TSTP Solution File: GRP128-4.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP128-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 6.66s 6.86s
% Output : Refutation 7.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP128-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 12:02:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 6.66/6.86
% 6.66/6.86 SPASS V 3.9
% 6.66/6.86 SPASS beiseite: Proof found.
% 6.66/6.86 % SZS status Theorem
% 6.66/6.86 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.66/6.86 SPASS derived 5841 clauses, backtracked 4012 clauses, performed 39 splits and kept 7124 clauses.
% 6.66/6.86 SPASS allocated 83446 KBytes.
% 6.66/6.86 SPASS spent 0:00:06.51 on the problem.
% 6.66/6.86 0:00:00.04 for the input.
% 6.66/6.86 0:00:00.00 for the FLOTTER CNF translation.
% 6.66/6.86 0:00:00.07 for inferences.
% 6.66/6.86 0:00:00.03 for the backtracking.
% 6.66/6.86 0:00:06.33 for the reduction.
% 6.66/6.86
% 6.66/6.86
% 6.66/6.86 Here is a proof with depth 15, length 318 :
% 6.66/6.86 % SZS output start Refutation
% 6.66/6.86 1[0:Inp] group_element(u) group_element(v) || -> product(e_3,v,u) product(e_2,v,u) product(e_1,v,u)*.
% 6.66/6.86 2[0:Inp] group_element(u) group_element(v) || -> product(v,e_3,u) product(v,e_2,u) product(v,e_1,u)*.
% 6.66/6.86 3[0:Inp] || -> group_element(e_1)*.
% 6.66/6.86 4[0:Inp] || -> group_element(e_2)*.
% 6.66/6.86 5[0:Inp] || -> group_element(e_3)*.
% 6.66/6.86 6[0:Inp] || equalish(e_1,e_2)*+ -> .
% 6.66/6.86 7[0:Inp] || equalish(e_1,e_3)*+ -> .
% 6.66/6.86 8[0:Inp] || equalish(e_2,e_1)*+ -> .
% 6.66/6.86 9[0:Inp] || equalish(e_2,e_3)*+ -> .
% 6.66/6.86 10[0:Inp] || equalish(e_3,e_1)*+ -> .
% 6.66/6.86 11[0:Inp] || equalish(e_3,e_2)*+ -> .
% 6.66/6.86 12[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 6.66/6.86 13[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 6.66/6.86 14[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 6.66/6.86 15[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 6.66/6.86 16[0:Inp] || product(u,v,w)*+ product(x,u,w)* -> product(x,v,u)*.
% 6.66/6.86 17[0:Inp] || product(u,v,w)*+ product(u,w,x)* -> product(w,v,x)*.
% 6.66/6.86 18[0:Inp] || product(u,v,w)*+ product(x,v,u)* -> product(x,u,w)*.
% 6.66/6.86 24[0:Res:1.4,18.0] group_element(u) group_element(v) || product(w,v,e_1)*+ -> product(e_3,v,u) product(e_2,v,u)* product(w,e_1,u)*.
% 6.66/6.86 26[0:Res:1.4,14.0] group_element(u) group_element(v) || product(e_1,w,u)*+ -> product(e_3,v,u) product(e_2,v,u)* equalish(w,v)*.
% 6.66/6.86 27[0:Res:1.4,15.0] group_element(u) group_element(v) || product(w,v,u)*+ -> product(e_3,v,u) product(e_2,v,u)* equalish(w,e_1).
% 6.66/6.86 28[0:Res:2.4,16.0] group_element(u) group_element(v) || product(w,v,u)*+ -> product(v,e_3,u) product(v,e_2,u)* product(w,e_1,v)*.
% 6.66/6.86 32[0:Res:2.4,14.0] group_element(u) group_element(v) || product(v,w,u)*+ -> product(v,e_3,u) product(v,e_2,u)* equalish(w,e_1).
% 6.66/6.86 35[0:Res:12.4,17.0] group_element(u) group_element(v) || product(v,e_1,w)*+ -> product(v,u,e_3) product(v,u,e_2)* product(e_1,u,w)*.
% 6.66/6.86 37[0:Res:12.4,13.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,e_1).
% 6.66/6.86 38[0:Res:12.4,14.0] group_element(u) group_element(v) || product(v,w,e_1)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,u)*.
% 6.66/6.86 39[0:Res:12.4,15.0] group_element(u) group_element(v) || product(w,u,e_1)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,v)*.
% 6.66/6.86 40[0:Res:1.4,27.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(e_3,v,u) product(e_2,v,u)* product(e_3,v,u) product(e_2,v,u)* equalish(e_1,e_1).
% 6.66/6.86 47[0:Obv:40.5] group_element(u) group_element(v) || -> product(e_3,v,u) product(e_2,v,u)* equalish(e_1,e_1).
% 6.66/6.86 50[0:Res:12.4,26.2] group_element(u) group_element(e_1) group_element(e_1) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_3,v,e_1) product(e_2,v,e_1)* equalish(u,v)*.
% 6.66/6.86 51[0:Obv:50.1] group_element(u) group_element(e_1) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_3,v,e_1) product(e_2,v,e_1)* equalish(u,v)*.
% 6.66/6.86 52[0:SSi:51.1,3.0] group_element(u) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_3,v,e_1) product(e_2,v,e_1)* equalish(u,v)*.
% 6.66/6.86 56[1:Spt:47.0,47.1,47.2,47.3] group_element(u) group_element(v) || -> product(e_3,v,u) product(e_2,v,u)*.
% 6.66/6.86 57[1:Res:56.3,16.0] group_element(u) group_element(v) || product(w,e_2,u)*+ -> product(e_3,v,u)* product(w,v,e_2)*.
% 6.66/6.86 60[1:Res:56.3,13.0] group_element(u) group_element(v) || product(e_2,v,w)*+ -> product(e_3,v,u)* equalish(w,u)*.
% 6.66/6.86 62[1:Res:56.3,15.0] group_element(u) group_element(v) || product(w,v,u)*+ -> product(e_3,v,u)* equalish(w,e_2).
