TSTP Solution File: GRP128-1.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP128-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:45:41 EDT 2022
% Result : Unsatisfiable 3.71s 3.89s
% Output : Refutation 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP128-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 07:46:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.71/3.89
% 3.71/3.89 SPASS V 3.9
% 3.71/3.89 SPASS beiseite: Proof found.
% 3.71/3.89 % SZS status Theorem
% 3.71/3.89 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.71/3.89 SPASS derived 4005 clauses, backtracked 940 clauses, performed 40 splits and kept 2487 clauses.
% 3.71/3.89 SPASS allocated 81549 KBytes.
% 3.71/3.89 SPASS spent 0:00:03.53 on the problem.
% 3.71/3.89 0:00:00.03 for the input.
% 3.71/3.89 0:00:00.00 for the FLOTTER CNF translation.
% 3.71/3.89 0:00:00.08 for inferences.
% 3.71/3.89 0:00:00.02 for the backtracking.
% 3.71/3.89 0:00:03.37 for the reduction.
% 3.71/3.89
% 3.71/3.89
% 3.71/3.89 Here is a proof with depth 21, length 375 :
% 3.71/3.89 % SZS output start Refutation
% 3.71/3.89 1[0:Inp] || -> group_element(e_1)*.
% 3.71/3.89 2[0:Inp] || -> group_element(e_2)*.
% 3.71/3.89 3[0:Inp] || -> group_element(e_3)*.
% 3.71/3.89 4[0:Inp] || equalish(e_1,e_2)*+ -> .
% 3.71/3.89 5[0:Inp] || equalish(e_1,e_3)*+ -> .
% 3.71/3.89 6[0:Inp] || equalish(e_2,e_1)*+ -> .
% 3.71/3.89 7[0:Inp] || equalish(e_2,e_3)*+ -> .
% 3.71/3.89 8[0:Inp] || equalish(e_3,e_1)*+ -> .
% 3.71/3.89 9[0:Inp] || equalish(e_3,e_2)*+ -> .
% 3.71/3.89 10[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 3.71/3.89 11[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 3.71/3.89 12[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 3.71/3.89 13[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 3.71/3.89 14[0:Inp] || product(u,v,w)*+ product(x,v,u)* -> product(x,u,w)*.
% 3.71/3.89 18[0:Res:10.4,14.0] group_element(u) group_element(v) || product(w,u,v)*+ -> product(v,u,e_3) product(v,u,e_2)* product(w,v,e_1)*.
% 3.71/3.89 19[0:Res:10.4,11.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,e_1).
% 3.71/3.89 20[0:Res:10.4,12.0] group_element(u) group_element(v) || product(v,w,e_1)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,u)*.
% 3.71/3.89 21[0:Res:10.4,13.0] group_element(u) group_element(v) || product(w,u,e_1)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,v)*.
% 3.71/3.89 22[0:Res:10.4,21.2] group_element(u) group_element(v) group_element(u) group_element(w) || -> product(v,u,e_3) product(v,u,e_2)* product(w,u,e_3) product(w,u,e_2)* equalish(v,w)*.
% 3.71/3.89 23[0:Obv:22.0] group_element(u) group_element(v) group_element(w) || -> product(u,v,e_3) product(u,v,e_2)* product(w,v,e_3) product(w,v,e_2)* equalish(u,w)*.
% 3.71/3.89 26[0:Res:10.4,19.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* product(v,u,e_3) product(v,u,e_2)* equalish(e_1,e_1).
% 3.71/3.89 27[0:Obv:26.5] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* equalish(e_1,e_1).
% 3.71/3.89 28[1:Spt:27.0,27.1,27.2,27.3] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)*.
% 3.71/3.89 29[1:Res:28.3,14.0] group_element(u) group_element(v) || product(w,u,v)*+ -> product(v,u,e_3)* product(w,v,e_2)*.
% 3.71/3.89 30[1:Res:28.3,11.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3)* equalish(w,e_2).
% 3.71/3.89 31[1:Res:28.3,12.0] group_element(u) group_element(v) || product(v,w,e_2)*+ -> product(v,u,e_3)* equalish(w,u)*.
% 3.71/3.89 33[1:Res:28.3,30.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(v,u,e_3)* product(v,u,e_3)* equalish(e_2,e_2).
% 3.71/3.89 34[1:Obv:33.4] group_element(u) group_element(v) || -> product(v,u,e_3)* equalish(e_2,e_2).
% 3.71/3.89 37[2:Spt:34.0,34.1,34.2] group_element(u) group_element(v) || -> product(v,u,e_3)*.
% 3.71/3.89 40[2:Res:37.2,12.0] group_element(u) group_element(v) || product(v,w,e_3)*+ -> equalish(w,u)*.
% 3.71/3.89 48[2:Res:37.2,40.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> equalish(u,w)*.
% 3.71/3.89 49[2:Obv:48.1] group_element(u) group_element(v) group_element(w) || -> equalish(u,v)*.
% 3.71/3.89 50[2:Con:49.2] group_element(u) group_element(v) || -> equalish(u,v)*.
% 3.71/3.89 56[2:Res:50.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 3.71/3.89 62[2:SSi:56.1,56.0,2.0,1.0] || -> .
% 3.71/3.89 63[2:Spt:62.0,34.3] || -> equalish(e_2,e_2)*.
% 3.71/3.89 74[1:Res:28.3,29.2] group_element(u) group_element(v) group_element(u) group_element(e_2) || -> product(v,u,e_3)* product(e_2,u,e_3)* product(v,e_2,e_2)*.
% 3.71/3.89 75[1:Obv:74.0] group_element(u) group_element(v) group_element(e_2) || -> product(u,v,e_3)* product(e_2,v,e_3)* product(u,e_2,e_2)*.
% 3.71/3.89 76[1:SSi:75.2,2.0] group_element(u) group_element(v) || -> product(u,v,e_3)* product(e_2,v,e_3)* product(u,e_2,e_2)*.
% 3.71/3.89 77[1:Fac:76.2,76.3] group_element(e_2) group_element(u) || -> product(e_2,u,e_3)* product(e_2,e_2,e_2)*.
% 3.71/3.89 98[1:SSi:77.0,2.0] group_element(u) || -> product(e_2,u,e_3)* product(e_2,e_2,e_2)*.
% 3.71/3.89 109[3:Spt:98.0,98.1] group_element(u) || -> product(e_2,u,e_3)*.
% 3.71/3.89 112[3:Res:109.1,12.0] group_element(u) || product(e_2,v,e_3)*+ -> equalish(v,u)*.
