TSTP Solution File: GRP133-2.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP133-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 1.42s 1.64s
% Output : Refutation 1.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP133-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.00/0.08 % Command : run_spass %d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 600
% 0.10/0.27 % DateTime : Mon Jun 13 06:44:56 EDT 2022
% 0.10/0.27 % CPUTime :
% 1.42/1.64
% 1.42/1.64 SPASS V 3.9
% 1.42/1.64 SPASS beiseite: Proof found.
% 1.42/1.64 % SZS status Theorem
% 1.42/1.64 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.42/1.64 SPASS derived 2665 clauses, backtracked 567 clauses, performed 27 splits and kept 1723 clauses.
% 1.42/1.64 SPASS allocated 79281 KBytes.
% 1.42/1.64 SPASS spent 0:00:01.36 on the problem.
% 1.42/1.64 0:00:00.03 for the input.
% 1.42/1.64 0:00:00.00 for the FLOTTER CNF translation.
% 1.42/1.64 0:00:00.05 for inferences.
% 1.42/1.64 0:00:00.01 for the backtracking.
% 1.42/1.64 0:00:01.24 for the reduction.
% 1.42/1.64
% 1.42/1.64
% 1.42/1.64 Here is a proof with depth 17, length 249 :
% 1.42/1.64 % SZS output start Refutation
% 1.42/1.64 1[0:Inp] || -> next(e_1,e_2)*.
% 1.42/1.64 3[0:Inp] || -> greater(e_2,e_1)*.
% 1.42/1.64 5[0:Inp] || -> greater(e_3,e_2)*.
% 1.42/1.64 6[0:Inp] || greater(u,v)* next(w,v)* product(w,e_1,u)*+ -> .
% 1.42/1.64 7[0:Inp] || -> group_element(e_1)*.
% 1.42/1.64 8[0:Inp] || -> group_element(e_2)*.
% 1.42/1.64 9[0:Inp] || -> group_element(e_3)*.
% 1.42/1.64 10[0:Inp] || equalish(e_1,e_2)*+ -> .
% 1.42/1.64 11[0:Inp] || equalish(e_1,e_3)*+ -> .
% 1.42/1.64 12[0:Inp] || equalish(e_2,e_1)*+ -> .
% 1.42/1.64 13[0:Inp] || equalish(e_2,e_3)*+ -> .
% 1.42/1.64 14[0:Inp] || equalish(e_3,e_1)*+ -> .
% 1.42/1.64 15[0:Inp] || equalish(e_3,e_2)*+ -> .
% 1.42/1.64 16[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 1.42/1.64 17[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 1.42/1.64 18[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 1.42/1.64 19[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 1.42/1.64 20[0:Inp] || product(u,v,w)*+ product(v,u,x)* -> product(x,w,v)*.
% 1.42/1.64 25[0:Res:16.4,20.0] 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)*.
% 1.42/1.64 26[0:Res:16.4,17.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,e_1).
% 1.42/1.64 27[0:Res:16.4,18.0] group_element(u) group_element(v) || product(v,w,e_1)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,u)*.
% 1.42/1.64 28[0:Res:16.4,19.0] group_element(u) group_element(v) || product(w,u,e_1)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,v)*.
% 1.42/1.64 30[0:Res:16.4,28.2] 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)*.
% 1.42/1.64 31[0:Obv:30.0] 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)*.
% 1.42/1.64 32[0:Res:16.4,27.2] 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)*.
% 1.42/1.64 33[0:Obv:32.1] 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)*.
% 1.42/1.64 34[0:Res:16.4,26.2] 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).
% 1.42/1.64 35[0:Obv:34.5] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* equalish(e_1,e_1).
% 1.42/1.64 36[0:Res:16.4,25.2] 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)*.
% 1.42/1.64 37[0:Obv:36.1] 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)*.
% 1.42/1.64 38[1:Spt:35.0,35.1,35.2,35.3] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)*.
% 1.42/1.64 40[1:Res:38.3,20.0] group_element(u) group_element(v) || product(u,v,w)*+ -> product(v,u,e_3)* product(w,e_2,u)*.
% 1.42/1.64 41[1:Res:38.3,17.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3)* equalish(w,e_2).