% 6.66/6.86 77[1:Res:56.3,62.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(e_3,v,u)* product(e_3,v,u)* equalish(e_2,e_2).
% 6.66/6.86 80[1:Obv:77.4] group_element(u) group_element(v) || -> product(e_3,v,u)* equalish(e_2,e_2).
% 6.66/6.86 93[2:Spt:80.0,80.1,80.2] group_element(u) group_element(v) || -> product(e_3,v,u)*.
% 6.66/6.86 97[2:Res:93.2,13.0] group_element(u) group_element(v) || product(e_3,v,w)*+ -> equalish(w,u)*.
% 6.66/6.86 103[2:Res:93.2,97.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> equalish(u,w)*.
% 6.66/6.86 106[2:Obv:103.1] group_element(u) group_element(v) group_element(w) || -> equalish(u,v)*.
% 6.66/6.86 107[2:Con:106.2] group_element(u) group_element(v) || -> equalish(u,v)*.
% 6.66/6.86 114[2:Res:107.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 6.66/6.86 120[2:SSi:114.1,114.0,4.0,3.0] || -> .
% 6.66/6.86 121[2:Spt:120.0,80.3] || -> equalish(e_2,e_2)*.
% 6.66/6.86 131[0:Res:2.4,32.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(v,e_3,u) product(v,e_2,u)* product(v,e_3,u) product(v,e_2,u)* equalish(e_1,e_1).
% 6.66/6.86 137[0:Obv:131.5] group_element(u) group_element(v) || -> product(v,e_3,u) product(v,e_2,u)* equalish(e_1,e_1).
% 6.66/6.86 138[3:Spt:137.0,137.1,137.2,137.3] group_element(u) group_element(v) || -> product(v,e_3,u) product(v,e_2,u)*.
% 6.66/6.86 143[3:Res:138.3,14.0] group_element(u) group_element(v) || product(v,w,u)*+ -> product(v,e_3,u)* equalish(w,e_2).
% 6.66/6.86 144[3:Res:138.3,15.0] group_element(u) group_element(v) || product(w,e_2,u)*+ -> product(v,e_3,u)* equalish(w,v)*.
% 6.66/6.86 299[3:Res:56.3,143.2] group_element(u) group_element(v) group_element(u) group_element(e_2) || -> product(e_3,v,u)* product(e_2,e_3,u)* equalish(v,e_2).
% 6.66/6.86 310[3:Obv:299.0] group_element(u) group_element(v) group_element(e_2) || -> product(e_3,u,v)* product(e_2,e_3,v)* equalish(u,e_2).
% 6.66/6.86 311[3:SSi:310.2,4.0] group_element(u) group_element(v) || -> product(e_3,u,v)* product(e_2,e_3,v)* equalish(u,e_2).
% 6.66/6.86 355[3:Res:56.3,144.2] group_element(u) group_element(e_2) group_element(u) group_element(v) || -> product(e_3,e_2,u)* product(v,e_3,u)* equalish(e_2,v).
% 6.66/6.86 362[3:Obv:355.0] group_element(e_2) group_element(u) group_element(v) || -> product(e_3,e_2,u)* product(v,e_3,u)* equalish(e_2,v).
% 6.66/6.86 363[3:SSi:362.0,4.0] group_element(u) group_element(v) || -> product(e_3,e_2,u)* product(v,e_3,u)* equalish(e_2,v).
% 6.66/6.86 370[0:Res:12.4,37.2] 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).
% 6.66/6.86 398[0:Obv:370.5] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* equalish(e_1,e_1).
% 6.66/6.86 439[4:Spt:398.0,398.1,398.2,398.3] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)*.
% 6.66/6.86 443[4:Res:439.3,13.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3)* equalish(w,e_2).
% 6.66/6.86 445[4:Res:439.3,15.0] group_element(u) group_element(v) || product(w,u,e_2)*+ -> product(v,u,e_3)* equalish(w,v)*.
% 6.66/6.86 706[0:Res:52.5,15.0] group_element(u) group_element(v) || product(w,v,e_1)*+ -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_3,v,e_1)* equalish(u,v)* equalish(w,e_2).
% 6.66/6.86 745[4:Res:311.3,443.2] group_element(u) group_element(v) group_element(e_3) group_element(e_2) || -> product(e_3,u,v)* equalish(u,e_2) product(e_2,e_3,e_3)* equalish(v,e_2).
% 6.66/6.86 756[4:SSi:745.3,745.2,4.0,5.0] group_element(u) group_element(v) || -> product(e_3,u,v)* equalish(u,e_2) product(e_2,e_3,e_3)* equalish(v,e_2).
% 6.66/6.86 985[4:Res:56.3,445.2] group_element(e_2) group_element(u) group_element(u) group_element(v) || -> product(e_3,u,e_2)* product(v,u,e_3)* equalish(e_2,v).
% 6.66/6.86 1008[4:Obv:985.1] group_element(e_2) group_element(u) group_element(v) || -> product(e_3,u,e_2)* product(v,u,e_3)* equalish(e_2,v).
% 6.66/6.86 1009[4:SSi:1008.0,4.0] group_element(u) group_element(v) || -> product(e_3,u,e_2)* product(v,u,e_3)* equalish(e_2,v).
% 6.66/6.86 1129[1:Res:56.3,57.2] group_element(u) group_element(e_2) group_element(u) group_element(v) || -> product(e_3,e_2,u)* product(e_3,v,u)* product(e_2,v,e_2)*.
% 6.66/6.86 1151[4:Res:1009.2,57.2] group_element(e_2) group_element(u) group_element(e_2) group_element(v) || -> product(u,e_2,e_3)* equalish(e_2,u) product(e_3,v,e_2)* product(e_3,v,e_2)*.
% 6.66/6.86 1155[1:Obv:1129.0] group_element(e_2) group_element(u) group_element(v) || -> product(e_3,e_2,u)* product(e_3,v,u)* product(e_2,v,e_2)*.
% 6.66/6.86 1156[1:SSi:1155.0,4.0] group_element(u) group_element(v) || -> product(e_3,e_2,u)* product(e_3,v,u)* product(e_2,v,e_2)*.
