TSTP Solution File: GRP134-2.003 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP134-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:45:52 EDT 2022
% Result : Unsatisfiable 1.66s 1.86s
% Output : Refutation 1.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP134-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n016.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 04:10:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.86
% 1.66/1.86 SPASS V 3.9
% 1.66/1.86 SPASS beiseite: Proof found.
% 1.66/1.86 % SZS status Theorem
% 1.66/1.86 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.66/1.86 SPASS derived 2771 clauses, backtracked 627 clauses, performed 27 splits and kept 1818 clauses.
% 1.66/1.86 SPASS allocated 79546 KBytes.
% 1.66/1.86 SPASS spent 0:00:01.52 on the problem.
% 1.66/1.86 0:00:00.03 for the input.
% 1.66/1.86 0:00:00.00 for the FLOTTER CNF translation.
% 1.66/1.86 0:00:00.05 for inferences.
% 1.66/1.86 0:00:00.02 for the backtracking.
% 1.66/1.86 0:00:01.39 for the reduction.
% 1.66/1.86
% 1.66/1.86
% 1.66/1.86 Here is a proof with depth 17, length 239 :
% 1.66/1.86 % SZS output start Refutation
% 1.66/1.86 1[0:Inp] || -> next(e_1,e_2)*.
% 1.66/1.86 3[0:Inp] || -> greater(e_2,e_1)*.
% 1.66/1.86 5[0:Inp] || -> greater(e_3,e_2)*.
% 1.66/1.86 6[0:Inp] || greater(u,v)* next(w,v)* product(w,e_1,u)*+ -> .
% 1.66/1.86 7[0:Inp] || -> group_element(e_1)*.
% 1.66/1.86 8[0:Inp] || -> group_element(e_2)*.
% 1.66/1.86 9[0:Inp] || -> group_element(e_3)*.
% 1.66/1.86 10[0:Inp] || equalish(e_1,e_2)*+ -> .
% 1.66/1.86 11[0:Inp] || equalish(e_1,e_3)*+ -> .
% 1.66/1.86 12[0:Inp] || equalish(e_2,e_1)*+ -> .
% 1.66/1.86 13[0:Inp] || equalish(e_2,e_3)*+ -> .
% 1.66/1.86 14[0:Inp] || equalish(e_3,e_1)*+ -> .
% 1.66/1.86 15[0:Inp] || equalish(e_3,e_2)*+ -> .
% 1.66/1.86 16[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 1.66/1.86 17[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 1.66/1.86 18[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 1.66/1.86 19[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 1.66/1.86 20[0:Inp] || product(u,v,w)*+ product(v,u,x)* -> product(x,w,u)*.
% 1.66/1.86 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,v)*.
% 1.66/1.86 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).
% 1.66/1.86 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)*.
% 1.66/1.86 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)*.
% 1.66/1.86 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)*.
% 1.66/1.86 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).
% 1.66/1.86 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).
% 1.66/1.86 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,u)*.
% 1.66/1.86 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,v)*.
% 1.66/1.86 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)*.
% 1.66/1.86 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,v)*.
% 1.66/1.86 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).
% 1.66/1.86 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,u)*.
% 1.66/1.86 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,v)*.
% 1.66/1.86 75[1:Fac:74.2,74.3] group_element(u) group_element(u) || -> product(u,u,e_3)* product(e_2,e_2,u)*.
% 1.66/1.86 98[1:Obv:75.0] group_element(u) || -> product(u,u,e_3)* product(e_2,e_2,u)*.
% 1.66/1.86 113[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)*.
% 1.66/1.86 128[1:SSi:113.0,7.0] || greater(e_3,u)+ next(e_1,u)* -> product(e_2,e_2,e_1)*.
% 1.66/1.86 139[1:Res:5.0,128.0] || next(e_1,e_2) -> product(e_2,e_2,e_1)*.
% 1.66/1.86 141[1:MRR:139.0,1.0] || -> product(e_2,e_2,e_1)*.
% 1.66/1.86 144[1:Res:141.0,17.0] || product(e_2,e_2,u)*+ -> equalish(u,e_1).
% 1.66/1.86 147[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).
