TSTP Solution File: GRP133-1.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP133-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:45:50 EDT 2022
% Result : Unsatisfiable 31.28s 31.47s
% Output : Refutation 37.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP133-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 12:19:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 31.28/31.47
% 31.28/31.47 SPASS V 3.9
% 31.28/31.47 SPASS beiseite: Proof found.
% 31.28/31.47 % SZS status Theorem
% 31.28/31.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.28/31.47 SPASS derived 11734 clauses, backtracked 5032 clauses, performed 68 splits and kept 9393 clauses.
% 31.28/31.47 SPASS allocated 95336 KBytes.
% 31.28/31.47 SPASS spent 0:0:31.12 on the problem.
% 31.28/31.47 0:00:00.04 for the input.
% 31.28/31.47 0:00:00.00 for the FLOTTER CNF translation.
% 31.28/31.47 0:00:00.23 for inferences.
% 31.28/31.47 0:00:00.13 for the backtracking.
% 31.28/31.47 0:0:30.67 for the reduction.
% 31.28/31.47
% 31.28/31.47
% 31.28/31.47 Here is a proof with depth 18, length 558 :
% 31.28/31.47 % SZS output start Refutation
% 31.28/31.47 1[0:Inp] || -> group_element(e_1)*.
% 31.28/31.47 2[0:Inp] || -> group_element(e_2)*.
% 31.28/31.47 3[0:Inp] || -> group_element(e_3)*.
% 31.28/31.47 4[0:Inp] || equalish(e_1,e_2)*+ -> .
% 31.28/31.47 5[0:Inp] || equalish(e_1,e_3)*+ -> .
% 31.28/31.47 6[0:Inp] || equalish(e_2,e_1)*+ -> .
% 31.28/31.47 7[0:Inp] || equalish(e_2,e_3)*+ -> .
% 31.28/31.47 8[0:Inp] || equalish(e_3,e_1)*+ -> .
% 31.28/31.47 9[0:Inp] || equalish(e_3,e_2)*+ -> .
% 31.28/31.47 10[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 31.28/31.47 11[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 31.28/31.47 12[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 31.28/31.47 13[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 31.28/31.47 14[0:Inp] || product(u,v,w)*+ product(v,u,x)* -> product(x,w,v)*.
% 31.28/31.47 18[0:Res:10.4,14.0] group_element(u) group_element(v) || product(u,v,w)*+ -> product(v,u,e_3) product(v,u,e_2)* product(w,e_1,u)*.
% 31.28/31.47 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).
% 31.28/31.47 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)*.
% 31.28/31.47 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)*.
% 31.28/31.47 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)*.
% 31.28/31.47 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)*.
% 31.28/31.47 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)*.
% 31.28/31.47 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)*.
% 31.28/31.47 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).
% 31.28/31.47 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).
% 31.28/31.47 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)*.
% 31.28/31.47 29[1:Res:28.3,14.0] group_element(u) group_element(v) || product(u,v,w)*+ -> product(v,u,e_3)* product(w,e_2,u)*.
% 31.28/31.47 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).
% 31.28/31.47 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)*.
% 31.28/31.47 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)*.
% 31.28/31.47 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).
% 31.28/31.47 34[1:Obv:33.4] group_element(u) group_element(v) || -> product(v,u,e_3)* equalish(e_2,e_2).
% 31.28/31.47 37[2:Spt:34.0,34.1,34.2] group_element(u) group_element(v) || -> product(v,u,e_3)*.
% 31.28/31.47 40[2:Res:37.2,12.0] group_element(u) group_element(v) || product(v,w,e_3)*+ -> equalish(w,u)*.
% 31.28/31.47 48[2:Res:37.2,40.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> equalish(u,w)*.
% 31.28/31.47 49[2:Obv:48.1] group_element(u) group_element(v) group_element(w) || -> equalish(u,v)*.
% 31.28/31.47 50[2:Con:49.2] group_element(u) group_element(v) || -> equalish(u,v)*.
% 31.28/31.47 56[2:Res:50.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 31.28/31.47 62[2:SSi:56.1,56.0,2.0,1.0] || -> .
% 31.28/31.47 63[2:Spt:62.0,34.3] || -> equalish(e_2,e_2)*.
% 31.28/31.48 74[1:Res:28.3,29.2] group_element(u) group_element(v) group_element(v) group_element(u) || -> product(v,u,e_3)* product(u,v,e_3)* product(e_2,e_2,v)*.
% 31.28/31.48 75[1:Obv:74.1] group_element(u) group_element(v) || -> product(u,v,e_3)* product(v,u,e_3)* product(e_2,e_2,u)*.
% 31.28/31.48 76[1:Fac:75.2,75.3] group_element(u) group_element(u) || -> product(u,u,e_3)* product(e_2,e_2,u)*.
% 31.28/31.48 95[1:Res:75.4,31.2] group_element(e_2) group_element(u) group_element(v) group_element(e_2) || -> product(e_2,u,e_3)* product(u,e_2,e_3)* product(e_2,v,e_3)* equalish(e_2,v).
% 31.28/31.48 96[1:Res:75.4,32.2] group_element(e_2) group_element(u) group_element(e_2) group_element(v) || -> product(e_2,u,e_3)* product(u,e_2,e_3)* product(v,e_2,e_3)* equalish(e_2,v).
% 31.28/31.48 97[1:Obv:76.0] group_element(u) || -> product(u,u,e_3)* product(e_2,e_2,u)*.
% 31.28/31.48 98[1:Obv:96.0] group_element(u) group_element(e_2) group_element(v) || -> product(e_2,u,e_3)* product(u,e_2,e_3)* product(v,e_2,e_3)* equalish(e_2,v).
% 31.28/31.48 99[1:SSi:98.1,2.0] group_element(u) group_element(v) || -> product(e_2,u,e_3)* product(u,e_2,e_3)* product(v,e_2,e_3)* equalish(e_2,v).
% 31.28/31.48 100[1:Obv:95.0] group_element(u) group_element(v) group_element(e_2) || -> product(e_2,u,e_3)* product(u,e_2,e_3)* product(e_2,v,e_3)* equalish(e_2,v).
% 31.28/31.48 101[1:SSi:100.2,2.0] group_element(u) group_element(v) || -> product(e_2,u,e_3)* product(u,e_2,e_3)* product(e_2,v,e_3)* equalish(e_2,v).
% 31.28/31.48 121[1:Res:97.2,30.2] group_element(u) group_element(e_2) group_element(e_2) || -> product(u,u,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 31.28/31.48 122[1:Res:97.2,31.2] group_element(e_2) group_element(u) group_element(e_2) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3)* equalish(e_2,u).
% 31.28/31.48 123[1:Res:97.2,32.2] group_element(e_2) group_element(e_2) group_element(u) || -> product(e_2,e_2,e_3)* product(u,e_2,e_3)* equalish(e_2,u).
% 31.28/31.48 124[1:Obv:123.0] group_element(e_2) group_element(u) || -> product(e_2,e_2,e_3)* product(u,e_2,e_3)* equalish(e_2,u).
% 31.28/31.48 125[1:SSi:124.0,2.0] group_element(u) || -> product(e_2,e_2,e_3)* product(u,e_2,e_3)* equalish(e_2,u).
% 31.28/31.48 126[1:Obv:122.0] group_element(u) group_element(e_2) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3)* equalish(e_2,u).
% 31.28/31.48 127[1:SSi:126.1,2.0] group_element(u) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3)* equalish(e_2,u).
% 31.28/31.48 128[1:Obv:121.1] group_element(u) group_element(e_2) || -> product(u,u,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 31.28/31.48 129[1:SSi:128.1,2.0] group_element(u) || -> product(u,u,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 31.28/31.48 134[3:Spt:125.0,125.2,125.3] group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u).
% 31.28/31.48 138[3:Res:134.1,12.0] group_element(u) || product(u,v,e_3)*+ -> equalish(e_2,u) equalish(v,e_2).
% 31.28/31.48 170[4:Spt:127.0,127.2,127.3] group_element(u) || -> product(e_2,u,e_3)* equalish(e_2,u).
% 31.28/31.48 179[5:Spt:129.0,129.1,129.3] group_element(u) || -> product(u,u,e_3)* equalish(u,e_2).
% 31.28/31.48 333[5:Res:179.1,138.1] group_element(u) group_element(u) || -> equalish(u,e_2)* equalish(e_2,u)* equalish(u,e_2)*.
% 31.28/31.48 340[5:Obv:333.2] group_element(u) || -> equalish(e_2,u)* equalish(u,e_2)*.
% 31.28/31.48 360[5:Res:340.2,4.0] group_element(e_1) || -> equalish(e_2,e_1)*.
% 31.28/31.48 363[5:SSi:360.0,1.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 364[5:MRR:363.0,6.0] || -> .
% 31.28/31.48 365[5:Spt:364.0,129.2] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 369[5:Res:365.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 31.28/31.48 441[5:Res:170.1,369.0] group_element(u) || -> equalish(e_2,u)* equalish(u,e_2)*.