% 3.71/3.89 158[3:Res:109.1,112.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 3.71/3.89 179[3:Res:158.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 3.71/3.89 185[3:SSi:179.1,179.0,2.0,1.0] || -> .
% 3.71/3.89 186[3:Spt:185.0,98.2] || -> product(e_2,e_2,e_2)*.
% 3.71/3.89 191[3:Res:186.0,12.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 3.71/3.89 192[3:Res:186.0,13.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 3.71/3.89 194[3:Res:186.0,31.2] group_element(u) group_element(e_2) || -> product(e_2,u,e_3)* equalish(e_2,u).
% 3.71/3.89 198[3:SSi:194.1,2.0] group_element(u) || -> product(e_2,u,e_3)* equalish(e_2,u).
% 3.71/3.89 204[3:Res:28.3,191.0] group_element(u) group_element(e_2) || -> product(e_2,u,e_3)* equalish(u,e_2).
% 3.71/3.89 206[3:SSi:204.1,2.0] group_element(u) || -> product(e_2,u,e_3)* equalish(u,e_2).
% 3.71/3.89 240[3:Res:28.3,192.0] group_element(e_2) group_element(u) || -> product(u,e_2,e_3)* equalish(u,e_2).
% 3.71/3.89 243[3:SSi:240.0,2.0] group_element(u) || -> product(u,e_2,e_3)* equalish(u,e_2).
% 3.71/3.89 249[3:Res:198.1,29.2] group_element(u) group_element(u) group_element(e_3) || -> equalish(e_2,u) product(e_3,u,e_3)* product(e_2,e_3,e_2)*.
% 3.71/3.89 252[3:Obv:249.0] group_element(u) group_element(e_3) || -> equalish(e_2,u) product(e_3,u,e_3)* product(e_2,e_3,e_2)*.
% 3.71/3.89 253[3:SSi:252.1,3.0] group_element(u) || -> equalish(e_2,u) product(e_3,u,e_3)* product(e_2,e_3,e_2)*.
% 3.71/3.89 268[3:Res:206.1,29.2] group_element(u) group_element(u) group_element(e_3) || -> equalish(u,e_2) product(e_3,u,e_3)* product(e_2,e_3,e_2)*.
% 3.71/3.89 271[3:Obv:268.0] group_element(u) group_element(e_3) || -> equalish(u,e_2) product(e_3,u,e_3)* product(e_2,e_3,e_2)*.
% 3.71/3.89 272[3:SSi:271.1,3.0] group_element(u) || -> equalish(u,e_2) product(e_3,u,e_3)* product(e_2,e_3,e_2)*.
% 3.71/3.89 302[3:Res:243.1,29.2] group_element(u) group_element(e_2) group_element(e_3) || -> equalish(u,e_2) product(e_3,e_2,e_3)* product(u,e_3,e_2)*.
% 3.71/3.89 305[3:SSi:302.2,302.1,3.0,2.0] group_element(u) || -> equalish(u,e_2) product(e_3,e_2,e_3)* product(u,e_3,e_2)*.
% 3.71/3.89 327[4:Spt:253.0,253.1,253.2] group_element(u) || -> equalish(e_2,u) product(e_3,u,e_3)*.
% 3.71/3.89 372[5:Spt:272.0,272.1,272.2] group_element(u) || -> equalish(u,e_2) product(e_3,u,e_3)*.
% 3.71/3.89 381[6:Spt:305.0,305.1,305.3] group_element(u) || -> equalish(u,e_2) product(u,e_3,e_2)*.
% 3.71/3.89 389[6:Res:381.2,29.2] group_element(u) group_element(e_3) group_element(e_2) || -> equalish(u,e_2) product(e_2,e_3,e_3)* product(u,e_2,e_2)*.
% 3.71/3.89 394[6:SSi:389.2,389.1,2.0,3.0] group_element(u) || -> equalish(u,e_2) product(e_2,e_3,e_3)* product(u,e_2,e_2)*.
% 3.71/3.89 395[6:MRR:394.3,192.0] group_element(u) || -> equalish(u,e_2)* product(e_2,e_3,e_3)*.
% 3.71/3.89 396[7:Spt:395.0,395.1] group_element(u) || -> equalish(u,e_2)*.
% 3.71/3.89 398[7:Res:396.1,4.0] group_element(e_1) || -> .
% 3.71/3.89 400[7:SSi:398.0,1.0] || -> .
% 3.71/3.89 401[7:Spt:400.0,395.2] || -> product(e_2,e_3,e_3)*.
% 3.71/3.89 405[7:Res:401.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_2).
% 3.71/3.89 528[7:Res:327.2,405.0] group_element(e_3) || -> equalish(e_2,e_3)* equalish(e_3,e_2).
% 3.71/3.89 533[7:SSi:528.0,3.0] || -> equalish(e_2,e_3)* equalish(e_3,e_2).
% 3.71/3.89 534[7:MRR:533.0,533.1,7.0,9.0] || -> .
% 3.71/3.89 537[6:Spt:534.0,305.2] || -> product(e_3,e_2,e_3)*.
% 3.71/3.89 540[6:Res:537.0,12.0] || product(e_3,u,e_3)* -> equalish(u,e_2).
% 3.71/3.89 544[6:MRR:372.2,540.0] group_element(u) || -> equalish(u,e_2)*.
% 3.71/3.89 546[6:Res:544.1,4.0] group_element(e_1) || -> .
% 3.71/3.89 548[6:SSi:546.0,1.0] || -> .
% 3.71/3.89 549[5:Spt:548.0,272.3] || -> product(e_2,e_3,e_2)*.
% 3.71/3.89 558[5:Res:549.0,191.0] || -> equalish(e_3,e_2)*.
% 3.71/3.89 559[5:MRR:558.0,9.0] || -> .
% 3.71/3.89 564[4:Spt:559.0,253.3] || -> product(e_2,e_3,e_2)*.
% 3.71/3.89 573[4:Res:564.0,191.0] || -> equalish(e_3,e_2)*.
% 3.71/3.89 574[4:MRR:573.0,9.0] || -> .
% 3.71/3.89 579[1:Spt:574.0,27.4] || -> equalish(e_1,e_1)*.
% 3.71/3.89 590[0:Res:10.4,18.2] group_element(u) group_element(v) group_element(u) group_element(e_1) || -> product(v,u,e_3) product(v,u,e_2)* product(e_1,u,e_3) product(e_1,u,e_2)* product(v,e_1,e_1)*.
% 3.71/3.89 591[0:Obv:590.0] group_element(u) group_element(v) group_element(e_1) || -> product(u,v,e_3) product(u,v,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* product(u,e_1,e_1)*.