% 6.66/6.86 1157[4:Obv:1151.6] group_element(u) group_element(e_2) group_element(v) || -> product(u,e_2,e_3)* equalish(e_2,u) product(e_3,v,e_2)*.
% 6.66/6.86 1158[4:SSi:1157.1,4.0] group_element(u) group_element(v) || -> product(u,e_2,e_3)* equalish(e_2,u) product(e_3,v,e_2)*.
% 6.66/6.86 1181[5:Spt:1158.1,1158.4] group_element(u) || -> product(e_3,u,e_2)*.
% 6.66/6.86 1185[5:Res:1181.1,13.0] group_element(u) || product(e_3,u,v)* -> equalish(v,e_2).
% 6.66/6.86 1197[5:MRR:756.2,1185.1] group_element(u) group_element(v) || -> equalish(u,e_2)* product(e_2,e_3,e_3)* equalish(v,e_2)*.
% 6.66/6.86 1222[5:Con:1197.1] group_element(u) || -> equalish(u,e_2)* product(e_2,e_3,e_3)*.
% 6.66/6.86 1225[6:Spt:1222.0,1222.1] group_element(u) || -> equalish(u,e_2)*.
% 6.66/6.86 1227[6:Res:1225.1,6.0] group_element(e_1) || -> .
% 6.66/6.86 1229[6:SSi:1227.0,3.0] || -> .
% 6.66/6.86 1230[6:Spt:1229.0,1222.2] || -> product(e_2,e_3,e_3)*.
% 6.66/6.86 1231[6:Res:1230.0,16.0] || product(u,e_2,e_3)*+ -> product(u,e_3,e_2).
% 6.66/6.86 1234[6:Res:1230.0,13.0] || product(e_2,e_3,u)*+ -> equalish(u,e_3).
% 6.66/6.86 1327[6:Res:56.3,1231.0] group_element(e_3) group_element(e_2) || -> product(e_3,e_2,e_3) product(e_2,e_3,e_2)*.
% 6.66/6.86 1334[6:SSi:1327.1,1327.0,4.0,5.0] || -> product(e_3,e_2,e_3) product(e_2,e_3,e_2)*.
% 6.66/6.86 1335[7:Spt:1334.0] || -> product(e_3,e_2,e_3)*.
% 6.66/6.86 1339[7:Res:1335.0,13.0] || product(e_3,e_2,u)*+ -> equalish(u,e_3).
% 6.66/6.86 1376[7:Res:1181.1,1339.0] group_element(e_2) || -> equalish(e_2,e_3)*.
% 6.66/6.86 1378[7:SSi:1376.0,4.0] || -> equalish(e_2,e_3)*.
% 6.66/6.86 1379[7:MRR:1378.0,9.0] || -> .
% 6.66/6.86 1380[7:Spt:1379.0,1334.0,1335.0] || product(e_3,e_2,e_3)* -> .
% 6.66/6.86 1381[7:Spt:1379.0,1334.1] || -> product(e_2,e_3,e_2)*.
% 6.66/6.86 1403[7:Res:1381.0,1234.0] || -> equalish(e_2,e_3)*.
% 6.66/6.86 1408[7:MRR:1403.0,9.0] || -> .
% 6.66/6.86 1420[5:Spt:1408.0,1158.0,1158.2,1158.3] group_element(u) || -> product(u,e_2,e_3)* equalish(e_2,u).
% 6.66/6.86 1426[5:Res:1420.1,17.0] group_element(u) || product(u,e_3,v)* -> equalish(e_2,u) product(e_3,e_2,v)*.
% 6.66/6.86 1441[5:MRR:363.3,1426.1] group_element(u) group_element(v) || -> product(e_3,e_2,u)* equalish(e_2,v)*.
% 6.66/6.86 1477[6:Spt:1441.1,1441.3] group_element(u) || -> equalish(e_2,u)*.
% 6.66/6.86 1479[6:Res:1477.1,8.0] group_element(e_1) || -> .
% 6.66/6.86 1481[6:SSi:1479.0,3.0] || -> .
% 6.66/6.86 1482[6:Spt:1481.0,1441.0,1441.2] group_element(u) || -> product(e_3,e_2,u)*.
% 6.66/6.86 1487[6:Res:1482.1,14.0] group_element(u) || product(e_3,v,u)* -> equalish(v,e_2).
% 6.66/6.86 1504[6:MRR:756.2,1487.1] group_element(u) group_element(v) || -> equalish(u,e_2)* product(e_2,e_3,e_3)* equalish(v,e_2)*.
% 6.66/6.86 1527[6:Con:1504.1] group_element(u) || -> equalish(u,e_2)* product(e_2,e_3,e_3)*.
% 6.66/6.86 1532[7:Spt:1527.0,1527.1] group_element(u) || -> equalish(u,e_2)*.
% 6.66/6.86 1534[7:Res:1532.1,6.0] group_element(e_1) || -> .
% 6.66/6.86 1536[7:SSi:1534.0,3.0] || -> .
% 6.66/6.86 1537[7:Spt:1536.0,1527.2] || -> product(e_2,e_3,e_3)*.
% 6.66/6.86 1538[7:Res:1537.0,16.0] || product(u,e_2,e_3)*+ -> product(u,e_3,e_2).
% 6.66/6.86 1586[7:Res:1482.1,1538.0] group_element(e_3) || -> product(e_3,e_3,e_2)*.
% 6.66/6.86 1587[7:SSi:1586.0,5.0] || -> product(e_3,e_3,e_2)*.
% 6.66/6.86 1592[7:Res:1587.0,14.0] || product(e_3,u,e_2)*+ -> equalish(u,e_3).
% 6.66/6.86 1605[0:Res:52.5,706.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_3,v,e_1)* equalish(u,v)* product(e_1,w,e_3) product(e_1,w,e_2)* product(e_3,v,e_1)* equalish(w,v)* equalish(e_2,e_2).
