TSTP Solution File: GRP376-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP376-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:47:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP376-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 13:33:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 471 clauses, backtracked 251 clauses, performed 11 splits and kept 474 clauses.
% 0.19/0.45 SPASS allocated 63466 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.04 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 4, length 238 :
% 0.19/0.45 % SZS output start Refutation
% 0.19/0.45 1[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 2[0:Inp] || -> equal(inverse(sk_c3),sk_c7)** equal(inverse(sk_c7),sk_c6).
% 0.19/0.45 3[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.45 4[0:Inp] || -> equal(inverse(sk_c4),sk_c6)** equal(inverse(sk_c7),sk_c6).
% 0.19/0.45 5[0:Inp] || -> equal(inverse(sk_c7),sk_c6) equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.45 6[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.45 11[0:Inp] || -> equal(inverse(sk_c1),sk_c7) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 16[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 17[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 18[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7)** equal(multiply(sk_c5,sk_c6),sk_c7).
% 0.19/0.45 19[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 20[0:Inp] || -> equal(multiply(sk_c4,sk_c5),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7).
% 0.19/0.45 21[0:Inp] || -> equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 22[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 23[0:Inp] || -> equal(multiply(sk_c3,sk_c6),sk_c7) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 24[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 26[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 27[0:Inp] || -> equal(inverse(sk_c3),sk_c7) equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.45 28[0:Inp] || -> equal(inverse(sk_c2),sk_c5) equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.45 29[0:Inp] || -> equal(inverse(sk_c4),sk_c6) equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.45 31[0:Inp] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c7) equal(inverse(w),sk_c5) equal(inverse(x),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c6),sk_c7)** equal(multiply(w,sk_c5),sk_c7)** equal(multiply(x,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.19/0.45 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.45 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.45 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.45 35[1:Spt:31.1,31.6] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c6),sk_c7)** -> .
% 0.19/0.45 36[2:Spt:1.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 40[3:Spt:2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.45 43[1:SpL:32.0,35.1] || equal(inverse(identity),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.45 46[4:Spt:3.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.45 48[4:SpL:46.0,35.1] || equal(inverse(sk_c3),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 49[4:Obv:48.1] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.45 50[4:Rew:40.0,49.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 51[4:Obv:50.0] || -> .
% 0.19/0.45 52[4:Spt:51.0,3.1,46.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.45 53[4:Spt:51.0,3.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 54[4:MRR:28.1,52.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.45 56[4:MRR:23.0,52.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 57[4:MRR:18.0,52.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 64[4:SpL:57.0,35.1] || equal(inverse(sk_c5),sk_c7)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 65[4:Obv:64.1] || equal(inverse(sk_c5),sk_c7)** -> .
% 0.19/0.45 70[4:SpR:53.0,33.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.45 71[4:SpR:54.0,33.0] || -> equal(multiply(sk_c5,sk_c2),identity)**.
% 0.19/0.45 73[1:SpL:33.0,35.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(identity,sk_c7) -> .
% 0.19/0.45 74[4:Rew:36.0,70.0] || -> equal(identity,sk_c5)**.
% 0.19/0.45 75[4:Rew:74.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 80[4:Rew:74.0,71.0] || -> equal(multiply(sk_c5,sk_c2),sk_c5)**.
% 0.19/0.45 83[4:Rew:75.0,80.0] || -> equal(sk_c2,sk_c5)**.
% 0.19/0.45 91[4:Rew:83.0,54.0] || -> equal(inverse(sk_c5),sk_c5)**.
% 0.19/0.45 92[4:Rew:83.0,56.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.45 93[4:Rew:91.0,65.0] || equal(sk_c5,sk_c7)** -> .
% 0.19/0.45 95[4:Rew:75.0,92.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 96[4:MRR:95.0,93.0] || -> .
% 0.19/0.45 101[3:Spt:96.0,2.0,40.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.45 102[3:Spt:96.0,2.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 103[3:MRR:27.0,101.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.45 105[3:MRR:22.0,101.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 106[3:MRR:17.0,101.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 119[3:SpR:102.0,33.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.45 120[3:SpR:103.0,33.0] || -> equal(multiply(sk_c5,sk_c2),identity)**.