% 31.28/31.48 612[5:Res:441.2,4.0] group_element(e_1) || -> equalish(e_2,e_1)*.
% 31.28/31.48 615[5:SSi:612.0,1.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 616[5:MRR:615.0,6.0] || -> .
% 31.28/31.48 617[4:Spt:616.0,127.1] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 644[4:Res:617.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 31.28/31.48 645[4:Res:617.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_2).
% 31.28/31.48 680[5:Spt:101.1,101.4,101.5] group_element(u) || -> product(e_2,u,e_3)* equalish(e_2,u).
% 31.28/31.48 714[5:Res:680.1,644.0] group_element(u) || -> equalish(e_2,u)* equalish(u,e_2)*.
% 31.28/31.48 876[5:Res:714.2,4.0] group_element(e_1) || -> equalish(e_2,e_1)*.
% 31.28/31.48 879[5:SSi:876.0,1.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 880[5:MRR:879.0,6.0] || -> .
% 31.28/31.48 881[5:Spt:880.0,101.0,101.2,101.3] group_element(u) || -> product(e_2,u,e_3)* product(u,e_2,e_3)*.
% 31.28/31.48 892[5:Res:881.1,644.0] group_element(u) || -> product(u,e_2,e_3)* equalish(u,e_2).
% 31.28/31.48 904[5:MRR:892.1,645.0] group_element(u) || -> equalish(u,e_2)*.
% 31.28/31.48 915[5:Res:904.1,4.0] group_element(e_1) || -> .
% 31.28/31.48 917[5:SSi:915.0,1.0] || -> .
% 31.28/31.48 918[3:Spt:917.0,125.1] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 929[3:Res:918.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 31.28/31.48 930[3:Res:918.0,13.0] || product(u,e_2,e_3)*+ -> equalish(u,e_2).
% 31.28/31.48 965[4:Spt:99.1,99.4,99.5] group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u).
% 31.28/31.48 1027[4:Res:965.1,930.0] group_element(u) || -> equalish(e_2,u)* equalish(u,e_2)*.
% 31.28/31.48 1158[4:Res:1027.2,4.0] group_element(e_1) || -> equalish(e_2,e_1)*.
% 31.28/31.48 1161[4:SSi:1158.0,1.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 1162[4:MRR:1161.0,6.0] || -> .
% 31.28/31.48 1163[4:Spt:1162.0,99.0,99.2,99.3] group_element(u) || -> product(e_2,u,e_3)* product(u,e_2,e_3)*.
% 31.28/31.48 1177[4:Res:1163.1,929.0] group_element(u) || -> product(u,e_2,e_3)* equalish(u,e_2).
% 31.28/31.48 1188[4:MRR:1177.1,930.0] group_element(u) || -> equalish(u,e_2)*.
% 31.28/31.48 1198[4:Res:1188.1,4.0] group_element(e_1) || -> .
% 31.28/31.48 1200[4:SSi:1198.0,1.0] || -> .
% 31.28/31.48 1201[1:Spt:1200.0,27.4] || -> equalish(e_1,e_1)*.
% 31.28/31.48 1212[0:Res:10.4,18.2] group_element(u) group_element(v) group_element(v) group_element(u) || -> product(v,u,e_3) product(v,u,e_2)* product(u,v,e_3) product(u,v,e_2)* product(e_1,e_1,v)*.
% 31.28/31.48 1213[0:Obv:1212.1] group_element(u) group_element(v) || -> product(u,v,e_3) product(u,v,e_2)* product(v,u,e_3) product(v,u,e_2)* product(e_1,e_1,u)*.
% 31.28/31.48 1214[0:Fac:1213.3,1213.5] group_element(u) group_element(u) || -> product(u,u,e_3) product(u,u,e_3) product(u,u,e_2)* product(e_1,e_1,u)*.
% 31.28/31.48 1215[0:Res:1213.3,18.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(u,v,e_3)* product(v,u,e_3) product(v,u,e_2)* product(e_1,e_1,u)* product(v,u,e_3) product(v,u,e_2)* product(e_2,e_1,u).
% 31.28/31.48 1221[0:Res:1213.5,18.2] group_element(u) group_element(v) group_element(v) group_element(u) || -> product(u,v,e_3) product(u,v,e_2)* product(v,u,e_3)* product(e_1,e_1,u)* product(u,v,e_3) product(u,v,e_2)* product(e_2,e_1,v)*.
% 31.28/31.48 1233[0:Res:1213.6,20.2] group_element(e_1) group_element(u) group_element(v) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* equalish(e_1,v).
% 31.28/31.48 1234[0:Res:1213.6,21.2] group_element(e_1) group_element(u) group_element(e_1) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* equalish(e_1,v).
% 31.28/31.48 1235[0:Obv:1214.2] group_element(u) || -> product(u,u,e_3) product(u,u,e_2)* product(e_1,e_1,u)*.
% 31.28/31.48 1236[0:Obv:1234.0] group_element(u) group_element(e_1) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* equalish(e_1,v).
% 31.28/31.48 1237[0:SSi:1236.1,1.0] group_element(u) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* equalish(e_1,v).
% 31.28/31.48 1238[0:Obv:1233.0] group_element(u) group_element(v) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* equalish(e_1,v).
% 31.28/31.48 1239[0:SSi:1238.2,1.0] group_element(u) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* equalish(e_1,v).
% 31.28/31.48 1246[0:Obv:1221.5] group_element(u) group_element(v) || -> product(u,v,e_3)* product(e_1,e_1,v)* product(v,u,e_3) product(v,u,e_2)* product(e_2,e_1,u)*.
% 31.28/31.48 1247[0:Obv:1215.6] group_element(u) group_element(v) || -> product(u,v,e_3)* product(e_1,e_1,u)* product(v,u,e_3) product(v,u,e_2)* product(e_2,e_1,u).
% 31.28/31.48 1249[0:Res:1235.2,14.0] group_element(u) || product(u,u,v)*+ -> product(u,u,e_3)* product(e_1,e_1,u)* product(v,e_2,u)*.
% 31.28/31.48 1250[0:Res:1235.2,11.0] group_element(u) || product(u,u,v)*+ -> product(u,u,e_3)* product(e_1,e_1,u)* equalish(v,e_2).
% 31.28/31.48 1251[0:Res:1235.2,12.0] group_element(u) || product(u,v,e_2)*+ -> product(u,u,e_3)* product(e_1,e_1,u)* equalish(v,u).
% 31.28/31.48 1258[0:Res:1235.3,13.0] group_element(u) || product(v,e_1,u)*+ -> product(u,u,e_3) product(u,u,e_2)* equalish(v,e_1).
% 31.28/31.48 1279[0:Res:25.6,18.2] group_element(u) group_element(v) group_element(w) group_element(w) group_element(v) || -> product(w,u,e_3) product(w,u,e_2)* product(w,v,e_3)* equalish(u,v)* product(v,w,e_3) product(v,w,e_2)* product(e_2,e_1,w)*.
% 31.28/31.48 1281[0:Res:25.6,11.0] group_element(u) group_element(v) group_element(w) || product(w,v,x)*+ -> product(w,u,e_3) product(w,u,e_2)* product(w,v,e_3)* equalish(u,v)* equalish(x,e_2).
% 31.28/31.48 1288[0:Obv:1279.2] group_element(u) group_element(v) group_element(w) || -> product(v,u,e_3) product(v,u,e_2)* product(v,w,e_3)* equalish(u,w)* product(w,v,e_3) product(w,v,e_2)* product(e_2,e_1,v)*.
% 31.28/31.48 1302[0:Res:1235.2,1250.1] group_element(u) group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)* product(u,u,e_3)* product(e_1,e_1,u)* equalish(e_2,e_2).
% 31.28/31.48 1306[0:Obv:1302.3] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)* equalish(e_2,e_2).
% 31.28/31.48 1312[2:Spt:1306.0,1306.1,1306.2] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)*.
% 31.28/31.48 1315[2:Res:1312.1,11.0] group_element(u) || product(u,u,v)*+ -> product(e_1,e_1,u)* equalish(v,e_3).
% 31.28/31.48 1322[2:Res:1312.2,12.0] group_element(u) || product(e_1,v,u)*+ -> product(u,u,e_3)* equalish(v,e_1).
% 31.28/31.48 1341[2:Res:1312.1,1315.1] group_element(u) group_element(u) || -> product(e_1,e_1,u)* product(e_1,e_1,u)* equalish(e_3,e_3).
% 31.28/31.48 1342[2:Res:1312.2,1315.1] group_element(u) group_element(e_1) || -> product(u,u,e_3)* product(e_1,e_1,e_1)* equalish(u,e_3).
% 31.28/31.48 1344[2:Obv:1341.2] group_element(u) || -> product(e_1,e_1,u)* equalish(e_3,e_3).
% 31.28/31.48 1345[2:SSi:1342.1,1.0] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,e_1)* equalish(u,e_3).
% 31.28/31.48 1373[3:Spt:1344.0,1344.1] group_element(u) || -> product(e_1,e_1,u)*.
% 31.28/31.48 1376[3:Res:1373.1,11.0] group_element(u) || product(e_1,e_1,v)*+ -> equalish(v,u)*.