% 1.42/1.64 73[1:Res:38.3,40.2] 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)*.
% 1.42/1.64 74[1:Obv:73.1] group_element(u) group_element(v) || -> product(u,v,e_3)* product(v,u,e_3)* product(e_2,e_2,u)*.
% 1.42/1.64 75[1:Fac:74.2,74.3] group_element(u) group_element(u) || -> product(u,u,e_3)* product(e_2,e_2,u)*.
% 1.42/1.64 98[1:Obv:75.0] group_element(u) || -> product(u,u,e_3)* product(e_2,e_2,u)*.
% 1.42/1.64 113[1:Res:98.1,6.2] group_element(e_1) || greater(e_3,u) next(e_1,u)* -> product(e_2,e_2,e_1)*.
% 1.42/1.64 128[1:SSi:113.0,7.0] || greater(e_3,u)+ next(e_1,u)* -> product(e_2,e_2,e_1)*.
% 1.42/1.64 139[1:Res:5.0,128.0] || next(e_1,e_2) -> product(e_2,e_2,e_1)*.
% 1.42/1.64 141[1:MRR:139.0,1.0] || -> product(e_2,e_2,e_1)*.
% 1.42/1.64 144[1:Res:141.0,17.0] || product(e_2,e_2,u)*+ -> equalish(u,e_1).
% 1.42/1.64 147[1:Res:141.0,41.2] group_element(e_2) group_element(e_2) || -> product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 1.42/1.64 148[1:Obv:147.0] group_element(e_2) || -> product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 1.42/1.64 149[1:SSi:148.0,8.0] || -> product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 1.42/1.64 150[1:MRR:149.1,10.0] || -> product(e_2,e_2,e_3)*.
% 1.42/1.64 188[1:Res:150.0,144.0] || -> equalish(e_3,e_1)*.
% 1.42/1.64 189[1:MRR:188.0,14.0] || -> .
% 1.42/1.64 198[1:Spt:189.0,35.4] || -> equalish(e_1,e_1)*.
% 1.42/1.64 212[0:Fac:37.3,37.5] 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)*.
% 1.42/1.64 214[0:Res:37.3,25.2] 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).
% 1.42/1.64 236[0:Obv:212.2] group_element(u) || -> product(u,u,e_3) product(u,u,e_2)* product(e_1,e_1,u)*.
% 1.42/1.64 250[0:Obv:214.6] 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).
% 1.42/1.64 253[0:Res:236.2,17.0] group_element(u) || product(u,u,v)*+ -> product(u,u,e_3)* product(e_1,e_1,u)* equalish(v,e_2).
% 1.42/1.64 254[0:Res:236.2,18.0] group_element(u) || product(u,v,e_2)*+ -> product(u,u,e_3)* product(e_1,e_1,u)* equalish(v,u).
% 1.42/1.64 255[0:Res:236.2,19.0] group_element(u) || product(v,u,e_2)*+ -> product(u,u,e_3)* product(e_1,e_1,u)* equalish(v,u).
% 1.42/1.64 257[0:Res:236.3,6.2] group_element(u) || greater(u,v)*+ next(e_1,v)* -> product(u,u,e_3) product(u,u,e_2)*.
% 1.42/1.64 279[0:Res:236.2,253.1] 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).
% 1.42/1.64 280[0:Obv:279.3] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)* equalish(e_2,e_2).
% 1.42/1.64 310[2:Spt:280.0,280.1,280.2] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)*.
% 1.42/1.64 313[2:Res:310.1,17.0] group_element(u) || product(u,u,v)*+ -> product(e_1,e_1,u)* equalish(v,e_3).
% 1.42/1.64 321[2:Res:310.2,18.0] group_element(u) || product(e_1,v,u)*+ -> product(u,u,e_3)* equalish(v,e_1).
% 1.42/1.64 336[2:Res:310.2,313.1] group_element(u) group_element(e_1) || -> product(u,u,e_3)* product(e_1,e_1,e_1)* equalish(u,e_3).
% 1.42/1.64 341[2:Res:310.1,313.1] group_element(u) group_element(u) || -> product(e_1,e_1,u)* product(e_1,e_1,u)* equalish(e_3,e_3).
