TSTP Solution File: GRP125-2.005 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP125-2.005 : TPTP v8.1.0. Released v1.2.0.
% 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 11:45:35 EDT 2022
% Result : Unsatisfiable 6.25s 6.49s
% Output : Refutation 11.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP125-2.005 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % 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 13:21:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.25/6.49
% 6.25/6.49 SPASS V 3.9
% 6.25/6.49 SPASS beiseite: Proof found.
% 6.25/6.49 % SZS status Theorem
% 6.25/6.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.25/6.49 SPASS derived 15300 clauses, backtracked 1431 clauses, performed 57 splits and kept 3427 clauses.
% 6.25/6.49 SPASS allocated 96488 KBytes.
% 6.25/6.49 SPASS spent 0:00:06.12 on the problem.
% 6.25/6.49 0:00:00.03 for the input.
% 6.25/6.49 0:00:00.00 for the FLOTTER CNF translation.
% 6.25/6.49 0:00:00.28 for inferences.
% 6.25/6.49 0:00:00.06 for the backtracking.
% 6.25/6.49 0:00:05.69 for the reduction.
% 6.25/6.49
% 6.25/6.49
% 6.25/6.49 Here is a proof with depth 23, length 418 :
% 6.25/6.49 % SZS output start Refutation
% 6.25/6.49 2[0:Inp] || -> next(e_2,e_3)*.
% 6.25/6.49 3[0:Inp] || -> next(e_3,e_4)*.
% 6.25/6.49 12[0:Inp] || -> greater(e_4,e_3)*.
% 6.25/6.49 13[0:Inp] || -> greater(e_5,e_3)*.
% 6.25/6.49 14[0:Inp] || -> greater(e_5,e_4)*.
% 6.25/6.49 15[0:Inp] || greater(u,v)* next(w,v)* product(w,e_1,u)*+ -> .
% 6.25/6.49 16[0:Inp] || -> group_element(e_1)*.
% 6.25/6.49 17[0:Inp] || -> group_element(e_2)*.
% 6.25/6.49 18[0:Inp] || -> group_element(e_3)*.
% 6.25/6.49 19[0:Inp] || -> group_element(e_4)*.
% 6.25/6.49 20[0:Inp] || -> group_element(e_5)*.
% 6.25/6.49 21[0:Inp] || equalish(e_1,e_2)*+ -> .
% 6.25/6.49 22[0:Inp] || equalish(e_1,e_3)*+ -> .
% 6.25/6.49 23[0:Inp] || equalish(e_1,e_4)*+ -> .
% 6.25/6.49 24[0:Inp] || equalish(e_1,e_5)*+ -> .
% 6.25/6.49 25[0:Inp] || equalish(e_2,e_1)*+ -> .
% 6.25/6.49 26[0:Inp] || equalish(e_2,e_3)*+ -> .
% 6.25/6.49 28[0:Inp] || equalish(e_2,e_5)*+ -> .
% 6.25/6.49 29[0:Inp] || equalish(e_3,e_1)*+ -> .
% 6.25/6.49 30[0:Inp] || equalish(e_3,e_2)*+ -> .
% 6.25/6.49 33[0:Inp] || equalish(e_4,e_1)*+ -> .
% 6.25/6.49 34[0:Inp] || equalish(e_4,e_2)*+ -> .
% 6.25/6.49 35[0:Inp] || equalish(e_4,e_3)*+ -> .
% 6.25/6.49 36[0:Inp] || equalish(e_4,e_5)*+ -> .
% 6.25/6.49 37[0:Inp] || equalish(e_5,e_1)*+ -> .
% 6.25/6.49 38[0:Inp] || equalish(e_5,e_2)*+ -> .
% 6.25/6.49 39[0:Inp] || equalish(e_5,e_3)*+ -> .
% 6.25/6.49 40[0:Inp] || equalish(e_5,e_4)*+ -> .
% 6.25/6.49 41[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_5) product(v,u,e_4) product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 6.25/6.49 42[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 6.25/6.49 43[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 6.25/6.49 44[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 6.25/6.49 45[0:Inp] || -> product(u,u,u)*.
% 6.25/6.49 46[0:Inp] || product(u,v,w)*+ product(v,u,x)* -> product(x,w,v)*.
% 6.25/6.49 57[0:Res:45.0,44.0] || product(u,v,v)*+ -> equalish(u,v).
% 6.25/6.49 59[0:Res:45.0,43.0] || product(u,v,u)*+ -> equalish(v,u).
% 6.25/6.49 61[0:Res:45.0,42.0] || product(u,u,v)*+ -> equalish(v,u).
% 6.25/6.49 67[0:Res:41.6,59.0] group_element(u) group_element(e_1) || -> product(e_1,u,e_5) product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 6.25/6.49 69[0:Res:41.6,46.0] group_element(u) group_element(v) || product(u,v,w)*+ -> product(v,u,e_5) product(v,u,e_4) product(v,u,e_3) product(v,u,e_2)* product(w,e_1,u)*.
% 6.25/6.49 71[0:Res:41.6,43.0] group_element(u) group_element(v) || product(v,w,e_1)*+ -> product(v,u,e_5) product(v,u,e_4) product(v,u,e_3) product(v,u,e_2)* equalish(w,u)*.
% 6.25/6.49 72[0:Res:41.6,44.0] group_element(u) group_element(v) || product(w,u,e_1)*+ -> product(v,u,e_5) product(v,u,e_4) product(v,u,e_3) product(v,u,e_2)* equalish(w,v)*.
% 6.25/6.49 73[0:Res:41.6,57.0] group_element(e_1) group_element(u) || -> product(u,e_1,e_5) product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 6.25/6.49 74[0:SSi:73.0,16.0] group_element(u) || -> product(u,e_1,e_5) product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 6.25/6.49 75[0:SSi:67.1,16.0] group_element(u) || -> product(e_1,u,e_5) product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 6.25/6.49 83[0:Res:74.4,59.0] group_element(e_2) || -> product(e_2,e_1,e_5) product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 6.25/6.49 87[0:Res:74.4,43.0] group_element(u) || product(u,v,e_2)*+ -> product(u,e_1,e_5) product(u,e_1,e_4) product(u,e_1,e_3)* equalish(u,e_1) equalish(v,e_1).
% 6.25/6.49 89[0:SSi:83.0,17.0] || -> product(e_2,e_1,e_5) product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 6.25/6.49 90[0:MRR:89.3,89.4,25.0,21.0] || -> product(e_2,e_1,e_5) product(e_2,e_1,e_4) product(e_2,e_1,e_3)*.
% 6.25/6.49 91[0:Res:90.2,15.2] || greater(e_3,u)+ next(e_2,u)* -> product(e_2,e_1,e_5) product(e_2,e_1,e_4)*.
% 6.25/6.49 92[0:Res:90.2,46.0] || product(e_1,e_2,u)* -> product(e_2,e_1,e_5) product(e_2,e_1,e_4) product(u,e_3,e_1)*.
% 6.25/6.49 95[0:Res:90.2,44.0] || product(u,e_1,e_3)* -> product(e_2,e_1,e_5) product(e_2,e_1,e_4)* equalish(u,e_2).
% 6.25/6.49 96[1:Spt:91.3] || -> product(e_2,e_1,e_4)*.
% 6.25/6.49 97[1:Res:96.0,15.2] || greater(e_4,u)+ next(e_2,u)* -> .
% 6.25/6.49 102[1:Res:12.0,97.0] || next(e_2,e_3)* -> .
% 6.25/6.49 105[1:MRR:102.0,2.0] || -> .
% 6.25/6.49 106[1:Spt:105.0,91.3,96.0] || product(e_2,e_1,e_4)*+ -> .
