TSTP Solution File: GRP129-1.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP129-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:45:43 EDT 2022
% Result : Unsatisfiable 18.03s 18.21s
% Output : Refutation 19.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP129-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.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 : Tue Jun 14 07:31:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 18.03/18.21
% 18.03/18.21 SPASS V 3.9
% 18.03/18.21 SPASS beiseite: Proof found.
% 18.03/18.21 % SZS status Theorem
% 18.03/18.21 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.03/18.21 SPASS derived 6582 clauses, backtracked 1713 clauses, performed 51 splits and kept 5043 clauses.
% 18.03/18.21 SPASS allocated 87302 KBytes.
% 18.03/18.21 SPASS spent 0:0:17.86 on the problem.
% 18.03/18.21 0:00:00.03 for the input.
% 18.03/18.21 0:00:00.00 for the FLOTTER CNF translation.
% 18.03/18.21 0:00:00.14 for inferences.
% 18.03/18.21 0:00:00.09 for the backtracking.
% 18.03/18.21 0:0:17.57 for the reduction.
% 18.03/18.21
% 18.03/18.21
% 18.03/18.21 Here is a proof with depth 22, length 529 :
% 18.03/18.21 % SZS output start Refutation
% 18.03/18.21 1[0:Inp] || -> group_element(e_1)*.
% 18.03/18.21 2[0:Inp] || -> group_element(e_2)*.
% 18.03/18.21 3[0:Inp] || -> group_element(e_3)*.
% 18.03/18.21 4[0:Inp] || equalish(e_1,e_2)*+ -> .
% 18.03/18.21 5[0:Inp] || equalish(e_1,e_3)*+ -> .
% 18.03/18.21 6[0:Inp] || equalish(e_2,e_1)*+ -> .
% 18.03/18.21 7[0:Inp] || equalish(e_2,e_3)*+ -> .
% 18.03/18.21 8[0:Inp] || equalish(e_3,e_1)*+ -> .
% 18.03/18.21 9[0:Inp] || equalish(e_3,e_2)*+ -> .
% 18.03/18.21 10[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 18.03/18.21 11[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 18.03/18.21 12[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 18.03/18.21 13[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 18.03/18.21 14[0:Inp] || product(u,v,w)*+ product(x,u,v)* -> product(v,x,w)*.
% 18.03/18.21 18[0:Res:10.4,14.0] group_element(u) group_element(v) || product(w,v,u)*+ -> product(v,u,e_3) product(v,u,e_2)* product(u,w,e_1)*.
% 18.03/18.21 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).
% 18.03/18.21 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)*.
% 18.03/18.21 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)*.
% 18.03/18.21 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)*.
% 18.03/18.21 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)*.
% 18.03/18.21 24[0:Res:10.4,20.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* product(v,w,e_3) product(v,w,e_2)* equalish(u,w)*.
% 18.03/18.21 25[0:Obv:24.1] group_element(u) group_element(v) group_element(w) || -> product(w,u,e_3) product(w,u,e_2)* product(w,v,e_3) product(w,v,e_2)* equalish(u,v)*.
% 18.03/18.21 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).
% 18.03/18.21 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).
% 18.03/18.21 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)*.
% 18.03/18.21 29[1:Res:28.3,14.0] group_element(u) group_element(v) || product(w,v,u)*+ -> product(v,u,e_3)* product(u,w,e_2)*.
% 18.03/18.21 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).
% 18.03/18.21 32[1:Res:28.3,13.0] group_element(u) group_element(v) || product(w,u,e_2)*+ -> product(v,u,e_3)* equalish(w,v)*.
% 18.03/18.21 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).
% 18.03/18.21 34[1:Obv:33.4] group_element(u) group_element(v) || -> product(v,u,e_3)* equalish(e_2,e_2).
% 18.03/18.21 37[2:Spt:34.0,34.1,34.2] group_element(u) group_element(v) || -> product(v,u,e_3)*.
% 18.03/18.21 40[2:Res:37.2,12.0] group_element(u) group_element(v) || product(v,w,e_3)*+ -> equalish(w,u)*.
% 18.03/18.21 48[2:Res:37.2,40.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> equalish(u,w)*.
% 18.03/18.21 49[2:Obv:48.1] group_element(u) group_element(v) group_element(w) || -> equalish(u,v)*.
% 18.03/18.21 50[2:Con:49.2] group_element(u) group_element(v) || -> equalish(u,v)*.
% 18.03/18.21 56[2:Res:50.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 18.03/18.21 62[2:SSi:56.1,56.0,2.0,1.0] || -> .
% 18.03/18.21 63[2:Spt:62.0,34.3] || -> equalish(e_2,e_2)*.
% 18.03/18.21 74[1:Res:28.3,29.2] group_element(u) group_element(v) group_element(e_2) group_element(u) || -> product(v,u,e_3)* product(u,e_2,e_3)* product(e_2,v,e_2)*.
% 18.03/18.21 75[1:Obv:74.0] group_element(u) group_element(e_2) group_element(v) || -> product(u,v,e_3)* product(v,e_2,e_3)* product(e_2,u,e_2)*.
% 18.03/18.21 76[1:SSi:75.1,2.0] group_element(u) group_element(v) || -> product(u,v,e_3)* product(v,e_2,e_3)* product(e_2,u,e_2)*.
% 18.03/18.21 83[1:Res:76.3,14.0] group_element(u) group_element(v) || product(w,v,e_2)* -> product(u,v,e_3)* product(e_2,u,e_2)* product(e_2,w,e_3)*.
% 18.03/18.21 87[1:Res:76.3,29.2] group_element(u) group_element(v) group_element(e_3) group_element(e_2) || -> product(u,v,e_3)* product(e_2,u,e_2)* product(e_2,e_3,e_3)* product(e_3,v,e_2)*.
% 18.03/18.21 104[1:SSi:87.3,87.2,2.0,3.0] group_element(u) group_element(v) || -> product(u,v,e_3)* product(e_2,u,e_2)* product(e_2,e_3,e_3)* product(e_3,v,e_2)*.
% 18.03/18.21 105[1:MRR:104.5,83.2] group_element(u) group_element(v) || -> product(u,v,e_3)* product(e_2,u,e_2)* product(e_2,e_3,e_3)*.
% 18.03/18.21 108[3:Spt:105.0,105.1,105.2,105.3] group_element(u) group_element(v) || -> product(u,v,e_3)* product(e_2,u,e_2)*.
% 18.03/18.21 119[3:Res:108.3,29.2] group_element(u) group_element(v) group_element(e_2) group_element(u) || -> product(u,v,e_3)* product(u,e_2,e_3)* product(e_2,e_2,e_2)*.
% 18.03/18.21 127[3:Obv:119.0] group_element(u) group_element(e_2) group_element(v) || -> product(v,u,e_3)* product(v,e_2,e_3)* product(e_2,e_2,e_2)*.
% 18.03/18.21 128[3:Con:127.0] group_element(e_2) group_element(u) || -> product(u,e_2,e_3)* product(e_2,e_2,e_2)*.
% 18.03/18.21 129[3:SSi:128.0,2.0] group_element(u) || -> product(u,e_2,e_3)* product(e_2,e_2,e_2)*.
% 18.03/18.21 132[4:Spt:129.0,129.1] group_element(u) || -> product(u,e_2,e_3)*.
% 18.03/18.21 133[4:Res:132.1,14.0] group_element(u) || product(v,u,e_2)* -> product(e_2,v,e_3)*.
% 18.03/18.21 137[4:Res:132.1,29.2] group_element(u) group_element(e_3) group_element(e_2) || -> product(e_2,e_3,e_3)* product(e_3,u,e_2)*.
% 18.03/18.21 140[4:SSi:137.2,137.1,2.0,3.0] group_element(u) || -> product(e_2,e_3,e_3)* product(e_3,u,e_2)*.
% 18.03/18.21 141[4:MRR:140.2,133.1] group_element(u) || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 162[4:EmS:141.0,1.0] || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 167[4:Res:162.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_3).
% 18.03/18.21 226[4:Res:132.1,167.0] group_element(e_2) || -> equalish(e_2,e_3)*.
% 18.03/18.21 228[4:SSi:226.0,2.0] || -> equalish(e_2,e_3)*.
% 18.03/18.21 229[4:MRR:228.0,7.0] || -> .
% 18.03/18.21 235[4:Spt:229.0,129.2] || -> product(e_2,e_2,e_2)*.