% 6.66/6.86 1611[0:Obv:1605.6] group_element(u) group_element(v) group_element(w) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,w)* product(e_1,v,e_3) product(e_1,v,e_2)* product(e_3,w,e_1)* equalish(v,w)* equalish(e_2,e_2).
% 6.66/6.86 1612[0:Con:1611.1] group_element(u) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,v)* product(e_3,v,e_1)* equalish(e_2,e_2).
% 6.66/6.86 1623[7:Res:1482.1,1592.0] group_element(e_2) || -> equalish(e_2,e_3)*.
% 6.66/6.86 1625[7:SSi:1623.0,4.0] || -> equalish(e_2,e_3)*.
% 6.66/6.86 1626[7:MRR:1625.0,9.0] || -> .
% 6.66/6.86 1627[4:Spt:1626.0,398.4] || -> equalish(e_1,e_1)*.
% 6.66/6.86 1909[1:Fac:1156.2,1156.3] group_element(u) group_element(e_2) || -> product(e_3,e_2,u)* product(e_2,e_2,e_2)*.
% 6.66/6.86 1951[1:SSi:1909.1,4.0] group_element(u) || -> product(e_3,e_2,u)* product(e_2,e_2,e_2)*.
% 6.66/6.86 1977[5:Spt:1951.0,1951.1] group_element(u) || -> product(e_3,e_2,u)*.
% 6.66/6.86 1981[5:Res:1977.1,13.0] group_element(u) || product(e_3,e_2,v)*+ -> equalish(v,u)*.
% 6.66/6.86 2019[5:Res:1977.1,1981.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 6.66/6.86 2026[5:Res:2019.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 6.66/6.86 2032[5:SSi:2026.1,2026.0,4.0,3.0] || -> .
% 6.66/6.86 2033[5:Spt:2032.0,1951.2] || -> product(e_2,e_2,e_2)*.
% 6.66/6.86 2038[5:Res:2033.0,14.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 6.66/6.86 2069[5:Res:56.3,2038.0] group_element(e_2) group_element(u) || -> product(e_3,u,e_2)* equalish(u,e_2).
% 6.66/6.86 2073[5:SSi:2069.0,4.0] group_element(u) || -> product(e_3,u,e_2)* equalish(u,e_2).
% 6.66/6.86 2221[5:Res:2073.1,143.2] group_element(u) group_element(e_2) group_element(e_3) || -> equalish(u,e_2)* product(e_3,e_3,e_2)* equalish(u,e_2)*.
% 6.66/6.86 2226[5:Obv:2221.3] group_element(u) group_element(e_2) group_element(e_3) || -> product(e_3,e_3,e_2)* equalish(u,e_2)*.
% 6.66/6.86 2227[5:SSi:2226.2,2226.1,5.0,4.0] group_element(u) || -> product(e_3,e_3,e_2)* equalish(u,e_2)*.
% 6.66/6.86 2230[6:Spt:2227.0,2227.2] group_element(u) || -> equalish(u,e_2)*.
% 6.66/6.86 2232[6:Res:2230.1,6.0] group_element(e_1) || -> .
% 6.66/6.86 2234[6:SSi:2232.0,3.0] || -> .
% 6.66/6.86 2235[6:Spt:2234.0,2227.1] || -> product(e_3,e_3,e_2)*.
% 6.66/6.86 2236[6:Res:2235.0,16.0] || product(u,e_3,e_2)*+ -> product(u,e_3,e_3).
% 6.66/6.86 2239[6:Res:2235.0,13.0] || product(e_3,e_3,u)*+ -> equalish(u,e_2).
% 6.66/6.86 2289[6:Res:2235.0,2236.0] || -> product(e_3,e_3,e_3)*.
% 6.66/6.86 2327[6:Res:2289.0,2239.0] || -> equalish(e_3,e_2)*.
% 6.66/6.86 2330[6:MRR:2327.0,11.0] || -> .
% 6.66/6.86 2335[3:Spt:2330.0,137.4] || -> equalish(e_1,e_1)*.
% 6.66/6.86 2348[4:Spt:1951.0,1951.1] group_element(u) || -> product(e_3,e_2,u)*.
% 6.66/6.86 2352[4:Res:2348.1,13.0] group_element(u) || product(e_3,e_2,v)*+ -> equalish(v,u)*.
% 6.66/6.86 2367[4:Res:2348.1,2352.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 6.66/6.86 2374[4:Res:2367.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 6.66/6.86 2380[4:SSi:2374.1,2374.0,4.0,3.0] || -> .
% 6.66/6.86 2381[4:Spt:2380.0,1951.2] || -> product(e_2,e_2,e_2)*.
% 6.66/6.86 2385[4:Res:2381.0,13.0] || product(e_2,e_2,u)*+ -> equalish(u,e_2).
% 6.66/6.86 2387[4:Res:2381.0,15.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 6.66/6.86 2389[4:Res:2381.0,60.2] group_element(u) group_element(e_2) || -> product(e_3,e_2,u)* equalish(e_2,u).
% 6.66/6.86 2395[4:SSi:2389.1,4.0] group_element(u) || -> product(e_3,e_2,u)* equalish(e_2,u).
% 6.66/6.86 2409[0:Res:2.4,38.2] group_element(e_1) group_element(u) group_element(v) group_element(u) || -> product(u,e_3,e_1) product(u,e_2,e_1)* product(u,v,e_3) product(u,v,e_2)* equalish(e_1,v).
% 6.66/6.86 2420[0:Obv:2409.1] group_element(e_1) group_element(u) group_element(v) || -> product(v,e_3,e_1) product(v,e_2,e_1)* product(v,u,e_3) product(v,u,e_2)* equalish(e_1,u).
% 6.66/6.86 2421[0:SSi:2420.0,3.0] group_element(u) group_element(v) || -> product(v,e_3,e_1) product(v,e_2,e_1)* product(v,u,e_3) product(v,u,e_2)* equalish(e_1,u).
% 6.66/6.86 2427[4:Res:56.3,2385.0] group_element(u) group_element(e_2) || -> product(e_3,e_2,u)* equalish(u,e_2).