% 1.66/1.86 148[1:Obv:147.0] group_element(e_2) || -> product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 1.66/1.86 149[1:SSi:148.0,8.0] || -> product(e_2,e_2,e_3)* equalish(e_1,e_2).
% 1.66/1.86 150[1:MRR:149.1,10.0] || -> product(e_2,e_2,e_3)*.
% 1.66/1.86 188[1:Res:150.0,144.0] || -> equalish(e_3,e_1)*.
% 1.66/1.86 189[1:MRR:188.0,14.0] || -> .
% 1.66/1.86 198[1:Spt:189.0,35.4] || -> equalish(e_1,e_1)*.
% 1.66/1.86 212[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)*.
% 1.66/1.86 214[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,v)* product(v,u,e_3) product(v,u,e_2)* product(e_2,e_1,v).
% 1.66/1.86 236[0:Obv:212.2] group_element(u) || -> product(u,u,e_3) product(u,u,e_2)* product(e_1,e_1,u)*.
% 1.66/1.86 250[0:Obv:214.6] 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,v).
% 1.66/1.86 253[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).
% 1.66/1.86 254[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).
% 1.66/1.86 255[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).
% 1.66/1.86 257[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)*.
% 1.66/1.86 277[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).
% 1.66/1.86 280[0:Obv:277.3] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)* equalish(e_2,e_2).
% 1.66/1.86 310[2:Spt:280.0,280.1,280.2] group_element(u) || -> product(u,u,e_3)* product(e_1,e_1,u)*.
% 1.66/1.86 313[2:Res:310.1,17.0] group_element(u) || product(u,u,v)*+ -> product(e_1,e_1,u)* equalish(v,e_3).
% 1.66/1.86 321[2:Res:310.2,18.0] group_element(u) || product(e_1,v,u)*+ -> product(u,u,e_3)* equalish(v,e_1).
% 1.66/1.86 336[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).
% 1.66/1.86 337[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).
% 1.66/1.86 342[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).
% 1.66/1.86 343[2:Obv:337.2] group_element(u) || -> product(e_1,e_1,u)* equalish(e_3,e_3).
% 1.66/1.86 348[3:Spt:343.0,343.1] group_element(u) || -> product(e_1,e_1,u)*.
% 1.66/1.86 349[3:Res:348.1,6.2] group_element(u) || greater(u,v)*+ next(e_1,v)* -> .
% 1.66/1.86 366[3:Res:5.0,349.1] group_element(e_3) || next(e_1,e_2)* -> .
% 1.66/1.86 369[3:SSi:366.0,9.0] || next(e_1,e_2)* -> .
% 1.66/1.86 370[3:MRR:369.0,1.0] || -> .
% 1.66/1.86 372[3:Spt:370.0,343.2] || -> equalish(e_3,e_3)*.
% 1.66/1.86 427[4:Spt:342.0,342.1,342.3] group_element(u) || -> product(u,u,e_3)* equalish(u,e_3).
% 1.66/1.86 428[4:Res:427.1,6.2] group_element(e_1) || greater(e_3,u) next(e_1,u)* -> equalish(e_1,e_3).
% 1.66/1.86 435[4:SSi:428.0,7.0] || greater(e_3,u) next(e_1,u)* -> equalish(e_1,e_3).
% 1.66/1.86 436[4:MRR:435.2,11.0] || greater(e_3,u)+ next(e_1,u)* -> .
% 1.66/1.86 439[4:Res:5.0,436.0] || next(e_1,e_2)* -> .
% 1.66/1.86 441[4:MRR:439.0,1.0] || -> .
% 1.66/1.86 442[4:Spt:441.0,342.2] || -> product(e_1,e_1,e_1)*.
% 1.66/1.86 446[4:Res:442.0,17.0] || product(e_1,e_1,u)*+ -> equalish(u,e_1).
% 1.66/1.86 450[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).
% 1.66/1.86 453[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).
% 1.66/1.86 478[4:Res:310.2,446.0] group_element(u) || -> product(u,u,e_3)* equalish(u,e_1).
% 1.66/1.86 536[4:Res:478.1,17.0] group_element(u) || product(u,u,v)*+ -> equalish(u,e_1) equalish(v,e_3).
