.48 364[4:Rew:362.0,342.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 367[4:MRR:364.0,341.0] || -> .
% 0.21/0.48 374[3:Spt:367.0,1.1,35.0] || equal(multiply(sk_c6,sk_c5),sk_c4)** -> .
% 0.21/0.48 375[3:Spt:367.0,1.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.48 376[3:MRR:4.1,374.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.48 377[3:MRR:2.1,374.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 378[3:MRR:5.1,374.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.48 379[3:MRR:3.1,374.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.48 381[3:SpR:375.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.48 400[3:SpR:378.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.21/0.48 402[3:Rew:376.0,400.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.48 404[3:SpR:379.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.21/0.48 406[3:Rew:377.0,404.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.48 407[3:SpR:402.0,29.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),multiply(sk_c4,u))**.
% 0.21/0.48 408[3:SpR:402.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.48 410[3:Rew:381.0,408.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.48 411[3:Rew:410.0,375.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.48 425[3:Rew:410.0,406.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.48 426[3:Rew:411.0,425.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.48 427[3:Rew:426.0,280.0] || equal(identity,sk_c6)** -> .
% 0.21/0.48 430[3:Rew:426.0,61.0] || -> equal(multiply(sk_c6,sk_c6),identity)**.
% 0.21/0.48 431[3:Rew:426.0,286.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.21/0.48 448[3:Rew:431.0,407.0,410.0,407.0,426.0,407.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.48 450[3:Rew:448.0,430.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 453[3:MRR:450.0,427.0] || -> .
% 0.21/0.48 458[2:Spt:453.0,11.0,31.0] || equal(inverse(sk_c6),sk_c4)** -> .
% 0.21/0.48 459[2:Spt:453.0,11.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.48 460[2:MRR:14.1,458.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.48 461[2:MRR:12.1,458.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 462[2:MRR:15.0,458.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.48 463[2:MRR:13.0,458.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.48 465[2:SpR:459.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.48 472[2:SpR:462.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.21/0.48 474[2:Rew:460.0,472.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.48 476[2:SpR:463.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.21/0.48 478[2:Rew:461.0,476.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.48 480[2:SpR:474.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.48 482[2:Rew:465.0,480.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.48 483[2:Rew:482.0,459.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.48 486[2:Rew:482.0,463.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.21/0.48 488[2:Rew:482.0,465.0] || -> equal(multiply(inverse(sk_c6),sk_c4),sk_c6)**.
% 0.21/0.48 493[2:Rew:482.0,478.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.48 494[2:Rew:483.0,493.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.48 495[2:Rew:494.0,458.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.21/0.48 502[2:Rew:28.0,488.0,494.0,488.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 506[2:Rew:502.0,273.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 509[2:Rew:506.0,486.0] || -> equal(sk_c2,sk_c6)**.
% 0.21/0.48 511[2:Rew:509.0,461.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.48 513[2:MRR:511.0,495.0] || -> .
% 0.21/0.48 526[1:Spt:513.0,26.0,26.1,26.3,26.4,26.5,26.7,26.8,26.9] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(inverse(sk_c6),sk_c4) equal(multiply(u,sk_c4),sk_c5)**+ equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) equal(multiply(sk_c5,sk_c4),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c4) -> .
% 0.21/0.48 528[2:Spt:11.0] || -> equal(inverse(sk_c6),sk_c4)**.
% 0.21/0.48 529[2:Rew:528.0,526.2] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(sk_c4,sk_c4) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) equal(multiply(sk_c5,sk_c4),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c4) -> .
% 0.21/0.48 531[2:Obv:529.2] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) equal(multiply(sk_c5,sk_c4),sk_c6)** equal(multiply(sk_c6,sk_c5),sk_c4) -> .
% 0.21/0.48 533[2:SpR:528.0,81.0] || -> equal(multiply(sk_c4,multiply(sk_c6,u)),u)**.
% 0.21/0.48 535[3:Spt:1.1] || -> equal(multiply(sk_c6,sk_c5),sk_c4)**.
% 0.21/0.48 537[3:Rew:535.0,531.6] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) equal(multiply(sk_c5,sk_c4),sk_c6)** equal(sk_c4,sk_c4) -> .
% 0.21/0.48 538[3:Obv:537.6] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4) equal(multiply(sk_c5,sk_c4),sk_c6)** -> .