% 18.03/18.21 242[4:Res:235.0,32.2] group_element(e_2) group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u).
% 18.03/18.21 245[4:SSi:242.0,2.0] group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u).
% 18.03/18.21 283[4:Res:245.1,14.0] group_element(u) || product(v,u,e_2)* -> equalish(e_2,u) product(e_2,v,e_3)*.
% 18.03/18.21 287[4:Res:245.1,29.2] group_element(u) group_element(e_3) group_element(e_2) || -> equalish(e_2,u) product(e_2,e_3,e_3)* product(e_3,u,e_2)*.
% 18.03/18.21 291[4:SSi:287.2,287.1,2.0,3.0] group_element(u) || -> equalish(e_2,u) product(e_2,e_3,e_3)* product(e_3,u,e_2)*.
% 18.03/18.21 292[4:MRR:291.3,283.1] group_element(u) || -> equalish(e_2,u)* product(e_2,e_3,e_3)*.
% 18.03/18.21 304[5:Spt:292.0,292.1] group_element(u) || -> equalish(e_2,u)*.
% 18.03/18.21 306[5:Res:304.1,6.0] group_element(e_1) || -> .
% 18.03/18.21 308[5:SSi:306.0,1.0] || -> .
% 18.03/18.21 309[5:Spt:308.0,292.2] || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 311[5:Res:309.0,11.0] || product(e_2,e_3,u)*+ -> equalish(u,e_3).
% 18.03/18.21 313[5:Res:309.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 344[5:Res:108.3,311.0] group_element(e_3) group_element(u) || -> product(e_3,u,e_3)* equalish(e_2,e_3).
% 18.03/18.21 348[5:SSi:344.0,3.0] group_element(u) || -> product(e_3,u,e_3)* equalish(e_2,e_3).
% 18.03/18.21 349[5:MRR:348.2,7.0] group_element(u) || -> product(e_3,u,e_3)*.
% 18.03/18.21 419[5:Res:349.1,313.0] group_element(e_3) || -> equalish(e_3,e_2)*.
% 18.03/18.21 424[5:SSi:419.0,3.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 425[5:MRR:424.0,9.0] || -> .
% 18.03/18.21 429[3:Spt:425.0,105.4] || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 432[3:Res:429.0,14.0] || product(u,e_2,e_3)* -> product(e_3,u,e_3)*.
% 18.03/18.21 433[3:Res:429.0,11.0] || product(e_2,e_3,u)*+ -> equalish(u,e_3).
% 18.03/18.21 435[3:Res:429.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 486[3:Res:76.4,433.0] group_element(e_3) group_element(u) || -> product(e_3,u,e_3)* product(u,e_2,e_3)* equalish(e_2,e_3).
% 18.03/18.21 490[3:SSi:486.0,3.0] group_element(u) || -> product(e_3,u,e_3)* product(u,e_2,e_3)* equalish(e_2,e_3).
% 18.03/18.21 491[3:MRR:490.3,7.0] group_element(u) || -> product(e_3,u,e_3)* product(u,e_2,e_3)*.
% 18.03/18.21 492[3:MRR:491.2,432.0] group_element(u) || -> product(e_3,u,e_3)*.
% 18.03/18.21 542[3:Res:492.1,435.0] group_element(e_3) || -> equalish(e_3,e_2)*.
% 18.03/18.21 543[3:SSi:542.0,3.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 544[3:MRR:543.0,9.0] || -> .
% 18.03/18.21 551[1:Spt:544.0,27.4] || -> equalish(e_1,e_1)*.
% 18.03/18.21 562[0:Res:10.4,18.2] group_element(u) group_element(v) group_element(e_1) group_element(u) || -> product(v,u,e_3) product(v,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,v,e_1)*.
% 18.03/18.21 563[0:Obv:562.0] group_element(u) group_element(e_1) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* product(e_1,u,e_1)*.
% 18.03/18.21 564[0:SSi:563.1,1.0] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* product(e_1,u,e_1)*.
% 18.03/18.21 571[0:Res:564.5,14.0] group_element(u) group_element(v) || product(w,v,e_1)* -> product(u,v,e_3) product(u,v,e_2)* product(v,e_1,e_3)* product(e_1,u,e_1)* product(e_1,w,e_2)*.
% 18.03/18.21 575[0:Res:564.5,18.2] group_element(u) group_element(v) group_element(e_2) group_element(e_1) || -> product(u,v,e_3) product(u,v,e_2)* product(v,e_1,e_3)* product(e_1,u,e_1)* product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,v,e_1)*.
% 18.03/18.21 592[0:SSi:575.3,575.2,1.0,2.0] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(v,e_1,e_3)* product(e_1,u,e_1)* product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,v,e_1)*.
% 18.03/18.21 593[0:MRR:592.8,571.2] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(v,e_1,e_3)* product(e_1,u,e_1)* product(e_1,e_2,e_3) product(e_1,e_2,e_2)*.
% 18.03/18.21 607[0:Res:23.6,18.2] group_element(u) group_element(v) group_element(w) group_element(e_2) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(w,v,e_3)* equalish(u,w)* product(v,e_2,e_3) product(v,e_2,e_2)* product(e_2,w,e_1)*.
% 18.03/18.21 612[0:Obv:607.1] group_element(u) group_element(v) group_element(e_2) group_element(w) || -> product(u,w,e_3) product(u,w,e_2)* product(v,w,e_3)* equalish(u,v)* product(w,e_2,e_3) product(w,e_2,e_2)* product(e_2,v,e_1)*.
% 18.03/18.21 613[0:SSi:612.2,2.0] 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(w,e_2,e_3) product(w,e_2,e_2)* product(e_2,v,e_1)*.
% 18.03/18.21 621[0:Res:25.4,18.2] group_element(u) group_element(v) group_element(w) group_element(e_2) group_element(u) || -> product(w,u,e_3)* product(w,v,e_3) product(w,v,e_2)* equalish(u,v)* product(u,e_2,e_3) product(u,e_2,e_2)* product(e_2,w,e_1)*.
% 18.03/18.21 634[0:Obv:621.0] group_element(u) group_element(v) group_element(e_2) group_element(w) || -> product(v,w,e_3)* product(v,u,e_3) product(v,u,e_2)* equalish(w,u)* product(w,e_2,e_3) product(w,e_2,e_2)* product(e_2,v,e_1)*.
% 18.03/18.21 635[0:SSi:634.2,2.0] group_element(u) group_element(v) group_element(w) || -> product(v,w,e_3)* product(v,u,e_3) product(v,u,e_2)* equalish(w,u)* product(w,e_2,e_3) product(w,e_2,e_2)* product(e_2,v,e_1)*.
% 18.03/18.21 679[2:Spt:593.0,593.1,593.2,593.3,593.4,593.5] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(v,e_1,e_3)* product(e_1,u,e_1)*.
% 18.03/18.21 686[2:Res:679.4,14.0] group_element(u) group_element(v) || product(w,v,e_1)* -> product(u,v,e_3) product(u,v,e_2)* product(e_1,u,e_1)* product(e_1,w,e_3)*.
% 18.03/18.21 690[2:Res:679.4,18.2] group_element(u) group_element(v) group_element(e_3) group_element(e_1) || -> product(u,v,e_3) product(u,v,e_2)* product(e_1,u,e_1)* product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,v,e_1)*.
% 18.03/18.21 707[2:SSi:690.3,690.2,1.0,3.0] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(e_1,u,e_1)* product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,v,e_1)*.
% 18.03/18.21 708[2:MRR:707.7,686.2] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(e_1,u,e_1)* product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 18.03/18.21 733[3:Spt:708.0,708.1,708.2,708.3,708.4] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(e_1,u,e_1)*.
% 18.03/18.21 744[3:Res:733.4,18.2] group_element(u) group_element(v) group_element(e_1) group_element(u) || -> product(u,v,e_3) product(u,v,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,e_1,e_1)*.
% 18.03/18.21 752[3:Obv:744.0] group_element(u) group_element(e_1) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* product(e_1,e_1,e_1)*.
% 18.03/18.21 753[3:Con:752.0] group_element(e_1) group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,e_1,e_1)*.
% 18.03/18.21 754[3:SSi:753.0,1.0] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,e_1,e_1)*.
% 18.03/18.21 757[4:Spt:754.0,754.1,754.2] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)*.
% 18.03/18.21 758[4:Res:757.2,14.0] group_element(u) || product(v,u,e_1)* -> product(u,e_1,e_3)* product(e_1,v,e_2)*.