% 31.28/31.48 1396[3:Res:1373.1,1376.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 31.28/31.48 1408[3:Res:1396.2,4.0] group_element(e_1) group_element(e_2) || -> .
% 31.28/31.48 1414[3:SSi:1408.1,1408.0,2.0,1.0] || -> .
% 31.28/31.48 1415[3:Spt:1414.0,1344.2] || -> equalish(e_3,e_3)*.
% 31.28/31.48 1466[4:Spt:1345.0,1345.1,1345.3] group_element(u) || -> product(u,u,e_3)* equalish(u,e_3).
% 31.28/31.48 1468[4:Res:1466.1,14.0] group_element(u) || product(u,u,v)*+ -> equalish(u,e_3) product(v,e_3,u)*.
% 31.28/31.48 1898[4:Res:1466.1,1468.1] group_element(u) group_element(u) || -> equalish(u,e_3) equalish(u,e_3) product(e_3,e_3,u)*.
% 31.28/31.48 1906[4:Obv:1898.2] group_element(u) || -> equalish(u,e_3) product(e_3,e_3,u)*.
% 31.28/31.48 1939[4:Res:1906.2,1315.1] group_element(u) group_element(e_3) || -> equalish(u,e_3)* product(e_1,e_1,e_3)* equalish(u,e_3)*.
% 31.28/31.48 1951[4:Obv:1939.2] group_element(u) group_element(e_3) || -> product(e_1,e_1,e_3)* equalish(u,e_3)*.
% 31.28/31.48 1952[4:SSi:1951.1,3.0] group_element(u) || -> product(e_1,e_1,e_3)* equalish(u,e_3)*.
% 31.28/31.48 1998[5:Spt:1952.0,1952.2] group_element(u) || -> equalish(u,e_3)*.
% 31.28/31.48 2000[5:Res:1998.1,5.0] group_element(e_1) || -> .
% 31.28/31.48 2002[5:SSi:2000.0,1.0] || -> .
% 31.28/31.48 2003[5:Spt:2002.0,1952.1] || -> product(e_1,e_1,e_3)*.
% 31.28/31.48 2005[5:Res:2003.0,14.0] || product(e_1,e_1,u)*+ -> product(u,e_3,e_1)*.
% 31.28/31.48 2148[5:Res:2003.0,2005.0] || -> product(e_3,e_3,e_1)*.
% 31.28/31.48 2156[5:Res:2148.0,11.0] || product(e_3,e_3,u)*+ -> equalish(u,e_1).
% 31.28/31.48 2232[5:Res:1906.2,2156.0] group_element(u) || -> equalish(u,e_3) equalish(u,e_1)*.
% 31.28/31.48 2244[5:Res:2232.2,6.0] group_element(e_2) || -> equalish(e_2,e_3)*.
% 31.28/31.48 2245[5:SSi:2244.0,2.0] || -> equalish(e_2,e_3)*.
% 31.28/31.48 2246[5:MRR:2245.0,7.0] || -> .
% 31.28/31.48 2247[4:Spt:2246.0,1345.2] || -> product(e_1,e_1,e_1)*.
% 31.28/31.48 2253[4:Res:2247.0,11.0] || product(e_1,e_1,u)*+ -> equalish(u,e_1).
% 31.28/31.48 2257[4:Res:2247.0,20.2] group_element(u) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 31.28/31.48 2279[4:SSi:2257.1,1.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 31.28/31.48 2325[4:Res:1312.2,2253.0] group_element(u) || -> product(u,u,e_3)* equalish(u,e_1).
% 31.28/31.48 2415[4:Res:2325.1,13.0] group_element(u) || product(v,u,e_3)* -> equalish(u,e_1) equalish(v,u).
% 31.28/31.48 2496[4:Res:2279.2,1322.1] group_element(u) group_element(e_2) || -> product(e_1,u,e_3)* equalish(e_1,u) product(e_2,e_2,e_3) equalish(u,e_1).
% 31.28/31.48 2499[4:SSi:2496.1,2.0] group_element(u) || -> product(e_1,u,e_3)* equalish(e_1,u) product(e_2,e_2,e_3) equalish(u,e_1).
% 31.28/31.48 2500[4:MRR:2499.1,2415.1] group_element(u) || -> equalish(e_1,u)* product(e_2,e_2,e_3)* equalish(u,e_1)*.
% 31.28/31.48 2531[5:Spt:2500.0,2500.1,2500.3] group_element(u) || -> equalish(e_1,u)* equalish(u,e_1)*.
% 31.28/31.48 2534[5:Res:2531.1,4.0] group_element(e_2) || -> equalish(e_2,e_1)*.
% 31.28/31.48 2537[5:SSi:2534.0,2.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 2538[5:MRR:2537.0,6.0] || -> .
% 31.28/31.48 2539[5:Spt:2538.0,2500.2] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 2542[5:Res:2539.0,14.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 31.28/31.48 2631[5:Res:2539.0,2542.0] || -> product(e_3,e_3,e_2)*.
% 31.28/31.48 2647[5:Res:2631.0,1315.1] group_element(e_3) || -> product(e_1,e_1,e_3)* equalish(e_2,e_3).
% 31.28/31.48 2648[5:SSi:2647.0,3.0] || -> product(e_1,e_1,e_3)* equalish(e_2,e_3).
% 31.28/31.48 2649[5:MRR:2648.1,7.0] || -> product(e_1,e_1,e_3)*.
% 31.28/31.48 2669[5:Res:2649.0,2253.0] || -> equalish(e_3,e_1)*.
% 31.28/31.48 2675[5:MRR:2669.0,8.0] || -> .
% 31.28/31.48 2694[2:Spt:2675.0,1306.3] || -> equalish(e_2,e_2)*.
% 31.28/31.48 3178[0:Res:1235.2,1249.1] group_element(u) group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)* product(u,u,e_3)* product(e_1,e_1,u)* product(e_2,e_2,u).
% 31.28/31.48 3184[0:Obv:3178.3] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)* product(e_2,e_2,u).
% 31.28/31.48 3198[0:Res:3184.1,11.0] group_element(u) || product(u,u,v)*+ -> product(e_1,e_1,u)* product(e_2,e_2,u) equalish(v,e_3).
% 31.28/31.48 3295[0:Res:3184.1,3198.1] group_element(u) group_element(u) || -> product(e_1,e_1,u)* product(e_2,e_2,u) product(e_1,e_1,u)* product(e_2,e_2,u) equalish(e_3,e_3).
% 31.28/31.48 3306[0:Obv:3295.3] group_element(u) || -> product(e_1,e_1,u)* product(e_2,e_2,u) equalish(e_3,e_3).
% 31.28/31.48 3317[3:Spt:3306.0,3306.1,3306.2] group_element(u) || -> product(e_1,e_1,u)* product(e_2,e_2,u).
% 31.28/31.48 3321[3:Res:3317.1,11.0] group_element(u) || product(e_1,e_1,v)*+ -> product(e_2,e_2,u)* equalish(v,u)*.
% 31.28/31.48 3322[3:Res:3317.1,12.0] group_element(u) || product(e_1,v,u)*+ -> product(e_2,e_2,u) equalish(v,e_1).
% 31.28/31.48 3337[3:Res:3317.1,1250.1] group_element(u) group_element(e_1) || -> product(e_2,e_2,u)* product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(u,e_2).
% 31.28/31.48 3347[3:SSi:3337.1,1.0] group_element(u) || -> product(e_2,e_2,u)* product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(u,e_2).
% 31.28/31.48 3386[3:Res:10.4,3322.1] group_element(u) group_element(e_1) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_2,e_2,e_1) equalish(u,e_1).
% 31.28/31.48 3401[3:Obv:3386.1] group_element(u) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_2,e_2,e_1) equalish(u,e_1).
% 31.28/31.48 3402[3:SSi:3401.1,1.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_2,e_2,e_1) equalish(u,e_1).
% 31.28/31.48 3596[4:Spt:3347.0,3347.1,3347.4] group_element(u) || -> product(e_2,e_2,u)* equalish(u,e_2).
% 31.28/31.48 3616[4:Res:3596.1,1250.1] group_element(u) group_element(e_2) || -> equalish(u,e_2)* product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(u,e_2)*.
% 31.28/31.48 3618[4:Obv:3616.2] group_element(u) group_element(e_2) || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(u,e_2)*.
% 31.28/31.48 3619[4:SSi:3618.1,2.0] group_element(u) || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(u,e_2)*.
% 31.28/31.48 3685[5:Spt:3619.0,3619.3] group_element(u) || -> equalish(u,e_2)*.
% 31.28/31.48 3687[5:Res:3685.1,4.0] group_element(e_1) || -> .
% 31.28/31.48 3689[5:SSi:3687.0,1.0] || -> .
% 31.28/31.48 3690[5:Spt:3689.0,3619.1,3619.2] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)*.
% 31.28/31.48 3691[6:Spt:3690.0] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 3696[6:Res:3691.0,11.0] || product(e_2,e_2,u)*+ -> equalish(u,e_3).