% 1.66/1.86 538[4:Res:478.1,19.0] group_element(u) || product(v,u,e_3)*+ -> equalish(u,e_1) equalish(v,u).
% 1.66/1.86 1194[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).
% 1.66/1.86 1199[4:SSi:1194.1,8.0] group_element(u) || -> product(e_1,u,e_3)* equalish(e_1,u) product(e_2,e_2,e_3) equalish(u,e_1).
% 1.66/1.86 1200[4:MRR:1199.1,538.1] group_element(u) || -> equalish(e_1,u)* product(e_2,e_2,e_3)* equalish(u,e_1)*.
% 1.66/1.86 1209[5:Spt:1200.0,1200.1,1200.3] group_element(u) || -> equalish(e_1,u)* equalish(u,e_1)*.
% 1.66/1.86 1212[5:Res:1209.1,10.0] group_element(e_2) || -> equalish(e_2,e_1)*.
% 1.66/1.86 1215[5:SSi:1212.0,8.0] || -> equalish(e_2,e_1)*.
% 1.66/1.86 1216[5:MRR:1215.0,12.0] || -> .
% 1.66/1.86 1217[5:Spt:1216.0,1200.2] || -> product(e_2,e_2,e_3)*.
% 1.66/1.86 1219[5:Res:1217.0,20.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 1.66/1.86 1307[5:Res:1217.0,1219.0] || -> product(e_3,e_3,e_2)*.
% 1.66/1.86 1322[5:Res:1307.0,536.1] group_element(e_3) || -> equalish(e_3,e_1) equalish(e_2,e_3)*.
% 1.66/1.86 1328[5:SSi:1322.0,9.0] || -> equalish(e_3,e_1) equalish(e_2,e_3)*.
% 1.66/1.86 1329[5:MRR:1328.0,1328.1,14.0,13.0] || -> .
% 1.66/1.86 1334[2:Spt:1329.0,280.3] || -> equalish(e_2,e_2)*.
% 1.66/1.86 1642[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)*.
% 1.66/1.86 1644[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)*.
% 1.66/1.86 1645[0:SSi:1642.0,9.0] || next(e_1,e_2) -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)*.
% 1.66/1.86 1646[0:MRR:1645.0,1.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2)*.
% 1.66/1.86 1647[0:SSi:1644.0,8.0] || next(e_1,e_1)+ -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 1.66/1.86 1649[0:Res:1646.1,20.0] || product(e_3,e_3,u)*+ -> product(e_3,e_3,e_3)* product(u,e_2,e_3)*.
% 1.66/1.86 1650[0:Res:1646.1,17.0] || product(e_3,e_3,u)*+ -> product(e_3,e_3,e_3)* equalish(u,e_2).
% 1.66/1.86 1652[0:Res:1646.1,19.0] || product(u,e_3,e_2)*+ -> product(e_3,e_3,e_3)* equalish(u,e_3).
% 1.66/1.86 1669[3:Spt:1650.0,1650.2] || product(e_3,e_3,u)*+ -> equalish(u,e_2).
% 1.66/1.86 1695[4:Spt:1652.0,1652.2] || product(u,e_3,e_2)*+ -> equalish(u,e_3).
% 1.66/1.86 1748[5:Spt:1649.0,1649.2] || product(e_3,e_3,u)*+ -> product(u,e_2,e_3)*.
% 1.66/1.86 1754[5:Res:1646.1,1748.0] || -> product(e_3,e_3,e_3) product(e_2,e_2,e_3)*.
% 1.66/1.86 1760[6:Spt:1754.0] || -> product(e_3,e_3,e_3)*.
% 1.66/1.86 1770[6:Res:1760.0,1669.0] || -> equalish(e_3,e_2)*.
% 1.66/1.86 1771[6:MRR:1770.0,15.0] || -> .
% 1.66/1.86 1787[6:Spt:1771.0,1754.0,1760.0] || product(e_3,e_3,e_3)*+ -> .
% 1.66/1.86 1788[6:Spt:1771.0,1754.1] || -> product(e_2,e_2,e_3)*.