% 18.03/18.21 762[4:Res:757.2,18.2] group_element(u) group_element(e_2) group_element(e_1) || -> product(u,e_1,e_3)* product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 765[4:SSi:762.2,762.1,1.0,2.0] group_element(u) || -> product(u,e_1,e_3)* product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 766[4:MRR:765.4,758.1] group_element(u) || -> product(u,e_1,e_3)* product(e_1,e_2,e_3) product(e_1,e_2,e_2)*.
% 18.03/18.21 779[5:Spt:766.0,766.1] group_element(u) || -> product(u,e_1,e_3)*.
% 18.03/18.21 783[5:Res:779.1,13.0] group_element(u) || product(v,e_1,e_3)*+ -> equalish(v,u)*.
% 18.03/18.21 885[5:Res:779.1,783.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 18.03/18.21 891[5:Res:885.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 18.03/18.21 897[5:SSi:891.1,891.0,2.0,1.0] || -> .
% 18.03/18.21 898[5:Spt:897.0,766.2,766.3] || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)*.
% 18.03/18.21 901[5:Res:898.1,11.0] || product(e_1,e_2,u)*+ -> product(e_1,e_2,e_3)* equalish(u,e_2).
% 18.03/18.21 902[5:Res:898.1,12.0] || product(e_1,u,e_2)* -> product(e_1,e_2,e_3)* equalish(u,e_2).
% 18.03/18.21 916[6:Spt:901.0,901.2] || product(e_1,e_2,u)*+ -> equalish(u,e_2).
% 18.03/18.21 919[6:Res:898.1,916.0] || -> product(e_1,e_2,e_3)* equalish(e_2,e_2).
% 18.03/18.21 942[7:Spt:919.0] || -> product(e_1,e_2,e_3)*.
% 18.03/18.21 949[7:Res:942.0,916.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 950[7:MRR:949.0,9.0] || -> .
% 18.03/18.21 951[7:Spt:950.0,919.0,942.0] || product(e_1,e_2,e_3)*+ -> .
% 18.03/18.21 952[7:Spt:950.0,919.1] || -> equalish(e_2,e_2)*.
% 18.03/18.21 954[7:MRR:902.1,951.0] || product(e_1,u,e_2)*+ -> equalish(u,e_2).
% 18.03/18.21 970[7:Res:757.2,954.0] group_element(e_1) || -> product(e_1,e_1,e_3)* equalish(e_1,e_2).
% 18.03/18.21 971[7:SSi:970.0,1.0] || -> product(e_1,e_1,e_3)* equalish(e_1,e_2).
% 18.03/18.21 972[7:MRR:971.1,4.0] || -> product(e_1,e_1,e_3)*.
% 18.03/18.21 1000[7:Res:972.0,14.0] || product(u,e_1,e_1)* -> product(e_1,u,e_3)*.
% 18.03/18.21 1002[7:Res:972.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 1004[7:Res:972.0,18.2] group_element(e_3) group_element(e_1) || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,e_1,e_1).
% 18.03/18.21 1007[7:SSi:1004.1,1004.0,1.0,3.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,e_1,e_1).
% 18.03/18.21 1008[7:MRR:1007.2,1000.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 18.03/18.21 1015[7:Res:1008.1,954.0] || -> product(e_1,e_3,e_3)* equalish(e_3,e_2).
% 18.03/18.21 1016[7:MRR:1015.1,9.0] || -> product(e_1,e_3,e_3)*.
% 18.03/18.21 1073[7:Res:1016.0,1002.0] || -> equalish(e_3,e_1)*.
% 18.03/18.21 1075[7:MRR:1073.0,8.0] || -> .
% 18.03/18.21 1076[6:Spt:1075.0,901.1] || -> product(e_1,e_2,e_3)*.
% 18.03/18.21 1077[6:Res:1076.0,14.0] || product(u,e_1,e_2)*+ -> product(e_2,u,e_3)*.
% 18.03/18.21 1079[6:Res:1076.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 1126[6:Res:757.2,1077.0] group_element(u) || -> product(u,e_1,e_3)* product(e_2,u,e_3)*.
% 18.03/18.21 1159[6:Res:1126.1,1079.0] group_element(e_1) || -> product(e_2,e_1,e_3)* equalish(e_1,e_2).
% 18.03/18.21 1167[6:SSi:1159.0,1.0] || -> product(e_2,e_1,e_3)* equalish(e_1,e_2).
% 18.03/18.21 1168[6:MRR:1167.1,4.0] || -> product(e_2,e_1,e_3)*.
% 18.03/18.21 1205[6:Res:1168.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 1206[6:Res:1168.0,13.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 1238[6:Res:1126.2,1205.0] group_element(u) || -> product(u,e_1,e_3)* equalish(u,e_1).
% 18.03/18.21 1273[6:Res:1238.1,1206.0] group_element(u) || -> equalish(u,e_1)* equalish(u,e_2).
% 18.03/18.21 1278[6:Res:1273.1,8.0] group_element(e_3) || -> equalish(e_3,e_2)*.
% 18.03/18.21 1280[6:SSi:1278.0,3.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 1281[6:MRR:1280.0,9.0] || -> .
% 18.03/18.21 1282[4:Spt:1281.0,754.3] || -> product(e_1,e_1,e_1)*.
% 18.03/18.21 1285[4:Res:1282.0,12.0] || product(e_1,u,e_1)*+ -> equalish(u,e_1).
% 18.03/18.21 1290[4:Res:1282.0,21.2] group_element(e_1) group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 18.03/18.21 1294[4:SSi:1290.0,1.0] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 18.03/18.21 1327[4:Res:733.4,1285.0] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* equalish(u,e_1).
% 18.03/18.21 1354[4:Res:1294.2,14.0] group_element(u) || product(v,u,e_1)* -> product(u,e_1,e_3)* equalish(e_1,u) product(e_1,v,e_2)*.
% 18.03/18.21 1359[4:Res:1294.2,18.2] group_element(u) group_element(e_2) group_element(e_1) || -> product(u,e_1,e_3)* equalish(e_1,u) product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 1369[4:SSi:1359.2,1359.1,1.0,2.0] group_element(u) || -> product(u,e_1,e_3)* equalish(e_1,u) product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 1370[4:MRR:1369.5,1354.1] group_element(u) || -> product(u,e_1,e_3)* equalish(e_1,u) product(e_1,e_2,e_3) product(e_1,e_2,e_2)*.
% 18.03/18.21 1468[5:Spt:1370.0,1370.1,1370.2] group_element(u) || -> product(u,e_1,e_3)* equalish(e_1,u).
% 18.03/18.21 1469[5:Res:1468.1,14.0] group_element(u) || product(v,u,e_1)* -> equalish(e_1,u) product(e_1,v,e_3)*.
% 18.03/18.21 1474[5:Res:1468.1,18.2] group_element(u) group_element(e_3) group_element(e_1) || -> equalish(e_1,u) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,u,e_1)*.
% 18.03/18.21 1482[5:SSi:1474.2,1474.1,1.0,3.0] group_element(u) || -> equalish(e_1,u) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,u,e_1)*.
% 18.03/18.21 1483[5:MRR:1482.4,1469.1] group_element(u) || -> equalish(e_1,u)* product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 18.03/18.21 1487[6:Spt:1483.0,1483.1] group_element(u) || -> equalish(e_1,u)*.
% 18.03/18.21 1489[6:Res:1487.1,4.0] group_element(e_2) || -> .
% 18.03/18.21 1491[6:SSi:1489.0,2.0] || -> .
% 18.03/18.21 1492[6:Spt:1491.0,1483.2,1483.3] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 18.03/18.21 1493[6:Res:1492.1,14.0] || product(u,e_1,e_3)* -> product(e_1,e_3,e_3)* product(e_3,u,e_2)*.
% 18.03/18.21 1494[6:Res:1492.1,11.0] || product(e_1,e_3,u)*+ -> product(e_1,e_3,e_3)* equalish(u,e_2).
% 18.03/18.21 1496[6:Res:1492.1,13.0] || product(u,e_3,e_2)* -> product(e_1,e_3,e_3)* equalish(u,e_1).
% 18.03/18.21 1531[7:Spt:1494.0,1494.2] || product(e_1,e_3,u)*+ -> equalish(u,e_2).
% 18.03/18.21 1540[7:Res:1492.1,1531.0] || -> product(e_1,e_3,e_3)* equalish(e_2,e_2).