% 3.71/3.89 592[0:SSi:591.2,1.0] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* product(u,e_1,e_1)*.
% 3.71/3.89 593[0:Fac:592.3,592.5] group_element(e_1) group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_3) product(e_1,u,e_2)* product(e_1,e_1,e_1)*.
% 3.71/3.89 614[0:Obv:593.2] group_element(e_1) group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_1,e_1,e_1)*.
% 3.71/3.89 615[0:SSi:614.0,1.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_1,e_1,e_1)*.
% 3.71/3.89 646[2:Spt:615.0,615.1,615.2] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)*.
% 3.71/3.89 647[2:Res:646.2,14.0] group_element(u) || product(v,u,e_1)*+ -> product(e_1,u,e_3)* product(v,e_1,e_2)*.
% 3.71/3.89 648[2:Res:646.2,11.0] group_element(u) || product(e_1,u,v)*+ -> product(e_1,u,e_3)* equalish(v,e_2).
% 3.71/3.89 649[2:Res:646.2,12.0] group_element(u) || product(e_1,v,e_2)*+ -> product(e_1,u,e_3)* equalish(v,u)*.
% 3.71/3.89 650[2:Res:646.2,13.0] group_element(u) || product(v,u,e_2)*+ -> product(e_1,u,e_3)* equalish(v,e_1).
% 3.71/3.89 652[2:Res:646.2,18.2] group_element(u) group_element(u) group_element(e_2) || -> product(e_1,u,e_3)* product(e_2,u,e_3) product(e_2,u,e_2) product(e_1,e_2,e_1)*.
% 3.71/3.89 654[2:Obv:652.0] group_element(u) group_element(e_2) || -> product(e_1,u,e_3)* product(e_2,u,e_3) product(e_2,u,e_2) product(e_1,e_2,e_1)*.
% 3.71/3.89 655[2:SSi:654.1,2.0] group_element(u) || -> product(e_1,u,e_3)* product(e_2,u,e_3) product(e_2,u,e_2) product(e_1,e_2,e_1)*.
% 3.71/3.89 659[2:Res:646.2,648.1] group_element(u) group_element(u) || -> product(e_1,u,e_3)* product(e_1,u,e_3)* equalish(e_2,e_2).
% 3.71/3.89 660[2:Obv:659.2] group_element(u) || -> product(e_1,u,e_3)* equalish(e_2,e_2).
% 3.71/3.89 664[3:Spt:660.0,660.1] group_element(u) || -> product(e_1,u,e_3)*.
% 3.71/3.89 667[3:Res:664.1,12.0] group_element(u) || product(e_1,v,e_3)*+ -> equalish(v,u)*.
% 3.71/3.89 695[0:Res:23.6,18.2] group_element(u) group_element(v) group_element(w) group_element(v) group_element(e_2) || -> product(u,v,e_3) product(u,v,e_2)* product(w,v,e_3)* equalish(u,w)* product(e_2,v,e_3) product(e_2,v,e_2)* product(w,e_2,e_1)*.
% 3.71/3.89 702[0:Obv:695.1] group_element(u) group_element(v) group_element(w) group_element(e_2) || -> product(u,w,e_3) product(u,w,e_2)* product(v,w,e_3)* equalish(u,v)* product(e_2,w,e_3) product(e_2,w,e_2)* product(v,e_2,e_1)*.
% 3.71/3.89 703[0:SSi:702.3,2.0] group_element(u) group_element(v) group_element(w) || -> product(u,w,e_3) product(u,w,e_2)* product(v,w,e_3)* equalish(u,v)* product(e_2,w,e_3) product(e_2,w,e_2)* product(v,e_2,e_1)*.
% 3.71/3.89 709[3:Res:664.1,667.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 3.71/3.89 715[3:Res:709.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 3.71/3.89 721[3:SSi:715.1,715.0,2.0,1.0] || -> .
% 3.71/3.89 722[3:Spt:721.0,660.2] || -> equalish(e_2,e_2)*.
% 3.71/3.89 759[2:Res:646.2,649.1] group_element(u) group_element(v) || -> product(e_1,u,e_3)* product(e_1,v,e_3)* equalish(u,v)*.
% 3.71/3.89 795[2:Res:10.4,647.1] group_element(u) group_element(v) group_element(u) || -> product(v,u,e_3) product(v,u,e_2)* product(e_1,u,e_3)* product(v,e_1,e_2)*.
% 3.71/3.89 796[2:Obv:795.0] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(e_1,v,e_3)* product(u,e_1,e_2)*.
% 3.71/3.89 806[2:Res:759.3,11.0] group_element(u) group_element(v) || product(e_1,v,w)*+ -> product(e_1,u,e_3)* equalish(u,v)* equalish(w,e_3).
% 3.71/3.89 808[2:Res:759.3,13.0] group_element(u) group_element(v) || product(w,v,e_3)*+ -> product(e_1,u,e_3)* equalish(u,v)* equalish(w,e_1).
% 3.71/3.89 868[4:Spt:655.0,655.1,655.2,655.3] group_element(u) || -> product(e_1,u,e_3)* product(e_2,u,e_3) product(e_2,u,e_2).
% 3.71/3.89 870[4:Res:868.1,11.0] group_element(u) || product(e_1,u,v)*+ -> product(e_2,u,e_3) product(e_2,u,e_2) equalish(v,e_3).
% 3.71/3.89 872[4:Res:868.1,13.0] group_element(u) || product(v,u,e_3)*+ -> product(e_2,u,e_3) product(e_2,u,e_2)* equalish(v,e_1).
% 3.71/3.89 886[4:Res:868.1,870.1] group_element(u) group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)* product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_3,e_3).
% 3.71/3.89 890[4:Obv:886.3] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_3,e_3).
% 3.71/3.89 898[5:Spt:890.0,890.1,890.2] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)*.
% 3.71/3.89 899[5:Res:898.2,14.0] group_element(u) || product(v,u,e_2)*+ -> product(e_2,u,e_3)* product(v,e_2,e_2)*.
% 3.71/3.89 903[5:Res:898.2,650.1] group_element(u) group_element(u) || -> product(e_2,u,e_3) product(e_1,u,e_3)* equalish(e_2,e_1).
% 3.71/3.89 906[5:Obv:903.0] group_element(u) || -> product(e_2,u,e_3) product(e_1,u,e_3)* equalish(e_2,e_1).
% 3.71/3.89 907[5:MRR:906.3,6.0] group_element(u) || -> product(e_2,u,e_3) product(e_1,u,e_3)*.
% 3.71/3.89 930[5:Res:907.2,11.0] group_element(u) || product(e_1,u,v)*+ -> product(e_2,u,e_3) equalish(v,e_3).