% 0.19/0.45 123[3:Rew:36.0,119.0] || -> equal(identity,sk_c5)**.
% 0.19/0.45 125[3:Rew:123.0,32.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 128[3:Rew:123.0,73.1] || equal(inverse(inverse(sk_c6)),sk_c7)** equal(sk_c5,sk_c7) -> .
% 0.19/0.45 129[3:Rew:123.0,120.0] || -> equal(multiply(sk_c5,sk_c2),sk_c5)**.
% 0.19/0.45 132[3:Rew:125.0,106.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 133[3:Rew:125.0,129.0] || -> equal(sk_c2,sk_c5)**.
% 0.19/0.45 134[3:Rew:132.0,102.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 141[3:Rew:133.0,105.0] || -> equal(multiply(sk_c5,sk_c5),sk_c7)**.
% 0.19/0.45 142[3:Rew:125.0,141.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 158[3:Rew:142.0,128.1,134.0,128.0,134.0,128.0,132.0,128.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 159[3:Obv:158.1] || -> .
% 0.19/0.45 160[2:Spt:159.0,1.1,36.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.45 161[2:Spt:159.0,1.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 163[2:MRR:11.1,160.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.45 166[2:MRR:6.0,160.0] || -> equal(multiply(sk_c1,sk_c7),sk_c6)**.
% 0.19/0.45 175[2:SpR:161.0,33.0] || -> equal(multiply(sk_c6,sk_c7),identity)**.
% 0.19/0.45 177[2:SpR:163.0,33.0] || -> equal(multiply(sk_c7,sk_c1),identity)**.
% 0.19/0.45 185[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.45 186[0:Rew:32.0,185.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.45 189[2:SpR:175.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(identity,u))**.
% 0.19/0.45 190[2:Rew:32.0,189.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 199[2:SpR:177.0,190.0] || -> equal(multiply(sk_c6,identity),sk_c1)**.
% 0.19/0.45 202[0:SpR:186.0,186.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.45 207[2:SpR:166.0,186.0] || -> equal(multiply(inverse(sk_c1),sk_c6),sk_c7)**.
% 0.19/0.45 210[0:SpR:33.0,186.0] || -> equal(multiply(inverse(inverse(u)),identity),u)**.
% 0.19/0.45 218[2:Rew:163.0,207.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.45 221[0:Rew:202.0,210.0] || -> equal(multiply(u,identity),u)**.
% 0.19/0.45 223[2:Rew:221.0,199.0] || -> equal(sk_c1,sk_c6)**.
% 0.19/0.45 225[2:Rew:223.0,166.0] || -> equal(multiply(sk_c6,sk_c7),sk_c6)**.
% 0.19/0.45 226[2:Rew:223.0,177.0] || -> equal(multiply(sk_c7,sk_c6),identity)**.
% 0.19/0.45 232[2:Rew:175.0,225.0] || -> equal(identity,sk_c6)**.
% 0.19/0.45 238[2:Rew:232.0,43.0] || equal(inverse(sk_c6),sk_c7)** equal(sk_c6,sk_c7) -> .
% 0.19/0.45 241[2:Rew:218.0,226.0,232.0,226.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 242[2:Rew:241.0,161.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 281[2:Rew:241.0,238.1,242.0,238.0,241.0,238.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 282[2:Obv:281.1] || -> .
% 0.19/0.45 285[1:Spt:282.0,31.0,31.2,31.3,31.4,31.5,31.7,31.8,31.9,31.10] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c5),sk_c6)**+ equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c6,sk_c7),sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.19/0.45 287[2:Spt:1.1] || -> equal(multiply(sk_c6,sk_c7),sk_c5)**.
% 0.19/0.45 288[2:Rew:287.0,285.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c5,sk_c5) equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.19/0.45 290[2:Obv:288.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.19/0.45 292[2:SpR:287.0,34.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),multiply(sk_c5,u))**.
% 0.19/0.45 293[2:SpR:287.0,186.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c7)**.
% 0.19/0.45 295[3:Spt:2.0] || -> equal(inverse(sk_c3),sk_c7)**.
% 0.19/0.45 296[3:SpR:295.0,186.0] || -> equal(multiply(sk_c7,multiply(sk_c3,u)),u)**.
