TSTP Solution File: GRP124-6.004 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP124-6.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:45:32 EDT 2022
% Result : Unsatisfiable 0.85s 1.06s
% Output : Refutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP124-6.004 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 : Mon Jun 13 14:09:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.85/1.06
% 0.85/1.06 SPASS V 3.9
% 0.85/1.06 SPASS beiseite: Proof found.
% 0.85/1.06 % SZS status Theorem
% 0.85/1.06 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.85/1.06 SPASS derived 2093 clauses, backtracked 224 clauses, performed 37 splits and kept 1077 clauses.
% 0.85/1.06 SPASS allocated 77858 KBytes.
% 0.85/1.06 SPASS spent 0:00:00.71 on the problem.
% 0.85/1.06 0:00:00.03 for the input.
% 0.85/1.06 0:00:00.00 for the FLOTTER CNF translation.
% 0.85/1.06 0:00:00.04 for inferences.
% 0.85/1.06 0:00:00.01 for the backtracking.
% 0.85/1.06 0:00:00.59 for the reduction.
% 0.85/1.06
% 0.85/1.06
% 0.85/1.06 Here is a proof with depth 14, length 251 :
% 0.85/1.06 % SZS output start Refutation
% 0.85/1.06 1[0:Inp] || -> group_element(e_1)*.
% 0.85/1.06 2[0:Inp] || -> group_element(e_2)*.
% 0.85/1.06 3[0:Inp] || -> group_element(e_3)*.
% 0.85/1.06 4[0:Inp] || -> group_element(e_4)*.
% 0.85/1.06 5[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.85/1.06 6[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.85/1.06 7[0:Inp] || equalish(e_1,e_4)*+ -> .
% 0.85/1.06 8[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.85/1.06 9[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.85/1.06 10[0:Inp] || equalish(e_2,e_4)*+ -> .
% 0.85/1.06 11[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.85/1.06 12[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.85/1.06 13[0:Inp] || equalish(e_3,e_4)*+ -> .
% 0.85/1.06 14[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.85/1.06 15[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.85/1.06 16[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.85/1.06 17[0:Inp] group_element(u) group_element(v) || -> product1(v,u,e_4) product1(v,u,e_3) product1(v,u,e_2) product1(v,u,e_1)*.
% 0.85/1.06 18[0:Inp] || product1(u,v,w)*+ product1(u,v,x)* -> equalish(x,w)*.
% 0.85/1.06 19[0:Inp] || product1(u,v,w)*+ product1(u,x,w)* -> equalish(x,v)*.
% 0.85/1.06 20[0:Inp] || product1(u,v,w)*+ product1(x,v,w)* -> equalish(x,u)*.
% 0.85/1.06 21[0:Inp] || -> product1(u,u,u)*.
% 0.85/1.06 22[0:Inp] group_element(u) group_element(v) || -> product2(v,u,e_4) product2(v,u,e_3) product2(v,u,e_2) product2(v,u,e_1)*.
% 0.85/1.06 23[0:Inp] || product2(u,v,w)*+ product2(u,v,x)* -> equalish(x,w)*.
% 0.85/1.06 24[0:Inp] || product2(u,v,w)*+ product2(u,x,w)* -> equalish(x,v)*.
% 0.85/1.06 25[0:Inp] || product2(u,v,w)*+ product2(x,v,w)* -> equalish(x,u)*.
% 0.85/1.06 26[0:Inp] || -> product2(u,u,u)*.
% 0.85/1.06 27[0:Inp] || product1(u,v,w)*+ product1(v,x,u)* -> product2(w,x,v)*.
% 0.85/1.06 35[0:Res:26.0,25.0] || product2(u,v,v)*+ -> equalish(u,v).
% 0.85/1.06 38[0:Res:26.0,24.0] || product2(u,v,u)*+ -> equalish(v,u).
% 0.85/1.06 39[0:Res:26.0,23.0] || product2(u,u,v)*+ -> equalish(v,u).
% 0.85/1.06 42[0:Res:21.0,20.0] || product1(u,v,v)*+ -> equalish(u,v).