% 31.28/31.48 3926[6:Res:3596.1,3696.0] group_element(u) || -> equalish(u,e_2)* equalish(u,e_3).
% 31.28/31.48 3997[6:Res:3926.1,4.0] group_element(e_1) || -> equalish(e_1,e_3)*.
% 31.28/31.48 3998[6:SSi:3997.0,1.0] || -> equalish(e_1,e_3)*.
% 31.28/31.48 3999[6:MRR:3998.0,5.0] || -> .
% 31.28/31.48 4000[6:Spt:3999.0,3690.0,3691.0] || product(e_2,e_2,e_3)*+ -> .
% 31.28/31.48 4001[6:Spt:3999.0,3690.1] || -> product(e_1,e_1,e_2)*.
% 31.28/31.48 4094[6:Res:3596.1,4000.0] group_element(e_3) || -> equalish(e_3,e_2)*.
% 31.28/31.48 4097[6:SSi:4094.0,3.0] || -> equalish(e_3,e_2)*.
% 31.28/31.48 4098[6:MRR:4097.0,9.0] || -> .
% 31.28/31.48 4101[4:Spt:4098.0,3347.2,3347.3] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)*.
% 31.28/31.48 4110[5:Spt:4101.0] || -> product(e_1,e_1,e_3)*.
% 31.28/31.48 4115[5:Res:4110.0,11.0] || product(e_1,e_1,u)*+ -> equalish(u,e_3).
% 31.28/31.48 4116[5:Res:4110.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_1).
% 31.28/31.48 4141[5:MRR:3402.1,4116.0] group_element(u) || -> product(e_1,u,e_2)* product(e_2,e_2,e_1) equalish(u,e_1).
% 31.28/31.48 4214[5:Res:3317.1,4115.0] group_element(u) || -> product(e_2,e_2,u)* equalish(u,e_3).
% 31.28/31.48 4725[6:Spt:4141.0,4141.1,4141.3] group_element(u) || -> product(e_1,u,e_2)* equalish(u,e_1).
% 31.28/31.48 4762[6:Res:4725.1,3322.1] group_element(u) group_element(e_2) || -> equalish(u,e_1)* product(e_2,e_2,e_2)* equalish(u,e_1)*.
% 31.28/31.48 4771[6:Obv:4762.2] group_element(u) group_element(e_2) || -> product(e_2,e_2,e_2)* equalish(u,e_1)*.
% 31.28/31.48 4772[6:SSi:4771.1,2.0] group_element(u) || -> product(e_2,e_2,e_2)* equalish(u,e_1)*.
% 31.28/31.48 4802[7:Spt:4772.0,4772.2] group_element(u) || -> equalish(u,e_1)*.
% 31.28/31.48 4804[7:Res:4802.1,6.0] group_element(e_2) || -> .
% 31.28/31.48 4806[7:SSi:4804.0,2.0] || -> .
% 31.28/31.48 4807[7:Spt:4806.0,4772.1] || -> product(e_2,e_2,e_2)*.
% 31.28/31.48 4812[7:Res:4807.0,11.0] || product(e_2,e_2,u)*+ -> equalish(u,e_2).
% 31.28/31.48 4856[7:Res:4214.1,4812.0] group_element(u) || -> equalish(u,e_3) equalish(u,e_2)*.
% 31.28/31.48 4964[7:Res:4856.2,4.0] group_element(e_1) || -> equalish(e_1,e_3)*.
% 31.28/31.48 4965[7:SSi:4964.0,1.0] || -> equalish(e_1,e_3)*.
% 31.28/31.48 4966[7:MRR:4965.0,5.0] || -> .
% 31.28/31.48 4967[6:Spt:4966.0,4141.2] || -> product(e_2,e_2,e_1)*.
% 31.28/31.48 4987[6:Res:4967.0,1250.1] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 31.28/31.48 4988[6:SSi:4987.0,2.0] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 31.28/31.48 4989[6:MRR:4988.2,4.0] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)*.
% 31.28/31.48 5001[7:Spt:4989.0] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 5006[7:Res:5001.0,11.0] || product(e_2,e_2,u)* -> equalish(u,e_3).
% 31.28/31.48 5017[7:MRR:4214.1,5006.0] group_element(u) || -> equalish(u,e_3)*.
% 31.28/31.48 5041[0:Res:1235.3,1281.3] group_element(u) group_element(v) group_element(e_1) group_element(e_1) || -> product(u,u,e_3) product(u,u,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* product(e_1,e_1,e_3)* equalish(v,e_1) equalish(u,e_2).
% 31.28/31.48 5064[0:Obv:5041.2] group_element(u) group_element(v) group_element(e_1) || -> product(u,u,e_3) product(u,u,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* product(e_1,e_1,e_3)* equalish(v,e_1) equalish(u,e_2).
% 31.28/31.48 5085[7:Res:5017.1,5.0] group_element(e_1) || -> .
% 31.28/31.48 5087[7:SSi:5085.0,1.0] || -> .
% 31.28/31.48 5088[7:Spt:5087.0,4989.0,5001.0] || product(e_2,e_2,e_3)* -> .
% 31.28/31.48 5089[7:Spt:5087.0,4989.1] || -> product(e_1,e_1,e_2)*.
% 31.28/31.48 5139[7:Res:5089.0,4115.0] || -> equalish(e_2,e_3)*.
% 31.28/31.48 5151[7:MRR:5139.0,7.0] || -> .
% 31.28/31.48 5186[5:Spt:5151.0,4101.0,4110.0] || product(e_1,e_1,e_3)*+ -> .
% 31.28/31.48 5187[5:Spt:5151.0,4101.1] || -> product(e_1,e_1,e_1)*.
% 31.28/31.48 5226[0:SSi:5064.2,1.0] group_element(u) group_element(v) || -> product(u,u,e_3) product(u,u,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* product(e_1,e_1,e_3)* equalish(v,e_1) equalish(u,e_2).
% 31.28/31.48 5283[5:Res:5187.0,3321.1] group_element(u) || -> product(e_2,e_2,u)* equalish(e_1,u).
% 31.28/31.48 5325[5:Res:3317.1,5186.0] group_element(e_3) || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 5330[5:SSi:5325.0,3.0] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 5339[5:Res:5330.0,11.0] || product(e_2,e_2,u)*+ -> equalish(u,e_3).
% 31.28/31.48 5985[5:Res:5283.1,5339.0] group_element(u) || -> equalish(e_1,u)* equalish(u,e_3)*.
% 31.28/31.48 6036[5:Res:5985.1,4.0] group_element(e_2) || -> equalish(e_2,e_3)*.
% 31.28/31.48 6037[5:SSi:6036.0,2.0] || -> equalish(e_2,e_3)*.
% 31.28/31.48 6038[5:MRR:6037.0,7.0] || -> .
% 31.28/31.48 6039[3:Spt:6038.0,3306.3] || -> equalish(e_3,e_3)*.
% 31.28/31.48 6048[4:Spt:1237.1,1237.6,1237.7,1237.8] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 31.28/31.48 6055[4:Res:6048.2,13.0] group_element(u) || product(v,e_1,e_2)*+ -> product(u,e_1,e_3)* equalish(e_1,u) equalish(v,u)*.
% 31.28/31.48 6284[4:Res:1235.3,6055.1] group_element(e_2) group_element(u) || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)* product(u,e_1,e_3)* equalish(e_1,u) equalish(e_1,u).
% 31.28/31.48 6289[4:Obv:6284.5] group_element(e_2) group_element(u) || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)* product(u,e_1,e_3)* equalish(e_1,u).
% 31.28/31.48 6290[4:SSi:6289.0,2.0] group_element(u) || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)* product(u,e_1,e_3)* equalish(e_1,u).
% 31.28/31.48 6306[5:Spt:1239.1,1239.6,1239.7,1239.8] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 31.28/31.48 6390[6:Spt:6290.0,6290.3,6290.4] group_element(u) || -> product(u,e_1,e_3)* equalish(e_1,u).
% 31.28/31.48 6397[6:Res:6390.1,13.0] group_element(u) || product(v,e_1,e_3)*+ -> equalish(e_1,u)* equalish(v,u)*.
% 31.28/31.48 6488[6:Res:1235.3,6397.1] group_element(e_3) group_element(u) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)* equalish(e_1,u)* equalish(e_1,u)*.
% 31.28/31.48 6493[6:Obv:6488.4] group_element(e_3) group_element(u) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)* equalish(e_1,u)*.
% 31.28/31.48 6494[6:SSi:6493.0,3.0] group_element(u) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)* equalish(e_1,u)*.
% 31.28/31.48 6632[7:Spt:6494.0,6494.3] group_element(u) || -> equalish(e_1,u)*.
% 31.28/31.48 6634[7:Res:6632.1,4.0] group_element(e_2) || -> .
% 31.28/31.48 6636[7:SSi:6634.0,2.0] || -> .
% 31.28/31.48 6637[7:Spt:6636.0,6494.1,6494.2] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)*.