% 3.71/3.89 988[5:Res:907.2,930.1] group_element(u) group_element(u) || -> product(e_2,u,e_3)* product(e_2,u,e_3)* equalish(e_3,e_3).
% 3.71/3.89 991[5:Obv:988.2] group_element(u) || -> product(e_2,u,e_3)* equalish(e_3,e_3).
% 3.71/3.89 1000[6:Spt:991.0,991.1] group_element(u) || -> product(e_2,u,e_3)*.
% 3.71/3.89 1003[6:Res:1000.1,12.0] group_element(u) || product(e_2,v,e_3)*+ -> equalish(v,u)*.
% 3.71/3.89 1037[6:Res:1000.1,1003.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 3.71/3.89 1043[6:Res:1037.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 3.71/3.89 1049[6:SSi:1043.1,1043.0,2.0,1.0] || -> .
% 3.71/3.89 1050[6:Spt:1049.0,991.2] || -> equalish(e_3,e_3)*.
% 3.71/3.89 1180[5:Res:898.2,899.1] group_element(u) group_element(u) || -> product(e_2,u,e_3)* product(e_2,u,e_3)* product(e_2,e_2,e_2)*.
% 3.71/3.89 1182[5:Obv:1180.2] group_element(u) || -> product(e_2,u,e_3)* product(e_2,e_2,e_2)*.
% 3.71/3.89 1199[7:Spt:1182.0,1182.1] group_element(u) || -> product(e_2,u,e_3)*.
% 3.71/3.89 1202[7:Res:1199.1,12.0] group_element(u) || product(e_2,v,e_3)*+ -> equalish(v,u)*.
% 3.71/3.89 1221[7:Res:1199.1,1202.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 3.71/3.89 1227[7:Res:1221.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 3.71/3.89 1233[7:SSi:1227.1,1227.0,2.0,1.0] || -> .
% 3.71/3.89 1234[7:Spt:1233.0,1182.2] || -> product(e_2,e_2,e_2)*.
% 3.71/3.89 1238[7:Res:1234.0,13.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 3.71/3.89 1239[7:Res:1234.0,650.1] group_element(e_2) || -> product(e_1,e_2,e_3)* equalish(e_2,e_1).
% 3.71/3.89 1242[7:SSi:1239.0,2.0] || -> product(e_1,e_2,e_3)* equalish(e_2,e_1).
% 3.71/3.89 1243[7:MRR:1242.1,6.0] || -> product(e_1,e_2,e_3)*.
% 3.71/3.89 1276[7:Res:1243.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_2).
% 3.71/3.89 1277[7:Res:1243.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_1).
% 3.71/3.89 1279[7:Res:1243.0,18.2] group_element(e_2) group_element(e_3) || -> product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_1,e_3,e_1)*.
% 3.71/3.89 1281[7:SSi:1279.1,1279.0,3.0,2.0] || -> product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_1,e_3,e_1)*.
% 3.71/3.89 1412[8:Spt:1281.0] || -> product(e_3,e_2,e_3)*.
% 3.71/3.89 1420[8:Res:1412.0,1277.0] || -> equalish(e_3,e_1)*.
% 3.71/3.89 1421[8:MRR:1420.0,8.0] || -> .
% 3.71/3.89 1423[8:Spt:1421.0,1281.0,1412.0] || product(e_3,e_2,e_3)*+ -> .
% 3.71/3.89 1424[8:Spt:1421.0,1281.1,1281.2] || -> product(e_3,e_2,e_2) product(e_1,e_3,e_1)*.
% 3.71/3.89 1425[9:Spt:1424.0] || -> product(e_3,e_2,e_2)*.
% 3.71/3.89 1434[9:Res:1425.0,1238.0] || -> equalish(e_3,e_2)*.
% 3.71/3.89 1435[9:MRR:1434.0,9.0] || -> .
% 3.71/3.89 1438[9:Spt:1435.0,1424.0,1425.0] || product(e_3,e_2,e_2)* -> .
% 3.71/3.89 1439[9:Spt:1435.0,1424.1] || -> product(e_1,e_3,e_1)*.
% 3.71/3.89 1450[9:Res:1439.0,648.1] group_element(e_3) || -> product(e_1,e_3,e_3)* equalish(e_1,e_2).
% 3.71/3.89 1451[9:SSi:1450.0,3.0] || -> product(e_1,e_3,e_3)* equalish(e_1,e_2).
% 3.71/3.89 1452[9:MRR:1451.1,4.0] || -> product(e_1,e_3,e_3)*.
% 3.71/3.89 1461[9:Res:1452.0,1276.0] || -> equalish(e_3,e_2)*.
% 3.71/3.89 1463[9:MRR:1461.0,9.0] || -> .
% 3.71/3.89 1465[5:Spt:1463.0,890.3] || -> equalish(e_3,e_3)*.
% 3.71/3.89 1631[2:Fac:796.3,796.5] group_element(u) group_element(e_1) || -> product(u,e_1,e_3) product(e_1,e_1,e_3)* product(u,e_1,e_2)*.
% 3.71/3.89 1682[2:SSi:1631.1,1.0] group_element(u) || -> product(u,e_1,e_3) product(e_1,e_1,e_3)* product(u,e_1,e_2)*.
% 3.71/3.89 1720[6:Spt:1682.0,1682.1,1682.3] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)*.
% 3.71/3.89 1730[6:Res:1720.2,650.1] group_element(u) group_element(e_1) || -> product(u,e_1,e_3)* product(e_1,e_1,e_3)* equalish(u,e_1).
% 3.71/3.89 1737[6:SSi:1730.1,1.0] group_element(u) || -> product(u,e_1,e_3)* product(e_1,e_1,e_3)* equalish(u,e_1).
% 3.71/3.89 1746[7:Spt:1737.0,1737.1,1737.3] group_element(u) || -> product(u,e_1,e_3)* equalish(u,e_1).
% 3.71/3.89 1752[7:Res:1746.1,808.2] group_element(u) group_element(v) group_element(e_1) || -> equalish(u,e_1)* product(e_1,v,e_3)* equalish(v,e_1) equalish(u,e_1)*.
% 3.71/3.89 1756[7:Res:1746.1,872.1] group_element(u) group_element(e_1) || -> equalish(u,e_1)* product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(u,e_1)*.
% 3.71/3.89 1767[7:Obv:1756.2] group_element(u) group_element(e_1) || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(u,e_1)*.
% 3.71/3.89 1768[7:SSi:1767.1,1.0] group_element(u) || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(u,e_1)*.