% 0.85/1.06 44[0:Res:21.0,19.0] || product1(u,v,u)*+ -> equalish(v,u).
% 0.85/1.06 49[0:Res:22.5,38.0] group_element(u) group_element(e_1) || -> product2(e_1,u,e_4) product2(e_1,u,e_3) product2(e_1,u,e_2)* equalish(u,e_1).
% 0.85/1.06 57[0:SSi:49.1,1.0] group_element(u) || -> product2(e_1,u,e_4) product2(e_1,u,e_3) product2(e_1,u,e_2)* equalish(u,e_1).
% 0.85/1.06 74[0:Res:17.5,44.0] group_element(u) group_element(e_1) || -> product1(e_1,u,e_4) product1(e_1,u,e_3) product1(e_1,u,e_2)* equalish(u,e_1).
% 0.85/1.06 78[0:Res:17.5,27.0] group_element(u) group_element(v) || product1(u,w,v)*+ -> product1(v,u,e_4) product1(v,u,e_3) product1(v,u,e_2)* product2(e_1,w,u)*.
% 0.85/1.06 81[0:Res:17.5,20.0] group_element(u) group_element(v) || product1(w,u,e_1)*+ -> product1(v,u,e_4) product1(v,u,e_3) product1(v,u,e_2)* equalish(w,v)*.
% 0.85/1.06 82[0:Res:17.5,42.0] group_element(e_1) group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3) product1(u,e_1,e_2)* equalish(u,e_1).
% 0.85/1.06 83[0:SSi:82.0,1.0] group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3) product1(u,e_1,e_2)* equalish(u,e_1).
% 0.85/1.06 85[0:SSi:74.1,1.0] group_element(u) || -> product1(e_1,u,e_4) product1(e_1,u,e_3) product1(e_1,u,e_2)* equalish(u,e_1).
% 0.85/1.06 93[0:Res:57.3,35.0] group_element(e_2) || -> product2(e_1,e_2,e_4) product2(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.85/1.06 95[0:SSi:93.0,2.0] || -> product2(e_1,e_2,e_4) product2(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.85/1.06 96[0:MRR:95.2,95.3,8.0,5.0] || -> product2(e_1,e_2,e_4) product2(e_1,e_2,e_3)*.
% 0.85/1.06 97[0:Res:96.1,23.0] || product2(e_1,e_2,u)*+ -> product2(e_1,e_2,e_4)* equalish(u,e_3).
% 0.85/1.06 100[1:Spt:97.0,97.2] || product2(e_1,e_2,u)*+ -> equalish(u,e_3).
% 0.85/1.06 112[0:Res:83.3,44.0] group_element(e_2) || -> product1(e_2,e_1,e_4) product1(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.85/1.06 118[0:Res:83.3,19.0] group_element(u) || product1(u,v,e_2)*+ -> product1(u,e_1,e_4) product1(u,e_1,e_3)* equalish(u,e_1) equalish(v,e_1).
% 0.85/1.06 120[0:SSi:112.0,2.0] || -> product1(e_2,e_1,e_4) product1(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.85/1.06 121[0:MRR:120.2,120.3,8.0,5.0] || -> product1(e_2,e_1,e_4) product1(e_2,e_1,e_3)*.
% 0.85/1.06 122[0:Res:121.1,27.0] || product1(e_1,u,e_2)+ -> product1(e_2,e_1,e_4) product2(e_3,u,e_1)*.
% 0.85/1.06 123[0:Res:121.1,18.0] || product1(e_2,e_1,u)*+ -> product1(e_2,e_1,e_4)* equalish(u,e_3).
% 0.85/1.06 125[0:Res:121.1,20.0] || product1(u,e_1,e_3)*+ -> product1(e_2,e_1,e_4)* equalish(u,e_2).
% 0.85/1.06 130[2:Spt:123.0,123.2] || product1(e_2,e_1,u)*+ -> equalish(u,e_3).
% 0.85/1.06 136[3:Spt:125.0,125.2] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.85/1.06 138[4:Spt:122.1] || -> product1(e_2,e_1,e_4)*.
% 0.85/1.06 143[4:Res:138.0,130.0] || -> equalish(e_4,e_3)*.