% 1.42/1.64 342[2:SSi:336.1,7.0] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,e_1)* equalish(u,e_3).
% 1.42/1.64 343[2:Obv:341.2] group_element(u) || -> product(e_1,e_1,u)* equalish(e_3,e_3).
% 1.42/1.64 348[3:Spt:343.0,343.1] group_element(u) || -> product(e_1,e_1,u)*.
% 1.42/1.64 349[3:Res:348.1,6.2] group_element(u) || greater(u,v)*+ next(e_1,v)* -> .
% 1.42/1.64 366[3:Res:5.0,349.1] group_element(e_3) || next(e_1,e_2)* -> .
% 1.42/1.64 369[3:SSi:366.0,9.0] || next(e_1,e_2)* -> .
% 1.42/1.64 370[3:MRR:369.0,1.0] || -> .
% 1.42/1.64 372[3:Spt:370.0,343.2] || -> equalish(e_3,e_3)*.
% 1.42/1.64 427[4:Spt:342.0,342.1,342.3] group_element(u) || -> product(u,u,e_3)* equalish(u,e_3).
% 1.42/1.64 428[4:Res:427.1,6.2] group_element(e_1) || greater(e_3,u) next(e_1,u)* -> equalish(e_1,e_3).
% 1.42/1.64 435[4:SSi:428.0,7.0] || greater(e_3,u) next(e_1,u)* -> equalish(e_1,e_3).
% 1.42/1.64 436[4:MRR:435.2,11.0] || greater(e_3,u)+ next(e_1,u)* -> .
% 1.42/1.64 439[4:Res:5.0,436.0] || next(e_1,e_2)* -> .
% 1.42/1.64 441[4:MRR:439.0,1.0] || -> .
% 1.42/1.64 442[4:Spt:441.0,342.2] || -> product(e_1,e_1,e_1)*.
% 1.42/1.64 446[4:Res:442.0,17.0] || product(e_1,e_1,u)*+ -> equalish(u,e_1).
% 1.42/1.64 450[4:Res:442.0,27.2] group_element(u) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 1.42/1.64 453[4:SSi:450.1,7.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(e_1,u).
% 1.42/1.64 478[4:Res:310.2,446.0] group_element(u) || -> product(u,u,e_3)* equalish(u,e_1).
% 1.42/1.64 536[4:Res:478.1,17.0] group_element(u) || product(u,u,v)*+ -> equalish(u,e_1) equalish(v,e_3).
% 1.42/1.64 538[4:Res:478.1,19.0] group_element(u) || product(v,u,e_3)*+ -> equalish(u,e_1) equalish(v,u).
% 1.42/1.64 1195[4:Res:453.2,321.1] 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).
% 1.42/1.64 1200[4:SSi:1195.1,8.0] group_element(u) || -> product(e_1,u,e_3)* equalish(e_1,u) product(e_2,e_2,e_3) equalish(u,e_1).
% 1.42/1.64 1201[4:MRR:1200.1,538.1] group_element(u) || -> equalish(e_1,u)* product(e_2,e_2,e_3)* equalish(u,e_1)*.
% 1.42/1.64 1210[5:Spt:1201.0,1201.1,1201.3] group_element(u) || -> equalish(e_1,u)* equalish(u,e_1)*.
% 1.42/1.64 1213[5:Res:1210.1,10.0] group_element(e_2) || -> equalish(e_2,e_1)*.
% 1.42/1.64 1216[5:SSi:1213.0,8.0] || -> equalish(e_2,e_1)*.
% 1.42/1.64 1217[5:MRR:1216.0,12.0] || -> .
% 1.42/1.64 1218[5:Spt:1217.0,1201.2] || -> product(e_2,e_2,e_3)*.
% 1.42/1.64 1220[5:Res:1218.0,20.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 1.42/1.64 1308[5:Res:1218.0,1220.0] || -> product(e_3,e_3,e_2)*.
% 1.42/1.64 1322[5:Res:1308.0,536.1] group_element(e_3) || -> equalish(e_3,e_1) equalish(e_2,e_3)*.