% 6.25/6.49 107[1:Spt:105.0,91.0,91.1,91.2] || greater(e_3,u)+ next(e_2,u)* -> product(e_2,e_1,e_5)*.
% 6.25/6.49 108[1:MRR:90.1,106.0] || -> product(e_2,e_1,e_5) product(e_2,e_1,e_3)*.
% 6.25/6.49 111[1:MRR:95.2,106.0] || product(u,e_1,e_3)* -> product(e_2,e_1,e_5)* equalish(u,e_2).
% 6.25/6.49 112[1:MRR:92.2,106.0] || product(e_1,e_2,u)* -> product(e_2,e_1,e_5) product(u,e_3,e_1)*.
% 6.25/6.49 115[0:Res:45.0,72.2] group_element(e_1) group_element(u) || -> product(u,e_1,e_5) product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 6.25/6.49 117[0:SSi:115.0,16.0] group_element(u) || -> product(u,e_1,e_5) product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 6.25/6.49 119[2:Spt:108.0] || -> product(e_2,e_1,e_5)*.
% 6.25/6.49 120[2:Res:119.0,15.2] || greater(e_5,u)+ next(e_2,u)* -> .
% 6.25/6.49 126[2:Res:13.0,120.0] || next(e_2,e_3)* -> .
% 6.25/6.49 129[2:MRR:126.0,2.0] || -> .
% 6.25/6.49 130[2:Spt:129.0,108.0,119.0] || product(e_2,e_1,e_5)*+ -> .
% 6.25/6.49 131[2:Spt:129.0,108.1] || -> product(e_2,e_1,e_3)*.
% 6.25/6.49 137[2:MRR:111.1,130.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 6.25/6.49 138[2:MRR:112.1,130.0] || product(e_1,e_2,u)*+ -> product(u,e_3,e_1)*.
% 6.25/6.49 151[0:Res:45.0,71.2] group_element(u) group_element(e_1) || -> product(e_1,u,e_5) product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 6.25/6.49 153[0:SSi:151.1,16.0] group_element(u) || -> product(e_1,u,e_5) product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 6.25/6.49 155[2:Res:41.6,138.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_5) product(e_1,e_2,e_4) product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_1,e_3,e_1).
% 6.25/6.49 156[2:SSi:155.1,155.0,16.0,17.0] || -> product(e_1,e_2,e_5) product(e_1,e_2,e_4) product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_1,e_3,e_1).
% 6.25/6.49 162[2:Res:156.3,57.0] || -> product(e_1,e_2,e_5) product(e_1,e_2,e_4) product(e_1,e_2,e_3)* product(e_1,e_3,e_1) equalish(e_1,e_2).
% 6.25/6.49 163[2:MRR:162.4,21.0] || -> product(e_1,e_2,e_5) product(e_1,e_2,e_4) product(e_1,e_2,e_3)* product(e_1,e_3,e_1).
% 6.25/6.49 164[2:Res:163.2,138.0] || -> product(e_1,e_2,e_5) product(e_1,e_2,e_4)* product(e_1,e_3,e_1) product(e_3,e_3,e_1).
% 6.25/6.49 169[3:Spt:164.0] || -> product(e_1,e_2,e_5)*.
% 6.25/6.49 171[3:Res:169.0,46.0] || product(e_2,e_1,u)*+ -> product(u,e_5,e_2)*.
% 6.25/6.49 173[3:Res:169.0,43.0] || product(e_1,u,e_5)*+ -> equalish(u,e_2).
% 6.25/6.49 197[0:Res:41.6,69.2] group_element(u) group_element(v) group_element(v) group_element(u) || -> product(v,u,e_5) product(v,u,e_4) product(v,u,e_3) product(v,u,e_2)* product(u,v,e_5) product(u,v,e_4) product(u,v,e_3) product(u,v,e_2)* product(e_1,e_1,v)*.
% 6.25/6.49 205[0:Obv:197.1] group_element(u) group_element(v) || -> product(u,v,e_5) product(u,v,e_4) product(u,v,e_3) product(u,v,e_2)* product(v,u,e_5) product(v,u,e_4) product(v,u,e_3) product(v,u,e_2)* product(e_1,e_1,u)*.
% 6.25/6.49 216[3:Res:131.0,171.0] || -> product(e_3,e_5,e_2)*.
% 6.25/6.49 236[3:Res:216.0,43.0] || product(e_3,u,e_2)*+ -> equalish(u,e_5).
% 6.25/6.49 237[3:Res:216.0,44.0] || product(u,e_5,e_2)*+ -> equalish(u,e_3).
% 6.25/6.49 240[3:Res:74.4,236.0] group_element(e_3) || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4) product(e_3,e_1,e_3)* equalish(e_3,e_1) equalish(e_1,e_5).
% 6.25/6.49 242[3:SSi:240.0,18.0] || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4) product(e_3,e_1,e_3)* equalish(e_3,e_1) equalish(e_1,e_5).
% 6.25/6.49 243[3:MRR:242.3,242.4,29.0,24.0] || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4) product(e_3,e_1,e_3)*.
% 6.25/6.49 244[3:Res:75.4,237.0] group_element(e_5) || -> product(e_1,e_5,e_5) product(e_1,e_5,e_4) product(e_1,e_5,e_3)* equalish(e_5,e_1) equalish(e_1,e_3).
% 6.25/6.49 246[3:SSi:244.0,20.0] || -> product(e_1,e_5,e_5) product(e_1,e_5,e_4) product(e_1,e_5,e_3)* equalish(e_5,e_1) equalish(e_1,e_3).
% 6.25/6.49 247[3:MRR:246.3,246.4,37.0,22.0] || -> product(e_1,e_5,e_5) product(e_1,e_5,e_4) product(e_1,e_5,e_3)*.
% 6.25/6.49 259[0:Res:117.4,44.0] group_element(u) || product(v,e_1,e_2)*+ -> product(u,e_1,e_5) product(u,e_1,e_4) product(u,e_1,e_3)* equalish(e_1,u) equalish(v,u)*.
% 6.25/6.49 270[3:Res:243.2,59.0] || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4)* equalish(e_1,e_3).
% 6.25/6.49 278[3:MRR:270.2,22.0] || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4)*.
% 6.25/6.49 283[3:Res:278.1,46.0] || product(e_1,e_3,u)* -> product(e_3,e_1,e_5) product(u,e_4,e_1)*.
% 6.25/6.49 284[3:Res:278.1,42.0] || product(e_3,e_1,u)*+ -> product(e_3,e_1,e_5)* equalish(u,e_4).
% 6.25/6.49 286[3:Res:278.1,44.0] || product(u,e_1,e_4)* -> product(e_3,e_1,e_5)* equalish(u,e_3).
% 6.25/6.49 297[0:Res:153.4,46.0] group_element(u) || product(u,e_1,v)*+ -> product(e_1,u,e_5) product(e_1,u,e_4) product(e_1,u,e_3)* equalish(e_1,u) product(v,e_2,u)*.
% 6.25/6.49 309[3:Res:247.2,42.0] || product(e_1,e_5,u)*+ -> product(e_1,e_5,e_5) product(e_1,e_5,e_4)* equalish(u,e_3).
% 6.25/6.49 310[3:Res:247.2,43.0] || product(e_1,u,e_3)*+ -> product(e_1,e_5,e_5) product(e_1,e_5,e_4)* equalish(u,e_5).
% 6.25/6.49 333[4:Spt:284.1] || -> product(e_3,e_1,e_5)*.
% 6.25/6.49 335[4:Res:333.0,15.2] || greater(e_5,u)+ next(e_3,u)* -> .
% 6.25/6.49 342[4:Res:14.0,335.0] || next(e_3,e_4)* -> .