% 0.85/1.06 144[4:MRR:143.0,16.0] || -> .
% 0.85/1.06 145[4:Spt:144.0,122.1,138.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.85/1.06 146[4:Spt:144.0,122.0,122.2] || product1(e_1,u,e_2)+ -> product2(e_3,u,e_1)*.
% 0.85/1.06 147[4:MRR:121.0,145.0] || -> product1(e_2,e_1,e_3)*.
% 0.85/1.06 161[0:Res:85.3,20.0] group_element(u) || product1(v,u,e_2)*+ -> product1(e_1,u,e_4) product1(e_1,u,e_3)* equalish(u,e_1) equalish(v,e_1).
% 0.85/1.06 162[0:Res:85.3,42.0] group_element(e_2) || -> product1(e_1,e_2,e_4) product1(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.85/1.06 163[4:Res:85.3,146.0] group_element(u) || -> product1(e_1,u,e_4) product1(e_1,u,e_3) equalish(u,e_1) product2(e_3,u,e_1)*.
% 0.85/1.06 164[0:SSi:162.0,2.0] || -> product1(e_1,e_2,e_4) product1(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.85/1.06 165[0:MRR:164.2,164.3,8.0,5.0] || -> product1(e_1,e_2,e_4) product1(e_1,e_2,e_3)*.
% 0.85/1.06 169[0:Res:165.1,20.0] || product1(u,e_2,e_3)*+ -> product1(e_1,e_2,e_4)* equalish(u,e_1).
% 0.85/1.06 201[0:Res:21.0,81.2] group_element(e_1) group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3) product1(u,e_1,e_2)* equalish(e_1,u).
% 0.85/1.06 203[0:SSi:201.0,1.0] group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3) product1(u,e_1,e_2)* equalish(e_1,u).
% 0.85/1.06 218[4:Res:163.4,39.0] group_element(e_3) || -> product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_1,e_3).
% 0.85/1.06 222[4:SSi:218.0,3.0] || -> product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_1,e_3).
% 0.85/1.06 223[4:MRR:222.1,222.2,222.3,42.0,11.0,6.0] || -> product1(e_1,e_3,e_4)*.
% 0.85/1.06 316[4:Res:147.0,78.2] group_element(e_2) group_element(e_3) || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.85/1.06 320[4:Res:223.0,78.2] group_element(e_1) group_element(e_4) || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2) product2(e_1,e_3,e_1)*.
% 0.85/1.06 321[4:SSi:320.1,320.0,4.0,1.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2) product2(e_1,e_3,e_1)*.
% 0.85/1.06 322[4:SSi:316.1,316.0,3.0,2.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.85/1.06 332[4:Res:321.3,38.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)* equalish(e_3,e_1).
% 0.85/1.06 339[4:MRR:332.3,11.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.85/1.06 342[4:Res:339.2,18.0] || product1(e_4,e_1,u)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_2).
% 0.85/1.06 344[4:Res:339.2,20.0] || product1(u,e_1,e_2)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_4).
% 0.85/1.06 351[4:Res:322.3,39.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)* equalish(e_2,e_1).
% 0.85/1.06 353[4:MRR:351.3,8.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)*.
% 0.85/1.06 360[4:Res:353.2,42.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)* equalish(e_3,e_2).
% 0.85/1.06 362[4:MRR:360.2,12.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)*.
% 0.85/1.06 380[4:Res:362.1,44.0] || -> product1(e_3,e_2,e_4)* equalish(e_2,e_3).
% 0.85/1.06 389[4:MRR:380.1,9.0] || -> product1(e_3,e_2,e_4)*.
% 0.85/1.06 395[4:Res:389.0,19.0] || product1(e_3,u,e_4)*+ -> equalish(u,e_2).
% 0.85/1.06 456[5:Spt:342.0,342.3] || product1(e_4,e_1,u)*+ -> equalish(u,e_2).
% 0.85/1.06 481[6:Spt:344.0,344.3] || product1(u,e_1,e_2)*+ -> equalish(u,e_4).