% 1.42/1.64 1329[5:SSi:1322.0,9.0] || -> equalish(e_3,e_1) equalish(e_2,e_3)*.
% 1.42/1.64 1330[5:MRR:1329.0,1329.1,14.0,13.0] || -> .
% 1.42/1.64 1335[2:Spt:1330.0,280.3] || -> equalish(e_2,e_2)*.
% 1.42/1.64 1643[0:Res:5.0,257.1] group_element(e_3) || next(e_1,e_2) -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)*.
% 1.42/1.64 1645[0:Res:3.0,257.1] group_element(e_2) || next(e_1,e_1) -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 1.42/1.64 1646[0:SSi:1643.0,9.0] || next(e_1,e_2) -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)*.
% 1.42/1.64 1647[0:MRR:1646.0,1.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)*.
% 1.42/1.64 1648[0:SSi:1645.0,8.0] || next(e_1,e_1)+ -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 1.42/1.64 1650[0:Res:1647.1,20.0] || product(e_3,e_3,u)*+ -> product(e_3,e_3,e_3)* product(u,e_2,e_3)*.
% 1.42/1.64 1651[0:Res:1647.1,17.0] || product(e_3,e_3,u)*+ -> product(e_3,e_3,e_3)* equalish(u,e_2).
% 1.42/1.64 1652[0:Res:1647.1,18.0] || product(e_3,u,e_2)*+ -> product(e_3,e_3,e_3)* equalish(u,e_3).
% 1.42/1.64 1653[0:Res:1647.1,19.0] || product(u,e_3,e_2)*+ -> product(e_3,e_3,e_3)* equalish(u,e_3).
% 1.42/1.64 1670[3:Spt:1651.0,1651.2] || product(e_3,e_3,u)*+ -> equalish(u,e_2).
% 1.42/1.64 1682[4:Spt:1652.0,1652.2] || product(e_3,u,e_2)*+ -> equalish(u,e_3).
% 1.42/1.64 1694[5:Spt:1653.0,1653.2] || product(u,e_3,e_2)*+ -> equalish(u,e_3).
% 1.42/1.64 1747[6:Spt:1650.0,1650.2] || product(e_3,e_3,u)*+ -> product(u,e_2,e_3)*.
% 1.42/1.64 1753[6:Res:1647.1,1747.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 1.42/1.64 1759[7:Spt:1753.0] || -> product(e_3,e_3,e_3)*.
% 1.42/1.64 1769[7:Res:1759.0,1670.0] || -> equalish(e_3,e_2)*.
% 1.42/1.64 1770[7:MRR:1769.0,15.0] || -> .
% 1.42/1.64 1786[7:Spt:1770.0,1753.0,1759.0] || product(e_3,e_3,e_3)*+ -> .
% 1.42/1.64 1787[7:Spt:1770.0,1753.1] || -> product(e_2,e_2,e_3)*.
% 1.42/1.64 1792[7:Res:1787.0,17.0] || product(e_2,e_2,u)*+ -> equalish(u,e_3).
% 1.42/1.64 1793[7:Res:1787.0,18.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 1.42/1.64 1794[7:Res:1787.0,19.0] || product(u,e_2,e_3)*+ -> equalish(u,e_2).
% 1.42/1.64 1855[7:Res:250.2,1793.0] group_element(e_2) group_element(u) || -> product(e_1,e_1,e_2)* product(u,e_2,e_3) product(u,e_2,e_2)* product(e_2,e_1,e_2) equalish(u,e_2).
% 1.42/1.64 1857[7:SSi:1855.0,8.0] group_element(u) || -> product(e_1,e_1,e_2)* product(u,e_2,e_3) product(u,e_2,e_2)* product(e_2,e_1,e_2) equalish(u,e_2).
% 1.42/1.64 1858[7:MRR:1857.2,1794.0] group_element(u) || -> product(e_1,e_1,e_2)* product(u,e_2,e_2)* product(e_2,e_1,e_2) equalish(u,e_2).
% 1.42/1.64 1904[8:Spt:1858.0,1858.2,1858.4] group_element(u) || -> product(u,e_2,e_2)* equalish(u,e_2).