% 0.19/0.45 298[4:Spt:4.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.45 299[4:SpR:298.0,186.0] || -> equal(multiply(sk_c6,multiply(sk_c4,u)),u)**.
% 0.19/0.45 301[5:Spt:3.1] || -> equal(multiply(sk_c3,sk_c6),sk_c7)**.
% 0.19/0.45 303[5:SpR:301.0,186.0] || -> equal(multiply(inverse(sk_c3),sk_c7),sk_c6)**.
% 0.19/0.45 305[5:Rew:295.0,303.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.45 309[6:Spt:5.1] || -> equal(multiply(sk_c4,sk_c5),sk_c6)**.
% 0.19/0.45 311[6:SpR:309.0,186.0] || -> equal(multiply(inverse(sk_c4),sk_c6),sk_c5)**.
% 0.19/0.45 313[6:Rew:298.0,311.0] || -> equal(multiply(sk_c6,sk_c6),sk_c5)**.
% 0.19/0.45 315[6:SpR:313.0,186.0] || -> equal(multiply(inverse(sk_c6),sk_c5),sk_c6)**.
% 0.19/0.45 317[6:Rew:293.0,315.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 318[6:Rew:317.0,287.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.45 319[6:Rew:317.0,298.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.45 321[6:Rew:317.0,305.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.45 322[6:Rew:317.0,309.0] || -> equal(multiply(sk_c4,sk_c5),sk_c7)**.
% 0.19/0.45 325[6:Rew:317.0,290.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(inverse(sk_c7),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(multiply(sk_c5,sk_c6),sk_c7)** -> .
% 0.19/0.45 326[6:Rew:317.0,293.0] || -> equal(multiply(inverse(sk_c7),sk_c5),sk_c7)**.
% 0.19/0.45 333[6:Rew:318.0,321.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 335[6:Rew:333.0,322.0] || -> equal(multiply(sk_c4,sk_c7),sk_c7)**.
% 0.19/0.45 337[6:Rew:33.0,326.0,333.0,326.0] || -> equal(identity,sk_c7)**.
% 0.19/0.45 339[6:Rew:337.0,221.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.45 343[6:Rew:339.0,335.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.45 345[6:Rew:343.0,319.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 355[6:Rew:333.0,325.7,339.0,325.7,317.0,325.7,339.0,325.6,317.0,325.6,339.0,325.5,333.0,325.5,339.0,325.4,333.0,325.4,317.0,325.4,345.0,325.3,333.0,325.1,317.0,325.0] || equal(inverse(u),sk_c7)** equal(inverse(v),sk_c7)** equal(inverse(w),sk_c7)** equal(sk_c7,sk_c7) equal(u,sk_c7) equal(v,sk_c7) equal(w,sk_c7) equal(sk_c7,sk_c7) -> .
% 0.19/0.45 356[6:Obv:355.7] || 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) -> .
% 0.19/0.45 357[6:Con:356.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.45 387[6:SpL:345.0,357.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 388[6:Obv:387.1] || -> .
% 0.19/0.45 389[6:Spt:388.0,5.1,309.0] || equal(multiply(sk_c4,sk_c5),sk_c6)** -> .
% 0.19/0.45 390[6:Spt:388.0,5.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 395[6:MRR:20.0,389.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 401[6:SpR:390.0,186.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 403[6:Rew:292.0,401.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 405[6:Rew:403.0,395.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 408[6:Rew:405.0,305.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.45 410[6:Rew:405.0,287.0] || -> equal(multiply(sk_c7,sk_c7),sk_c5)**.
% 0.19/0.45 413[6:Rew:405.0,389.0] || equal(multiply(sk_c4,sk_c5),sk_c7)** -> .
% 0.19/0.45 414[6:Rew:405.0,299.0] || -> equal(multiply(sk_c7,multiply(sk_c4,u)),u)**.
% 0.19/0.45 420[6:Rew:408.0,410.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 423[6:Rew:420.0,403.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.45 426[6:Rew:420.0,413.0] || equal(multiply(sk_c4,sk_c7),sk_c7)** -> .
% 0.19/0.45 428[6:Rew:423.0,414.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.45 429[6:UnC:428.0,426.0] || -> .