% 1.66/1.86 1793[6:Res:1788.0,17.0] || product(e_2,e_2,u)*+ -> equalish(u,e_3).
% 1.66/1.86 1794[6:Res:1788.0,18.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 1.66/1.86 1795[6:Res:1788.0,19.0] || product(u,e_2,e_3)*+ -> equalish(u,e_2).
% 1.66/1.86 1861[6:Res:250.2,1795.0] group_element(u) group_element(e_2) || -> product(e_1,e_1,e_2)* product(e_2,u,e_3) product(e_2,u,e_2)* product(e_2,e_1,e_2) equalish(u,e_2).
% 1.66/1.86 1863[6:SSi:1861.1,8.0] group_element(u) || -> product(e_1,e_1,e_2)* product(e_2,u,e_3) product(e_2,u,e_2)* product(e_2,e_1,e_2) equalish(u,e_2).
% 1.66/1.86 1864[6:MRR:1863.2,1794.0] group_element(u) || -> product(e_1,e_1,e_2)* product(e_2,u,e_2)* product(e_2,e_1,e_2) equalish(u,e_2).
% 1.66/1.86 1905[7:Spt:1864.0,1864.2,1864.4] group_element(u) || -> product(e_2,u,e_2)* equalish(u,e_2).
% 1.66/1.86 1915[7:Res:1905.1,1695.0] group_element(e_3) || -> equalish(e_3,e_2) equalish(e_2,e_3)*.
% 1.66/1.86 1923[7:SSi:1915.0,9.0] || -> equalish(e_3,e_2) equalish(e_2,e_3)*.
% 1.66/1.86 1924[7:MRR:1923.0,1923.1,15.0,13.0] || -> .
% 1.66/1.86 1939[7:Spt:1924.0,1864.1,1864.3] || -> product(e_1,e_1,e_2)* product(e_2,e_1,e_2).
% 1.66/1.86 1940[8:Spt:1939.0] || -> product(e_1,e_1,e_2)*.
% 1.66/1.86 1944[8:Res:1940.0,20.0] || product(e_1,e_1,u)*+ -> product(u,e_2,e_1)*.
% 1.66/1.86 2074[8:Res:1940.0,1944.0] || -> product(e_2,e_2,e_1)*.
% 1.66/1.86 2092[8:Res:2074.0,1793.0] || -> equalish(e_1,e_3)*.
% 1.66/1.86 2093[8:MRR:2092.0,11.0] || -> .
% 1.66/1.86 2100[8:Spt:2093.0,1939.0,1940.0] || product(e_1,e_1,e_2)*+ -> .
% 1.66/1.86 2101[8:Spt:2093.0,1939.1] || -> product(e_2,e_1,e_2)*.
% 1.66/1.86 2118[8:Res:2101.0,20.0] || product(e_1,e_2,u)*+ -> product(u,e_2,e_2)*.
% 1.66/1.86 2120[8:Res:2101.0,18.0] || product(e_2,u,e_2)*+ -> equalish(u,e_1).
% 1.66/1.86 2124[8:Res:2101.0,255.1] group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_2,e_1).
% 1.66/1.86 2131[8:SSi:2124.0,7.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_2,e_1).
% 1.66/1.86 2132[8:MRR:2131.2,12.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)*.
% 1.66/1.86 2143[8:Res:33.6,2100.0] 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).
% 1.66/1.86 2147[8:Obv:2143.1] 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).
% 1.66/1.86 2148[8:SSi:2147.1,7.0] 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).
% 1.66/1.86 2153[9:Spt:2132.0] || -> product(e_1,e_1,e_3)*.
% 1.66/1.86 2154[9:Res:2153.0,6.2] || greater(e_3,u)+ next(e_1,u)* -> .
% 1.66/1.86 2243[9:Res:5.0,2154.0] || next(e_1,e_2)* -> .
% 1.66/1.86 2245[9:MRR:2243.0,1.0] || -> .
% 1.66/1.86 2246[9:Spt:2245.0,2132.0,2153.0] || product(e_1,e_1,e_3)*+ -> .
% 1.66/1.86 2247[9:Spt:2245.0,2132.1] || -> product(e_1,e_1,e_1)*.