% 3.71/3.89 1773[7:Obv:1752.3] group_element(u) group_element(v) group_element(e_1) || -> product(e_1,v,e_3)* equalish(v,e_1) equalish(u,e_1)*.
% 3.71/3.89 1774[7:Con:1773.0] group_element(u) group_element(e_1) || -> product(e_1,u,e_3)* equalish(u,e_1).
% 3.71/3.89 1775[7:SSi:1774.1,1.0] group_element(u) || -> product(e_1,u,e_3)* equalish(u,e_1).
% 3.71/3.89 1824[8:Spt:1768.0,1768.3] group_element(u) || -> equalish(u,e_1)*.
% 3.71/3.89 1826[8:Res:1824.1,6.0] group_element(e_2) || -> .
% 3.71/3.89 1828[8:SSi:1826.0,2.0] || -> .
% 3.71/3.89 1829[8:Spt:1828.0,1768.1,1768.2] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 3.71/3.89 1837[8:Res:1829.1,650.1] group_element(e_1) || -> product(e_2,e_1,e_3) product(e_1,e_1,e_3)* equalish(e_2,e_1).
% 3.71/3.89 1842[8:SSi:1837.0,1.0] || -> product(e_2,e_1,e_3) product(e_1,e_1,e_3)* equalish(e_2,e_1).
% 3.71/3.89 1843[8:MRR:1842.2,6.0] || -> product(e_2,e_1,e_3) product(e_1,e_1,e_3)*.
% 3.71/3.89 1848[9:Spt:1843.0] || -> product(e_2,e_1,e_3)*.
% 3.71/3.89 1852[9:Res:1848.0,13.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 3.71/3.89 2029[9:Res:1746.1,1852.0] group_element(u) || -> equalish(u,e_1)* equalish(u,e_2).
% 3.71/3.89 2043[9:Res:2029.1,8.0] group_element(e_3) || -> equalish(e_3,e_2)*.
% 3.71/3.89 2045[9:SSi:2043.0,3.0] || -> equalish(e_3,e_2)*.
% 3.71/3.89 2046[9:MRR:2045.0,9.0] || -> .
% 3.71/3.89 2047[9:Spt:2046.0,1843.0,1848.0] || product(e_2,e_1,e_3)*+ -> .
% 3.71/3.89 2048[9:Spt:2046.0,1843.1] || -> product(e_1,e_1,e_3)*.
% 3.71/3.89 2056[9:Res:2048.0,12.0] || product(e_1,u,e_3)* -> equalish(u,e_1).
% 3.71/3.89 2073[9:MRR:1775.1,2056.0] group_element(u) || -> equalish(u,e_1)*.
% 3.71/3.89 2097[9:Res:2073.1,6.0] group_element(e_2) || -> .
% 3.71/3.89 2099[9:SSi:2097.0,2.0] || -> .
% 3.71/3.89 2100[7:Spt:2099.0,1737.2] || -> product(e_1,e_1,e_3)*.
% 3.71/3.89 2103[7:Res:2100.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_1).
% 3.71/3.89 2147[7:Res:868.1,2103.0] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)* equalish(u,e_1).
% 3.71/3.89 2210[7:Res:2147.2,650.1] group_element(u) group_element(u) || -> product(e_2,u,e_3) equalish(u,e_1) product(e_1,u,e_3)* equalish(e_2,e_1).
% 3.71/3.89 2218[7:Obv:2210.0] group_element(u) || -> product(e_2,u,e_3) equalish(u,e_1) product(e_1,u,e_3)* equalish(e_2,e_1).
% 3.71/3.89 2219[7:MRR:2218.3,2218.4,2103.0,6.0] group_element(u) || -> product(e_2,u,e_3)* equalish(u,e_1).
% 3.71/3.89 2228[7:Res:2219.1,14.0] group_element(u) || product(v,u,e_2)*+ -> equalish(u,e_1) product(v,e_2,e_3)*.
% 3.71/3.89 2429[7:Res:646.2,2228.1] group_element(u) group_element(u) || -> product(e_1,u,e_3)* equalish(u,e_1) product(e_1,e_2,e_3)*.
% 3.71/3.89 2433[7:Obv:2429.0] group_element(u) || -> product(e_1,u,e_3)* equalish(u,e_1) product(e_1,e_2,e_3)*.
% 3.71/3.89 2434[7:MRR:2433.1,2103.0] group_element(u) || -> equalish(u,e_1)* product(e_1,e_2,e_3)*.
% 3.71/3.89 2458[8:Spt:2434.0,2434.1] group_element(u) || -> equalish(u,e_1)*.
% 3.71/3.89 2460[8:Res:2458.1,6.0] group_element(e_2) || -> .
% 3.71/3.89 2462[8:SSi:2460.0,2.0] || -> .
% 3.71/3.89 2463[8:Spt:2462.0,2434.2] || -> product(e_1,e_2,e_3)*.
% 3.71/3.89 2479[8:Res:2463.0,2103.0] || -> equalish(e_2,e_1)*.
% 3.71/3.89 2485[8:MRR:2479.0,6.0] || -> .
% 3.71/3.89 2487[6:Spt:2485.0,1682.2] || -> product(e_1,e_1,e_3)*.
% 3.71/3.89 2492[6:Res:2487.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_1).
% 3.71/3.89 2493[6:Res:2487.0,13.0] || product(u,e_1,e_3)*+ -> equalish(u,e_1).
% 3.71/3.89 2502[6:Res:2487.0,18.2] group_element(e_1) group_element(e_3) || -> product(e_3,e_1,e_3) product(e_3,e_1,e_2) product(e_1,e_3,e_1)*.
% 3.71/3.89 2511[6:SSi:2502.1,2502.0,3.0,1.0] || -> product(e_3,e_1,e_3) product(e_3,e_1,e_2) product(e_1,e_3,e_1)*.
% 3.71/3.89 2629[7:Spt:2511.0] || -> product(e_3,e_1,e_3)*.
% 3.71/3.89 2644[7:Res:2629.0,2493.0] || -> equalish(e_3,e_1)*.
% 3.71/3.89 2645[7:MRR:2644.0,8.0] || -> .
% 3.71/3.89 2652[7:Spt:2645.0,2511.0,2629.0] || product(e_3,e_1,e_3)*+ -> .
% 3.71/3.89 2653[7:Spt:2645.0,2511.1,2511.2] || -> product(e_3,e_1,e_2) product(e_1,e_3,e_1)*.
% 3.71/3.89 2654[8:Spt:2653.0] || -> product(e_3,e_1,e_2)*.