% 0.19/0.45 434[5:Spt:429.0,3.1,301.0] || equal(multiply(sk_c3,sk_c6),sk_c7)** -> .
% 0.19/0.45 435[5:Spt:429.0,3.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 436[5:MRR:28.1,434.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.45 438[5:MRR:23.0,434.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 439[5:MRR:18.0,434.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 445[5:SpR:435.0,186.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 447[5:Rew:292.0,445.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 448[5:Rew:447.0,439.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 454[5:Rew:448.0,434.0] || equal(multiply(sk_c3,sk_c7),sk_c7)** -> .
% 0.19/0.45 466[5:SpR:436.0,186.0] || -> equal(multiply(sk_c5,multiply(sk_c2,u)),u)**.
% 0.19/0.45 468[5:Rew:447.0,466.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.45 469[5:Rew:468.0,438.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 471[5:Rew:469.0,447.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.45 478[5:Rew:471.0,296.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.45 479[5:UnC:478.0,454.0] || -> .
% 0.19/0.45 483[4:Spt:479.0,4.0,298.0] || equal(inverse(sk_c4),sk_c6)** -> .
% 0.19/0.45 484[4:Spt:479.0,4.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 485[4:MRR:29.0,483.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.45 487[4:MRR:24.0,483.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 488[4:MRR:19.0,483.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 490[4:Rew:488.0,290.7,484.0,290.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 491[4:Obv:490.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.45 494[4:SpR:484.0,186.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 496[4:Rew:292.0,494.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.45 497[4:Rew:496.0,488.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.45 499[4:Rew:497.0,484.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.45 504[4:Rew:497.0,491.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.45 508[4:Rew:497.0,504.5,497.0,504.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.45 511[4:SpR:485.0,186.0] || -> equal(multiply(sk_c5,multiply(sk_c2,u)),u)**.
% 0.19/0.45 513[4:Rew:496.0,511.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.45 514[4:Rew:513.0,487.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.45 516[4:Rew:514.0,496.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.45 519[4:Rew:514.0,508.1] || 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_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.45 523[4:Con:519.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.45 524[4:Rew:514.0,523.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.45 525[4:Con:524.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.45 548[0:SpR:33.0,221.0] || -> equal(inverse(identity),identity)**.
% 0.19/0.45 550[3:SpR:295.0,33.0] || -> equal(multiply(sk_c7,sk_c3),identity)**.
% 0.19/0.45 555[4:Rew:516.0,550.0] || -> equal(identity,sk_c3)**.
% 0.19/0.45 556[4:Rew:555.0,221.0] || -> equal(multiply(u,sk_c3),u)**.
% 0.19/0.45 559[4:Rew:555.0,548.0] || -> equal(inverse(sk_c3),sk_c3)**.
% 0.19/0.45 560[4:Rew:295.0,559.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.45 572[4:Rew:560.0,556.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.45 573[4:Rew:572.0,525.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.45 601[4:SpL:499.0,573.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.45 602[4:Obv:601.1] || -> .
% 0.19/0.45 603[3:Spt:602.0,2.0,295.0] || equal(inverse(sk_c3),sk_c7)** -> .
% 0.19/0.45 604[3:Spt:602.0,2.1] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.45 606[3:MRR:27.0,603.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.45 608[3:MRR:22.0,603.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.45 609[3:MRR:17.0,603.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.45 612[3:Rew:609.0,290.7,604.0,290.3] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(sk_c6,sk_c6) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** equal(sk_c7,sk_c7) -> .
% 0.19/0.45 613[3:Obv:612.7] || equal(inverse(u),sk_c6) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.45 616[3:SpR:604.0,186.0] || -> equal(multiply(sk_c6,multiply(sk_c7,u)),u)**.
% 0.19/0.45 618[3:Rew:292.0,616.0] || -> equal(multiply(sk_c5,u),u)**.
% 0.19/0.46 619[3:Rew:618.0,609.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 621[3:Rew:619.0,604.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 625[3:Rew:619.0,613.0] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c6)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c6)** -> .
% 0.19/0.46 629[3:Rew:619.0,625.5,619.0,625.3] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c5) equal(inverse(w),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.46 632[3:SpR:606.0,186.0] || -> equal(multiply(sk_c5,multiply(sk_c2,u)),u)**.