% 1.42/1.64 1918[8:Res:1904.1,1682.0] group_element(e_3) || -> equalish(e_3,e_2) equalish(e_2,e_3)*.
% 1.42/1.64 1921[8:SSi:1918.0,9.0] || -> equalish(e_3,e_2) equalish(e_2,e_3)*.
% 1.42/1.64 1922[8:MRR:1921.0,1921.1,15.0,13.0] || -> .
% 1.42/1.64 1935[8:Spt:1922.0,1858.1,1858.3] || -> product(e_1,e_1,e_2)* product(e_2,e_1,e_2).
% 1.42/1.64 1936[9:Spt:1935.0] || -> product(e_1,e_1,e_2)*.
% 1.42/1.64 1941[9:Res:1936.0,20.0] || product(e_1,e_1,u)*+ -> product(u,e_2,e_1)*.
% 1.42/1.64 2065[9:Res:1936.0,1941.0] || -> product(e_2,e_2,e_1)*.
% 1.42/1.64 2088[9:Res:2065.0,1792.0] || -> equalish(e_1,e_3)*.
% 1.42/1.64 2089[9:MRR:2088.0,11.0] || -> .
% 1.42/1.64 2096[9:Spt:2089.0,1935.0,1936.0] || product(e_1,e_1,e_2)*+ -> .
% 1.42/1.64 2097[9:Spt:2089.0,1935.1] || -> product(e_2,e_1,e_2)*.
% 1.42/1.64 2114[9:Res:2097.0,20.0] || product(e_1,e_2,u)*+ -> product(u,e_2,e_1)*.
% 1.42/1.64 2119[9:Res:2097.0,255.1] group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_2,e_1).
% 1.42/1.64 2126[9:SSi:2119.0,7.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_2,e_1).
% 1.42/1.64 2127[9:MRR:2126.2,12.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)*.
% 1.42/1.64 2139[9:Res:33.6,2096.0] 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_1,e_1,e_3)* equalish(u,e_1).
% 1.42/1.64 2143[9:Obv:2139.1] group_element(u) group_element(e_1) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_1,e_1,e_3)* equalish(u,e_1).
% 1.42/1.64 2144[9:SSi:2143.1,7.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* product(e_1,e_1,e_3)* equalish(u,e_1).
% 1.42/1.64 2148[10:Spt:2127.0] || -> product(e_1,e_1,e_3)*.
% 1.42/1.64 2150[10:Res:2148.0,6.2] || greater(e_3,u)+ next(e_1,u)* -> .
% 1.42/1.64 2237[10:Res:5.0,2150.0] || next(e_1,e_2)* -> .
% 1.42/1.64 2239[10:MRR:2237.0,1.0] || -> .
% 1.42/1.64 2240[10:Spt:2239.0,2127.0,2148.0] || product(e_1,e_1,e_3)*+ -> .
% 1.42/1.64 2241[10:Spt:2239.0,2127.1] || -> product(e_1,e_1,e_1)*.
% 1.42/1.64 2246[10:MRR:2144.3,2240.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 1.42/1.64 2301[10:Res:2246.2,1694.0] group_element(e_3) || -> product(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_1,e_3).
% 1.42/1.64 2302[10:SSi:2301.0,9.0] || -> product(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_1,e_3).
% 1.42/1.64 2303[10:MRR:2302.1,2302.2,14.0,11.0] || -> product(e_1,e_3,e_3)*.
% 1.42/1.64 2320[10:Res:2303.0,18.0] || product(e_1,u,e_3)*+ -> equalish(u,e_3).
% 1.42/1.64 2606[10:Res:2246.2,2114.0] group_element(e_2) || -> product(e_1,e_2,e_3)* equalish(e_2,e_1) product(e_2,e_2,e_1).
% 1.42/1.64 2607[10:SSi:2606.0,8.0] || -> product(e_1,e_2,e_3)* equalish(e_2,e_1) product(e_2,e_2,e_1).
% 1.42/1.64 2608[10:MRR:2607.1,12.0] || -> product(e_1,e_2,e_3)* product(e_2,e_2,e_1).
% 1.42/1.64 2656[10:Res:2608.0,2320.0] || -> product(e_2,e_2,e_1)* equalish(e_2,e_3).