% 31.28/31.48 6641[7:Res:6637.1,14.0] || product(e_3,e_3,u)*+ -> product(e_3,e_3,e_3)* product(u,e_2,e_3)*.
% 31.28/31.48 6642[7:Res:6637.1,11.0] || product(e_3,e_3,u)*+ -> product(e_3,e_3,e_3)* equalish(u,e_2).
% 31.28/31.48 6730[8:Spt:6642.0,6642.2] || product(e_3,e_3,u)*+ -> equalish(u,e_2).
% 31.28/31.48 6822[9:Spt:6641.0,6641.2] || product(e_3,e_3,u)*+ -> product(u,e_2,e_3)*.
% 31.28/31.48 6828[9:Res:6637.1,6822.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 31.28/31.48 6834[10:Spt:6828.0] || -> product(e_3,e_3,e_3)*.
% 31.28/31.48 6853[10:Res:6834.0,6730.0] || -> equalish(e_3,e_2)*.
% 31.28/31.48 6854[10:MRR:6853.0,9.0] || -> .
% 31.28/31.48 6876[10:Spt:6854.0,6828.0,6834.0] || product(e_3,e_3,e_3)*+ -> .
% 31.28/31.48 6877[10:Spt:6854.0,6828.1] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 6894[10:Res:6877.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 31.28/31.48 6978[10:Res:6390.1,6894.0] group_element(e_2) || -> equalish(e_1,e_2)* equalish(e_1,e_2)*.
% 31.28/31.48 6980[10:Obv:6978.1] group_element(e_2) || -> equalish(e_1,e_2)*.
% 31.28/31.48 6981[10:SSi:6980.0,2.0] || -> equalish(e_1,e_2)*.
% 31.28/31.48 6982[10:MRR:6981.0,4.0] || -> .
% 31.28/31.48 6985[9:Spt:6982.0,6641.1] || -> product(e_3,e_3,e_3)*.
% 31.28/31.48 7003[9:Res:6985.0,6730.0] || -> equalish(e_3,e_2)*.
% 31.28/31.48 7004[9:MRR:7003.0,9.0] || -> .
% 31.28/31.48 7026[8:Spt:7004.0,6642.1] || -> product(e_3,e_3,e_3)*.
% 31.28/31.48 7032[8:Res:7026.0,12.0] || product(e_3,u,e_3)*+ -> equalish(u,e_3).
% 31.28/31.48 7067[8:Res:6390.1,7032.0] group_element(e_3) || -> equalish(e_1,e_3)* equalish(e_1,e_3)*.
% 31.28/31.48 7069[8:Obv:7067.1] group_element(e_3) || -> equalish(e_1,e_3)*.
% 31.28/31.48 7070[8:SSi:7069.0,3.0] || -> equalish(e_1,e_3)*.
% 31.28/31.48 7071[8:MRR:7070.0,5.0] || -> .
% 31.28/31.48 7074[6:Spt:7071.0,6290.1,6290.2] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 31.28/31.48 7079[6:Res:7074.1,11.0] || product(e_2,e_2,u)*+ -> product(e_2,e_2,e_3)* equalish(u,e_2).
% 31.28/31.48 7080[6:Res:7074.1,12.0] || product(e_2,u,e_2)*+ -> product(e_2,e_2,e_3)* equalish(u,e_2).
% 31.28/31.48 7081[6:Res:7074.1,13.0] || product(u,e_2,e_2)*+ -> product(e_2,e_2,e_3)* equalish(u,e_2).
% 31.28/31.48 7256[7:Spt:7079.0,7079.2] || product(e_2,e_2,u)*+ -> equalish(u,e_2).
% 31.28/31.48 7271[8:Spt:7080.0,7080.2] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 31.28/31.48 7288[9:Spt:7081.0,7081.2] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 31.28/31.48 7397[9:Res:6306.2,7288.0] group_element(e_2) || -> product(e_1,e_2,e_3)* equalish(e_1,e_2) equalish(e_1,e_2).
% 31.28/31.48 7407[9:Obv:7397.2] group_element(e_2) || -> product(e_1,e_2,e_3)* equalish(e_1,e_2).
% 31.28/31.48 7408[9:SSi:7407.0,2.0] || -> product(e_1,e_2,e_3)* equalish(e_1,e_2).
% 31.28/31.48 7409[9:MRR:7408.1,4.0] || -> product(e_1,e_2,e_3)*.
% 31.28/31.48 7438[9:Res:7409.0,18.2] group_element(e_1) group_element(e_2) || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* product(e_3,e_1,e_1).
% 31.28/31.48 7439[9:Res:7409.0,14.0] || product(e_2,e_1,u)*+ -> product(u,e_3,e_2)*.
% 31.28/31.48 7441[9:Res:7409.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_2).
% 31.28/31.48 7456[9:SSi:7438.1,7438.0,2.0,1.0] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* product(e_3,e_1,e_1).
% 31.28/31.48 7584[9:Res:3184.2,7441.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 31.28/31.48 7590[9:SSi:7584.0,3.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 31.28/31.48 7591[9:MRR:7590.2,4.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 31.28/31.48 7598[10:Spt:7591.0] || -> product(e_3,e_3,e_3)*.
% 31.28/31.48 7603[10:Res:7598.0,11.0] || product(e_3,e_3,u)*+ -> equalish(u,e_3).
% 31.28/31.48 7931[11:Spt:7456.0] || -> product(e_2,e_1,e_3)*.
% 31.28/31.48 7951[11:Res:7931.0,7439.0] || -> product(e_3,e_3,e_2)*.
% 31.28/31.48 7995[11:Res:7951.0,7603.0] || -> equalish(e_2,e_3)*.
% 31.28/31.48 7996[11:MRR:7995.0,7.0] || -> .
% 31.28/31.48 8025[11:Spt:7996.0,7456.0,7931.0] || product(e_2,e_1,e_3)*+ -> .
% 31.28/31.48 8026[11:Spt:7996.0,7456.1,7456.2] || -> product(e_2,e_1,e_2)* product(e_3,e_1,e_1).
% 31.28/31.48 8040[12:Spt:8026.0] || -> product(e_2,e_1,e_2)*.
% 31.28/31.48 8076[12:Res:8040.0,7271.0] || -> equalish(e_1,e_2)*.
% 31.28/31.48 8077[12:MRR:8076.0,4.0] || -> .
% 31.28/31.48 8103[12:Spt:8077.0,8026.0,8040.0] || product(e_2,e_1,e_2)*+ -> .
% 31.28/31.48 8104[12:Spt:8077.0,8026.1] || -> product(e_3,e_1,e_1)*.
% 31.28/31.48 8116[12:Res:8104.0,11.0] || product(e_3,e_1,u)*+ -> equalish(u,e_1).
% 31.28/31.48 8194[12:Res:23.4,8103.0] group_element(e_2) group_element(e_1) group_element(u) || -> product(e_2,e_1,e_3)* product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_2,u).
% 31.28/31.48 8195[12:SSi:8194.1,8194.0,1.0,2.0] group_element(u) || -> product(e_2,e_1,e_3)* product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_2,u).
% 31.28/31.48 8196[12:MRR:8195.1,8025.0] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_2,u).
% 31.28/31.48 8483[12:Res:8196.2,8116.0] group_element(e_3) || -> product(e_3,e_1,e_3)* equalish(e_2,e_3) equalish(e_2,e_1).
% 31.28/31.48 8484[12:SSi:8483.0,3.0] || -> product(e_3,e_1,e_3)* equalish(e_2,e_3) equalish(e_2,e_1).
% 31.28/31.48 8485[12:MRR:8484.1,8484.2,7.0,6.0] || -> product(e_3,e_1,e_3)*.
% 31.28/31.48 8540[12:Res:8485.0,8116.0] || -> equalish(e_3,e_1)*.
% 31.28/31.48 8542[12:MRR:8540.0,8.0] || -> .
% 31.28/31.48 8549[10:Spt:8542.0,7591.0,7598.0] || product(e_3,e_3,e_3)* -> .
% 31.28/31.48 8550[10:Spt:8542.0,7591.1] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 8588[10:Res:8550.0,7256.0] || -> equalish(e_3,e_2)*.
% 31.28/31.48 8590[10:MRR:8588.0,9.0] || -> .
% 31.28/31.48 8616[9:Spt:8590.0,7081.1] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 8639[9:Res:8616.0,7256.0] || -> equalish(e_3,e_2)*.
% 31.28/31.48 8640[9:MRR:8639.0,9.0] || -> .
% 31.28/31.48 8664[8:Spt:8640.0,7080.1] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 8685[8:Res:8664.0,7256.0] || -> equalish(e_3,e_2)*.
% 31.28/31.48 8686[8:MRR:8685.0,9.0] || -> .
% 31.28/31.48 8702[7:Spt:8686.0,7079.1] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 8706[7:Res:8702.0,14.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 31.28/31.48 8954[7:Res:8702.0,8706.0] || -> product(e_3,e_3,e_2)*.
% 31.28/31.48 8964[7:Res:8954.0,11.0] || product(e_3,e_3,u)*+ -> equalish(u,e_2).