% 0.19/0.46 634[3:Rew:618.0,632.0] || -> equal(multiply(sk_c2,u),u)**.
% 0.19/0.46 635[3:Rew:634.0,608.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 636[3:Rew:635.0,606.0] || -> equal(inverse(sk_c2),sk_c7)**.
% 0.19/0.46 640[3:Rew:635.0,629.1] || 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_c5),sk_c7)** equal(multiply(w,sk_c7),sk_c7)** -> .
% 0.19/0.46 643[3:Con:640.1] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c5),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.46 644[3:Rew:635.0,643.2] || equal(inverse(u),sk_c7) equal(inverse(v),sk_c7) equal(multiply(u,sk_c7),sk_c7)** equal(multiply(v,sk_c7),sk_c7)** -> .
% 0.19/0.46 645[3:Con:644.1] || equal(inverse(u),sk_c7) equal(multiply(u,sk_c7),sk_c7)** -> .
% 0.19/0.46 672[3:SpR:634.0,221.0] || -> equal(identity,sk_c2)**.
% 0.19/0.46 674[3:Rew:672.0,548.0] || -> equal(inverse(sk_c2),sk_c2)**.
% 0.19/0.46 676[3:Rew:672.0,221.0] || -> equal(multiply(u,sk_c2),u)**.
% 0.19/0.46 678[3:Rew:636.0,674.0] || -> equal(sk_c2,sk_c7)**.
% 0.19/0.46 683[3:Rew:678.0,676.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 684[3:Rew:683.0,645.1] || equal(inverse(u),sk_c7)** equal(u,sk_c7) -> .
% 0.19/0.46 706[3:SpL:621.0,684.0] || equal(sk_c7,sk_c7)* equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 707[3:Obv:706.1] || -> .
% 0.19/0.46 708[2:Spt:707.0,1.1,287.0] || equal(multiply(sk_c6,sk_c7),sk_c5)** -> .
% 0.19/0.46 709[2:Spt:707.0,1.0] || -> equal(inverse(sk_c7),sk_c6)**.
% 0.19/0.46 710[2:MRR:26.1,708.0] || -> equal(inverse(sk_c2),sk_c5)**.
% 0.19/0.46 712[2:MRR:21.0,708.0] || -> equal(multiply(sk_c2,sk_c5),sk_c7)**.
% 0.19/0.46 713[2:MRR:16.0,708.0] || -> equal(multiply(sk_c5,sk_c6),sk_c7)**.
% 0.19/0.46 725[2:SpR:712.0,186.0] || -> equal(multiply(inverse(sk_c2),sk_c7),sk_c5)**.
% 0.19/0.46 727[2:Rew:710.0,725.0] || -> equal(multiply(sk_c5,sk_c7),sk_c5)**.
% 0.19/0.46 736[2:SpR:727.0,186.0] || -> equal(multiply(inverse(sk_c5),sk_c5),sk_c7)**.
% 0.19/0.46 738[2:Rew:33.0,736.0] || -> equal(identity,sk_c7)**.
% 0.19/0.46 739[2:Rew:738.0,548.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.46 740[2:Rew:738.0,221.0] || -> equal(multiply(u,sk_c7),u)**.
% 0.19/0.46 741[2:Rew:738.0,32.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.46 743[2:Rew:709.0,739.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.46 745[2:Rew:743.0,713.0] || -> equal(multiply(sk_c5,sk_c7),sk_c7)**.
% 0.19/0.46 747[2:Rew:743.0,708.0] || equal(multiply(sk_c7,sk_c7),sk_c5)** -> .
% 0.19/0.46 755[2:Rew:740.0,745.0] || -> equal(sk_c5,sk_c7)**.
% 0.19/0.46 764[2:Rew:741.0,747.0,755.0,747.0] || equal(sk_c7,sk_c7)* -> .
% 0.19/0.46 765[2:Obv:764.0] || -> .
% 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_11 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_26 prove_this_27 prove_this_28 prove_this_29 prove_this_31 left_identity left_inverse associativity
% 0.19/0.46
%------------------------------------------------------------------------------