% 6.25/6.49 346[4:MRR:342.0,3.0] || -> .
% 6.25/6.49 347[4:Spt:346.0,284.1,333.0] || product(e_3,e_1,e_5)*+ -> .
% 6.25/6.49 348[4:Spt:346.0,284.0,284.2] || product(e_3,e_1,u)*+ -> equalish(u,e_4).
% 6.25/6.49 355[4:MRR:286.1,347.0] || product(u,e_1,e_4)*+ -> equalish(u,e_3).
% 6.25/6.49 356[4:MRR:283.1,347.0] || product(e_1,e_3,u)*+ -> product(u,e_4,e_1)*.
% 6.25/6.49 390[4:Res:41.6,356.0] group_element(e_3) group_element(e_1) || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_1,e_4,e_1).
% 6.25/6.49 392[4:Res:75.4,356.0] group_element(e_3) || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_3,e_1) product(e_2,e_4,e_1).
% 6.25/6.49 393[4:SSi:392.0,18.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_3,e_1) product(e_2,e_4,e_1).
% 6.25/6.49 394[4:MRR:393.3,29.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3)* product(e_2,e_4,e_1).
% 6.25/6.49 395[4:SSi:390.1,390.0,16.0,18.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_1,e_4,e_1).
% 6.25/6.49 396[5:Spt:394.0] || -> product(e_1,e_3,e_5)*.
% 6.25/6.49 398[5:Res:396.0,173.0] || -> equalish(e_3,e_2)*.
% 6.25/6.49 405[5:MRR:398.0,30.0] || -> .
% 6.25/6.49 406[5:Spt:405.0,394.0,396.0] || product(e_1,e_3,e_5)*+ -> .
% 6.25/6.49 407[5:Spt:405.0,394.1,394.2,394.3] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)* product(e_2,e_4,e_1).
% 6.25/6.49 408[5:MRR:395.0,406.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_1,e_4,e_1).
% 6.25/6.49 410[6:Spt:407.0] || -> product(e_1,e_3,e_4)*.
% 6.25/6.49 417[6:Res:410.0,356.0] || -> product(e_4,e_4,e_1)*.
% 6.25/6.49 418[6:Res:417.0,61.0] || -> equalish(e_1,e_4)*.
% 6.25/6.49 429[6:MRR:418.0,23.0] || -> .
% 6.25/6.49 434[6:Spt:429.0,407.0,410.0] || product(e_1,e_3,e_4)*+ -> .
% 6.25/6.49 435[6:Spt:429.0,407.1,407.2] || -> product(e_1,e_3,e_3)* product(e_2,e_4,e_1).
% 6.25/6.49 436[6:MRR:408.0,434.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_1,e_4,e_1).
% 6.25/6.49 438[7:Spt:435.0] || -> product(e_1,e_3,e_3)*.
% 6.25/6.49 445[7:Res:438.0,57.0] || -> equalish(e_1,e_3)*.
% 6.25/6.49 447[7:MRR:445.0,22.0] || -> .
% 6.25/6.49 448[7:Spt:447.0,435.0,438.0] || product(e_1,e_3,e_3)*+ -> .
% 6.25/6.49 449[7:Spt:447.0,435.1] || -> product(e_2,e_4,e_1)*.
% 6.25/6.49 450[7:MRR:436.0,448.0] || -> product(e_1,e_3,e_2)* product(e_1,e_4,e_1).
% 6.25/6.49 456[7:Res:449.0,42.0] || product(e_2,e_4,u)*+ -> equalish(u,e_1).
% 6.25/6.49 458[7:Res:449.0,44.0] || product(u,e_4,e_1)*+ -> equalish(u,e_2).
% 6.25/6.49 466[7:Res:450.0,42.0] || product(e_1,e_3,u)*+ -> product(e_1,e_4,e_1) equalish(u,e_2).
% 6.25/6.49 555[8:Spt:466.0,466.2] || product(e_1,e_3,u)*+ -> equalish(u,e_2).
% 6.25/6.49 556[8:Res:41.6,555.0] group_element(e_3) group_element(e_1) || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* equalish(e_1,e_2).
% 6.25/6.49 562[8:SSi:556.1,556.0,16.0,18.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* equalish(e_1,e_2).
% 6.25/6.49 563[8:MRR:562.0,562.1,562.2,562.4,406.0,434.0,448.0,21.0] || -> product(e_1,e_3,e_2)*.
% 6.25/6.49 568[8:Res:563.0,43.0] || product(e_1,u,e_2)*+ -> equalish(u,e_3).
% 6.25/6.49 573[8:Res:75.4,568.0] group_element(u) || -> product(e_1,u,e_5) product(e_1,u,e_4) product(e_1,u,e_3)* equalish(u,e_1) equalish(u,e_3).
% 6.25/6.49 601[0:Res:205.9,57.0] group_element(e_2) group_element(u) || -> product(e_2,u,e_5) product(e_2,u,e_4) product(e_2,u,e_3) product(e_2,u,e_2)* product(u,e_2,e_5) product(u,e_2,e_4) product(u,e_2,e_3)* product(e_1,e_1,e_2)* equalish(u,e_2).
% 6.25/6.49 630[0:SSi:601.0,17.0] group_element(u) || -> product(e_2,u,e_5) product(e_2,u,e_4) product(e_2,u,e_3) product(e_2,u,e_2)* product(u,e_2,e_5) product(u,e_2,e_4) product(u,e_2,e_3)* product(e_1,e_1,e_2)* equalish(u,e_2).
% 6.25/6.49 631[0:MRR:630.4,59.0] group_element(u) || -> product(e_2,u,e_5) product(e_2,u,e_4) product(e_2,u,e_3)* product(u,e_2,e_5) product(u,e_2,e_4) product(u,e_2,e_3)* product(e_1,e_1,e_2)* equalish(u,e_2).
% 6.25/6.49 763[9:Spt:309.0,309.3] || product(e_1,e_5,u)*+ -> equalish(u,e_3).
% 6.25/6.49 863[10:Spt:310.0,310.3] || product(e_1,u,e_3)*+ -> equalish(u,e_5).
% 6.25/6.49 2149[10:Res:573.3,863.0] group_element(u) || -> product(e_1,u,e_5) product(e_1,u,e_4)* equalish(u,e_1) equalish(u,e_3) equalish(u,e_5).
% 6.25/6.49 2181[10:Res:2149.2,57.0] group_element(e_4) || -> product(e_1,e_4,e_5)* equalish(e_4,e_1) equalish(e_4,e_3) equalish(e_4,e_5) equalish(e_1,e_4).
% 6.25/6.49 2189[10:SSi:2181.0,19.0] || -> product(e_1,e_4,e_5)* equalish(e_4,e_1) equalish(e_4,e_3) equalish(e_4,e_5) equalish(e_1,e_4).
% 6.25/6.49 2190[10:MRR:2189.1,2189.2,2189.3,2189.4,33.0,35.0,36.0,23.0] || -> product(e_1,e_4,e_5)*.
% 6.25/6.49 2195[10:Res:2190.0,173.0] || -> equalish(e_4,e_2)*.
% 6.25/6.49 2201[10:MRR:2195.0,34.0] || -> .
% 6.25/6.49 2203[10:Spt:2201.0,310.1,310.2] || -> product(e_1,e_5,e_5) product(e_1,e_5,e_4)*.
% 6.25/6.49 2215[10:Res:2203.1,763.0] || -> product(e_1,e_5,e_5)* equalish(e_4,e_3).
% 6.25/6.49 2216[10:MRR:2215.1,35.0] || -> product(e_1,e_5,e_5)*.
% 6.25/6.49 2262[10:Res:2216.0,763.0] || -> equalish(e_5,e_3)*.