% 18.03/18.21 1560[8:Spt:1540.0] || -> product(e_1,e_3,e_3)*.
% 18.03/18.21 1570[8:Res:1560.0,1531.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 1571[8:MRR:1570.0,9.0] || -> .
% 18.03/18.21 1573[8:Spt:1571.0,1540.0,1560.0] || product(e_1,e_3,e_3)*+ -> .
% 18.03/18.21 1574[8:Spt:1571.0,1540.1] || -> equalish(e_2,e_2)*.
% 18.03/18.21 1577[8:MRR:1496.1,1573.0] || product(u,e_3,e_2)*+ -> equalish(u,e_1).
% 18.03/18.21 1578[8:MRR:1493.1,1573.0] || product(u,e_1,e_3)*+ -> product(e_3,u,e_2)*.
% 18.03/18.21 1647[8:Res:1468.1,1578.0] group_element(u) || -> equalish(e_1,u) product(e_3,u,e_2)*.
% 18.03/18.21 1698[8:Res:1647.2,1577.0] group_element(e_3) || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 18.03/18.21 1699[8:SSi:1698.0,3.0] || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 18.03/18.21 1700[8:MRR:1699.0,1699.1,5.0,8.0] || -> .
% 18.03/18.21 1713[7:Spt:1700.0,1494.1] || -> product(e_1,e_3,e_3)*.
% 18.03/18.21 1714[7:Res:1713.0,14.0] || product(u,e_1,e_3)*+ -> product(e_3,u,e_3)*.
% 18.03/18.21 1717[7:Res:1713.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 1755[7:Res:1468.1,1714.0] group_element(u) || -> equalish(e_1,u) product(e_3,u,e_3)*.
% 18.03/18.21 1767[7:Res:1755.2,1717.0] group_element(e_3) || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 18.03/18.21 1768[7:SSi:1767.0,3.0] || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 18.03/18.21 1769[7:MRR:1768.0,1768.1,5.0,8.0] || -> .
% 18.03/18.21 1777[5:Spt:1769.0,1370.3,1370.4] || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)*.
% 18.03/18.21 1780[5:Res:1777.1,14.0] || product(u,e_1,e_2)* -> product(e_1,e_2,e_3)* product(e_2,u,e_2)*.
% 18.03/18.21 1781[5:Res:1777.1,11.0] || product(e_1,e_2,u)*+ -> product(e_1,e_2,e_3)* equalish(u,e_2).
% 18.03/18.21 1783[5:Res:1777.1,13.0] || product(u,e_2,e_2)* -> product(e_1,e_2,e_3)* equalish(u,e_1).
% 18.03/18.21 1812[6:Spt:1781.0,1781.2] || product(e_1,e_2,u)*+ -> equalish(u,e_2).
% 18.03/18.21 1818[6:Res:733.4,1812.0] group_element(e_2) group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_1,e_2).
% 18.03/18.21 1821[6:Res:1777.1,1812.0] || -> product(e_1,e_2,e_3)* equalish(e_2,e_2).
% 18.03/18.21 1822[6:SSi:1818.0,2.0] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_1,e_2).
% 18.03/18.21 1823[6:MRR:1822.3,4.0] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)*.
% 18.03/18.21 1855[7:Spt:1821.0] || -> product(e_1,e_2,e_3)*.
% 18.03/18.21 1866[7:Res:1855.0,1812.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 1868[7:MRR:1866.0,9.0] || -> .
% 18.03/18.21 1869[7:Spt:1868.0,1821.0,1855.0] || product(e_1,e_2,e_3)*+ -> .
% 18.03/18.21 1870[7:Spt:1868.0,1821.1] || -> equalish(e_2,e_2)*.
% 18.03/18.21 1873[7:MRR:1783.1,1869.0] || product(u,e_2,e_2)*+ -> equalish(u,e_1).
% 18.03/18.21 1874[7:MRR:1780.1,1869.0] || product(u,e_1,e_2)*+ -> product(e_2,u,e_2)*.
% 18.03/18.21 1947[7:Res:1327.3,1873.0] group_element(u) group_element(e_2) || -> product(u,e_2,e_3)* equalish(u,e_1) equalish(u,e_1).
% 18.03/18.21 1955[7:Obv:1947.3] group_element(u) group_element(e_2) || -> product(u,e_2,e_3)* equalish(u,e_1).
% 18.03/18.21 1956[7:SSi:1955.1,2.0] group_element(u) || -> product(u,e_2,e_3)* equalish(u,e_1).
% 18.03/18.21 2008[7:Res:1823.2,1874.0] group_element(e_1) || -> product(e_2,e_1,e_3)* product(e_2,e_2,e_2).
% 18.03/18.21 2011[7:SSi:2008.0,1.0] || -> product(e_2,e_1,e_3)* product(e_2,e_2,e_2).
% 18.03/18.21 2067[8:Spt:2011.0] || -> product(e_2,e_1,e_3)*.
% 18.03/18.21 2070[8:Res:2067.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 2157[8:Res:1956.1,2070.0] group_element(e_2) || -> equalish(e_2,e_1)* equalish(e_2,e_1)*.
% 18.03/18.21 2159[8:Obv:2157.1] group_element(e_2) || -> equalish(e_2,e_1)*.
% 18.03/18.21 2160[8:SSi:2159.0,2.0] || -> equalish(e_2,e_1)*.
% 18.03/18.21 2161[8:MRR:2160.0,6.0] || -> .
% 18.03/18.21 2162[8:Spt:2161.0,2011.0,2067.0] || product(e_2,e_1,e_3)* -> .
% 18.03/18.21 2163[8:Spt:2161.0,2011.1] || -> product(e_2,e_2,e_2)*.
% 18.03/18.21 2183[8:Res:2163.0,1873.0] || -> equalish(e_2,e_1)*.
% 18.03/18.21 2187[8:MRR:2183.0,6.0] || -> .
% 18.03/18.21 2206[6:Spt:2187.0,1781.1] || -> product(e_1,e_2,e_3)*.
% 18.03/18.21 2209[6:Res:2206.0,14.0] || product(u,e_1,e_2)*+ -> product(e_2,u,e_3)*.
% 18.03/18.21 2210[6:Res:2206.0,11.0] || product(e_1,e_2,u)*+ -> equalish(u,e_3).
% 18.03/18.21 2211[6:Res:2206.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 2212[6:Res:2206.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 2239[6:Res:733.4,2210.0] group_element(e_2) group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_1,e_3).
% 18.03/18.21 2243[6:SSi:2239.0,2.0] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_1,e_3).
% 18.03/18.21 2244[6:MRR:2243.3,5.0] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)*.
% 18.03/18.21 2246[0:Fac:635.5,635.8] group_element(e_2) group_element(u) group_element(u) || -> product(u,u,e_3)* product(u,e_2,e_3) equalish(u,e_2) product(u,e_2,e_3) product(u,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 2327[0:Obv:2246.4] group_element(e_2) group_element(u) || -> product(u,u,e_3)* equalish(u,e_2) product(u,e_2,e_3) product(u,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 2328[0:SSi:2327.0,2.0] group_element(u) || -> product(u,u,e_3)* equalish(u,e_2) product(u,e_2,e_3) product(u,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 2444[6:Res:2244.2,2209.0] group_element(e_1) || -> product(e_2,e_1,e_3)* product(e_2,e_2,e_3).
% 18.03/18.21 2448[6:SSi:2444.0,1.0] || -> product(e_2,e_1,e_3)* product(e_2,e_2,e_3).
% 18.03/18.21 2636[7:Spt:2448.0] || -> product(e_2,e_1,e_3)*.
% 18.03/18.21 2637[7:Res:2636.0,14.0] || product(u,e_2,e_1)* -> product(e_1,u,e_3)*.
% 18.03/18.21 2639[7:Res:2636.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 2642[7:Res:2636.0,18.2] group_element(e_3) group_element(e_1) || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,e_2,e_1).
% 18.03/18.21 2652[7:SSi:2642.1,2642.0,1.0,3.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,e_2,e_1).
% 18.03/18.21 2653[7:MRR:2652.2,2637.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 18.03/18.21 2657[8:Spt:2653.0] || -> product(e_1,e_3,e_3)*.
% 18.03/18.21 2669[8:Res:2657.0,2211.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 2673[8:MRR:2669.0,9.0] || -> .
% 18.03/18.21 2684[8:Spt:2673.0,2653.0,2657.0] || product(e_1,e_3,e_3)*+ -> .