% 1.42/1.64 2659[10:MRR:2656.1,13.0] || -> product(e_2,e_2,e_1)*.
% 1.42/1.64 2672[10:Res:2659.0,1792.0] || -> equalish(e_1,e_3)*.
% 1.42/1.64 2673[10:MRR:2672.0,11.0] || -> .
% 1.42/1.64 2680[6:Spt:2673.0,1650.1] || -> product(e_3,e_3,e_3)*.
% 1.42/1.64 2700[6:Res:2680.0,1670.0] || -> equalish(e_3,e_2)*.
% 1.42/1.64 2701[6:MRR:2700.0,15.0] || -> .
% 1.42/1.64 2718[5:Spt:2701.0,1653.1] || -> product(e_3,e_3,e_3)*.
% 1.42/1.64 2728[5:Res:2718.0,1670.0] || -> equalish(e_3,e_2)*.
% 1.42/1.64 2729[5:MRR:2728.0,15.0] || -> .
% 1.42/1.64 2740[4:Spt:2729.0,1652.1] || -> product(e_3,e_3,e_3)*.
% 1.42/1.64 2750[4:Res:2740.0,1670.0] || -> equalish(e_3,e_2)*.
% 1.42/1.64 2751[4:MRR:2750.0,15.0] || -> .
% 1.42/1.64 2756[3:Spt:2751.0,1651.1] || -> product(e_3,e_3,e_3)*.
% 1.42/1.64 2760[3:Res:2756.0,17.0] || product(e_3,e_3,u)*+ -> equalish(u,e_3).
% 1.42/1.64 2761[3:Res:2756.0,18.0] || product(e_3,u,e_3)*+ -> equalish(u,e_3).
% 1.42/1.64 2762[3:Res:2756.0,19.0] || product(u,e_3,e_3)*+ -> equalish(u,e_3).
% 1.42/1.64 2781[3:Res:250.2,2761.0] group_element(e_3) group_element(u) || -> product(e_1,e_1,e_3)* product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,e_3) equalish(u,e_3).
% 1.42/1.64 2783[3:SSi:2781.0,9.0] group_element(u) || -> product(e_1,e_1,e_3)* product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,e_3) equalish(u,e_3).
% 1.42/1.64 2784[3:MRR:2783.2,2762.0] group_element(u) || -> product(e_1,e_1,e_3)* product(u,e_3,e_2)* product(e_2,e_1,e_3) equalish(u,e_3).
% 1.42/1.64 2821[4:Spt:1648.1] || -> product(e_2,e_2,e_3)*.
% 1.42/1.64 2824[4:Res:2821.0,20.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 1.42/1.64 2900[4:Res:2821.0,2824.0] || -> product(e_3,e_3,e_2)*.
% 1.42/1.64 2923[4:Res:2900.0,2760.0] || -> equalish(e_2,e_3)*.
% 1.42/1.64 2924[4:MRR:2923.0,13.0] || -> .
% 1.42/1.64 2937[4:Spt:2924.0,1648.1,2821.0] || product(e_2,e_2,e_3)*+ -> .
% 1.42/1.64 2938[4:Spt:2924.0,1648.0,1648.2] || next(e_1,e_1)+ -> product(e_2,e_2,e_2)*.
% 1.42/1.64 2943[5:Spt:2784.0,2784.2,2784.4] group_element(u) || -> product(u,e_3,e_2)* equalish(u,e_3).
% 1.42/1.64 2945[5:Res:2943.1,25.2] group_element(u) group_element(u) group_element(e_3) || -> equalish(u,e_3) product(e_3,u,e_3) product(e_3,u,e_2) product(e_2,e_1,u)*.
% 1.42/1.64 2967[5:Obv:2945.0] group_element(u) group_element(e_3) || -> equalish(u,e_3) product(e_3,u,e_3) product(e_3,u,e_2) product(e_2,e_1,u)*.
% 1.42/1.64 2968[5:SSi:2967.1,9.0] group_element(u) || -> equalish(u,e_3) product(e_3,u,e_3) product(e_3,u,e_2) product(e_2,e_1,u)*.