% 0.85/1.06 482[6:Res:203.3,481.0] group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3)* equalish(e_1,u) equalish(u,e_4).
% 0.85/1.06 719[6:Res:482.2,44.0] group_element(e_3) || -> product1(e_3,e_1,e_4)* equalish(e_1,e_3) equalish(e_3,e_4) equalish(e_1,e_3).
% 0.85/1.06 735[6:Obv:719.2] group_element(e_3) || -> product1(e_3,e_1,e_4)* equalish(e_3,e_4) equalish(e_1,e_3).
% 0.85/1.06 736[6:SSi:735.0,3.0] || -> product1(e_3,e_1,e_4)* equalish(e_3,e_4) equalish(e_1,e_3).
% 0.85/1.06 737[6:MRR:736.1,736.2,13.0,6.0] || -> product1(e_3,e_1,e_4)*.
% 0.85/1.06 809[6:Res:737.0,395.0] || -> equalish(e_1,e_2)*.
% 0.85/1.06 810[6:MRR:809.0,5.0] || -> .
% 0.85/1.06 812[6:Spt:810.0,344.1,344.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.85/1.06 818[6:Res:812.1,136.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.85/1.06 821[6:MRR:818.0,818.1,456.0,15.0] || -> .
% 0.85/1.06 824[5:Spt:821.0,342.1,342.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.85/1.06 830[5:Res:824.1,136.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.85/1.06 832[5:MRR:830.1,15.0] || -> product1(e_4,e_1,e_4)*.
% 0.85/1.06 834[5:Res:832.0,44.0] || -> equalish(e_1,e_4)*.
% 0.85/1.06 842[5:MRR:834.0,7.0] || -> .
% 0.85/1.06 844[3:Spt:842.0,125.1] || -> product1(e_2,e_1,e_4)*.
% 0.85/1.06 854[3:Res:844.0,130.0] || -> equalish(e_4,e_3)*.
% 0.85/1.06 855[3:MRR:854.0,16.0] || -> .
% 0.85/1.06 859[2:Spt:855.0,123.1] || -> product1(e_2,e_1,e_4)*.
% 0.85/1.06 863[2:Res:859.0,78.2] group_element(e_2) group_element(e_4) || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.85/1.06 867[2:Res:859.0,20.0] || product1(u,e_1,e_4)*+ -> equalish(u,e_2).
% 0.85/1.06 871[2:SSi:863.1,863.0,4.0,2.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.85/1.06 936[3:Spt:169.0,169.2] || product1(u,e_2,e_3)*+ -> equalish(u,e_1).
% 0.85/1.06 969[2:Res:871.3,39.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)* equalish(e_2,e_1).
% 0.85/1.06 971[2:MRR:969.3,8.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.85/1.06 978[2:Res:971.2,42.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.85/1.06 980[2:MRR:978.2,15.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.85/1.06 982[2:Res:980.1,78.2] group_element(e_4) group_element(e_3) || -> product1(e_4,e_2,e_4) product1(e_3,e_4,e_4) product1(e_3,e_4,e_3) product1(e_3,e_4,e_2) product2(e_1,e_2,e_4)*.
% 0.85/1.06 987[3:Res:980.1,936.0] || -> product1(e_4,e_2,e_4)* equalish(e_4,e_1).
% 0.85/1.06 989[3:MRR:987.1,14.0] || -> product1(e_4,e_2,e_4)*.
% 0.85/1.06 1005[3:Res:989.0,44.0] || -> equalish(e_2,e_4)*.
% 0.85/1.06 1013[3:MRR:1005.0,10.0] || -> .
% 0.85/1.06 1015[3:Spt:1013.0,169.1] || -> product1(e_1,e_2,e_4)*.
% 0.85/1.06 1016[2:SSi:982.1,982.0,3.0,4.0] || -> product1(e_4,e_2,e_4) product1(e_3,e_4,e_4) product1(e_3,e_4,e_3) product1(e_3,e_4,e_2) product2(e_1,e_2,e_4)*.
% 0.85/1.06 1024[4:Spt:980.0] || -> product1(e_4,e_2,e_4)*.