% 3.71/3.89 2655[8:Res:2654.0,14.0] || product(u,e_1,e_3)*+ -> product(u,e_3,e_2).
% 3.71/3.89 2747[8:Res:2487.0,2655.0] || -> product(e_1,e_3,e_2)*.
% 3.71/3.89 2786[8:Res:2747.0,13.0] || product(u,e_3,e_2)*+ -> equalish(u,e_1).
% 3.71/3.89 2802[8:Res:2747.0,870.1] group_element(e_3) || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2)* equalish(e_2,e_3).
% 3.71/3.89 2810[8:SSi:2802.0,3.0] || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2)* equalish(e_2,e_3).
% 3.71/3.89 2811[8:MRR:2810.2,7.0] || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2)*.
% 3.71/3.89 2820[9:Spt:2811.0] || -> product(e_2,e_3,e_3)*.
% 3.71/3.89 2821[9:Res:2820.0,14.0] || product(u,e_3,e_2)+ -> product(u,e_2,e_3)*.
% 3.71/3.89 3143[9:Res:2747.0,2821.0] || -> product(e_1,e_2,e_3)*.
% 3.71/3.89 3167[9:Res:3143.0,2492.0] || -> equalish(e_2,e_1)*.
% 3.71/3.89 3173[9:MRR:3167.0,6.0] || -> .
% 3.71/3.89 3176[9:Spt:3173.0,2811.0,2820.0] || product(e_2,e_3,e_3)* -> .
% 3.71/3.89 3177[9:Spt:3173.0,2811.1] || -> product(e_2,e_3,e_2)*.
% 3.71/3.89 3204[9:Res:3177.0,2786.0] || -> equalish(e_2,e_1)*.
% 3.71/3.89 3209[9:MRR:3204.0,6.0] || -> .
% 3.71/3.89 3230[8:Spt:3209.0,2653.0,2654.0] || product(e_3,e_1,e_2)* -> .
% 3.71/3.89 3231[8:Spt:3209.0,2653.1] || -> product(e_1,e_3,e_1)*.
% 3.71/3.89 3264[8:Res:3231.0,648.1] group_element(e_3) || -> product(e_1,e_3,e_3)* equalish(e_1,e_2).
% 3.71/3.89 3266[8:SSi:3264.0,3.0] || -> product(e_1,e_3,e_3)* equalish(e_1,e_2).
% 3.71/3.89 3267[8:MRR:3266.1,4.0] || -> product(e_1,e_3,e_3)*.
% 3.71/3.89 3288[8:Res:3267.0,2492.0] || -> equalish(e_3,e_1)*.
% 3.71/3.89 3294[8:MRR:3288.0,8.0] || -> .
% 3.71/3.89 3304[4:Spt:3294.0,655.4] || -> product(e_1,e_2,e_1)*.
% 3.71/3.89 3325[4:Res:3304.0,806.2] group_element(u) group_element(e_2) || -> product(e_1,u,e_3)* equalish(u,e_2) equalish(e_1,e_3).
% 3.71/3.89 3332[4:Res:3304.0,648.1] group_element(e_2) || -> product(e_1,e_2,e_3)* equalish(e_1,e_2).
% 3.71/3.89 3337[4:SSi:3332.0,2.0] || -> product(e_1,e_2,e_3)* equalish(e_1,e_2).
% 3.71/3.89 3338[4:MRR:3337.1,4.0] || -> product(e_1,e_2,e_3)*.
% 3.71/3.89 3339[4:SSi:3325.1,2.0] group_element(u) || -> product(e_1,u,e_3)* equalish(u,e_2) equalish(e_1,e_3).
% 3.71/3.89 3340[4:MRR:3339.3,5.0] group_element(u) || -> product(e_1,u,e_3)* equalish(u,e_2).
% 3.71/3.89 3523[4:Res:3338.0,12.0] || product(e_1,u,e_3)* -> equalish(u,e_2).
% 3.71/3.89 3542[4:MRR:3340.1,3523.0] group_element(u) || -> equalish(u,e_2)*.
% 3.71/3.89 3548[4:Res:3542.1,4.0] group_element(e_1) || -> .
% 3.71/3.89 3550[4:SSi:3548.0,1.0] || -> .
% 3.71/3.89 3551[2:Spt:3550.0,615.3] || -> product(e_1,e_1,e_1)*.
% 3.71/3.89 3567[2:Res:3551.0,11.0] || product(e_1,e_1,u)*+ -> equalish(u,e_1).
% 3.71/3.89 3568[2:Res:3551.0,12.0] || product(e_1,u,e_1)*+ -> equalish(u,e_1).
% 3.71/3.89 3569[2:Res:3551.0,13.0] || product(u,e_1,e_1)*+ -> equalish(u,e_1).
% 3.71/3.89 3578[2:Res:3551.0,20.2] group_element(u) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 3.71/3.89 3579[2:Res:3551.0,21.2] group_element(e_1) group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 3.71/3.89 3583[2:SSi:3578.1,1.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 3.71/3.89 3584[2:SSi:3579.0,1.0] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 3.71/3.89 3623[2:Res:10.4,3568.0] group_element(u) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 3.71/3.89 3627[2:SSi:3623.1,1.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 3.71/3.89 3758[2:Res:10.4,3569.0] group_element(e_1) group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 3.71/3.89 3761[2:SSi:3758.0,1.0] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 3.71/3.89 3763[2:Res:3583.2,11.0] group_element(u) || product(e_1,u,v)*+ -> product(e_1,u,e_3)* equalish(e_1,u) equalish(v,e_2).
% 3.71/3.89 3765[2:Res:3583.2,13.0] group_element(u) || product(v,u,e_2)*+ -> product(e_1,u,e_3)* equalish(e_1,u) equalish(v,e_1).
% 3.71/3.89 3810[2:Res:3584.2,12.0] group_element(u) || product(u,v,e_2)*+ -> product(u,e_1,e_3)* equalish(e_1,u) equalish(v,e_1).
% 3.71/3.89 3850[2:Res:3627.2,11.0] group_element(u) || product(e_1,u,v)*+ -> product(e_1,u,e_3)* equalish(u,e_1) equalish(v,e_2).
% 3.71/3.89 3943[2:Res:3761.2,12.0] group_element(u) || product(u,v,e_2)*+ -> product(u,e_1,e_3)* equalish(u,e_1) equalish(v,e_1).
% 3.71/3.89 4046[2:Res:3583.2,3763.1] group_element(u) group_element(u) || -> product(e_1,u,e_3)* equalish(e_1,u) product(e_1,u,e_3)* equalish(e_1,u) equalish(e_2,e_2).