% 18.03/18.21 2685[8:Spt:2673.0,2653.1] || -> product(e_1,e_3,e_2)*.
% 18.03/18.21 2692[8:Res:2685.0,13.0] || product(u,e_3,e_2)*+ -> equalish(u,e_1).
% 18.03/18.21 2940[0:Fac:613.4,613.8] group_element(e_2) group_element(u) group_element(e_2) || -> product(e_2,e_2,e_3) product(u,e_2,e_3)* equalish(e_2,u) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 3030[0:Obv:2940.3] group_element(u) group_element(e_2) || -> product(u,e_2,e_3)* equalish(e_2,u) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 3114[8:Res:2244.2,2692.0] group_element(e_3) || -> product(e_2,e_3,e_3)* equalish(e_2,e_1).
% 18.03/18.21 3118[8:SSi:3114.0,3.0] || -> product(e_2,e_3,e_3)* equalish(e_2,e_1).
% 18.03/18.21 3119[8:MRR:3118.1,6.0] || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 3133[8:Res:3119.0,2639.0] || -> equalish(e_3,e_1)*.
% 18.03/18.21 3137[8:MRR:3133.0,8.0] || -> .
% 18.03/18.21 3145[7:Spt:3137.0,2448.0,2636.0] || product(e_2,e_1,e_3)* -> .
% 18.03/18.21 3146[7:Spt:3137.0,2448.1] || -> product(e_2,e_2,e_3)*.
% 18.03/18.21 3161[7:Res:3146.0,2212.0] || -> equalish(e_2,e_1)*.
% 18.03/18.21 3162[7:MRR:3161.0,6.0] || -> .
% 18.03/18.21 3173[3:Spt:3162.0,708.5,708.6] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 18.03/18.21 3174[0:SSi:3030.1,2.0] group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 3211[3:Res:3173.1,14.0] || product(u,e_1,e_3)* -> product(e_1,e_3,e_3)* product(e_3,u,e_2)*.
% 18.03/18.21 3212[3:Res:3173.1,11.0] || product(e_1,e_3,u)*+ -> product(e_1,e_3,e_3)* equalish(u,e_2).
% 18.03/18.21 3213[3:Res:3173.1,12.0] || product(e_1,u,e_2)* -> product(e_1,e_3,e_3)* equalish(u,e_3).
% 18.03/18.21 3214[3:Res:3173.1,13.0] || product(u,e_3,e_2)* -> product(e_1,e_3,e_3)* equalish(u,e_1).
% 18.03/18.21 3216[3:Res:3173.1,18.2] group_element(e_2) group_element(e_3) || -> product(e_1,e_3,e_3)* product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_2,e_1,e_1).
% 18.03/18.21 3234[3:SSi:3216.1,3216.0,3.0,2.0] || -> product(e_1,e_3,e_3)* product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_2,e_1,e_1).
% 18.03/18.21 3251[4:Spt:3212.0,3212.2] || product(e_1,e_3,u)*+ -> equalish(u,e_2).
% 18.03/18.21 3265[4:Res:3173.1,3251.0] || -> product(e_1,e_3,e_3)* equalish(e_2,e_2).
% 18.03/18.21 3274[5:Spt:3265.0] || -> product(e_1,e_3,e_3)*.
% 18.03/18.21 3289[5:Res:3274.0,3251.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 3290[5:MRR:3289.0,9.0] || -> .
% 18.03/18.21 3303[5:Spt:3290.0,3265.0,3274.0] || product(e_1,e_3,e_3)*+ -> .
% 18.03/18.21 3304[5:Spt:3290.0,3265.1] || -> equalish(e_2,e_2)*.
% 18.03/18.21 3305[5:MRR:3173.0,3303.0] || -> product(e_1,e_3,e_2)*.
% 18.03/18.21 3306[5:MRR:3213.1,3303.0] || product(e_1,u,e_2)*+ -> equalish(u,e_3).
% 18.03/18.21 3307[5:MRR:3214.1,3303.0] || product(u,e_3,e_2)*+ -> equalish(u,e_1).
% 18.03/18.21 3308[5:MRR:3211.1,3303.0] || product(u,e_1,e_3)*+ -> product(e_3,u,e_2)*.
% 18.03/18.21 3309[5:MRR:3234.0,3303.0] || -> product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_2,e_1,e_1)*.
% 18.03/18.21 3395[6:Spt:3174.0,3174.1,3174.2,3174.5] group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u) product(e_2,u,e_1)*.
% 18.03/18.21 3469[7:Spt:3309.0] || -> product(e_3,e_2,e_3)*.
% 18.03/18.21 3470[7:Res:3469.0,14.0] || product(u,e_3,e_2)*+ -> product(e_2,u,e_3)*.
% 18.03/18.21 3471[7:Res:3469.0,11.0] || product(e_3,e_2,u)*+ -> equalish(u,e_3).
% 18.03/18.21 3588[7:Res:3305.0,3470.0] || -> product(e_2,e_1,e_3)*.
% 18.03/18.21 3610[7:Res:3588.0,3308.0] || -> product(e_3,e_2,e_2)*.
% 18.03/18.21 3638[7:Res:3610.0,3471.0] || -> equalish(e_2,e_3)*.
% 18.03/18.21 3639[7:MRR:3638.0,7.0] || -> .
% 18.03/18.21 3666[7:Spt:3639.0,3309.0,3469.0] || product(e_3,e_2,e_3)*+ -> .
% 18.03/18.21 3667[7:Spt:3639.0,3309.1,3309.2] || -> product(e_3,e_2,e_2) product(e_2,e_1,e_1)*.
% 18.03/18.21 3674[8:Spt:3667.0] || -> product(e_3,e_2,e_2)*.
% 18.03/18.21 3675[8:Res:3674.0,14.0] || product(u,e_3,e_2)*+ -> product(e_2,u,e_2)*.
% 18.03/18.21 3678[8:Res:3674.0,13.0] || product(u,e_2,e_2)*+ -> equalish(u,e_3).
% 18.03/18.21 3772[8:Res:3305.0,3675.0] || -> product(e_2,e_1,e_2)*.
% 18.03/18.21 3846[8:Res:3772.0,14.0] || product(u,e_2,e_1)*+ -> product(e_1,u,e_2)*.
% 18.03/18.21 3851[8:Res:3772.0,18.2] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,e_2,e_1).
% 18.03/18.21 3869[8:SSi:3851.1,3851.0,1.0,2.0] || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,e_2,e_1).
% 18.03/18.21 3870[8:MRR:3869.2,3846.0] || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)*.
% 18.03/18.21 3883[9:Spt:3870.0] || -> product(e_1,e_2,e_3)*.
% 18.03/18.21 3884[9:Res:3883.0,14.0] || product(u,e_1,e_2)*+ -> product(e_2,u,e_3)*.
% 18.03/18.21 3887[9:Res:3883.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 4005[4:Res:679.5,3251.0] group_element(e_3) group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)* product(u,e_1,e_3)* equalish(e_1,e_2).
% 18.03/18.21 4006[4:SSi:4005.0,3.0] group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)* product(u,e_1,e_3)* equalish(e_1,e_2).
% 18.03/18.21 4007[5:MRR:4006.3,4006.4,3308.0,4.0] group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)*.
% 18.03/18.21 4331[9:Res:3772.0,3884.0] || -> product(e_2,e_2,e_3)*.
% 18.03/18.21 4356[9:Res:4331.0,3887.0] || -> equalish(e_2,e_1)*.
% 18.03/18.21 4357[9:MRR:4356.0,6.0] || -> .
% 18.03/18.21 4391[9:Spt:4357.0,3870.0,3883.0] || product(e_1,e_2,e_3)* -> .
% 18.03/18.21 4392[9:Spt:4357.0,3870.1] || -> product(e_1,e_2,e_2)*.
% 18.03/18.21 4435[9:Res:4392.0,3678.0] || -> equalish(e_1,e_3)*.
% 18.03/18.21 4437[9:MRR:4435.0,5.0] || -> .
% 18.03/18.21 4460[8:Spt:4437.0,3667.0,3674.0] || product(e_3,e_2,e_2)*+ -> .
% 18.03/18.21 4461[8:Spt:4437.0,3667.1] || -> product(e_2,e_1,e_1)*.
% 18.03/18.21 4472[8:Res:4461.0,12.0] || product(e_2,u,e_1)*+ -> equalish(u,e_1).