% 0.21/0.48 544[4:Spt:6.1] || -> equal(multiply(sk_c5,sk_c4),sk_c6)**.
% 0.21/0.48 546[4:Rew:544.0,538.5] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4)** equal(sk_c6,sk_c6) -> .
% 0.21/0.48 547[4:Obv:546.5] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c4)** -> .
% 0.21/0.48 552[5:Spt:21.0] || -> equal(inverse(sk_c1),sk_c6)**.
% 0.21/0.48 553[5:SpR:552.0,81.0] || -> equal(multiply(sk_c6,multiply(sk_c1,u)),u)**.
% 0.21/0.48 558[6:Spt:16.1] || -> equal(multiply(sk_c1,sk_c6),sk_c4)**.
% 0.21/0.48 560[6:SpR:558.0,81.0] || -> equal(multiply(inverse(sk_c1),sk_c4),sk_c6)**.
% 0.21/0.48 562[6:Rew:552.0,560.0] || -> equal(multiply(sk_c6,sk_c4),sk_c6)**.
% 0.21/0.48 567[6:SpR:562.0,81.0] || -> equal(multiply(inverse(sk_c6),sk_c6),sk_c4)**.
% 0.21/0.48 569[6:Rew:528.0,567.0] || -> equal(multiply(sk_c4,sk_c6),sk_c4)**.
% 0.21/0.48 571[6:SpR:569.0,81.0] || -> equal(multiply(inverse(sk_c4),sk_c4),sk_c6)**.
% 0.21/0.48 573[6:Rew:28.0,571.0] || -> equal(identity,sk_c6)**.
% 0.21/0.48 574[6:Rew:573.0,27.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.48 575[6:Rew:573.0,273.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.48 578[6:Rew:574.0,562.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.48 579[6:Rew:574.0,535.0] || -> equal(sk_c4,sk_c5)**.
% 0.21/0.48 586[6:Rew:578.0,528.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.48 592[6:Rew:578.0,547.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c6)** -> .
% 0.21/0.48 596[6:Rew:578.0,579.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.48 609[6:Rew:596.0,592.4,575.0,592.4,575.0,592.3,596.0,592.3,575.0,592.2,578.0,592.2,596.0,592.2,596.0,592.0] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) equal(sk_c6,sk_c6) -> .
% 0.21/0.48 610[6:Obv:609.4] || equal(inverse(u),sk_c6)** equal(inverse(v),sk_c6)** equal(u,sk_c6) equal(v,sk_c6) -> .
% 0.21/0.48 611[6:Con:610.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.21/0.48 680[6:SpL:586.0,611.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.21/0.48 682[6:Obv:680.1] || -> .
% 0.21/0.48 683[6:Spt:682.0,16.1,558.0] || equal(multiply(sk_c1,sk_c6),sk_c4)** -> .
% 0.21/0.48 684[6:Spt:682.0,16.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.48 685[6:MRR:19.1,683.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.48 686[6:MRR:17.1,683.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.48 687[6:MRR:20.1,683.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.48 688[6:MRR:18.1,683.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.48 694[6:SpR:684.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.48 705[6:SpR:687.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.21/0.48 707[6:Rew:685.0,705.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.48 719[6:SpR:688.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.21/0.48 721[6:Rew:686.0,719.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.48 725[6:SpR:707.0,29.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),multiply(sk_c4,u))**.
% 0.21/0.48 726[6:SpR:707.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.48 728[6:Rew:694.0,726.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.48 729[6:Rew:728.0,684.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.48 749[6:Rew:728.0,721.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 750[6:Rew:729.0,749.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.49 752[6:Rew:750.0,683.0] || equal(multiply(sk_c1,sk_c6),sk_c6)** -> .
% 0.21/0.49 753[6:Rew:750.0,533.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.21/0.49 761[6:Rew:753.0,725.0,728.0,725.0,750.0,725.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 765[6:Rew:761.0,553.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.21/0.49 766[6:UnC:765.0,752.0] || -> .
% 0.21/0.49 775[5:Spt:766.0,21.0,552.0] || equal(inverse(sk_c1),sk_c6)** -> .
% 0.21/0.49 776[5:Spt:766.0,21.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.49 777[5:MRR:24.1,775.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.49 778[5:MRR:22.1,775.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 779[5:MRR:25.0,775.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.49 780[5:MRR:23.0,775.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.49 781[5:Rew:776.0,547.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** equal(sk_c4,sk_c4) -> .