% 1.66/1.86 2252[9:MRR:2148.3,2246.0] group_element(u) || -> product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 1.66/1.86 2669[9:Res:2252.2,2118.0] group_element(e_2) || -> product(e_1,e_2,e_3)* equalish(e_2,e_1) product(e_2,e_2,e_2).
% 1.66/1.86 2670[9:SSi:2669.0,8.0] || -> product(e_1,e_2,e_3)* equalish(e_2,e_1) product(e_2,e_2,e_2).
% 1.66/1.86 2671[9:MRR:2670.1,12.0] || -> product(e_1,e_2,e_3)* product(e_2,e_2,e_2).
% 1.66/1.86 2680[9:Res:2671.0,1795.0] || -> product(e_2,e_2,e_2)* equalish(e_1,e_2).
% 1.66/1.86 2686[9:MRR:2680.1,10.0] || -> product(e_2,e_2,e_2)*.
% 1.66/1.86 2704[9:Res:2686.0,2120.0] || -> equalish(e_2,e_1)*.
% 1.66/1.86 2706[9:MRR:2704.0,12.0] || -> .
% 1.66/1.86 2716[5:Spt:2706.0,1649.1] || -> product(e_3,e_3,e_3)*.
% 1.66/1.86 2736[5:Res:2716.0,1669.0] || -> equalish(e_3,e_2)*.
% 1.66/1.86 2737[5:MRR:2736.0,15.0] || -> .
% 1.66/1.86 2754[4:Spt:2737.0,1652.1] || -> product(e_3,e_3,e_3)*.
% 1.66/1.86 2764[4:Res:2754.0,1669.0] || -> equalish(e_3,e_2)*.
% 1.66/1.86 2765[4:MRR:2764.0,15.0] || -> .
% 1.66/1.86 2778[3:Spt:2765.0,1650.1] || -> product(e_3,e_3,e_3)*.
% 1.66/1.86 2782[3:Res:2778.0,17.0] || product(e_3,e_3,u)*+ -> equalish(u,e_3).
% 1.66/1.86 2783[3:Res:2778.0,18.0] || product(e_3,u,e_3)*+ -> equalish(u,e_3).
% 1.66/1.86 2784[3:Res:2778.0,19.0] || product(u,e_3,e_3)*+ -> equalish(u,e_3).
% 1.66/1.86 2823[3:Res:250.2,2784.0] 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,e_3) equalish(u,e_3).
% 1.66/1.86 2825[3:SSi:2823.1,9.0] 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,e_3) equalish(u,e_3).
% 1.66/1.86 2826[3:MRR:2825.2,2783.0] group_element(u) || -> product(e_1,e_1,e_3)* product(e_3,u,e_2)* product(e_2,e_1,e_3) equalish(u,e_3).
% 1.66/1.86 2840[4:Spt:1647.1] || -> product(e_2,e_2,e_3)*.
% 1.66/1.86 2843[4:Res:2840.0,20.0] || product(e_2,e_2,u)*+ -> product(u,e_3,e_2)*.
% 1.66/1.86 2919[4:Res:2840.0,2843.0] || -> product(e_3,e_3,e_2)*.
% 1.66/1.86 2964[4:Res:2919.0,2782.0] || -> equalish(e_2,e_3)*.
% 1.66/1.86 2982[4:MRR:2964.0,13.0] || -> .
% 1.66/1.86 2995[4:Spt:2982.0,1647.1,2840.0] || product(e_2,e_2,e_3)*+ -> .
% 1.66/1.86 2996[4:Spt:2982.0,1647.0,1647.2] || next(e_1,e_1)+ -> product(e_2,e_2,e_2)*.
% 1.66/1.86 3001[5:Spt:2826.0,2826.2,2826.4] group_element(u) || -> product(e_3,u,e_2)* equalish(u,e_3).
% 1.66/1.86 3007[5:Res:3001.1,25.2] group_element(u) group_element(e_3) group_element(u) || -> equalish(u,e_3) product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,u)*.
% 1.66/1.86 3029[5:Obv:3007.0] group_element(e_3) group_element(u) || -> equalish(u,e_3) product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,u)*.