% 0.85/1.06 1025[4:Res:1024.0,44.0] || -> equalish(e_2,e_4)*.
% 0.85/1.06 1033[4:MRR:1025.0,10.0] || -> .
% 0.85/1.06 1035[4:Spt:1033.0,980.0,1024.0] || product1(e_4,e_2,e_4)*+ -> .
% 0.85/1.06 1036[4:Spt:1033.0,980.1] || -> product1(e_4,e_2,e_3)*.
% 0.85/1.06 1041[4:MRR:1016.0,1035.0] || -> product1(e_3,e_4,e_4) product1(e_3,e_4,e_3) product1(e_3,e_4,e_2) product2(e_1,e_2,e_4)*.
% 0.85/1.06 1205[4:Res:1041.3,100.0] || -> product1(e_3,e_4,e_4) product1(e_3,e_4,e_3) product1(e_3,e_4,e_2)* equalish(e_4,e_3).
% 0.85/1.06 1206[4:MRR:1205.1,1205.3,44.0,16.0] || -> product1(e_3,e_4,e_4) product1(e_3,e_4,e_2)*.
% 0.85/1.06 1209[4:Res:1206.1,18.0] || product1(e_3,e_4,u)*+ -> product1(e_3,e_4,e_4)* equalish(u,e_2).
% 0.85/1.06 1210[4:Res:1206.1,19.0] || product1(e_3,u,e_2)*+ -> product1(e_3,e_4,e_4)* equalish(u,e_4).
% 0.85/1.06 1215[5:Spt:1209.0,1209.2] || product1(e_3,e_4,u)*+ -> equalish(u,e_2).
% 0.85/1.06 1242[6:Spt:1210.0,1210.2] || product1(e_3,u,e_2)*+ -> equalish(u,e_4).
% 0.85/1.06 1244[6:Res:203.3,1242.0] group_element(e_3) || -> product1(e_3,e_1,e_4) product1(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_1,e_4).
% 0.85/1.06 1252[6:SSi:1244.0,3.0] || -> product1(e_3,e_1,e_4) product1(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_1,e_4).
% 0.85/1.06 1253[6:MRR:1252.1,1252.2,1252.3,44.0,6.0,7.0] || -> product1(e_3,e_1,e_4)*.
% 0.85/1.06 1263[6:Res:1253.0,867.0] || -> equalish(e_3,e_2)*.
% 0.85/1.06 1265[6:MRR:1263.0,12.0] || -> .
% 0.85/1.06 1275[6:Spt:1265.0,1210.1] || -> product1(e_3,e_4,e_4)*.
% 0.85/1.06 1283[6:Res:1275.0,1215.0] || -> equalish(e_4,e_2)*.
% 0.85/1.06 1285[6:MRR:1283.0,15.0] || -> .
% 0.85/1.06 1287[5:Spt:1285.0,1209.1] || -> product1(e_3,e_4,e_4)*.
% 0.85/1.06 1293[5:Res:1287.0,42.0] || -> equalish(e_3,e_4)*.
% 0.85/1.06 1295[5:MRR:1293.0,13.0] || -> .
% 0.85/1.06 1297[1:Spt:1295.0,97.1] || -> product2(e_1,e_2,e_4)*.
% 0.85/1.06 1298[1:Res:1297.0,23.0] || product2(e_1,e_2,u)*+ -> equalish(u,e_4).
% 0.85/1.06 1302[2:Spt:165.0] || -> product1(e_1,e_2,e_4)*.
% 0.85/1.06 1303[2:Res:1302.0,78.2] group_element(e_1) group_element(e_4) || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2) product2(e_1,e_2,e_1)*.
% 0.85/1.06 1307[2:Res:1302.0,20.0] || product1(u,e_2,e_4)*+ -> equalish(u,e_1).
% 0.85/1.06 1309[2:SSi:1303.1,1303.0,4.0,1.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2) product2(e_1,e_2,e_1)*.
% 0.85/1.06 1310[3:Spt:121.0] || -> product1(e_2,e_1,e_4)*.