% 18.03/18.21 4506[8:Res:23.6,4460.0] group_element(u) group_element(e_2) group_element(e_3) || -> product(u,e_2,e_3) product(u,e_2,e_2)* product(e_3,e_2,e_3)* equalish(u,e_3).
% 18.03/18.21 4509[8:SSi:4506.2,4506.1,3.0,2.0] group_element(u) || -> product(u,e_2,e_3) product(u,e_2,e_2)* product(e_3,e_2,e_3)* equalish(u,e_3).
% 18.03/18.21 4510[8:MRR:4509.3,3666.0] group_element(u) || -> product(u,e_2,e_3) product(u,e_2,e_2)* equalish(u,e_3).
% 18.03/18.21 4528[8:Res:4510.2,3306.0] group_element(e_1) || -> product(e_1,e_2,e_3)* equalish(e_1,e_3) equalish(e_2,e_3).
% 18.03/18.21 4537[8:SSi:4528.0,1.0] || -> product(e_1,e_2,e_3)* equalish(e_1,e_3) equalish(e_2,e_3).
% 18.03/18.21 4538[8:MRR:4537.1,4537.2,5.0,7.0] || -> product(e_1,e_2,e_3)*.
% 18.03/18.21 4565[8:Res:4538.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 4602[8:Res:3395.3,4472.0] group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u) equalish(u,e_1).
% 18.03/18.21 4605[8:MRR:4602.1,4565.0] group_element(u) || -> equalish(e_2,u)* equalish(u,e_1)*.
% 18.03/18.21 4809[8:Res:4605.1,7.0] group_element(e_3) || -> equalish(e_3,e_1)*.
% 18.03/18.21 4811[8:SSi:4809.0,3.0] || -> equalish(e_3,e_1)*.
% 18.03/18.21 4812[8:MRR:4811.0,8.0] || -> .
% 18.03/18.21 4813[6:Spt:4812.0,3174.3,3174.4] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 18.03/18.21 4814[7:Spt:4813.0] || -> product(e_2,e_2,e_3)*.
% 18.03/18.21 4815[7:Res:4814.0,14.0] || product(u,e_2,e_2)*+ -> product(e_2,u,e_3)*.
% 18.03/18.21 4818[7:Res:4814.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 5053[7:Res:4007.2,4815.0] group_element(e_2) || -> product(e_3,e_2,e_3) product(e_2,e_3,e_3)*.
% 18.03/18.21 5054[5:Res:4007.2,3307.0] group_element(e_3) || -> product(e_3,e_3,e_3)* equalish(e_3,e_1).
% 18.03/18.21 5055[5:SSi:5054.0,3.0] || -> product(e_3,e_3,e_3)* equalish(e_3,e_1).
% 18.03/18.21 5056[5:MRR:5055.1,8.0] || -> product(e_3,e_3,e_3)*.
% 18.03/18.21 5057[7:SSi:5053.0,2.0] || -> product(e_3,e_2,e_3) product(e_2,e_3,e_3)*.
% 18.03/18.21 5081[5:Res:5056.0,14.0] || product(u,e_3,e_3)* -> product(e_3,u,e_3)*.
% 18.03/18.21 5083[5:Res:5056.0,12.0] || product(e_3,u,e_3)*+ -> equalish(u,e_3).
% 18.03/18.21 5095[7:MRR:5057.1,5081.0] || -> product(e_3,e_2,e_3)*.
% 18.03/18.21 5226[7:Res:5095.0,4818.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 5227[7:MRR:5226.0,9.0] || -> .
% 18.03/18.21 5232[7:Spt:5227.0,4813.0,4814.0] || product(e_2,e_2,e_3)*+ -> .
% 18.03/18.21 5233[7:Spt:5227.0,4813.1] || -> product(e_2,e_2,e_2)*.
% 18.03/18.21 5267[7:Res:5233.0,13.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 18.03/18.21 5507[7:Res:4007.2,5267.0] group_element(e_2) || -> product(e_3,e_2,e_3)* equalish(e_3,e_2).
% 18.03/18.21 5516[7:SSi:5507.0,2.0] || -> product(e_3,e_2,e_3)* equalish(e_3,e_2).
% 18.03/18.21 5517[7:MRR:5516.1,9.0] || -> product(e_3,e_2,e_3)*.
% 18.03/18.21 5718[7:Res:5517.0,5083.0] || -> equalish(e_2,e_3)*.
% 18.03/18.21 5722[7:MRR:5718.0,7.0] || -> .
% 18.03/18.21 5737[4:Spt:5722.0,3212.1] || -> product(e_1,e_3,e_3)*.
% 18.03/18.21 5738[4:Res:5737.0,14.0] || product(u,e_1,e_3)*+ -> product(e_3,u,e_3)*.
% 18.03/18.21 5739[4:Res:5737.0,11.0] || product(e_1,e_3,u)*+ -> equalish(u,e_3).
% 18.03/18.21 5740[4:Res:5737.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_3).
% 18.03/18.21 5741[4:Res:5737.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_1).
% 18.03/18.21 5743[4:Res:5737.0,18.2] group_element(e_3) group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_3,e_1,e_1)*.
% 18.03/18.21 5752[4:Obv:5743.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_3,e_1,e_1)*.
% 18.03/18.21 5753[4:SSi:5752.0,3.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_3,e_1,e_1)*.
% 18.03/18.21 5771[4:Res:679.5,5739.0] group_element(e_3) group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)* product(u,e_1,e_3)* equalish(e_1,e_3).
% 18.03/18.21 5779[4:SSi:5771.0,3.0] group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)* product(u,e_1,e_3)* equalish(e_1,e_3).
% 18.03/18.21 5780[4:MRR:5779.4,5.0] group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)* product(u,e_1,e_3)*.
% 18.03/18.21 5781[4:MRR:5780.3,5738.0] group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)*.
% 18.03/18.21 5803[5:Spt:3174.0,3174.1,3174.2,3174.5] group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u) product(e_2,u,e_1)*.
% 18.03/18.21 5815[5:Res:5803.1,5740.0] group_element(e_1) || -> equalish(e_2,e_1) product(e_2,e_1,e_1)* equalish(e_2,e_3).
% 18.03/18.21 5835[5:SSi:5815.0,1.0] || -> equalish(e_2,e_1) product(e_2,e_1,e_1)* equalish(e_2,e_3).
% 18.03/18.21 5836[5:MRR:5835.0,5835.2,6.0,7.0] || -> product(e_2,e_1,e_1)*.
% 18.03/18.21 5875[5:Res:5836.0,13.0] || product(u,e_1,e_1)*+ -> equalish(u,e_2).
% 18.03/18.21 6298[5:Res:5753.2,5875.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)* equalish(e_3,e_2).
% 18.03/18.21 6299[5:MRR:6298.2,9.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)*.
% 18.03/18.21 6305[6:Spt:6299.0] || -> product(e_3,e_3,e_3)*.
% 18.03/18.21 6320[6:Res:6305.0,5741.0] || -> equalish(e_3,e_1)*.
% 18.03/18.21 6321[6:MRR:6320.0,8.0] || -> .
% 18.03/18.21 6332[6:Spt:6321.0,6299.0,6305.0] || product(e_3,e_3,e_3)*+ -> .
% 18.03/18.21 6333[6:Spt:6321.0,6299.1] || -> product(e_3,e_3,e_2)*.
% 18.03/18.21 6336[6:Res:6333.0,14.0] || product(u,e_3,e_3)*+ -> product(e_3,u,e_2)*.
% 18.03/18.21 6338[6:Res:6333.0,12.0] || product(e_3,u,e_2)*+ -> equalish(u,e_3).
% 18.03/18.21 6600[6:Res:5737.0,6336.0] || -> product(e_3,e_1,e_2)*.
% 18.03/18.21 6792[6:Res:6600.0,6338.0] || -> equalish(e_1,e_3)*.
% 18.03/18.21 6800[6:MRR:6792.0,5.0] || -> .
% 18.03/18.21 6815[5:Spt:6800.0,3174.3,3174.4] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 18.03/18.21 6829[6:Spt:6815.0] || -> product(e_2,e_2,e_3)*.
% 18.03/18.21 6830[6:Res:6829.0,14.0] || product(u,e_2,e_2)*+ -> product(e_2,u,e_3)*.
% 18.03/18.21 6833[6:Res:6829.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 6844[6:MRR:2328.3,6833.0] group_element(u) || -> product(u,u,e_3)* equalish(u,e_2) product(u,e_2,e_2)* product(e_2,u,e_1)*.