% 31.28/31.48 8965[7:Res:8954.0,12.0] || product(e_3,u,e_2)*+ -> equalish(u,e_3).
% 31.28/31.48 8966[7:Res:8954.0,13.0] || product(u,e_3,e_2)*+ -> equalish(u,e_3).
% 31.28/31.48 9345[7:Res:6306.2,8966.0] group_element(e_3) || -> product(e_1,e_3,e_3)* equalish(e_1,e_3) equalish(e_1,e_3).
% 31.28/31.48 9347[7:Obv:9345.2] group_element(e_3) || -> product(e_1,e_3,e_3)* equalish(e_1,e_3).
% 31.28/31.48 9348[7:SSi:9347.0,3.0] || -> product(e_1,e_3,e_3)* equalish(e_1,e_3).
% 31.28/31.48 9349[7:MRR:9348.1,5.0] || -> product(e_1,e_3,e_3)*.
% 31.28/31.48 9358[7:Res:9349.0,14.0] || product(e_3,e_1,u)*+ -> product(u,e_3,e_3)*.
% 31.28/31.48 9774[7:Res:6048.2,8965.0] group_element(e_3) || -> product(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_1,e_3).
% 31.28/31.48 9776[7:Obv:9774.2] group_element(e_3) || -> product(e_3,e_1,e_3)* equalish(e_1,e_3).
% 31.28/31.48 9777[7:SSi:9776.0,3.0] || -> product(e_3,e_1,e_3)* equalish(e_1,e_3).
% 31.28/31.48 9778[7:MRR:9777.1,5.0] || -> product(e_3,e_1,e_3)*.
% 31.28/31.48 10121[7:Res:9778.0,9358.0] || -> product(e_3,e_3,e_3)*.
% 31.28/31.48 10154[7:Res:10121.0,8964.0] || -> equalish(e_3,e_2)*.
% 31.28/31.48 10156[7:MRR:10154.0,9.0] || -> .
% 31.28/31.48 10184[5:Spt:10156.0,1239.0,1239.2,1239.3,1239.4,1239.5] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)*.
% 31.28/31.48 10219[5:Fac:10184.2,10184.4] group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 31.28/31.48 10288[5:Obv:10219.1] group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 31.28/31.48 10289[5:SSi:10288.0,1.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 31.28/31.48 10346[6:Spt:10289.0] || -> product(e_1,e_1,e_3)*.
% 31.28/31.48 10350[6:Res:10346.0,14.0] || product(e_1,e_1,u)*+ -> product(u,e_3,e_1)*.
% 31.28/31.48 10353[6:Res:10346.0,13.0] || product(u,e_1,e_3)*+ -> equalish(u,e_1).
% 31.28/31.48 10485[0:Fac:1288.4,1288.9] group_element(e_1) group_element(e_2) group_element(u) || -> product(e_2,e_1,e_3) product(e_2,u,e_3)* equalish(e_1,u) product(u,e_2,e_3) product(u,e_2,e_2)* product(e_2,e_1,e_2)*.
% 31.28/31.48 10628[0:SSi:10485.1,10485.0,2.0,1.0] group_element(u) || -> product(e_2,e_1,e_3) product(e_2,u,e_3)* equalish(e_1,u) product(u,e_2,e_3) product(u,e_2,e_2)* product(e_2,e_1,e_2)*.
% 31.28/31.48 10849[6:Res:10346.0,10350.0] || -> product(e_3,e_3,e_1)*.
% 31.28/31.48 10867[6:Res:10849.0,11.0] || product(e_3,e_3,u)*+ -> equalish(u,e_1).
% 31.28/31.48 10875[6:Res:10849.0,20.2] group_element(u) group_element(e_3) || -> product(e_3,u,e_3) product(e_3,u,e_2)* equalish(e_3,u).
% 31.28/31.48 10886[6:SSi:10875.1,3.0] group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)* equalish(e_3,u).
% 31.28/31.48 11176[6:Res:10886.2,1258.1] group_element(e_1) group_element(e_2) || -> product(e_3,e_1,e_3) equalish(e_3,e_1) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* equalish(e_3,e_1).
% 31.28/31.48 11179[6:Obv:11176.3] group_element(e_1) group_element(e_2) || -> product(e_3,e_1,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* equalish(e_3,e_1).
% 31.28/31.48 11180[6:SSi:11179.1,11179.0,2.0,1.0] || -> product(e_3,e_1,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* equalish(e_3,e_1).
% 31.28/31.48 11181[6:MRR:11180.0,11180.3,10353.0,8.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 31.28/31.48 11217[7:Spt:11181.0] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 11221[7:Res:11217.0,14.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 31.28/31.48 11505[7:Res:11217.0,11221.0] || -> product(e_3,e_3,e_2)*.
% 31.28/31.48 11548[7:Res:11505.0,10867.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 11549[7:MRR:11548.0,6.0] || -> .
% 31.28/31.48 11576[7:Spt:11549.0,11181.0,11217.0] || product(e_2,e_2,e_3)*+ -> .
% 31.28/31.48 11577[7:Spt:11549.0,11181.1] || -> product(e_2,e_2,e_2)*.
% 31.28/31.48 11591[7:Res:11577.0,12.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 31.28/31.48 11834[7:Res:6048.2,11591.0] group_element(e_2) || -> product(e_2,e_1,e_3)* equalish(e_1,e_2) equalish(e_1,e_2).
% 31.28/31.48 11840[7:Obv:11834.2] group_element(e_2) || -> product(e_2,e_1,e_3)* equalish(e_1,e_2).
% 31.28/31.48 11841[7:SSi:11840.0,2.0] || -> product(e_2,e_1,e_3)* equalish(e_1,e_2).
% 31.28/31.48 11842[7:MRR:11841.1,4.0] || -> product(e_2,e_1,e_3)*.
% 31.28/31.48 11888[7:Res:11842.0,10353.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 11889[7:MRR:11888.0,6.0] || -> .
% 31.28/31.48 11923[6:Spt:11889.0,10289.0,10346.0] || product(e_1,e_1,e_3)*+ -> .
% 31.28/31.48 11924[6:Spt:11889.0,10289.1] || -> product(e_1,e_1,e_2)*.
% 31.28/31.48 12030[6:Res:11924.0,14.0] || product(e_1,e_1,u)*+ -> product(u,e_2,e_1)*.
% 31.28/31.48 12032[6:Res:11924.0,12.0] || product(e_1,u,e_2)*+ -> equalish(u,e_1).
% 31.28/31.48 12033[6:Res:11924.0,13.0] || product(u,e_1,e_2)*+ -> equalish(u,e_1).
% 31.28/31.48 12164[6:Res:3184.2,11923.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 31.28/31.48 12166[6:Res:1247.3,11923.0] group_element(e_3) group_element(u) || -> product(e_3,u,e_3)* product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,e_3)*.
% 31.28/31.48 12170[6:SSi:12164.0,3.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 31.28/31.48 12175[6:SSi:12166.0,3.0] group_element(u) || -> product(e_3,u,e_3)* product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,e_3)*.
% 31.28/31.48 12300[7:Spt:12170.0] || -> product(e_3,e_3,e_3)*.
% 31.28/31.48 12306[7:Res:12300.0,12.0] || product(e_3,u,e_3)*+ -> equalish(u,e_3).
% 31.28/31.48 12307[7:Res:12300.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_3).
% 31.28/31.48 12459[8:Spt:12175.0,12175.1,12175.2,12175.3] group_element(u) || -> product(e_3,u,e_3)* product(u,e_3,e_3) product(u,e_3,e_2)*.
% 31.28/31.48 12514[8:Res:12459.3,12032.0] group_element(e_1) || -> product(e_3,e_1,e_3) product(e_1,e_3,e_3)* equalish(e_3,e_1).
% 31.28/31.48 12515[8:SSi:12514.0,1.0] || -> product(e_3,e_1,e_3) product(e_1,e_3,e_3)* equalish(e_3,e_1).
% 31.28/31.48 12516[8:MRR:12515.2,8.0] || -> product(e_3,e_1,e_3) product(e_1,e_3,e_3)*.
% 31.28/31.48 12625[7:Res:1246.2,12307.0] group_element(u) group_element(e_3) || -> product(e_1,e_1,e_3)* product(e_3,u,e_3) product(e_3,u,e_2) product(e_2,e_1,u)* equalish(u,e_3).
% 31.28/31.48 12626[8:Res:12516.1,12307.0] || -> product(e_3,e_1,e_3)* equalish(e_1,e_3).
% 31.28/31.48 12628[8:MRR:12626.0,12626.1,12306.0,5.0] || -> .
% 31.28/31.48 12629[7:SSi:12625.1,3.0] group_element(u) || -> product(e_1,e_1,e_3)* product(e_3,u,e_3) product(e_3,u,e_2) product(e_2,e_1,u)* equalish(u,e_3).
% 31.28/31.48 12630[7:MRR:12629.1,12629.2,11923.0,12306.0] group_element(u) || -> product(e_3,u,e_2) product(e_2,e_1,u)* equalish(u,e_3).