% 6.25/6.49 2265[10:MRR:2262.0,39.0] || -> .
% 6.25/6.49 2269[9:Spt:2265.0,309.1,309.2] || -> product(e_1,e_5,e_5) product(e_1,e_5,e_4)*.
% 6.25/6.49 2272[9:Res:2269.1,46.0] || product(e_5,e_1,u)*+ -> product(e_1,e_5,e_5)* product(u,e_4,e_5)*.
% 6.25/6.49 2273[9:Res:2269.1,42.0] || product(e_1,e_5,u)*+ -> product(e_1,e_5,e_5)* equalish(u,e_4).
% 6.25/6.49 2278[10:Spt:2273.0,2273.2] || product(e_1,e_5,u)*+ -> equalish(u,e_4).
% 6.25/6.49 2344[11:Spt:2272.1] || -> product(e_1,e_5,e_5)*.
% 6.25/6.49 2353[11:Res:2344.0,2278.0] || -> equalish(e_5,e_4)*.
% 6.25/6.49 2356[11:MRR:2353.0,40.0] || -> .
% 6.25/6.49 2360[11:Spt:2356.0,2272.1,2344.0] || product(e_1,e_5,e_5)*+ -> .
% 6.25/6.49 2361[11:Spt:2356.0,2272.0,2272.2] || product(e_5,e_1,u)*+ -> product(u,e_4,e_5)*.
% 6.25/6.49 2371[11:Res:74.4,2361.0] group_element(e_5) || -> product(e_5,e_1,e_5) product(e_5,e_1,e_4) product(e_5,e_1,e_3) equalish(e_5,e_1) product(e_2,e_4,e_5)*.
% 6.25/6.49 2376[11:SSi:2371.0,20.0] || -> product(e_5,e_1,e_5) product(e_5,e_1,e_4) product(e_5,e_1,e_3) equalish(e_5,e_1) product(e_2,e_4,e_5)*.
% 6.25/6.49 2377[11:MRR:2376.3,37.0] || -> product(e_5,e_1,e_5) product(e_5,e_1,e_4) product(e_5,e_1,e_3) product(e_2,e_4,e_5)*.
% 6.25/6.49 2392[12:Spt:2377.0] || -> product(e_5,e_1,e_5)*.
% 6.25/6.49 2394[12:Res:2392.0,59.0] || -> equalish(e_1,e_5)*.
% 6.25/6.49 2402[12:MRR:2394.0,24.0] || -> .
% 6.25/6.49 2403[12:Spt:2402.0,2377.0,2392.0] || product(e_5,e_1,e_5)* -> .
% 6.25/6.49 2404[12:Spt:2402.0,2377.1,2377.2,2377.3] || -> product(e_5,e_1,e_4) product(e_5,e_1,e_3) product(e_2,e_4,e_5)*.
% 6.25/6.49 2407[13:Spt:2404.0] || -> product(e_5,e_1,e_4)*.
% 6.25/6.49 2415[13:Res:2407.0,355.0] || -> equalish(e_5,e_3)*.
% 6.25/6.49 2417[13:MRR:2415.0,39.0] || -> .
% 6.25/6.49 2418[13:Spt:2417.0,2404.0,2407.0] || product(e_5,e_1,e_4)* -> .
% 6.25/6.49 2419[13:Spt:2417.0,2404.1,2404.2] || -> product(e_5,e_1,e_3) product(e_2,e_4,e_5)*.
% 6.25/6.49 2422[14:Spt:2419.0] || -> product(e_5,e_1,e_3)*.
% 6.25/6.49 2430[14:Res:2422.0,137.0] || -> equalish(e_5,e_2)*.
% 6.25/6.49 2432[14:MRR:2430.0,38.0] || -> .
% 6.25/6.49 2433[14:Spt:2432.0,2419.0,2422.0] || product(e_5,e_1,e_3)* -> .
% 6.25/6.49 2434[14:Spt:2432.0,2419.1] || -> product(e_2,e_4,e_5)*.
% 6.25/6.49 2439[14:Res:2434.0,456.0] || -> equalish(e_5,e_1)*.
% 6.25/6.49 2445[14:MRR:2439.0,37.0] || -> .
% 6.25/6.49 2448[10:Spt:2445.0,2273.1] || -> product(e_1,e_5,e_5)*.
% 6.25/6.49 2456[10:Res:2448.0,57.0] || -> equalish(e_1,e_5)*.
% 6.25/6.49 2458[10:MRR:2456.0,24.0] || -> .
% 6.25/6.49 2462[8:Spt:2458.0,466.1] || -> product(e_1,e_4,e_1)*.
% 6.25/6.49 2480[8:Res:2462.0,458.0] || -> equalish(e_1,e_2)*.
% 6.25/6.49 2483[8:MRR:2480.0,21.0] || -> .
% 6.25/6.49 2486[3:Spt:2483.0,164.0,169.0] || product(e_1,e_2,e_5)*+ -> .
% 6.25/6.49 2487[3:Spt:2483.0,164.1,164.2,164.3] || -> product(e_1,e_2,e_4)* product(e_1,e_3,e_1) product(e_3,e_3,e_1).
% 6.25/6.49 2514[4:Spt:2487.0] || -> product(e_1,e_2,e_4)*.
% 6.25/6.49 2518[4:Res:2514.0,46.0] || product(e_2,e_1,u)*+ -> product(u,e_4,e_2)*.
% 6.25/6.49 2520[4:Res:2514.0,43.0] || product(e_1,u,e_4)*+ -> equalish(u,e_2).
% 6.25/6.49 2684[4:Res:131.0,2518.0] || -> product(e_3,e_4,e_2)*.
% 6.25/6.49 2774[4:Res:2684.0,44.0] || product(u,e_4,e_2)*+ -> equalish(u,e_3).
% 6.25/6.49 2775[4:Res:2684.0,87.1] group_element(e_3) || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4) product(e_3,e_1,e_3)* equalish(e_3,e_1) equalish(e_4,e_1).
% 6.25/6.49 2776[4:SSi:2775.0,18.0] || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4) product(e_3,e_1,e_3)* equalish(e_3,e_1) equalish(e_4,e_1).
% 6.25/6.49 2777[4:MRR:2776.3,2776.4,29.0,33.0] || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4) product(e_3,e_1,e_3)*.
% 6.25/6.49 2806[4:Res:75.4,2774.0] group_element(e_4) || -> product(e_1,e_4,e_5) product(e_1,e_4,e_4) product(e_1,e_4,e_3)* equalish(e_4,e_1) equalish(e_1,e_3).
% 6.25/6.49 2821[4:SSi:2806.0,19.0] || -> product(e_1,e_4,e_5) product(e_1,e_4,e_4) product(e_1,e_4,e_3)* equalish(e_4,e_1) equalish(e_1,e_3).
% 6.25/6.49 2822[4:MRR:2821.3,2821.4,33.0,22.0] || -> product(e_1,e_4,e_5) product(e_1,e_4,e_4) product(e_1,e_4,e_3)*.
% 6.25/6.49 2851[4:Res:2777.2,59.0] || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4)* equalish(e_1,e_3).
% 6.25/6.49 2860[4:MRR:2851.2,22.0] || -> product(e_3,e_1,e_5) product(e_3,e_1,e_4)*.
% 6.25/6.49 2865[4:Res:2860.1,69.2] group_element(e_3) group_element(e_1) || -> product(e_3,e_1,e_5) product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_4,e_1,e_3).
% 6.25/6.49 2866[4:Res:2860.1,46.0] || product(e_1,e_3,u)*+ -> product(e_3,e_1,e_5) product(u,e_4,e_1)*.