% 0.21/0.49 782[5:Obv:781.4] || equal(inverse(u),sk_c5) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** -> .
% 0.21/0.49 786[5:SpR:776.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.49 805[5:SpR:779.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.21/0.49 807[5:Rew:777.0,805.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.49 809[5:SpR:780.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.21/0.49 811[5:Rew:778.0,809.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.49 812[5:SpR:807.0,29.0] || -> equal(multiply(sk_c5,multiply(sk_c5,u)),multiply(sk_c4,u))**.
% 0.21/0.49 813[5:SpR:807.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.49 815[5:Rew:786.0,813.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 816[5:Rew:815.0,776.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.49 832[5:Rew:815.0,782.0] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c4),sk_c5)** equal(multiply(v,sk_c5),sk_c6)** -> .
% 0.21/0.49 836[5:Rew:815.0,811.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 837[5:Rew:816.0,836.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.49 838[5:Rew:837.0,528.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.49 839[5:Rew:837.0,533.0] || -> equal(multiply(sk_c6,multiply(sk_c6,u)),u)**.
% 0.21/0.49 847[5:Rew:839.0,812.0,815.0,812.0,837.0,812.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.21/0.49 856[5:Rew:815.0,832.3,837.0,832.2,815.0,832.2] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c6) equal(multiply(u,sk_c6),sk_c6)** equal(multiply(v,sk_c6),sk_c6)** -> .
% 0.21/0.49 857[5:Con:856.1] || equal(inverse(u),sk_c6) equal(multiply(u,sk_c6),sk_c6)** -> .
% 0.21/0.49 867[5:SpR:778.0,28.0] || -> equal(multiply(sk_c6,sk_c2),identity)**.
% 0.21/0.49 869[5:Rew:847.0,867.0] || -> equal(identity,sk_c2)**.
% 0.21/0.49 871[5:Rew:869.0,28.0] || -> equal(multiply(inverse(u),u),sk_c2)**.
% 0.21/0.49 872[5:Rew:869.0,273.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.21/0.49 895[5:SpR:838.0,871.0] || -> equal(multiply(sk_c6,sk_c6),sk_c2)**.
% 0.21/0.49 896[5:Rew:847.0,895.0] || -> equal(sk_c2,sk_c6)**.
% 0.21/0.49 902[5:Rew:896.0,872.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.49 903[5:Rew:902.0,857.1] || equal(inverse(u),sk_c6)** equal(u,sk_c6) -> .
% 0.21/0.49 954[5:SpL:838.0,903.0] || equal(sk_c6,sk_c6)* equal(sk_c6,sk_c6)* -> .
% 0.21/0.49 956[5:Obv:954.1] || -> .
% 0.21/0.49 957[4:Spt:956.0,6.1,544.0] || equal(multiply(sk_c5,sk_c4),sk_c6)** -> .
% 0.21/0.49 958[4:Spt:956.0,6.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.49 961[4:MRR:9.1,957.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.49 962[4:MRR:7.1,957.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 964[4:MRR:10.1,957.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.49 965[4:MRR:8.1,957.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.49 967[4:SpR:958.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.49 983[4:SpR:964.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.21/0.49 985[4:Rew:961.0,983.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.49 987[4:SpR:965.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.21/0.49 989[4:Rew:962.0,987.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.49 991[4:SpR:985.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.49 993[4:Rew:967.0,991.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 994[4:Rew:993.0,958.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.49 1002[4:Rew:993.0,957.0] || equal(multiply(sk_c6,sk_c4),sk_c6)** -> .
% 0.21/0.49 1010[4:Rew:993.0,989.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 1011[4:Rew:994.0,1010.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.49 1014[4:Rew:1011.0,994.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 1018[4:Rew:1014.0,1002.0,1011.0,1002.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.49 1019[4:Obv:1018.0] || -> .
% 0.21/0.49 1029[3:Spt:1019.0,1.1,535.0] || equal(multiply(sk_c6,sk_c5),sk_c4)** -> .