% 31.28/31.48 12631[8:Spt:12628.0,12175.4] || -> product(e_2,e_1,e_3)*.
% 31.28/31.48 12636[8:Res:12631.0,11.0] || product(e_2,e_1,u)*+ -> equalish(u,e_3).
% 31.28/31.48 12653[8:MRR:12630.2,12636.0] group_element(u) || -> product(e_3,u,e_2)* equalish(u,e_3).
% 31.28/31.48 12839[6:Res:11924.0,12030.0] || -> product(e_2,e_2,e_1)*.
% 31.28/31.48 12950[6:Res:12839.0,11.0] || product(e_2,e_2,u)*+ -> equalish(u,e_1).
% 31.28/31.48 13120[8:Res:12653.1,12033.0] group_element(e_1) || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 31.28/31.48 13123[8:SSi:13120.0,1.0] || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 31.28/31.48 13124[8:MRR:13123.0,13123.1,5.0,8.0] || -> .
% 31.28/31.48 13168[7:Spt:13124.0,12170.0,12300.0] || product(e_3,e_3,e_3)* -> .
% 31.28/31.48 13169[7:Spt:13124.0,12170.1] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 13201[7:Res:13169.0,12950.0] || -> equalish(e_3,e_1)*.
% 31.28/31.48 13202[7:MRR:13201.0,8.0] || -> .
% 31.28/31.48 13219[4:Spt:13202.0,1237.0,1237.2,1237.3,1237.4,1237.5] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)*.
% 31.28/31.48 13238[4:Fac:13219.2,13219.4] group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 31.28/31.48 13307[4:Obv:13238.1] group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 31.28/31.48 13308[4:SSi:13307.0,1.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 31.28/31.48 13366[5:Spt:10628.0,10628.2,10628.3,10628.4,10628.5] group_element(u) || -> product(e_2,u,e_3)* equalish(e_1,u) product(u,e_2,e_3) product(u,e_2,e_2)*.
% 31.28/31.48 13470[6:Spt:13308.0] || -> product(e_1,e_1,e_3)*.
% 31.28/31.48 13474[6:Res:13470.0,14.0] || product(e_1,e_1,u)*+ -> product(u,e_3,e_1)*.
% 31.28/31.48 13476[6:Res:13470.0,12.0] || product(e_1,u,e_3)*+ -> equalish(u,e_1).
% 31.28/31.48 13477[6:Res:13470.0,13.0] || product(u,e_1,e_3)*+ -> equalish(u,e_1).
% 31.28/31.48 13815[6:Res:13470.0,13474.0] || -> product(e_3,e_3,e_1)*.
% 31.28/31.48 13833[6:Res:13815.0,11.0] || product(e_3,e_3,u)*+ -> equalish(u,e_1).
% 31.28/31.48 13841[6:Res:13815.0,20.2] group_element(u) group_element(e_3) || -> product(e_3,u,e_3) product(e_3,u,e_2)* equalish(e_3,u).
% 31.28/31.48 13852[6:SSi:13841.1,3.0] group_element(u) || -> product(e_3,u,e_3) product(e_3,u,e_2)* equalish(e_3,u).
% 31.28/31.48 14172[6:Res:13852.2,1258.1] group_element(e_1) group_element(e_2) || -> product(e_3,e_1,e_3) equalish(e_3,e_1) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* equalish(e_3,e_1).
% 31.28/31.48 14175[6:Obv:14172.3] group_element(e_1) group_element(e_2) || -> product(e_3,e_1,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* equalish(e_3,e_1).
% 31.28/31.48 14176[6:SSi:14175.1,14175.0,2.0,1.0] || -> product(e_3,e_1,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2)* equalish(e_3,e_1).
% 31.28/31.48 14177[6:MRR:14176.0,14176.3,13477.0,8.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 31.28/31.48 14213[7:Spt:14177.0] || -> product(e_2,e_2,e_3)*.
% 31.28/31.48 14217[7:Res:14213.0,14.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 31.28/31.48 14516[7:Res:14213.0,14217.0] || -> product(e_3,e_3,e_2)*.
% 31.28/31.48 14784[7:Res:14516.0,13833.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 14785[7:MRR:14784.0,6.0] || -> .
% 31.28/31.48 14812[7:Spt:14785.0,14177.0,14213.0] || product(e_2,e_2,e_3)*+ -> .
% 31.28/31.48 14813[7:Spt:14785.0,14177.1] || -> product(e_2,e_2,e_2)*.
% 31.28/31.48 14851[7:Res:14813.0,12.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 31.28/31.48 14852[7:Res:14813.0,13.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 31.28/31.48 15238[7:Res:13219.2,14852.0] group_element(e_2) || -> product(e_1,e_2,e_3)* product(e_2,e_1,e_3) product(e_2,e_1,e_2) equalish(e_1,e_2).
% 31.28/31.48 15244[7:SSi:15238.0,2.0] || -> product(e_1,e_2,e_3)* product(e_2,e_1,e_3) product(e_2,e_1,e_2) equalish(e_1,e_2).
% 31.28/31.48 15245[7:MRR:15244.2,15244.3,14851.0,4.0] || -> product(e_1,e_2,e_3)* product(e_2,e_1,e_3).
% 31.28/31.48 15280[8:Spt:15245.0] || -> product(e_1,e_2,e_3)*.
% 31.28/31.48 15301[8:Res:15280.0,13476.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 15302[8:MRR:15301.0,6.0] || -> .
% 31.28/31.48 15342[8:Spt:15302.0,15245.0,15280.0] || product(e_1,e_2,e_3)* -> .
% 31.28/31.48 15343[8:Spt:15302.0,15245.1] || -> product(e_2,e_1,e_3)*.
% 31.28/31.48 15399[8:Res:15343.0,13477.0] || -> equalish(e_2,e_1)*.
% 31.28/31.48 15400[8:MRR:15399.0,6.0] || -> .
% 31.28/31.48 15440[6:Spt:15400.0,13308.0,13470.0] || product(e_1,e_1,e_3)*+ -> .
% 31.28/31.48 15441[6:Spt:15400.0,13308.1] || -> product(e_1,e_1,e_2)*.
% 31.28/31.48 15639[6:Res:15441.0,14.0] || product(e_1,e_1,u)*+ -> product(u,e_2,e_1)*.
% 31.28/31.48 15641[6:Res:15441.0,12.0] || product(e_1,u,e_2)*+ -> equalish(u,e_1).
% 31.28/31.48 15805[6:Res:3184.2,15440.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 31.28/31.48 15807[6:Res:1247.3,15440.0] group_element(e_3) group_element(u) || -> product(e_3,u,e_3)* product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,e_3)*.
% 37.70/37.91 15811[6:SSi:15805.0,3.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 37.70/37.91 15816[6:SSi:15807.0,3.0] group_element(u) || -> product(e_3,u,e_3)* product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,e_3)*.
% 37.70/37.91 15945[7:Spt:15811.0] || -> product(e_3,e_3,e_3)*.
% 37.70/37.91 15951[7:Res:15945.0,12.0] || product(e_3,u,e_3)*+ -> equalish(u,e_3).
% 37.70/37.91 15952[7:Res:15945.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_3).
% 37.70/37.91 16123[8:Spt:15816.0,15816.1,15816.2,15816.3] group_element(u) || -> product(e_3,u,e_3)* product(u,e_3,e_3) product(u,e_3,e_2)*.
% 37.70/37.91 16178[8:Res:16123.3,15641.0] group_element(e_1) || -> product(e_3,e_1,e_3) product(e_1,e_3,e_3)* equalish(e_3,e_1).
% 37.70/37.91 16179[8:SSi:16178.0,1.0] || -> product(e_3,e_1,e_3) product(e_1,e_3,e_3)* equalish(e_3,e_1).
% 37.70/37.91 16180[8:MRR:16179.2,8.0] || -> product(e_3,e_1,e_3) product(e_1,e_3,e_3)*.
% 37.70/37.91 16295[8:Res:16180.1,15952.0] || -> product(e_3,e_1,e_3)* equalish(e_1,e_3).
% 37.70/37.91 16298[8:MRR:16295.0,16295.1,15951.0,5.0] || -> .
% 37.70/37.91 16310[8:Spt:16298.0,15816.4] || -> product(e_2,e_1,e_3)*.
% 37.70/37.91 16316[8:Res:16310.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_1).
% 37.70/37.91 16733[6:Res:15441.0,15639.0] || -> product(e_2,e_2,e_1)*.
% 37.70/37.91 16786[6:Res:16733.0,11.0] || product(e_2,e_2,u)*+ -> equalish(u,e_1).
% 37.70/37.91 16829[6:Res:13366.4,16786.0] group_element(e_2) || -> product(e_2,e_2,e_3)* equalish(e_1,e_2) product(e_2,e_2,e_3)* equalish(e_2,e_1).
% 37.70/37.91 16832[6:Obv:16829.1] group_element(e_2) || -> equalish(e_1,e_2) product(e_2,e_2,e_3)* equalish(e_2,e_1).