% 1.42/1.64 2969[5:MRR:2968.2,2761.0] group_element(u) || -> equalish(u,e_3) product(e_3,u,e_2) product(e_2,e_1,u)*.
% 1.42/1.64 2988[5:Res:2969.3,255.1] group_element(e_2) group_element(e_1) || -> equalish(e_2,e_3) product(e_3,e_2,e_2) product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_2,e_1).
% 1.55/1.79 2997[5:Res:2969.3,254.1] group_element(e_2) group_element(e_2) || -> equalish(e_2,e_3) product(e_3,e_2,e_2) product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.55/1.79 2998[5:Obv:2997.0] group_element(e_2) || -> equalish(e_2,e_3) product(e_3,e_2,e_2) product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.55/1.79 2999[5:SSi:2998.0,8.0] || -> equalish(e_2,e_3) product(e_3,e_2,e_2) product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.55/1.79 3000[5:MRR:2999.0,2999.2,2999.4,13.0,2937.0,10.0] || -> product(e_3,e_2,e_2) product(e_1,e_1,e_2)*.
% 1.55/1.79 3001[5:SSi:2988.1,2988.0,7.0,8.0] || -> equalish(e_2,e_3) product(e_3,e_2,e_2) product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_2,e_1).
% 1.55/1.79 3002[5:MRR:3001.0,3001.4,13.0,12.0] || -> product(e_3,e_2,e_2) product(e_1,e_1,e_3) product(e_1,e_1,e_1)*.
% 1.55/1.79 3023[6:Spt:3000.0] || -> product(e_3,e_2,e_2)*.
% 1.55/1.79 3031[6:Res:3023.0,255.1] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_3,e_2).
% 1.55/1.79 3042[6:SSi:3031.0,8.0] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_3,e_2).
% 1.55/1.79 3043[6:MRR:3042.0,3042.2,2937.0,15.0] || -> product(e_1,e_1,e_2)*.
% 1.55/1.79 3054[6:Res:3043.0,18.0] || product(e_1,u,e_2)*+ -> equalish(u,e_1).
% 1.55/1.79 3216[6:Res:2943.1,3054.0] group_element(e_1) || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 1.55/1.79 3217[6:SSi:3216.0,7.0] || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 1.55/1.79 3218[6:MRR:3217.0,3217.1,11.0,14.0] || -> .
% 1.55/1.79 3227[6:Spt:3218.0,3000.0,3023.0] || product(e_3,e_2,e_2)*+ -> .
% 1.55/1.79 3228[6:Spt:3218.0,3000.1] || -> product(e_1,e_1,e_2)*.
% 1.55/1.79 3229[6:MRR:3002.0,3227.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)*.
% 1.55/1.79 3246[6:Res:3228.0,17.0] || product(e_1,e_1,u)*+ -> equalish(u,e_2).
% 1.55/1.79 3322[7:Spt:3229.0] || -> product(e_1,e_1,e_3)*.
% 1.55/1.79 3396[7:Res:3322.0,3246.0] || -> equalish(e_3,e_2)*.
% 1.55/1.79 3402[7:MRR:3396.0,15.0] || -> .
% 1.55/1.79 3408[7:Spt:3402.0,3229.0,3322.0] || product(e_1,e_1,e_3)* -> .
% 1.55/1.79 3409[7:Spt:3402.0,3229.1] || -> product(e_1,e_1,e_1)*.
% 1.55/1.79 3413[7:Res:3409.0,3246.0] || -> equalish(e_1,e_2)*.
% 1.55/1.79 3430[7:MRR:3413.0,10.0] || -> .
% 1.55/1.79 3439[5:Spt:3430.0,2784.1,2784.3] || -> product(e_1,e_1,e_3)* product(e_2,e_1,e_3).
% 1.55/1.79 3442[6:Spt:3439.0] || -> product(e_1,e_1,e_3)*.
% 1.55/1.79 3444[6:Res:3442.0,6.2] || greater(e_3,u)+ next(e_1,u)* -> .
% 1.55/1.79 3492[6:Res:5.0,3444.0] || next(e_1,e_2)* -> .
% 1.55/1.79 3494[6:MRR:3492.0,1.0] || -> .