% 6.25/6.49 2867[4:Res:2860.1,42.0] || product(e_3,e_1,u)*+ -> product(e_3,e_1,e_5)* equalish(u,e_4).
% 6.25/6.49 2868[4:Res:2860.1,43.0] || product(e_3,u,e_4)*+ -> product(e_3,e_1,e_5)* equalish(u,e_1).
% 6.25/6.49 2869[4:Res:2860.1,44.0] || product(u,e_1,e_4)*+ -> product(e_3,e_1,e_5)* equalish(u,e_3).
% 6.25/6.49 2873[4:SSi:2865.1,2865.0,16.0,18.0] || -> product(e_3,e_1,e_5) product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_4,e_1,e_3).
% 6.25/6.49 2962[4:Res:2822.2,46.0] || product(e_4,e_1,u)*+ -> product(e_1,e_4,e_5) product(e_1,e_4,e_4)* product(u,e_3,e_4)*.
% 6.25/6.49 2963[4:Res:2822.2,42.0] || product(e_1,e_4,u)*+ -> product(e_1,e_4,e_5) product(e_1,e_4,e_4)* equalish(u,e_3).
% 6.25/6.49 2964[4:Res:2822.2,43.0] || product(e_1,u,e_3)*+ -> product(e_1,e_4,e_5) product(e_1,e_4,e_4)* equalish(u,e_4).
% 6.25/6.49 2999[5:Spt:2867.0,2867.2] || product(e_3,e_1,u)*+ -> equalish(u,e_4).
% 6.25/6.49 3011[6:Spt:2868.0,2868.2] || product(e_3,u,e_4)*+ -> equalish(u,e_1).
% 6.25/6.49 3016[7:Spt:2869.0,2869.2] || product(u,e_1,e_4)*+ -> equalish(u,e_3).
% 6.25/6.49 3111[8:Spt:2866.1] || -> product(e_3,e_1,e_5)*.
% 6.25/6.49 3120[8:Res:3111.0,2999.0] || -> equalish(e_5,e_4)*.
% 6.25/6.49 3121[8:MRR:3120.0,40.0] || -> .
% 6.25/6.49 3123[8:Spt:3121.0,2866.1,3111.0] || product(e_3,e_1,e_5)*+ -> .
% 6.25/6.49 3124[8:Spt:3121.0,2866.0,2866.2] || product(e_1,e_3,u)*+ -> product(u,e_4,e_1)*.
% 6.25/6.49 3125[8:MRR:2860.0,3123.0] || -> product(e_3,e_1,e_4)*.
% 6.25/6.49 3130[8:MRR:2873.0,3123.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_4,e_1,e_3).
% 6.25/6.49 3133[8:Res:75.4,3124.0] group_element(e_3) || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_3,e_1) product(e_2,e_4,e_1).
% 6.25/6.49 3142[8:SSi:3133.0,18.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_3,e_1) product(e_2,e_4,e_1).
% 6.25/6.49 3143[8:MRR:3142.3,29.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3)* product(e_2,e_4,e_1).
% 6.25/6.49 3159[9:Spt:3143.0] || -> product(e_1,e_3,e_5)*.
% 6.25/6.49 3162[9:Res:3159.0,46.0] || product(e_3,e_1,u)*+ -> product(u,e_5,e_3)*.
% 6.25/6.49 3163[9:Res:3159.0,42.0] || product(e_1,e_3,u)*+ -> equalish(u,e_5).
% 6.25/6.49 3164[9:Res:3159.0,43.0] || product(e_1,u,e_5)*+ -> equalish(u,e_3).
% 6.25/6.49 3165[9:Res:3159.0,44.0] || product(u,e_3,e_5)*+ -> equalish(u,e_1).
% 6.25/6.49 3386[9:Res:3125.0,3162.0] || -> product(e_4,e_5,e_3)*.
% 6.25/6.49 3391[9:Res:3386.0,43.0] || product(e_4,u,e_3)*+ -> equalish(u,e_5).
% 6.25/6.49 3537[10:Spt:2963.0,2963.3] || product(e_1,e_4,u)*+ -> equalish(u,e_3).
% 6.25/6.49 3672[11:Spt:2962.2] || -> product(e_1,e_4,e_4)*.
% 6.25/6.49 3682[11:Res:3672.0,3537.0] || -> equalish(e_4,e_3)*.
% 6.25/6.49 3685[11:MRR:3682.0,35.0] || -> .
% 6.25/6.49 3689[11:Spt:3685.0,2962.2,3672.0] || product(e_1,e_4,e_4)*+ -> .
% 6.25/6.49 3690[11:Spt:3685.0,2962.0,2962.1,2962.3] || product(e_4,e_1,u)*+ -> product(e_1,e_4,e_5)* product(u,e_3,e_4)*.
% 6.25/6.49 3693[12:Spt:3690.0,3690.2] || product(e_4,e_1,u)*+ -> product(u,e_3,e_4)*.
% 6.25/6.49 3694[12:Res:41.6,3693.0] group_element(e_1) group_element(e_4) || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) product(e_4,e_1,e_2) product(e_1,e_3,e_4)*.
% 6.25/6.49 3703[12:Res:74.4,3693.0] group_element(e_4) || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) equalish(e_4,e_1) product(e_2,e_3,e_4)*.
% 6.25/6.49 3708[12:SSi:3703.0,19.0] || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) equalish(e_4,e_1) product(e_2,e_3,e_4)*.
% 6.25/6.49 3709[12:MRR:3708.3,33.0] || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) product(e_2,e_3,e_4)*.
% 6.25/6.49 3710[12:SSi:3694.1,3694.0,19.0,16.0] || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) product(e_4,e_1,e_2) product(e_1,e_3,e_4)*.
% 6.25/6.49 3727[13:Spt:3709.0] || -> product(e_4,e_1,e_5)*.
% 6.25/6.49 3737[13:Res:3727.0,3693.0] || -> product(e_5,e_3,e_4)*.
% 6.25/6.49 3777[13:Res:3737.0,44.0] || product(u,e_3,e_4)*+ -> equalish(u,e_5).
% 6.25/6.49 6197[8:Res:3125.0,297.1] group_element(e_3) || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_1,e_3) product(e_4,e_2,e_3).
% 6.25/6.49 15968[14:Spt:631.0,631.1,631.2,631.3,631.4,631.5,631.6,631.8] group_element(u) || -> product(e_2,u,e_5) product(e_2,u,e_4) product(e_2,u,e_3)* product(u,e_2,e_5) product(u,e_2,e_4) product(u,e_2,e_3)* equalish(u,e_2).
% 6.25/6.49 15978[14:Res:15968.3,57.0] group_element(e_3) || -> product(e_2,e_3,e_5) product(e_2,e_3,e_4)* product(e_3,e_2,e_5) product(e_3,e_2,e_4) product(e_3,e_2,e_3) equalish(e_3,e_2) equalish(e_2,e_3).
% 6.25/6.49 16002[14:SSi:15978.0,18.0] || -> product(e_2,e_3,e_5) product(e_2,e_3,e_4)* product(e_3,e_2,e_5) product(e_3,e_2,e_4) product(e_3,e_2,e_3) equalish(e_3,e_2) equalish(e_2,e_3).
% 6.25/6.49 16003[14:MRR:16002.4,16002.5,16002.6,59.0,30.0,26.0] || -> product(e_2,e_3,e_5) product(e_2,e_3,e_4)* product(e_3,e_2,e_5) product(e_3,e_2,e_4).
% 6.25/6.49 16494[15:Spt:16003.0] || -> product(e_2,e_3,e_5)*.
% 6.25/6.49 16502[15:Res:16494.0,3165.0] || -> equalish(e_2,e_1)*.
% 6.25/6.49 16504[15:MRR:16502.0,25.0] || -> .