% 37.70/37.91 16833[6:SSi:16832.0,2.0] || -> equalish(e_1,e_2) product(e_2,e_2,e_3)* equalish(e_2,e_1).
% 37.70/37.91 16834[8:MRR:16833.0,16833.1,16833.2,4.0,16316.0,6.0] || -> .
% 37.70/37.91 16839[7:Spt:16834.0,15811.0,15945.0] || product(e_3,e_3,e_3)* -> .
% 37.70/37.91 16840[7:Spt:16834.0,15811.1] || -> product(e_2,e_2,e_3)*.
% 37.70/37.91 16874[7:Res:16840.0,16786.0] || -> equalish(e_3,e_1)*.
% 37.70/37.91 16875[7:MRR:16874.0,8.0] || -> .
% 37.70/37.91 16890[5:Spt:16875.0,10628.1,10628.6] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 37.70/37.91 16891[6:Spt:16890.0] || -> product(e_2,e_1,e_3)*.
% 37.70/37.91 16896[6:Res:16891.0,11.0] || product(e_2,e_1,u)*+ -> equalish(u,e_3).
% 37.70/37.91 16897[6:Res:16891.0,12.0] || product(e_2,u,e_3)*+ -> equalish(u,e_1).
% 37.70/37.91 16898[6:Res:16891.0,13.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 37.70/37.91 16911[6:Res:16891.0,1258.1] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)* equalish(e_2,e_1).
% 37.70/37.91 16913[6:SSi:16911.0,3.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)* equalish(e_2,e_1).
% 37.70/37.91 16914[6:MRR:16913.2,6.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)*.
% 37.70/37.91 16922[7:Spt:13308.0] || -> product(e_1,e_1,e_3)*.
% 37.70/37.91 17274[6:Res:3184.2,16898.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 37.70/37.91 17281[7:Res:16922.0,16898.0] || -> equalish(e_1,e_2)*.
% 37.70/37.91 17287[7:MRR:17281.0,4.0] || -> .
% 37.70/37.91 17288[6:SSi:17274.0,3.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 37.70/37.91 17289[6:MRR:17288.2,4.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 37.70/37.91 17312[7:Spt:17287.0,13308.0,16922.0] || product(e_1,e_1,e_3)*+ -> .
% 37.70/37.91 17313[7:Spt:17287.0,13308.1] || -> product(e_1,e_1,e_2)*.
% 37.70/37.91 17331[7:MRR:5226.6,17312.0] group_element(u) group_element(v) || -> product(u,u,e_3) product(u,u,e_2)* product(e_1,v,e_3) product(e_1,v,e_2)* equalish(v,e_1) equalish(u,e_2).
% 37.70/37.91 17455[7:Res:17313.0,12.0] || product(e_1,u,e_2)*+ -> equalish(u,e_1).
% 37.70/37.91 17456[7:Res:17313.0,13.0] || product(u,e_1,e_2)*+ -> equalish(u,e_1).
% 37.70/37.91 17520[7:MRR:17331.5,17455.0] group_element(u) group_element(v) || -> product(u,u,e_3) product(u,u,e_2)* product(e_1,v,e_3)* equalish(v,e_1) equalish(u,e_2).
% 37.70/37.91 17592[8:Spt:17520.1,17520.4,17520.5] group_element(u) || -> product(e_1,u,e_3)* equalish(u,e_1).
% 37.70/37.91 17658[9:Spt:17289.0] || -> product(e_3,e_3,e_3)*.
% 37.70/37.91 17665[9:Res:17658.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_3).
% 37.70/37.91 18035[9:Res:17592.1,17665.0] group_element(e_3) || -> equalish(e_3,e_1) equalish(e_1,e_3)*.
% 37.70/37.91 18037[9:SSi:18035.0,3.0] || -> equalish(e_3,e_1) equalish(e_1,e_3)*.
% 37.70/37.91 18038[9:MRR:18037.0,18037.1,8.0,5.0] || -> .
% 37.70/37.91 18042[9:Spt:18038.0,17289.0,17658.0] || product(e_3,e_3,e_3)* -> .
% 37.70/37.91 18043[9:Spt:18038.0,17289.1] || -> product(e_2,e_2,e_3)*.
% 37.70/37.91 18079[9:Res:18043.0,16897.0] || -> equalish(e_2,e_1)*.
% 37.70/37.91 18080[9:MRR:18079.0,6.0] || -> .
% 37.70/37.91 18096[8:Spt:18080.0,17520.0,17520.2,17520.3,17520.6] group_element(u) || -> product(u,u,e_3) product(u,u,e_2)* equalish(u,e_2).
% 37.70/37.91 18108[9:Spt:16914.0] || -> product(e_3,e_3,e_3)*.
% 37.70/37.91 18114[9:Res:18108.0,12.0] || product(e_3,u,e_3)*+ -> equalish(u,e_3).
% 37.70/37.91 18115[9:Res:18108.0,13.0] || product(u,e_3,e_3)*+ -> equalish(u,e_3).
% 37.70/37.91 18359[9:Res:1246.2,18115.0] group_element(u) group_element(e_3) || -> product(e_1,e_1,e_3)* product(e_3,u,e_3) product(e_3,u,e_2) product(e_2,e_1,u)* equalish(u,e_3).
% 37.70/37.91 18361[9:SSi:18359.1,3.0] group_element(u) || -> product(e_1,e_1,e_3)* product(e_3,u,e_3) product(e_3,u,e_2) product(e_2,e_1,u)* equalish(u,e_3).
% 37.70/37.91 18362[9:MRR:18361.1,18361.2,18361.4,17312.0,18114.0,16896.0] group_element(u) || -> product(e_3,u,e_2)* equalish(u,e_3).
% 37.70/37.91 18699[9:Res:18362.1,17456.0] group_element(e_1) || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 37.70/37.91 18702[9:SSi:18699.0,1.0] || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 37.70/37.91 18703[9:MRR:18702.0,18702.1,5.0,8.0] || -> .
% 37.70/37.91 18747[9:Spt:18703.0,16914.0,18108.0] || product(e_3,e_3,e_3)*+ -> .
% 37.70/37.91 18748[9:Spt:18703.0,16914.1] || -> product(e_3,e_3,e_2)*.
% 37.70/37.91 18749[9:MRR:17289.0,18747.0] || -> product(e_2,e_2,e_3)*.
% 37.70/37.91 18834[9:Res:18749.0,16897.0] || -> equalish(e_2,e_1)*.
% 37.70/37.91 18837[9:MRR:18834.0,6.0] || -> .
% 37.70/37.91 18856[6:Spt:18837.0,16890.0,16891.0] || product(e_2,e_1,e_3)*+ -> .
% 37.70/37.91 18857[6:Spt:18837.0,16890.1] || -> product(e_2,e_1,e_2)*.
% 37.70/37.91 18953[6:Res:18857.0,13.0] || product(u,e_1,e_2)*+ -> equalish(u,e_2).
% 37.70/37.91 18977[6:Res:18857.0,1251.1] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 37.70/37.91 19025[6:SSi:18977.0,2.0] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 37.70/37.91 19026[6:MRR:19025.2,4.0] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)*.
% 37.70/37.91 19055[7:Spt:13308.0] || -> product(e_1,e_1,e_3)*.
% 37.70/37.91 19059[7:Res:19055.0,14.0] || product(e_1,e_1,u)*+ -> product(u,e_3,e_1)*.
% 37.70/37.91 19139[8:Spt:19026.0] || -> product(e_2,e_2,e_3)*.
% 37.70/37.91 19143[8:Res:19139.0,14.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 37.70/37.91 20073[7:Res:19055.0,19059.0] || -> product(e_3,e_3,e_1)*.
% 37.70/37.91 20092[7:Res:20073.0,11.0] || product(e_3,e_3,u)*+ -> equalish(u,e_1).
% 37.70/37.91 20364[8:Res:19139.0,19143.0] || -> product(e_3,e_3,e_2)*.
% 37.70/37.91 20418[8:Res:20364.0,20092.0] || -> equalish(e_2,e_1)*.
% 37.70/37.91 20419[8:MRR:20418.0,6.0] || -> .
% 37.70/37.91 20444[8:Spt:20419.0,19026.0,19139.0] || product(e_2,e_2,e_3)* -> .
% 37.70/37.91 20445[8:Spt:20419.0,19026.1] || -> product(e_1,e_1,e_2)*.
% 37.70/37.91 20521[8:Res:20445.0,18953.0] || -> equalish(e_1,e_2)*.
% 37.70/37.91 20527[8:MRR:20521.0,4.0] || -> .
% 37.70/37.91 20579[7:Spt:20527.0,13308.0,19055.0] || product(e_1,e_1,e_3)* -> .
% 37.70/37.91 20580[7:Spt:20527.0,13308.1] || -> product(e_1,e_1,e_2)*.
% 37.70/37.91 20725[7:Res:20580.0,18953.0] || -> equalish(e_1,e_2)*.
% 37.70/37.91 20730[7:MRR:20725.0,4.0] || -> .
% 37.70/37.91 % SZS output end Refutation
% 37.70/37.91 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
% 37.70/37.91
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