% 18.03/18.21 6931[6:Res:6844.1,5740.0] group_element(e_1) || -> equalish(e_1,e_2) product(e_1,e_2,e_2)* product(e_2,e_1,e_1) equalish(e_1,e_3).
% 18.03/18.21 6975[6:SSi:6931.0,1.0] || -> equalish(e_1,e_2) product(e_1,e_2,e_2)* product(e_2,e_1,e_1) equalish(e_1,e_3).
% 18.03/18.21 6976[6:MRR:6975.0,6975.3,4.0,5.0] || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_1).
% 18.03/18.21 7031[7:Spt:6976.0] || -> product(e_1,e_2,e_2)*.
% 18.03/18.21 7035[7:Res:7031.0,13.0] || product(u,e_2,e_2)*+ -> equalish(u,e_1).
% 18.03/18.21 7259[7:Res:5781.2,7035.0] group_element(e_2) || -> product(e_3,e_2,e_3)* equalish(e_3,e_1).
% 18.03/18.21 7273[7:SSi:7259.0,2.0] || -> product(e_3,e_2,e_3)* equalish(e_3,e_1).
% 18.03/18.21 7274[7:MRR:7273.1,8.0] || -> product(e_3,e_2,e_3)*.
% 18.03/18.21 7301[7:Res:7274.0,6833.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 7302[7:MRR:7301.0,9.0] || -> .
% 18.03/18.21 7310[7:Spt:7302.0,6976.0,7031.0] || product(e_1,e_2,e_2)*+ -> .
% 18.03/18.21 7311[7:Spt:7302.0,6976.1] || -> product(e_2,e_1,e_1)*.
% 18.03/18.21 7514[6:Res:5781.2,6830.0] group_element(e_2) || -> product(e_3,e_2,e_3) product(e_2,e_3,e_3)*.
% 18.03/18.21 7527[6:SSi:7514.0,2.0] || -> product(e_3,e_2,e_3) product(e_2,e_3,e_3)*.
% 18.03/18.21 7537[8:Spt:7527.0] || -> product(e_3,e_2,e_3)*.
% 18.03/18.21 7552[8:Res:7537.0,6833.0] || -> equalish(e_3,e_2)*.
% 18.03/18.21 7553[8:MRR:7552.0,9.0] || -> .
% 18.03/18.21 7555[8:Spt:7553.0,7527.0,7537.0] || product(e_3,e_2,e_3)* -> .
% 18.03/18.21 7556[8:Spt:7553.0,7527.1] || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 7578[8:Res:7556.0,5741.0] || -> equalish(e_2,e_1)*.
% 18.03/18.21 7580[8:MRR:7578.0,6.0] || -> .
% 18.03/18.21 7598[6:Spt:7580.0,6815.0,6829.0] || product(e_2,e_2,e_3)*+ -> .
% 18.03/18.21 7599[6:Spt:7580.0,6815.1] || -> product(e_2,e_2,e_2)*.
% 18.03/18.21 7627[6:Res:7599.0,13.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 18.03/18.21 7652[6:MRR:2328.4,7627.0] group_element(u) || -> product(u,u,e_3)* equalish(u,e_2) product(u,e_2,e_3)* product(e_2,u,e_1)*.
% 18.03/18.21 7759[6:Res:5781.2,7627.0] group_element(e_2) || -> product(e_3,e_2,e_3)* equalish(e_3,e_2).
% 18.03/18.21 7772[6:SSi:7759.0,2.0] || -> product(e_3,e_2,e_3)* equalish(e_3,e_2).
% 18.03/18.21 7773[6:MRR:7772.1,9.0] || -> product(e_3,e_2,e_3)*.
% 18.03/18.21 7805[6:Res:7652.1,5740.0] group_element(e_1) || -> equalish(e_1,e_2) product(e_1,e_2,e_3)* product(e_2,e_1,e_1) equalish(e_1,e_3).
% 18.03/18.21 7841[6:SSi:7805.0,1.0] || -> equalish(e_1,e_2) product(e_1,e_2,e_3)* product(e_2,e_1,e_1) equalish(e_1,e_3).
% 18.03/18.21 7842[6:MRR:7841.0,7841.3,4.0,5.0] || -> product(e_1,e_2,e_3)* product(e_2,e_1,e_1).
% 18.03/18.21 7890[6:Res:7773.0,14.0] || product(u,e_3,e_2)*+ -> product(e_2,u,e_3)*.
% 18.03/18.21 7919[7:Spt:7842.0] || -> product(e_1,e_2,e_3)*.
% 18.03/18.21 7931[7:Res:7919.0,5740.0] || -> equalish(e_2,e_3)*.
% 18.03/18.21 7935[7:MRR:7931.0,7.0] || -> .
% 18.03/18.21 7942[7:Spt:7935.0,7842.0,7919.0] || product(e_1,e_2,e_3)*+ -> .
% 18.03/18.21 7943[7:Spt:7935.0,7842.1] || -> product(e_2,e_1,e_1)*.
% 18.03/18.21 8494[6:Res:5781.2,7890.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_2,e_3,e_3)*.
% 18.03/18.21 8500[6:SSi:8494.0,3.0] || -> product(e_3,e_3,e_3) product(e_2,e_3,e_3)*.
% 18.03/18.21 8511[8:Spt:8500.0] || -> product(e_3,e_3,e_3)*.
% 18.03/18.21 8527[8:Res:8511.0,5741.0] || -> equalish(e_3,e_1)*.
% 18.03/18.21 8529[8:MRR:8527.0,8.0] || -> .
% 18.03/18.21 8540[8:Spt:8529.0,8500.0,8511.0] || product(e_3,e_3,e_3)* -> .
% 18.03/18.21 8541[8:Spt:8529.0,8500.1] || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 8569[8:Res:8541.0,5741.0] || -> equalish(e_2,e_1)*.
% 18.03/18.21 8570[8:MRR:8569.0,6.0] || -> .
% 18.03/18.21 8590[2:Spt:8570.0,593.6,593.7] || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)*.
% 18.03/18.21 8641[3:Spt:8590.0] || -> product(e_1,e_2,e_3)*.
% 18.03/18.21 8642[3:Res:8641.0,14.0] || product(u,e_1,e_2)*+ -> product(e_2,u,e_3)*.
% 18.03/18.21 8644[3:Res:8641.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 8647[3:Res:8641.0,18.2] group_element(e_3) group_element(e_2) || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2)* product(e_3,e_1,e_1).
% 18.03/18.21 8661[3:SSi:8647.1,8647.0,2.0,3.0] || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2)* product(e_3,e_1,e_1).
% 18.03/18.21 8964[4:Spt:8661.0] || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 8965[4:Res:8964.0,14.0] || product(u,e_2,e_3)*+ -> product(e_3,u,e_3)*.
% 18.03/18.21 8968[4:Res:8964.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_2).
% 18.03/18.21 9255[4:Res:8641.0,8965.0] || -> product(e_3,e_1,e_3)*.
% 18.03/18.21 9332[4:Res:9255.0,14.0] || product(u,e_3,e_1)*+ -> product(e_1,u,e_3)*.
% 18.03/18.21 9337[4:Res:9255.0,18.2] group_element(e_3) group_element(e_1) || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,e_3,e_1).
% 18.03/18.21 9346[4:SSi:9337.1,9337.0,1.0,3.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,e_3,e_1).
% 18.03/18.21 9347[4:MRR:9346.2,9332.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 18.03/18.21 9352[5:Spt:9347.0] || -> product(e_1,e_3,e_3)*.
% 18.03/18.21 9369[5:Res:9352.0,8968.0] || -> equalish(e_1,e_2)*.
% 18.03/18.21 9371[5:MRR:9369.0,4.0] || -> .
% 18.03/18.21 9383[5:Spt:9371.0,9347.0,9352.0] || product(e_1,e_3,e_3)*+ -> .
% 18.03/18.21 9384[5:Spt:9371.0,9347.1] || -> product(e_1,e_3,e_2)*.
% 18.03/18.21 9406[5:Res:9384.0,14.0] || product(u,e_1,e_3)*+ -> product(e_3,u,e_2)*.
% 18.03/18.21 9409[5:Res:9384.0,13.0] || product(u,e_3,e_2)*+ -> equalish(u,e_1).
% 18.03/18.21 9851[5:Res:9255.0,9406.0] || -> product(e_3,e_3,e_2)*.