% 6.25/6.49 16506[15:Spt:16504.0,16003.0,16494.0] || product(e_2,e_3,e_5)*+ -> .
% 6.25/6.49 16507[15:Spt:16504.0,16003.1,16003.2,16003.3] || -> product(e_2,e_3,e_4)* product(e_3,e_2,e_5) product(e_3,e_2,e_4).
% 6.25/6.49 16508[16:Spt:16507.0] || -> product(e_2,e_3,e_4)*.
% 6.25/6.49 16515[16:Res:16508.0,3777.0] || -> equalish(e_2,e_5)*.
% 6.25/6.49 16516[16:MRR:16515.0,28.0] || -> .
% 6.25/6.49 16518[16:Spt:16516.0,16507.0,16508.0] || product(e_2,e_3,e_4)*+ -> .
% 6.25/6.49 16519[16:Spt:16516.0,16507.1,16507.2] || -> product(e_3,e_2,e_5) product(e_3,e_2,e_4)*.
% 6.25/6.49 16521[16:Res:16519.1,3011.0] || -> product(e_3,e_2,e_5)* equalish(e_2,e_1).
% 6.25/6.49 16528[16:MRR:16521.1,25.0] || -> product(e_3,e_2,e_5)*.
% 6.25/6.49 16531[16:Res:16528.0,69.2] group_element(e_3) group_element(e_2) || -> product(e_2,e_3,e_5) product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2)* product(e_5,e_1,e_3).
% 6.25/6.49 16536[16:SSi:16531.1,16531.0,17.0,18.0] || -> product(e_2,e_3,e_5) product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2)* product(e_5,e_1,e_3).
% 6.25/6.49 16537[16:MRR:16536.0,16536.1,16506.0,16518.0] || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2)* product(e_5,e_1,e_3).
% 6.25/6.49 16957[17:Spt:16537.0] || -> product(e_2,e_3,e_3)*.
% 6.25/6.49 16966[17:Res:16957.0,57.0] || -> equalish(e_2,e_3)*.
% 6.25/6.49 16969[17:MRR:16966.0,26.0] || -> .
% 6.25/6.49 16971[17:Spt:16969.0,16537.0,16957.0] || product(e_2,e_3,e_3)* -> .
% 6.25/6.49 16972[17:Spt:16969.0,16537.1,16537.2] || -> product(e_2,e_3,e_2)* product(e_5,e_1,e_3).
% 6.25/6.49 16986[17:Res:16972.0,59.0] || -> product(e_5,e_1,e_3)* equalish(e_3,e_2).
% 6.25/6.49 16999[17:MRR:16986.1,30.0] || -> product(e_5,e_1,e_3)*.
% 6.25/6.49 17007[17:Res:16999.0,137.0] || -> equalish(e_5,e_2)*.
% 6.25/6.49 17015[17:MRR:17007.0,38.0] || -> .
% 6.25/6.49 17022[14:Spt:17015.0,631.7] || -> product(e_1,e_1,e_2)*.
% 6.25/6.49 17051[14:Res:17022.0,61.0] || -> equalish(e_2,e_1)*.
% 6.25/6.49 17091[14:MRR:17051.0,25.0] || -> .
% 6.25/6.49 17107[13:Spt:17091.0,3709.0,3727.0] || product(e_4,e_1,e_5)*+ -> .
% 6.25/6.49 17108[13:Spt:17091.0,3709.1,3709.2,3709.3] || -> product(e_4,e_1,e_4) product(e_4,e_1,e_3) product(e_2,e_3,e_4)*.
% 6.25/6.49 17109[13:MRR:3710.0,17107.0] || -> product(e_4,e_1,e_4) product(e_4,e_1,e_3) product(e_4,e_1,e_2) product(e_1,e_3,e_4)*.
% 6.25/6.49 17138[14:Spt:17108.0] || -> product(e_4,e_1,e_4)*.
% 6.25/6.49 17148[14:Res:17138.0,3016.0] || -> equalish(e_4,e_3)*.
% 6.25/6.49 17154[14:MRR:17148.0,35.0] || -> .
% 6.25/6.49 17160[14:Spt:17154.0,17108.0,17138.0] || product(e_4,e_1,e_4)*+ -> .
% 6.25/6.49 17161[14:Spt:17154.0,17108.1,17108.2] || -> product(e_4,e_1,e_3) product(e_2,e_3,e_4)*.
% 6.25/6.49 17162[14:MRR:17109.0,17160.0] || -> product(e_4,e_1,e_3) product(e_4,e_1,e_2) product(e_1,e_3,e_4)*.
% 6.25/6.49 17164[15:Spt:17161.0] || -> product(e_4,e_1,e_3)*.
% 6.25/6.49 17176[15:Res:17164.0,3391.0] || -> equalish(e_1,e_5)*.
% 6.25/6.49 17179[15:MRR:17176.0,24.0] || -> .
% 6.25/6.49 17184[15:Spt:17179.0,17161.0,17164.0] || product(e_4,e_1,e_3)*+ -> .
% 6.25/6.49 17185[15:Spt:17179.0,17161.1] || -> product(e_2,e_3,e_4)*.
% 6.25/6.49 17186[15:MRR:17162.0,17184.0] || -> product(e_4,e_1,e_2) product(e_1,e_3,e_4)*.
% 6.25/6.49 17216[16:Spt:17186.0] || -> product(e_4,e_1,e_2)*.
% 6.25/6.49 17227[16:Res:17216.0,44.0] || product(u,e_1,e_2)*+ -> equalish(u,e_4).
% 6.25/6.49 17521[16:Res:117.4,17227.0] group_element(u) || -> product(u,e_1,e_5) product(u,e_1,e_4) product(u,e_1,e_3)* equalish(e_1,u) equalish(u,e_4).
% 6.25/6.49 17974[16:Res:17521.3,137.0] group_element(u) || -> product(u,e_1,e_5) product(u,e_1,e_4)* equalish(e_1,u) equalish(u,e_4) equalish(u,e_2).
% 6.25/6.49 18030[16:Res:17974.2,3016.0] group_element(u) || -> product(u,e_1,e_5)* equalish(e_1,u) equalish(u,e_4) equalish(u,e_2) equalish(u,e_3).
% 6.25/6.49 18079[16:Res:18030.1,59.0] group_element(e_5) || -> equalish(e_1,e_5)* equalish(e_5,e_4) equalish(e_5,e_2) equalish(e_5,e_3) equalish(e_1,e_5)*.
% 6.25/6.49 18102[16:Obv:18079.1] group_element(e_5) || -> equalish(e_5,e_4) equalish(e_5,e_2) equalish(e_5,e_3) equalish(e_1,e_5)*.
% 6.25/6.49 18103[16:SSi:18102.0,20.0] || -> equalish(e_5,e_4) equalish(e_5,e_2) equalish(e_5,e_3) equalish(e_1,e_5)*.
% 6.25/6.49 18104[16:MRR:18103.0,18103.1,18103.2,18103.3,40.0,38.0,39.0,24.0] || -> .
% 6.25/6.49 18120[16:Spt:18104.0,17186.0,17216.0] || product(e_4,e_1,e_2)* -> .
% 6.25/6.49 18121[16:Spt:18104.0,17186.1] || -> product(e_1,e_3,e_4)*.
% 6.25/6.49 18134[16:Res:18121.0,3163.0] || -> equalish(e_4,e_5)*.
% 6.25/6.49 18141[16:MRR:18134.0,36.0] || -> .
% 6.25/6.49 18147[12:Spt:18141.0,3690.1] || -> product(e_1,e_4,e_5)*.
% 6.25/6.49 18158[12:Res:18147.0,3537.0] || -> equalish(e_5,e_3)*.