% 0.85/1.06 1311[3:Res:1310.0,78.2] group_element(e_2) group_element(e_4) || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.85/1.06 1315[3:Res:1310.0,20.0] || product1(u,e_1,e_4)*+ -> equalish(u,e_2).
% 0.85/1.06 1319[3:SSi:1311.1,1311.0,4.0,2.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.85/1.06 1468[2:Res:1309.3,38.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)* equalish(e_2,e_1).
% 0.85/1.06 1476[2:MRR:1468.3,8.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.85/1.06 1509[2:Res:1476.2,27.0] || product1(e_1,u,e_4)+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product2(e_2,u,e_1)*.
% 0.85/1.06 1510[2:Res:1476.2,18.0] || product1(e_4,e_1,u)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_2).
% 0.85/1.06 1520[3:Res:1319.3,39.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)* equalish(e_2,e_1).
% 0.85/1.06 1525[3:MRR:1520.3,8.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.85/1.06 1534[3:Res:1525.2,42.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.85/1.06 1536[3:MRR:1534.2,15.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.85/1.06 1540[3:Res:1536.1,18.0] || product1(e_4,e_2,u)*+ -> product1(e_4,e_2,e_4)* equalish(u,e_3).
% 0.85/1.06 1541[3:Res:1536.1,19.0] || product1(e_4,u,e_3)*+ -> product1(e_4,e_2,e_4)* equalish(u,e_2).
% 0.85/1.06 1565[4:Spt:1540.0,1540.2] || product1(e_4,e_2,u)*+ -> equalish(u,e_3).
% 0.85/1.06 1572[5:Spt:1541.0,1541.2] || product1(e_4,u,e_3)*+ -> equalish(u,e_2).
% 0.85/1.06 1686[6:Spt:1510.0,1510.3] || product1(e_4,e_1,u)*+ -> equalish(u,e_2).
% 0.85/1.06 1882[7:Spt:1509.0,1509.3] || product1(e_1,u,e_4)+ -> product2(e_2,u,e_1)*.
% 0.85/1.06 1885[7:Res:1302.0,1882.0] || -> product2(e_2,e_2,e_1)*.
% 0.85/1.06 1889[7:Res:1885.0,39.0] || -> equalish(e_1,e_2)*.
% 0.85/1.06 1893[7:MRR:1889.0,5.0] || -> .
% 0.85/1.06 1897[7:Spt:1893.0,1509.1,1509.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.85/1.06 1905[7:Res:1897.1,1686.0] || -> product1(e_4,e_1,e_4)* equalish(e_3,e_2).
% 0.85/1.06 1907[7:MRR:1905.1,12.0] || -> product1(e_4,e_1,e_4)*.
% 0.85/1.06 1920[7:Res:1907.0,1686.0] || -> equalish(e_4,e_2)*.
% 0.85/1.06 1923[7:MRR:1920.0,15.0] || -> .
% 0.85/1.06 1942[6:Spt:1923.0,1510.1,1510.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.85/1.06 1951[6:Res:1942.1,1572.0] || -> product1(e_4,e_1,e_4)* equalish(e_1,e_2).
% 0.85/1.06 1952[6:MRR:1951.1,5.0] || -> product1(e_4,e_1,e_4)*.
% 0.85/1.06 1988[6:Res:1952.0,1315.0] || -> equalish(e_4,e_2)*.
% 0.85/1.06 1992[6:MRR:1988.0,15.0] || -> .
% 0.85/1.06 2001[5:Spt:1992.0,1541.1] || -> product1(e_4,e_2,e_4)*.
% 0.85/1.06 2011[5:Res:2001.0,1565.0] || -> equalish(e_4,e_3)*.
% 0.85/1.06 2014[5:MRR:2011.0,16.0] || -> .
% 0.85/1.06 2019[4:Spt:2014.0,1540.1] || -> product1(e_4,e_2,e_4)*.
% 0.85/1.06 2027[4:Res:2019.0,1307.0] || -> equalish(e_4,e_1)*.
% 0.85/1.06 2030[4:MRR:2027.0,14.0] || -> .
% 0.85/1.06 2035[3:Spt:2030.0,121.0,1310.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.85/1.06 2036[3:Spt:2030.0,121.1] || -> product1(e_2,e_1,e_3)*.