% 0.21/0.49 1030[3:Spt:1019.0,1.0] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.49 1031[3:MRR:4.1,1029.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.49 1032[3:MRR:2.1,1029.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 1033[3:MRR:5.1,1029.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.49 1034[3:MRR:3.1,1029.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.49 1036[3:SpR:1030.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.49 1045[3:SpR:1033.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.21/0.49 1047[3:Rew:1031.0,1045.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.49 1049[3:SpR:1034.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.21/0.49 1051[3:Rew:1032.0,1049.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.49 1053[3:SpR:1047.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.49 1055[3:Rew:1036.0,1053.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 1056[3:Rew:1055.0,1030.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.49 1061[3:Rew:1055.0,1029.0] || equal(multiply(sk_c6,sk_c6),sk_c4)** -> .
% 0.21/0.49 1067[3:Rew:1055.0,1051.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 1068[3:Rew:1056.0,1067.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.49 1071[3:Rew:1068.0,1056.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 1073[3:Rew:1071.0,1061.0,1068.0,1061.0] || equal(sk_c6,sk_c6)* -> .
% 0.21/0.49 1074[3:Obv:1073.0] || -> .
% 0.21/0.49 1082[2:Spt:1074.0,11.0,528.0] || equal(inverse(sk_c6),sk_c4)** -> .
% 0.21/0.49 1083[2:Spt:1074.0,11.1] || -> equal(multiply(sk_c5,sk_c6),sk_c4)**.
% 0.21/0.49 1084[2:MRR:14.1,1082.0] || -> equal(inverse(sk_c3),sk_c5)**.
% 0.21/0.49 1085[2:MRR:12.1,1082.0] || -> equal(inverse(sk_c2),sk_c6)**.
% 0.21/0.49 1086[2:MRR:15.0,1082.0] || -> equal(multiply(sk_c3,sk_c4),sk_c5)**.
% 0.21/0.49 1087[2:MRR:13.0,1082.0] || -> equal(multiply(sk_c2,sk_c5),sk_c6)**.
% 0.21/0.49 1089[2:SpR:1083.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c6)**.
% 0.21/0.49 1096[2:SpR:1086.0,81.0] || -> equal(multiply(inverse(sk_c3),sk_c5),sk_c4)**.
% 0.21/0.49 1098[2:Rew:1084.0,1096.0] || -> equal(multiply(sk_c5,sk_c5),sk_c4)**.
% 0.21/0.49 1100[2:SpR:1087.0,81.0] || -> equal(multiply(inverse(sk_c2),sk_c6),sk_c5)**.
% 0.21/0.49 1102[2:Rew:1085.0,1100.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.21/0.49 1104[2:SpR:1098.0,81.0] || -> equal(multiply(inverse(sk_c5),sk_c4),sk_c5)**.
% 0.21/0.49 1106[2:Rew:1089.0,1104.0] || -> equal(sk_c5,sk_c6)**.
% 0.21/0.49 1107[2:Rew:1106.0,1083.0] || -> equal(multiply(sk_c6,sk_c6),sk_c4)**.
% 0.21/0.49 1110[2:Rew:1106.0,1087.0] || -> equal(multiply(sk_c2,sk_c6),sk_c6)**.
% 0.21/0.49 1112[2:Rew:1106.0,1089.0] || -> equal(multiply(inverse(sk_c6),sk_c4),sk_c6)**.
% 0.21/0.49 1117[2:Rew:1106.0,1102.0] || -> equal(multiply(sk_c6,sk_c6),sk_c6)**.
% 0.21/0.49 1118[2:Rew:1107.0,1117.0] || -> equal(sk_c4,sk_c6)**.
% 0.21/0.49 1119[2:Rew:1118.0,1082.0] || equal(inverse(sk_c6),sk_c6)** -> .
% 0.21/0.49 1122[2:Rew:28.0,1112.0,1118.0,1112.0] || -> equal(identity,sk_c6)**.
% 0.21/0.49 1124[2:Rew:1122.0,273.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.21/0.49 1129[2:Rew:1124.0,1110.0] || -> equal(sk_c2,sk_c6)**.
% 0.21/0.49 1131[2:Rew:1129.0,1085.0] || -> equal(inverse(sk_c6),sk_c6)**.
% 0.21/0.49 1133[2:MRR:1131.0,1119.0] || -> .
% 0.21/0.49 % SZS output end Refutation
% 0.21/0.49 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_10 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_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 left_identity left_inverse associativity
% 0.21/0.49
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