% 6.66/6.86 2430[4:SSi:2427.1,4.0] group_element(u) || -> product(e_3,e_2,u)* equalish(u,e_2).
% 6.66/6.86 2451[4:Res:2395.1,39.2] group_element(e_1) group_element(e_2) group_element(u) || -> equalish(e_2,e_1) product(u,e_2,e_3) product(u,e_2,e_2)* equalish(e_3,u).
% 6.66/6.86 2456[4:SSi:2451.1,2451.0,4.0,3.0] group_element(u) || -> equalish(e_2,e_1) product(u,e_2,e_3) product(u,e_2,e_2)* equalish(e_3,u).
% 6.66/6.86 2457[4:MRR:2456.1,8.0] group_element(u) || -> product(u,e_2,e_3) product(u,e_2,e_2)* equalish(e_3,u).
% 6.66/6.86 2490[4:Res:2430.1,13.0] group_element(u) || product(e_3,e_2,v)* -> equalish(u,e_2)* equalish(v,u)*.
% 6.66/6.86 2538[4:Res:2457.2,2387.0] group_element(u) || -> product(u,e_2,e_3)* equalish(e_3,u) equalish(u,e_2).
% 6.66/6.86 2569[4:Res:2538.1,62.2] group_element(u) group_element(e_3) group_element(e_2) || -> equalish(e_3,u)* equalish(u,e_2)* product(e_3,e_2,e_3)* equalish(u,e_2)*.
% 6.66/6.86 2579[4:Obv:2569.4] group_element(u) group_element(e_3) group_element(e_2) || -> equalish(e_3,u)* product(e_3,e_2,e_3)* equalish(u,e_2)*.
% 6.66/6.86 2580[4:SSi:2579.2,2579.1,4.0,5.0] group_element(u) || -> equalish(e_3,u)* product(e_3,e_2,e_3)* equalish(u,e_2)*.
% 6.66/6.86 2581[4:MRR:2580.2,2490.1] group_element(u) || -> equalish(e_3,u)* equalish(u,e_2)*.
% 6.66/6.86 2585[4:Res:2581.2,6.0] group_element(e_1) || -> equalish(e_3,e_1)*.
% 6.66/6.86 2587[4:SSi:2585.0,3.0] || -> equalish(e_3,e_1)*.
% 6.66/6.86 2588[4:MRR:2587.0,10.0] || -> .
% 6.66/6.86 2589[1:Spt:2588.0,47.4] || -> equalish(e_1,e_1)*.
% 6.66/6.86 2659[0:Res:2.4,24.2] group_element(e_1) group_element(u) group_element(v) group_element(e_1) || -> product(u,e_3,e_1) product(u,e_2,e_1) product(e_3,e_1,v) product(e_2,e_1,v)* product(u,e_1,v)*.
% 6.66/6.86 2662[0:Obv:2659.0] group_element(u) group_element(v) group_element(e_1) || -> product(u,e_3,e_1) product(u,e_2,e_1) product(e_3,e_1,v) product(e_2,e_1,v)* product(u,e_1,v)*.
% 6.66/6.86 2663[0:SSi:2662.2,3.0] group_element(u) group_element(v) || -> product(u,e_3,e_1) product(u,e_2,e_1) product(e_3,e_1,v) product(e_2,e_1,v)* product(u,e_1,v)*.
% 6.66/6.86 2698[2:Spt:1612.0,1612.1,1612.2,1612.3,1612.4,1612.5] group_element(u) group_element(v) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,v)* product(e_3,v,e_1)*.
% 6.66/6.86 2707[2:Res:2698.3,35.2] group_element(e_1) group_element(u) group_element(v) group_element(e_1) || -> product(e_1,e_1,e_3)* equalish(e_1,u) product(e_3,u,e_1)* product(e_1,v,e_3) product(e_1,v,e_2)* product(e_1,v,e_2)*.
% 6.66/6.86 2764[2:Obv:2707.8] group_element(u) group_element(v) group_element(e_1) || -> product(e_1,e_1,e_3)* equalish(e_1,u) product(e_3,u,e_1)* product(e_1,v,e_3) product(e_1,v,e_2)*.
% 6.66/6.86 2765[2:SSi:2764.2,3.0] group_element(u) group_element(v) || -> product(e_1,e_1,e_3)* equalish(e_1,u) product(e_3,u,e_1)* product(e_1,v,e_3) product(e_1,v,e_2)*.
% 6.66/6.86 2979[3:Spt:2765.0,2765.3,2765.4] group_element(u) || -> equalish(e_1,u) product(e_3,u,e_1)*.
% 6.66/6.86 2980[3:Res:2979.2,16.0] group_element(u) || product(v,e_3,e_1)* -> equalish(e_1,u) product(v,u,e_3)*.
% 6.66/6.86 2983[3:Res:2979.2,13.0] group_element(u) || product(e_3,u,v)*+ -> equalish(e_1,u) equalish(v,e_1).
% 6.66/6.86 3001[3:MRR:2421.2,2980.1] group_element(u) group_element(v) || -> product(v,e_2,e_1)* product(v,u,e_3) product(v,u,e_2)* equalish(e_1,u).
% 6.66/6.86 3069[3:Res:3001.4,2983.1] group_element(u) group_element(e_3) group_element(u) || -> product(e_3,e_2,e_1)* product(e_3,u,e_3)* equalish(e_1,u) equalish(e_1,u) equalish(e_2,e_1).
% 6.66/6.86 3071[3:Obv:3069.5] group_element(e_3) group_element(u) || -> product(e_3,e_2,e_1)* product(e_3,u,e_3)* equalish(e_1,u) equalish(e_2,e_1).
% 6.66/6.86 3072[3:SSi:3071.0,5.0] group_element(u) || -> product(e_3,e_2,e_1)* product(e_3,u,e_3)* equalish(e_1,u) equalish(e_2,e_1).
% 6.66/6.86 3073[3:MRR:3072.4,8.0] group_element(u) || -> product(e_3,e_2,e_1)* product(e_3,u,e_3)* equalish(e_1,u).
% 6.66/6.86 3107[4:Spt:3073.0,3073.2,3073.3] group_element(u) || -> product(e_3,u,e_3)* equalish(e_1,u).