% 4.22/4.44 4053[2:Obv:4046.3] group_element(u) || -> product(e_1,u,e_3)* equalish(e_1,u) equalish(e_2,e_2).
% 4.22/4.44 4070[3:Spt:4053.0,4053.1,4053.2] group_element(u) || -> product(e_1,u,e_3)* equalish(e_1,u).
% 4.22/4.44 4073[3:Res:4070.1,12.0] group_element(u) || product(e_1,v,e_3)*+ -> equalish(e_1,u)* equalish(v,u)*.
% 4.22/4.44 4296[3:Res:4070.1,4073.1] group_element(u) group_element(v) || -> equalish(e_1,u)* equalish(e_1,v)* equalish(u,v)*.
% 4.22/4.44 4356[3:Res:4296.2,5.0] group_element(e_3) group_element(u) || -> equalish(e_1,u)* equalish(e_3,u).
% 4.22/4.44 4363[3:SSi:4356.0,3.0] group_element(u) || -> equalish(e_1,u)* equalish(e_3,u).
% 4.22/4.44 4368[3:Res:4363.1,4.0] group_element(e_2) || -> equalish(e_3,e_2)*.
% 4.22/4.44 4369[3:SSi:4368.0,2.0] || -> equalish(e_3,e_2)*.
% 4.22/4.44 4370[3:MRR:4369.0,9.0] || -> .
% 4.22/4.44 4371[3:Spt:4370.0,4053.3] || -> equalish(e_2,e_2)*.
% 4.22/4.44 4423[2:Res:703.9,3850.1] group_element(u) group_element(e_1) group_element(v) group_element(e_2) || -> product(u,v,e_3) product(u,v,e_2)* product(e_1,v,e_3)* equalish(u,e_1) product(e_2,v,e_3) product(e_2,v,e_2) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 4.22/4.44 4448[2:Con:4423.0] group_element(e_1) group_element(u) group_element(e_2) || -> product(e_1,u,e_3)* product(e_2,u,e_3) product(e_2,u,e_2) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 4.22/4.44 4449[2:SSi:4448.2,4448.0,2.0,1.0] group_element(u) || -> product(e_1,u,e_3)* product(e_2,u,e_3) product(e_2,u,e_2) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 4.22/4.44 4450[2:MRR:4449.5,4449.6,6.0,4.0] group_element(u) || -> product(e_1,u,e_3)* product(e_2,u,e_3) product(e_2,u,e_2) product(e_1,e_2,e_3)*.
% 4.22/4.44 4918[4:Spt:4450.0,4450.1,4450.2,4450.3] group_element(u) || -> product(e_1,u,e_3)* product(e_2,u,e_3) product(e_2,u,e_2).
% 4.22/4.44 4934[4:Res:4918.1,3567.0] group_element(e_1) || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(e_3,e_1).
% 4.22/4.44 4940[4:SSi:4934.0,1.0] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(e_3,e_1).
% 4.22/4.44 4941[4:MRR:4940.2,8.0] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 4.22/4.44 5019[5:Spt:4941.0] || -> product(e_2,e_1,e_3)*.
% 4.22/4.44 5021[5:Res:5019.0,14.0] || product(u,e_1,e_2)*+ -> product(u,e_2,e_3).
% 4.22/4.44 5024[5:Res:5019.0,13.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 4.22/4.44 5033[5:Res:5019.0,18.2] group_element(e_1) group_element(e_3) || -> product(e_3,e_1,e_3) product(e_3,e_1,e_2) product(e_2,e_3,e_1)*.
% 4.22/4.44 5046[5:SSi:5033.1,5033.0,3.0,1.0] || -> product(e_3,e_1,e_3) product(e_3,e_1,e_2) product(e_2,e_3,e_1)*.
% 4.22/4.44 5104[6:Spt:5046.0] || -> product(e_3,e_1,e_3)*.
% 4.22/4.44 5120[6:Res:5104.0,5024.0] || -> equalish(e_3,e_2)*.
% 4.22/4.44 5124[6:MRR:5120.0,9.0] || -> .
% 4.22/4.44 5125[6:Spt:5124.0,5046.0,5104.0] || product(e_3,e_1,e_3)*+ -> .
% 4.22/4.44 5126[6:Spt:5124.0,5046.1,5046.2] || -> product(e_3,e_1,e_2) product(e_2,e_3,e_1)*.
% 4.22/4.44 5132[6:Res:5126.1,14.0] || product(u,e_3,e_2)+ -> product(e_3,e_1,e_2)* product(u,e_2,e_1)*.
% 4.22/4.44 5199[7:Spt:5132.0,5132.2] || product(u,e_3,e_2)+ -> product(u,e_2,e_1)*.
% 4.22/4.44 5217[7:Res:3583.2,5199.0] group_element(e_3) || -> product(e_1,e_3,e_3) equalish(e_1,e_3) product(e_1,e_2,e_1)*.
% 4.22/4.44 5220[7:SSi:5217.0,3.0] || -> product(e_1,e_3,e_3) equalish(e_1,e_3) product(e_1,e_2,e_1)*.
% 4.22/4.44 5221[7:MRR:5220.1,5.0] || -> product(e_1,e_3,e_3) product(e_1,e_2,e_1)*.
% 4.22/4.44 5237[8:Spt:5221.0] || -> product(e_1,e_3,e_3)*.
% 4.22/4.44 5242[8:Res:5237.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_1).
% 4.22/4.44 5251[8:Res:5237.0,18.2] group_element(e_3) group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_3,e_1)*.
% 4.22/4.44 5256[8:Obv:5251.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_3,e_1)*.
% 4.22/4.44 5257[8:SSi:5256.0,3.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_3,e_1)*.
% 4.22/4.44 5352[9:Spt:5257.0] || -> product(e_3,e_3,e_3)*.
% 4.22/4.44 5369[9:Res:5352.0,5242.0] || -> equalish(e_3,e_1)*.
% 4.22/4.44 5370[9:MRR:5369.0,8.0] || -> .
% 4.22/4.44 5383[9:Spt:5370.0,5257.0,5352.0] || product(e_3,e_3,e_3)* -> .
% 4.22/4.44 5384[9:Spt:5370.0,5257.1,5257.2] || -> product(e_3,e_3,e_2) product(e_1,e_3,e_1)*.
% 4.22/4.44 5408[9:Res:5384.1,3568.0] || -> product(e_3,e_3,e_2)* equalish(e_3,e_1).
% 4.22/4.44 5416[9:MRR:5408.1,8.0] || -> product(e_3,e_3,e_2)*.