% 0.85/1.06 2037[3:MRR:125.1,2035.0] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.85/1.06 2113[4:Spt:1476.0] || -> product1(e_4,e_1,e_4)*.
% 0.85/1.06 2114[4:Res:2113.0,44.0] || -> equalish(e_1,e_4)*.
% 0.85/1.06 2123[4:MRR:2114.0,7.0] || -> .
% 0.85/1.06 2126[4:Spt:2123.0,1476.0,2113.0] || product1(e_4,e_1,e_4)*+ -> .
% 0.85/1.06 2127[4:Spt:2123.0,1476.1,1476.2] || -> product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.85/1.06 2131[4:MRR:1509.1,2126.0] || product1(e_1,u,e_4) -> product1(e_4,e_1,e_3) product2(e_2,u,e_1)*.
% 0.85/1.06 2134[5:Spt:2127.0] || -> product1(e_4,e_1,e_3)*.
% 0.85/1.06 2140[5:Res:2134.0,2037.0] || -> equalish(e_4,e_2)*.
% 0.85/1.06 2143[5:MRR:2140.0,15.0] || -> .
% 0.85/1.06 2152[5:Spt:2143.0,2127.0,2134.0] || product1(e_4,e_1,e_3)*+ -> .
% 0.85/1.06 2153[5:Spt:2143.0,2127.1] || -> product1(e_4,e_1,e_2)*.
% 0.85/1.06 2157[5:MRR:2131.1,2152.0] || product1(e_1,u,e_4)+ -> product2(e_2,u,e_1)*.
% 0.85/1.06 2210[5:Res:1302.0,2157.0] || -> product2(e_2,e_2,e_1)*.
% 0.93/1.09 2232[5:Res:2210.0,39.0] || -> equalish(e_1,e_2)*.
% 0.93/1.09 2236[5:MRR:2232.0,5.0] || -> .
% 0.93/1.09 2240[2:Spt:2236.0,165.0,1302.0] || product1(e_1,e_2,e_4)*+ -> .
% 0.93/1.09 2241[2:Spt:2236.0,165.1] || -> product1(e_1,e_2,e_3)*.
% 0.93/1.09 2244[2:MRR:169.1,2240.0] || product1(u,e_2,e_3)*+ -> equalish(u,e_1).
% 0.93/1.09 2256[3:Spt:121.0] || -> product1(e_2,e_1,e_4)*.
% 0.93/1.09 2257[3:Res:2256.0,78.2] group_element(e_2) group_element(e_4) || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.93/1.09 2266[3:SSi:2257.1,2257.0,4.0,2.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.93/1.09 2430[3:Res:2266.3,39.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)* equalish(e_2,e_1).
% 0.93/1.09 2438[3:MRR:2430.3,8.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.93/1.09 2448[3:Res:2438.2,42.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.93/1.09 2452[3:MRR:2448.2,15.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.93/1.09 2459[3:Res:2452.1,2244.0] || -> product1(e_4,e_2,e_4)* equalish(e_4,e_1).
% 0.93/1.09 2461[3:MRR:2459.1,14.0] || -> product1(e_4,e_2,e_4)*.
% 0.93/1.09 2494[3:Res:2461.0,44.0] || -> equalish(e_2,e_4)*.
% 0.93/1.09 2502[3:MRR:2494.0,10.0] || -> .
% 0.93/1.09 2506[3:Spt:2502.0,121.0,2256.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.93/1.09 2507[3:Spt:2502.0,121.1] || -> product1(e_2,e_1,e_3)*.
% 0.93/1.09 2508[3:MRR:125.1,2506.0] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.93/1.09 2514[3:Res:2507.0,78.2] group_element(e_2) group_element(e_3) || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.93/1.09 2521[3:SSi:2514.1,2514.0,3.0,2.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.93/1.09 2592[3:Res:2521.3,39.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)* equalish(e_2,e_1).
% 0.93/1.09 2600[3:MRR:2592.3,8.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)*.