% 6.66/6.86 3124[4:Res:3107.1,2983.1] group_element(u) group_element(u) || -> equalish(e_1,u)* equalish(e_1,u)* equalish(e_3,e_1).
% 6.66/6.86 3126[4:Obv:3124.2] group_element(u) || -> equalish(e_1,u)* equalish(e_3,e_1).
% 6.66/6.86 3127[4:MRR:3126.2,10.0] group_element(u) || -> equalish(e_1,u)*.
% 6.66/6.86 3136[4:Res:3127.1,6.0] group_element(e_2) || -> .
% 6.66/6.86 3138[4:SSi:3136.0,4.0] || -> .
% 6.66/6.86 3139[4:Spt:3138.0,3073.1] || -> product(e_3,e_2,e_1)*.
% 6.66/6.86 3140[4:Res:3139.0,16.0] || product(u,e_3,e_1)+ -> product(u,e_2,e_3)*.
% 6.66/6.86 3143[4:Res:3139.0,13.0] || product(e_3,e_2,u)*+ -> equalish(u,e_1).
% 6.66/6.86 3336[4:Res:2979.2,3140.0] group_element(e_3) || -> equalish(e_1,e_3) product(e_3,e_2,e_3)*.
% 6.66/6.86 3354[4:SSi:3336.0,5.0] || -> equalish(e_1,e_3) product(e_3,e_2,e_3)*.
% 6.66/6.86 3355[4:MRR:3354.0,7.0] || -> product(e_3,e_2,e_3)*.
% 6.66/6.86 3377[4:Res:3355.0,3143.0] || -> equalish(e_3,e_1)*.
% 6.66/6.86 3381[4:MRR:3377.0,10.0] || -> .
% 6.66/6.86 3397[3:Spt:3381.0,2765.1,2765.2,2765.5,2765.6] group_element(u) || -> product(e_1,e_1,e_3)* product(e_1,u,e_3) product(e_1,u,e_2)*.
% 6.66/6.86 3399[4:Spt:3397.0,3397.2,3397.3] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)*.
% 6.66/6.86 3400[4:Res:3399.2,16.0] group_element(u) || product(v,e_1,e_2)*+ -> product(e_1,u,e_3)* product(v,u,e_1)*.
% 6.66/6.86 3403[4:Res:3399.2,13.0] group_element(u) || product(e_1,u,v)*+ -> product(e_1,u,e_3)* equalish(v,e_2).
% 6.66/6.86 3509[4:Res:3399.2,3403.1] group_element(u) group_element(u) || -> product(e_1,u,e_3)* product(e_1,u,e_3)* equalish(e_2,e_2).
% 6.66/6.86 3511[4:Obv:3509.2] group_element(u) || -> product(e_1,u,e_3)* equalish(e_2,e_2).
% 6.66/6.86 3526[5:Spt:3511.0,3511.1] group_element(u) || -> product(e_1,u,e_3)*.
% 6.66/6.86 3531[5:Res:3526.1,14.0] group_element(u) || product(e_1,v,e_3)*+ -> equalish(v,u)*.
% 6.66/6.86 3693[5:Res:3526.1,3531.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 6.66/6.86 3701[5:Res:3693.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 6.66/6.86 3707[5:SSi:3701.1,3701.0,4.0,3.0] || -> .
% 6.66/6.86 3708[5:Spt:3707.0,3511.2] || -> equalish(e_2,e_2)*.
% 6.66/6.86 3827[4:Res:3399.2,3400.1] group_element(e_1) group_element(u) || -> product(e_1,e_1,e_3)* product(e_1,u,e_3) product(e_1,u,e_1)*.
% 6.66/6.86 3828[4:SSi:3827.0,3.0] group_element(u) || -> product(e_1,e_1,e_3)* product(e_1,u,e_3) product(e_1,u,e_1)*.
% 6.66/6.86 3885[6:Spt:3828.0,3828.2,3828.3] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_1)*.
% 6.66/6.86 3909[6:Res:3885.2,3403.1] group_element(u) group_element(u) || -> product(e_1,u,e_3)* product(e_1,u,e_3)* equalish(e_1,e_2).
% 6.66/6.86 3911[6:Obv:3909.2] group_element(u) || -> product(e_1,u,e_3)* equalish(e_1,e_2).
% 6.66/6.86 3912[6:MRR:3911.2,6.0] group_element(u) || -> product(e_1,u,e_3)*.
% 6.66/6.86 3933[6:Res:3912.1,14.0] group_element(u) || product(e_1,v,e_3)*+ -> equalish(v,u)*.
% 6.66/6.86 4083[6:Res:3912.1,3933.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 6.66/6.86 4090[6:Res:4083.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 6.66/6.86 4096[6:SSi:4090.1,4090.0,4.0,3.0] || -> .
% 6.66/6.86 4097[6:Spt:4096.0,3828.1] || -> product(e_1,e_1,e_3)*.
% 6.66/6.86 4098[6:Res:4097.0,16.0] || product(u,e_1,e_3)+ -> product(u,e_1,e_1)*.
% 6.66/6.86 4101[6:Res:4097.0,13.0] || product(e_1,e_1,u)*+ -> equalish(u,e_3).
% 6.66/6.86 4212[6:Res:4097.0,4098.0] || -> product(e_1,e_1,e_1)*.
% 6.66/6.86 4288[6:Res:4212.0,4101.0] || -> equalish(e_1,e_3)*.
% 6.66/6.86 4289[6:MRR:4288.0,7.0] || -> .
% 6.66/6.86 4301[4:Spt:4289.0,3397.1] || -> product(e_1,e_1,e_3)*.
% 6.66/6.86 4306[4:Res:4301.0,16.0] || product(u,e_1,e_3)+ -> product(u,e_1,e_1)*.
% 6.66/6.86 4309[4:Res:4301.0,13.0] || product(e_1,e_1,u)*+ -> equalish(u,e_3).
% 6.66/6.86 4419[4:Res:4301.0,4306.0] || -> product(e_1,e_1,e_1)*.