% 6.25/6.49 18160[12:MRR:18158.0,39.0] || -> .
% 6.25/6.49 18171[10:Spt:18160.0,2963.1,2963.2] || -> product(e_1,e_4,e_5) product(e_1,e_4,e_4)*.
% 6.25/6.49 18187[10:Res:18171.1,2520.0] || -> product(e_1,e_4,e_5)* equalish(e_4,e_2).
% 6.25/6.49 18197[10:MRR:18187.1,34.0] || -> product(e_1,e_4,e_5)*.
% 6.25/6.49 18200[10:Res:18197.0,3164.0] || -> equalish(e_4,e_3)*.
% 6.25/6.49 18209[10:MRR:18200.0,35.0] || -> .
% 6.25/6.49 18220[9:Spt:18209.0,3143.0,3159.0] || product(e_1,e_3,e_5)*+ -> .
% 6.25/6.49 18221[9:Spt:18209.0,3143.1,3143.2,3143.3] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)* product(e_2,e_4,e_1).
% 6.25/6.49 18223[9:MRR:3130.0,18220.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_4,e_1,e_3).
% 6.25/6.49 18224[8:SSi:6197.0,18.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_1,e_3) product(e_4,e_2,e_3).
% 6.25/6.49 18225[8:MRR:18224.2,18224.3,57.0,22.0] || -> product(e_1,e_3,e_5) product(e_1,e_3,e_4)* product(e_4,e_2,e_3).
% 6.25/6.49 18226[9:MRR:18225.0,18220.0] || -> product(e_1,e_3,e_4)* product(e_4,e_2,e_3).
% 6.25/6.49 18261[10:Spt:18221.0] || -> product(e_1,e_3,e_4)*.
% 6.25/6.49 18263[10:Res:18261.0,2520.0] || -> equalish(e_3,e_2)*.
% 6.25/6.49 18273[10:MRR:18263.0,30.0] || -> .
% 6.25/6.49 18279[10:Spt:18273.0,18221.0,18261.0] || product(e_1,e_3,e_4)*+ -> .
% 6.25/6.49 18280[10:Spt:18273.0,18221.1,18221.2] || -> product(e_1,e_3,e_3)* product(e_2,e_4,e_1).
% 6.25/6.49 18281[10:MRR:18226.0,18279.0] || -> product(e_4,e_2,e_3)*.
% 6.25/6.49 18283[10:MRR:18223.0,18279.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_4,e_1,e_3).
% 6.25/6.49 18284[11:Spt:18280.0] || -> product(e_1,e_3,e_3)*.
% 6.25/6.49 18292[11:Res:18284.0,57.0] || -> equalish(e_1,e_3)*.
% 6.25/6.49 18297[11:MRR:18292.0,22.0] || -> .
% 6.25/6.49 18303[11:Spt:18297.0,18280.0,18284.0] || product(e_1,e_3,e_3)*+ -> .
% 6.25/6.49 18304[11:Spt:18297.0,18280.1] || -> product(e_2,e_4,e_1)*.
% 6.25/6.49 18306[11:MRR:18283.0,18303.0] || -> product(e_1,e_3,e_2)* product(e_4,e_1,e_3).
% 6.25/6.49 18319[10:Res:18281.0,46.0] || product(e_2,e_4,u)*+ -> product(u,e_3,e_2)*.
% 6.25/6.49 18568[12:Spt:18306.0] || -> product(e_1,e_3,e_2)*.
% 6.25/6.49 18577[12:Res:18568.0,43.0] || product(e_1,u,e_2)*+ -> equalish(u,e_3).
% 6.25/6.49 19082[12:Res:153.4,18577.0] group_element(u) || -> product(e_1,u,e_5) product(e_1,u,e_4) product(e_1,u,e_3)* equalish(e_1,u) equalish(u,e_3).
% 6.25/6.49 19206[11:Res:18304.0,18319.0] || -> product(e_1,e_3,e_2)*.
% 6.25/6.49 19476[13:Spt:2822.0] || -> product(e_1,e_4,e_5)*.
% 6.25/6.49 19479[13:Res:19476.0,46.0] || product(e_4,e_1,u)*+ -> product(u,e_5,e_4)*.
% 6.25/6.49 19635[13:Res:41.6,19479.0] group_element(e_1) group_element(e_4) || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) product(e_4,e_1,e_2) product(e_1,e_5,e_4)*.
% 6.25/6.49 19648[13:Res:117.4,19479.0] group_element(e_4) || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) equalish(e_1,e_4) product(e_2,e_5,e_4)*.
% 6.25/6.49 19659[13:SSi:19648.0,19.0] || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) equalish(e_1,e_4) product(e_2,e_5,e_4)*.
% 6.25/6.49 19660[13:MRR:19659.1,19659.3,59.0,23.0] || -> product(e_4,e_1,e_5) product(e_4,e_1,e_3) product(e_2,e_5,e_4)*.
% 6.25/6.49 19661[13:SSi:19635.1,19635.0,19.0,16.0] || -> product(e_4,e_1,e_5) product(e_4,e_1,e_4) product(e_4,e_1,e_3) product(e_4,e_1,e_2) product(e_1,e_5,e_4)*.
% 6.25/6.49 19662[14:Spt:19660.0] || -> product(e_4,e_1,e_5)*.
% 6.25/6.49 19674[14:Res:19662.0,19479.0] || -> product(e_5,e_5,e_4)*.
% 6.25/6.49 19687[14:Res:19674.0,61.0] || -> equalish(e_4,e_5)*.
% 6.25/6.49 19696[14:MRR:19687.0,36.0] || -> .
% 6.25/6.49 19699[14:Spt:19696.0,19660.0,19662.0] || product(e_4,e_1,e_5)*+ -> .
% 6.25/6.49 19700[14:Spt:19696.0,19660.1,19660.2] || -> product(e_4,e_1,e_3) product(e_2,e_5,e_4)*.
% 6.25/6.49 19701[14:MRR:19661.0,19699.0] || -> product(e_4,e_1,e_4) product(e_4,e_1,e_3) product(e_4,e_1,e_2) product(e_1,e_5,e_4)*.
% 6.25/6.49 19703[15:Spt:19700.0] || -> product(e_4,e_1,e_3)*.
% 6.25/6.49 19712[15:Res:19703.0,137.0] || -> equalish(e_4,e_2)*.
% 6.25/6.49 19719[15:MRR:19712.0,34.0] || -> .
% 6.25/6.49 19724[15:Spt:19719.0,19700.0,19703.0] || product(e_4,e_1,e_3)*+ -> .
% 6.25/6.49 19725[15:Spt:19719.0,19700.1] || -> product(e_2,e_5,e_4)*.
% 6.25/6.49 19726[15:MRR:19701.1,19724.0] || -> product(e_4,e_1,e_4) product(e_4,e_1,e_2) product(e_1,e_5,e_4)*.
% 6.25/6.49 19733[15:Res:19725.0,44.0] || product(u,e_5,e_4)*+ -> equalish(u,e_2).
% 6.25/6.49 20077[16:Spt:19726.0] || -> product(e_4,e_1,e_4)*.
% 6.25/6.49 20087[16:Res:20077.0,3016.0] || -> equalish(e_4,e_3)*.
% 6.25/6.49 20094[16:MRR:20087.0,35.0] || -> .
% 6.25/6.49 20100[16:Spt:20094.0,19726.0,20077.0] || product(e_4,e_1,e_4)*+ -> .
% 6.25/6.49 20101[16:Spt:20094.0,19726.1,19726.2] || -> product(e_4,e_1,e_2) product(e_1,e_5,e_4)*.
% 6.25/6.49 20103[17:Spt:20101.0] || -> product(e_4,e_1,e_2)*.