% 0.93/1.09 2611[3:Res:2600.2,42.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)* equalish(e_3,e_2).
% 0.93/1.09 2615[3:MRR:2611.2,12.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)*.
% 0.93/1.09 2662[3:Res:2615.1,44.0] || -> product1(e_3,e_2,e_4)* equalish(e_2,e_3).
% 0.93/1.09 2671[3:MRR:2662.1,9.0] || -> product1(e_3,e_2,e_4)*.
% 0.93/1.09 2674[3:Res:2671.0,78.2] group_element(e_3) group_element(e_4) || -> product1(e_4,e_3,e_4) product1(e_4,e_3,e_3) product1(e_4,e_3,e_2) product2(e_1,e_2,e_3)*.
% 0.93/1.09 2680[3:SSi:2674.1,2674.0,4.0,3.0] || -> product1(e_4,e_3,e_4) product1(e_4,e_3,e_3) product1(e_4,e_3,e_2) product2(e_1,e_2,e_3)*.
% 0.93/1.09 2816[3:Res:2680.3,1298.0] || -> product1(e_4,e_3,e_4) product1(e_4,e_3,e_3) product1(e_4,e_3,e_2)* equalish(e_3,e_4).
% 0.93/1.09 2817[3:MRR:2816.0,2816.3,44.0,13.0] || -> product1(e_4,e_3,e_3) product1(e_4,e_3,e_2)*.
% 0.93/1.09 2823[3:Res:2817.1,118.1] group_element(e_4) || -> product1(e_4,e_3,e_3) product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(e_4,e_1) equalish(e_3,e_1).
% 0.93/1.09 2824[3:Res:2817.1,161.1] group_element(e_3) || -> product1(e_4,e_3,e_3) product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_4,e_1).
% 0.93/1.09 2826[3:SSi:2824.0,3.0] || -> product1(e_4,e_3,e_3) product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_4,e_1).
% 0.93/1.09 2827[3:MRR:2826.3,2826.4,11.0,14.0] || -> product1(e_4,e_3,e_3) product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)*.
% 0.93/1.09 2828[3:SSi:2823.0,4.0] || -> product1(e_4,e_3,e_3) product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(e_4,e_1) equalish(e_3,e_1).
% 0.93/1.09 2829[3:MRR:2828.3,2828.4,14.0,11.0] || -> product1(e_4,e_3,e_3) product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.93/1.09 2871[4:Spt:2827.0] || -> product1(e_4,e_3,e_3)*.
% 0.93/1.09 2877[4:Res:2871.0,42.0] || -> equalish(e_4,e_3)*.
% 0.93/1.09 2879[4:MRR:2877.0,16.0] || -> .
% 0.93/1.09 2881[4:Spt:2879.0,2827.0,2871.0] || product1(e_4,e_3,e_3)*+ -> .
% 0.93/1.09 2882[4:Spt:2879.0,2827.1,2827.2] || -> product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)*.
% 0.93/1.09 2887[4:MRR:2829.0,2881.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.93/1.09 2945[4:Res:2887.1,2508.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.93/1.09 2948[4:MRR:2945.1,15.0] || -> product1(e_4,e_1,e_4)*.
% 0.93/1.09 2951[4:Res:2948.0,44.0] || -> equalish(e_1,e_4)*.
% 0.93/1.09 2960[4:MRR:2951.0,7.0] || -> .
% 0.93/1.09 % SZS output end Refutation
% 0.93/1.09 Formulae used in the proof : element_1 element_2 element_3 element_4 e_1_is_not_e_2 e_1_is_not_e_3 e_1_is_not_e_4 e_2_is_not_e_1 e_2_is_not_e_3 e_2_is_not_e_4 e_3_is_not_e_1 e_3_is_not_e_2 e_3_is_not_e_4 e_4_is_not_e_1 e_4_is_not_e_2 e_4_is_not_e_3 product1_total_function1 product1_total_function2 product1_right_cancellation product1_left_cancellation product1_idempotence product2_total_function1 product2_total_function2 product2_right_cancellation product2_left_cancellation product2_idempotence qg2a
% 0.93/1.09
%------------------------------------------------------------------------------