% 6.66/6.86 4445[4:Res:4419.0,4309.0] || -> equalish(e_1,e_3)*.
% 6.66/6.86 4446[4:MRR:4445.0,7.0] || -> .
% 6.66/6.86 4458[2:Spt:4446.0,1612.6] || -> equalish(e_2,e_2)*.
% 6.66/6.86 5503[0:Fac:2663.5,2663.6] group_element(e_2) group_element(u) || -> product(e_2,e_3,e_1) product(e_2,e_2,e_1) product(e_3,e_1,u) product(e_2,e_1,u)*.
% 6.66/6.86 5549[0:SSi:5503.0,4.0] group_element(u) || -> product(e_2,e_3,e_1) product(e_2,e_2,e_1) product(e_3,e_1,u) product(e_2,e_1,u)*.
% 6.66/6.86 5696[3:Spt:5549.0,5549.3,5549.4] group_element(u) || -> product(e_3,e_1,u) product(e_2,e_1,u)*.
% 6.66/6.86 5699[3:Res:5696.2,18.0] group_element(u) || product(v,e_1,e_2)*+ -> product(e_3,e_1,u)* product(v,e_2,u)*.
% 6.66/6.86 5701[3:Res:5696.2,14.0] group_element(u) || product(e_2,v,u)*+ -> product(e_3,e_1,u) equalish(v,e_1).
% 6.66/6.86 5992[3:Res:5696.2,5699.1] group_element(e_2) group_element(u) || -> product(e_3,e_1,e_2) product(e_3,e_1,u) product(e_2,e_2,u)*.
% 6.66/6.86 5993[3:SSi:5992.0,4.0] group_element(u) || -> product(e_3,e_1,e_2) product(e_3,e_1,u) product(e_2,e_2,u)*.
% 6.66/6.86 5997[4:Spt:5993.0,5993.2,5993.3] group_element(u) || -> product(e_3,e_1,u) product(e_2,e_2,u)*.
% 6.66/6.86 6004[4:Res:5997.2,5701.1] group_element(u) group_element(u) || -> product(e_3,e_1,u)* product(e_3,e_1,u)* equalish(e_2,e_1).
% 6.66/6.86 6020[4:Obv:6004.2] group_element(u) || -> product(e_3,e_1,u)* equalish(e_2,e_1).
% 6.66/6.86 6021[4:MRR:6020.2,8.0] group_element(u) || -> product(e_3,e_1,u)*.
% 6.66/6.86 6033[4:Res:6021.1,13.0] group_element(u) || product(e_3,e_1,v)*+ -> equalish(v,u)*.
% 6.66/6.86 6266[4:Res:6021.1,6033.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 6.66/6.86 6272[4:Res:6266.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 6.66/6.86 6278[4:SSi:6272.1,6272.0,4.0,3.0] || -> .
% 6.66/6.86 6279[4:Spt:6278.0,5993.1] || -> product(e_3,e_1,e_2)*.
% 6.66/6.86 6280[4:Res:6279.0,16.0] || product(u,e_3,e_2)+ -> product(u,e_1,e_3)*.
% 6.66/6.86 6282[4:Res:6279.0,18.0] || product(u,e_1,e_3)*+ -> product(u,e_3,e_2).
% 6.66/6.86 6283[4:Res:6279.0,13.0] || product(e_3,e_1,u)*+ -> equalish(u,e_2).
% 6.66/6.86 6291[4:Res:6279.0,28.2] group_element(e_2) group_element(e_1) || -> product(e_1,e_3,e_2) product(e_1,e_2,e_2)* product(e_3,e_1,e_1).
% 6.66/6.86 6302[4:SSi:6291.1,6291.0,3.0,4.0] || -> product(e_1,e_3,e_2) product(e_1,e_2,e_2)* product(e_3,e_1,e_1).
% 6.66/6.86 6487[4:Res:5696.2,6282.0] group_element(e_3) || -> product(e_3,e_1,e_3) product(e_2,e_3,e_2)*.
% 7.50/7.71 6489[4:SSi:6487.0,5.0] || -> product(e_3,e_1,e_3) product(e_2,e_3,e_2)*.
% 7.50/7.71 6500[4:Res:6489.1,16.0] || product(u,e_2,e_2)* -> product(e_3,e_1,e_3)* product(u,e_3,e_2).
% 7.50/7.71 6505[4:Res:6489.1,15.0] || product(u,e_3,e_2)* -> product(e_3,e_1,e_3)* equalish(u,e_2).
% 7.50/7.71 6506[4:Res:6489.1,6280.0] || -> product(e_3,e_1,e_3) product(e_2,e_1,e_3)*.
% 7.50/7.71 6514[5:Spt:6506.0] || -> product(e_3,e_1,e_3)*.
% 7.50/7.71 6533[5:Res:6514.0,6283.0] || -> equalish(e_3,e_2)*.
% 7.50/7.71 6534[5:MRR:6533.0,11.0] || -> .
% 7.50/7.71 6554[5:Spt:6534.0,6506.0,6514.0] || product(e_3,e_1,e_3)*+ -> .
% 7.50/7.71 6555[5:Spt:6534.0,6506.1] || -> product(e_2,e_1,e_3)*.
% 7.50/7.71 6559[5:MRR:6505.1,6554.0] || product(u,e_3,e_2)*+ -> equalish(u,e_2).
% 7.50/7.71 6560[5:MRR:6500.1,6554.0] || product(u,e_2,e_2)* -> product(u,e_3,e_2).
% 7.50/7.71 6597[5:MRR:6302.1,6560.0] || -> product(e_1,e_3,e_2)* product(e_3,e_1,e_1).
% 7.50/7.71 6694[6:Spt:6597.0] || -> product(e_1,e_3,e_2)*.
% 7.50/7.71 7178[6:Res:6694.0,6559.0] || -> equalish(e_1,e_2)*.
% 7.50/7.71 7179[6:MRR:7178.0,6.0] || -> .
% 7.50/7.71 7180[6:Spt:7179.0,6597.0,6694.0] || product(e_1,e_3,e_2)* -> .