% 1.55/1.79 3495[6:Spt:3494.0,3439.0,3442.0] || product(e_1,e_1,e_3)*+ -> .
% 1.55/1.79 3496[6:Spt:3494.0,3439.1] || -> product(e_2,e_1,e_3)*.
% 1.55/1.79 3524[6:Res:3496.0,25.2] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_3,e_1,e_2).
% 1.55/1.79 3525[6:Res:3496.0,20.0] || product(e_1,e_2,u)*+ -> product(u,e_3,e_1)*.
% 1.55/1.79 3533[6:SSi:3524.1,3524.0,7.0,8.0] || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_3,e_1,e_2).
% 1.55/1.79 3821[7:Spt:3533.0] || -> product(e_1,e_2,e_3)*.
% 1.55/1.79 3833[7:Res:3821.0,3525.0] || -> product(e_3,e_3,e_1)*.
% 1.55/1.79 3912[7:Res:3833.0,2760.0] || -> equalish(e_1,e_3)*.
% 1.55/1.79 3913[7:MRR:3912.0,11.0] || -> .
% 1.55/1.79 3923[7:Spt:3913.0,3533.0,3821.0] || product(e_1,e_2,e_3)*+ -> .
% 1.55/1.79 3924[7:Spt:3913.0,3533.1,3533.2] || -> product(e_1,e_2,e_2)* product(e_3,e_1,e_2).
% 1.55/1.79 3931[8:Spt:3924.0] || -> product(e_1,e_2,e_2)*.
% 1.55/1.79 3937[8:Res:3931.0,18.0] || product(e_1,u,e_2)*+ -> equalish(u,e_2).
% 1.55/1.79 3941[8:Res:3931.0,255.1] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.55/1.79 3956[8:SSi:3941.0,8.0] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.55/1.79 3957[8:MRR:3956.0,3956.2,2937.0,10.0] || -> product(e_1,e_1,e_2)*.
% 1.55/1.79 4074[8:Res:3957.0,3937.0] || -> equalish(e_1,e_2)*.
% 1.55/1.79 4088[8:MRR:4074.0,10.0] || -> .
% 1.55/1.79 4102[8:Spt:4088.0,3924.0,3931.0] || product(e_1,e_2,e_2)*+ -> .
% 1.55/1.79 4103[8:Spt:4088.0,3924.1] || -> product(e_3,e_1,e_2)*.
% 1.55/1.79 4113[8:Res:4103.0,18.0] || product(e_3,u,e_2)*+ -> equalish(u,e_1).
% 1.55/1.79 4191[8:Res:31.4,4102.0] group_element(e_1) group_element(e_2) group_element(u) || -> product(e_1,e_2,e_3)* product(u,e_2,e_3) product(u,e_2,e_2)* equalish(e_1,u).
% 1.55/1.79 4192[8:SSi:4191.1,4191.0,8.0,7.0] group_element(u) || -> product(e_1,e_2,e_3)* product(u,e_2,e_3) product(u,e_2,e_2)* equalish(e_1,u).
% 1.55/1.79 4193[8:MRR:4192.1,3923.0] group_element(u) || -> product(u,e_2,e_3) product(u,e_2,e_2)* equalish(e_1,u).
% 1.55/1.79 4276[8:Res:4193.2,4113.0] group_element(e_3) || -> product(e_3,e_2,e_3)* equalish(e_1,e_3) equalish(e_2,e_1).
% 1.55/1.79 4279[8:SSi:4276.0,9.0] || -> product(e_3,e_2,e_3)* equalish(e_1,e_3) equalish(e_2,e_1).
% 1.55/1.79 4280[8:MRR:4279.1,4279.2,11.0,12.0] || -> product(e_3,e_2,e_3)*.
% 1.55/1.79 4342[8:Res:4280.0,2761.0] || -> equalish(e_2,e_3)*.
% 1.55/1.79 4343[8:MRR:4342.0,13.0] || -> .
% 1.55/1.79 % SZS output end Refutation
% 1.55/1.79 Formulae used in the proof : e_1_then_e_2 e_2_greater_e_1 e_3_greater_e_2 no_redundancy 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
% 1.55/1.79
%------------------------------------------------------------------------------