% 1.66/1.86 3030[5:SSi:3029.0,9.0] group_element(u) || -> equalish(u,e_3) product(u,e_3,e_3) product(u,e_3,e_2)* product(e_2,e_1,u)*.
% 1.66/1.86 3031[5:MRR:3030.2,2784.0] group_element(u) || -> equalish(u,e_3) product(u,e_3,e_2)* product(e_2,e_1,u)*.
% 1.66/1.86 3097[5:Res:3031.3,254.1] group_element(e_2) group_element(e_2) || -> equalish(e_2,e_3) product(e_2,e_3,e_2) product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.66/1.86 3099[5:Res:3031.3,255.1] group_element(e_2) group_element(e_1) || -> equalish(e_2,e_3) product(e_2,e_3,e_2) product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_2,e_1).
% 1.66/1.86 3108[5:SSi:3099.1,3099.0,7.0,8.0] || -> equalish(e_2,e_3) product(e_2,e_3,e_2) product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_2,e_1).
% 1.66/1.86 3109[5:MRR:3108.0,3108.4,13.0,12.0] || -> product(e_2,e_3,e_2) product(e_1,e_1,e_3) product(e_1,e_1,e_1)*.
% 1.66/1.86 3110[5:Obv:3097.0] group_element(e_2) || -> equalish(e_2,e_3) product(e_2,e_3,e_2) product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.66/1.86 3111[5:SSi:3110.0,8.0] || -> equalish(e_2,e_3) product(e_2,e_3,e_2) product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.66/1.86 3112[5:MRR:3111.0,3111.2,3111.4,13.0,2995.0,10.0] || -> product(e_2,e_3,e_2) product(e_1,e_1,e_2)*.
% 1.66/1.86 3144[6:Spt:3112.0] || -> product(e_2,e_3,e_2)*.
% 1.66/1.86 3152[6:Res:3144.0,254.1] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_3,e_2).
% 1.66/1.86 3164[6:SSi:3152.0,8.0] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_3,e_2).
% 1.82/2.04 3165[6:MRR:3164.0,3164.2,2995.0,15.0] || -> product(e_1,e_1,e_2)*.
% 1.82/2.04 3179[6:Res:3165.0,19.0] || product(u,e_1,e_2)*+ -> equalish(u,e_1).
% 1.82/2.04 3464[6:Res:3001.1,3179.0] group_element(e_1) || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 1.82/2.04 3465[6:SSi:3464.0,7.0] || -> equalish(e_1,e_3)* equalish(e_3,e_1).
% 1.82/2.04 3466[6:MRR:3465.0,3465.1,11.0,14.0] || -> .
% 1.82/2.04 3471[6:Spt:3466.0,3112.0,3144.0] || product(e_2,e_3,e_2)*+ -> .
% 1.82/2.04 3472[6:Spt:3466.0,3112.1] || -> product(e_1,e_1,e_2)*.
% 1.82/2.04 3473[6:MRR:3109.0,3471.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)*.
% 1.82/2.04 3501[6:Res:3472.0,17.0] || product(e_1,e_1,u)*+ -> equalish(u,e_2).
% 1.82/2.04 3597[7:Spt:3473.0] || -> product(e_1,e_1,e_3)*.
% 1.82/2.04 3640[7:Res:3597.0,3501.0] || -> equalish(e_3,e_2)*.
% 1.82/2.04 3641[7:MRR:3640.0,15.0] || -> .
% 1.82/2.04 3647[7:Spt:3641.0,3473.0,3597.0] || product(e_1,e_1,e_3)* -> .
% 1.82/2.04 3648[7:Spt:3641.0,3473.1] || -> product(e_1,e_1,e_1)*.
% 1.82/2.04 3652[7:Res:3648.0,3501.0] || -> equalish(e_1,e_2)*.
% 1.82/2.04 3671[7:MRR:3652.0,10.0] || -> .
% 1.82/2.04 3684[5:Spt:3671.0,2826.1,2826.3] || -> product(e_1,e_1,e_3)* product(e_2,e_1,e_3).
% 1.82/2.04 3688[6:Spt:3684.0] || -> product(e_1,e_1,e_3)*.