% 4.22/4.44 5430[9:Res:5416.0,3943.1] group_element(e_3) || -> product(e_3,e_1,e_3)* equalish(e_3,e_1) equalish(e_3,e_1).
% 4.22/4.44 5463[9:Obv:5430.2] group_element(e_3) || -> product(e_3,e_1,e_3)* equalish(e_3,e_1).
% 4.22/4.44 5464[9:SSi:5463.0,3.0] || -> product(e_3,e_1,e_3)* equalish(e_3,e_1).
% 4.22/4.44 5465[9:MRR:5464.0,5464.1,5125.0,8.0] || -> .
% 4.22/4.44 5484[8:Spt:5465.0,5221.0,5237.0] || product(e_1,e_3,e_3)* -> .
% 4.22/4.44 5485[8:Spt:5465.0,5221.1] || -> product(e_1,e_2,e_1)*.
% 4.22/4.44 5511[8:Res:5485.0,3568.0] || -> equalish(e_2,e_1)*.
% 4.22/4.44 5516[8:MRR:5511.0,6.0] || -> .
% 4.22/4.44 5531[7:Spt:5516.0,5132.1] || -> product(e_3,e_1,e_2)*.
% 4.22/4.44 5561[7:Res:5531.0,5021.0] || -> product(e_3,e_2,e_3)*.
% 4.22/4.44 5577[7:Res:5561.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_3).
% 4.22/4.44 5806[7:Res:4918.1,5577.0] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)* equalish(e_1,e_3).
% 4.22/4.44 5807[7:SSi:5806.0,2.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)* equalish(e_1,e_3).
% 4.22/4.44 5808[7:MRR:5807.2,5.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 4.22/4.44 5809[8:Spt:5808.0] || -> product(e_2,e_2,e_3)*.
% 4.22/4.44 5825[8:Res:5809.0,5577.0] || -> equalish(e_2,e_3)*.
% 4.22/4.44 5827[8:MRR:5825.0,7.0] || -> .
% 4.22/4.44 5845[8:Spt:5827.0,5808.0,5809.0] || product(e_2,e_2,e_3)* -> .
% 4.22/4.44 5846[8:Spt:5827.0,5808.1] || -> product(e_2,e_2,e_2)*.
% 4.22/4.44 5864[8:Res:5846.0,3765.1] group_element(e_2) || -> product(e_1,e_2,e_3)* equalish(e_1,e_2) equalish(e_2,e_1).
% 4.22/4.44 5875[8:SSi:5864.0,2.0] || -> product(e_1,e_2,e_3)* equalish(e_1,e_2) equalish(e_2,e_1).
% 4.22/4.44 5876[8:MRR:5875.1,5875.2,4.0,6.0] || -> product(e_1,e_2,e_3)*.
% 4.22/4.44 5910[8:Res:5876.0,5577.0] || -> equalish(e_1,e_3)*.
% 4.22/4.44 5914[8:MRR:5910.0,5.0] || -> .
% 4.22/4.44 5922[5:Spt:5914.0,4941.0,5019.0] || product(e_2,e_1,e_3)*+ -> .
% 4.22/4.44 5923[5:Spt:5914.0,4941.1] || -> product(e_2,e_1,e_2)*.
% 4.22/4.44 5942[5:Res:5923.0,14.0] || product(u,e_1,e_2)*+ -> product(u,e_2,e_2).
% 4.22/4.44 6054[5:Res:5923.0,5942.0] || -> product(e_2,e_2,e_2)*.
% 4.22/4.44 6080[5:Res:6054.0,3810.1] group_element(e_2) || -> product(e_2,e_1,e_3)* equalish(e_1,e_2) equalish(e_2,e_1).
% 4.22/4.44 6100[5:SSi:6080.0,2.0] || -> product(e_2,e_1,e_3)* equalish(e_1,e_2) equalish(e_2,e_1).
% 4.22/4.44 6101[5:MRR:6100.0,6100.1,6100.2,5922.0,4.0,6.0] || -> .
% 4.22/4.44 6123[4:Spt:6101.0,4450.4] || -> product(e_1,e_2,e_3)*.
% 4.22/4.44 6131[4:Res:6123.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_1).
% 4.22/4.44 6140[4:Res:6123.0,18.2] group_element(e_2) group_element(e_3) || -> product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_1,e_3,e_1)*.
% 4.22/4.44 6159[4:SSi:6140.1,6140.0,3.0,2.0] || -> product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_1,e_3,e_1)*.
% 4.22/4.44 6221[5:Spt:6159.0] || -> product(e_3,e_2,e_3)*.
% 4.22/4.44 6236[5:Res:6221.0,6131.0] || -> equalish(e_3,e_1)*.
% 4.22/4.44 6237[5:MRR:6236.0,8.0] || -> .
% 4.22/4.44 6238[5:Spt:6237.0,6159.0,6221.0] || product(e_3,e_2,e_3)*+ -> .
% 4.22/4.44 6239[5:Spt:6237.0,6159.1,6159.2] || -> product(e_3,e_2,e_2) product(e_1,e_3,e_1)*.
% 4.22/4.44 6261[5:Res:6239.1,3568.0] || -> product(e_3,e_2,e_2)* equalish(e_3,e_1).
% 4.22/4.44 6266[5:MRR:6261.1,8.0] || -> product(e_3,e_2,e_2)*.
% 4.22/4.44 6276[5:Res:6266.0,3810.1] group_element(e_3) || -> product(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_2,e_1).
% 4.22/4.44 6296[5:SSi:6276.0,3.0] || -> product(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_2,e_1).
% 4.22/4.44 6297[5:MRR:6296.1,6296.2,5.0,6.0] || -> product(e_3,e_1,e_3)*.
% 4.22/4.44 6312[5:Res:6297.0,14.0] || product(u,e_1,e_3)*+ -> product(u,e_3,e_3).
% 4.22/4.44 6314[5:Res:6297.0,12.0] || product(e_3,u,e_3)*+ -> equalish(u,e_1).
% 4.22/4.44 6587[5:Res:6297.0,6312.0] || -> product(e_3,e_3,e_3)*.
% 4.22/4.44 6605[5:Res:6587.0,6314.0] || -> equalish(e_3,e_1)*.
% 4.22/4.44 6606[5:MRR:6605.0,8.0] || -> .
% 4.22/4.44 % SZS output end Refutation
% 4.22/4.44 Formulae used in the proof : element_1 element_2 element_3 e_1_is_not_e_2 e_1_is_not_e_3 e_2_is_not_e_1 e_2_is_not_e_3 e_3_is_not_e_1 e_3_is_not_e_2 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation qg3
% 4.22/4.44
%------------------------------------------------------------------------------