% 18.03/18.21 9877[5:Res:9851.0,9409.0] || -> equalish(e_3,e_1)*.
% 18.03/18.21 9878[5:MRR:9877.0,8.0] || -> .
% 18.03/18.21 9903[4:Spt:9878.0,8661.0,8964.0] || product(e_2,e_3,e_3)*+ -> .
% 18.03/18.21 9904[4:Spt:9878.0,8661.1,8661.2] || -> product(e_2,e_3,e_2)* product(e_3,e_1,e_1).
% 18.03/18.21 9917[5:Spt:9904.0] || -> product(e_2,e_3,e_2)*.
% 18.03/18.21 9919[5:Res:9917.0,14.0] || product(u,e_2,e_3)*+ -> product(e_3,u,e_2)*.
% 18.03/18.21 10060[5:Res:8641.0,9919.0] || -> product(e_3,e_1,e_2)*.
% 18.03/18.21 10099[5:Res:10060.0,8642.0] || -> product(e_2,e_3,e_3)*.
% 18.03/18.21 10100[5:MRR:10099.0,9903.0] || -> .
% 18.03/18.21 10111[5:Spt:10100.0,9904.0,9917.0] || product(e_2,e_3,e_2)*+ -> .
% 18.03/18.21 10112[5:Spt:10100.0,9904.1] || -> product(e_3,e_1,e_1)*.
% 18.03/18.21 10116[5:Res:10112.0,14.0] || product(u,e_3,e_1)*+ -> product(e_1,u,e_1)*.
% 18.03/18.21 10119[5:Res:10112.0,13.0] || product(u,e_1,e_1)*+ -> equalish(u,e_3).
% 18.03/18.21 10121[5:Res:10112.0,18.2] group_element(e_1) group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)* product(e_1,e_3,e_1).
% 18.03/18.21 10134[5:Obv:10121.0] group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)* product(e_1,e_3,e_1).
% 18.03/18.21 10135[5:SSi:10134.0,1.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)* product(e_1,e_3,e_1).
% 18.03/18.21 10233[6:Spt:10135.0] || -> product(e_1,e_1,e_3)*.
% 18.03/18.21 10246[6:Res:10233.0,8644.0] || -> equalish(e_1,e_2)*.
% 18.03/18.21 10251[6:MRR:10246.0,4.0] || -> .
% 18.03/18.21 10266[6:Spt:10251.0,10135.0,10233.0] || product(e_1,e_1,e_3)*+ -> .
% 18.03/18.21 10267[6:Spt:10251.0,10135.1,10135.2] || -> product(e_1,e_1,e_2)* product(e_1,e_3,e_1).
% 18.03/18.21 10288[7:Spt:10267.0] || -> product(e_1,e_1,e_2)*.
% 18.03/18.21 10292[7:Res:10288.0,12.0] || product(e_1,u,e_2)*+ -> equalish(u,e_1).
% 18.03/18.21 10315[7:Res:10288.0,8642.0] || -> product(e_2,e_1,e_3)*.
% 18.03/18.21 10342[7:Res:10315.0,14.0] || product(u,e_2,e_1)* -> product(e_1,u,e_3)*.
% 18.03/18.21 10347[7:Res:10315.0,18.2] group_element(e_3) group_element(e_1) || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,e_2,e_1).
% 18.03/18.21 10356[7:SSi:10347.1,10347.0,1.0,3.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* product(e_3,e_2,e_1).
% 18.03/18.21 10357[7:MRR:10356.2,10342.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 19.96/20.16 10387[8:Spt:10357.0] || -> product(e_1,e_3,e_3)*.
% 19.96/20.16 10400[8:Res:10387.0,8644.0] || -> equalish(e_3,e_2)*.
% 19.96/20.16 10405[8:MRR:10400.0,9.0] || -> .
% 19.96/20.16 10419[8:Spt:10405.0,10357.0,10387.0] || product(e_1,e_3,e_3)*+ -> .
% 19.96/20.16 10420[8:Spt:10405.0,10357.1] || -> product(e_1,e_3,e_2)*.
% 19.96/20.16 10594[8:Res:10420.0,10292.0] || -> equalish(e_3,e_1)*.
% 19.96/20.16 10595[8:MRR:10594.0,8.0] || -> .
% 19.96/20.16 10608[7:Spt:10595.0,10267.0,10288.0] || product(e_1,e_1,e_2)*+ -> .
% 19.96/20.16 10609[7:Spt:10595.0,10267.1] || -> product(e_1,e_3,e_1)*.
% 19.96/20.16 10638[7:Res:10609.0,10116.0] || -> product(e_1,e_1,e_1)*.
% 19.96/20.16 10712[7:Res:10638.0,10119.0] || -> equalish(e_1,e_3)*.
% 19.96/20.16 10713[7:MRR:10712.0,5.0] || -> .
% 19.96/20.16 10725[3:Spt:10713.0,8590.0,8641.0] || product(e_1,e_2,e_3)*+ -> .
% 19.96/20.16 10726[3:Spt:10713.0,8590.1] || -> product(e_1,e_2,e_2)*.
% 19.96/20.16 10768[3:Res:10726.0,13.0] || product(u,e_2,e_2)*+ -> equalish(u,e_1).
% 19.96/20.16 10770[3:Res:10726.0,18.2] group_element(e_2) group_element(e_2) || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_2,e_1,e_1)*.
% 19.96/20.16 10806[3:Obv:10770.0] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_2,e_1,e_1)*.
% 19.96/20.16 10807[3:SSi:10806.0,2.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_2,e_1,e_1)*.
% 19.96/20.16 11161[4:Spt:10807.0] || -> product(e_2,e_2,e_3)*.
% 19.96/20.16 11163[4:Res:11161.0,14.0] || product(u,e_2,e_2)*+ -> product(e_2,u,e_3)*.
% 19.96/20.16 11165[4:Res:11161.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 19.96/20.16 11357[4:Res:10726.0,11163.0] || -> product(e_2,e_1,e_3)*.
% 19.96/20.16 11377[4:Res:11357.0,11165.0] || -> equalish(e_1,e_2)*.
% 19.96/20.16 11382[4:MRR:11377.0,4.0] || -> .
% 19.96/20.16 11394[4:Spt:11382.0,10807.0,11161.0] || product(e_2,e_2,e_3)*+ -> .
% 19.96/20.16 11395[4:Spt:11382.0,10807.1,10807.2] || -> product(e_2,e_2,e_2) product(e_2,e_1,e_1)*.
% 19.96/20.16 11443[5:Spt:11395.0] || -> product(e_2,e_2,e_2)*.
% 19.96/20.16 11470[5:Res:11443.0,10768.0] || -> equalish(e_2,e_1)*.
% 19.96/20.16 11471[5:MRR:11470.0,6.0] || -> .
% 19.96/20.16 11517[5:Spt:11471.0,11395.0,11443.0] || product(e_2,e_2,e_2)*+ -> .
% 19.96/20.16 11518[5:Spt:11471.0,11395.1] || -> product(e_2,e_1,e_1)*.
% 19.96/20.16 11532[5:Res:11518.0,11.0] || product(e_2,e_1,u)*+ -> equalish(u,e_1).
% 19.96/20.16 11576[5:Res:25.4,11517.0] group_element(e_2) group_element(u) group_element(e_2) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_2,u).
% 19.96/20.16 11584[5:Obv:11576.0] group_element(u) group_element(e_2) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_2,u).
% 19.96/20.16 11585[5:SSi:11584.1,2.0] group_element(u) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_2,u).
% 19.96/20.16 11586[5:MRR:11585.1,11394.0] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)* equalish(e_2,u).
% 19.96/20.16 11689[5:Res:11586.2,11532.0] group_element(e_1) || -> product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_2,e_1).
% 19.96/20.16 11690[5:Obv:11689.2] group_element(e_1) || -> product(e_2,e_1,e_3)* equalish(e_2,e_1).
% 19.96/20.16 11691[5:SSi:11690.0,1.0] || -> product(e_2,e_1,e_3)* equalish(e_2,e_1).
% 19.96/20.16 11692[5:MRR:11691.1,6.0] || -> product(e_2,e_1,e_3)*.
% 19.96/20.16 11739[5:Res:11692.0,11532.0] || -> equalish(e_3,e_1)*.
% 19.96/20.16 11740[5:MRR:11739.0,8.0] || -> .
% 19.96/20.16 % SZS output end Refutation
% 19.96/20.16 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
% 19.96/20.16
%------------------------------------------------------------------------------