% 6.25/6.49 20125[17:Res:20103.0,259.1] group_element(u) || -> product(u,e_1,e_5) product(u,e_1,e_4) product(u,e_1,e_3)* equalish(e_1,u) equalish(e_4,u).
% 6.25/6.49 21053[17:Res:20125.3,137.0] group_element(u) || -> product(u,e_1,e_5) product(u,e_1,e_4)* equalish(e_1,u) equalish(e_4,u) equalish(u,e_2).
% 6.25/6.49 21112[17:Res:21053.2,3016.0] group_element(u) || -> product(u,e_1,e_5)* equalish(e_1,u) equalish(e_4,u) equalish(u,e_2) equalish(u,e_3).
% 6.25/6.49 21166[17:Res:21112.1,59.0] group_element(e_5) || -> equalish(e_1,e_5)* equalish(e_4,e_5) equalish(e_5,e_2) equalish(e_5,e_3) equalish(e_1,e_5)*.
% 6.25/6.49 21191[17:Obv:21166.1] group_element(e_5) || -> equalish(e_4,e_5) equalish(e_5,e_2) equalish(e_5,e_3) equalish(e_1,e_5)*.
% 6.25/6.49 21192[17:SSi:21191.0,20.0] || -> equalish(e_4,e_5) equalish(e_5,e_2) equalish(e_5,e_3) equalish(e_1,e_5)*.
% 6.25/6.49 21193[17:MRR:21192.0,21192.1,21192.2,21192.3,36.0,38.0,39.0,24.0] || -> .
% 6.25/6.49 21212[17:Spt:21193.0,20101.0,20103.0] || product(e_4,e_1,e_2)* -> .
% 6.25/6.49 21213[17:Spt:21193.0,20101.1] || -> product(e_1,e_5,e_4)*.
% 6.25/6.49 21223[17:Res:21213.0,19733.0] || -> equalish(e_1,e_2)*.
% 6.25/6.49 21229[17:MRR:21223.0,21.0] || -> .
% 6.25/6.49 21238[13:Spt:21229.0,2822.0,19476.0] || product(e_1,e_4,e_5)*+ -> .
% 6.25/6.49 21239[13:Spt:21229.0,2822.1,2822.2] || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3)*.
% 6.25/6.49 21241[13:MRR:2964.1,21238.0] || product(e_1,u,e_3)* -> product(e_1,e_4,e_4)* equalish(u,e_4).
% 6.25/6.49 21245[14:Spt:21239.0] || -> product(e_1,e_4,e_4)*.
% 6.25/6.49 21254[14:Res:21245.0,57.0] || -> equalish(e_1,e_4)*.
% 6.25/6.49 21260[14:MRR:21254.0,23.0] || -> .
% 6.25/6.49 21263[14:Spt:21260.0,21239.0,21245.0] || product(e_1,e_4,e_4)*+ -> .
% 6.25/6.49 21264[14:Spt:21260.0,21239.1] || -> product(e_1,e_4,e_3)*.
% 6.25/6.49 21266[14:MRR:21241.1,21263.0] || product(e_1,u,e_3)*+ -> equalish(u,e_4).
% 6.25/6.49 21323[14:Res:19082.3,21266.0] group_element(u) || -> product(e_1,u,e_5) product(e_1,u,e_4)* equalish(e_1,u) equalish(u,e_3) equalish(u,e_4).
% 11.06/11.27 22970[14:Res:21323.2,2520.0] group_element(u) || -> product(e_1,u,e_5)* equalish(e_1,u) equalish(u,e_3) equalish(u,e_4) equalish(u,e_2).
% 11.06/11.27 23051[14:Res:22970.1,57.0] group_element(e_5) || -> equalish(e_1,e_5)* equalish(e_5,e_3) equalish(e_5,e_4) equalish(e_5,e_2) equalish(e_1,e_5)*.
% 11.06/11.27 23073[14:Obv:23051.1] group_element(e_5) || -> equalish(e_5,e_3) equalish(e_5,e_4) equalish(e_5,e_2) equalish(e_1,e_5)*.
% 11.06/11.27 23074[14:SSi:23073.0,20.0] || -> equalish(e_5,e_3) equalish(e_5,e_4) equalish(e_5,e_2) equalish(e_1,e_5)*.
% 11.06/11.27 23075[14:MRR:23074.0,23074.1,23074.2,23074.3,39.0,40.0,38.0,24.0] || -> .
% 11.06/11.27 23100[12:Spt:23075.0,18306.0,18568.0] || product(e_1,e_3,e_2)* -> .
% 11.06/11.27 23101[12:Spt:23075.0,18306.1] || -> product(e_4,e_1,e_3)*.
% 11.06/11.27 23102[12:MRR:23100.0,19206.0] || -> .
% 11.06/11.27 23103[7:Spt:23102.0,2869.1] || -> product(e_3,e_1,e_5)*.
% 11.06/11.27 23117[7:Res:23103.0,2999.0] || -> equalish(e_5,e_4)*.
% 11.06/11.27 23118[7:MRR:23117.0,40.0] || -> .
% 11.06/11.27 23131[6:Spt:23118.0,2868.1] || -> product(e_3,e_1,e_5)*.
% 11.06/11.27 23157[6:Res:23131.0,2999.0] || -> equalish(e_5,e_4)*.
% 11.06/11.27 23158[6:MRR:23157.0,40.0] || -> .
% 11.06/11.27 23171[5:Spt:23158.0,2867.1] || -> product(e_3,e_1,e_5)*.
% 11.06/11.27 23173[5:Res:23171.0,15.2] || greater(e_5,u)+ next(e_3,u)* -> .
% 11.06/11.27 23197[5:Res:14.0,23173.0] || next(e_3,e_4)* -> .
% 11.06/11.27 23201[5:MRR:23197.0,3.0] || -> .
% 11.06/11.27 23202[4:Spt:23201.0,2487.0,2514.0] || product(e_1,e_2,e_4)* -> .
% 11.06/11.27 23203[4:Spt:23201.0,2487.1,2487.2] || -> product(e_1,e_3,e_1)* product(e_3,e_3,e_1).
% 11.06/11.27 23263[5:Spt:23203.0] || -> product(e_1,e_3,e_1)*.
% 11.06/11.27 23267[5:Res:23263.0,59.0] || -> equalish(e_3,e_1)*.
% 11.06/11.27 23281[5:MRR:23267.0,29.0] || -> .
% 11.06/11.27 23290[5:Spt:23281.0,23203.0,23263.0] || product(e_1,e_3,e_1)* -> .
% 11.06/11.27 23291[5:Spt:23281.0,23203.1] || -> product(e_3,e_3,e_1)*.
% 11.06/11.27 23316[5:Res:23291.0,61.0] || -> equalish(e_1,e_3)*.
% 11.06/11.27 23327[5:MRR:23316.0,22.0] || -> .
% 11.06/11.27 % SZS output end Refutation
% 11.06/11.27 Formulae used in the proof : e_2_then_e_3 e_3_then_e_4 e_4_greater_e_3 e_5_greater_e_3 e_5_greater_e_4 no_redundancy element_1 element_2 element_3 element_4 element_5 e_1_is_not_e_2 e_1_is_not_e_3 e_1_is_not_e_4 e_1_is_not_e_5 e_2_is_not_e_1 e_2_is_not_e_3 e_2_is_not_e_5 e_3_is_not_e_1 e_3_is_not_e_2 e_4_is_not_e_1 e_4_is_not_e_2 e_4_is_not_e_3 e_4_is_not_e_5 e_5_is_not_e_1 e_5_is_not_e_2 e_5_is_not_e_3 e_5_is_not_e_4 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation product_idempotence qg3
% 11.06/11.27
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