% 7.50/7.71 7181[6:Spt:7179.0,6597.1] || -> product(e_3,e_1,e_1)*.
% 7.50/7.71 7218[6:Res:7181.0,6283.0] || -> equalish(e_1,e_2)*.
% 7.50/7.71 7219[6:MRR:7218.0,6.0] || -> .
% 7.50/7.71 7252[3:Spt:7219.0,5549.1,5549.2] || -> product(e_2,e_3,e_1) product(e_2,e_2,e_1)*.
% 7.50/7.71 7253[4:Spt:7252.0] || -> product(e_2,e_3,e_1)*.
% 7.50/7.71 7254[4:Res:7253.0,16.0] || product(u,e_2,e_1)*+ -> product(u,e_3,e_2).
% 7.50/7.71 7255[4:Res:7253.0,17.0] || product(e_2,e_1,u)+ -> product(e_1,e_3,u)*.
% 7.50/7.71 7258[4:Res:7253.0,14.0] || product(e_2,u,e_1)*+ -> equalish(u,e_3).
% 7.50/7.71 7259[4:Res:7253.0,15.0] || product(u,e_3,e_1)*+ -> equalish(u,e_2).
% 7.50/7.71 7264[4:Res:7253.0,28.2] group_element(e_1) group_element(e_3) || -> product(e_3,e_3,e_1) product(e_3,e_2,e_1) product(e_2,e_1,e_3)*.
% 7.50/7.71 7287[4:SSi:7264.1,7264.0,5.0,3.0] || -> product(e_3,e_3,e_1) product(e_3,e_2,e_1) product(e_2,e_1,e_3)*.
% 7.50/7.71 7353[4:Res:1.4,7254.0] group_element(e_1) group_element(e_2) || -> product(e_3,e_2,e_1) product(e_2,e_2,e_1) product(e_1,e_3,e_2)*.
% 7.50/7.71 7359[4:SSi:7353.1,7353.0,4.0,3.0] || -> product(e_3,e_2,e_1) product(e_2,e_2,e_1) product(e_1,e_3,e_2)*.
% 7.50/7.71 7424[5:Spt:7287.0] || -> product(e_3,e_3,e_1)*.
% 7.50/7.71 7441[5:Res:7424.0,7259.0] || -> equalish(e_3,e_2)*.
% 7.50/7.71 7442[5:MRR:7441.0,11.0] || -> .
% 7.50/7.71 7456[5:Spt:7442.0,7287.0,7424.0] || product(e_3,e_3,e_1)*+ -> .
% 7.50/7.71 7457[5:Spt:7442.0,7287.1,7287.2] || -> product(e_3,e_2,e_1) product(e_2,e_1,e_3)*.
% 7.50/7.71 7458[6:Spt:7457.0] || -> product(e_3,e_2,e_1)*.
% 7.50/7.71 7467[6:Res:7458.0,7254.0] || -> product(e_3,e_3,e_2)*.
% 7.50/7.71 7482[6:Res:7467.0,16.0] || product(u,e_3,e_2)*+ -> product(u,e_3,e_3).
% 7.50/7.71 7485[6:Res:7467.0,13.0] || product(e_3,e_3,u)*+ -> equalish(u,e_2).
% 7.50/7.71 8107[6:Res:7467.0,7482.0] || -> product(e_3,e_3,e_3)*.
% 7.50/7.71 8123[6:Res:8107.0,7485.0] || -> equalish(e_3,e_2)*.
% 7.50/7.71 8125[6:MRR:8123.0,11.0] || -> .
% 7.50/7.71 8134[6:Spt:8125.0,7457.0,7458.0] || product(e_3,e_2,e_1)*+ -> .
% 7.50/7.71 8135[6:Spt:8125.0,7457.1] || -> product(e_2,e_1,e_3)*.
% 7.50/7.71 8137[6:MRR:7359.0,8134.0] || -> product(e_2,e_2,e_1) product(e_1,e_3,e_2)*.
% 7.50/7.71 8163[6:Res:8135.0,7255.0] || -> product(e_1,e_3,e_3)*.
% 7.50/7.71 8179[6:Res:8163.0,13.0] || product(e_1,e_3,u)*+ -> equalish(u,e_3).
% 7.50/7.71 8233[7:Spt:8137.0] || -> product(e_2,e_2,e_1)*.
% 7.50/7.71 8251[7:Res:8233.0,7258.0] || -> equalish(e_2,e_3)*.
% 7.50/7.71 8252[7:MRR:8251.0,9.0] || -> .
% 7.50/7.71 8264[7:Spt:8252.0,8137.0,8233.0] || product(e_2,e_2,e_1)*+ -> .
% 7.50/7.71 8265[7:Spt:8252.0,8137.1] || -> product(e_1,e_3,e_2)*.
% 7.50/7.71 8830[7:Res:8265.0,8179.0] || -> equalish(e_2,e_3)*.
% 7.50/7.71 8831[7:MRR:8830.0,9.0] || -> .
% 7.50/7.71 8834[4:Spt:8831.0,7252.0,7253.0] || product(e_2,e_3,e_1)*+ -> .
% 7.50/7.71 8835[4:Spt:8831.0,7252.1] || -> product(e_2,e_2,e_1)*.
% 7.50/7.71 8837[4:Res:8835.0,16.0] || product(u,e_2,e_1)*+ -> product(u,e_2,e_2).
% 7.50/7.71 8840[4:Res:8835.0,13.0] || product(e_2,e_2,u)*+ -> equalish(u,e_1).
% 7.50/7.71 8954[4:Res:8835.0,8837.0] || -> product(e_2,e_2,e_2)*.
% 7.50/7.71 9019[4:Res:8954.0,8840.0] || -> equalish(e_2,e_1)*.
% 7.50/7.71 9023[4:MRR:9019.0,8.0] || -> .
% 7.50/7.71 % SZS output end Refutation
% 7.50/7.71 Formulae used in the proof : row_surjectivity column_surjectivity 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_1 qg3_2 qg3
% 7.50/7.71
%------------------------------------------------------------------------------