% 1.82/2.04 3689[6:Res:3688.0,6.2] || greater(e_3,u)+ next(e_1,u)* -> .
% 1.82/2.04 3767[6:Res:5.0,3689.0] || next(e_1,e_2)* -> .
% 1.82/2.04 3769[6:MRR:3767.0,1.0] || -> .
% 1.82/2.04 3770[6:Spt:3769.0,3684.0,3688.0] || product(e_1,e_1,e_3)*+ -> .
% 1.82/2.04 3771[6:Spt:3769.0,3684.1] || -> product(e_2,e_1,e_3)*.
% 1.82/2.04 3801[6:Res:3771.0,25.2] 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_1).
% 1.82/2.04 3802[6:Res:3771.0,20.0] || product(e_1,e_2,u)*+ -> product(u,e_3,e_2)*.
% 1.82/2.04 3811[6:SSi:3801.1,3801.0,7.0,8.0] || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_3,e_1,e_1).
% 1.82/2.04 4051[6:Res:16.4,3802.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_1,e_3,e_2).
% 1.82/2.04 4055[6:SSi:4051.1,4051.0,7.0,8.0] || -> product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_1,e_3,e_2).
% 1.82/2.04 4060[7:Spt:3811.0] || -> product(e_1,e_2,e_3)*.
% 1.82/2.04 4073[7:Res:4060.0,3802.0] || -> product(e_3,e_3,e_2)*.
% 1.82/2.04 4134[7:Res:4073.0,2782.0] || -> equalish(e_2,e_3)*.
% 1.82/2.04 4158[7:MRR:4134.0,13.0] || -> .
% 1.82/2.04 4175[7:Spt:4158.0,3811.0,4060.0] || product(e_1,e_2,e_3)*+ -> .
% 1.82/2.04 4176[7:Spt:4158.0,3811.1,3811.2] || -> product(e_1,e_2,e_2)* product(e_3,e_1,e_1).
% 1.82/2.04 4177[7:MRR:4055.0,4175.0] || -> product(e_1,e_2,e_2)* product(e_1,e_3,e_2).
% 1.82/2.04 4183[8:Spt:4176.0] || -> product(e_1,e_2,e_2)*.
% 1.82/2.04 4189[8:Res:4183.0,18.0] || product(e_1,u,e_2)*+ -> equalish(u,e_2).
% 1.82/2.04 4193[8:Res:4183.0,255.1] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.82/2.04 4213[8:SSi:4193.0,8.0] || -> product(e_2,e_2,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 1.82/2.04 4214[8:MRR:4213.0,4213.2,2995.0,10.0] || -> product(e_1,e_1,e_2)*.
% 1.82/2.04 4353[8:Res:4214.0,4189.0] || -> equalish(e_1,e_2)*.
% 1.82/2.04 4355[8:MRR:4353.0,10.0] || -> .
% 1.82/2.04 4369[8:Spt:4355.0,4176.0,4183.0] || product(e_1,e_2,e_2)*+ -> .
% 1.82/2.04 4370[8:Spt:4355.0,4176.1] || -> product(e_3,e_1,e_1)*.
% 1.82/2.04 4371[8:MRR:4177.0,4369.0] || -> product(e_1,e_3,e_2)*.
% 1.82/2.04 4380[8:Res:4370.0,19.0] || product(u,e_1,e_1)*+ -> equalish(u,e_3).
% 1.82/2.04 4402[8:Res:4371.0,254.1] group_element(e_1) || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_3,e_1).
% 1.82/2.04 4418[8:SSi:4402.0,7.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_1)* equalish(e_3,e_1).
% 1.82/2.04 4419[8:MRR:4418.0,4418.2,3770.0,14.0] || -> product(e_1,e_1,e_1)*.
% 1.82/2.04 4545[8:Res:4419.0,4380.0] || -> equalish(e_1,e_3)*.
% 1.82/2.04 4547[8:MRR:4545.0,11.0] || -> .
% 1.82/2.04 % SZS output end Refutation
% 1.82/2.04 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 qg4
% 1.82/2.04
%------------------------------------------------------------------------------